X-Ray Absorption and Emission William I . Campbell, U. College Park, Md.
S.
Department o f the Interior, Bureau of Mines, College Park Metallurgy Research Center,
lames D. Brown, University o f Western Ontario, Faculty o f Engineering Science, london, Ontario, Canada
A s
IK OUR 1964 (116) and 1966 (117)
reviews, we continue to use the format established by our predecessors Liebhafsky, Winslow, and Pfeiffer (413). This 1968 review consists of a critical evaluation of new developments and tabular summaries of X-ray spectrography and electron probe microanalysis. Stoddart and Dowden (614) recently compiled a comprehensive bibliography on fluorescent X-ray spectrography. Their bibliography is indexed by the element determined, matrix analyzed, author, equipment, method, and theory. At present the principal application of X-ray emission and absorption techniques is to determine the concentration of specific elements. I n the future X-ray emission techniques will find additional applications as analytical chemistry becomes more sophisticated in characterizing materials. The Committee on Characterization of Materials, Materials Advisory Board, National Research Council developed the following definition (441): “Characterization describes those features of the composition and structure (including defects) of a material that are significant for a particular preparation, study of properties, or use, and suffice for reproduction of the material.” Lowenergy X-ray spectroscopy supplemented by photoelectron and Auger spectroscopy can provide information regarding valence, coordination, bonding energy, and the composition of surface layers. We agree with Liebhafsky et al. (412) that the future of low energy X-rays lies in the interpretation of spectra rather than the determination of concentration. Low-energy X-ray and electron emission techniques are emphasized in this review. Energy dispersion techniques using radioactive isotopes as the source of excitation have grown rapidly during the past two years. This growth is due, in large part, to improvements in detector technology and to the commercial availability of a wide selection of isotopic sources. The lithium-drifted semiconductor detector with its high resolution capability opens new avenues of X-ray analysis. Energy dispersion and the semiconductor detector are extensively covered in this review. I n electron probe microanalysis, there has been significant progress in defining and evaluating the parameters that are used to relate measured X-ray intensi-
346 R
ANALYTICAL CHEMISTRY
ties to composition. The evaluation of these parameters and their effect on the calculated concentration have been greatly accelerated by the use of computers. Heinrich outlined a plan for cooperative action on the determination of X-ray mass absorption coefficients (300). Better knowledge of mass absorption coefficients is necessary for theoretically reliable methods for computing concentration. Cooperative efforts in determination of the various parameters, such as mass absorption and fluorescent yield, are to our mutual advantage. Your support is requested in these efforts. The critical tabulation of K, L, RI, N, and 0 spectral lines by Bearden was recently published in Review of JIodern Physics (47). This tabulation was available previously as an AEC report. Atomic energy levels were compiled by Bearden and Burr (48). I n their calculations, the wavelengths of all available emission lines of an element were used to form a n overdetermined set of equations that were solved by least squares to give a best set of relative energy levels. These values were then placed on an absolute scale by X-ray photoelectron measurements or by using wavelengths of the absorption edges. X-ray wavelength and absorption edge tabies were computed by Dewey for use in electron probe microanalyzer calculations (183). Brockman and Whittem (90) compiled a condensed 28 table for first order spectral lines. As stated in our 1966 review, there are excellent wavelength and 28 tables already available. We recommend the use of Bearden’s tables (47, 48) for any additional 28 tables. Recent textbooks and conference proceedings are listed in Table I. “Advances in X-Ray Analysis” (430, 474) provides excellent summaries of recent developments in X-ray emission and electron probe microanalysis. There are three new textbooks on X-ray emission techniques (5, 354, 468) and two books on electron microprobe analysis (496, 631). Hopefully some publisher will make Muller’s book available in English (468). There is occasionally a duplication of effort in the translation of textbooks. The book by Ulokhin (73), recently made available in English by Pergamon Press, was translated into English in 1962 by the Hindustan The Publishing Company (117).
“Handbook of X-Rays” was approximately five years in preparation. This comprehensive book covers all aspects of X-ray analysis, including X-ray emission and microanalyzer instrumentation and techniques (358). Because of the desire to achieve more rapid and detailed communications regarding their research, the Spectrochemical Section of the Kational Bureau of Standards is preparing detailed summaries of yearly progress (563, 664). These reports summarize facilities, publications, personnel, and more important, research in progress. Reports of this type from all of the major laboratories engaged in X-ray research would aid in reducing duplication of effort. Continuing education is becoming a way of life for most scientists, including those whose interest lies in X-ray methods of analysis. Excellent introductory courses are provided by several of the instrument manufacturers a t their plants or a t various locations throughout the United States. Summer workshops at various universities provide an excellent introduction to X-ray emission and electron probe microanalysis. Technical societies are offering short intensive courbes as part of professional development programs. For example, the Washington-Baltimore Section of the Society of Applied Spectroscopy is presenting a series of five 2-hour lectures on X-ray emission techniques. RIore emphasis on radiation safety is strongly recommended, particularly as there will be a significant increase in the use of isotopes for energy dispersion analysis and in applications involving X-rays in the 50- to 100-key range. INSTRUMENTATION
General. The manufacturers have continued the trend toward completely automated and programmed X-ray spectrometers. Instruments are now available t h a t can detect all elements from fluorine u p through t h e periodic table. T h e program ill automatically select the 28 angle, analyzing crystal, Soller slit, detector, and pulse height analyzer setting, and then print out both the counts collected and the concentration. Obviously the accuracy of the analysis is no better than the match between standard and un-
known, or the reliability of the mathematical correction procedures used. During the past two years more attention has been given to two possible souices of instrumental error. The crystal chamber must be kept constant to k0.5OC to avoid systematic errors resulting from small shifts in peak position due to changes in d-spacing of the crystal. This problem becomes more serious when using high resolution optics with aut omat ed spectrometers. Also, the temperature and pressure of the counting gas in flow proportional counters must be stabilized because the gas amplification factor is affected by both of these variables. Because of the difficulty and cost of obtaining an adequate supply of helium, the vacuum spectrometer is widely used outside the United States. This vacuum system results in slightly higher intendies owing to increased X-ray transmission of lowenergy Xrays; however, liquid samples are awkward t o analyze in a vacuum spectrograph. Squirrel1 (608) modified a P W 1540 spectrometer to use either a partial vacuum-helium atmosphere or helium only. Excellent results were obtained with volatile organic liquids using the helium path. Campbell and Hammond (114) automated a commercial X-ray spectrograph for continuous operation. The objective was to obtain the lowest possible limit of detection and to optimize analytical precision by taking 100 to 200 measurements over extended counting periods. A unique spectrograph was described by Zeitz (698) which uses a very thin transmission-scatter biological sample enclosed in a vacuum chamber. The amount of the element present is determined by intensity measurements using a curved-crystal spectrometer. The characteristic X-rays are transmitted through the sample to a slit on the focusing circle. The sample weight is obtained from scattered X-rays using a propo~tionalcounter readout. The Henke X-ray tube has been adapted to fit on a commercially available vacuum spectrometer (257). Samples are e x i t e d by low-energy X-rays, thus avoiding the problems of decomposition that occur when unstable compounds are subjected to electron bombardment. Although the grating spectrograph of Holliday (328) offers superior resolving power, the flat crystal spectrometer using an oriented soap film for dispersion is adequate for most applications (3f3). Probably the most versatile spectrograph for the lowenergy X-ray region is the instrument designed by Mattson and Ehlert (55, 449). By changing voltage on either the cathode or anode, samples can be excited by electrons or X-rays. I n another configuration wires suspended
Table I.
Author Adler, I. Blokhin, M. A. Brown, J. G. Castaing, R., Descamps, J., Philibert, J., Eds. Elion, H. A.
Summary of Recent Books
Title X-Ray Emission Spectrography in Geology Methods of X-Ray Spectroscopic Research X-Rays and Their Applications X-Ray Optics and X-Ray Microanalysis Instrument and Chemical Analysis Aspects of Electron Microanalysis and Macroanalysis Practical X-Ray Spectrometry Handbook of X-Rays Elektronenstrahl-Mikroanalyse
Advances in X-Ray Analysis, Vol. 9
Newkirk, J. B., Mallett', G. R., Eds. Theisen, R. h e r . SOC.Testing Materials Baker, P. S., Gerrard, N., Eds. International Atomic Energy Agency Parrish, W., Ed. Siegbahn, K.
Spektrochemische Analysen mit Rontgenfluoreszenz Advances in X-Ray Analysis, Vol. 10 Quantitative Electron Microprobe Analysis Sections on X-Rays Fifty Years of Progress in Metallographic Techniques Second Symposium on Low Energy X- and Gamma Sources and Applications Radioisotope Instruments in Industry and Geophysics-Vol. 1 X-Ray and Electron Methods of Analysis Alpha, Beta, and Gamma Ray SpectrosCOPY
across two insulators are excited by electrons. The temperature of the wire can be varied by ohmic heating to remove any surface contamination. Gases can be introduced into the chamber containing the wire to investigate gas-solid reactions at selected temperatures. It is also possible to ionize gases at low pressures by electron excitation. The sample chamber and X-ray optical system are designed so that X-ray photons emitted by the chamber material do not enter the X-ray spectrometer optics. Their instrument has been used for surveying a wide variety of materials (2O4,443). Campbell et al. constructed a soft X-ray spectrometer for the study of valence bands of metals (112). Their instrument uses a blazed concave replica grating at grazing incidence, with a photomultiplier as the detector. A moderately low-energy Xray spectrometer was employed t o measure X-ray emission from the deuterium plasma of a theta pinch reaction (395)*
Direct electron excitation X-ray spectrometers are commercially available. The Telesec instrument can be preset for any combination of six elements (37). The manufacturers state that in the past there were three major objections to electron excitation-need for high vacuum around the electron gun, instability of system, and high background. According to Telesec, these objections have been eliminated in their instrument. Japan Electron Optics Laboratory (379) also developed a primary X-ray analyzer. The electron
beam diameter is approximately 5 millimeters; the incident electron power is 0.5 to 5 watts in normal operation. Specimen holders are insulated from ground by a Teflon bushing enabling the absorbed electrons to be measured by a micro-microampere meter. Signalto-noise ratios of 1700 to 1 and 1100 t o 1 were obtained for silicon K a and aluminum Ka,respectively, using pure element standards. Further information on electron excitation can be obtained from publications on electron probe microanalysis ($3). Excitation. There has been increased activity in t h e development of more efficient excitation on both t h e low- and high-energy X-ray regions. T h e stability of a commercially available X-ray generator was critically evaluated by Ashby and Proctor (28). Over a 23.5-hour test with line voltage fluctuations of *15% the X-ray tube current and voltage were constant to 1 0 . 0 2 and +0.05%, respectively. During these evaluations Ashby and Proctor observed drifts in X-ray intensity which could not be explained by electronic instability. These drifts in intensity were found to be a result of changes in the X-ray transmission of the air path between the sample and the detector. The density of the air was changing with variations in temperature and pressure, Because of the high electronic stability, this small temperature-pressure effect could be observed. Yee and Deslattes (691) found that a transistorized current stabilizer for X-ray tubes using directly heated cathodes was operational over VOL. 40, NO. 5, APRIL 1968
347 R
the 20- to 1000-mA range. The X-ray tube current was constant to =kO.l% for periods of a t least one-half hour. Linear polarization of X-rays was investigated by Huffman (558). The linear polarization of X-rays produced in a mercury vapor target tube was analyzed by measuring the scattered intensity from beryllium parallel and perpendicular to the emission plane. Because fluorescent X-rays are isotropic, line-to-background ratios can be optimized by viewing the sample so that scattering of primary X-rays is minimized. Machlett Laboratories (382) announced the development of an experimental thin-window platinum target X-ray tube. K i t h a 0.005-inch-thick beryllium window, this tube has characteristics equivalent to the conventional tungsten tube and the thin window chromium target tube. The dissipation of heat arising from backscattered electrons limits the size of their window to 0.5-inch diameter. Soviet scientists (594) designed a rhenium target X-ray tube that could operate up to a load of 3.5 kilowatts. The distance from the focal spot to the beryllium mindow is approximately 11 millimeters-about one half the distance of the Machlett OEG 60 tube. Operating at maximum power the beryllium window reached a temperature of 350°C. Electrostatic deflection of the backscattered electrons reduced the window temperature to 12O-15O0C. Taylor designed a highintensity rotating-anode X-ray tube that could be operated at 250-275 milliamperes at 30 kilovolts or 150 milliamperes a t 50 kilovolts (625). The focal spot is 10 by 1 millimeters, and the rotational speed is 1750 revolutions per minute. H e anticipated construction of a 25-kilowatt X-ray tube for spectrographic analysis. Kathren (362) utilized a 200-kilovolt industrial X-ray unit to generate “monochromatic” X-rays. The “monochromatic” X-rays were generated by bombarding secondary sources Ivith a high-energy primary beam. A 150kilovolt industrial unit was used to excite uranium K lines for detection of uranium contamination (561). With the significant improvements in detector technology, we anticipate many new applications of 50- to 100-keV X-rays. Small X-ray tubes (30-mm diameter) were evaluated for drill hole logging of minerals. These tubes could be operated up to 100 kilovolts, giving a n X-ray output of 1Olo to lo1’ photons per second ( 2 ) . Gas-filled tubes operated intermittently and their output was only one half to one fourth that of a heated-filament X-ray tube. Miniaturized X-ray tubes were evaluated for excitation of low atomic number elements on the lunar surface (172, 198, 464). 348 R * ANALYTICAL CHEMISTRY
The Cristallobloc 31 X-ray tube has a cylindrical rotatable anode with six faces for fluorescent excitation (635). When the primary excitation mode is used, the sample is placed in slits machined in the copper block. The Raymax demountable tube (580) was used to evaluate excitation parameters in the lowenergy X-ray region. Maximum intensity was obtained with high takeoff angle, low angle of incidence of the electron beam, and optimum voltage setting. Losev et al. (417) made similar studies on the escitation of silicon K radiation. I n addition they evaluated the output from 10 anodes ranging from beryllium to gold. Walker (659) used a commercially available demountable X-ray tube in a windowless configuration. Results were compared with those obtained with 30- and 100-micron beryllium windows. When the window was absent deflection plates were used to eliminate scattered electrons. One relatively simple way to increase intensity of the low-energy X-rays is to eliminate the plastic film holding the sample. Beard and Proctor (45) designed a windowless solution holder that gave a reproducible height of solution. The uncovered holders gave a 3- and 6-fold increase for sulfur and aluminum K a , respectively, compared with holders with 1/4-mil mylar windows. Davidson and Wyckoff (176) reexamined the cold cathode gas tube for use in the low-energy X-ray region. Contamination of the target was not a problem, in contrast to the buildup of impurities using the heated cathode. Their air-cooled tube could be operated up to 200 watts. A demountable X-ray tube was operated at 10 to 20 kilovolts and 200 to 300 milliamperes (182). The power on the tube is limited by the rate of dissipation of heat; this power can be increased by using pressurized coolant. Dispersion. Activity reported on t h e development of improved analyzing crystals has decreased during t h e past two years. Resolution and intensity of spectral lines are directly related t o t h e analyzing crystal; therefore a greater research effort is warranted. Isomet Corporation recently announced the commercial availability of OHM (octadecyl hydrogen maleate) crystals for use in the long wavelength region. These crystals offer high r,eflectivity and a 2d spacing of 63.5 4. Sparks (598) found that oriented hoteressed pyrolytic graphite, 2d = 6.70 A, has excellent potential as an X-ray monochromator. The diffraction efficiency of the 002 reflection for copper K a is approximately 50% if the divergence of the X-ray beam does not exceed the mosaic spread of the graphite. The peak width is full-width half-maximum. Sparks found that graphite
