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JOU RNAL OF RESEARCH of the Notional Bureau of Standards - A. Physics and Chemistry Vol. 79A, No. 6, Novem ber- December 1975 Absolute Isotopic Abundance Ratios and the Atomic Weight of a Reference Sample of Silicon

I. L. Barnes, L. J. Moore, L. A. Machlan, T. J. Murphy, and W. R. Shields*

Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234

( August 27,1 975 )

Absolute values have been obtained for the isotopic a bundance ratios of a reference sample of silicon using e lectron impact spectrometry. Samples of known isoto pi c composit ion pre pared fro m nearly isotopically pure sepa rated sili con were used to calibrate the mass spectrometers. The result ing absolute ,sSi/,JOS i ratio= 29.74320± 0.00747 and the 29S i/,,°S i ratio= 1. 50598 ± 0.00086 whic h yield atom percents of '"Si = 92.229:n . 0.00155. "'Si =,1.()6982 I 0.00124 and :l IISi = :). 10085 I 0.00074. The atomic weight calc ulated from this isotopic composition is 28.085526 · 0.000056. The indi cated un certainties are overall limit s of error based on 95 percent confidence limit s for th e means and a ll owances for th e effects of kn own sources of possibl e s yste matic e rror. A study of natural '"Si/,IIIS i ratio variations reported in the literature extends tb e estimat ed uncert aint y in the atomic weight of natural sili con to ' 0.000.3 9.

Key words: Absolut e ratios; atomi c weight: isotopic abundance: sili con .

• Present aJdrt:ss: Teledyne Isutopcs. Ti monium. Maryland 2 1200.

1. Introduction as a candidate for the measurement of its unit cell dimension s, and atomic weight, with desired The Analytical Spectrometry Sect.ion of the National measurement uncertainties for each of these at the Bureau of Standards is conducting a long term program parts-per-million level or less. Since sili con in nature of absolute isotopic abundance ratios and atomic consists of a mixture of three stable and nonradioactive weight determinations using thermal ionization mass isotopes ("8S i, :!~ 'Si. :lOS i). the uncertainty of the relative spectrometry. Previous ele ments studied include proportions of these masses immediately became the [1] ,1 [2] , [3] , [4] , [5], limiting error in the precis e characterization of the [6], [7], r8], rubidium [9], silicon crys tal. rhenium [10], and [I1J. This present work As a secondary objective, the atomic weight of extends the study to silicon and demonstrates an ex­ silicon could also be combined with the param­ pansion of the technique to include impact eter measurements by the IBS to permit a new and mass spectrometry. direct redetermination of Avogadro's Constant [12]. Interest in the atomic weight of silicon was stimu­ Finally, also unanswered was the question of whether lated by the long-term project of the NBS Institute for the atomic weight of the silicon crystal had been dis­ Basic Standards to replace the kilogram as a standard torted during the zone purification process. of mass. Mass is the remaining triumvir of the m-k-s To achieve these objectives a project was begun to measurement system whose definition is expressed in determine the absolute silicon abundance terms of an artifact physical unit- the platinum-iridium ratios and, hence. the atomic weight of a reference I-kg mass that resides in Paris. The meter and second sample of silicon, with an intermediate goal of ~ 10 have been redefined as multiples of measurable natural parts- per-million (ppm) uncertainty in the atomic phenomena. weight. As a mil estone in achieving this goal, a high purity To obtain absolute isotopic ratios from the observed silicon crystal of high lattice perfection was selected or relative measurements made on a mass spectrometer it is necessary to calibrate the instrument using samples

