Determination of Impurities in Silicon by Neutron Activation Analysis ARTHUR KANT', J. PAUL CALI, and HARRIET D. THOMPSON Air Research and Development Command, Air Force Cambridge Research Center, Bedford, Mass.
A method of determining trace elements in silicon in the concentration range of lo-* to p.p.m. by neutron activation analysis involves radiochemical separations, and the characterization and determination of the elements by their induced beta activities. The elements determined are: phosphorus, iron, copper, zinc, gallium, arsenic, silver, cadmium, indium, antimony, thallium, and bismuth. The method of treating phosphorus presents a special problem, because phosphorus-31 is formed in the neutron activation process.
T
HE development of silicon transistors is largely dependent on the production of ultra-high-purity silicon metal, because as little as 1012 to 1014 atoms of impurities per ce. can seriously affect transistor properties. For example, the resistivity of a bar of single-crystal silicon containing l O I 4 atoms of antimony per cc. is, a t room temperature, approximately 52 ohm-em. If the number of antimony atoms is increased to 5 X 10': the resistivity is decreased to 10.4 ohm-cm. Therefore, as little as 0.01 p.p,m. of donor- or acceptor-type impurity has a marked effect upon transistor properties. In like manner, other important electrical properties of transistors can be shonm to vary markedly n ith very small amounts of impurity atoms. In order to control the amounts of impurities in high-purity silicon, some means of control analysis must be available. In the concentrations xith which this discussion is concerned, spectroscopic or colorimetric analyses are too insensitive, because the limits of detection for these methods are usually of the order of 1 p.p.m. The neutron radioactivation method (11) is used in this laboratory for the determination of trace impurities in silicon metal. Other methods may be employed for the determination of the individual elements considered herein, which viould give a sensitivity as good as if not better than 1p.p.m. Hon-ever, it was the object of the authors to employ a single method which might be applied satisfactorily to a majority of the possible elements present in silicon. The neutron activation method was chosen for this reason. Historically, radioactivation n-as first used by Hevesy and Levi (8). The basic principles involved in this technique have been well set forth by Boyd ( 1 ) . hlany papers give general and specific information on the method (?, 3, 6-10]. Two methods of approach to the activation method are possible in determining the concentrations of the activated impurities in silicon. The first involves the techniques of gamma spectrometry and is well exemplified in the work of hlorrison and Cosgrove (16). This technique has the advantage of speed, especially because no radiochemical separations must be performed, but it is useless nhere the activated impurity is a beta emitter. Intrinsically the method is not so sensitive as the second technique, as the sensitivity of any activation technique is eventually limited by the background count of the detector. In gamma counting the background rate is 20 to 50 times that of a beta detector; the gamma spectrometric method, in general, i q therefore several times as insensitive as the beta method. Also contributing to the lesser sensitivity of the gamma spectrometric method is the fact that only 5 to 10% of the total available counting rate is recorded, as in this technique the usual procedure is to count on a specific gamma peak. 1