gives a 5-fold increase in intensity as compared to lithium fluoride. Crystals and oriented soap films used for X-ray analyzers are summarized in Tables I1 and I11 taken from a paper by Baun and Fischer (41). Of the newer crystals, clinochlore (a naturally occurring cLystal) looks promising for the 10 to 20 A region. As there appears to be a useful upper limit to the d-spacing of soap films, Baun and Fischer suggest alternate deposition of a thin film of a strong scatterer and a precisely controlled sandwich layer of a low scatterer. Although their approach is restricted by the present art of vacuum deposition, the suggestion merits further study. Chan (142, 143) found that certain PET crystals grown in his laboratory gave 2.5 times the reflectivity of E D d T and 9 times that of mica for silicon K a radiation. For a pure silicon sample, count rates in escess of 106 counts per second were achieved. Chan cautions that PET crystals should be kept in a desiccator when not in use. Advantages of soap films and gratings are compared by Henke (309). Previously, lowenergy X-ray spectroscopy was accomplished by diffraction gratings a t grazing incidence. Xew techniques for making low-angle blaze gratings have greatly improved intensities. More recently most of the research in lowenergy X-ray spectroscopy has been accomplished using Langmuir-Blodgett type of analyzers. Using the oriented soap films at a high B r a g angle, a significantly larger total solid angle of radiation is viewed as compared to the small angle grazing incidence geometry. Excellent discussions on the preparation and properties of soap films were presented by Ehlert and 3lattson (203, 205). Optimization of slit width for focusing spectrometers is discussed by Lavrent’ev and Vainshtein (405). Detectors. During the past two years there has been significant research on the pulse amplitude shift as a function of X-ray intensity (227). Burkhalter, Brown, and Nyklebust (104) compared a variety of sealed and flowproportional counters for peak shift as a function of counting rate. The two significant findings were that peak shifts were larger for flom-proportional counters than for sealed detectors and that the peak shift was a strong function of anode voltage. For esamole, a t 1500 volts the peak shift is 5 7 , coinpared with a 50% shift a t 1900 volts. I n contrast a sealed detector operated at 1750 volts gave no observable shift from 500 to 50,000 counts per second. Sanford and Cclhane (654) found that performance at high count rate could be improved by using a n inert gas of low atomic number, by increasing the detector capacitance (increasing the anode wire diameter), and by operating at a low gas multiplication factor. Spiel-
beig (601) concluded that the density 1011 space charge depends on the aiiode nile diameter, as most of thc charge multiplication in the detector takes place close to the anode wire. Therefole the peak shift should be reduced by incieasing the wire diameter. Veiy little shift was observed using a 0.012-cni-diameter wire. Higher ope1 atiiig voltage \\as required, but did not create any special problems. The type of anode material (602) was also found to have an effect on pulse shift. A detector using an anode wire of 50-,udiameter tungsten had a significantly loner shift thaii the same detector with a 50-p-diameter stainless steel wire. d gas pressuie control system for the flow counter was described by Spielberg (600). He concluded that, in an airconditioned room, additional temperature control on the flow counter gas was not required. Practical techniques for casting thin formvar films on water nere described by LIeriitt and Agazzi (.@2), A ruggedized thin window counter was designed for space applications (559). The variation of gain and resolution with time for a sealed thin window counter was investigated by Culhane et al. (166). The deterioration in gain and resolution mas restored by either placing the counter in a desiccator with phosphorus pentoside or by bubjecting the counter to dry ice temperature. dpparently the counter deterioration resulted from water vapor leaking through the windo\\. .ipplications of gas-flow and sealed proportional counters ale described in the following papers (111, 113, 15'9, 467, 654). An excellent source of information on scintillation counters is the recently revised book by I3irks (64). There have been major improvemeiits in the lithium-drifted silicon and germanium detectors during the past two years These detectors offer escellent resolution in the medium- and highenergy X-ray region. Excellent review paperq on the state of the art have been published recently (177, 270, 325327). If the reader is not familiar with the new detectors, the introductory papers by 13oanian et al. (83) aiid Heath (2Y6) are recommended. The active counting volume of a lithium-drifted detector is formed by drifting lithium into a p-type silicon or gernianiuni crystal under carefully controlled conditions (260). The function of the lithium i, to compensate for the effect of impurities The detector is coniprised of a region of compensated silicon or germanium sandwiched betneeii a very thin 1,-type and n-type region. 13y applying a bias voltage to the detector in the reverse direction, the detector becomes a high-impedance device. This electric field depletes the compensated region of free charge carot the po,itivc
Table
Name
II.
Analyzing Crystals ( 4 7 )
2d,
A
Topaz Lithium fluoride Sodium chloride Calcite Silicon
2.71 4.02 5.64 6.06 6.28
Fluorite Germanium
6.30 6.53 6.58 7.50 8.74 8.80 8.80 10.64 14.15 14.92 15.12 15.18 15.96 18.50 19.91 26.63 28.42 32.84
Potassium bromide Ammonium phosphate Pentaerythritol Ammonium tartrate Ethylene diamine d-tartrate Ammonium phosphate Ammonium tartrate Ammonium citrate Sucrose Gypsum Beryl Itaconic acid Mica Potassium acid phthalate Clinochlore Bismuth titanate Octadecyl hydrogen maleate Octadecyl hydrogen succinate
Table 111.
Lead Lead Lead Lead Lead Lead Lead
Name laurate myristate palmitate stearate arachidate lignocerate mellissate
Soap Film-Multilayer Analyzers ( 4 7 )
Number of carbon atoms 12 14 16 18 20
24 30
Notes Natural mineral Durable, strong reflection Cleavage, easily bent Durable natural mineral, cleavage Semiconductor slices may be used, suppressed second order Cleavage Semiconductor slices may be used, suppressed second order N o cleavage, easily bent Large natural growth face Soft, difficult to grow, intense reflections Cleavage, easy to grow from HzO solution No cleavage Easy to grow from H20solution Large natural growth face Natural growth face Difficult to grow, spontaneous nucleation Dehydrates in high vacuum, easily bent Natural mineral Cleavage Natural mineral, cleavage, easily bent Growth from H20 solution, cleavage Natural mineral, cleavage, easily bent Platelets, may be bent Both difficult to grow, long growth cycles, spontaneous nucleation
2d Spacing,
70 80.5 90 100.79 110 131.45 165
riers (electrons and holes). This depleted region is the radiation-sensitive volume of the detector. Typical detector areas and depths are 30 to 100 square millimeters and 2 to 5 millimeters, respectively. A large number of ion pairs are formed per incident photon, but these semiconductor detectors do not have the high multiplication typical of the pulse formed in the gas proportional type counter. Therefore, a very low-noise, high-gain preamplification is required (207, 208). This preamplification is achieved b y operating a field effect transistor a t liquid nitrogen temperature (661). The detection efficiency is the function of the depletion depth and the atomic number of the semiconductor. A 3-millimeter-thick silicon diode will absorb approximately 50% of 30-keV X-ray photons; however the photoelectric absorption of silicon decreases rapidly with increasing X-ray energy. For higher energy X-rays, germanium is the detector of choice because of its higher photoelectric absorption coefficient.
-1
Notes Possible degradation in vacuum Easy to prepare Easy to prepare Easy t o prepare More difficult to prepare More difficult to prepare and usually poor quality
The principal advantage of the lithium-drifted detector is the significant improvement in resolving power as compared to proportional and scintillation counters. The theoretical width of the measured pulse is related to the statistical spread in the number of electron-hole pairs formed by photoelectric absorption. Resolution is conventionally expressed by the following relationship FTVHM (keV) = 2 . 3 5 5 a (1) where E = energy of incident electron or X-ray photon in keV e = average energy to create electron-hole pair = 3.6 eV for silicon, F = the Fano factor For small-diameter detectors, the Fano factors for germanium and silicon are 0.15 and 0.20, respectively (296). The observed line width also includes contributions from various sources of noise in the detector and in the electronics, Resolutions of 0.5 to 0.7 keV ( F W H M ) have been reported for silicon detectors in the 5- to 30-keV region. The exVOL. 40,
NO. 5 ,
APRIL 1968
* 349 R
celIent resolution of the germanium detector for high-energy K X-rays is shown in Figure 1 (83). Of particular significance is the separation of the Kala2doublets of thorium and uranium. By using amplifiers with pole zero cancellation, the problem of peak broadening at high count rate has been virtually eliminated. Pulse widths did not show any apparent broadening for count rates up to 15,000 counts per second (296). The lithium-drifted detectors have great potential for energy dispersion analysis. Information can be obtained in a few minutes regarding the overall sample composition using a lithium-drifted detector coupled with a multichannel analyzer. We predict these detectors will find extensive appli-
b
a z
:w:
Figure 1 . K X-ray spectra of high atomic number elements using a lithium-drifted germanium detector (83)
In
a W a In I-
z
3
0 V
2
Lr,
I
K82
LL
0
m a
z
a
-
In 3
I
I-
,
,
0
60
70
Table IV.
In cement materials (178) In minerals and ores (184, 199, 384, 477, 653, 677) In miscellaneous materials (59, 376, 464, 616, 626, 642) In organics (54, 210, 263) In soils (360) Lead In alloys and metals (171, 432, 466, 697) In minerals and ores (666) In miscellaneous materials (433, 616, 630, 667) In organics (608) Magnesium In metals (372, 697) In minerals and ores (565) In miscellaneous materials (360, 394) In slags (178) Manganese (52, 77, 202, 372, 411, 466, 697, 677) Mercury (433)
350 R
ANALYTICAL CHEMISTRY
100
,
110
120
ENE'RGY.'keV
Specific X-Ray Spectrographic Analysis
Aluminum In alloys and metals (146, 162, 227, 234, 236, 400, 466) I n minerals and ores (199,360,384, 663, 677) In miscellaneous materials ( I 78, 394, 526) Antimony (400,457,479,681) Arsenic (431, 433, 457, 681 ) Barium (126, 372, 613) Beryllium (204) Bismuth (433) Boron (204, 230, 233) Bromine (542, 671, 608, 657) Calcium In cement materials (178. 677) In minerals and ores (199, 384, 477, 653, 677) In miscellaneous materials (394, 516, 626, 642) In organics (12, 54, 1.61, 499) Carbqn (230, 238, 370) Chlorine (12, 181, 384, 642, 668, 657) Chromium In alloys and metals (77, 202, 280, 372, 411, 457) In miscellaneous materials (64) Cobalt In metals and alloys (163, 411, 457, 697) In miscellaneous materials (464, 606, 630, 686) In organics (64) Copper In alloys (32, 171, 306, 229, 380, /ill,469) In metals (146, 372, 642, 697) In miscellaneous materials (184, 464) Fluorine (56, 443) Germanium (681) Gold (89, 144, 171, 206) Hafnium (3, 240, 259) Iron In alloys and metals (77, 1.45, 163, 234, 280, 372, 411, 466, 628, 597)
90
80 X-RAY
,
Molybdenum In alloys (457) I n miscellaneous materials (52, 184, 421, 668) I n steels (202) Nickel In alloys and metals (145, 153, 236, 280, 372, 466, 697) In miscellaneous materials (52, 63, 59, 163, 199, 464, 626, 642, 658)
Niobium I n alloys (400, 457) In miscellaneous materials (506. ~, 685) Nitrogen (230, 238) Oxvnen (LLc?) ar r Palladium (206) Phosphorus (12, 241, 400, 626, 677) Platinum (206) Potassium (12, 199, 384, 477, 499, 626) Rare earths In metals (146, 381, 628) In miscellaneous mixtures (11, 616, 683) Rhenium (457) Rubidium (621) Selenium (431, 433, 681 ) Silicon In alloys (202, 372, 400, 636) In cement materials (178) In minerals and ores (161, 199, 384, 653, 677) In miscellaneous materials (142, 143, 360, 394, 626) Silver (171, 206, 535) Sodium (59L 655) Strontium (740, 457, 621, 639, 682) Sulfur (12, 230, 262, 384, 451, 472, 658, 674, 608, 672, 673) Tantalum (457, 506) Technetium (421) Tellurium (103) Thallium (ASS. L57) Thorium (69, $0, 386, 683) Thulium (340) Tin (126, 139,400, 467, 465, 479, 630, 692, 681) Titanium In metals (400, 411) I n minerals and ores (384, 477, 563, 677) In miscellaneous materials (54, 506, 626, 683) Tungsten (31) Uranium (69, 293, 372, 386, 683) Vanadium (53, 180, 400, 457) Yttrium (27, 586, 578, 683) Zinc In metals (32, 77, 206, ?29, 372, 380, 434, 466, 697) In miscellaneous materials (69, 626, 666) In organics (263, $17,698) Zirconium In metals (269, 400, 624) In minerals and ores (3) In miscellaneous materials (464, 630) I
Y
~
\
I
cations in several phases of X-ray emission analysis. Grodski (272) and Uaun and Fischer (39)recently summarized the state of the art for photoelectric-type detectors. There are four basic types of these detectors : multidynode, secondary electron multipliers; resistance strip magnetic multipliers; continuous channel multipiers; and detectors in which photoelectrons are accelerated and subsequently counted. The detectors differ in the method by which the photoelectric signal is collected and amplified. All of the detectors are windowless-the incident X-ray photons are the direct cause of the photoelectric emission from a cathode. The photocathode material has a very pronounced effect on the detector efficiency. These detectors have a poorer signal-to-noise ratio than proportional counters, but their fast pulse rise time permits very high count rates, Presently application of the photoelectric detector is limited to the very low energy X-ray region. Characteristics of avalanche type semiconductor detectors are summarized by Huth and Locker (342). Possible advantages of the avalanche-type detectors are small size, ruggedness, and speed of response. At the present stage of development resolution is poorer than for the gas-filled proportional counters. QUANTITATIVE ANALYSIS
Emission. X-ray spectrography continues t o be used for a n increasing number of applications, both for research and for quality and process control (674). Methods for specific elements are listed in Table IV. Analysis of various classes of samples are summarized in Table V. In the comprehensive bibliography by Stoddart and Dowden (614), there is an index listing the element determined and the matrix being analyzed. Another excellent source of methods is the Applications Review, pnblished by Analytical Chemistry every two years. X-ray emission methods were compared to chemical (402) and optical (201) techniques with regard to accuracy, precision, range of application, difficulty, time, and cost. Although there has not been any major development, there has been steady progress in quantitative aspects of X-ray analysis. These applications range from incinerator slags (626) to logging minerals in situ (45.5) and the analysis of the Moon’s surface (172, 637). Backerud (32) presented a critical discussion of the determination of copper in complex brasses. The ratio of copper Kpl to zinc K a was used to eliminate dependence on surface preparation, sample size, and samp1e-to-Xray tube distance. Applications of various techniques were described in the following papers-
addition (425), dilution (167, 584), emission-transmission (410), external standard (507), fusion (184, 287, 690), line to scatter (74), and solutions (655). Smagunova et al. (585) compared the accuracy of seven standard methods for analyzing ores. Their studies included absorption correction, addition, dilution, internal standard, and line-tobackground. They concluded that the internal standard approach gave the most reliable values. Czamanske et al. (167) compared dilution techniques with simple briquetting for powdered samples. They reported that uncertainties associated with undiluted Samples, moderate dilution, and moderate dilution-fusion methods, make these techniques less generally applicable than suggested in the literature. They conclude that the analyst must either account for absorption and enhancement effects or create an essentially identical matrix for sample and standard. Formulas for the calculation of optimum amounts of diluent are covered by Duimakaev and Blokhin (193). Champion and Whittem (141) compared solution analysis on a weight basis rather than the conventional volume basis. Their paper merits widespread consideration because their approach reduces systematic errors. Matrix effects, the magnitude of which are related to the type and amount of acid or base added, are significantly reduced when samples are compared on a weight basis rather than by volume. A critical investigation of their approach is recommended. Applications of computer techniques to achieve quantitative results continue to increase in the production and control laboratories. The Lucas-Tooth computer program is the one that is widely used (206, 260, 390, 419, 553). Sanderson and Yeck list a program for use with a small computer (553). Their program is used for ferrotitanium ores and residues of widely varying composition. Alley and Myers (13) used multiple regression to analyze ingredients in a rocket propellant mix. Another regression technique (324) was used to obtain estimates of mass absorption coefficients as a function of wavelength. These coefficients were then employed in the calculation of concentration from measured X-ray intensities. A semi-theoretical method was proposed by Andermann (16) for obtaining exponential correction factors for calculation of interelement effects. His method is based on ratios of the difference in mass absorption coefficients between unknown and standard. According to Andermann, his method does not require a large library of standards and the direction of change from interelement effects is easily predicted. Disadvantages are that all elements present in the sample must be considered
Table V.