I Fi gures in brackets indi cate the li terature references at the e nd of thi s paper. of accurately known isotopic ratios of the element 727 under study. These synthetic isotopic standards, pre­ The operating parameters of the source were as pared from chemically pure and very nearly isotopically follows: pure separated isotope. provide a bias or fractionation Electron energy 50 e V correction (calculated isotope ratio·observed isotope Accelerating potential 4780 V ratio) which when applied to the observed isotope ratio Emission current 85 /-LA of the reference sample being calibrated allow an Trap current 80 /-LA absolute ratio to be calculated for this sample. The Filament current 3.0 A atomic weight can then be calculated from the absolute isotopic abundances and the atomic masses reported The various samples of reference materials and of by Wapstra and Gove [13]. separated isotopes prepared as described below were Prior to 1948 the accepted atomic weight of silicon processed for analysis using essentially the system was 28.06 based on the work of Baxter et a!. [14] meas' described by Reynolds and Verhoogen [23] in which uring the ratios SiCL: 4 Ag and SiBr4: 4 Ag. Based on barium fluosilicate (BaSiF(;) was heated to produce the isotopic ratios measured by White and Cameron BaF 2 and gaseous SiF4 • The was [15] and others the value 28.086 ± 0.001 was accepted collected and introduced into the mass spectrometer [16] but the error limits were expanded to ~ 0.003 [17] to become the source of the SiF1 ions which were based on the report of lhe variations of silicon isotopes measured. by Allenby [18]. The vacuum system used for the preparation of the SiF4 was constructed of nickel and copper tubing instead of the system used by Reynolds and 2. Experimental Procedure Verhoogen since it was believed that the glass itself might be the source of small amounts of which 2.1. Mass Spectrometry might lead to the formation of SiF20 I . SiF~HO + and SiF~H~O ' ions as noted by them (see below). Isotope ratio measurements were made on a 60° The sample was placed in a 3/4·inch nickel tube extended fli ght path 15 cm (6 inch) mass spectrometer. approximately 30 cm long which was attached to a The mass spectrometer was equipped with a "2" vacuum line through a "" fitting with an alum· focusing thin lens source [19] (see below). The collector inum gasket. The vacuum line constructed of 5/s·inch was a deep bucket Faraday Cage type equipped with copper tubing contained a U·tube trap which was cooled a 50 percent transmission grid shadowing a series of with a mixture of dry ice- during processing electron suppression grids [20]. The measuring circuit of the sample. The silicon tetrafluoride gas was col· consisted of two state·of·the·art vibrating reed elec­ lected in a nickel sample tube cooled with liquid trometers with provisions for automatic range switch· . ing. The output of the measuring system was fed into In a typical sample preparation cycle a new sample both an expanded scale recorder [21] and a digital tube was placed on the vacuum system evacuated to a system consisting of a voltage to frequency converter pressure of < 10- 5 Pa (10 - 7 torr), the trap cooled, a and a precision scaler-timer. In general both systems tube furnace placed around the sample container and were used redundantly. The digital system and the the tube baked at a temperature of 700 °C for 1 hr. The range switching systems were under control. furnace was then turned off and the tube was allowed to Mass measurements were made by magnetic field cool to room temperature. The tube was removed from switching. The magnetic field was controlled and the system and 100 mg of the BaSiF» was added. The changed with the use of a gaussmeter·controller. Source tube was reattached to the system and evacuated with a and collector slits were arranged so that complete sample collecting tube attached to the system. When a resolution of each of the masses of interest was obtained. pressure of < 10- 5 Pa (10 - 7 torr) was reached the The electron impact source used was similar to the U·tube trap was cooled and liquid nitorgen placed on thermal emission source normally used in our labora­ the sample collecting tube. At this point the vacuum tory except that the shield was replaced with an elec· system was valved off, the furnace turned on and the tron impact section consisting of a filament, sample heated to 410 °C (± 5 °C measured with a cali­ impact chamber or "cage" and an electron trap. The brated chromel- thermocouple) at a rate of trap plate was provided with an external electrical approximately r /min. Previous experiments had circuit so that it could be continuously heated to about shown that at a temperature of 400 °C the sample had 300 °C which reduced the background to negligible completely decomposed and the SiF4 produced was levels. quantitatively removed and collected. This was sub­ The sample gas was admitted to the impact region stantially in agreement with the results of Reynolds and through a short section of Teflon 2 tubing from a leak Verhoogen. After a of 10 min at 410 °C the fur­ of the type described by Shields [22]. nace was turned off and allowed to cool to below 200 °C after which the main vacuum system valve was opened

2 Certain commerc ial products are identified in order 10 adequately specify the experi ­ and the system pumped out for 15 min to remove any mental procedure. In no case does such id entification imply recommendation or endorse­ other gases in the system not held at liquid nitrogen ment by the National Bureau of Standards. nor does it imply that the products identified are necessaril y the best available for the purpose, temperature in the sample collecting tube. The sample

