Interaction of Beta Particles with Matter Quantitative Determination of Hydrogen, Carbon, Nitrogen, Oxygen, and Fluorine Materials PETER R. GRAY, DONALD
H. CLAREY, and WILLIAM H. BEAMER
Radiochemistry laboratory, The Dow Chemical Co., Midlond, Mich.
b Binary and ternary compounds and mixtures can be uniquely analyzed by a measurement of their @-ray transmittance and backscatter intensities. A rnathematicol equation for P-ray backscattering has been developed which correlates the experimental data with the theoretical sample analysis. The standard deviation in the experimentally determined weight fraction of hydrogen in hydrocarbons and in hydrogen-containing ternary compounds is less than 0.03%. Analysis of ternary compounds is fast, simple, accurate, and nondestructive.
B
incident upon mattcr are affected by different processes. Some are scattered, lose their energy, and are absorbed by the material. Others, with their full energy or partially degraded in energy, are transmitted through the material if it is thin enough, and still others are reflected or backscattered in the direction they came from. All these processes have been studied aiid attempts at quantitative interpretations have been made. Recent publications have described these analytical applications of p-ray interactions with matter (1, R, 4, 6, 7 ) . Two-component systems-e.g., hydrocarbons-can be analyzed by P-ray transmittance or absorption techniques and P-ray backscattering. While capable of approximately the same precision, p-ray backscattering is simpler, principally because sample mass densities must be known to only 0.01 gram per cc. (Transmission measurements require =!=0.0001gram per cc. precision.) Because both p-ray transmission and &ray backscattering intensities are dependent upon the atomic number of the material-see for example (S)-it is conceivable that complete quantitative analyses of three-component compounds or mixtures can be made by a transmission and backscatter intensity mcnsurenicnt on the same sample. Appropriate analytirul expressions showing this dependence upon the atomic number are available for the transmission iiitensities, but no such uscful cxprrssions have heretofore been
devised for the p-ray backscatter intensities. The quantitative expressions developed by Smith and Otvos (12) for the transmission of p-rays through matter are used herein, except that appropriate elemental absorption cross sections are found for the system geometry, as is the esperimcntally determined function, R = f(A). These absorption equations: R =f(A)
(1)
and
ETA-RATS
582
ANALYTICAL CHEMISTRY
state that the intensity, R, of the transmitted P-rays is a function of the total cross section, A. A is defined in Equation 2, in which p is the mass density of the material and wf,, S,, and Ai are the weight fraction, atomic absorption cross section, and atomic weight of element i, respectively. Equation 1 is evaluated graphically after determining the elemental cross sections, S,, from the analyses of known compounds. A functional analytical expression for p-ray backscatter was developed independently and found to be consistent with the P-ray scattering theory. P-Ray backscattering is primarily due to interactions of incident p-rays with the coulombic field of the atomic nuclei of the scattering media. Scattering by the extranuclear electrons of the atom is relatively less important except in the very lightest elements-for example, hydrogen. A typical two-body scattering equation giving the number of electrons scattered (single scattering events) through an angle 6 is: 1
tered through an angle
e
n, = number of incident p-rays N = number of scattering centers or nuclei 2 = atomic number of the scattering center e = electronic charge mu2 = energy of the incident P-ray p = ratio of the velocity of the incident @-ray to the velocity of light a = atomic fine structure constant C’ and C” = weighting constants Equation 3 is composed of two parts: the scattering of the incident P-rays by the nuclei of the scattering material, or more precisely, by the coulombic field of the nuclei, and the Scattering due to the extranuclear electrons. The nuclear coulombic field scattering is proportional to Z2, 1%-hilethe scattering from the extranuclear electrons or orbital electrons is proportional to 2 . Therefore the coulombic field scattering becomes increasingly more important as the atomic number, Z, of the scattering media increases. The nuclear coulombic field and the extranuclear electrons contribute approximately equally to the scattering from hydrogen, and thereafter the electron-electron scattering decreases rapidly. After combining angular functions and other constant values and summing to include multi-elemental scatterers (compounds and mixtures), the scattering Equation
r
where n(e) = number of electrons scat-
Angular terms and terms dependent
Ronqe Selector
SUPPIY
Trorifoimer
Figure 1. Schematic diagram of the P-ray
L
-
D C E ecliomtlei Arpl
Recorder
cr
f
-
I1
!t
1’
S I der Tcp
Tronamirrian
only upon the energetics of the incident P-rays can be treated as constants, as the geometry of the system is essentially invariant as are the pparticle characteristics. Only the scattering centers change. Equation 5 is derived by regrouping the terms of Equation 4
‘
source
Vier
Apparofua
Replacement of FNiZi, the total nuclear 1
charge per cubic centimeter, by the charge density (numerically equal to the electron density) gives a n equation independent of mass density. The charge density (c.d.) is defined as:
EXPERIMENTAL
+
iAz,[f(e) + B Z , ~
n(e) = z
cf’(e)lN , Z ,
(5)
-4sthe bracketed portions of Equation 5 are dependent only on the atomic SZ,l Cf’(0’i) number, {AZ,ff(B) is constant for any specific element and
+
+
where Ki is a n elemental constant. According to Equation 6, the number of electrons scattered through a n angle, 0, is equal to the summation of the total nuclear charge per cubic centimeter, NiZi, times a constant, KI, dependent upon the atomic number. @-Raybackscattering has been shown to be essentially independent of the mass density of the scattering material (5). Very small density effects which have been noted (of the order of a few hundredths of 1% in backscatter intensity) are believed to be caused by slight geometry changes in the system and are not caused b y the backscattering phenomenon itself (6,10, 11). ZNiZi, t
i
the total nuclear charge per cubic centimeter, however, is dependent upon sample mass density (Equation 7),
N - deneity X Avogadro’s constant (7) molecular weight
where wfi, Zi, and A , are the weight fraction, atomic number, and atomic weight of element i, respectively. Because electrons have so small a mass, they may be deflected through reasonably large angles by the electric field in a n atom without passing in the immediate neighborhood of the nucleus as a heavy charged particle of the same velocity would have to do. For the scattering of electrons by atoms, therefore, we expect the shielding of the nuclear charge by the orbital electrons in the atom to be important. This orbital electron shielding eff ectively reduces 2, the nuclear charge, by a factor A, giving a n cffective atomic number, 2, for scattering of electrons by the coulombic field of the atom. Replacement of 2 by 2 in the scattering equation, or more specifically in the charge density term (Equation 8), gives a final scattering equation (Equation 9), independent of mass density and dependent upon two elemental constants, Xi, an elemental backscatter coefficient or cross section, and Z,. mfi
Zi
x
xw*
40) = i
necessitating a modification in Equation 6 before it can be applied successfully to the intensity of backscattered P-rays.
