I n the case of the derivative of 2methyl-1-butanethiol, a considerable discrepancy exists (20’). Since the melting point value obtained seems t o agree quite well with that of the isomeric 1-pentanethiol, it was thought that perhaps the Eastman sample was mislabeled. However, a mixed melting point determination of the derivative of 1-pentanethiol and the supposed 2methyl-1-butanethiol gave a substantial depression. Furthermore, a n intensive N M R study of the questionable derivative, the mercaptan from which it was prepared, and the sulfone of the derivative. established unequivocally its identity as the 2,4-dinitrophenyl thioether of 2-methyl-1-butanethiol. Diffraction Data. The diffraction data for all t h e derivatives of t h e mercaptans included in this study a r e given in Table 111. Many strong lines characteristic of t h e respective derivative were obtained in all samples, making qualitative identification quite simple. The unique character of the diffraction patterns of mercaptans which are quite similar in structure is demon-
strated by the spectrometer traces of the isomeric 1-pentanethiol and 2methyl-1-butanethiol derivatives, Figure 1. Disulfides. The 2,4-dinitrophenyl thioethers of representative aliphatic and aromatic disulfides have been prepared. Those chosen were the n-butyl disulfide and phenyl disulfide. They were prepared by the method described in t h e experimental section a n d gave derivatives which checked exactly with their respective thiol derivatives in regard to melting point and x-ray diffraction patterns. Therefore, the identification of disulfides may also be accomplished quite readily by this same procedure. ACKNOWLEDGMENT
The authors thank Robert Culmo for the elemental analyses and Harry Agahiginn and George Vickers for their NMR interpretations. LITERATURE CITED
(1) Brock, M. J., Hannum, M. J., ANAL.
CHEJI.27, 1374 (1955).
(2) Charles, R. G., Johnston, ‘8. D., Ibid.,
29, 1145 (1957).
(3) Cheronis, K. D., Entrikin, J. B.,
“Semimicro Qualitative Organic Analysis,” p. 321, Crowell, Kew York, 1947. (4) Ibid., p. 441. ( 5 ) Clark, G. L., Kaye, W.I., Parks, T. D., ANAL.CHEW18,310 (1946). (6) DeLange, J. J., Houtman, J. P. W., X e c . trav. c h i m . 65, 891 (1946). (7) Garska, K. J., Douthit, R. C., Yarbroueh. V. A s AXAL. CHEX 33,. 392,. (196ij.’ (8) Gordon, B. E., Vopat, F., Jr., Burnham, H. D., Jones, L. C., Jr., Ibid., 23, 1754 (1951). (9) Gould, C. IT,,Gross, S. T., I b i d . , 25, 749 (1953). (10) Hofer. L. J. E.. Peebles. TI-. C . , I b i d . , 27, 1852’(1955). ’ (11) McKinley, J. B., Kckels, J. E., Sidhu, S. S., IND.ENG.CHEM.,ANAL. ED. 16,301(1944). (12) .Matthews, F. W., hlichell, J. H., Ibzd., 18, 662 (1946). (13) Rose, H. A4.JVan Camp, A. J., A N A L . CHEM. 28, 1430 (1956). (14) Stahl, C. R., Siggia, S., Ibid., 29, 154-5 (1957). (15) Warren, G. G., hlatthews, F. IT7., I b i d . , 26, 1986 (1954). (16) Wurtz, D. H., Sharpless, K. E., Zbid., 21, 1446 (1949). RECEIVEDfor revie-, October 11, 1961. Accepted December 13, 1961. ~
Precision in X-Ray Spectrochemical Analysis Fixed-Time vs. Fixed-Count L. S. BIRKS and D. M. BROWN
U. S.
Naval Research laboratory, Washington 25,
A comparison of the statistics for fixed-time and fixed-count rneasurernents o f line minus background in x-ray spectrochemical analysis shows that the relative standard deviation for fixed-time operation i s never greater than 1.1 times that for fixedcount operation. Therefore, the more convenient fixed-time mode of operation is recommended for all measurements.