The second method of approach, the one utilized in this laboratory, involves the following steps: 1. Irradiation of silicon samples together with weighed amounts of the elements to be used as standards. 2. Dissolution of the irradiated sample together with microgram amounts of inactive isotopes of the elements to be determined and removal of silicon activity by fuming with nitrichydrofluoric acid mixture. 3. Separation of the activated impurities by radiochemical techniques. 4. Measurement of the beta intensity of the separated activated impurity element. 5. Verification of the measured isotope by half life and energy determination. The comparative method was used in determining the concentration of impurity elements. The silicon samples are placed in aluminum irradiation capsules together with small quartz needles containing weighed amounts of the oxides of the elements to be determined. The activity of the separated impurity element is compared to the activity of the standard and because the mass of the standard is known, the mass of the impurity element can be calculated. Utilizing this method, uncertainties in the values of the cross section, neutron flux, half life, and the detection coefficient of the counting setup are eliminated, as each parameter is identical in both the standard and the corresponding impurity element. EXPERIMEYTAL
Elements Determined. The following elements were chosen for determination: phosphorus, iron, copper, zinc, gallium, arsenic, silver, cadmium, indium, antimony, thallium, and bismuth. The Group I11 and T' elements are especially important, as they are added in known quantities to pure silicon metal, as either acceptor or donor elements, to produce transistor properties. Zinc is evpected to be present, as a present-day process involves the zinc reduction of silicon tetrachloride to produce silicon metal. The remainder are important, in that they markedly affect the lifetime of transistors. Nuclear Data. Samples of silicon were irradiated in the Brookhaven Sational Laboratory reactor. Khen a nucleus is subjected to a thermal neutron flus,the main nuclear process is the n, y reaction. The target nuclei bombarded, together n-ith the cross section for the n, */ reaction, the isotope produced, together with its half life, and the maximum energy of the emitted beta rays are given in Table I (10, 16). In addition to the activities listed, other radioisotopes of iron, copper, zinc, gallium, silver, cadmium, indium, antimony, and thallium are produced; however, they are eliminated from Consideration because of the shortness of the
Table I. Target Nucleus
Nuclear Data for Elements Determined
Cross Section, Barns 0.23 0.7 3.9 0.10 3.4 4.2 2.8 1.1
56
6.8 8.0 0.0017
Present address. Watertown Arsenal Laboratory, Watertown Mass.
1867
Fraction Isotopic Abundance 1.0 0,0033 0.69 0.187 0.398 1.0 0.487 0.288 0.042 0.572 0.295 1.0
Isotope formed by n,y
Ti/a 14.3d 47d 12.9h 14h 14h 27h 270d 2.3d 50d 2.8d 2.7y 5d
Max. Energy of B - , A1.e.v. 1 .7 0 . 2 6 : 0.46 0.57 0.90 0.14; 3.15 1 . 3 ;2 . 5 ; 3 . 1 0.09: 0.53 0 6; 1 . 1 2.05 1.4;1 . 9 0.71 1.17
ANALYTICAL CHEMISTRY
1868 half life or their very low cross sections or because they have other types of decay than beta decay. Samples. Gram quantities of silicon metal commercially available from E. I. du Pont de Nemours 8: Co., T\‘ilmington, Del., were used. The silicon is Du Pont’s densified material bearing the label “hyperpure silicon semiconductor grade.” Two different lots, both spectroscopically pure, were analyzed-A and B. The oxides of the elements to be determined in the silicon samples were encapsulated in small quartz needles. The silicon samples were irradiated so that the standards and sample were subjected to the same neutron flux. Irradiation Data. The samples and standards were irradiated for approximately 15 days in the Brookhaven Kational Laboratory reactor at a neutron flux of 3 X 10l2 neutrons per sq. cm. per second. The principal nuclear reaction occurring under the conditions of irradiation is the n, y reaction. I t is important to consider the n, y reaction occurring with the overwhelming number of silicon atoms, as compared to the n, y reaction on the smaller numbers of impurity atoms. The following occurs:
n,Y
Si30 -+ Si31
8-
P3l
2.6 hr.
(stable)
n,
-/ p31 -+
P-
p32 -+
S32
(4)
If this value of NIAl is substituted in Equation 2, the result is:
3 = No+ul(1 - e - h l t ) - N2+u2 dt
(5)
The solution of Equation 5 subject to the above stated conditions is :
R
where
=
NO+Ul.
