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Abstract ü Problem Status ü Authorization ü
INTRODUCTION 1 I
MATHEMATICAL FORMuLATION 2 f
NUMERICAL CALCULATIONS 3
GENERAL DESCRIPTION OF THE PROGRAM
ACKNOWLEDGMENT f
REFERENCES 5
APPENDIX A-Program Listing 6
APPENDIX B - Sample Program Output 9
APPENDIX C - Data Coding Form 11
ABSTRACT
To determine impurity concentrations in solids using mass spectrographs, ion-sensitive emulsions are used. The principal problem it. obtaining quantitative results from a mass spectrum recorded on a photographic plate is deter- mining the characteristic response curve. Calculations required to determine the parameters in an empirical func- tion which accurately represents the response curve of Ilford Q2 emulsions are programmed in FORTRAN language. The program input data consists of the impurity-ion mass, line density, and exposure; the impurity-ion concentration and the detection limit are calculated and printed as output.
PROBLEM STATUS
This is a final report en the computer program tor determining impurity concentrations in solids.
AUTHORIZATION
NRL Problem P03-07A Project ARPA Order Number 418
Manuscript submitted October 4, 1967.
ii
A COMPUTER PROGRAM FOR THE QUANTITATIVE INTERPRETATION OF MASS SPECTROGRAPHIC PHOTOPLATES
INTRODUCTION
Solid-state mass spectrographs norm&ily use ion-sensitive photographic plates as the ou'put detector, due to the wide variation in ion intensity of the rf vacuum npark source. In addition, the photoplate is an excellent ion integrator and has the ability to detect and to record a wide range of masses simultaneously.
There are two principal procedures used for tha analytical interpretation of photo- graphic plates: (a) visual inspection (1), where an experienced analyst visually compares line densities and calculates concentrations from relative exposures, and (b) the photo- metric method (1-3), where a microdeuJfometer is used to determine line densities and the data are pro« ssed by manual calculations. The first method produces semiquantita- tlve results; the latter method, by eliminating errors arising from visually matching densities, line width, emulsion background, etc., can produce quantitative results.
This report is aot interded to argue in favor of one method over the other. Both methods are useful. However, if the densltometric meihod is used, the manual labor re- quired to process the data is so gr^at that the routine computation can be done best by a digital computer.
The primary problem in obtaining a quantitative analysis of a mass spectrurii re- corded on a photoplate is deverminlng the characteristic response curve of the emulsion. There are several "functlonless" methods (4) for obtaining the characteristic response curve, but the method most widely associated with mass spectrography is the modifica- tion by Duke (2), based on the "two-line technique" described by Churchill (5) for use in optical spectrography. The characteristic response curve may also be obtained by a "functional" niethod. An empirical function given by Hull (6) accurately represents the entire response range of Ilford Q2 emulsions, thus permitting all analytical data to be evaluated.
Both the functionless and the functional method have individual merit. The Churchill two-line method is applicable only for elements possessing an appropriate isotopic dis- tribution, and it requires many pairs of measurements o! two lines having a known inten- sity ratio (such as isotopes whose abundance ratio falls within the requisite range). In addition, only inlormalioa from a single element is used to construct the characteristic cuiv"?. but Owens and Giardino (7) have demonstrated that emulsion response exhibits ion-mass ■>pendence, ion-energy dependence, and, possibly, chemical dependence. How- ever, Kennicott (8) has described a computer program using this method.
The functional method, in which the data are fitted to aji empirical curve, is easier to program. Hovever, it teixs.s to force the data into a predetermined formula, and any errors of the ion-beam integrator are not corrected. Woolston (9) has described a com- puter program written in assembly-system language, using tlie functional method.
The program described below is modeled after Woolston's program, but it is written in FORTRAN IV, because NRL's CDC 3800 computer is more receptive to FORTRAN language. Generally the mathemaucal functions and symbols of both Woolston's program and our program are the same; there are slight additions or deletions that suited our
BEY AND ALLARD
personal approach. However, the parameters calculated from the same data are essen- tially the same.