728 collecting tube valve was closed, the liquid nitrogen The 1 g of ~HSiC insoluble residue resulting from the removed and the tu be was allowed to warm to room filtration of the solution was decom­ temperature after which it was connected to the mass posed by sodium carbonate fusion. About 5 g of sodium spectrometer inlet manifold. carbonate was added to a 20-ml platinum and During subsequent analyses of the gas the sample about 50 mg of the ~8SiC was added. The crucible was collection tube was always cooled in a dry ice-ethanol covered with a platinum cover and heated over a bath to ensure that no water vapor would enter the Meeker burner at moderate heat to fuse the Na~CO:; spectrometer. Examination of the mass region of inter­ and react with the 28SiC. After a few min utes the heat est and for seven or eight mass units both above and was raised to the full Meeker burner temperature [or below showed no sign of interfering peaks. about 5 min. The crucible and contents were then One further precaution was observed during sample cooled. the cover removed, a second 50 mg portion of preparation to ensure that no inadvertant isotopic con­ ~8SiC added. and the Na2CO:; fusion repeated. This tamination could occur. A number of sample tubes, procedure was repeated until the entire sample of sample collection tubes, and vacuum manifold U-traps ~HSiC had been added and fused. One gram of Na2CO:l were constructed, marked and tagged. A separate set was added to the original platinum crucible and fused was used for the preparation of each different sample. to react with any remaining 28SiC. The sodium car­ bonate melts were dissol ved in about 400 ml of H20 in a 2.2. Purification of Separated Silicon Isotopes 500-ml Teflon beaker. The solution was titrated with The final goal of achieving stoichiometric assays of the (l + 4) HCl to PH 5-6 (as determined by pH indicating enriched isotopes at the 0.01 percent precision and paper), the CO 2 expelled by rapid stirring, and the solu­ accuracy level is strongly dependent on the chemical tion was made alkaline with dilute sodium hydroxide to purity of each isotope. The enrichment of the ~HSi and about pH 9. The solution was then passed through a :IOSi isotopes was done by electromagnetic separation at cation exchange column as described for the sodium Oak Ridge National Laboratory (Union hydroxide solution of the soluble silica. The eluate was Nuclear Company). Collection of each high energy sep­ caught in a Teflon beaker, evaporated to dryness and arated Si ion beam was effected with a faraday the resulting hydrated silica was transferred to the cup. Thus the removal of the separated isotope from platinum crucible that contained the previously sepa­ the graphite cup resulted in a material, as received at rated silica. The crucible was then covered with a NBS, that was a mixture of SiO~. SiC and graphite. The platinum cover and ignited in an electric muffle furnace silicon 28 was designated sam pIe 900390 and consisted at 800 °C for several hours. The total recovered ~8SiO~ of 4.452 g of mixed Si02 and SiC along with some weighed 4.185 g equivalent to 1.952 g of 28Si. graphite from the collector. The silicon 30 was desig­ The :!OSi separated isotope mixture was taken into nated sample 900490 and consisted of 200 mg of the solution in a manner similar to the ~8Si procedure same type mixture. except on a reduced scale because of the smaller sam­ The ~RSi separated isotope sample was transferred to ple size. The total sample was transferred to a 100-ml a 100 ml FEP-Teflon beaker and the FEP-Teflon beaker and the silicon dioxide and silicon along with any silicon present in the material was metal were dissolved by adding 2 g of 50 percent dissolved by adding 16 g of 50 percent sodium hydrox­ sodium hydroxide and diluting to 50 ml. After overnight ide solution and diluting to 50 ml. The solution was digestion on a hot plate at about 80°C, the solution was digested overnight on a hot plate at about 80 °C and filtered through a close textured filter paper. The insol­ filtered through a close textured filter paper. The insol­ uble residue and filter paper were washed with H 20, uble residue and filter paper were washed with water. transferred to a platinum crucible, and ignited over a transferred to a platinum crucible and the paper and Meeker burner. About 50 percent (97 mg) of the original residue were ignited over a Meeker burner. About material remained and was assumed to be :wSiC. 25 percent (l g) of the original material remained and The filtrate containing the sodium hydroxide soluble was assumed to be . (silicon was passed through a strongly acidic cation ex­ The filtrate was split into two equal portions and each change column constructed from polypropylene and portion was diluted to 500 ml in Teflon beakers. Each containing about 35 ml of Bio-Rad AG50 X 8 , portion was passed through a strongly acidic cation 100-200 mesh_ The column was washed with 70 ml exchange column to remove sodium and other cations_ of water to completely remove the silicic acid, The columns were constructed from polystyrene and Hz 305i03, from the column and the eluate and wash­ were approximately 33 cm long and of 2.5 cm inside ings were evaporated to dryness. The residue was trans­ diameter. They were filled to a height of 25 cm with ferred to a lO-ml platinum crucible and ignited to Bio-Rad AG50 X 8, 100-200 mesh, cation exchange :30 5i02 over a Meeker burner. resin. The eluates were caught in Teflon beakers. Each The silicon carbide insoluble residue resulting from column was washed with about 150 ml of water to com­ the filtration of the sodium hydroxide solution was pletely remove the silicic acid, H/HSiO:;, from the decomposed by sodium carbonate fusion in the same column. The eluates and washings were then evapo­ manner as the ~8SiC except that only 1 g of Na2CO:l rated to dryness on a hot plate and the resulting was used_ Any :wSiC remaining in the original platinum hydrated silica, ~HSiO~ 'xH 2 0, was transferred to a crucible was dissolved by fusion with 0.2 g Na2CO:l . 50-ml platinum crucible. The sodium carbonate melts were dissolved in about