centei-Le., a pure element-as the charge density is unity for a single element. The two elemental constants are evaluated experimentally from the analysis of 6-ray backscatter intensities of known materials. Equation 9 was derived from an analysis of single scattering events. The bnckscatter phenomenon, hoivever, is believed to be due primarily to multiple scattering, wherein a single particle undergoes a large number of scattering collisions before leaving the scattering material. The estimation of the mean angular deflection of the p r a y s is obtained by applying statistical methods to the single scattering equation. This does not alter our basic equation and Equation 9 adequately describes the backscattering intensity of (3-raj.s in this system. The backscattering equation (Equation 9), together with the transmission equations (Equations 1 and 2) form the basis for the complete quantitative determination of ternary compounds. The necessary third relation is that the weight fractions of the sample components equal unity.
i
ICi
(0)
Ai
Equation 9 reduces to n(0) = K I for scattering from a single scattering
Apparatus. T h e apparatus used for t h e determination of t h e p r a y backscatter intensities has been described ( 5 ) . KO changes have been made in its operation. Many of the components of the P-ray transmission instrument are duplicates of that used for the backscatter studies. The methods of measurement-Le., the ionization chamber detector, electrometer, electrometer-amplifier, and potentiometer-recorder system-are exact duplicates, The source, source mount, and sample cell are different. The (3rays incident on the sample corn(’ from a source (30-mc. strontium-90-yttrium90) mounted on the axis of the cylindrical ionization chamber detector. The hermetically sealed 30-mc. Sr-90-Y-90 b-ray source, $/s-inch outer diameter, inch high, has a n active spot 4(‘ inch in diameter covered with a ll/pmrl stainless steel window. The source is doubly sealed in 10-mil aluminum. Strontium-90 was chosen as the radioactive source material because it is abundant and fairly inexpensive, has a rtJlatively long half life (27.7 years) (IS), and emits only p-radiation, thereby reducing the radiation shielding problem. The principal p-radiation has a n energy of 2.26 m.e.v. (IS) (from Y-90, in transient equilibrium with Sr-90), which minimizes the effects of the source window, sample cell windows, and detector window, I n contrast with the p r a y backscatter instrument where the source and detector are on the same side of the sample cell, the 6-ray transmission sample cell is identically positioned between the @-raysource and thc ionization chamber (Figure 1). VOL. 32,
NO. 6, MAY 1960
e
583
Because the P-ray transmission intensities of a large number of materials of varying atomic numbers and densities were dctcrmined, two sample cells of different thicknesses were used t o obtain bettcr sensitivities. One cell, whose active volume is 3/18 inch thick (total volume = 1.2 cc.), isused in the measurements on hydrocarbons and other light, low atomic number liquids. The second cell, l / g inch thick (volume = 0.8 cc.), is used for heavier liquids and liquids of highcr atomic number. Both cells are of stainless steel construction with the exception of the two windows, each 5/g inch in diameter and covered
Table I. 8-Ray Backscatter Elemental Constants Effective Atomic Atomic Backscatter Cross Xum- Number, Section, K Element ber, 2 2 -748.1 Hydrogen 1 1,000 Carbon 6 3.704 641.6 Nitrogen 7 3.987 1087.8 1605.1 Oxygen 8 4.234 2024.3 Fluorine 9 4.835 The compounds and mixtures listed below were used in the calculation of the conB tan t s : HYDROCARBONS Iso-octane n-Octane Pentane Ethylcyclohexane Methylcyclohexane Isoprene Cumene Phenylcyclohexane p-Xylene Toluene Benzene Ethynylbenzene OXYOEY COMPOUNDS
n-Octyl alcohol sec-0ct 1 alcohol n-Butyr et her Isoamyl alcohol n-Amyl alcohol Diethyl ether n-Butyl alcohol tert-Butyl alcohol Isopropyl alcohol clohexanone ethyl ethyl ketone Ethyl alcohol Acetone m-Cresol Benzyl alcohol Anisole 1,3-Propanediol Dimethoxvmethane Butyric aiid Dioxane Ethyl acetate Acetic acid Water NITROGEN COMPOUNDS Dibutylamine 99.5 17 0 triethylamine, 0 -49 H20 99.23% diethylamine, O.77y0 HzO 98.7170 n-butylamine, 1.2970 HzO 99.26y0 pyridine, O.74Y0 H20 Dimethylformamide FLUORISE COhfPOUSDS o-Fluorotoluene 1-Fluoronaphthalene
2
Fluorobenzcne
p-Fluoronnisole
584
ANALYTICAL CHEMISTRY
with 0.005-inch mica, through which the 0-rays are transmitted. The cells are 11/2 inches by 11Q/32 inches by 1/2 inch thick. The source-to-detector disinch and the sample cell is tance is positioned identically between the source and detector by a slider which carries the cell into the measurement position. The entire assembly-Le., the ionisation chamber detector, source, electrometer, and sample cell-is incorporated in a large thermally insulated box maintained at 30" & 0.1' C. Whereas thermostating of the backscatter equipment was necessary primarily for stable electrometer operation, the thermostating of the transmission assembly is necessary not only for the stability of the electronics, but also for maintaining the samples a t a constant temperature. As the intensity of the transmitted Prays is more dependent upon the mass density of the sample than on the ratio of the elemental constituents, the temperature of the sample must be constant during the measurements so that the density of the sample is constant and the results are reproducible. Because the sample temperature must be stabilized at 30' C., approximately 10 minutes are required for a measurement of the transmitted P-ray intensity. Density Measurements. Precise sample mass densities at 30.0' 0.1' C. were determined to *0.0001 gram per cc. for the p r a y transmission measurements. T h e p r a y backscatter measurements require a density precision of only hO.01 gram per cc. Samples. Standardizing liquids (liquids used in the determination of elemental constants) were of the highest obtainable purity. Samples were carefully distilled and successive distillation fractions were analyzed for purity on vapor phase chromatography columns. If desirable or if the purity of the sample mas questioned, infrared and mass spectrographic analyses were obtained also. Only those samples which analyzed to be better than 99.9% pure were used to establish the p-ray backscatter and P-ray elemental constants. Standard solid samples were of analytical reagent grade wherever possible.