Applications to a Specific Class of Samples
Alloys Copper base (32, 380, 466) Ferrous (419) General (280, 318, 634) High temperature (403) Light metals (77) Platinum group (206) Titanium (L67) Aluminum (372)’ hlqminum oxide (463) Archaeology (127, 171) Biology (12, 1.40, 141, 263, 692) Boron (107, 642) Carbides (409, 606, 668, 686) Catalysts (616) Cement (463) Clay (360) Clinical chemistry (28, 473) Coal (108, 384) Electronics (375) Flue dusts (666) Foods (499) Gases (181. 668) Geochemistry ( f l ,140, 288, 477) Glass (139, 394) Gold (693) Incinerator slags and fly ash (262, 626) Industrial hygiene (464, 667) Iron and steel (202., 400) . . Iron ores (677)‘ Meteorites (690) Nickel (411) Ores (11, 169, 184, 287, 634, 663) Organics (64, 143) Paints (647) Petroleum (63, 210, 674) Plastics (608) Protective coatings (163, 186) Radioactive materials (293, 361, 464, 683) Rare earths (628,678) Rocket propellants (13, 469) Silicates (161, 390, 394) Slags (162, 178, 677) Soils (646)
and enhancement effects are not corrected. The use of scattered X-rays for matrix correction should expand rapidly, particularly in conjunction with energy dispersion techniques. Hahn-Weinheimer et al. (278) investigated the relationship of scatter to mass absorption coefficients of the sample. Myers et al. developed a mathematical procedure for correcting for particle size and matrix based on scattered X-rays (469). They analyzed mixtures of potassium perchlorate, titanium, aluminum, and a binder. Matrix effects can be corrected by the use of Compton scatter measurements (420). The Compton scatter intensity is dependent on matrix composition in the same manner as fluorescent X-rays. This approach to matrix correction warrants further consideration. Most mathematical procedures for calculating concentration from measured intensities use an “effective wavelength.” Grothe and Krause (274) found that 50% of the excitation of a cobalt-nickel sample was accounted for by the tungsten L radiation and 50% by the continuum. For a 50-50 nickelVOL 40, NO. 5, APRIL 1968
* 351 R
cobalt mixture, 8% of the cobalt radiation resulted from excitation by nickel Kp radiation generated in the sample (275). Obviously the use of a single “effective” wavelength gives incorrect results. Salem and Zarlingo (552) found that, with thick targets, indirect ionization contributes to line production; with very thin targets, line emission results from direct collisions only. The spectral composition of the exciting radiation strongly affects the accuracy of analysis according to Pavlinskii (497). They compared results obtained from yttrium and strontium samples mixed with different filters using molybdenum (characteristic plus continuum) and tungsten (continuum only) radiation. I\‘hen determining a high atomic number element in a low atomic number matrix, the calibration curve is nonlinear because of the strong absorption of the high atomic number element for its characteristic K or L radiation. One way to extend the linear portion of the calibration curve is to use a longwavelength AI spectral line. I n this wavelength region, low atomic number elements make a significant contribution to the absorption coefficient of the sample (273). Particle size and matrix effects are the principal parameters to be considered when preparing samples for X-ray spectrographic analysis. High-speed impact mills provide a 1- to 10-micron particle size range for low atomic number elements (424). Materials must be physically homogeneous initialry, because the milling is highly selective to hardness, cleavage, and fracture. Based on our experience, the recommended method for minimizing particle size and matrix effects is dilution plus fusion. Pyrosulfate fusion and its advantages are summarized by Diae and Anderson (184). Borax fusion continues to be the most widely used technique (287, 390, 401, 690). A minus 100-mesh low-melting, low-viscosity glass composition, composed of six parts boric oxide, two parts sodium carbonate, and one part lithium tetraborate, is available from Corning Glass. One of the principal problems with borax fusion has been the adherence of a portion of the sample to the crucible. This results in a loss of sample plus a difficult, time-consuming cleaning step. Using a Palau crucible (800/, gold-20% palladium), the borax fusion pours cleanly out of the crucible (590). Other promising alloys are platinum %%-gold 5% and platinum 80%-gold 5%-rhodium 157, (private communication with Colin Van Zyl, Anglo American Research Laboratories). Surface preparation is a critical step in the analysis of leaded copper alloys (432). The primary reason for inaccurate analysis is the presence of a
352 R
ANALYTICAL CHEMISTRY
damaged surface layer that is depleted in lead. Metallographic polishing of the samples tends to minimize this problem. One of the reviewers (W.J.C.) is presently evaluating the use of lead K a radiation for analytical problems such as the leaded alloys. The use of high-energy K radiation, penetration of approximately ‘/8-’/4 inch, will minimize grain size and surface preparation variables. Natelson (472) developed a sulfur densitometer for scanning paper electrophoretic strips to determine serum protein. Electrophoresis of the serum protein was accomplished using conventional paper tape. This tape was fed continuously into a vacuum X-ray spectrograph to monitor the sulfur intensity. Preparation of biological samples is described by Zeitz (692) and Anspaugh et al. (22). Determination of halogens and sulfur in gaseous samples was accomplished by Schnell (568). The chromatographic effluent (carrier gas plus constituents being determined) is passed through a capillary that is irradiated by an intense X-ray beam. The elements present in the effluent are determined by measuring the secondary X-rays leaving the capillary. With a 50-mm capillary, the detection limit was 5 x 10-7 gram of carbon disulfide per milliliter of carrier gas. Applications, advantages, and limitations of various plastic binders were considered (650). One application is to convert lipophilic liquids plus an internal standard into a solid sample. Karttunen (361) developed a technique for handling radioactive materials. The dissolved materials are placed in a glass cell and this cell is covered with a Mylar sack; then the Mylar is heat-sealed to prevent leakage. Sample preparation techniques for various types of samples are described in the following papers: nonmetallics (677), minute mineral specimens (288),slimes (418), and sediments (161). Process and Quality Control. T h e characteristics of X-ray emission methods-specific, rapid, and nondestructive-are ideally suited for process and quality control analysis. x’ow t h a t isotopic sources and energy dispersion systems are becoming widely available, dynamic analysis should be greatly accelerated. T h e isotopic source eliminates the need for a n expensive and bulky power supply and X-ray tube; in addition, isotopes are stable sources of X-rays. The principal difference between online and laboratory-type analysis is in the sample preparation and presentation. Obviously, sample preparation must be held to a minimum for on-line analysis. Fusion or dilution techniques are not possible without seriously delaying the time between sampling and analysis. The best approach for ma-
trix correction is to use backscattered or transmitted X-rays to obtain knowledge regarding the absorption characteristics of the sample. The Elliott automatic double path spectrometer is used for quality control of brass and bronze production (580). Samples are either large solid pieces or briquetted drillings. Excellent results are obtained using the ratio of copper to zinc K intensity. Craig (162) presented a thorough discussion on application of X-ray emission methods to control analysis of lead blast furnace slags. Examples of quality control instrumentation using both fixed and programmed spectrometers were described by Davidson and coworkers (174) and Furbee (265). Apparatus for sampling a number of continuously flowing streams of materials was patented by Pick and Bingham (604). Samples can be in the form of powders, slurries, or solutions. Details of wet and dry methods of sample preparation and presentation for dynamic analysis were summarized by Shequen and Smallbone (672). Olie way to handle slurries is to place the sample on a fast-moving belt; the approximate speed is 3 meters per second, and the thickness of the slurry layer is 1.5 to 2 nim (618). No X-ray window is required between the slurry and the X-ray tube. Another approach to slurry presentation is to centrifuge out the solid material by a tangential injector. Then the solid material is passed in front of the X-ray tube. With this technique, the per cent of the element in the solid is independent of the solid content of the slurry (124). Smallbone used scattered radiation at 0.45 A to correct for pulp density and matrix (586). Carr-Urion concluded that an onstream analyzer using radioisotopic sources and energy dispersion analysis gave excellent results (122). Various techniques to correct for or to minimize particle size effects in slurry analysis were described by Carr-13rion el al. (121, 123, 125). Trace Analysis. Fluorescent X-ray spectrography continues t o be used for an increasing number of applications in t h e trace element range (8). Trace elements are determined in the original sample (Class 1) or as isolated microgram quantities chemically separated from the host material (Class 2). Recent publications on allplications and techniques of trace element analysis are listed in Table VI. Natelson and Whitford (473) prepared a thorough review of clincial applications. They offer a number of practical suggestions regarding optimization of signal to noise, sample preparation techniques, and the use of primary X-ray filters. Probably the most extensive application of trace analysis is directed toward
biological problems. Anspaugh et al. (88) are attempting t o correlate trace element concentration and disease; for example, the relationship of diabetes to copper content in the serum and the age of the patient. Standardization of analysis for these biological fluids is accomplished by the addition method. These “standard” samples are subsequently lyophilized and pressed into wafers as are the unknowns. Zeitz (698) determined the zinc content in tissue sections. I n his procedure the zinc KCZradiation is transmitted through thin specimens. Sample weight is determined by scattered radiation measured nondispersively. Very high sensitivity is achieved using his transmission sample-curved crystal focusing geometry. Direct electron excitation of trace elements was evaluated by Toussaint and Vos (635). Detection limits were 0.7 and 11 ppm for silicon and magnesium in aluminum, respectively. The relative sensitivity of direct electron excitation] as compared to secondary X-ray excitation, is still debatable (65). However, in our opinion, X-ray excitation with its greater signal-to-noise ratio is equal or superior in sensitivity to electron excitation. Applications to Class 2 samples are limited only by the complexity of the analytical chemistry required to concentrate and isolate the elements of interest. For example, low concentrations of hafnium dioxide in zirconium dioxide are determined by melting the oxide with sodium thiosulfate] dissolving the melt in aqueous ammonium thiocyanide, and concentrating the hafnium oxide by a three-stage liquidliquid extraction process (240). Trace toxic elements in water are determined by chelating the elements with the ammonium salt of pyrrolidine dithiocarbamate, extracting into chloroform, and evaporating the chloroform extract on filter paper (433). Based on our experience, the ionexchange resin-loaded papers offer the best general approach to Class 2 samples. Principles, general instructions, and applications are described in two publications by the Bureau of Mines (118, 597). By using smaller ionexchange resin paper disks, other researchers achieved sensitivity €or fractional microgram quantities of nickel and vanadium in petroleum products and terephthalic acid (63, 54). Absorption. There were no major developments in quantitative analysis based on absorption techniques during t h e past two years. Radioactive isotopes such as beta (165, 514) and gamma (508) emitters provide a stable, inexpensive source of X-rays. Pruess et al. (514) suggest applications for beta sources using copper, iron, and molybdenum targets. Their compila-
tion of beta-excited X-ray spectra (615‘) is an excellent contribution to the literature. Spectra are presented for calcium-45, phosphorus-32, and promethium-147 in various source configurations. A three-wavelength X-ray absorption edge method was developed for the determination of plutonium in a nitrate medium (279). Two of the wavelengths bracket the plutonium LIlr edge; the third wavelength is used to minimize the systematic error in determining the value of a constant used in the calculation of concentration. The relative standard deviation was +0.6% for concentrations of 10 to 25 mg per ml. Absorption techniques M ere employed to determine composition of rhodiumberyllium alloys (360) and metals in hydrocarbons (165). North (482) adapted an older model Philips fluorescent X-ray spectrograph for absorption analysis. Thin Films and Coatings. Composition and thickness of thin films and coatings can be determined by either X-ray emission or absorption techniques. For ultra-thin films, several monolayers or less, newer techniques described in subsequent sections of this review are applicable; however, proton excitation, photoelectron spectroscopy, and Auger spectroscopy are not so well developed as the conventional X-ray methods. Ebel, Jax, and Perez (200) developed an absolute method for film thickness measurements in the 50 to 5000 .k range. They measured X-ray intensities a t two or more takeoff angles and used these data to calculate thickness; no standards were required. Cline and Schwartz (152) determined the thickness of aluminum on silicon in the range of 0 to 4 microns. Two methods were compared-aluminum K emission, and absorption of silicon K a . The aluminum K emission method was concluded to give the best results; the sensitivity was = t 6A of aluminum. Various methods for determining thickness of tin plate were compared (692). The two methods giving the beat results were measurement of characteristic X-rays from the coating layer (tin) and of characteristic X-rays for the base material (iron). The latter measurement is preferred for on-line control because of its higher intensity output and lower background. Sickel-chromium films are of importance for their magnetic properties. Values obtained by X-ray emission and absorption methods are in excellent agreement with those obtained by colorimetric and interferometric methods (604). Films of noble metals were determined using a molybdenum X-ray tube. The calculation of thickness was based on the assumption that the exciting wavelength was independent of film thickness (186). Thin films, 600 to 1300 A, of nickel,
Table VI.