729 100 ml of H 20 in a T eflon beaker. The solution was there was no signifi cant diffe re nce in the purity of the titrated with (1 + 4) HCI to pH 5--6 (as determined by two isotope solutions at a level th at could interfere with pH indicating paper), the C O 2 was expell ed by rapid the assay method for sili con which was based on the stirring , and the solution was made alkaline with dilute gravimetric de termination of Cs2SiF,;. The princi pal sodium hydroxide solution to about pH 9. This solution interfere nces are the e le ment s that form insolublc was then passed through the same cation column as fluo sili cates s uch as th e alk ali es and a lk a line . the sodium hydroxide fraction and the column was In addition to the e le ments re ported in table 1, washed with about 70 ml of H20. The eluate and tun ),!:s te n was detected in the •. Si-30" solution. S ub­ washings were caught in a T eflon beaker. evaporated sequent analysis of CS2 :l oSiF 6 from the assay using a to dryness, and the residue was transferred to the lH:1 W s pi ke s howed that the t un),!:sten concentrati on platinum crucible that contained the pre vi ously sepa­ was negli),!:ibl e at less than 3 ppm. rated 30Si02. The crucible was then covered with a platinum cover and ignited to an electric muffle furnace 2.4. Assay of the Separated Isotope Solutions at 1000 °C for 1/2 h. The ~ oSi0 2 recovered weighed 0.1814 g equivalent to 87.8 mg of aOSi. Four we i),!:h e d portions each containin),!: about 10 mg Through out these procedures , the utmost care was of sili con, were withdra wn from e ac h separated isotope used to prevent contamination of the isotopes with solution in the followin),!: ma nner. A lO- c m platinum natural silic on. All of the be akers, ion-exc hange columns needl e was inserted throu ),!: h a No. 2 polye thyle ne ion-exchange resin s and filter papers were cleaned with stopper and used to re pl ace the cap in the bottle . A dilute high-purity hydroflu oric acid before use. All of 10-ml polyethylene hypodermic syringe with the plunger the chemical reagents were selected for low silicon covered with a thin s heet of cj'e fl on was att ached to content. For example, the total system blank for the the Kel-F hub of the n eedle and the desired amount of solution was withdrawn. The syrin),!:e was then d is­ purification of the 30Si isotope amounted to 4 fL g of natural sili con or about 0.0003 percent of the :loSi. connected from the hub a nd the tip was capped with a Ke l-F ·cap. An y stati c chargc that mi),!:ht be present 2 .3 . Preparation and Analysis of the Separated Isotope on the plasti c syrini!e was di ssipated by wi pin),!: it with Solutions a d amp lint less towel. The s yrin ge and conte nts were weighed on a semi microbalance to ± 0.02 m),!:. The The 4.18 ),!: of purifie d 2H Si02 was transferred to a solution was then delivered from th e syrin ),!:e into a 250-ml T e fl on beaker and di ssolved in a mixture of 50-ml T e flon-FE!> beak er and the syrin oe was aoain 130 ml of water and 30 ml of hi gh-p urity 48 percent cappe d , wiped a nd weighed. The wei),!: ht :f the sa ~p l e hydroflu ori c acid a t room te mperature. The solution was dete rmined from the wei),!: ht of the syrin ),!:e before was transferred to a tare d 500-ml Teflon bottle and and aft er de liv ery of the sample. Two assay s am ples diluted to a pproximately 300 g with water containin),!: were withdra wn from each solution before and aft er 30 ml of co ncentrated hydroflu ori c acid to ),!:i ve a solu ­ tion containing a pproxim ate ly 0.18 mmol/),!: of H 2 2HS iF,; TABI.E 1. Alwlysis of silicol1 is%lJeS in 3N hydroflu ori c acid. This solution was desi),!: nated "Si-28" . ··S i-28·· ··Si-30· · Et emen t The 0.181 g of purified :1 0 Si02 was transferred to a PI' III PI' III 100-ml T e fl on beaker and di ssolved in a mixture of A)! 7 2 35 ml of water and 7 ml of 48 percent hydroflu ori c acid " AI .5 3 at roo m te mpe rature. The solution was transferred to a "As 3 :2 125 ml tare d FEP-Te fl on bottle and diluted with water Ba 0 ..5 1 to approximate ly 55 g to give a solution approximately Ca 5 3 Cd 1 4 0.05 mmol/g of H 2 30SiF(; in 3N . The Cr ]0 30 solution was design ated "Si-30". Cu 4 4 Samples of the " Si-28" and " Si-30" were analyze d Fe 18 26 for impurity ele ments by isotope-dilution spark source J-.: 1 7 :V1)! 