even a t a single thickness. However, this in the method may be useful in other systems, and it does offer a rapid method of obtaining results ranging from semiquantitative to quantitative for a wide range of element concentrxtions. LITERATURE CITED
( 1 ) Adler, I., Axelrod, J. M., Spectrochim.
Acla7,91(1955).
(2) Beattie, H. J., Brissie, R. M., ANAL. CHEM.26, 980 (1054).
(11) Pfeiffer, H. G., Zemany, P. D., . v ~ J ( ( 3 ) Birks, L.S., Brooks, E. J., Friedman, H., Zbid., 25, 692 (1953). t w e 174,397 (1954). (4) Claisse, F., Norelco Reptr. 3, 3 (1957). (12) Rhodin, T. N., ANAL.CHEM.27, (5) Cullity, B, D,, "Elements of x : R ~ ~ 1857 (1955). Diffraction," Addison-Wesley Publishing Co., Reading, Mass., 1956. (6) G'Jnn, E. L.1 A N A L . CHEM. 29, 184 ( 1957). RECEIVED for review October 22, 1958. ( 7 ) .Kaufman, H. S., private communicaAccepted August 7, 1959. Division of tion. Analytical Chemistry, 132nd Meeting, (8) Kohl P. K., Caugherty, B., J . Appl. ACS, New York, N . Y., September 1957 Phys. 23, 427 (1952). Taken from a thesis submitted by E . J. (9) Kokotailo, G . T., Damon, G. F., Felten to the Polytechnic Institute of ANAL.CHEM.2 5 , 1185 (1953). Brooklyn in partial fulfillment of the (10) Parrish, W., Philips Tech. Rev. 17, requirements for the degree of doctor of 269 (1956). philosophy in chemistry in June 1958.
Precision in X-Ray Emission Spectrography Background Present PAUL
D. ZEMANY,
HEINZ G. PFEIFFER, and HERMAN A. LIEBHAFSKY
General Electric Co., Schenectady,
N. Y,
Considerations stemming from the probability theory and from the theory of errors determine the best precision attainable in x-ray emission spectrography under realizable operating conditions, even when the background is significant. This statement is supported by 90 res,ilts for a spot containing less than 2 X lo-' gram of zinc and by 216 results for another containing 4 X lop5 gram of strontium.
V% for N e . According to the rule for the error of a difference, the counting error for N T - N g is: ~-
SC =
d.TT
f
.vg
(2)
The complexity of sc increases with the number of quantities counted to establish it. One objective of this investigation is to see whether s = sc
(3)
the units being identical for both.
P
( 2 ) has shown that x-ray emission spectrography under ideal operating conditions and with background nrgligible is a random process, simibr in this respect to radioactive decay. Undw such conditions, the individual counts N , . . . N , lie upon the unique Gaussian distribulion of mean and standard deviation sc = V% The present investigation deals with the practically more important case in which the background N e is not negligiblc and mav be comparable with the total count N T mqde a t the goniometer position corresponding to the peak of the chararteristic line being used 2,s the analytical line. Samples for the experiments were standard spots (3) of zinc and strontium on filter paper. For these samples, the amount of elemcnt E present may be assumed proportion21 to N T - N e . If n detcrminations of E give the results el?-", the standard deviation is. RPVIOUS WORK
N
The counting error, due to statistical fluctuations only, is for N T and
4%
1776
ANALYTICAL CHEMISTRY
Another objective is to see \\hether
N r - N e is distributed according to the
unique Gaussian for which the standprd deviation is sc. Achievement of either objective indicatcs that precision in x-ray emission spectrography as actunlly practiced can be calculatcd satisfactorily from counting data. Establishment of distribution is the niorr conclusive and time-consuming test. EXPERIMENTS WITH ZINC, 1954
Instrumental Details. The tungsten-target tube was operated a t 50 kv. and 50 ma. A crystal of lithium fluoride was used. The detector was an argon-filled Geiger counter. The analytical line was zinc K , a t 28 = 41.77', with a n auxiliary setting for background determination a t 39.80'. Formation and Counting of Zinc Spot. About 0.02 ml. of aqueous zinc nitrate (zinc content near 10 y per ml.) was evaporated upon a 1.25-cm. square of Whatman No. 1 filter paper supported in the sample holder of the x-ray siectrograph upon a strip of Mylar, 0.001 cm. thick and 0.6 cm. wide. Ninety values of NT a t 28 = 41.77' and 90 values of N e a t 28 = 39.80' were obtained for this spot, each N r alternating