Trace Analysis-Samples and Techniques
Samples (Class 1) Biological and clinical (22, 140, 263, 472, 475,692)
Inorganic solutions (381, 421, 433, 464, 613,682) (59, 98, 103, 293, 400, 697, 694) Metals Minerals (11, 140, 288) Nonmetals (107. 120. 1 3 .4.) Organics (63, 64, 421) Oxides (69, 240) Thin films (472) Techni ues (Class 2) Ashe\ residues (263, 667) Evaporated residues (22, 433, 516) Impregnated papers (64, 472) Ion-exchange papers and membranes
(62, 63, 98, 118, 139, 293, 385, 464, 697) llicropore filters (103) Precipitation (624, 681 )
cobalt, and iron were determined by stripping the films and analyzing the resultant solutions (153). This approach can be used for any film that can readily be dissolved. The use of backscattered beta rays, backscattered X-rays, and fluorescent X-rays was discussed in two excellent papers on the use of radioisotopes (110, 529). Rhodes (529) covers principles and applications and lists characteristics of various isotopic sources. Margolinas (484) evaluated a radioisotopic gauge for determining zinc coating produced in a galvanizing process. A 100-mCi Xm241source was used with a proportional counter readout. The accuracy of the measurements is = t l micron over the range 50 to 210 g/m2 and = t 2 microns over the range 160 to 350 g/mZ. Margolinas estimates that a gauge costing 40 to 60 thousand dollars can be paid for in 10 months by the improvement in process control. X-Ray Probes. X-ray macroprobes are a n excellent supplement t o t h e electron probe microanalyzer. Konconductors can be analyzed, and surface preparation is not so critical for X-ray excitation as for electron probe measurements. Most of the X-ray probes are attachments to commercial X-ray spectrographs. Reduction in spot size is accomplished by collimation of either the primary or secondary X-ray beam. Bertin compared four slit systems for selected area analysis (60). H e concluded that the inclined slit is preferred because this slit combines high sensitivity, excellent resolution, and narrow spectral lines. .Li modified Siemens Crystalloflex IV was used to study segregation of chromium in steel (355). .1 wide range of applications of the X-ray probe was described by Loomis and Storks (416). One of their problems was to determine the source of lead in cow stomachs. A unique focusing spectrometer X-ray probe was designed by Garton, Campbell, and Watling (258). Other probe designs were VOL 40, NO. 5 , APRIL 1968
0
353 R
discussed in our previous reviews. Commercial X-ray probe attachments were used to investigate thin mineral sections (314) and electroplated diffusion couples (545).
DYSPROSIUM 30' Takeoff
Ma
LOW-ENERGY X-RAYS A N D ELECTRONS
Low-Energy X-Rays. T h e lowenergy X-ray region is becoming increasingly important as the characterization of materials becomes more sophisticated. For many characterization problems, elemental analyses must be supplemented b y information regarding valence, oxidation state, a n d coordination. Information of this type can be derived from changes in the shape and energy of X-ray band and line spectra. A good example is the detailed study on sulfur for clinical information (672, 673). Research in the lowenergy X-ray region has been limited to a few key investigators; however, the number should increase rapidly as the essential instrumentation is now commercially available. Progress in instrumentation and applications of low-energy X-rays is summarized in a special issue of the Norelco Reporter (20'7, SIO). Instrumentation for samples in a gaseous phase was designed by Deslattes and LaVilla (181). Relative intensities of L and 11 spectra in the 2 to 85 range were determined by Davidson and Wyckoff (17 6 ) . Holliday ($57, 328) has made very careful measurements in the low energy X-ray region to relate wavelength shift and intensity profiles of band spectra to the bond strength. The change in shape and energy of the carbon K band was used to identify carbon precipitated in iron, carbon dissolved in iron, and carbon combined with iron as Fe3C. The measurements were obtained with a high-resolution focusing spectrometer having a curved blazed replica grating. Because emission bands are more sensitive to bonding than to structure, spectral data will supplement diffraction. For example, although strontium titanate and titanium dioxide are structurally different, their emission band spectra indicate that the Ti-0 band is similar in the two compounds. Baun and Fischer measured lowenergy X-ray spectra using electron excitation and nonfocusing X-ray optics with oriented soap films as the analyzer. Their very extensive studies include spectra of the following elements and their compounds: boron (232, 2S5), carbon (238), nitrogen (238), and aluminum alloys (38, 231, 2S4236, 2391, and first series transition elements (269). As they accumulate large numbers of spectra, Baun and Fischer are beginning to formulate rules regarding changes in intensity and peak shape as a function of chemical state. For
354 R *
ANALYTICAL CHEMISTRY
\.A eV
9.63 I
1280
~
I
9.40 '
13CO
I
~
I
1320
9.20 ~
I
'
1340
I
'
I
Figure 2. Dysprosium M a and M/3 emission spectra as a function of electron energy (237)
example, in the aluminum binary alloys the aluminum E; band position and the aluminum Kar/Kar intensity ratio are linearly dependent on alloy composition (239). One reason progress in interpretation of spectra has been slow is the poor agreement between investigators. For example, Merritt and Agazzi (452) found that the sulfur L bands they measured by X-ray excitation differed markedly from the band spectra measured by Fischer and Baun using electron excitation. Although some of the conflicting data in the literature can be attributed to sample decomposition using electron excitation, the principal reason for the differences in measured spectra is probably self-absorption of low-energy X-ray lines. The depth at which X-rays are generated is related to the energy of the incident electrons or X-rays. Changes in the takeoff angle significantly affect the "effective" depth from which the X-rays can escape (40). The effects of variation in energy and takeoff angle were very pronounced for the Copper LIlr band spectra. Spectra were measured for energies ranging from 1.4 to 10 keV and takeoff angles ranging from 1" to 70". A more extreme case of self-absorption exists in the Mol and M p emission lines of the rare earth elements (237). Fischer and Baun demonstrated that the complicated structure reported in the earlier literature is a result of the mode of measurement rather than a true characteristic of the M spectrum. Figure 2, taken from their paper, shows that as the electron energy (and hence depth of penetration) is reduced, the spectrum shows less structure. At a high takeoff angle (30") and low voltage (1.5 kV) both the M a and M p are simple line
'
spectra. The complex structure observed at low takeoff angles and high electron energy results from self-absorption and a complex absorption edge structure. For future publications, we urge authors to give their operating parameters in detail so that data can be critically compared by other investigators. Also the data should be obtained under experimental conditions that minimize self-absorption. High-resolution absorption techniques can also be utilized to gain information regarding bonding. Xzaroff discussed the application of low-energy absorption methods to the study of alloys (30). White and RlcKinstry (669) measured the K absorption fine structure of 40 simple oxides of six elements. They found the following factors to be most I : bond character, nearest significant neighbor environment (primary coordination number), and valence. Longrange ordering apparently has little or no effect on the fine structure. Excitation by Heavy Particles. Although excitation b y protons and alpha particles has not been applied t o many analytical problems, these techniques offer several significant advantages over electron excitation. Efficiency of X-ray production b y proton excitation increases with decreasing X-ray energy. Also t h e bremsstrahlung radiation is reduced by a factor of the square of the electron mass to that of the proton or alpha particle. Therefore excitation by heavy charged particles should yield essentially monochromatic low-energy radiation (86, 370, 435, 567, 611, 612). Production efficiency for lowenergy X-rays can be calculated from the following equation:
N
=
kK.~,jIZ-6.82 exp (0.062 E,)
(2)
where N = X-ray yield in photons/ proton, kx = 0.192, k~ = lo2, k v = 3.4 x 108, and E , = proton energy, keV. The line-to-background r?tio for copper L a to background at 3.5 h is 37,000 to 1 when filter attenuation and counter efficiency are considered (612). The thick-target X-ray yield was found to be a function of the crystallographic orientation of single-crystal samples (371). The single-crystal yield exceeded the polycrystalline sample yield by 30% a t certain orientations. For single crystals of copper, the largest observed maximum-to-minimum yield was 15 to 1 in the vicinity of the 001 direction. Channeling of low energy protons is strongly related to the crystallographic orientation of the sample. The sensitivity of the X-ray yield to orientation suggests that this technique will provide significant information re-
garding the interaction of positive ions and ordered arrays of atoms. Surface chemical analysis by alpha particle bonibardnient recently received world-wide attention when the first in situ lunar analysis was performed. The instrument designed by Turkevich et al. (640) utilizes the variation in backscatter of monoenergetic alpha particles with matter as a function of atomic number. The energy spectra of backscattered alpha particles from curium-242 were measured with semiconductor detectors. Other detectors measured protons from CY, p reactions. Surface density of very thin films can be determined by proton excitation techniques. Thin films of aluminum, copper, and ytterbium were determined using the instrumentation shown in Figure 3 (146, $69). The X-ray yields from the unknowns were compared with those obtained from films of known thickness. Using a 10-p-4 current incident on a thick aluminum target, a typical detection system would record 10,000 counts per second with a counter signal-to-noise ratio of io4. ;\t a signalto-noise ratio of unity, the calculated surface density is 0.005 pg/cm2. The range of surface density that can be measured by proton excitation spans four orders of magnitude. Lower limit of the surface density measurement is established by the magnitude of the proton capture cross-section and the counter background. The upper limit is a function of the proton energy. Auger and Photoelectrons. -4uger and photoelectron spectroscopy are excellent complementary methods t o loiv energy X-ray spectrography. These techniques have been known for many years, b u t found very limited application because of experimental difficulties. Rapid growth is predicted because simple reliable electron spectrometers will be available a t a price competitive with low-energy X-ray spectrometers. Lowenergy electron zpectroscopy can be used to determine composition of layers as thin as one tenth of a monolayer. Depth of penetration is usually less than a few hundred A; the depth can be varied by changing the energy of the exiting radiation and the takeoff angle. All elements above beryllium are detectable and the method has high sensitivity, particularly if the element sought tends to segregate on the surface. Semiquantitative and qualitative analyses are readily obtained; however, quantitative results are difficult to achieve because of the problems inherent in preparing ultra-thin samples and standards. When an atom is excited by electrons, the atom can return to the ground state by emission of characteristic X-rays or by a radiationless process in which Auger electrons are emitted (102, 21'7,
221). The energies of Auger electrons are specific for the element but not so well defined as X-rays. The observed huger spectrum consids of comparatively broad peaks of slightly leas energy than the transition energies of the atoms. Although these peaks are broad, the -4uger spectra look very promising for determination of low atomic number elements. The Auger electron yield is very high for low atomic number elements, whereas the X-ray fluorescent yield is Ion. Experimental difficulties for low-energy X-rays and Auger electrons are comparable. Because of the low energies used for escitation and observation, .4uger analysis provides information about extremely thin surface layers. This loiv penetration provides information on surface segregation, surface contamination, and diffusion in solids (289-291 ). Instrumentation for .4uger spectroscopy, shown in Figure 4, consists of an electron gun, sample holder, electron-energy analyzer, and electron multiplier. The system is evacuated with sorption-ion pumping and sealed with metal gaskets to avoid organic contamination. Because of the thin layers being examined, cleanliness of the vacuum and surface preparation of the sample are very important (291). In photoelectron spectroscopic chemical analysis (ESC-A), low energy Xrays such as aluminum KCYare used to eject photoelectrons from the sample surface (218). T h e photoelectron energy is given by the folloiving relationship : Ephotoeieetron
=
Ex-rayphoton - E b i n d l n g energy
E w o r k function o f spectrometer housing material
(3)
Therefore, the photoelectron energy is a function of the binding energy of the atom for the ejected electron. Because this binding energy varies ith chemical state, photoelectrons can be used to determine valence and olidation state. These changes in binding energy are easier to detect by photoelectrons than by X-rays for the following reason: I n X-ray emission the X-ray photon energy represents the difference in energy between two levels, whereas the photoelectron energy represents directly the change in binding energy. ;Ilthough there may be relatively large changes in binding energy between K and L electron levels, there will be only a small change in X-ray energy if the shifts are compaiable and in the same direction. I n contrast, using ESC;\, a change in binding energy of several electron volts is easy to detect. For example, photoelectrons for Sz- and S6& in sodium thiosulfate are easily resolved. -4uger spectra give additional information; two lines with a 4.3-electron-volt separation for S2-and S6+nere observed (218). ESCA tech-
PROTONS
I COLLIMATORS
1
I
I
Figure 3. Schematic of proton excitation instrumentation ( 7 46)
niques can be applied to E; shell photoelectron emission of low Z elements (219) and to L and 11 shell emission for medium and high Z elements (129, 620, 481). Some characteristics of ESCA are: Electron binding energies of inner shells increase with increasing oxidation number; all three levels, K, LI and L I ~ , ~have ~ I ,an energy shift of approximately 1 eV per degree of oxidation, and shifts are approximately the same regardless of the cation-e.g., potassium+
Table VII. Energy Dispersion Instrumentation and Applications
Instrumentation Detectors (64, 83, 105, 296) Filters (49, 91, 133, 198, 199, 285, 383, 548)
General (67, 82, 110, 123, 126, 440, 492, 531, 536, 565, 622, 633, 666)
Principles (110, 438, 532) Radiation safety (21, 492, 637) Sniirres "__
Alpha (566, 637, 641 ) Beta (109, 21 1, 409, 437, 622) General (21, 357, 515, 566, 696, 622, 6.41. 6 6 1 4 6 6 )
Spectral convolution (9, 66, 271, ,276, 295, 565, 676, 637)
Applications Alloys (56, 534, 636) Cement (534, 6 4 1 ) Coal and coal ash (57, 108, 363, 470, 534, 535, 638)
Coating thickness and composition (58, 110, 138, 363, 434, 463, 529, 638, 666) Foods (57) Gases (615) General (61, 385, 439, 491) High purity elements (593) In situ ore analysis (2, 9, 455, 568) Low atomic number elements (133) Mail sorting (168, 544) Metal identification (89, 351) JIicroanalysis (343) Ores (66, 82, 1.84, 126, 158, 169, 170, 455, 478, 479, 492, 633, 534, 565, 637, 666) Petroleum and hydrocarbons (210, 492) Slurries (121, 122, 124-1 26, 610) Solutions (57, 386, 670)
VOL 40, NO. 5 APRIL 1968
355 R
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COLLIMATOR
ELECTRON EMITTER FOR SAMPLE HEATING
TRA
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CRYSTAL7
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DETECTOR
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WAVE L E N G T H D I S P E R S I ON
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Y
ENERGY DISPERSION
Figure 5. Comparison of X-ray spectrometer optics and energy dispersion (66)
MULTIPLIER
-+ Figure 4.
