use of DMSO as a solvent also enhances the chemical shift separation of the individual dichloroacetyl resonances as well as the tertiary, secondary, and primary group separations. A change in solvent does cause a significant change in chemical shift of the dichloroacetyl resonances,-e.g., shifts in DMSOd 6 are approximately 0.8 ppm to lower field than those in CDCI,. Concentration variations affect the resonance positions only slightly. Other dichloroacetates derived from primary alcohols have been studied which are not included in Figure 1, a and b. The dichloroacetyl resonances of these esters, without exception and independent of degree of branching, fall to lower field than the dichloroacetyl resonance of ethyl dichloroacetate. The advantage of this method lies in the fact that with a single scan of the proton spectrum of a dichloroacetylated alcohol not only may the primary, secondary, and tertiary dichloroacetyl resonances be observed, but also alpha proton
paramagnetic shifts may be noted as additional diagnostic features. An additional advantage of the dichloroacetylation-” method over the I9F method ( I ) is that it can be performed using the more accessible proton spectrometer systems. The trifluoroacetylation-lgFmethod ( I ) for alcohol characterization provides larger chemical shift differences between primary, secondary, and tertiary resonances but approximately the same separations within each group. The same chemical shift tendencies within groups have been noted when compared with the 19F results. The dichloroacetylation-lH method has been applied with success to polymer systems containing hydroxyl groups, specifically polyethers derived from various initiators. In addition to obtaining the types of hydroxyl groups present in these polyethers, one can obtain the amount of hydroxyl with respect to initiator and monomer. RECEIVED for review November 2,1967. Accepted December 11,1967.
Rapid Precision Determination of Composition of Continuous Solid Solutions by X-Ray Techniques Paul Cherin, E. A. Davis, and C. Bielan Xerox Corp., Research Laboratories, Rochester, N. Y SOLIDSOLUTIONS have found considerable application commercially as phosphors, photoconductors, etc. By varying the composition of such solutions, it is possible to adjust their properties-for example, to control the band gap. Thus, it has become increasingly more important to be able to determine precisely and promptly the composition of solid solutions. A continuous series of solid solutions can form whenever the atoms or ions involved are similar in size and have similar electronic structure. Because this generally means similar chemical properties, problems frequently arise when chemical techniques are used for composition determination. In general, physical methods can be both more rapid and precise. In addition, they frequently require less material than chemical methods. The techniques we have used are based on X-ray diffraction and fluorescence spectrometry. Basically, the net intensity of X-ray emission by the constituent atoms of the solid solution is calibrated against emission from physical mixtures, These solid solutions are then used as secondary standards for Debye-Scherrer photographs, which can be measured rapidly and require less than 0.1 mg of sample. The X-ray fluorescence spectrometry method utilizes a ratio technique-Le., a ratio of the net emission intensities of the constituents a and b (a binary system is assumed here), It can be shown ( I ) that
It is also possible to prepare solid pellets with a nonabsorbing dilutant (2). Although X-ray emission spectrometry frequently yields precise results, greater relative precision can be achieved through the use of X-ray diffraction in a rapid technique which we call the “inner ring” method. “Inner rings” refer to Debye-Scherrer diffraction rings having high 20 values, which are highly sensitive to changes in lattice spacings, and, therefore, in most solid solutions, are highly sensitive to changes in composition. This technique is most useful when the solid solution gives reasonably sharp diffraction lines in the back-reflection region and when the constituents of the solid solution have appreciably different lattice parameters. If the diameter of an inner ring is defined in terms of S, the line separation, where S is measured in the same units as the camera radius, and d is the lattice spacing, then
so = -x
cos 4
2d
where n and K are constants. If the materials being analyzed can be put into solution, then the matrix effect is considerably reduced and the relationship between the ratio of emitted intensities and the ratio of concentrations is virtually linear.
For a continuous series of solid solutions crystallizing in the cubic phase and obeying Vegard‘s law-Le., having lattice constant proportional to the mole per cent of the constituents, a plot of (cos S/4)-’ us. Xi,the mole fraction of the ith component, is linear. The same is true of hexagonal and tetragonal systems when the c/a ratio is independent of the composition. As the latter is generally a good approximation in most systems, the plot of (cos S/4)-’ us. X r is a very useful one. Greater precision can be achieved if care is taken to eliminate errors due to film shrinkage, absorption, etc. (see Appendix). To utilize the inner ring method, a set of standard solid solutions is necessary. Their compositions can be determined
(1) E. P. Berth, ANAL.CHEM., 36,826 (1964).