By substituting this value of N Z in Equation 3 and solving, Equation 7 is obtained. NSA2 - = 1 - (1
R
-
+u&4
+ B)e-x21 - . # q X 2 A e - + ~ 2+~ Be-Ai1 (7)
where 1
1
and
The initial production of silicon activity in comparatively large amounts presents no serious problem: Its short half life causes the bulk of silicon-31 to decay to stable phosphorus before separation nork begins; and most of the silicon is lost by evolution as silicon tetrafluoride during dissolution with hydrofluoric acid. Furthermore, silicon-31 activity is very effectively removed in the radio-chemical purification schemes. In the determination of phosphorus the above reaction must be considered, as can be seen if the entire reaction is written, starting with silicon-30:
n,Y PSi30 -+ Si31 -+. 2.6 hr
iCT1X1 = No+q(1 - e - h t )
(stable)
14.3 d
From the above, it is evident that there will be two sources of phosphorus-32 activity: any impurity phosphorus-31 originally present in the silicon, and the above reaction. It is, therefore, necessary to compute the amount of phosphorus-32 formed by this latter reaction. In order to obtain the amount of phosphorus-32 as a function of the number of atoms of silicon-30, the neutron flux, and the time of irradiation, it is necessary to solve the following set of equations:
where N o = number of atoms of silicon-30 initially present N 1 = number of atoms of silicon-31 formed by n , y on silicon-30 N 2 = number of atoms of phosphorus-31 formed by decay of silicon-31 N J = number of atoms formed by n , y on phosphorus-31 u1 = cross section for silicon-30 ( n , r ) silicon-31 reaction, sq. em. uz = cross section for phosphorus-31 (n,y ) phosphorus-32 reaction, sq. em. X1 = decay constant for silicon-31, see.-’ X2 = decay constant for phosphorus-32, see. -l + = thermal flux, neutrons per sq. em. per second t = time of irradiation, seconds The value sought is N&, which is the activity of phosphorus32. The initial conditions for the solutions of Equations 1, 2, and 3 are N1 = 0, N2 = 0, and N3 = 0 at t = 0 and the assumption that A’o is essentially constant. The solution of Equation 1 subject to the initial conditions is:
Equation 7 is the general solution for Equation 3. However, several conditions are present for this system which simplify Equation 7 : t
> 1- >> ‘5, and t >> 1
A1 XlAZ When simplified, Equation 7 reduces to:
+uz
A2
Activity of P32 = -V3A2
=
At’
(5)
AT0+u1
(Ad
+ e--X2t
- 1) (8)
For the irradiation time used, the contribution of phosphorus-31 from silicon-30 is negligible if the phosphorus is initially present to an extent greater than 0.1 p.p.m. For phosphorus concentrations less than 0.1 p.p.m. the phosphorus as formed from silicon30, according to Equation 8, must be subtracted from the total phosphorus-32 activity. In the latter case, the comparative method is not applicable, and absolute beta-counting techniques must be used. I n order to obtain the high sensitivity required, it is necessary to irradiate relatively large quantities of silicon. Because of the low neutron absorption cross section of silicon, it is possible to use relatively large amounts of silicon without appreciable neutron beam attenuation. Calculations indicate that as much as 10 grams of silicon Till cause an inappreciable beam attenuation throughout the sample (of the order of 1%). The amount of standard elements used was sufficiently small to cause no appreciable beam attenuation. In the case of indium, which has the largest neutron absorption cross section of any of the elements determined, the attenuation due to the indium standard is no more than 1%. Treatment of Silicon Sample after Irradiation. After irradiation, the silicon samples are removed from the irradiation capsule. A 1- to 2-gram piece of silicon metal is placed in a platinum dish and the surface is completely etched in nitric acid-hydrofluoric acid to remove any surface contaminants which might possibly have been present and would now be activated. In the submicro concentration regions the introduction of surface impurities is an obvious and important source of anomalous results. The above method of etching obviates this source of error and only bulk impurities are then determined. The sample is then transferred to another platinum dish and microgram amounts of carriers are added. Sample and carriers are then dissolved in a 50-50 mixture of concentrated nitric acidhydrofluoric acid, Repeated fumings with hydrofluoric acid are carried out until all visible traces of silicon are removed. The residue-i.e., carriers-is then dissolved in a suitable medium,
V O L U M E 28, NO. 12, D E C E M B E R 1 9 5 6 usually hydrochloric acid, and the resulting solution is made up to volume in a volumetric flask. The platinum crucible is monitored a t this point to make certain that all of the activities present are in solution and have been transferred. Suitable aliquots are then taken from the volumetric flask for the radiochemical separation and purification of the elements to be determined. It is a t this point that known amounts of stable isotopic carriers are added, usually of the order of 10 mg. per determination. In order to ensure the isotopic exchange of the carrier and the activity, the carrier is added in its highest oxidation state, since in general the activity will also be in this state (having been fumed with concentrated nitric acid in the dissolution process). The solution is then m r m e d and allowed to stand for a t least 15 minutes, Chemical Procedures. The radiochemical procedures described below were designed with the follom ing considerations. The procedure for each element must, in its entirety, be specific-that is, the final precipitate must be entirely free of all possible contaminating or interfering radioactive species. Because phosphorus-32 is formed from the irradiation of silicon-30, each radiochemical procedure must have a specific step for the removal of this interfering element. Each procedure must effectively remove silicon-31 activity. The procedures for gallium, copper, zinc, and arsenic must be fairly rapid, as these isotopes are relatively short-lived. The following references were found useful in the preparation of these procedures (12, 17-20, 2.2). GROUP SEPARATIONS
In order to simplify the radiochemical separations the following groupings were used: Group A. Group B. Group C. Group D. Group E.