-
Schematic of Auger electron spectrometer (291 )
as compared to sodium+-when anions are the source of photoelectrons. Instrumentation for photoelectron spectroscopy is similar to that for Auger spectroscopy, the difference being that X-rays are the source of excitation in ESCA. In one arrangement (216) radiation from the X-ray tube is filtered with aluminum foil before striking the sample. Photoelectrons from the sample leave through a defining slit into the spectrometer. By varying the current in the spectrometer coils, electrons of a selected energy are brought to a focus a t the detector slit. The coil current is varied step-wise and the photoelectron pulses are stored in a multichannel analyzer. Instrumentation for a permanent magnet ESCX spectrograph was described by Fahlman and Siegbahn (222). Recent techniques for producing electron beams with narroiv energy resolution and various methods for measuring these energies are summarized by Klemperer (388). ENERGY DISPERSION X-RAY ANALYSIS USING RADIOACTIVE SOURCES
During the past two years there has been a very significant increase in instrumentation and applications of Xray analysis using isotopic X-ray sources coupled with energy dispersion techniques based on electronic pulse amplitude discrimination and selective X-ray filters. Progress in various countries was summarized in the following re(666),France (440), ports-Australia Japan (363), Poland (491), and the Cnited Kingdom ( 2 1 ) . In the United States, the research and development of isotopic X-ray analyzers has been accelerated by the strong support of the Division of Isotope Development of the
356 R
ANALYTICAL CHEMISTRY
Atomic Energy Commission. Major symposia on uses of low-energy X-ray sources were held in Warsaw, Poland (348), Chicago, Ill. ( J 4 ) , and Austin, Texas (35). General review papers were prepared by Campbell (115), Holynska ( @ I ) , Martinelli (43S), and Rhodes (530). Publications on various aspects of instrumentation and application are listed in Table VII. In conventional X-ray spectrography the sample is subjected to a very intense X-ray flux of approximately 10’3 photons per second. The resultant fluorescent X-rays are dispersed by a crystal analyzer (see Figure 5 ) . This wavelength dispersion technique gives excellent spectral resolution, but the geometrical losses and low diffraction efficiency reduce the X-ray intensity by a t least lo6. The fluorescent X-ray spectrograph requires a stable 2- to 3-kW power supply, a precision goniometer, and an electronic readout. A moderately priced spectrograph costs 15 to 20 thousand dollars. Energy dispersion systems using a radioactive isotopic source can be very simple, as shown in Figure 5 . This basic system may be augmented by filters placed either between the source and the sample, or between the sample and the detector. The detector can be a gasfilled proportional counter, a scintillation counter, or one of the new lithiumdrifted silicon or germanium detectors. An instrument using proportional or scintillation counters costs two to four thousand dollars; with the lithiumdrifted detectors, the cost is increased by a factor of two. The photon flus available from isotopic sources is in the IO6 to IO8 range. Because of the close coupling of the source-sample-detector
assembly, the overall collection efficiency is approximately 1%. Therefore, isotopic sources provide useable intensities for energy dispersion analysis. Sources. There are three types of isotopes used for energy dispersion analysis-alpha, beta, and gamma emitters. Alpha emitters such as polonium-210 and curium-242 are used to excite low-energy X-rays. They offer the advantage of high signal-tonoise, but are potent health hazards. Beta emitters are normally used to generate bremsstrahlung plus characteristic X-rays that collectively excite fluorescent radiation from the sample. These sources may be in the form of a thin layer of the isotope on a suitable target material, or a mechanical or chemical mixing of isotope and target. Pruess et al. (525) compiled extensive data on three beta emitters-promethium-147, calcium-45, and phosphorus-32. Sources that decay by electron capture yield essentially monoenergetic radiation, e.?., cadmium-109 emits silver K radiation. By selecting an isotope whose characteristic radiation just exceeds the absorption edge energy of the element being determined, high signal-to-noise ratios can be achieved. High-energy gamma emitters are usually used in a source-target configuration where the gamma radiation excites lower energy X-ray5 characteristic of the target. These X-rays are then utilized to excite X-rays characteristic of the sample. “The Isotope Index” (596) is an annual listing of source suppliers and prices. Detailed information on source design and fabrication of special sources is available from various companies engaged in source development. Catalogs of spectra of various isotopes have been compiled that are a valuable aid for selecting a source for a particular application (85,294, 515). The Isotope Information Center a t the Oak Ridge Sational Laboratory provides assistance in obtaining information regarding the availability of isotopes. Their excellent quarterly publication “Isotopes and
,SAMPLE
60
I
I
I
P A 2 BAND
DETECTOR WINDOW
A
dSAMP 15
C
XD-ERTAEYC T FILTER OR F
~
C
O
U
O
ANNULAR A R R A Y F SOORCES
h
SCINTILLATION T L R
20
25
30
35
40
X - R A Y E N E R G Y , kev
Figure 7.
Balanced filters for Tin K a radiation (82)
VilNDOW
B
Figure 6. Central and annular source geometries (530)
Radiation Technology” reviews progress in industrial and research applications of isotopes. T n o soul ce-sample-detector geometries used ~ i t beta, h gamma, and X-ray emitting isotopes are shoivn in Figure 6. The central source arrangement is the one most M idely used in radioisotopic X-ray analysis. The important parameters are the sample-source-detector distances and the relative sizes of the three components. The X-ray filters are usually placed between the qource and the detector \\indow. Using the central source geometry, overall efficiencj is lo-* to lO-‘so that counting rates of l o 3 to IO5 counts per second are obtained from pure elements. Shielding is provided by a shutter and by the sample being analyzed. ;inother useful geometry is the annular source in ahich the sources are arranged in a doughnut-like array around the outside of the detector window. This type of source arrangement is necessary to prevent the source from blocking excited radiation from the sample reaching the detector. Source-target assemblies are used n i t h beta and gamma emitters to give a characteristic spectra of the target element. This target element is selected so that the energy of its principal X-ray line just exceeds the absorption edge of the element to be determined. The source, a high-intensity gamma emitter, is positioned in a cup formed by the target element. The high-energy gamma radiation from the source excites X-raj s characteristic of the target element These characteriftic X-rays superimpoied over a acattered gamma background are the source of excitation. Resolution. T h e resolution in energy dispersion techniques is provided by Ross filters, a detector whose out-
put pulse is proportional t o t h e photon energy, or some combination of the two. T h e Ross filter in combination with a low-resolution detector-the scintillation counter-is the system used for most energy dispersion applications. Instrumentation of this type is available from several manufacturers. Other instrument manufacturers have adapted Ross filters for use with proportional counters. These balanced (Ross) filters were developed 30 to 40 years ago (385, 548);however, they were not required for conventional X-raj spectrography utilizing crystal spectrometers. The balanced filters generally consist of two thin metallic folds that have absorption edges on the low- and high- energy side of the X-ray spectral line of interest. For example, the filters for tin K a radiation are thin sheets of silver and palladium (see Figure 7 ) . The energy of the tin K a line just exceeds the K edge of palladium, a strong abforber of tin K a , while the tin K a radiation is highly transmitted by the silver. The thickness of the two filters is carefully controlled so that their ab3orption characteristics are similar for all X-rays except those in the narrow pass band. The difference in measured intensity, using first the silver and then the palladium filter, is related to the tin content of the sample. In general, the balanced filter technique is limited to major, and in favorable cases, minor constituents, as the analytical line intensity is a small difference betneeri two large intensities. Any spectral line whose energy falls within the pass band is a potential source of error. The Ross filter is a single-element analyzer; therefore, each element requires a unique set of filters. The Ross principle is eaiy to apply and can be used n i t h broad spectrum sources and wide band detectors. Broquet, Robin, and T’acher (91) presented an ewellent discussion on filter preparation, choice of filters, and possible spectral interferences. They prepared filters by mechanically rolling metallic foils, chemical etching, electrodeposition, and encapsulation in
plastic. Preparation of foils for the 1to 15-keV region is discussed by Halliday et al. (286). Other researchers have prepared filters of strontium (49) and filters for low atomic number elements (198, 199). The low atomic number filters were dried slurries of the powdered compounds plus polystyrene. The use of gases for X-ray filters was investigated by Castaing and Pichoir (133) for the nondispersive analysis of low atomic number elements. Their filter assembly is a cylindrical container closed a t both ends by collodion windows. Pressure of the circulating gases can be continuously adjusted to vary the transmission of low-energy X-rays. During the past two years, the lithium-drifted silicon and germanium detectors became commercially available. The high resolution provided by these detectors makes it possible to achieve multi-element analysis using energy dispersion techniques. The resolving power of various detectors is compared n i t h spectral resolution by Rosi filters and crystal diffraction in Table VI11 (103). The resolution of adjacent spectral lines is proportional t o the dispersion and inversely proportional to line width. T o compare resolution achieved by various techniques, a figure of merit, R , was formulated that is equal to the separation of the peaks of characteristic Ka lines of adjacent atomic number elements divided by the line width at one-half maximum intensity. For Ross filters, the line width corresponds to the pass band. The resolving power of conventional flatcrystal optics was evaluated for typical collimator-crystal combinations. Four sets of spectral lines were evaluated covering X-ray energies from .ilE(al, 1.49 keV, to -iuKal, 68.8 keV. I n the soft X-ray region, 50 keV, the lithium-drifted silicon detector results in higher resolution than can be obtained by conventional flat crystal optics. Analyzing crystals with very small d-spacing and high reflectivity are not available so that pulse amplitude discrimination using a lithium-drifted detector and balanced filter techniques are recommended for evaluation in the high-energy X-ray region. Applications. T h e principal problem in conventional X-ray spectrography-the matrix effect-is equally important in energy dispersion. When t h e sample is analyzed in t h e laboratory and t h e sensitivity is adequate, t h e matrix effect can be reduced or effectively eliminated b y dilution. For in situ analysis, or when sample handling is to be minimized, alternative methods are required. Probably the best approach is to use the intensity of backscattered X-rays as a means for matrix correction. Although there have been many successful applications of hackscattered Xrays, the analyst must first establish the validity of this approach for his particular problem. Several theoretical and semi-empirical formulas have been derived to describe the relationship between the properties of the scattering medium and the gauge geometry (Z'), Lubecki et nl. (420) found that Compton scatter behaved similarly to fluorescent X-rays and could be used for matrix correction. Other analytical problems in conventional X-ray spectrography such as particle-size effect, surface preparation, and chemical effects are also present i n energy dispersion, but to a different degree. The use of high-energy K series X-ray lines minimizes variations in intensity duc to surface roughness or
particle size because the penetration of the characteristic X-rays has increased from microns to millimeters. In the soft X-ray region, peak shifts resulting from chemical effects will not be observed because of the much poorer resolution of the energy dispersion method. Obviously, this poorer resolution is not always advantageous. There are many limitations to applications of energy dispersion imposed by inadequate resolution of spectral lines, particularly when determining low concentrations. Energy dispersive X-ray systems are being used for many of the research and control analyses that were provided by conventional X-ray spectrographs. The acceptance of these new techniques is demonstrated by the large number of applications listed in Table VII. These applications range from in situ analysis of the lunar surface to the meat-fat ratio of animals. Industry is beginning to use these simple instruments for widespread quality and process control analysis. X-ray emitting isotopes, produced by neutron activation, ran also be used for encrgy dispersion analysis; for example, K capture isotopes emit radiation that is specific for the element being determined (505, 571). Following the excellent introductory paper by Bowman et al. (83) a number of publications have described energy dispersion applications of the semi-conductor detector (298, 530, 344, 356, 533). For isolated microgram quantities of elements deposited on filter papers the limit of detection is the 10- to 100- microgram range. Limits of detection for samples as powders, solids, or solutions, are in the order of 100 ppm. Lower detection limits can be achieved by using isotopic sources of higher strength, improved source-sample-detector geometry, and longer counting times.
~
Table VIII.
Comparison of Spectral Resolution by Diffraction and Energy Dispersion Techniques
R=-D W"2
Scint ilLi-drifted Proportional lation Ross Energy, Crystal Jectral silicon counter counter filter keV diffraction lines 43." ... 0.3 ... 0.9 1.49 AlKcvi 1.74 SiKw 1.0 0.5 0.2 1 .o 12.b 7.48 NiKal 8.05 CuKcri 1.1 0.5 0.2 1.0 2.3b 21.18 PdKai 1.3 0.4 0.2 1.0 1.oc 22.16 AgKw 66.83 PtKai 68.80 AuKoli a EDdT crystal - coarse collimation 0.8'28 = TY1'2. * LiF crystal - fine collimation 0.3"28 = Wi/z. c LiF crystal - fine collimation 0.3'28 = W 1 / 2 2nd order lines were used. D = distance between K a peaks for adjacent atomic number elements. W ' Z = width of peak at l / ~maximum intensity. D and TY are expressed in 28 for crystal diffraction and keV for energy dispersion.