P
in x-ray spectrochemical analysis depends on both the linepeak intensity, I L , and on the background intensity, I B , where IL and I B are in arbitrary units such as counts per second or counts per minute. Mack and Spielberg (3) showed equations for the optimum division of counting time for the peak and background positions in order to obtain maximum precision in the peak minus background, ILl e , measurement. For routine analysis, it is not convenient to make the necessary calculations for each line in the spectrum and even less convenient to readjust the counting time for each RECISION
240
ANALYTICAL CHEMISTRY
D. C.
measurement. Thus, the only commonly used modes of operation are fixed-time and fixed-count. I n fixedtime operation, the number of counts, iYL, collected a t the line peak is larger than the number of counts, N B , collected at the background position. I n fixed-count operation, the number of background counts, N E ‘ , is arbitrarily made equal to the peak counts, NL‘, by extending the measurement time a t the background position. It is well recognized that precision of the ILIo value is better for fixed-count operation. The question that has not been answered heretofore in a simple fashion is: “Just how much better is the precision for fixed-count operation and how does i t depend on the relative intensity of the background?” To answer the question, one must consider the relative standard deviations for the fixed-time and fixed-count modes of operation. CALCULATIONS
be the standard deviaLet U L and tions of measurements a t the line peak
and a t the background position, respectively. The standard deviation of the peak minus background value is obtained by the usual rule for adding variance U,?,
-E
=
(UL2
+
UB’)’
*
The relative standard deviation is U L -E%
100 ( U L *
+
UB’)’
‘/(IL - I B )
(I)
So far this is completely general and holds for any distribution of counting time. The difference in the results for fixed-time and fixed-count operation will depend on changes in U L or U B values. Some relationships may be expressed that will simplify the evaluation. First, in order to normalize the comparison, N L should be made equal to NL‘ by choosing the proper counting interval. If this is not done, then either fixed-time or fixed-count operation can be more precise dependent only on the particular value of N L or NL’ for each individual measurement. Sec-
1.10
T
1.08
-L
cJL=
1,/rJy2 1.06
1.04
1.02
1.00
0.2
0
ondly. by the definition of fixed-count,
Using Equation 3,
( U L -B%)F.T.
Third, let .c represent the background/ line-peak intensity ratio, IB/IL
=
IB2
x21L2 and
=
1 0 0 1 ~ N ~ - ”( *1
+ z ) ” ~ / ( I L- I B )
(9)
Fixed-count : (3)
= NB/LvL
U L and U B are standard deviations rather than relative standard deviations, and UL
= uL%IL;
UB
=
U
B
~
~
B
Fised-time:
Fixed-count: Substituting
NL’
=
NL=
NB’ UL
= IL/NL“~
(6)
Figure 1 shows the values of U L and U B for the two modes of operation. U B for fixed-count is smaller than for fixed-time because the denominator is N L instead of NB. Substituting the values for uL and U B into Equation 1, we obtain Fixed-time : ( U L -B%)F
T
oa
I.o
Figure 2. Ratio of relative standard deviations for fixed-time and fixed-count vs. relative background intensity
N B = X ~ V Equation L, 8 simplifies to
=
0.6
Fixed Count
F i x e d Time
Figure 1. Relative standard deviations for line and background intensities
x
0.4
= 100(IL2/NL
+
IB~/-VB)’/’/(IL - IB)
(8)
Figure 2 s h o w a plot of U J U , for the full range of I B / I L from zero to unity. The fixed-time mode of operation is always nearly as good as the fixed-count mode, the maximum value of the ratio being less than 1.1 a t I B / I L = 0.4. This means that for fixedtime, the precision is always within 10% of that for fixed-count.
CONCLUSION
Again substituting IB‘ tion 10 becomes
=
x 2 I L ~Equa,
What is the ratio of precision for fixedtime-fixed-count? For simplicity, write uf for (UL-B%)F.T. and u,for ( U L - B % ) F . C . The desired ratio is Equation 9/Equation 11, or Uf/UC
= (1
+ s)”2/(1 +
Z2)”Z
(12)
Equation 12 has the interesting property that the number of counts drops out entirely leaving the background/ line ratio as the only parameter. Therefore, it is completely general for comparing fixed-time and fixed-count measurements a t any counting rate or time provided only that the data are normalized by making N L = NL’.
Fixed-time operation in x-ray spectrochemical analysis is much faster than fixed-count operation because N B is not required to be as large as N L . Since the relative standard deviation for fixed-time operation is never greater than 1.1 times that for fixed-count operation, fixed-time operation is recommended for all routine analysis.
REFERENCES
(1) Birks, L. S., “X-ray Spectrochemical Analysis,” p. 53, Interscience, New York, 1959. (2) Liebhafsky, H. A., Pfeiffer, H. G., Winslow, E. H., Zemany, P. D., “X-ray
Absorption and Emission in Analytical Chemistry,” p. 278, Wiley, New York,
1960. (3) Mack, hl., Spielberg, N., Spectrochim. Acta 12, 169 (1958).
RECEIVED for review October 6, 1961. Accepted November 30, 1961.
VOL 34, NO. 2, FEBRUARY 1962
241