*
RESULTS
Elemental Backscatter Constants. T h e analytical p-ray backscatter equation (Equation 9) can be expressed in a n alternate form which is better adapted t o t h e determination of the elemental constants] 2, t h e effective atomic number, and K , t h e backscatter coefficient. If the charge density of the compound A,B,C, is expressed in terms of number and kinds of atoms rather than weight fractions, the resultant equation (Equation 11) can be used to obtain a series of simultaneous equations which can be solved for the elemental constants. R =
+
+
X Z A K A Y Z B K B z&Kc XZ.4
+
yZB
+
ZZC
(11)
To obtain the highest possible accuracy and most representative values for the constants, the constants were obtained from a least squares analysis of the series of simultaneous equations using a Burroughs Datatron 204 digital computer. The mathematical computer program allows a least squares analysis to be made of up to 60 equations containing as many as 20 parameters. The values for the elemental constants of hydrogen, carbon, and oxygen were obtained from the analysis of 13 hydrocarbons and 23 oxygen compounds. The calculated elemental P-ray backscatter constants of hydrogen, carbon, and oxygen are tabulated in Table I. The effective atomic number of hydrogen is arbitrarily given a value equal to its actual atomic number, one. The calculated constants of hydrogen, carbon, and oxygen were used in the determination of the nitrogen and fluorine constants. Six nitrogen compounds and four fluorine compounds were used as standards. The calculated constants are given in Table I. Foul of the nitrogen compounds had small amounts of water associated with them. The water analysis was done by a Karl Fischer titration. Elemental Transmission Constants. T h e @-ray transmission constants cannot b e calculated in so rigorous a method as were the backscatter constants. T h e transmission values were obtained in a similar manner as t h a t used by Smith and Otvos (12). P-Ray transmission intensities through the S/,e-inch transmission cell mere measured for 13 hydrocarbons a t 29.9" C. The amplifier-recorder output voltage was expressed as arbitrary scale divisions as indicated by the range selector and recorder of the transmission instrument. Using the atomic weights of hydrogen and carbon, the calculated weight fractions of hydrogen and carbon in the individual hydrocarbons, and the accurate mass densities (&0.0001 gram per cc.) a t 29.9" C., a value A ( A = p T s ) w a s computed for each hydrocarbon ' using several different values of the relative atomic cross sections, Si. The' atomic cross section for 8-ray transmission through hydrogen was assigned the value of 1.00 and the cross section value of carbon varied from 6.00 to 7.00. It was found that SC = 6.500 gave the smoothest plot of R us. A for the 3/l.3inch transmission cell. The atomic absorption cross section of oxygen in the same cell was established by measuring the p-ray transmission intensities through 15 oxygencontaining compounds. A value of the total absorption cross section, A , was calculated for each compound, using the values of 1.000 and 6.500 for the atomic absorption cross sections of
hydrogen and carbon, respectivply. The value of SOwas varied between 8.5 and 9.5 to establish the value of SO; this gave values of A which best fit the curve of A vs. R determined above for the hydrocarbons. SO = 9.046 was selected as the best value for the atomic cross section of oxygen. Similarly, SN was calculated from four nitrogen compounds and determined to be 7.778 SF,calculated from only one fluorine compound, was 10.35. (Most of the fluorine compounds were too heavy and contained too much fluorine to be measured on this thicker cell.) The values of the atomic absorption cross sections for hydrogen, carbon, nitrogen, oxygen, and fluorine in the '/s-inch cell were 'determined in a similar manner. With the exception of water, all the standards were three- or four-element compounds. This necessitated varying SCand SOsimultaneously between 6.0 and 7.0 and 8.5 and 9.5, respectively. It was expected that the atomic cross sections would be very similar to those of the thicker cell, as the difference in geometry between the two cells is small. The best values of SCand SOwere determined from the analysis of eight osygen-containing compounds. The value of SN which best fit the curve of A zs. R determined above for the osygen compounds was calculated from the analysis of five nitrogen-containing compounds and mixtures Similarly, SFmas calculated from four fluorine compounds. The SC,SN, SO,and Sa for the values of SH, '/s-inch P-ray transmission cell are tabulated in Table 11,together with the atomic absorption cross sections for the S/16-inchcell. Quantitative Analyses. T h e complete quantitative analyses of twoand three-element compounds a n d mixtures can be accomplished using these elemental @-ray backscattering and transmission constants. Twoelement compounds-e.g., hydrocarbons-can be analyzed on either of t h e instruments singly; t h e complete analysis of ternary compounds requires a, 8-ray intensity determination on both instruments. Compounds and mixtures containing four or more elements cannot be uniquely determined unless the quantitative analysis on a t least one element is known, but intensity determinations on one or both instruments establishes the accuracy or feasibility of an empirical formula. While it is conceivable that more than one compound would yield identical @-ray intensities on either the backscatter or transmission instruments, i t is improbable that more than one, or a t the most very few compounds, would give equal P-ray intensities on both the backscatter and transmission instruments. The analyses of the standard hydro-
Table 11.