MATHEMATICAL FORMULATION
The equation for tie photographic calibration curve given by Hull (6) rnay be ex- pressed by
/ 100- ff \
\'z, 'SAT' (1)
where, for a sample component x,
Kx is directly proportional to the component concentration In the total ion beam striking the plate aid to the photoplate sensitivity,
aZi i is the abundance of isotope i of the sample component,
Ex Is the exposure, indicated by the b?am-monltor Integrator, in nanocoulombs,
T, Is the percent line transmission (corrected for background) of the spectral line i,
TSAT Is the percent transmission of the spectral line i for an Infinite (saturation) exposure, and
RI Is proportional to the maximum slope of the photographic response curve.
The corrected line transmission rL In Eq. (1) Is given by
/ loo- r^ \l/rf / loo- TR \1/Ä]
loo + r,.,. -r ~^-] - -——^ !
1 t /ioo-^By " / loo-rg
where TLB IS the measured line transmission and TB Is the measi; 'd background trans- mission, both In percent transmission.
The sensitivity of the emulsion is proportional to M0-6, where M Is the mass of the Ion. When this factor Is Included the equation for calculating the Impui Ity-lon concen- tration c, in ppma Is determined from Eq. (I) and becomes
lOfilHFr)osSrKrCr C, = * L^_l . (3)
{IUFr)0-sSjeKl,
where tfF is a factor proportional to the mass in atomic mass units, c. Is the fractional concentration of the reference Ion, and s 12 the relative sensitivity coefficient (unless both 5, and Sr are known, they are taken to be unity).
When the lines have finite width the concentr; ilons are corrected by a factor equal to the line width. Thus, Eq. (3) must be multlplifd by ■,, , «r.;, where w is the width of
NRL REPORT 6655
the line as determined at the points of haU-maxlmum on the Intensity profile. When the background Is considered, these points correspond to the transmission
100 ♦ TSAr
Lw U 100 hB\
Mft.
LB TSAT' \TB-TSATI J 1 (xm
1 +
(4)
i /^o-rta\1/y?' ! /ioo-ra\'//f']
2 ^LB-TSAT' 2 ^B'TSATI J
NUMERICAL CALCULATIONS
When only one data point Is available, R4 Is taken to be 1. (1 and 2) Rx Is determined from the relationship
For two data points
log
R. - vrtl - r5/4rM loo
's/sr oo- r
/.2
'"«(IX)
(5)
which may be derived from Eq. (1). Only three data points are allowed In the prog^im. When three points are used, an average value of fiz (equal to the root-mean-square of RZ
obtained from the calculation for the three combinations of pairs of data points) Is calcu- lated and Is designated as nIV. If Rx Is either greater than 1.25 or less than 1, RAV is set equal to 1.0. Upon substituting RAy into Eq. (1). numerical values of KX are calculated for each data point, and the root mean square of this result, denoted by A ,,, is substi- tuted into Eq. (3) to determine the Ion concentration.
Numerical values of r^, are calculated from Eq. (4) for each data point; an_average value of the correction for line width can be determined by the densitometrlc measure- ments, and the factor wx i «■,.. ^ can be applied to Eq. (3).
The detection limit Is determined by using «,. to calculate Kx for the maximum component exposure, setting Tl = 100% and Tg = 98% in Eq. (1) and substituting these values of K, in Eq. (3).
GENERAL DESCRIPTION OF THE PROGRAM
Expressions are programmed for the calculations described in the previous section for experimental data read in from punched cards. Tables of isotope abundances and Identifications are punched on IBM cards and are read in preceding the experimental data cards. If an incorrect isotope identification is made on the corresponding data card, NO ISOTOPE LISTED is printed, and the calculation for that isotope is bypassed. Other errors are determined by the system err ^r identifiers. Formats of the experimental data cards are given in Table I.
The input data are punched on cards. A table of isotope abundances Is read in with the measured data. Table 2 gives a definition of the symbols used in the program.
Cards 3 through 4 + (N- I) are included, in order, for each isotope Three cards (identified as 23-1, 23-2, and 23-3) may be Inserted into the program between cards 23 and 24. The data are then punched in as optical density.