358 R
ANALYTICAL CHEMISTRY
JYe predict a very rapid increase in the application of energy dispersion Xray techniques using radioisotope excitation sources. This increase will be a result of the advantages offered by these techniques : lower cost, excitation selectivity, and stability, portability, and simplicity of operation. These new instruments cost 2 to 5 times less than conventional X-ray spectrographic equipment: therefore, they can be purchased economically for specific problems. There is the opportunity for much greater selectivity in excitation conditions as numerous isotopic sources are available a t moderate cost. The isotopic sources eliminate the need for voltage and current stabilizers and the electrical and water requirements of the conventional sealed X-ray tube. The battery-operated energy dispersion systems are compact lightweight instruments; thus, the portability can be used to advantage in many applications. Finally, the simplicity of operation should increase the utilization by loner skilled personnel working in metallurgical, chemical, and mining industries and in clinical laboratories. ELECTRONPROBEMICROANALYSIS
In the past two years significant progress has been made in defining and characterizing the parameters that are important in relating measured X-ray intensities quantitatively to composition. For X-rayo wavelengths of approximately 3 A and shorter, the methods of quantitative analysis are reasonably well defined. In this region analyses to within 2 per cent relative are possible using pure elements as standards, provided mass absorption coefficients, fluorescent yields, and atomic number parameters are accurately known. The most significant barriers to better analyses are no longer the theories of quantitative analysis but rather the basic physical parameters such as the mass absorption coefficients and the depth distribution of X-ray production required in these theories. Until better values are available, it will be impossible to distinguish unequivocally between the merits of the theories as finer and finer distinctions are made. The same problem is arising in the Monte Carlo and transport equation treatments of quantitative microanalysis. Data for use in these equations are simply not sufficiently accurate to determine the agreement between theory and measurements. Thus the evaluation of further advances in these theoretical treatments must await more careful measurements. We can, therefore, expect a greater emphasis on the accurate measurement of X-ray parameters in the next few years. The situation is not so satisfactory foroanalytical wavelengths longer than 3 A. The seriousness of the problems
of wavelength shifts, band shapes, self absorption, and variation in transition probabilities is just beginning to be realized. Coupled with the lack of truly accurate maqs absorption coefficients and other parameters, analyses that can be called quantitative are not very often realized. On the positive side, almost all manufacturers have available spectrometers for routine measuremen; of X-ray wavelengths to a t least 50 A. The ease of measuring these wavelengths will stimulate research into the factors affecting quantitative analysis. Indeed, in the past two years the first attempts at defining application and limitations of methods for quantitative analysis using long wavelengths have appeared. Rapid progress can be expected. This emphasis on the use of longer and longer analytical wavelengths has placed a greater burden on the operator of an electron probe microanalyzer in that he must know more and more about the physics of X-rays. Many analyses could be in error by a factor of 2 or more because of improper operation of the electron microprobe, unsuspected wavelength shifts, or the use of inapplicable calculation methods. More thorough training must be available to ensure that gross errors are not committed by inexperienced microprobers. The many users groups and the Electron Probe Analysis Society of ..imerica should take an active role in this educational process. The use of computers to reduce the manual labor in converting X-ray intensities to composition has become commonplace. Many different programs based on the many published correction equations have been mritten. More and more, automatic data collection systems are being used in connection with electron probe microanalyzers and computer programs. This relieves the operator of the routine operations in connection with microanalysis but at the same time requires a greater diligence to ensure that the results have meaning. The danger with these programs is that the arithmetic accuracy of the computer tends to be equated with the accuracy of the Xray measurements and the equations used in the program; the results, therefore, are viewed with much greater significance than they may merit. Inexperienced operators particularly are a p t to use such program< as a crutch, which impedes their quest for better understanding of factors involved in quantitative analysis. -i number of neir instruments have been developed. Mainly these are improved instruments by existing manufacturers M hich reflert the trend toward modularity of design and simplicity of operation. In recognition of the importance of qualitative analpis, these new
instruments all have excellent beam scanning systems with the ability to display a variety of electron current and X-ray signals with biasing to enhance contrast. The emphasis on long wavelength analysis is also reflected by the fact that spectrometers for detection and measurement of wavelengths to a t least 50 A are available with all of these instruments. Another interesting development is the appearance of commercial instruments combining the functions of an electron microscope and electron probe microanalyzer. Evaluation of the contributions of these combination instruments must await their more widespread use in the nest few years. Publications and Meetings. Several new books on electron probe microanalysis have been published. These are included in the list of books given in Table I. T h e most important of these is the Proceedings of t h e Fourth International Conference on X-ray optics and X-ray microanalysis held a t .irsay3 France, in September 1965 (131). This book includes reports of the most significant research in the field of electron probe microanalysis in the past few years, and reflects the continuing high quality of these international meetings and of the published proceedings. Papers presented a t four other meetings have been the subject of separate issues of a journal or will have been published as books by the time this review article appears. Proceedings of two meetings held in Vienna, Austria, in 1964 and 1965 have been published as separate issues of Mikrochimica Acta (456). A number of papers presented a t the First Sational Conference on Electron Probe Microanalysis have been collected and will be published in the series “Advances in Electronics and Electron Physics,” published by Academic Press. The review papers presented as part of the 69th annual meeting of ASTM in Atlantic City, ?;. J., June 1966, also will be published as part of a Special Technical Publication of .1STlI ( 1 4 ) . .A brief summary of a meeting on applications of electron probe microanalysis sponsored by the Institute of Metals was given by Swindells (619). H. l l a l i s a (426) has written a general book on electron probe microanalysis in German. Heinrich (298) recently reviewed this book and comments that its strength lies in the practical approach of the author toward experimental details of microanalysis. The treatment of quantitative analysis, however, tends to be descriptive rather than critical. The book by Theisen (630) on quantitative analysis is disappointing. I t presents the equation, for a system of quantitative corrections which he has developed arid lengthy tables to expedite the corrections. However, both
typographical errors and errors in the derivations of the equations limit the usefulness of an already limited book. Poole (609) in reviewing the book is particularly critical and warns of possible danger in ready acceptance of the equations and tables. Eliori (209) has also written a general book on electron probe microanalysis. Unfortunately, this book also gives a very biased view, particularly in the section on instrumentation. KO effort has been made to compare or even describe the many different types of instruments presently available, which vary widely in their characteristics. Also, discussion of quantitative analysis is rather limited. For the geologist, Adler ( 5 ) in his book on X-ray analysis devotes several chapters to electron probe microanalysis with particular application to geological samples. These are easily understood and well written and present a good introduction to electron probe microanalysis. Anderson (20) noted that the extensive work of Smith et al. (537,687-690) on the use of standards for establishing quantitative relationships in the analysis of silicate minerals was not discussed in ;Idler’s book. An annual series of conferences was instituted in the United States in 1966, to bring together a t one meeting the many electron microprobe papers which previously were presented a t scattered meetings throughout S o r t h America. At the first conference a t College Park, Md., in May 1966, a committee headed by Dr. L. L. Marton of the Xational Bureau of Standards was commissioned to investigate the desirability of forming an organized society. Impetus was given to this action by the success of the First Conference and the difficulties experienced in organizing such a conference without formal backing. The recommendation of the committee to the attendees of the Second Conference in Boston, June 1967, that a Society be organized was approved by a large majority. The Electron Probe -4nalysis Society of America was thus formed. The election of the executive board will have taken place by the time this review is published. The third national meeting will take place in the Chicago area in 1968. A major problem in electron probe microanalysis continues to be the proper training of operators and of analysts concerned with interpreting the data from electron probe microanalyzers. With the ever increaiing sales of new instruments this promises to be a continuing problem. Education would seem an important area where a significant contribution could be made by the Electron Probe Analysis Society of America. Probe users groups now exist in practically every area of the United States, VOL. 40, NO. 5 , APRIL 1968
359 R
in Canada, in Japan, and in many areas of Europe. These groups have proved a useful forum for the discussion of analytical and instrumental problems. The two major areas which these groups are attacking are the analysis of standard samples to establish reproducibility of results on a variety of instruments and the establishment of performance standards for instruments so that new operators can have some basis for judging how well an instrument is performing (62). Some comments of the Washington probe users group on the pitfalls in the analysis of standard samples were presented at the 69th annual ASTM meeting (14). Reports of the activities of several users’ groups have been given a t the national meetings in College Park and Boston. Quantitative Analysis. T o relate measured X-ray intensity t o concentration, corrections must be applied for absorption, fluorescence due t o characteristic lines, and atomic number. Several general discussions of quantitative probe microanalysis have been published in the past two years (18, 23, 28, 66, 480, 498, 579, 694). Smith (587) has recently reviewed the various factors that are important in theories relating X-ray intensity to composition. A correction for fluorescence due to absorption of the continuum is acknowledged but seldom applied. The rationale used in ignoring a continuum fluorescence correction is that the contribution is a more or less constant fraction of the intensity generated in the sample and pure element standard, or that it is included in the atomic number correction. Up to 15% of the measured intensity from gold a t 30 kV is reported to be due to continuum fluorescence. From the same source, a correction of 6.5% to the calculated composition in InAs is necessary (92). These data would indicate that a more careful evaluation of fluorescence due to the continuum would be fruitful. Important criteria in quantitative analyses are the sensitivity or limit of detection of a method and the precision of analysis. Ziebold (695) pointed out that far more is involved in the estimation of precision and sensitivity than simply counting statistics. One of the major additional factors is the height of the sample relative to the spectrometer. This sample height is extremely critical for instruments in which the sample surface is tangent t o the focusing circle for the spectrometer. Ziebold developed expressions which can be used to estimate sensitivity and precision based on the Ziebold-Ogilvie relation between intensity ratio and concentration. This Ziebold-Ogilvie equation has been used in the analysis of ternary samples (346). Sensitivity of two kinds of instruments have been 360 R
ANALYTICAL CHEMISTRY
compared by .irlt and Bloch (25) based on peak and background measurements. They found a very strong dependence of sensitivity on electron voltage. .1 number of evaluations of the correction procedures have been made in the past two years. These evaluations are based on comparison of known compositions with those calculated form the measured X-ray intensities. ;ill of these claim to be critical, and most dram conclusions about which correction procedure is best. The significance of these evaluations must be carefully considered. Some of the important criteria are: (a) What equations are being evaluated and is the comparison made between the most recent form of each equation? Quite frequently evaluations are biased by the use of equations which have been modified from an admittedly limited form. -1s an example, Helgesson (307) compares the absorption correction of Philibert with that of Tong. The modification of Duncumb and Shields to the Philibert equation is not used, although, for the samples containing aluminum, the Duncumb and Shields modification has already been shown to be important. (b) Are the efferts for which the evaluation is made the only significant corrections in the sample? Evaluations of the atomic number effect have been plagued with errors because uncertainty in the absorption correction due to possible error in mass absorption coefficients completely masks the existence of an atomic number effect. The existence of an atomic number effect for copper in the Cu-Si system as reported by Ranzetta and Scott (517) has been proved because the mass absorption coefficients for C u K a are essentially identical and small for both elements. Unfortunately a possible fluorescence effect by the Kp line of copper was not taken into account and the demonstration of any atomic number effect for nickel in the same system cannot be considered as proven. (c) T h a t experimental measurements were used for the evaluation? Quite frequently, on the basis of analysis using a single instrument for a single binary System, or even on a single sample, recommendations are given as to which correction procedure is best. Such recommendations can hardly bear any weight a t all as many errors could bias the results toward the equations which are not suitable except for very limited analyses. (d) K h a t data such as mas9 absorption coefficients, fluorescence yields, etc., have been used in the evaluations? -1gain, because of the u?rertainties in the parameters, comparisons can be biased because of the particular values used. The beat method of circumventing this latter problem would appear to be to compare correction procedures applied to a large volume of data, using a histogram to plot errors. This procedure was first used by Poole (610)
and has since become quite popular (51, 307, 630). (e) Do the equations that are compared really apply to the measurements which have been made? Many comparisons are made in which the approximate methods such as those of Belk (51) are evaluated for much data for which they were never intended to apply. Beaman (43) has done extensive calculations, many of which proved the inaccuracies of equations that were already pointed out in the original papers. In evaluating the advances made in quantitative analysis, the X-ray wavelengths should be divided into shortand long-wavelength regions +th the division falling roughly a t 3 A. The choice of this division is predicated by a number of factors. For the shortwavelength region, using the best of the presently available correction equations, analyses to within l or 2% are generally possible using pure elements as standards. The absorption correction is limited to moderate values by the largest mass absorptign coefficient for wavelengths up to 3 -4. is approximately 1000. Finally, 3 A represents the longest wavelength for which efiects such as wavelength shifts due to chemical bonding may be safely ignored. I n the long-wavelength region, lower accuracy must be expected because a whole host of new effects must be carefully considered. These effects will be discussed in a later section. Absorption Correction. The absorption correction equation proposed by Philibert and as modified b y Duncumb and Shields has become the most widely used absorption correction equation. The form of this equation was given in our 1966 review (117). Evaluations such as those by Beaman (43),Colby and Conleg (154), and Heinrich (301) support the view that this equation is the best currently available for quantitative analysis in the short-wavelength region. J. V. Smith (587) has evaluated the use of various absorption correction equations for quantitative analysis of mineralogical specimens. For elements of atomic number greater than Si in the Periodic Table, p d hence wavelengths shorter than 7 A, he recommends the m e of Philibert’s equation or f ( x ) tables. Adler and Goldstein ( 6 , 7 ) have prepared tables of the modified Philibert equation, so that this absorption correction can be applied quickly by finding two values in the tables. Similar tables have been prepared by Ranzetta and Scott (520). Theisen (629, 631) proposed alternate parameters for u and h in Philibert’s equation. These values are ,J
8.9 (Eo
x 105 - E,)*
= ~-
(4)
where E , and E, are the electron energy and absorption edge energy, respectively, and
Eo2 A ( E , - E J 25
h = 1.5308-
(5)
where A and Z are atoniic weight and atomic number. Theisen supports the use of these parameters on the basis of agreement known and calculated compositions for data from over 100 samples of published data. It is unfortunate that the errors and inaccuracies in his book (630) have tended to discredit this correction equation so that few evaluations have been made. Beaman (43) rates the Theisen equation as quite low in accuracy. I n Russia, Il’in and Loseva (345) have proposed an absorption correction based on a concept of an effective depth for X-ray production which is an extension of a similar concept of Kupriyanova (397). The form of this proposed correction is that
KA
=
CAfi
where K A is the ratio of the measured X-ray intensity of a characteristic line of element A in a sample to the intensity in the pure element A ,
Cn is the concentration of element A , and
f,is given by Equation 7 : I n this equation x i and x i are the product of mass absorption coefficient and cosecant of the X-ray take-off angle for sample and pure element, respectively. The factors z& and x& are the effective depths of production of X-rays. If it is assumed that the effective depth has the same value x* in the sample and pure element, then it can be evaluated from the intensity ratios (KA’s) for the KCYand Kp lines for the same element, and f i can be writ ten f1
= exp
( [ x i - x i 1 z*)
(8)
An identical linear relationship was found between the value of x* and overvoltage for two iron-nickel samples with x values which differed by a factor of 2. The equation found for relating z* to overvoltage in the iron-nickel system was X* = 0.194 X
(E, - E A )
(9)
where E , and EA are the electron voltage and the excitation potential, respectively. Il’in and Loseva claim that this absorption correction can be applied to any sample with x less than 1000 using the above equation for effective depth. For samples in which x is greater than 1000, the effective depth