Elemental P-Ray Absorption Cross Sections
3/16-Inch '/*-Inch Element Cell Cell 1,000 1 .ooo Hydrogen Carbon 6.500 6.550 Xitrogen 7,778 7.777 9.046 9.109 Oxygen Fluorine 10.35 10.43 The compounds and mixtures listed below were used in the calculation of the absorption constants: 3/16-InchCell 13Y DROC ARB o ss Pentene Isoprene Iso-octane Octene Methylcyclohexnne Cyclohexane Ethylcyclohexane Toluene
p-Xylene Benzene Ethi nylbenzene Cumene P henylcyclohexane OXYGESCOMPOUSDS Diethyl ether %-Butylether Acetone tert-Butyl alcohol Isopropyl alcohol Methyl ethyl ketone Ethyl alcohol n-Butyl alcohol Isoamyl alcohol n-Amyl alcohol sec-Octyl alcohol n-Octy1 alcohol Dimethoxymethane Ethyl acetate Cyclohexanone NITROGEX COMPOUNDS: Diethylamine and water Triethylamine and water Butylamine and water Dibut ylamine FLUORINE COMPOUSD Fluorohexane 1/8-Inch cell OXYGEXCOMPOUNDS
Butyric acid Anisole m-Cresol Benzyl alcohol Dioxane Acetic acid Water 1,3-Propanediol Sucrose and water NITROGEN COMPOUNDS Dimethylformamide Pyridine and water Urea and water FLUORINE COMPOUNDS o-Fluorotoluene Fluorobenzene p-fluoronnisole 1-Fluoronaphthalene m-Difluorobenzene carbons on both instruments are tabulated in Table 111. The 3/la-inch cell was used in the 8-ray transmission analyses. The complete analyses of the osygencontaining compounds are given in Table W . Water is analyzed on either
Table 111. Hydrocarbon Analysis by P-Ray Backscatter and Transmission Techniques
Weight Fraction Carbon Experimental @-Ray @-Ray HydroTheobacktyanscarbon retical scatter mission Iso-octane 0.8412 0.8412 0.8417 Pentene 0.8563 0,8562 0.8563 Octene 0,8563 0.8567 0 8567 0.8565 Cyclohexane 0.8563 Methylcyclohexane 0.8563 0.8563 0,8565 Ethylcyclohexane 0,8563 0.8561 0.8563 Isoprene 0.8812 0.8815 0.8816 Cumene 0.8994 0.8997 0.8995 Phenylcyclo0.8994 0 8998 0.8989 hexane 0.9051 0.9052 0 9051 p-Xylene Toluene 0.9125 0 0126 0.9128 Benzene 0,9226 0.9228 0.9224 Ethynylbenzene 0.9408 0,9407 0,9406 0,02370 0.029% Std. dev. I
the p-ray backscatter or transmission instruments. Both instruments are used in the analyses of the ternary oxygen compounds. The rather 11 itle variety of osygen compounds necessitated using both transmission cells. Compounds reading less than 2300 scale divisions when analyzed with the 3/16inch cell were reanalyzed on the '/8inch cell for greater sensitivity. Only one of the standard nitrogen compounds can be completely determined, because the other nitrogen conipounds and mistures used contained four elements. The weight fractions of nitrogen in the four-element compounds and mistures n ere calculated from the known sample compositions and the weight fractions of hydrogen, carbon, and osygen calculated from their p-ray backscatter and transmission intensities (Table V). Three of the fluorine compounds were uniquely determined, while the weight fraction of fluorine in p-fluoroanisole n a s calculated from the known sample composition. The analyses of these fluorine standards are given in Table VI. Several other samples not used as standards on both instruments have also been analyzed (Table VII). These compounds hnd been analyzed by vapor phase chromatography and found to be essentially free of impurities. Diethylbenzene was determined sep:irately on both instruments. A hydrocarbon sample, thought to be essentially 2,3-dimethylpenta11e, :is analyzed on both instruments. The n eight fraction of carbon dctwniined esperimentnlly, 0.8368 and 0.8372 on the transmission 2nd bacLscnttcr instruments, respectively, differed from the theoretical value of 0.8300. SubVOL. 32, NO. 6 , M A Y 1960
* 585
Table IV.