with an ATB. Counts obtained o v w longer periods on other samplw showed that no significant error due to resetting the goniometcr was present. The true zinc content of the spot and the background adjustmrnt factor wercb determined by extended counting to a precision much greater than that of an!. individual difference N T - N e . Determination of Ne. A filter paper was treated as in the formation of the zinc spot, but with the zinc, omitted. The following data wcrc, obtained . times for 16,384 counts, 1366.99 seconds a t 39.80" and 1159.72 seconds a t 41.77". For the individual determinations, N e was estimated h!. multiplying a count made a t 39.80' on the zinc spot by the br.ckground correction factor 1366.99/1159.72, or 1.179. Counting Rate for Zinc. Spots containing large amounts of zinc (-1 containing 4.0 y each, and 4 more containing 8 y each) were prepared and counted as described above. These were averaged to give the true counting rate for zinc. The result is:
Rzn = 16.0 counts per second per
7
(4J
Zinc Content of Spot. The fol1on.ing data give the zinc content of thc spot. Time for .VT = 16,384 counts at 4 1 . i i 0 , 970.33 seconds. From preceding data, N E for this intervd is 13,829. Zinr content of spot: t)Iz,, = (16,384 - 13,829)/ (970.33 X 16.0) = 0.165 7 ( 5 1 Individual Experiments. A counting interval, At, of approximately 40 seconds was selected for the individual experiments. On the zinc snot, counts a t 39.80" were alternated with counts a t
41.77" until data for BO individual determinations were at hand. The counts a t 39.80" are the N's of Table I. Individual values of Ne wrre obt:iined h!. multiplying these N's by 1.179. Results. BACKGROUND. Thcs i i i i l i vidual valurs of AI should lie up011 the Gaussian for which sc = and s should approxirnatrly equal Sc (Equ:ition 3) ( 1 ) . The data in Table I shot\ that both expectations are realized. ZINC DKTERMINATIONS. The individual valucs of N g were estimatcd b!multiplying thr N ' s in Table I by l . l i 9 . Ninety v:ilurs of N T - Il'g w r e t h m obtaincd by subtracting each N,, front the NT preccding it. From thrscb differcnccs, individu:i.l v:tlurs of m z , , could h a w bwn cdcu1atc.d according to Equation 5 , but this ivzs unnrccwir). for the statistic:il treatrnmt. \vhic*li follows the pattrrn of Table I. From thc 90 individual v a l u i ~ of ~ N T - N e , thc folhving data werv cal____ culatcd: nirnn, N T - A'g, 118.2 couiit3; sc = d R T = 35 Coutlts; 8 (Equation 1 ) = 39 rounts; r m g r of N T - - N o , 36 to 204 counts. The zinc rontcmt of thc spot ~ Y W - -~ responcling to N T - h g is:
dz,
COUNTS
Figure 1. Theoretical frequency distributions of results from repetitive counting experiments with appreciable background Numbers have been arbitrarily chosen for purposes of illustration
N,- F,
z
+
iTiz,, = 118.2/(40 X 16.0) =
W c* Y
1
3s,---?s,--*'
I
VALUES OF NT-NH F R O M INDIVIDUAL EXPERIMENTS ON Z I N C SPOT'
Figure 2. Comparison of distribution of experimental results from analysis of a zinc spot with distribution predicted from theory Note effect of simple background correction on standard counting error
5or-NORMAL
CURVE
ks a0
U.195 ,. I l i ~
The agrcwiicmt brtwcm I'qu:itioiih 5 and 6 is satisfactory. Thc >ni:ill(xst valuc. of A'T - h l g \\auld h:i\.ia gi\.c>ii mzn :IS about 0.06 7 ,whic*h slioi\- tlii. nced for a statisticnl :!ppr dctrrrninations by x-r:ty ( \ trography. Thc data arr nlso >:itisfactory in that Equr,tion 3 is s:iti-ficxil. T o trst thc distribution of thi, (1:it:i. Figure 1 sholvs thc id(dizvd ilistri1)iitions to br rxpcctrd from statisti(8:iI considerations. A c.oinp:trism wit11 Figure 2, in ivhich thr intlividu:rl N T - N B valuw h:iw bccn plottchtl around the C:tussi:ln for \ v h i i . l i N T - n l g = 118.2 find sr = 3.5; slinivq that thr agrccmcmt is srtisf:i.ctorj.. The rcsults of the work on zini: coilform to cxpcictations hrscd on statistical considwations and tho tlirorv of rrroi'>. I t \v,os possible to maintain satinf:ic*tor!operating conditions in thc x-r:i!- s p w trograph sjxtrrn ovvr tho timcb r w ~ i i i r ~ ~ ( I for all th(5 tl(.tcmiinntions. EXPERIMENTS W I T H STRONTIUM
J
216 DETERMINATIONS OF STRONTIUM
Figure 3. Comparison of distribution of experimental results from analysis of a strontium spot with distribution predicted from theory Note effect of complex background correction on standard counting error a n d compare with Figure 2
'The i~sperimcnts with stiuntiuiii (1957) w r r mor(, eutmsivc, than thosib with zinc and diKcwd from thml i i i O I I ( ' importmt rcspcct. In thc strontium work, all the data. ncrdcd to rstal)lisli NT and N e were obtaincld in c : d i iiitlividual cxperimcnt. Ecch such ( y w r i ment thus constitutrd a solf-coiit:iiiicd determination of the elemrnt E in R spot. The strontium work is not given in detail because it closely r r s c n i t h that of zinc. VOL 31, NO. 1 1 , NOVEMBER 1 9 5 9
1777
Table 1. =
478.4-,
Statistical Analysis of sc =
90 Values of N
dz = 22, s = 26 (Equation 1).
from Filter Paper
Range of A', 418-530.