Arsenic, Bismuth, and Gallium Indium, Thallium, and Antimony Silver, Cadmium, and Iron Zinc and Copper Phosphorus
The elements listed above are not separated as in a qualitative scheme. Rather, separations are made only within the groups. At no time is more than one group determined in a single aliquot of the solution to be analyzed. One aliquot is taken for the separation and determination of Group A, another aliquot for Group B, etc. All procedures start with the initial aliquot for that group. Group A Separation. Arsenic, bismuth, and gallium are separated as follows: the arsenic as arsenic trisulfide; the gallium by extraction with ether. The bismuth remains in the original solution. GALLIUM.The gallium is extracted from the ether with water, preci itated as the hydroxide, twice scavenged with arsenic trisulfiz and bismuth trisulfide, scavenged with barium carbonate and ferric hydroxide, again extracted with ether using phosphorus as a holdback carrier, re-extracted with water and precipitated as gallium hydroxyquinolate, washed, dried, weighed, and mounted for counting. ARSENIC. The arsenic trisulfide is dissolved in ammonia and scavenged with lanthanum hydroxide, precipitated as arsenic trisulfide using gallium, antimony, and phosphorus as holdback carriers dissolved, distilled as arsenic trichloride, reduced to the metal, dltered, washed. dried, weighed, and mounted for counting as arsenic metal. BISMUTH. The bismuth is precipitated several times as the hydroxide using arsenic, antimony, barium, strontium, and copper as holdback carriers, then precipitated as bismuth phosphate using arsenic, antimony, gallium, indium, and thallium as holdback carriers. The bismuth is then precipitated as bismuth trisulfide using strontium, indium, gallium, barium, and yttrium as holdback carriers, and finally precipitated as bismuth metal, filtered, washed, dried, weighed and mounted for counting as the metal. Group B Separation. The thallium, indium, and antimony are separated as follows: the thallium as thallous iodide; the antimony as antimony trisulfide (at p H 1); the indium as indium trisulfide (at p H 3 to 4). THALLIUM. Thallium is extracted with isopropyl ether using phosphorus, bismuth, chromium, and yttrium as holdback carriers, scavenged with cupric sulfide, bismuth trisulfide, arsenic trisulfide, and antimony trisulfide, and scavenged with the
1869 hydroxides of indium, gallium, and iron The thallium is then precipitated as thallous iodide with indium, gallium, and molybdenum as holdback carriers, and finally precipitated, filtered, washed, dried, weighed, and mounted for counting as thallous chromate. INDIUM The indium solution is scavenged several times with arsenic trisulfide, cupric sulfide, bismuth trisulfide, and antimony trisulfide, precipitated several times as indium trisulfide, extracted by 8-hydroxyquinoline in chloroform, and re-extracted into hydrochloric acid by boiling off the chloroform. The indium is then precipitated, filtered, washed, dried, weighed, and mounted for counting as indium quinolinate. ANTIMONY.The antimony solution is scavenged with arsenic trisulfide, extracted with isopropyl ether, using phosphorus as 3 holdback carrier, extracted from the ether with 3N potassium hydroxide, and precipitated as antimony trisulfide. The antimony is distilled as antimony trichloride using tin as a holdback carrier, and finally precipitated, filtered, washed, dried, weighed. and mounted for counting as antimony metal. Group C Separation. The silver and cadmium are separated as follows: The silver is precipitated as silver chloride; the cadmium is precipitated as cadmium sulfide in 0.3N acid. Iron in the supernatant solution is precipitated as ferric hydroxide. SILVER. The silver is precipitated