1 1 mass s pectro metry. Sam ples equi valent to about 5 mg :'11" 3 20 of sili con were spik ed with 10 - 7 cr of "A" 1:!7 Ba 44 Ca ,. Na '·30 '·50 lll Cd 53C r W;C u 54 F e 41K 26 M- IT !I7 M ~' (i2N i '20(Q>b' Ni 2 7 123S b ,' H2Se: 117 S n', H6S r', 120 T e, 2 ' ~ TI , (;7in. A f~ e r th e' I' ll 1 2 dS b 21 7 additio n of 0.5 ml of perc hl ori c acid to each sam ple, th e Se 3 0.2 sili con m atrix was volatilized as S iF 4 by evaporati on to S n 1 5 a s mall drop of perchl oric acid. The drop was trans­ Sr 0.2 0.3 ferred to a pai r of gold wires, evaporated onto the Te 0.5 1 1'1 I 1 wires, and th e deposit was analyzed by s pa rk source Zn 1 8 mass s pectrometry. In addition to the ele ments determined by isotope " Ve rsu- "; \'1 .. dilution, AI, As, Na, and S b were estimated by com­ h Ve r s u ~ x:! S; ,. Versus ·11 h pari son to isotopes of other e le me nts. T abl e I s hows d Ve rsus "'Sn the result of these analyses. The results showed that l" Valu e not signi fican tl y different fro m bl ank. 730 withdrawing the calibration samples to e nsure that re moved by e vaporating the solution to approximate ly no change in concentrati on had occurred during this ] 5 ml. time interval (about 3 h). The solution was tra nsferred to a 100-ml FEP-Tc fl on Each weighed portion was then assayed as follows : beaker a nd 40 g of bori c acid solution (5 gil 00 ml ) and The "Si-28" solutions were diluted to a pproximately 4 g of molybdi c acid solution (25 1£ of a mmoniu m 6 ml with I N HF. The "Si-30" aliquots we re 6 ml so molybdate tetrahydrate di ssolved in 200 ml of H 2 SO-l no further dilution was required. A weighed aliquot 0 + 9) a nd dilute d to 250 ml with wat E' r) we re added. of CsCl solution (100 mg CsCI/g) was added to the Aft er mixing, the pH of the solution was adjusted to separated isotope assay solution in an a mount to give 1. 7-1.8 with NH .,OH 0 + 1). After a ll owin g th e so lu ­ a pproximately 10 percent excess of the stoichiometric ti on to stand for 10 min , 4 1£ of tart ari c acid solution a mount required to yield cesium fluosilicate , Cs2SiFf;. (25 1£/100 ml ) was added. The solution was mi xed a nd Twenty grams of were added to the beaker, the 4 g of reducing so lution (27 1£ of sodium bi s ul fi te, 2 1£ of solution was covered and stored in a plastic box with sodium hydro xid e and 0.5 1£ of I -a mino 2-n apthol 4-s ul ­ an open beaker of acetone to prevent excessive loss foni c acid di ssolv ed in 250 ml of wate r and filt e red of acetone from the assay solution. After allowing through a close-textured pa pe r) was added. The solu­ the solution to stand at least 48 h (the " Si-28" solution tion was trans ferred to a 100-ml volumetri c fl as k, fill ed stood [or 5 days) it was filt ered through a weighed 15-ml to the mark with wate r a nd thoroughl y mi xed. The Munroe cruc ibl e and washed with approximately 20 ml absorbancy was measured on a spectrophotome ter at o[ a 90 percent acetone/l0 percent water (v/v) solution. 650 nm usin g a 2-c m cell with wa ter in th e re fe re nce (The filtrate and washings were transferred back to cell. The mi cromoles of sili con we re calc ul a ted from a the original beaker and reserved for the dete rminati on curve plotted by carrying known amounts of s ili con of di ssolved a nd untransfen;ed sili con. ) The crucible through the same procedure. The sili con fo und was and contents were dried for 2 h at 110 °C, allowed to added to the sili con from the gravim ctri c dete rminati on cool in a desiccator, tra nsferred to the case of a micro­ to yie ld the tota l sili con in the sam ple. Ta bl e 2 shows balance and allowed to stand for at least 1 h. The the results of these ana lyses. crucible and conte nts were we ighed to -+:- 0.Q02 mg. A This me th od of de te rmining th e concentrati on of combination bl a nk and buoyancy correcti on was made s ili con so lutions was pre vi ous ly tested on solutions con­ by averaging three that had been used to taining kn ow n amounts of s ili con. T wo so lutions we re filter blank samples carried through the procedure. The pre pared from hi gh purit y sili co n, SRM 990. Three sets drying, cooling a nd weighing were re peated until of four samples each conta ining fro m 320 to 420 }.Lm ol constant weight was reached. The air weight of the of sili con were withdrawn from cach soluti on a nd the Cs2SiF f; was the n determined and converted to vacuum sili con concent rat ions were deter m i ned as describ ed we ight usin g a C hemi cal Rubber Handbook (54 th above. Compari son of th e calcul ated and measured edition) value o[ 3.372 as the density of the salt. The concentrati ons showed biases of - 0.01 7 a nd - 0.032 mi cromoles of sili con present in the salt were deter­ percent fo r the t wo solutions. The s ili co n was dissolve d mined using a calculated atomi c weight for silicon and in diluted HNO:; and HF a nd there was appare ntly a 1973 atomi c weight values [or the other two eleme nts. greate r loss of S i as S iF ., from one so lutio n th a n the The fo rmula weights used were 407.7782 for CS 2 ~HSiF6 other. The concentration determin ed for each solution and 409.7463 for CS 2 :lOS iFf; . was intern ail y consis te nt with concentrati ons of The filt rate [rom the precipitati on of the cesiu m 0.107778 ± 0.000012 and 0.106541 ± 0 .00001 }.Lm ol/g flu osili cate was trans fe rred to the ori gin a l beaker and for 12 dete rminati ons on each solution. about 15 ml of wate r was added to ins ure th at any P ooling the res ult s of the "Si-28" separated isotope untra nsferred salt was dissol ved. The acetone was solutions with the results of the si x sets descri bed