Analyses of Oxygen Compounds by P-Ray Backscatter and Transmission Techniques
Compound Water (transmission) Water (backscatter) Acetone Cyclohexanone Isoamyl alcohol IEopropyl alcohol n-Amyl alcohol fed-Butyl alcohol Ethyl alcohol Methyl ethyl ketone n-Octyl alcohol sec-Octyl alcohol n-Butyl ether Ethyl acetate Butyric acid Dioxane n-Butyl alcohol Diethyl ether Methylal 1,3-Propanediol Anisole m-Cresol Benzyl alcohol Acetic acid
Theoretical n-fo = 0.88810 wfH O.lllgb m-fo = 0.8881 wfH = 0.1119 wfc = 0.6204O n f o = 0.2755 wfH = 0.1041 wfc = 0.7343 wfo = 0.1630 wfH = 0.1027 wfc = 0.6813 wfo = 0.1815 W f H = 0.1372 wfc = O.599G wfo = 0.2662 \ v f H = 0.1342 vifc = 0.6813 410 = 0.1815 n'fH = 0.1372 wfc = 0,6482 \yfo = 0.2158 w f H = 0.1360 W'fC = 0,5214 wfo = 0.3473 wfH = 0.1313 wfc = 0.6663 n7fo = 0.2219 WfH 0.1118 wfc = 0.7378 wfo = 0.1229 WfH = 0,1393 wfc = 0.7378 RTfo = 0.1229 \vfH = 0.1393 wfc = 0,7379 wfo = 0.1229 \?fH = 0.1393 wfc = 0.5453 d o = 0,3632 WfH = 0.0915 wfo = 0.5453 Wfo = 0.3632 !%'fa = 0.0915 wfc = 0,5453 wfo = 0.3632 W f H = 0.0915 wfc = 0.6482 wfo = 0.2158 W f H = 0.1360 wfc = 0.6482 wfo = 0.2158 &'fa = 0.1360 wfc = 0.4735 wfo = 0.4208 wfH = 0,1060 wfc = 0,4735 wfo = 0.4205 wfH = 0,1060 wfc = 0.7775 wfo = 0.1480 Wfa = 0.0746 wfc = 0.7775 wfo = 0.1480 wfH = 0.0746 wfc = 0.7775 wfo = 0.1480 wfH = 0.0746 wfc = 0.4000 Wfo = 0,5328 wfH 0.0671
Std. dev. Oxygen Carbon Hydrogen . a wfo = weight fraction of oxygen. * WfH = weight fraction of hydrogen. wfc = weight fraction of carbon.
586
ANALYTICAL CHEMISTRY
Experj mental wfo = 0,8879 TvfH = 0.1121 wfo = 0 8879 WfH 0.1121 wfc = 0.6161 wfo = 0,2794 wfH = 0.1045 wfc = 0.7351 Wfo = 0.1622 wfH = 0,1027 wfc = 0.6827 W f o = 0.1804 K f H = 0.1369 wfc = 0,6036 wfo = 0.2626 wfH = 0.1338 wfc = 0.6797 wfo = 0.1831 WfH = 0,1372 wfc = 0.6478 wfo = 0.2163 W f H = 0.1359 a f c = 0.5233 wfo = 0.3455 wfH = 0.1312 wfc = 0.6680 wfo = 0.2199 wftr = 0,1115 wfc = 0.7399 wfo = 0.1209 wfR = 0.1392 wfo = 0.7369 wfo = 0.1233 W ~ E= 0.1398 wfc = 0.7405 wfo = 0.1207 wfH = 0.1388 wfc = 0.5444 wfo = 0,3643 WfH = 0,0913 wfc = 0.5453 wfo = 0.3634 w f H = 0.0913 wfc = 0.5421 wfo = 0.3661 WfH = 0,0918 wfc = 0.6493 wfo = 0.2150 W f H = 0.1357 wfc = 0.6402 wfo = 0,2225 WfH = 0,1373 wfc = 0.4716 wfo = 0.4225 W f H = 0,1059 wfc = 0.4739 wfo = 0.4200 WfH = 0,1061 wfc = 0.7764 wfo = 0.1490 WfH = 0.0746 wfc = 0,7790 wfo = 0.1465 WfH = 0,0745 wfc = 0.7768 wfo = 0.1484 U'fH = 0,0748 wfc = 0.4018 d o = 0,5305 WfH = 0.0677
sequent analyses by vapor phase chromatography and mass spectrographic analysis shoned the sample to be a mixture of isomers of heptane (wfc = 0.8390) and hexane (wfc = 0.8362), \+ith approsimntely tnice as much hexane isomers as heptane isomers on a weight basis. This agrem very ne11 nith the @-rayresults. i\Iethyl isopropenyl kptone \\as analyzed using both instruinenta. Thc difference betneen the experimentally detcrmiiied weight fractions and the theoretical values seemed excessively large for this type of compound, especially in thc w i g h t friiction of hydrogen. Mass spectrographic analysis revealed a small quantity of water in the sample, which amounted to l . l O ~ oby weight as determined by a Karl Fischer titration. For comparative purposes, a sample of this same methyl isopropenyl ketone was analyzed by classical microchemical methods. The results of these analyses are tabulated in Table VIII. Compounds ?nd mi\tures containing four or more 'rments cannot be comd unless the weight fractions of all elcments in ?\cess of three is knonn. However, the feasibility of a suggested empirical formula and a knowledge of the purity can be determined by measuring the intensities of the backscattered and transmitted 0-rays and comparing these with their theoretical intensities from the compound. For example, nitrobenzene containing hydrogen, carbon. nitrogen, and oxygen cannot be uniquely analyzed by @-ray transmission and backscatter alone. However, the observed 8-ray backscatter intensity. 715 scale divisions, is close to the predicted intensity for nitrobenzene, 717 scale divisions. The total P-ray absorption cross section A , as determined experimentally, is 0.6816 compared with the predicted value of 0.68155. From these results, the sample of nitrobenzene is thought to be of very high purity. Several solid compounds have been analyzed by dissolving them in suitable solvents. Although the resultant solutions often contain four or more elements, the solid sample can be completely analyzed if it contains no more than three elements of unknown analysis, as the weight fractions of the elements introduced by the solvent are known. Examples of the analysis of solid samples are given in Table IX. The analysis of the first four examples is given as the total weight fraction of the element-Le., including both solvent and solute. The next example, hexamethylenetetramine dissolved in water, is shown both as a total elemental analysis and a n analysis of the solute only, the effect of the solvent having been subtracted from the total @-rayintensities. Obviously, the greatest accuracy is obtained when a maximum amount of 1
unknown solute is dissolved in a minimum amount of knoiyn solvent. Similarly, liquid samples of insufficient volume t o be analyzed in the backscatter instrument (26 cc.) can be diluted with a known amount of solvent. A small sample of dibutyl phthalate (less than 7 ml.) mas diluted with isooctane and analyzed. The quantitative analysis is given in Table IX. Again, both the total analysis and the analysis of the dibutyl phthalate is given. Several mivtures of p-xylene and isooctane were prepared from the pure materials and analyzed on the transmission and backscatter instruments. Several of the mixtures mere analyzed on the backscatter instrument alone (Table X). Similarly, several mixtures of cumene and isoamyl alcohol were prepared and analyzed. The results are shown in Table XI. Cumene, isoamyl alcohol, and their mixtures give equal P-,ay backscatter intensities, but different transmission intensities.