as silver chloride using phosphorus as a holdback carrier, scavenged with ferric hydroxide, precipitated, filtered, washed, dried, weighed, and mounted for counting as silver iodate. CADwchf. The cadmium is precipitated twice as cadmium sulfide, using phosphorus as a holdback carrier, scavenged with palladium sulfide, precipitated as cadmium sulfide, and twice scavenged with ferric hydroxide. The cadmium is finally precipitated, filtered, washed, dried, weighed, and mounted for counting as cadmium ammonium phosphate. IRON.Ferric hydroxide is precipitated, washed, and dissolved in hydrochloric acid, and ferrous sulfide is precipitated in the presence of phosphorus as a holdback. The iron is extracted with ether; ferric hydroxide is reprecipitated and ignited to the oxide, then filtered, dried, weighed, and mounted for counting. Group D Separation. The copper and zinc are separated a3 follows: the copper as cupric sulfide in 1N hydrochloric acid; the zinc as zinc sulfide at p H 7 . COPPER. The copper solution is scavenged twice with ferric phosphate and ferric hydroxide, precipitated as cuprous thiocyanate, reprecipitated as copper a-benzoinoxime, and finally precipitated, filtered, washed, dried, weighed, and mounted for counting as cuprous thiocyanate. ZINC. The zinc is precipitated twice as zinc mercury thiocyanate, using phosphorus as a holdback carrier and oxalic acid as a complexing agent. The solution is scavenged with the excess mercury as mercuric sulfide; the zinc is precipitated as zinc sulfide, dissolved, scavenged twice with ferric hydroxide, and finally precipitated, washed, dried, weighed, and mounted for counting as zinc mercury thiocyanate. Group E Separation. PHOSPHORUS. Yttrium, arsenic, and copper carriers are added to the phosphorus solution and arsenic and copper are precipitated with hydrogen sulfide. Magnesium ammonium phosphate is then precipitated, washed, dissolved in hydrochloric acid, and scavenged with arsenic, antimony, copper, and palladium, and magnesium ammonium phosphate is reprecipitated. This precipitate is dissolved and scavenged with lanthanum oxalate. Finally, magnesium ammonium phosphate is precipitated, washed, dried, weighed, mounted, and counted. The standards are dissolved in suitable solvents and made to volume, and suitable aliquots are taken for determination of their radioactive content. In general, no radiochemical purification procedure is necessary. The standards are precipitated for mounting, using the same final precipitate as the unknown, and then the two are counted consecutively. Instrumentation. The samples and standards are filtered on 1-inch circles of No. 42 Whatman paper. The paper containing the precipitate is placed on an aluminum planchet of the same diameter and approximately 3/8 inch thick. A thin sheet of rubber hydrochloride (0.7 mg. per sq. cm.) is placed over the filter paper and an outer aluminum retaining ring is forced over the entire assembly. The sample is now ready for counting The samples and standards are counted using Tracerlab’s auto-
ANALYTICAL CHEMISTRY
1870 matic sample changer (SC-6-4) and TGC-2 Geiger tube (window 1.7 mg. per sq. cm.), and a Tracerlab SC-51 Autoscaler is used to record the counting rate. The time required for a predetermined number of counts is recorded on Tracerlab's Tracergraph
sc-5D.
Counting rates are corrected for background and coincidence loss. In addition, a normalizing factor is used which corrects for variations in the day to day operation of the setup. Atomic Instrument hlultiscaler Model 1070 operated in conjunction with Tracerlab's shielded manual sample changer and a TGC-2 Geiger tube is used to determine the maximum beta energy. For this determination the Feather analysis is utilized (5).