TAB LE 2. Concentration a/silicon isotope sa int ions

Sili con Sampl e Weight Total Cone. No. solution g From ppt From so l sili con solution Solution J1.m ol J1.m ol J1.m ol J1. mol Sijg "Si-28" 1 2.20065 390.482 0.182 390.664 177.522 2 2.08974 370.552 .332 370.884 177.479 3 2. 03935 361.606 .379 36 l.985 177.500 4 2. 09052 370. 763 .283 371.046 177.490 Avera[!;e ...... 177.498

"Si-30" 1 6.64491 355.205 0.374 355.579 53.5115 2 6.27097 335.1 54 .387 335.541 53.5070 3 6.62758 354.344 .242 354.586 53.501 6 4 6.63155 354.524 .317 354.841 53.5080 Average ...... , ...... 53.5070

731

L_ above yields a value of 0.0000126 /Lm ol/g for the stand· separated isotopes and the micromoles of silicon from ard deviation of an individual measurement. each separated isotope solution as determined from the assay and weight of solution taken. 2.5. Isotopic Analysis of Separated Isotopes Each calibration sample was thoroughly mixed and a weighed aliquot of BaCI~ solution (l00 mg BaCl~/ g) The quantities of " Si- 28" and "Si-30" were trans­ was added in an amount to give a 1 percent excess of felTed as th e barium compound and decomposed to the stoichiometric amount required to yield barium SiF 4 as described above. Because of the very large fluosilicate. BaSiF6. The solution was evaporated to ratios these compounds were measured using a 30 cm dryness at low heat (-80 QC) on a hot plate. Each radius mass spectrometer which was otherwise iden­ sample was evaporated separately to avoid any pos­ tical to the 15 cm radius used for the remaining sibility of cross-contamination. measurements. The results of these measurements are giv en in table 3. 2.7. Measurement of the Relative Ratios of the Reference Material TABLE 3. Measurements of the separated isotopes To determine the relative, or uncalibrated. isotopic abundances of the reference material, SRM 990 sam­ Sili con-28 ples were prepared as described above and the isotopic Sample No. '"Si/'''Si " Si/""Si ratios measured. To ensure that no instrumental memory effects were observed a careful background I 15500 45040 scan of the measured region was made before the 2 15450 43890 3 15740 46690 introduction of each sample. No sample was examined Avcra~ (' ...... 15563 45207 if the mass 85 position showed a detectable signal of S.D ...... 155 1407 more than 3 X 10' 15 A. Sufficient sample was introduced to give a total sili con beam intensity of 3 X 10- 11 A and Sili con·30 the ratios measured in a pattern of 10 ~ 8 Sir'Si ratio Sample No. ""Si/"'Si ""S i/ '"Si measurements, 20 30Sij2HSi ratios and 10 ~8SifHSi ratios. Additional sample was then introduced to give 1 71.8 1 883.4 a signal intensity of 7 X 10- 11 A and the ratio measure­ 2 71.50 888.8 3 71.29 879.4 ment repeated. After this the pattern was repeated at AveraJ,!c ...... 7 1.53 883.9 signal intensities of 3 X 10- 10 A and 7 X 10- 11 A. In no S.D ...... 0.26 4.7 case did the ratios show a change outside of experi­ mental error for each of the four different runs on each sample. The results of the relative measurements of 2.6. Preparation of Calibration Samples the reference samples are shown in table 5.

Three calibration samples were prepared by mixing 2.S. Comparison of the Isotopic Ratios of the Calibra­ weighed portions of the "Si -28" and " Si-30" solutions. tion Mixes and the Reference Sample One mixture was within 0.25 percent of the observed natural ~HSirlOSi ratio of 29.7 and the other two mixtures In the measurements of the isotopic ratios of gases bracketed the natural ratio by 2 percent. The portions such as silicon tetrafluoride using electron impact were withdrawn from the bottles and weighed in the ionization sources the problem of memory is nearly manner previously described for the assay of the solu­ always encountered. Although large and efficient tion. To ensure that there had been no change in con­ vacuum systems help alleviate the problem the gas centration of an isotope solution with time. the portions molecules adsorb on components of the source and for the calibration samples were withdrawn from the are released with the introduction of subsequent sam­ bottles between the samples taken for assay. ples causing an unpredictable alteration of the isotopic Table 4 shows the concentration of the calibration composition of the sample. To eliminate these effects samples calculated from the isotopic analysis of the the so-called "constant" background or interpolative

TABLE 4. Composition of silicon calibration samples

Sample Isotope Weight '"Si ""S i Isotope ratio No. solution solution g ILm ol ILm ol '"Si/""Si

1 "Si-28" 9.41413 1.6708450 0.0000369 30.389838 "Si- 30" 1.04286 0.0007393 .0549688

2 "Si-28" 9.47683 1.6819732 0.0000372 29.149102 "Si-30" 1.09454 0.0008074 .0576929

3 " Si-28" 9.16645 1.6268861 0.0000360 29.815019 " Si-30" 1.03502 0.0007635 .0545556

732 TABLE 5. Determination of relative ratios of reference sample and the standard related to the known values for the (SRM 990) standards through

Determination No. 28/29 :\0/:29 /\.\ = R/) (K II - K,.) + /'.1.

I 19.74689 0.665180 It is also possible to correct for a small amount of :2 19.74790 .664296 residual bias by use of an end point measurement. 3 19.7:3(i78 .664621 For this the standards are substituted for the unknown 4 19.74016 . 66:W:30 5 19.73'118 .66:\806 sample in a sequence A-A- 8 - 8 - 8 - 8 - A- A and the 6 19.7:\143 .6632114 reverse from which the end point bias may be cal­ 7 19. 74:16 ~ .664.')62 culated as: 8 19.74626 .664026 19.7:,565 .664692 9 R _ Rx.I-R.1 10 19.7:{7;30 .6646.')0 /).1 - RII-R.I II 19.7:>281 .66-1-752 12 19.74000 .6647.'):\ Average ...... 19.7:393(i .664379 R - R.\/I-R.I S.D ...... 0.00.')77 .OOO"2(i /)/1 - RII-R I