Table V.
Analysis of Nitrogen Compounds
Compound Pyridine water"
+
Di butylamine Dimethylformamide@ Diethylamine
+ watera
Triethylamine
+ watera + water5
n-Butylamine
Urea and water5 Urea and watera
Experimental wfc = 0.7582 wfo = 0.0021 wfH = 0,0639 wfc = 0.7434 wfs = 0.1084 T f H = 0,1482 W f c = 0.4908 wfo = 0.2208 R'fH = 0.0968 wfc = 0.6511 Y f O = 0.0074 Rfrr = 0,1515
wfa = 0.1492 wfc = 0,6484
WfH
= 0,1491
wfc wfo wfH
= 0.6527 = 0.0073 = 0.1510
wfc
=
wfo wfn wfc
= =
wfo
=
DISCUSSION
=
wfo
=
Std. dev. Oxygen Carbon Hydrogen ' '61 (weight fraction nitrogen) known. Table VI.
=
wfH wfc wfa wfc wfo n'fH
Urea and watera The use of @-ray backscattering and 8-ray transmission in the analysis of liquids is accurate, rapid, simple, and nondestructive. Tiyo-element compounds, such as hydrocarbons, can be completely analyzed on either of the instruments, whereas three-element compounds require p r a y intensity measurements on both the backscatter and transmission instruments for a complete quantitative analysis. Compounds and mixtures containing more than three elements cannot be analyzed unless quantitative data are available for all elements in eycess of three. Empirical formula can be verified for a compound containing any number of elemental components if the elemental @-ray constants are known for all the constituents. A t present, this is limited to compounds and mixtures containing hydrogen, carbon, nitrogen, oxygen, and fluorine. Because the P-ray backscattering intensity is proportional t o Zz, a sample to be analyzed must be free of higher atomic number elements, such as chlorine and bromine. It is expected t h a t a very small contamination of a higher atomic number elementfor example, 0.1% bromine by weightwould cause a considerable error in the analysis of a lighter liquid. When the elemental constants for these heavier elements are calculated and available, the contribution of such contaminations can be readily determined and the subsequent analysis corrected. Hydrocarbons are analyzed with approsimately the same precision on the transmission and backscatter instruments. The standard deviation in the weight fraction of carbon on hydrogen for the standard hydrocarbons, includ-
Theoretical wfc = 0.7536 wfo = 0.0066 wfH = 0,0641 dvfc= 0.7453 wfx = 0.1068 wfH = 0.1479 wfc = 0.4930 a f o = 0.2189 wfH = 0.0966 a7fc = 0.6518 wfo = 0.0068 WfH 0.1513 wfc = 0.7037 wfo = 0,0043
=
= = = =
0.0115 0.1511 0.0383 0.7691 0.1033 0.0583 0.7053 0.0987 0.0789 0.6429 0.0942
x f c = 0.7060
wfo
Yfo
R'fH
wfc wfo
=
0.0062
0.0397
= 0,7676 = 0,1034 = =
W ~ H=
wfc = Wfo = nfa =
0.0610 0,7032 0.0986 0.0786 0.6430 0,0944
0.0025 0,0025 0,0002
Analyses of Standard Fluorine Compounds
Compound 0-Fluorotoluene Fluorobenzene I-Fluoronaphthalene
Theoretical wfc = 0,7634 \vfF 0.1725 \vfz = 0,0641 wfc = 0,7499 ivfF = 0 . 1977
Std. dev. Carbon Fluorine Hydrogen
\vfc wfc
\vfF =
R'fF
\vfc wfo wfH
= = =
0.1300 0.0483 0.6666 0.1268 0,0559
=
WfF = \vfH =
\vfH = 0.0524 n f c = 0.8217
\vfB =
p-Fluoroanisole ( W f F known)
Experimental wfc = 0.7612 V-fF 0 . 1738 \vfH = 0.0650
0.7486 0,1989
0.0525 0,8244
= wfH =
0,1276
wfc \vfo
0.6683 0.1254 0,0557
\vfH
= =
0,0480
0,0021 0,0017 0.0005 ,-
Table VII.
Analyses by @Ray Transmission and Backscatter Intensities
Compound Diethyl benzene (transmission) Diethyl benzene (backscatter) Acetonitrile Fluorohexane m-Difluorobenzene Std. dev. Carbon Hydrogen
Theoretical wfc = 0.8949 wfH 0.1051 wfc = 0.8949 WfH = 0,1051 wfc = 0.5851 wfN = 0.3412 wfE = 0,0737 v f c = 0.6918 "fF = 0.1824 1VfH = 0,1258 wfc = 0.6316 wfF = 0.3330 wfH = 0.0353
Experimental wfc = 0.8947 \vfH = 0,1053 wfc = 0.8957 wfn = 0,1043 wfc = 0.5839 WfN = 0.3428 wfH = 0.0733 tvfo = 0.6890 wfF = 0.1851 W f H = 0 . 1259 wfc = 0.6354 F'fF = 0,3293 W f H = 0,0353
0,0024 0.0002
VOL. 32, NO. 6, MAY 1960
e
587
Table VIII.
Analyses of Methyl lsopropenyl Ketone
Theore tical Assuming pure Corrected for compound water content 0.7139 0.7061 0.1902 0.1979 0.0959 0.0960
wfc wfo WfH
Experimental Chemical B-Ray 0.7092 0,7086 0.1964 0,1959 0,0955 0.0930
~~~~
Table IX.