A
second
N = number of atoms of target nucleus 6 = thermal neutron flux, neutrons per sq. cm. per second u =
activation capture cross section, sq. cm.
X = decay constant of isotope formed, set.-'.
t = time of irradiation, seconds The minimum detectable activity is taken as 1 disintegration per second.
RESULTS AND DISCUSSION
Table I1 gives the results of the activation analysis on silicon samples A and B.
Table 11. Results of Activation Analysis on Silicon 31easured T I I S Bnalysis, P.P.M. Isotope
P
Fe cu Zn Ga As AP Cd In Ob
Measured Pa2
Sample .4 14d
NSA 26 hr.
Sample
B
14d Long 12 5 hr. 14 6 hr.
SSA 27 hr. Long
Sample A 0 01
(9)
.4 = disintegration rate of isotope formed, disintegrations per
RESULTS OF ANALYSES
Element Determined
= No$(l - ,-At)
where
Sample
B
0 01 and 0 02
0.0001~ 0.00005
KS.4
NSA NS.4 0.00030 2.8d 0.0001 2 Pd TI N S .4 SSA 0,oo:. KS.4 KSA 0.01 Bi A blank indicates no analysis. NSA. Not sufficient activity detected t o be able t o characterize half life. Where two results are given, two separate analyses were performed. 0 No activity found (see discussion of results). Background of detector was 20 counts per minute.
Discussion of Results. Spectrographic analyses of both lots detected no impurities whatsoever. This is in agreement with the activation analysis, as the impurities found by the latter method are in every case well below the limit of sensitivity for the spectrographic method. I n the determination of arsenic, phosphorus, and copper in sample B two results are given; t n o different chunks of silicon metal from the same lot number were analyzed. The differences are real and must be attributed to a certain degree of nonhomogeneity within the lot. In the measurements of the half lives of the various isotopes, KSA (not sufficient activity) indicates that the activity for these samples was well below the background activity of the detector. The statistical variations in such cases preclude a determination of the half life with any degree of certainty. However, the half life found even in these cases was of the right order of magnitude. One of the criteria for determining the purity of the final separated isotope was to have been the measurement of the mayimum beta energy. Unfortunately, in order to accomplish this by nieans of a Feather analysis, several hundred counts per minute of activity v-ere required. In only two cases x-as sufficient activity present for an energy determination. In sample B sufficient copper activity rras found, and a Feather analysis gave an indicated maximum beta energy of 0.60 m.e.v. as against a reported (10, 16) energy of 0.57 m.e.v. Similarly for phosphorus, the measured beta energy was 1.8 m.e.v. as against a reported (10, 16) energy of 1.71 m.e.v. The Feather method is usually considered accurate n ithin about 10% for uncomplicated cases. TT7hereno activity --as found, the minimum amount detectable is reported in Table 11. This represents the maximum amount of impurity that could possibly be present. The value is obtained from the equation:
Discussion of Errors. The precision and accuracy of the activation method of analysis in the range from 1000 to 0.1 p.p,m. of trace impurities have been well established (IS,14). Duplicate determinations of indium in silicon dioxide were done comparing the activation method with the spectrographic method (Table 111). Many of the errors involved in this method have been evaluated, and several of the possible sources of errors are discussed below. 1. ERRORDUE T O ISCOAIPLETE EXCHANGE OF ACTIVATED ISOTOPIC CARRIER. Many references ISOTOPE A X D INACTIVE (4, 21) show the steps that must be taken to obviate any difficulty on this account. The main source of error here exists nhen the carrier and the active species esist or can exist in different valence Etates. In every case where this could occur the chemistry I S so designed that the carrier and active isotope are swept through all the oxidation states possible. 2. ERROR EXISTING BY Loss OF ACTIVITY DURISG DISSOLVTION. In the procedures described, the sample is dissolved i n concentrated nitric acid-hydrofluoric acid in the presence of microgram amounts of carriers. The possibility of loss of activity during dissolution, either by the volatility of certain fluorides or through some other mechanism, exists. An experiment was designed and performed to evaluate this loss. A small piece of silicon to which was added a known amount of arsenic earlier was dissolved in the manner described in the dissolution procedure. After being treated several times n-ith hydrofluoric acid, the residue was dissolved in concentrated hydrochloric acid and arsenic trisulfide precipitated. The loss of arsenic by the volatility of the fluorides was negligible. As arsenic trifluoride is the most volatile of any of the fluorides of the elements determined, it seems safe to assume that none of the other fluorides will be lost through volatility at this point in the procedure.