Composition (Atom % ) If no bias exists R liA will be equal to zero and R tUI 28 92.22389 equal to 1. Normally this is not the case and the ratio 29 4.67:208 '10 :3.10403 of differences. R /) is corrected as: R/) - R/).I 28/30 = 29.71099 R /)(corrected) = R R :29/30 = 1.50517 /)/1- /). 1 The value of /\·x. the true isotopic ratio of the sample corrected for residual bias may then be calculated method was chosen for these measurements. The from the formula given for 1\.\ above. When this value interpolati ve method which has been in use by the of the true ~HSi/,wSi ratio is obtained a correction factor nuclear fuels industry for many years has been de­ for the filament bias may be calculated using that and scribed in detail by Smith et al. [24] and by Rodden [25]. the observed ratio. This may be used to correct all It consists essentially in the analysis of accurately other measured values to a "true" scale. known standards and samples in a prescribed and In addition to the above sequence another synthetic carefully timed pattern which permits the calculation mix (C) had been prepared with isotopic ratios nearly of the precise ratio difference between samples and identical to the reference material. This sample could standards regardless of the actual isotopic ratios meas­ be directly compared using the same timing program ured. The samples may be given accurate values as given above in a C-X-C-X ... sequence. The through the differences measured and the known values of X. the true ~HSirwSi ratio in the reference and values of the standards. In this case two of the pre­ the correction factor obtained are shown in table 6. pared synthetic mixes (A and B) were chosen with As a test of the validity of the above system this compositions slightly above and below the composi­ third mix C was substituted for the reference material tion of the standard. The three samples were prepared X. in a A- C- 8 - 8 - C- A- A- . .. sequence. The in separate sample containers to contain exactly the value for the 2HSi/,wSi ratio calculated from this meas­ same quantity of gas (within ± 0.5 percent) and the urement agreed with that known from the chemical three containers were attached to the mass spectrom­ preparation to within 0.001 percent. eter and were analyzed in the following manner. Sample A was introduced into the instrument to give a total TABLE 6. Sammary of filament correction factor calculation silicon ion beam of 3 X 10- 11 A. The ion beam was allowed to stabilize for exactly 2 min (all times given 1. From comparison of mixes 2. 4 and SRM 990 were controlled to " 1 s) after which 10 ratio measure­ R"leDrrected) = 0.48115 S.O.= 0.00428 ments were made. The pump on the sample manifold True ("Sif!IJSi)"",, = :29.74608 was then opened and the system allowed to evacuate for 5 min after which the sample X was introduced 2. From comparison of mix 5 and SRM 990 as above. These measurements were repeated in the R . ('"Si/,lIISi)",1O 1.002.')12 order A- X- 8 - 8 - X - A- A- X ... until a minimum atlo ("5i/,,"Si)-, of 10 A- X- 8 - 8 - X - A cycles were completed. From S.D. 0.000260 each cycle a ratio of differences may be calculated as True ('"Si/""Si j,.,!It = 29.74031

3. Average true value = 29.74:320

. 29.74:320 4. Correc tion factor= 29.71099= 1.001084 where Rx= average reading for sample entries 5. Correction factor/mass unit = 1.000.')42 R ..• = average reading for low standard entries 6. True (,"Si/,"'Si ),."" = 1.50598 R II = average reading [or high standard entries 733 3. Results and Discussion Tilles suggested that laboratory fractionation in the Calculation of Reference Sample sample preparation system used by Allenby may have Atomic Weight been the cause of the larger variation noted by him. In view of the excellent agreement between the results Using the corrected or true values for the isotopic of Tilles and Reynolds and Verhoogen and the much ratios determined for the reference sample and the larger variety of samples analyzed it seems that a values of the nuclidic masses given by Wapstra and maximum variation in nature of 0.5 percent is most Cove [12] the atomic weight of- this reference sample probable. may be calculated. The summary of the calculations are shown in table 7. As mentioned above Allenby reported a variation in The authors are indebted to P. 1. Paulsen who per· the ~8Si/~oSi ratios of 1.4 percent within the samples formed the spark source mass spectrometric analysis he analyzed. Reynolds and Verhoogen however, found of the reference material and of the separated isotopes only a maximum variation of 0.3 percent in materials and to Hsien H. Ku who provided the statistical analy· very similar to those analyzed by Allenby. In an at· sis of the experimental data but also studied the experi· tempt to resolve this discrepancy Tilles [26] analyzed ment and provided helpful guidance. a large variety of samples including a number of both The authors also acknowledge the help of the Divi· biological and meteoric origin. His results agreed very sion of Research US AEC (now ERDA) and the per~ well with those of Reynolds and Verhoogen but ex· sonnel of the Office of Isotope Sales, ORNL, for the tended the maximum range slightly to 0.53 percent. use of the separated isotopes.

TABLE 7. Summary calculations of atomic weight of a silicon reference sample

------Uncertainty components ------

Possible systematic Value 95% L.E. on the Possible bias on error in com- Possible Overall limit of ratio measurements determination of position of systematic error error a the end point separated in chemical correction isotopes analysis

Atomic weight = 28.0855258 ± 0.000055S ± O.0000202 ± 0.0000097 ± 0.0000073 ± 0.0000183

Nuclidic masses (12) (12C = 12) "Si = 27 .9769286 "'Si = 28.9764969 :l°Si = 29.9737722

Atomic percent '·Si = 92.22933 ± 0.00383 ± 0.OOJ55 ± 0.00063 ± 0.00047 ± 0.00118 "'Si = 4.66982 ± .00218 ± 0.00124 ± .00026 ± .00019 ± .00049 :lUS i= 3.10085 ± .00205 ± 0.00074 ± .00036 ± .00027 ± .00068 Isotopic ratios 2'Si/"oSi 29.74320 ± 0.021 Ol ± 0.00747 ± 0.00373 ± 0.00278 ± 0.00703 29Si/""Si 1.50598 ± .00119 ± .00086 ± .00009 ± .00007 ± .00047

a The overall limit of error is the sum of the 95 percent confidence limits for the ratio determinations and terms covering effects of known sources of possible systematic error.