(2) J. Leroux and M. Mahmud, ANAL.CHEM., 38,76 (1966).
In
ca 5 E In K + n In Ib
(1)
c b
VOL. 40, NO. 3, MARCH 1968
61 1
by means of the X-ray fluorescence spectrometry technique previously described. Once this standard set is completed, the composition of other solid solutions can be determined rapidly and with extremely high precision. As the Bragg angle of the inner ring approaches 90°, differences of 0.2 mole are easily observed. In the remainder of this paper, we discuss the application of the aforementioned techniques to the (Cdl-,Zn,)S system. This is a hexagonal system in which both axes nearly obey Vegard's law and the cja ratio ranges from 1.637 in ZnS to 1.623 in CdS.
r l
I
I
I
I
I
I
I
-!in
I
1'-
"O t
EXPERIMENTAL
Preparation of Standards. Physical mixtures of CdS and ZnS were carefully weighed to prepare standards. The mixtures were dissolved and digested in concentrated HCI, then diluted and transferred to test cells. The solid solutions were treated in the same manner. Measurement of Intensity Ratios. A Norelco 8-position vacuum X-ray spectrograph equipped with a lithium fluoride analyzing crystal with fine collimation slits was used to measure intensity. The pulse height analyzing techniques were optimized for the ZnKw (second order) and CdKal (second order) emission lines. The scintillation counter was positioned at the 28 value which gave the maximum number of counts. Multiple measurements were made. Similar measurements were made of the background at f2" in 20 off the main peak. Debye-Scherrer Technique. The usual Debye-Scherrer technique was used, except that a Lindemann capillary was thinly coated with a layer of petroleum jelly and then with a thin layer of powdered (Cdl-,Zn,)S. This procedure minimizes absorption effects (3) and requires only about 0.1 mg of sample. CuKa (Ni filtered) radiation was used. RESULTS
The variation of emitted X-rays as a function of composition in carefully weighed out mixtures of CdS and ZnS was determined. A plot of the I Z n l I m ratio us. the known mole ratio x z , / x c d is linear. The plot was subsequently used to determine the composition of the standard solid solutions. The diameters of several inner rings are plotted as a function of composition in Figure 1. The curves are labeled with the appropriate Miller indices. The sensitivity of this method can be appreciated by noting that the diameter of the (403) ring, for example, varies between about 0.25 mm per mole % near CdS to almost 1 mm per mole % near ZnS. When this ring approaches
(
cos
3 -
-l
=
1.017 and the precision falls,
the (321) ring can be followed. Similarly, when the composition is about 50% ZnS, the (315) diffraction ring can be observed and utilized. At most compositions, the diameters of three or more rings can be usefully measured to check for consistency. Relative compositions can usually be determined to i=O.ZX. The accuracy of this method for determining absolute compositions is clearly limited by the accuracy of the secondary standard-Le., the ratio of emission intensity us. mole ratio. Assuming the standards have been carefully prepared, the precision attainable from X-ray emission data is significantly affected by the counting rates. It can be shown ( 4 ) that the (3) M. E. Straumanis,J . Appl. Phys., 20,726(1949). (4) H. P. Klug and L. E. Alexander, "X-ray Diffraction Procedures," Wiley, New York, 1962.
612
ANALYTICAL CHEMISTRY
6
5
tz a, \
4
\
-
1. .0 00 0 1 0
I IO
I
I
20
30
I
40 50 60 70 MOLE PERCENT Z n S ( X z n )
:3 2
I
I
71
83
90
100
I
I
Figure 1. Variation of diameter of Debye-Scherrer diffraction rings in (Cd,- .Zn,)S (camera diameter
=
360 mm, X
= 1.5405
A
standard deviation in the emission intensity ratio due to statistical variation in the counting rate can be expressed as : (3) where
up =
1/Ncd and
UB
=
dBCd,
N C d is the total number of counts at the maximum of the CdKal (second order) emission line, B C d is the average background 2" off the CdKal (second order) maximum. The corresponding symbols for the Zn terms have similar significance. In the worst case (10 mole % of zinc) the standard deviation in the ratio of mole per cents is approximately 2.5%, based on Equation 3 and Figure 1. This value rises rapidly as the concentration of one of the constituents approaches zero. When the composition ratio is unity, the standard deviation is approximately 0.8%. When the inner ring method is utilized, the precision is not dependent on the composition but on the 28 value of the innermost ring. In addition, the procedure of drawing a smooth curve in Figure 1 averages, and therefore minimizes, the effect of random error in the composition determination of the standards. Thus, the precision attainable with the inner ring method should clearly be greater than with X-ray fluorescence spectrometry techniques in the ranges where the concentration of one of the constituents is low.