Below Distribution 413 413-434 435-456 457-478 479-500 Interval Frequency found None 3 14 27 27 Frcquency expected* None 2 13 30 30 Units for all data are counts. .i\ccortiing to Gaussian distribution for total population (area under curve) of 90.
l'hc strontium spot contained about 40 y of the element. To ensure large fluctuations in I\'T - NE, N B \vas deliberately increased by placing thc filter pslpcr to bc counted over an aluminum block; scattering of x-rays by the aluniinuni cnh:mces the background. T\vo standard smiple holders w r c used in thew esperiments. One rontained an aluniinuni block ovrr which was stretched the filter p q w r carrying the sample strontium spot. The other, a blank, contained a filter paper similarly treatctl but. with strontium omitted. The goniometer settings were: for the nnalyticnl line, strontium K m , 24.15"; auxilinr\. setting for the drtermination of Imkground, 25.15" (3). Four kinds of counts :ire nwded for a stblf-contained t~xprriment, three to establish N B (one a t ( w l i angle on the blank and one a t 25.15" on the sample) and onr on the sample at 24.15" to establish X T . Therefore, each experiment consists of counting the blank a t two angles, changing sample holders, and count,ing the sample a t the same two angles. The standard counting error sc will be more complex hcre than in Equation 2.
The estimated background is given by : LVB=
h'2j
Iso
(sample) x
iV?4i s o (blank)/N2s,l,o(blank) ( i )
As Ne is f0rmt.d by taking a product and a quotient, the expression given by thr law of combining errors for the standard counting error of N T - N B is cumbersome. For present purposes, the approximation suffices. So long as the three Fs on the right-hand side of Equation 7 are about equal, Equation 8 can be used with confidence. Equation 8 shows how the standard counting error increases with the number of kinds of counts needed to establish N T - N g , a point sometimes overlooked. I n all, 216 self-contained determidations, each requiring the four kinds of counts, were made. The following data were calculated from the individual results. mean, N T - N E , 696.9 counts; si (Equation 8), 270.4 counts; s (Equation l ) , 274.3 counts; range of NT N e , -5 to 1505 counts.
501 -592 15 13
523-544 4 2
Above 544 None None
The experimcmtzl results are to be tested for agreement between sk and s, which is satisfactory, and for distribution upon the Gaussian nith mean N T - N B and standard deviation sk; Figure 3 shows that the distribution is also satisfactory. CONCLUSION
The prrscnt investigation shows that precision is predictable and controllable in x-ray emission spectrography under satisfactory operating conditions even when the background is a significant factor. As a result, confidence in the method should increase, and its advantages for trace determinations under $iniple conditions should bccome increasingly apparent. LITERATURE CITED
Fagel, J. E., Jr., Liebhafsky, H. A,, Zemany, P. I)., ~ ~ N A LCHEM. . 30, 1918 (1958). ( 2 ) Liebhafsky, H. A,, Pfeiffer, H. G . , Zemany, 1'. I)., Ibid., 27, 1257 (1955). ( 3 ) Pfeiffer, H. G., Zemany, P. I)., Nature 174,307 (1954). (1)
RECEIVEDfor review May 27, 1959. Accepted August 20, 1959.
Determination of Free Hydrofluoric Acid in Tanta Ium-Niobium-Hyd rof Iuoric Acid Solutions by Near-lnf rared Spectrophotometry W. J. ALLAN and A.
R. GAHLER
Technology Department, Union Carbide Metals Co., Division of Union Carbide Corp., Niagara Falls, N. Y.
b A method for the determination of the free hydrofluoric acid concentration in tantalum-niobium-hydrofluoric acid solutions measures the absorbance at 1835 mp in a thin cell with sapphire windows. An anomalous effect of cell size was observed. Interferences caused by other acids, ammonium ion, various inorganic compounds, and hexone were studied. 1778
ANALYTICAL CHEMISTRY
I
N THE processing of niobium and
tantalum ores by liquid extraction procedures, it is important to know the free hydrofluoric acid concentration in the aqueous phase (4, 6). Because these aqueous solutions contain complex fluorides of tantalum and niobium, as well as silicon, iron, titanium, zirconium, and other metals in chemical equilibrium with hydrofluoric acid, the determina-
tion of free hydrofluoric acid is difficult. The problem is further complicated because the ionic species at various acid and metal concentrations have not been identified. Determination of free hydrofluoric acid by titration with sodium hydroxide disturbs the chemical equilibrium and gives erroneous results. Measurement of p H as a function of acidity, as proposed in the literature (a),