4. References 453-458 (Nov.-Dec. 1966). [7j Catanzaro, E. J.. Murphy, T . .J.. Shields. W. R.. and Garner. [1] Shields, W. R. , Garner. E. L.. and Dibeler. V. H .. J. Res. Nat. E. L.. J. Res. Nat. Bur. Stand. (U.S.) 72A (phys. and Chern.) Bur. Stand. (U.S.) 66A Whys. and Chem.) 1- 3 (jan. - Feb. 261-267 (May-June 1968). 1962). [8] Catanzaro. E. ]., Champion, C. E .. Garner. E. L., Marinenko. [2] Shields. W. R. . Murphy. T. J .. Garner. E. L. . and Dibeler, V. H .• G., Sappenfield. K. M., and Shields, W. R. , Nat. Bur. Stand. J. Am. Chem. ~oc. 84, 1519- 1522 (1962). (U.S.). Spec. Pub!. 260 - 17.70 pages (Feb. 1969). 13j Shields. W. R.. Murphy. T. J.. and Garner. E. L. . .r. Res. Nat. 19] Catanzaro, E. J. , Murphy, T. ].. Garner, E. L. . and Shields. Bur. Stand. (U.S.) 68A Whys. and Chem.) 589 - 592 (Nov.­ W. R. , J. Res. Nat. Bur. Stand. (U.S.) 73A (phys. and Chern.) Dec. 1964). 511 - 516 (Sept. - Oct. 1969). 14] Catanzaro. E. J .• Murphy. T. J., Garner. E. L. . and Shields, [10] Gramlich, ]. W. , Murphy. T. J .. Garner. E. L .. and Shields. W. R., J. Res. Nat. Bur. Stand. (U.S.) 68A Whys. and Chem.) W. R., J. Res. Nat. Bur. Stand. (U.S.) 77 A Whys. and Chern.) 593-599 (Nov. - Dec. 1964). 691 - 698 (Nov. - Dec. 1973). [5] Shields, W. R.. Murphy. T. J.. Catanzaro, E. ] ., and Garner, [11] Garner, E. L., Murphy. T. ].. Gramlich. J. WoO Paulsen. P. ] .. E. L.. ]. Res. Nat. Bur. Stand. (U.S.) 70A (phys. and Chern.) and Barnes, I. L. , Absolute Isotopic Abundance Ratios and 193 - 197 (March - April 1966). the Atomic Weight of a Reference Sample of Potassium. to [6J Catanzaro. E. J., Murphy. T. J.. Garner. E. L.. and Shields. be published in ]. Res. Nat. Bur. Stand. (U.S.). 79A (phys. W. R., J. Res. Nat. Bur. Stand. (U.S.) 70A (phys. and Chern.) and Chern.) No.6. (Nov. - Dec. 1975). 734 112J Deslattes. R. D .. Henins. A., Bowman.H. A., Schoonover. R. M.. [20] Shields, W. R. , (Ed.), Nat. ·Bur. Stand: (U.S.) Tech. Note 277, Carrol. C. L.. Barnes. 1. L.. Machlan. L. A., Moore, L. .J.. p. 8 (July 1966). and Shi eld s, W. R .. Phys. Rev. Lett. 33,463- 466 (1974). 121] Shields. W. R.. (Ed.). Nat. Bur. Stand. (U.S.) Tec h. Note 277. 113] Wapstra. A. H .. and Cove. N. B .. Nuclear Data Tables 9, p. !O (july 1966). 265-30 1 (l971). 122] Shields. W. R.. U.S. Patent 2.956.771 (1960). 114] Baxter. G. P .. Weatherill. P. r .. and Scripture. E. W .. .Jr.. Proc. 1231 Reynold s. J. 11 .. and Verhoogen. J.. Geochim. Cosmochim. Am. Acad. Arts Sci. 58, 24.5 - 268 (1923). Acta 3,224-234 (1953). 115J White. J. R.. and Cameron. A. E .. Phys. Rev. 74,991 - 1000 1241 Smith. R. L.. Shields. W. R .. and Tabor. C. D .. US AEC Report (1948). GAT- l7Il Rev. I (1956). 116] Cameron , A. E .. a nd Wichers. E .. .lA CS 84,4175- 4] 97 (1962). 125] Rodden, C. J.. (Ed.). Selected Measurement Methods for Plu· InJ Atomic Weights of the Elements- 1969, Pure App!. Chem. 21, tonium and in the Nuclear Fuel Cycle. 2nd ed. U.S. 93 - 107 (1970). Atomic Energy Commission (1972). 1]8J Allenby. R . .1 .. Geochim. Cosmochim. Acta 5, 40 - 48 (1954). 126] Tilles. 0 .. .J. Ceophy s. Res. 66,3003- 3013 (l961). 119] Shi elds. W. R .. (Ed.), Nat. Bur. Stand. (U .S.) Tech. Note 426. 53 pages (Sept. 1967). (Paper 79A6 - 870)

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