may be determined from any sample of known composition whose x is close to the unknown. The accuracy of the absorption equations can be evaluated by comparison with more fundamental data. The values of f(x) can be measured as a function of x by measuring the X-ray intensity as a function of take-off angles. T o place these values on a n absolute basis it is necessary to extrapHeinrich (301) olate to x = 0. pointed out that a plot of l/f(x) against x is a better method of extrapolation than the log f against x usually used. Taylor (626) has measured f(x) curves for aluminum and copper a t several electron voltages in a geometry in which the sample surface is not perpendicular to the electron beam. By rotation of such a sample about an axis parallel to the electron beam, the takeoff angle can be varied. His results do tend toward the values predicted by the modified Philibert equation as the electron incidence angle approaches 90 degrees. No analytic method for using the Philibert equations a t non-normal electron incidence is given. Wittry and Andersen (679) have evaluated measured values of f(x), excluding those for which the electron incidence is not normal to the specimen surface. They find a systematic dependence of f(x) on accelerating voltage, atomic number, and excitation ratio, E,/EA. By plotting f(x) on an appropriate scale, extrapolation to small values of f(x) was possible for use in the long-wavelengt h region, The absorption correction can also be calculated if the number of X-rays produced as a function of depth in a sample is known. The sandwich sample technique originally used by Castaing and Descamps (130) provides the means for such measurements of this distribution (d (pz) curve). During the past two years, four groups of measurements have been made. Castaing and Henoc (138) measured curves for aluminum a t five electron voltages using magnesium as the tracer element. The f(x) values obtained from these 6 (pz) curves differ by several per cent from the f(x) values calculated from the modified Philibert expression for the A1 K a line. Shimizu, Murata, and Shinoda (575) measured (pa) curves for a zinc tracer in copper a t electron voltages ranging from 24 to 37 kV in two different electron probe microanalyzers which had different takeoff angles. f(x) values were not calculated from these curves for comparison with the modified Philibert equation. Vignes and Dez (653) measured 6 (pz) curves for titanium using a vanadium tracer and for lead using a bismuth tracer, again a t several electron voltages. For these somewhat shorter wavelengths, good agreement was ob-
tained with the modified Philibert expression. 6 (pz) curves for zinc tracer in copper a t several electron voltages were also measured by Brown (Q6),but in an instrument in which the electron beam was incident on the sample a t an angle of 60 degrees. Using the geometrical factor to take into account the reduced depth of penetration in the inclined sample, the curve measured at 27.5 kV was in good agreement with the original 29 kV curve of Castaing and Descamps (f30). The f(x) values calculated from the 6 (pz) curve at 27.5 kV agree to within 1% of the modified Philibert equation, provided the x values are multiplied by the factor (1 cos2 8) where 8 is the angle between the electron beam and normal to the sample surface. A t lower electron voltages, this factor will no longer bring values from the modified Philibert equation a t normal electron incidence into coincidence with values at nonnormal electron incidence. This difficulty in using the absorption correction equations should be recognized by those having electron probe microanalyzers in which the sample is tilted relative to the electron beam. Cosslett (160) has used measurements of electron transmission through thin films to generate a 6 (pz) curve for copper a t 29 kV. Good agreement was obtained with the copper curve measured by Castaing. The most important physical parameters used in the absorption correction are mass absorption coefficients. Heinrich and Yakowitz (305) have evaluated the errors associated with the absorption correction and show that uncertainties in p / p values are one of the greatest potential sources of error in the absorption correction. T o minimize these errors, they recommend that f(x) values be kept larger than 0.7 by using low electron accelerating voltages and high take-off angles. Kelley (368) also emphasized the importance of accurate p / p values. Heinrich (302) prepared a table of mass absorption coefficients ( p / p ) based on a computer fit of a logarithmic equation to experimental data. Coefficients to calculate p/p for the various elements were then correlated by wavelength region and atomic number to obtain the best table of p / p values based on available experimental data. This table, the accompanying paper, and an additional discussion of p / p measurements by Heinrich (300) have stimulated the measurement of p / p values during the past two years. Bearden (43, Hughes and Woodhouse (359), Carter et al. (128), and AlcCrary et al. (446) have all made gxtensive measurements in the 1 to 10 A wavelength range with claimed accuracies of 1 to 3%. These authors have provided considerVOL. 40, NO 5 , APRIL 1968
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able new data, some of which are not in particularly good agreement with the tables prepared by Heinrich. The appearance of Heinrich’s tables has also stimulated the production of p / p tables using some sort of computer interpolation and extrapolation. Many of these efforts would appear to overlap or a t best be a dubious addition to an already sufficiently confused area. While it is evident, as more accurate p / p measurements are made, that Heinrich’s tables have significant errors in certain wavelength and atomic number regions, it is equally evident that a proliferation of tables can only lead to a completely chaotic condition where any attempts a t evaluating the accuracy of correction equations will degenerate into arguments over which table of p / p values to use. Some sort of coordination in the preparation of these tables would be desirable. An extensive table of p / p values is being prepared by McMaster et al. (447). This table extends from X-ray energies of 1000 keV down to 1 keV. Frazer (245) has prepared a set of coefficients for calculating p / ~ values similar to those of Heinrich evcept that a different weighting scheme and additional recent measurements were used in the computer fitting procedure. Taylor (625) suggests that a relationship between p / p values of an element for its own radiation can be used as an aid in interpolation. An additional table of values has also been published by Theisen and Vollath (632). Kelley (368) has prepared a graph from which p / p values for any element for any wavelength can be obtained. Such a graph contains an averaging procedure similar to that used in the computer techniques for obtaining best fit for p / p values. Guttmann and Wagenfeld (277) have calculated p / p values for most elements a t 10 wavelengths of interest to microanalysts from theoretical considerations of electronic wave functions. These calculated values agree to within about 5% of measured values and perhaps offer the hope that theory may supply accurate p / p values. I n the long-wavelength X-ray region, Henke et al. (312) have published a table of p / p values. This table represents the best and almost the only source for coefficients in this wavelength region. The table has been republished recently in the il’orelco Reporter (257). Fluorescent Correction. T h e most suitable correction for fluorescence due t o absorption of characteristic lines is a procedure suggested by Reed (523),which is a modification of an equation originally proposed by Castaing. This modification to Castaing’s equation will presumably remove the bias a t low kilovoltages which was the 362 R
ANALYTICAL CHEMISTRY
main criticism of Castaing’s equation in an evaluation by Colby and Conley (154). Criss (164) has developed a correction equation stated in terms of the absorption parameter f(x), and specifically has generated such an equation from the modified equation of Philibert for f(x). This kind of equation, which has yet to be evaluated, would free the fluorescence correction from the approximation of the primary 6 ( p z ) curves that is necessary for other types of fluorescence corrections. The distribution of fluorescence radiation as a function of depth in the sample has been measured by Brown (96). By measuring the 6 (pz) curve in a sandwich sample for a tracer element which is excited by the characteristic radiation of the matrix element, and subtracting the 0 (pa) curve for a tracer element which is not excited by the characteristic radiation of the same matrix element, the distribution of fluorescence radiation is obtained. Using iron, cobalt, nickel, and zinc tracers in copper, the fluorescence distribution was obtained. The same distribution was obtained in a single sample where the tracer element dysprosium was chosen so that the K a line of the copper matrix could excite the Lal but not the Lfl, line of dysprosium. I n the same paper, I3ronn gives a computer program that can be used to calculate the fluorescence distribution from a measured primary distribution. Fluorescence due to characteristic lines can seriously affect results in inhomogeneous samples such as diffusion couples or samples containing inclusions of elements which are excited by the characteristic radiation of the matrix. Smith (587) has reviewed attempts to evaluate the contribution of fluorescence in the context of the large inhomogeneities usually experienced in mineral samples. Maurice, Seguin, and Henoc (444) havc investigated the effect of fluorescence due to characteristic lines on the results from diffusion couples. Calculated values were compared with experimental curves from couples prepared by placing two metals in contact, one of which is capable of exciting the characteristic lines of the second. Reed (524) has considered the effect of fluorescence effects on spatial resolution of electron probe microanalysis. For homogeneous samples, Heinrich and Yakovvitz (306) have evaluated the errors introduced into quantitative analysis by possible errors in the many parameters which are necessary in the fluorescence correction. The most significant source of error is introduced by uncertainties in the fluorescent yield values. Most other errors can be expected to affect the calculated composition by 0.1 to 0.2% of the amount
present. Fink et al. (118) have recently reviewed the status of measurements of fluorescent yields. Fluorescence due to absorption of continuum radiation has been studied by Afonin and Pavlinskii (10). They claim that up to 207, of the intensity of .4gKa line is generated by absorption of continuum radiation for an electron accelerating voltage of 40 kV and compare experimental results with calculations from an equation derived in the paper. Hink (316) has measured the contribution due to continuum fluorescence in copper and tungsten. Similar magnitudes to that of Afonin and Pavlinskii for the continuum fluorescence were observed. Atomic Number Effect. The greatest effort in quantitative analysis during the past two years has gone into understanding and characterizing the atomic number correction. Significant progress has been made. From a situation in which it was frequently argued t h a t the atomic number correction was only the result of uncertainties in mass absorption coefficients, the existence of an atomic number correction is universally accepted and the physical basis of this correction is known. Castaing was the first to propose what has become known as the atomic number effect. In his second approximation, the ratio Kal of intensity generated within the sample compared to that generated in the pure element was related to concentration Ca by the equation
where and a s are constants. The values of these factors depend on atomic number and electron accelerating voltage, and the ratio aa/as is increasingly important with increasing difference between the average atomic number of sample and pure element standard. The origin of this dependence on atomic number is that the number of characteristic X-rays generated per incident electron for a given concentration of an element in matrices of varying atomic number is not constant as a result of differing backscattering and electron retardation properties of different elements. Thus the a coefficients can be written as
s
a = -
R
where S is related to the stopping power of an element and R is a backscatter coefficient which takes into account the loss of ionization in the sample as a result of the energy carried off by backscattered electrons. The differences i n the proposed atomic number corrections result from
different methods of evaluating S and R . Duncumb and Reed (297) have proposed the following method of calculatiiig these factors. The stopping power S is defined by
where p is density and dE/dx is the mean change in energy for an electron travelling a distance dx. Stopping power of an element is approximately constant for a particular element regardless of its physical or chemical state. The most suitable formula to date for stopping power is
S = const. - - In AE
(l'lJGiiE) -
(13)
where J is the mean ionization potential. Duncumb and DaCasa (194) have used J as an adjustable parameter to improve agreement between observed and calculated compositions. A table for J as a function of atomic number for this best fit can be found in the paper by Duncumb and Reed (197). If the electrons were backscattered with no loss in energy, then the 1 - R would be equal to the electron backscatter coefficient 7 which is the fraction of incident electrons which are backscattered. Because the electrons do lose some energy in the backscatter process the value of 1 - R is less than 7 b y an amount which depends on the energy distribution of backscattered electrons. The factor 1 - R can be calculated from the expression
where Q is the ionization cross-section, S is the stopping power mentioned above. C7 is the ratio of the electron energy E, to the absorption edge energy EA. q ( U ) is the number of backscattered electrons n i t h energy greater than E K . Thiq number can be calculated from measurements of the energy distribution of backscattered electrons. Duncumb and Reed (197) have prepared a table of values of R as a function of voltage ratio I: and atomic number Z based on Bishop's measurements (68). These values are for normal electron incidence with the effect of an inclined sample on these values being unknown a t the present time. Springer (605607) has taken a similar approach to evaluation of S and R for the atomic number effect, but his R values are based on earlier measurements for electron backscattering. Castaing and Derian (129) have used a special sample
for determining directly the values of 1 - R . A small cavity, 400 microns in diameter and 20 to 30 microns deep, was cut into the surface of a sample. This cavity was covered with a thin layer (approximately 2 mg 'cm2 thick) of the same element. The thin layer was formed by vacuum evaporation. h small hole was made in this thin layer so that the incident electron< could enter the cavity, but then would be trapped, giving up all their energy within the sample. Comparing the x-ray intensity generated in such a sample with the intensity from a normal flat sample allows the direct experimental measurement of the factor 1 - R. Smith (587) has developed a formula for S baqed on empirical fitting to a large number of standard samples. This formula is
This formula for S was obtained in an Applied Research Laboratories instrument and should not be used indiscriminately with other instruments until thoroughly checked. For values of R , Smith uses the values from measurements of backscattered electrons of Green. A graph reproduced in Smith's paper can be used to obtain R values for any electron voltage and atomic number. -4number of evaluations of the atomic number effect have been made. Because of the possible errors in the absorption and fluorescence corrections, these evaluations usually are based on statistical analysis of a large volume of data in which calculated compoqitions are compared with the known coniposition of standards. The success of any atomic number correction is judged on the basis of how successful the correction is in reducing the difference between known and calculated compositions. Poole (510) has compared several corrections for atomic number and plotted error histograms for each based on 229 analyses. Based on these data, the moit successful atomic number corrections were that of Thomas and that of Duncumb and Reed (197) d2scribed above. Another error histogram plotted by Duncumb and Reed s h o w clearly the improvement in agreement between known and calculated composition using the fitted value of J in the calculation of the stopping powerh. Belk (51) proposed a simplified correction for atomic number which can be applied to a great percentage of microanalyses. Csing an error histogram, the results on 150 analyses using the simplified method were comparable to the results obtained with more complicated correction procedures. Theisen (629-691) in his proposed correction procedure has included a part of the atomic number effect;
namely, the energy loss due to backscattering. Because no correction is made at the same time for stopping power and the R and S factors act in opposite directions to partially offset each other, application of a correction for backscattering alone would not appear to be successful. Indeed the comparison by Poole (,510) confirms this view. illthough in general the atomic number effect can only be evaluated by statistical means, in some samples the absorption and fluorescence corrections are sufficiently small that any difference between measured and calculated composition will be the result of the atomic number effect. Such samples are not common. One interesting case, however, is the copper-nickel system. Although adjacent elements in the Periodic Table are involved, a small but significant atomic number effect is expected because the Z I A ratios of copper and nickel are considerably different. Ranzetta and Scott (617 ) were able to show the existence of the atomic number effect for the analysis of copper in copper-nickel alloys because the absorption coefficients for the C u K a line are small and almost equal. The small contribution of fluorescence by the CuKP line to the XiKO intensity weakens the evidence for an atomic number correction in the analysis of nickel in these alloys. Computer Techniques. Computers are used in two main areas of application for electron probe microanalysis. On t h e one hand, high-speed computers are needed for t h e solution of t h e complicated equations relating t h e interactions of electrons with matter t o X-ray production. On t h e other hand, computers are being used simply as a labor-saving device in the less-complicated equations used to relate measured X-ray intensities to composition. Bishop (67, 68) used Monte Carlo techniques to follow trajectories for a large number of electrons. The paths of the electrons were divided into 25 equal steps. The scattering in each step waq calculated from inelastic and elastic scattering laws. Except for carbon the backscatter coefficients a t 30 kT' calculated by Bishop are 8% greater than measured values. I t is interesting that this 8% difference could be removed by adjusting the J factor in Bethe's equation for energy loss, similar to the adjustment required by Duncumb and DaCasa (194) to improve the agreement of the atomic number correction. =it 10 kV, an increase in the backscatter coefficient is predicted, although for large Z the backscatter coefficient actually decreases with decreasing electron voltage. Bishop believes that these discrepancies could be removed by better VOL 40, NO. 5, APRIL 1968
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approximations to the scattering process. 6 ( p a ) and f ( ~curves ) calculated by Monte Carlo technique show similar differences. D. B. Brown and Ogilvie (93, 94, 484) described an electron transport equation that is used to predict the distribution of depth of X-ray production, 6 ( p z ) , the absorption correction, f ( x ) , and the energy distribution of backscattered electrons. The values predicted by this approach are in good agreement with the experimental curves for 6 ( p a ) and f ( x ) as well as for the backscatter coefficients. The predicted distribution of the energies of backscattered electrons, however, does differ somewhat from measured distributions. This type of calculation has reached the point where improvements in the model cannot be evaluated because the improvements lead to differences in the predicted values which are of the same order of magnitude as the errors in the measurement of the values. More accurate measurements of such properties as 6 (pz), f ( x ) , and backscatter coefficients are required so that continued improvements of this model can be made. It is impractical a t the moment to use the Monte Carlo method of transport equation for routine quantitative analysis because of prohibitive calculation times. At the same time these theoretical approaches are very important in testing the simplified equations actually used for quantitative analysis. These simplified equations have been programmed to relieve the analyst from the chore of the iterative calculations required to relate X-ray intensities to composition. One of the important considerations in any such program is the convergence of the iterative procedure. Reed and Mason (525) have proposed an iteration procedure which they claim will have a much larger probability of convergence than other techniques which have been used. I n several hundred analyses for which a program written by Brown (95) has been used, less than 10 have failed to converge within the limit of 20 iterations set in the program using simple but small convergence limits. The program of Brown (95) is quite general for calculating composition from measured X-ray intensities. Either pure elements or compounds may be used as standards. Corrections for dead time and background are applied to the measured intensities. Several different absorption, fluorescence, and atomic number corrections are programmed which can be selected by code number. Frazer, Fitzgerald, and Reid (247) have published a program which has only a single absorption and fluorescence correction. The strength of this program lies in its very versatile data input
