~
considered, the corrections are of negligible magnitude. Figure 1 indicates that the importance of correction decreases with increasing 1 because of the increase in 1 of coal which constitutes d 5 Y c of the total matrix. In addition to the above work, the effect of the change in composition of the total matrix on the emission intensity of the elements wtw directly observed by adding various compounds to the coal. The observed decrease in intensity was 1@-20% (relative value) smaller than that calculated from the change in p of the total matrix. This discrepancy is possibly due to the approximations involved in the 1 correction procedure which tends to give a slightly high factor. On the other hand, these results confirm that the simple correction procedure accounts for a t least 80% of the error due to difference in matrices. The sensitivity of the method can be judged from the observed count rates given in Table 11. This shows that background measurements can be sensibly ignored in routine coal analysis. The background measurements have to be taken into account only when high precision analysis is required a t very low concentration levels. ACCURACY AND PRECISION OF RESULTS
With accepted methods of coal analysis, the precision of a determination is denoted by the tolerance limit set for that determination ( 7 ) . The tolerances are defined for any particular situation-e.g., within laboratory, etc.-as the maximum permissible difference in results of duplicate determinations by the same method and are given as absolute percentages. The tolerances used are the 95% confidence limits of the standard deviation of observed differences. It should be noted that tolerances are precision limits for methods which are believed to give accurate results ( 7 ) . The precision of the x-ray results is a time- and count-rate dependent quantity. Using fixed-time counts, the relative precision is dependent on the concentration. We have found no difficulty in reproducing results from replicate samples within the limits expected from counting statistics. As the precision of the x-ray results do not necessarily indicate accuracy, a comparison of x-ray and chemical results is desirable. Tolerance limits can be defined in this case as the maximum permissible difference between the results of the two methods. The standard deviation of the difference was calculated according to Nalirnov (15) from a number of samples analyzed in a routine manner. Each sample represented a composite of twenty feet of brown cod. The results
Table 111.
Element Fe Ti Ca K e1 S Si A1
a
~
~
~
Comparison of Results of Chemical and X-Ray Analysis
Concentration range of samples o/o c.d.b.
ma
Sb
32c
112 112 112 112 112 112 44 112
0.042 0.0023 0.024 0.0019 0.017 0.020 0.020 0.028
+0.013 -0.0011 +0.006 - 0.0008
0.16 -2.54 0.001-0.100 0.02 -0.35 0.002-0.052 0.04 -0.20 0.18 -0.74 0.01 -2.00 0 . 0 1 -0.73
+0.007 -0.006
+0.003 -0.003
m, number of samples compared. s, standard deviation of difference of
b chemical and x-ray results on a coal dry basis as absolute yo. c 3, mean of difference of chemical minus x-ray results on a coal dry basis.
expressed as the element on a coal dry basis yo are given in Table 111. The tolerances for the major elements are: 0.03Y0 for C1; 0,04’% for S, Si; 0.05% for Ca; 0.06% for Al; and 0.08% for Fe. For the minor elements Ti and K, the tolerance is 0.005%. Considering that the above tolerances are derived from results obtained by two different methods, they compare favorably with the values quoted by the British Standards Institution (Y)--i.e., 0.05% for S and 0.02% for C1 for results derived by the same method. From the practical point of view all the x-ray figures appear satisfactory for their use in evaluating coal quality. The mean of the differences, 2 , which is positive when x-ray figures are higher, shows no serious systematic bias of the calibration lines derived from standard coal samples. In the case of iron there may be a systematic bias giving a higher x-ray result. This may be due to the error in the total iron determined via ash analysis as it has been reported (9) that some iron can be lost by fusion with the ashing dish. On the whole, the above comparison of results confirm all aspects of the x-ray method and indicates its acceptability for use in routine analysis. The increase in the number of analyses can be gauged by our experience where three technicians using atomic absorption and x-ray methods produce results at the same rate as eighteen skilled analysts using standard methods of ash analysis (6). ACKNOWLEDGMENT
The author thanks R. Charlesworth, B. Willianls for experimental assistance, R. Forster for advice on statistical matters, and S. Burrows and R. Deed for criticizing the manuscript. LITERATURE CITED
(1) Baragwanath, G. E., Proc. Australian Inst. Mining and Metallurgy NO. 202, (1962). (2) Bernstein, F., “Advances in X-Ray Analysis,” Vol. 5, Plenum Press, New York, 1962.
(3) Ibid., Vol. 6, Plenum Press, New York, 1963. (4) British Standards Institution. B.S. 1016. ~ .Part ~6 (1958). . (5) Ibih., Part 8 (1959). (6) Ibid., Part 14 (1963). (7) Ibid., Part 16 (1961). I
,
\ - - - - ,
(8) Claisse, F., Samson, C., “Advances in X-Rav Analvsis.” Yol. 5. Plenum Press. Xiw Yo&. 1962. (9) Duiie, R. A., Norrish, K., Sweatman,
T. R., C.S.I.R.O. Divn. Coal Res., Misc. Rept. 177 (1963). (10) Durie, R. A., Schafer, H. N. S., Swaine, 1). J., C.S.I.R.O. Divn. Coal Res., Misc. Rept. 178 (1963).
(ll).Liebhafsky, H. A., Pfeiffer, H. G., Winslow, E. H., Zemany, P. D., “X-Kay Absorption and Emission in Analytical Chemistry,” 1st ed. pp. 167-8, Wiley, New York, 1960. (12) Ibid., pp. 153-8. (13) Muller, R., Spectrochim. Acta 2 0 , 143 (1964). (14) Nalimov, V. V., “The Application of
Mathematical Statistics to Chemical Analysis,” 1st ed., p. 195, Pergamon Press, London, England, 1963.
(15) Ibid., p. 24.
RECEIVEDfor review June 6, 1966. Accepted July 28, 1966. The work described above is part of the program of brown coal investigation of the Scientific Investigations Branch of the State Electricity Commission of Victoria.
Correction Qualitative An a lysis Petroleum and Related Materials Using Linear Elution Adsorption Chromatography I n this article by L. R. Snyder [ANAL.CHEM.38, 1319 (1966)l on page 1320, column 1, the quantities €1 (0.1) and (0.9) are incorrectly defined. The correct definitions are as follows: ~i(O.1) =
€1
+ [logio (Ro,i/_R0)I/0.64 A*
and ~i(O.9)=
€1
+ [logio (Ro.9I_RO)l/0.64A*
VOL. 38, NO. 12, NOVEMBER 1966
1735