BEY AND ALLARD
Table 1 Input Data Format
Data Card Number Format Symbols
1
2
3
4 through
4 + (N-l)
(55H )
!lx. 14. lOx. E11.4. 2x. F10.4)
(Ix, F4.1. 9x. F7.2. lOx. 12. lOx. A8. Al. 7x. F5.2)
(A8 Ix. F8.4. 2 (2x. F8.4). 3^, E10.3)
Rim Identification
NO RUNS, REF CONC, EI1V K
CHG, ATWT, M, Q, S"
ID, TLB, TB, TSAT, El
The sequence of cards 3 through 4 +(N - 1) is repeated a number of times equal to the number of runs.
Table 2 Definition of Symbols
Card Number
Symbol Definition
2 NO RUNS The number of isotopes processed
2 Ref Cone The concentration of the reference isotope
2 EIMAX The maximum photoplat" exposure in nanocoulombs
3 CHG The isotoplc charge
3 ATWT The average atomic weight of the element
3 N The number of data points used for the Isotope processed
3 Q The comments
3 S (Defined In text)
4 ID The atomic symbol and mass number
4 TLB, TB, TSAT, El (Defined In text)
The first 1-2 characters In the A8 specification of ID refers to the atomic symbol, and tiie last 1-3 characters correspond to the atomic mass.
ACKNOWLEDGMENT
Mr. Kenneth Moran of the NRL Computer Center Is gratefully acknowledged for his programming assistance.
REFERENCES
1. Craig, R.D., Enock, G.A., and Waldion, J.D., in "Advances In Mass Spectrometry," J.D. Waldron, ed., New York:Pergamon, 1959, p. 145
2. EHike, J.F., in "Ultrapurificatlon of Semiconductor Materials," M.S. Brookes and J.K. Kennedy, editors, New York:MacmlUan, 1962, p. 294
3. Perkins, CD., and Poilack, D.H., U.S. Department of Commerce, ASD-TDR-62--275, 1962
4. Owens, E.B., in "Mass Spectrometric Analysis of Solids," A.J. Ahearn, ed.. New York:Elsevier, 1966, p. 56
5. Churchill, J.R., Ind. Eng. Chem. (Anal. Edition) 16:653 (1944)
6. Hull, C.W., "Photographic Quantitative Analysis with a Solids Spark Mass Spectro- graph," Mass Spectrometry Conference, ASTM Committee 14, Paper No. 72, New Orleans, La., June 3-8, 1962
7. Owens, E.B., and Giardino, N.A.. "Quantitative Mass Spectrometry of Solids," Anal. Chem. 35:(No. 9):1172 (1963)
8. Kennicott, P.R., "A Computer Program for the Quantitative Interpretation of Mass Spectrograph Plates," 12th Annual Conference on Mass Spectrometry and Allied Topi 3, Montreal, Canada, June 7-12, 1964
9. Woolston, J.R., "Data Processing for the Mass Spectrographic Analysis of Solids," 13th Annuai Conference on Mass Spectrometry and Allied Topics, St. Louis, Mo., May 10-21, 1965
Appendix A
PROGRAM LISTING
PROGRAM SPECTRA 1 DIMENSION .■LEJ(3).TB(3).TSAT(3)!TUW(3ljTLi3ljJlL3J_iliAllljJJ22L2J-»_ 2 -