Analyses of Samples Dissolved in a Suitable Solvent
Sample System Acenaphthene and toluene (backscatter)
Theoretical
0.0600 m.fx = 0.0466 WfH = 0.1089 w f c = 0.8012 wfo = 0.0609 WfH 0.1378
Experimental vfc = 0.9177 wfE 0.0823 R-fc = 0 5527 \Vfo = 0 3311 wfa = 0 1162 wfc = 0 1566 Wfo = 0 7486 wfH = 0 0948 wfo = 0 8193 wfy = 0 0820 wfH = 0 0987 R f C = 0 5126 w f ~= 0 4003 m f ~= 0 0870 wfc = 0 0598 Wfv = 0 0467 wfn = 0 1090 wfc = 0 8041 Wfo = 0 0584 w f ~= 0 1375
Dibutyl hthalate (DBP) and iso-octane (analysis of D B ~ only) : wfc = 0.6004 n'fo = 0.2299 TfH = 0.0797
wfc = 0.7013 wfn = 0,2204 wfH = 0.0783
wfc = 0.9178
wfH 0.0822 wfc = 0.5522 wfo = 0.331G WfH = 0.1162 \Vfc = 0.1535 Sucrose and water wfo = 0.7518 wfH = 0,0947 Ammonium nitrate and water wfo = 0.8253 wfN = 0.0762 WfH = 0.0985 Hexamethylenetetramine and water (solute only) wfc = 0.5140 W f N = 0 3997
Benzoic acid and ethyl alcohol
0,0863
wfH
Rexamethylenet8etramineand water (total analysis) mfc Dibutyl phthalate and {so-octane (total analysis)
Table X. Analyses of Mixtures of p-Xylene and Iso-octane
Mixture Iso-octane p-xylene Mixture 2 Mixture Mixture 3 Mixture 4 Mixture 6 5 Mixture
Mixture 7
Thee- Experimental, wfc retical, Back- Transwfc scatter mission 0.8412 0.8412 0.8412 0,9051 0.9050 0,9051 0'8922 8927 0'8922 0.8921 0.8925 .., 0.8792 0.8794 0.8iG5 0.8763 0.8767 0.8657 0.8658 o,ii96 o,8591 o,8589 0.8545 0.8547 ...
Table XI.
ing the mixtures of p-xylene and isooctane, is less than 0.03% for both instruments. As the density has a very much smaller effect on the backscatter intensity than on the transmission intensity, the use of the backscatter instrument is preferred for hydrocarbon analysis. Densities must be measured to only 1 0 . 0 1 gram per cc. for backscatter analysis, compared to a necessary precision of &0.0001 gram per cc. for p r a y transmission. Backscatter analysis does have one obvious disadvant,age. A rather large sample
Analyses of Cumene and Isoamyl Alcohol Solutions
Mixture Cumene (backscatter) Cumene (transmission) Isoamyl alcohol Mixture 1 Mixture 2 Mixture 3
588
=
ANALYTICAL CHEMISTRY
Theoretical wfo = 0.8994 wfa = 0.1006 ~ f = c 0,8994 WfH = 0.1006 wfc = 0.6813 wfo = 0.1815 w f ~= 0.1372 wfc = 0.7363 wfo = 0.1357 V& = 0.1280 n*fc = 0,7921 wfo = 0.0893 wfa = 0.1186 wfc = 0.8471 wfo = 0.0435 wfa = 0.1094
Experimental wfc = 0.8997 wfH = 0.1003 wfc = 0.8995 w f ~= 0.1005 wfc = 0.6829 wfo = 0.1804 wfH = 0,1367 wfc = 0.7368 wfo = 0.1355 W ~ H= 0.1277 wfc"= 0.7936 wfo = 0.0883 wfH = 0.1181 wfc = 0.8476 wfo = 0,0434 WfH = 0,1090
volume (26 cc.) is necessary for the intensity determination, compared to only 0.8 and 1.2 cc. for the transmission measurements. I n general, the quantitative analysis of ternary compounds is not so precise as in the case of the hydrocarbons. This is to be expected because the errors are multiplied as a result of the two different measured p-ray intensities. The standard deviations of the carbon, oxygen, and hydrogen content in 27 oxygen compounds and mixtures are tabulated in Table XI1 together with the standard deviation of hydrogen in the hydrocarbons, nitrogen compounds, and fluorine compounds. Diethyl ether, which gave abnormally high deviations from the theoretical values, is not included in Table XII. The outstanding feature of Table XI1 is the consistently low standard deviation in the weight fraction of hydrogen. I n 45 ternary compounds and mixtures and 21 hydrocarbon systems, the standard deviation in the weight fraction of hydrogen is less than 0.03% on an absolute 11-eightbasis. This is significantly much lower than the standard deviations of carbon and oxygen in the carbon-oxygen-hydrogen systems. The errors in the carbon and oxygen analysis almost exactly compensate each other, thereby making the hydrogen analysis very good. Similarly, in the nitrogen and fluorine compounds, the hydrogen analysis is good because of compensating errors in the analysis of the other two elements. The reported anomalous behavior of hydrogen in p r a y backscattering (8) cannot be supported or disproved in this study as the absolute magnitude of the backscatter intensity is unknown. This reported anomaly-that hydrogen exhibits negative backscattering that is less than zero scattering, presumably because of absorption effects-has not been found to be a factor in the current investigations. Hydrogen, like the other elements, has been assigned a n effective atomic number and backscatter cross section which have been consistent with all the analytical data. [The negative value of the backscatter cross section of hydrogen (-748.1 scale divisions) does not imply negative backscatter per se, as the cross section values are expressed in arbitrary scale divisions and a different scale choice could give hydrogen a positive cross section.] After additional p-ray backscatter cross sections are available, it may be that theoretical considerations and experimental data would indicate negative backscattering for hydrogen. Very preliminary theoretical considerations and our limited data do seem to indicate that the experimental cross section of hydrogen is lower than TI h a t might be predicted. The concept of a n effective atomic number wherein a compound or mixture
can be regarded as being built of one kind of particle called atoms with atomic number 2 has been used in the analysis of ?-ray backscattering (9, 8, 11). Various formulas for the calculation of the effective atomic number have been suggested and correlated with ehperimental data. AIuller (Q), n i t h marked success in his system, used a formula such that