Comparison of Spectrographic and .\ctivation Determination of Indium in Silicon Sample Theoretica1.a Spectrographic, Activation, P.P.M. P.P.M. KO, P.P.M. 1 1640 1640 I160 1565 i 157 2 164 164 +, 16 147 zk 15 3 16 Faint line 15 + 2 4 1.6 Xot detected 3 . 9 i~ 0 . 4 * a Prepared by doping silicon dioxide r i t h weighed amounts of indium oxide. * Value high by approximately 2 p.p.m., indicating indium impurity background in silicon dioxide base material of about this amount. Table 111.
3. ERRORS OF REPRODUCIBILITY. In order to determine this error, a sample of silicon containing an unknown amount of phosphorus was irradiated as described above and siu determinations of the activated phosphorus were performed (Table IV). 4. ERRORFRORI CONTAVIN.4TISG -4CTIVITIES. The radiochemical procedures described herein are specific enough so that errors from this source are small. In substantiation of this state-
1871
V O L U M E 28, NO. 1 2 , D E C E M B E R 1 9 5 6 Table IV.
Reproducibility of Method for Phosphorus in Silicon Sample G. P/G. Si No. ( x 109 1 8 28 2 7 75 3 7 87 7 so 7 72 7 93 7 89
4
5
6
.Iverage Standard erior 2 401,
laboratory in performing many of the radiochemical separations. The silicon samples described were analyzed by the spectrographic section of Metal Hydrides, Inc., Beverly, Mass , under AF contract A F 19(604)-1416. LITERATURE CITED
(1) (2) (3) (4) (5) (6) (7)
(8) merit the folloA ing evidence is cited. I n the determination of galiium, indium, thallium, and bismuth, no activity whatsoever Kas found in the final counting form (Table 11). This is prima facie evidence that in these cases a t least, no contaminating activity could have been present. I n the case of phosphorus, iron, copper, zinc, silver, and antimony sufficient activity n-as found to be able to characterize the half life with a precision a t least within 10%. Errors from this source are considered to be no more than 10% (standard error). 5 . ERRORS RESULTING FROM STATISTICAL VARIATIONS IN THE PROCESS. The standard error of a disintegration rate is given by where N is the total number of events recorded. I n all cases a sufficient number of counts was taken to give a Standard error of no more than 10%. I n cases of high activity the standard error p a s approximately 1%. The over-all error of the method is estimated as approximately 50% for the absolute method and 10% for the comparative method.