APPENDIX
Assuming a shrinkage of 1 mm,
Calculations to show the effect of errors in measured line positions on the compositions determined are given below. Corrections, which minimize the effect of many of these errors, can be made. Reading Error.
A0
=
=
0.10"
(
A@= 1 + -
R
r sin 4 ~
D)
8R
(T
- 24) cos 24
cos 4
Assuming a 1 % error,
A0
+ sin 24
+ (sin 24) In(tan 4/2)
where4 = a12 - 0 = 5.83' D = the target-to-specimen distance, = 127.3 mm r = the radius of the capillary, 0.3 mm
A0 = 0.018' The error in composition is negligible. Film Shrinkage Error (6)
AS A0=-4 S ( 5 ) B. E. Warren, J . Appl. Phys., 16,614 (1945). (6) A. J. Bradley and A. H. Jay, Proc. Phys. SOC.,44, 563 (1932).
=
0.029'
The error in composition is about 0.005 mole Displacement from Center Error (6)
A0
and the error in composition is 0.1 mole %. Absorption Error. It can be shown (5) that for the case of a diverging beam and high absorption.
0.032'.
AR A0=--4 R
R
=
The error in composition is about 0.05 mole %. Camera Radius Error (6)
AS
where A S = the error in line separation A0 = the consequent error in the Bragg angle R = the radius of the camera, 180/.rr Assuming AS = 0.1 mm and 0 = 84.17' [(cos S/4)-' = 1.0051. then
A0
A0
%.
AX sin 4 cos 4 R
= -
where A X is the displacement of the sample from the center in the direction parallel to the beam. If the displacement is 0.5 mm,
A0 = 0.001" which has a negligible effect on the composition determination.
ACKNOWLEDGMENT The authors acknowledge the assistance of George Fekete, Fred Knier, and Phyllis Unger. The powders and crystals used in these experiments were prepared and grown by Edward Lind. RECEIVED for review June 22, 1967. Accepted December 22, 1967.
Determination of Fluoride iln Bone with the Fluoride Electrode Leon Singer and W. D. Armstrong Department of Biochemistry, CoIlege of Medical Sciences, University of Minnesota, Minneapolis, Minn. 55455
ELECTRODES made from single-crystal sections of rare earth fluoride have been developed to measure fluoride ion activity in solutions (I). The potential of the electrode generated against a reference electrode can be calibrated with standard fluoride solutions to reflect fluoride ion concentrations. However, the fluoride ion activity measurements in the solutions are influenced by factors such as pH, ionic strength, temperature, and by some extraneous ions. Therefore, these factors must be rigorously controlled in both standard and unknown solutions to obtain meaningful results. The fluoride ion electrode has been used for determination of fluoride in tungsten (2), and in chromium plating baths (3). Preliminary communications have described the use of the electrode for determination of fluoride in urine (4), (1) M. S. Frant and J. W. Ross, Science, 154,1553 (1966). (2) B. A. Roby and W. E. Sunderland, ANAL.CHEM.,39, 1304 (1967). (3) M. S. Frant, Plafittg, 54,702 (1967). (4) Leon Singer, W. D. Armstrong and J. J. Vogel, Abstr. 45th General Meeting of Inter. Assoc. Dental Research, p. 77 (March 1967).
enamel of teeth ( 3 ,and saliva (6). Durst and Taylor (7) modified the construction of the electrode to permit the use of SO-pl volumes of sample. This report described a simple direct method for determination of fluoride in bone which is rapid and accurate.
EXPERIMENTAL Apparatus. The Orion Model 94-09 fluoride ion electrode and a conventional potassium chloride electrode were employed with a Corning Model 12 research pH meter, which is provided with an expanded scale, for measurements of the fluoride ion activity of the solutions. Reagents. The standard fluoride solutions were made from sodium fluoride and each standard solution contained 0.05M sodium chloride and 0.005M sodium acetate-acetic acid buffer (pH 4.7). When the bone ash was expected to contain no more than 0.2% fluoride, standard solutions ( 5 ) B. Richardson and H. G. McCann, Zbid., p . 77. (6) P. Grgn, F. Brudevold, and H . G. McCann, Zbid., p . 79. 39,1483 (1967). (7) A. Durst and J. K. Taylor, ANAL.CHEM., VOL. 40, NO. 3, MARCH 1968
613