z
[(weight fraction),Z,]
=
(12)
1
Saldick and Allen’s (11) formula fori? [(electron density),Z,]
. i ? =
(13)
i
is a special case of the more general formula ( 6 ) 1
2
[(electron density),Z,”]’
=
(14)
1
nherein 2 = 1. Effective atomic numbers were calculated according to Equations 12 and 13 for all the compounds and mixtures studied herein, and correlation was attempted with the observed backscatter intensities. MullerJs effective atomic number (Equation 12) showed the poorest correlation with marked scatter of the points even after correcting for hydrogen content. The hydrocarbon systems indicated that some correlation existed, but the ternary compound data disputed any general correlation for all compounds. The results of plotting backscatter intensities us. the effective atomic numbers calculated using Equation 13 were much better, but there was still some scattering of the data from a smooth curve. Effective atomic numbers were calculated from Equation 14 with z = 0.93 and found to give a very good correlation n i t h the experimental P-ray backscatter intensities. A graphical representation could be used to obtain an effective atomic number from a backscatter intensity and could subsequently be used to individualize the compound or mixture. However, in view of the success of the mathematical approach this graphical interpretation should principally be of academic interest. The marked discrepancy between the data of Muller and ours in the lack of correlation of the effective atomic numbers can probably be attrib-
uted to the different experimental systems used in each case. The geometry is different as is also the method of detection of the backscattered 0-rays. Muller’s intensity data, obtained with a proportional counter, would be relatively free of ?-ray energy effects; whereas our ionization chamber detector integrates the energy loss of the ?-rays in transversing the active volume of the chamber. Because our data have been limited to the light elements (2 6 9), our effective atomic number calculations have not included values near the inflection points a t 2 = 10, 18, 36, and 54 noted by Muller. The quantitative analysis of binary compounds by either p-ray transmission or backscattering is rapid and accurate. The average time per sample is approximately 10 minutes for backscattering analysis and slightly longer for transmission analysis. The precise density requirements and the necessity of sample temperature being at 30” C. require the longer analysis time for the transmission determinations. Analysis of ternary compounds and mixtures is likewise rapid. The complete analysis of ternary compounds takes less than 30 minutes. If sufficient sample is available for the simultaneous determination of the sample density and backscatter and transmission p-ray intensities, the analysis can be done in less than 20 minutes. This is to be compared with the 3 to 4 hours for a complete analysis by classical microchemical methods. Investigations are continuing on the extension of these B-ray interactions t o higher atomic number materials. ACKNOWLEDGMENT
The authors are indebted to J. R. Scherer for the compilation of the computer program used in the calculation of the elemental backscatter constants. Acknowledgment is also extended t o E. D. Ruby and L. B. Westover for the vapor phase chromatography and mass spectrographic analyses. LITERATURE CITED
(1) Berthold, R., “Proceedings of the
Second United Nations International Conference on the Peaceful Uses of Atomic Energy,” P/983, Vol. 19, p. 288, United Hations, Geneva, 1958.
XII.
Table
Standard Deviations in P-Ray Analyses
Weight Element Fraction Carbon in C-H-0 compounds 0.0018 Oxygen in C;H-O compounds 0.0018 Hydrogen in C-H-0 compounds 0.0003 Hydrogen in nitrogen compounds 0,0002 Hydrogen in fluorine compounds 0,0005 Hydrogen in hydrocarbons (transmissjon) 0.0003 Hydrogen in hydrocarbons (backscatter) 0.0003 Hydrogen in 45 ternary compounds and mixtures 0.0003 (2) Danguy, L., Qiiivy, R., J . phys. radium 17, 320 (1956). (3) Evans, R. D., “The Atomic Nucleus ” Chaps. 19-21, McGraw-Hill, New York, 19.59.
(4) Fodor, J., Varga, C., “Proceedings of the Second United Nations International Conference on,, the Peaceful Uses of Atomic Energy, P/2241, Vol. 19, p. 215, United nations, Geneva, 19.58.
(5) Gray, P. R., Clarey, D. H., Beamer, w.H., ANAL.CHEM. 31, 2065 (1959). (6) Henricksen, T., Baarli, J., Radiation Research 6, 415 (1957). (7) Husain, S. A., Putman, J. L., Proc. Phys. SOC.( L o n d o n ) 70,304 (1957). ( 8 ) Muller, D. C.,ANAL.CHEM.29, 975 (1957). (9) Muller, R. H. Ibid., 29, 969 (1957). (10) Muller, R. k., Phys. Rev. 93, 891 (1954). (11) Saldick, J., Allen, A. O., J. Chem. Ph s. 22, 438 (1954). (12) mith, V. K.,Otvos, J. W., ANAL. CHEM.26,359 (1954). (13) Strominger, D., Hollander, J. &‘I., Seaborg, G. T., Revs. Modern Phys. 30, 585 (1958). RECEIVED for review September 23,. 1959. Accepted December 18, 1959. Division of Anal tical Chemistry, 137th Meeting, ACS, Cikeland, Ohio, April 1960.
4!
Correction Eva1ua t ion of St and ard Model D Keston Polarimetric Attachment for the Beckman DU Spectrophotometer I n this article b y Knud G. Poulsen [ANAL.CHEM.32, 410 (1960)], on page 413, the second line after the Literature Cited section should read Accepted December 17,1959.
VOL. 32, NO. 6, MAY 1960
589