364 R
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requirements and the extensive choice of output format. Beaman (44) has also developed a program in which mass absorption coefficients, jump ratios, fluorescent yields, and atomic number parameters are internal to the program. Hobby and Wood (319) have programmed absorption and fluorescence corrections. Hanneman and Lifshin (286) use computer-generated theoretical curves, fitted to the ZieboldOgilvie linear relation for quantitative analysis. Their program can also generate diffusion coefficients from the calculated compositions for data from diffusion couples. Similarly, Hoff and Gregory (323) include in their program the ability to calculate diffusion coefficients. A number of evaluations of correction procedures refer to computer programs (43, 154, 307, 510), and indeed the only practical method of handling the large amount of data required for significant evaluations of the atomic number effect is by computer. R e must not forget, however, that all the errors of mass absorption coefficients, etc., are not overcome by some magical property of the computer. The results printed in neat rows by a high-speed printer must be subject to the same scrutiny and skepticism as any hand-calculated results. Instrumentation and Sample Techniques. Several new instruments have been developed by t h e manufacturers of electron probe microanalyzers during the past two years. All of these represent second- or third-generation microanalyzers which will do the same analyses as the earlier instruments but are easier t o operate and more stable. The number of accessories available for the various instruments is increasing. dll have soft X-ray spectrometers and beam scanning with a variety of signals, and most have Kossel cameras. Sorton (483) has outlined some of the characteristics necessary for a research microanalyzer to be used for a wide variety of problems. S o t all of these characteristics can be found in every instrument. One of the interesting developments over the past five or six years has been the combination of an electron microprobe and electron microscope in a single instrument. W. C. Nixon and P. Duncumb in England have been pioneers in this kind of instrument in which an electron micrograph of quite good resolution can be obtained at the same time as compositional information from the X-rays generated in the sample. Two commercial manufacturers (156, 556) are now marketing combination instruments which have been developed by adding projection lenses to an electron microprobe. I n Russia, Vasichev (648, 649) has built a combination instrument which has two semifocusing spectrometers. The electron column
of this instrument is described in another paper (650),and techniques for aligning the column are reported (595). The opposite approach has also been taken. Starting with an electron microscope, X-ray detection systems have been added to give the combination instrument. Fuchs (252, 253) has attached a semifocusing spectrometer to a Siemens electron microscope. A nondispersive system was attached to a similar microscope by Giraud-Heraud, Sifferlen, and Saulnier (261). Using a flow proportional counter, elements having a difference of atomic number of a t least 2 in the region of copper in the periodic table could be separated. Koffman, Schippert, Moll, and Hamill (392) have developed a spectrometer attachment for a Philips EM-200 electron microscope which uses a mica crystal whose bending radius is varied for focusing. These instruments permit the direct correlation of composition with a magnified image, but thin samples are required for the transmission electron micrographs. T o examine bulk specimens by electron microscopy and microanalysis, Estill and Robertson (213) have used the contamination layer formed during analysis in an electron probe microanalyzer as a replica for subsequent examination in an electron microscope, thus achieving the often difficult task of relating data from both techniques to the same area of sample. An interesting new electron probe microanalyzer, which incorporates a mini-lens as the objective lens, has been developed by -4.B. Bok, L. A. Fontijn, and J. B. LePoole a t the Technisch Physische Dienst, T.S.O. Delft, Holland. The intriguing feature of this instrument is the small size of the electron optical column, leaving a great deal of space available in the vicinity of the sample. The mini-lens used as the objective lens of the electron column is only 50 mm high and 46 mm in diameter. The electron beam diameter a t the sample surface is less than 1 micron. Because of its small size and the equally small bore, the optical microscope cannot be placed concentrically with the electron optical column. Instead the electron column is tilted a t 45 degrees to the sample surface so that a standard optical microscope outside the vacuum system can be used to look directly down on the sample through a window above the sample. Two spectrometers having 30 degree take-off angles are placed on opposite sides of the sample. Because of the small size of the objective lens, X-ray take-off angles of up to 60 degrees are possible with the optical microscope in position, and one spectrometer with a take-off angle of 90 degrees would be feasible if the optical microscope were removed. Beam scanning is an important technique for qualitative analysis. The
signals nhich can be displayed are alniost limitless (299). Kimoto et al. (376), by using electron detectors symmetrically located on either side of the sample, removed contributions due to surface irregularities from beam scanning pictures. Scanning techniques have been applied to quantitative inclusion counting. Melford and JT7hittington (448) and Dorfler et al. (188-190) have developed auxiliary instrumentation for determining the number, size, and approximate composition of inclusions in the area scanned. Melford and Whittington combine data from two X-ray spectrometers and backscattered electron current, using logic circuits to recognize a maximum of three types of inclusions. The size of the inclusions is determined by using clock signals which are gated on and off with the appearance of X-ray signals related to a given type of inclusion. Dorfler et al. are developing a similar system except they propose to record the data for later analysis by computer. Any microprobe inclusion counter should have the advantage over optical systems, of determining inclusion type on the basis of composition. To improve the information conveyed by beam scanning pictures, a number of techniques have been used for displaying data. Wittry and Vancowering (680) described a system for stereoscopic display using, as an example, cathodoluminescence from G a l s . An isometric display is formed by using the rasters which drive the beam scanning to drive the 5 and y axes of the oscilloscope. XOK, however, a small component of the y (slowly varying) raster is applied to the z deflection and the signal, instead of modulating the intensity of the oscilloscope trace, is added to the y deflection. Stereoscopic pairs of images can be obtained by increasing the contribution of the y raster to the T deflection to vary the angle between the z and y coordinates of the display. Dorsey (192) used a similar technique, but with a single display, to demonstrate the existence of an effect of magnetic fields in a sample on backscattered electron intensities. Heinrich (299) has stored data in a multichannel analyzer memory, then used a similar display technique for readout of data. Heinrich (299) first described a technique for placing limits on the signal displayed on the oscilloscope screens, calling the technique concentration mapping. Christian and Schaaber (149) have developed a similar instrumentation for a Cambridge microanalyzer. They have applied the techniques to studies of surface engraved pictures (147, 148).
Resolution of beam-scanning pictures is directly related to the electron beam diameter when electron images are recorded and indirectly related through
the volume in which X-rays are generated when X-ray images are recorded. Beam diameters have been measured from the shape of the profile of the sample current os. distance in crossing a discontinuity in the sample or from the size of the contamination spot formed on a sample. The size of the contamination spot is consistently larger than the beam diameter determined by traversing a discontinuity (24). Hehenkamp (897) described a sample composed of alternate copper and gold layers on a copper block which was sectioned and polished to reveal the edges of the layers. This sample can be used to determine the effective electron beam diameter by noting the minimum thickness of layer which will give the same intensity as the bulk specimen. h similar sample of Cu-Si layers has been described by Belk and Clayton (52). Rapperport (622) has used a deconvolution technique to increase the resolution of electron probe microanalysis beyond what would be expected on the basis of the electron beam diameter. Abelmann and Jones (4) have investigated the effects of X-ray take-off angle and electron incidence angle on peak to background ratios and the applicability of the correction equations. They found that after removing the effect of back-scattered electrons. the beak to background ratio was almost independent of X-ray take-off angle. The electron incidence angle is more of a problem because no simple relation was found for relating the absorption equation used for normal electron incidence to non-normal incidence. Several sample stages have been described for heating microprobe specimens during analysis for studies of (ompositional changes a t elevated temperatures. Kimoto, Hashimoto, and Tada (377) describe a stage using a porcelain crucible which can be used a t temperatures up to 110' C. Miller and Wittry (458) developed a sample stage in nhich the temperature can be controlled to +4' over a temperature range of 100 to 500' K. This stage would permit the analysis of materials that are sensitive to heating by the electron beam, such as gallium metal. The flow proportional counter continues to be the most suitable detector for electron probe microanalysis, particularly in the long-wavelength region. A design of a typical counter can be found in the paper by Braybrook et al. (88). The major difficulty with the flow detector is the now well-documented decrease in pulse amplitude with increasing counting rate (42, 104,603). Spielberg (603) found that the important factors in the pulse shifts were the size and cleanliness of the anode wire and the gas gain in the detector. By increasing the diameter of the anode wire to 125 microns, no shifts were ob-
served for counting rates up to approximately 10,000 counts per second, whereas with very small anode wires significant shifts can be detected for counting rates as low as 500 counts per second. Beaman ( 4 Z ) has found decreases of up to 25% from the true intensity ratio because of pulse amplitude shifts when using a pulse height analyzer with a rather narrow window. Errors can be avoided by using wider windows, changing the gain in the amplifier, or decreasing the base line in the pulse height analyzer. Heinrich, Veith, and Yakowitz (304) have studied methods of correcting for dead time in the detection system. They found that the best equation for dead time correction is
where NT and No are the actual observed counting rates and t is the dead time of the total counting circuits. Several methods of determining dead time are evaluated in their paper. Multichannel analyzers are finding increased use for data storage and display from analyses of large numbers of sample points. Heinrich (299) gives several examples of application to concentration mapping. Fergason (296) has used a multichannel analyzer for storage of data along linear traverses. Background is corrected automatically by rescanning along the same line with the angle of the spectrometer appropriately adjusted. A method for determining extremely low concentrations of elements also utilizes a multichannel analyzer (226). The electron beam is caused to jump back and forth between two areas of a sample, one of which may be a standard. The data from the two areas are stored in different quadrants of the memory of a 400-channel analyzer. Concentrations of Al, Si, Ni, and Fe in U have been determined a t the 100-ppm level with precisions of i.10 ppm 2a using this technique. The analysis of radioactive specimens requires special techniques-both in the protection of the operator and in the preparation of the sample to avoid contamination of the instrument. Scotti, Johnson, and Cunningham (562) describe modifications to a microprobe for handling hot samples. The modifications consist for the most part in the provision for additional radiation shielding. Padden, I h r t o n , and Campbell (493) circumvent the shielding problems by using very small samples. Hudgens and Roesch (337) describe techniques to contain the activity of alpha active specimens. thus avoiding contamination of their electron microprobe. Sample preparation is probably the single most important step in electron VOL. 40, NO. 5 , APRIL 1968
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probe microanalysis and is doubly important in the case of standards to be used in evaluations of quantitative analysis. These must be homogeneous and of accurately known composition. Goldstein, Xajeske, and Yakowitz (264, 265) have used a splat cooling technique for preparation of standards. .A molten alloy is dropped onto a cooled copper plate, where it cools instantly and solidifies. Because of the rapid cooling, segregation is prevented. They report that standards can be prepared in which the variation between pieces and within pieces closely approximates the expected standard deviation owing to counting statistics alone. Standards prepared in this way are not necessarily stable and may segregate with time. The composition of the standard should be determined chemically, because it can vary significantly from that espected on the basis of the weight of the elements mixed together in forming the alloy. Yakowitz et al. (689) have continued the evaluation of present Sational Bureau of Standards standard samples for possible use as electron microprobe standards. Cartridge brass standards were found to be quite homogeneous and very suitable as microprobe standards; low-alloy steels on the other hand show segregation of some of the minor elements. Thus, the steel samples can be used as standards for some elements which form homogeneous solid solutions with the iron matrix, but not for others which are found localized in inclusions. Walter (660) deqcribed a method of preparing silicate standards using an aqueous silica gel solution which is sprayed onto a heated platinum foil to produce a homogeneous powder. Elements such as AI, Mg, Ca, K, Xa, and Fe are added to the solution a'. nitrates. The powder is pressed into a dense translucent pellet whose surface is quite suitable for analysis. Some variation (up to about 7% using a submicron electron beam) was found in the standards, indicating some inhomogeneity is still present. J. V. Smith (687) described a method of mounting mineral standards by placing the mineral grains in holes drilled into 1-inch-diameter brass cylinders. Epoxy resin was then carefully poured over the grains and allowed to harden. Polishing wa5 achieved using paper or copper laps, but if cloth laps were used, especially with an excess of lubricant, considerable relief resulted. Smith also described a method of preparing thin sections suitable for microprobe analysis. Hooper (336) studied various embedding compounds suitable for preparing samples of foraminifera. He desired an embedding medium which is transparent, stable under the electron beam, and of hardness 3 on the Moh's scale. Styrene was found to satisfy these requirements, al366 R
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though the embedding procedure required several days to complete. Silicate glasses have been found to be unstable under bombardment with the electron beam. The sodium or potassium intensity usually decreases with time of bombardment with the electron beam ('79, 647), although both Borom and Hanneman ('79) and Fredriksson (251) found samples in which the S a K a intensity increased by a factor of three. A mechanism for this increase in X a concentration has been suggested ('79). Xoving the sample during analysis can help to reduce these changes in X-ray intensity, but stable and meaningful intensity readings are not obtained. A symposium on sample preparation was held a t the First National Conference on Electron Probe Microanalysis with major papers on geological, biological, and metallurgical specimen preparation. Pickleseimer and Hallerman a t that symposium quantitatively assessed the effects of sample roughness by measuring the intensity across thin copper grids mounted on copper blocks. They found that a ridge of only 1 or 2 microns can significantly affect the measured X-ray intensities, while steps of 4 and 12 microns can reduce the measured X-ray intensity by 5070 for takeoff angles of 15.5' and 35', respectively. Pickleseimer and Hallerman also examined the problem of smearing soft phases over ha,rder ones during polishing. Layers of pure element less than one atomic layer thick, spread over one another, could be detected. Etching was recommended to remove any smeared material in any samples where smearing was suspected. Many of the techniques with regard to biological samples which Tousimis described at the symposium were published in a review article (634). Low-Energy X-Rays. The fact that every electron microprobe manufacturer has available a spectrometer for measuring the intensity of lowenergy X-rays has spurred interest in analysis using these wavelengths. Three methods are used in the separation and detection of these wavelengths. Crystals made up of layers of soap molecules are used as the dispersing element of the most common type of curved crystal spectrometers presently used (f34.4, 369, 619). Interest has also been shown in the use of gratings a t grazing incidence for separating wavelengths (88, 416). The intensities obtained by the two typey of spectrometers appear to be comparable, but the soap crystals are more commonly used because they are somewhat easier to produce. The third method of wavelength separation utilizes the fact that the output pulses from a proportional detector are proportional to the energy of the incident X-rays. Cooke
and Duncumb (157) and Wardell (661) use an electronic system to select narrow output voltage ranges characteristic of up to three element.. The intensity related to each element is determined by solving three simultaneous equations, again using electronic circuitry. Cooke and Duncumb point out the advantages of the nondispersive system when low intensities are encountered. Kimoto and Hert (378) have compared the use of dispersive and nondispersive techniques for low atomic number elements. Castaing and Pichoir (134) described a nondispersive system for analysis using low-energy X-rays in which a Ross filter technique is used. The filters are gases which are contained in gas cells. The method was applied to the detection of oxygen Ka radiation. A linear curve was obtained for intensity of oxygen K a us. concentration for 7 oxide samples for oxygen concentrations of less than 10 up to more than 50 weight per cent. Although detection of low-energy X rays has become almost routine, the problems of quantitative analysis are quite formidable. Some of these problems have been reviewed by Henke ( S l l ) , ilrrhenius (66), Koffman, 11011, and Norton (391) and Scott (561). Many authors have measured the shifts in wavelengths due to chemical binding. .A review of recent measurements can be found in the X-ray section of this paper: The changing shape of the emission lines iy also a problem, and it has not been settled whether peak intensities or integrated intensities over the entire line should be uqed in the quantitative equations. I n additional problem has been pointed out by Haun and Fischer (40). Self-absorlbtion of emission bands in the 10 to 50 A wavelength region can alter significantly the shape of emission bands a3 a function of electron voltage (see Figure 2). With such problem