a,
ACKNOWLEDGMENT
(9) (IO) (11)
(12) (13) (14) (15) (16) (17) (18)
(19) (20)
~
(21) (22)
The authors nish to express their thanks for the valuable assistance given by Lester F. Lon-e and Elinor hi. Reilly of this
Boyd, G. E., ANAL. CHEY.21, 335 (1949). Bron-n, H., Goldberg, E., Science 109, 347 (1949). Cohn, W.E., - 1 3 - 4 ~ .CHEX 20, 498 (1948). Friedlander, G., Kennedy, J. W., “Introduction t o Radiocheniistry,” Wiley, S e w York, 1949. Glendenin, L. E., Nucleonics 2 , 12 (1948). Goldberg, E. D., Brown, H., ANAL. CHEM.22, 308 (1950). Gordon, C. L., Ibid., 21, 96 (1949). Hevesy, G., Levi, H., Kgl. D a n s k e V i d e n s k a b . Selskab. Math.F y s . M e d d . 14, 5 (1936); 15, 11 (1938). Hudgens, J. E., Jr., Cali, J. P., . ~ N A L .CHEM.24, 171 (1952). Hughes, D. J., “Pile Seutron Research,” Addison-Werley Publishing Co., Cambridge, Nass., 1953. Kant, .irthur, Cali, J. P., Thompson, H. D., “Detailed Radiochemical Procedures for the Determination of Several Elements by Xeutron Activation Analysis,” Air Force Cambridge Research Center, Bedford, Mass. lleinke, W.W.,“Chemical Procedures Used in Bombardment Work at Berkeley,’’ U. S. -1tomic Energy Commission, Rept. AECD-2738 (19491. XIeinke, W.W:,Science 121, 177 (1955). Meinke, W.W., Anderson, R. E., AI^.*^. CHEX.25, 778 (1953). Morrison, G. H., Cosgrove, J. F., I b i d . , 27, 810 (1955). Satl. Bur. Standards Circ. 499 (September 1950). Soyes, A. X.,Bray, IT. C., “System of Qualitative Analysis for the Rare Elements.” AIacinillan. Kea York. 1948. Scott, W. W.,“Standard Methods of Chemical Analysis,” Van Sostrand, Kew York, 1939. Tobias, C. rl., Dunn, R. IT.,Science 109, 109 (1949). Vogel, rl., “Quantitative Inorganic ..inalysis,” Longmans, Green 6- Co.,-London, 1961. Wahl, A . C., Bonner, S . A,, “Radioactivity Applied to Chemistry,” lt‘iley, New York, 1961. Welcher, F. J., “Organic Analytical Reagents,” Van Nostrand. Sew York, 1947.
RECEIVED for review September 24, 195.5. Accepted October 2, 1956.
Amperometry with Two Platinum Electrodes with the Cu prous-Cu pric, Bromine-B romide System JAMES J. LINGANE and FRED C. ANSON Department of Chemistry, Harvard University, Cambridge 38, Mass.
The behavior of the indicator current observed with two polarized indicator electrodes during coulometric titration with bromine or cuprous copper in acidic cupric bromide solutions has been critically examined. The interpretation of the indicator current, and the relation between the observed minimum current and the equilibrium constant of the reaction 2Cu++ 7Br- = 2CuBri Bri, given by prebious authors has been shown to be inadequate. Correct relations for this system have been derived; these lead to an apparent equilibrium constant more nearly in accord with the value deduced from the observed formal potentials of the half-reactions involved. However, because the bromine-bromide couple does not behave with the thermodynamic reversibility demanded by the correct treatment, the apparent equilibrium constant from the amperometric measurements is considerably larger than the true value. Two-electrode amperometry, although very useful as an empirical means of end point detection in titrations, is not appealing as a technique for measuring equilibrium constan ts.
+
+
A
S ORIGINALLY demonstrated by Foulk and Bawden (6), the change in current between two platinum indicator electrodes subjected to a constant, small applied voltage can be used to recognize titration end points. During the past decade this technique has been applied very successfully (albeit empirically) for end point detection in divers types of coulometric titration, particularly by Swift and his collaborators. The principles and applications of the method are reviewed in the monographs of Lingane (9) and Delahay (3) and in articles by Duyckaerts (4), Bradbury (I), and Kolthoff (7). Our interest here is with the application of amperometry \\-ith two polarized platinum electrodes to end point detection in the particular case of coulometric titration with bromine and cuprous copper as dual intermediates, as originally used by Buck and Swift (3) for slom bromination reactions. The titration cell is essentially as indicated in Figure 1. The electrolyte contains relatively large concentrations of bromide ion and cupric ion, and is acidified with sulfuric acid. By appropriate selection of the polarity of the generator electrode in the test solution bromine can be generated via anodic oxidation of bromide ion, or cuprous copper (CuBrz-) can be generated by cathodic reduction of cupric ion. Starting Fith either excess bromine or excess cu-
