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"
(
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.
A@= 1 + -
AR A0=--4 R
R
= 0.032'.
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
Table I. Reproducibility of the Electrode Method for Analysis for Fluoride in Pooled Bone Ash ExperiNo. of aliquots F Content, ment analyzed f SE 1 8a 0.241 f 0.0011 2 6" 0.225 f 0.0014 3 1O a 0 . 2 3 6 f 0.0006 4 Ten 4- to 6-mg samples 0.225 -f 0.0023 Average 0.231 Aliquots of one solution of bone ash (see text).
z
0
~~
Table 11. Fluoride Contents of Bone Ash Obtained by Two Procedures Fluoride content, No. of Range of fluoride Electrode Reference method (8) bones contents, 9 0.036-0.050 1.07 k 0.014 (SE) 10 0.1884.259 0.98 f 0.019 (SE) 5 0,4734,635 0.99 f 0.010 (SE)
z
containing 0.1 to 0.7 ppm fluoride were used. Standard solutions with fluoride concentrations of 1 to 10 ppm fluoride were employed with bone ash samples containing higher than 0.2% fluoride. Materials. Dry, fat-free bones of rats were ashed overnight at 550' C. The pooled and mixed bone ash of several animals was used in one series of replicate analyses. In another series of analyses the ash of a single humerus from animals of different exposure to water-borne fluoride were employed in order to evaluate the reliability of the procedure with bones of widely different fluoride contents. Procedures. Four to 6 mg of bone ash were weighed in a small glass boat, transferred to a 50-ml polyethylene beaker, and dissolved by addition of 1 ml of 0.25M hydrochloric acid. The excess acid was nearly neutralized by addition of 1.1 ml of 0.125M sodium hydroxide solution and a final adjustment of the solution to pH 4.7, using a pH meter, was effected by titration, with 0.05M sodium acetate solution. The total volume of the solution was made up to 5 ml by addition of distilled water. These procedures produced essentially the same ionic strength and pH in the bone solutions as those of the standard solutions. The two electrodes were inserted into the solution which was stirred until a constant millivoltage reading on the meter was obtained. This required 5 to 10 minutes, The millivoltage readings with the standard solutions were plotted on the rectangular axis against their fluoride concentrations on the logarithmic axis of semilogarithmic paper. The curves so obtained were straight lines. These standard curves were used to translate the millivoltage readings of the bone ash solutions to concentration of fluoride. The fluoride contents of all bone ash samples were also determined by a previously described method (8) which depends upon isolation of the fluoride by diffusion of hydrogen fluoride and colorimetric determination of the evolved fluoride. RESULTS AND DISCUSSION The results given in Table I were obtained with the pooled bone ash. In each of Experiments 1-3, 60 mg of bone ash were dissolved in 12 ml of 0.25M hydrochloric acid. The indicated number of 1 .O-ml aliquots from each solution were separately adjusted to pH 4.7, diluted to 5 ml, and individually analyzed for fluoride by the described procedure. The re(8) Leon Singer and W. D. Armstrong, Anal. Biochem., 10, 495
(1965). 614
ANALYTICAL CHEMISTRY
sults of analyses of 10 indivihally weighed samples of the pooled bone ash are shown as Experiment 4. A mean percentage fluoride content of the same pooled bone ash of 0.235 0.0021 standard error of the mean was obtained by the reference procedure (8). The ash of the individual humeri of different fluoride contents were each analyzed by the electrode method and by the standard procedure (8). The results in Table I1 give the range of fluoride contents among the individual bones as obtained by the electrode method. A comparison of these results with those obtained with the same bone ash samples analyzed by the standard procedure are given as a ratio in the same table. The information in Table I shows a high degree of reproducibility of the results obtained on replicate analyses of a single solution of bone ash and the concordance of these results with those obtained by analyses of separate samples of the bone ash (Experiment 4). The average of the mean results obtained by the electrode procedure, 0.231 fluoride, compares well with the mean result, 0.235 % fluoride, found by the reference method. The variation of the mean results among Experiments 1-3 cannot be attributed entirely to the inherent errors of the electrode measurements because of the low values of the standard errors of the means, and may have resulted from inhomogeneity of the pooled bone ash. The results in Table I1 show excellent agreement between the results obtained by the two procedures with samples containing 0.188% or more fluoride, but that slightly higher fluoride contents were indicated by the electrode procedure with bone ash of low fluoride concentration than by the reference method (8). The latter findings are not to be attributed to an effect of phosphate ion in the bone ash solutions on the electrode or upon the activity of the fluoride ion in the bone ash solutions. The bone ash solutions contained 5-6 mmoles per liter phosphate and it was found that up to 20 mmoles of phosphate per liter added to standard solutions of low fluoride content had no effect on the millivoltage output of the electrode. These observations of lack of interference of phosphate were made with three-times recrystallized KH2POr. Reagent grade Na3P04contains sufficient fluoride to affect the results when added in the above-mentioned concentration to standard fluoride solutions. It would appear that the procedures described would also be applicable to determination of fluoride in the ash of other normal and pathological calcifications such as kidney stones and in minerals such as rock phosphate. The calcium, magnesium and phosphorus contents of bone ash are each nearly constant among specimens. Thus, the final dilutions of the bone ash solutions contained 7-11 mmoles calcium per liter and 0.3-0.4 mmoles magnesium per liter. Calcium and magnesium concentrations appreciably greater than these produce measurable negative errors in the results for fluoride contents and the magnitude of the errors increase with increasing concentration of divalent cation. With specimens whose calcium or magnesium contents are greater than that of bone ash (36-38z Ca; 0.4-0.8z Mg) a smaller sample should be used, if its fluoride content will permit. Alternately the standard solutions should be made to contain the approximate calcium and magnesium concentrations expected to be present in the solution of the samples and with appropriate adjustment of the ionic strength of the standard solutions by alteration of their sodium chloride contents.
*
RECEIVED for review December 1 1 , 1967. Accepted December 26, 1967. Work supported by Grant DE-01850 from the National Institutes of Health.