CID(3)»Ab(287 I,I DEN(237).MASSi2 87).MI(3).El (3).AI (3).0(2) 3 TYPE REAL /.FACTOR.ICAV,H.X.MI,HOL,ICAVR 4
2^1 FORMAT(7FU..5) 5 2w_2 F0RMAT(9Aet 6_- 2w3 F0RMAT( 19U) 7 20* FORMAT(2(016) ) ... _ 9
RFA0201,AB q READ2C2.IDEN .. . ._ ._ 10 REA0203.MASS 11 READ20'».MSICliMilt^_ . 12 LINE5=*7 13 READ 2v6 .... _._. 14 PRINT 205 15 PRINT 2C6 .._... _ . 16 CALL HEADlNf: 17
_.RFAD30 .NO RUNSiREf—COJiC.EIMA^ .. Ifl fO 26 I»1 .NO "UNS 1Q READ 31.CHG,AT WT.N.Q.S . MFAtTOR=(AT WT/(3P.0»CHG))•»C.6 21 DO 4 J*].N _ 2Z READ 32.iO( J).TLb(J) .Tu( J),TSAT( Jj.EKJ) ' 23 TLB( J)»lC.t»Jti-TLB( J)_)*lo0.y 22-1 TB(J)«lu,0»»(-TlJ( J) )*liJ0.0 23-2
TSAT(J)-10.C»»(-TSAT(J))»1C0.0 ■ _ _ _ 23-3 ID2(J)«MSK.2.ANU,ID(J) 24 L»0 25
1 L=L+1 26 IF(L.6T.287)33.2 _ 27
2 IFtIOiJ),E(J.IDEN(L) )3.1 28 3 AI!Jl«Ab(L)/100.0 29
Mi (JüMASSIL) 30 CALL CALC TL'TLPIJ).TB(Jl.TSAKJ),TL(J)i __ _ 31
4 CONTINUE 32 IDl«MSiU,AND«IC-. 33.— IF(N«E0.1i5,6 34
5 R*!«^ ._ _ _ 35 __ R(2)=1.0 36 RAV-l.C . . _ 31 CALL CALC K(R.TL.TSAT.EI .AI.KX) 38 CALL CALC TLW(N.TLB>TB.TSAT,TLX) 39 ICAV = MFACTÖR»KX 40 GO TO 11 _ 41
6 IFCN.EÜ.2)7.9 42 7 CALL CALC R(TL.TL(2).A1»£I.AI(2)»EI(2).TSAT.TSAT(2».R) 43 R!2)*R 44 RAV = R . 45 DO 8 Mrl,2 46 CALL CALC K(R,TL(M) tTSAT{M> .EI (M) ,AIjM)jK,X(MJ ) 47
8 CALL CALC TLW(R.TLb(W).TbtM).TSAI(M).TLW(M)) 48 KAV= SQRTF(K.X»ICX(2) )*MFACTOR __ 49 GO TO 11 50
V. DO 10 M»2J.2 il
NFL REPORT 6655
10 CALL CALC R(TL.TL(M) ,AI»CI .AI (N1 )»t I (M! ,TSAT jTSAKM) ,R(M-i ) ) 52 CALL CALC R(TL(2).TL(31.AIl2l»Ell2).A Ij 3! *f I(3)ttSAT12UTSAT«3) t 51.
CR(3n 5<t Z]L'JL±SI/J1MS1 55_
RAVs(RtR(2)*R(3li«»EX 56 JjQlSO. M=LiJ . 5X. CALL CALC K(RAV,TL(M).ISAT(M; ,tl (M) ,AI(M) .XX(M) ) 58
Kl CALL CALC TLW ( HA V t TLB ( M ) , To ( M ) . TbAT ( M ) . I LA ( M 1 ) :__ . ) i9 __ KAV=(K;X*KX(2)«S.X( 3) )»»tX»MKACTOR 60
U IF* I.ECI.p 12.13 __.... 61 12 CI=RFF CONC 62
_ SÄsS. -. - ._ ji» — KAVR=KAV 64
SQ-TOLJiai. - . fi5__ 13 Cl« 5R«K;AV/(S»KAVRI» REF CONC 66
13i_lFtN.E0olJl'».15 _ hi . U "1=1 6a
GO TO 20 69 15 Nl=N-l 70 DO .I8.ä«l.«.Nl-- -71
IF(AI(M),LT.A!(M+lI)16.17 72 _I6 M1=M+1 73
GO TO IB 74 17 M1«M . _ . 75 18 CONTINUE 76 tFtN.EQ.ailg.gO _ __ 27
19 RX=RAV 78 CO TO 21 . 79
20 RXaR 80 _21_CALL CALC K ( RX.98.0f n.o ,E IMAX . AI {,/.l ) ,<DL 1 81
DET LIM=:SR»<l)L/(<AVR«S)» REF CuNC« MFACTÜR 82 PR INJ 2 7ilDJL» ^1. DtJ_ LJJfL, (j i IJ . J ( 2 ) . 10 2 ( 1 1 . T UiJAJ ,J ü( 11 .i^AT (J } , 8 3. _
CTL(l).TLWI1).R()).KX(1).MFACTüR.S.EI (1 ) 84 IF(N.E0.1)24.23 85
23 DO 231 LN=2.N 86 PRINT 28,Iü2(LN).rLb(LN) .Tb(LN) ,TSAT(Lfi) ,TL(LN) .TLWKN! ,R(LN) t 87
CKXtLN)»El(LN) 88 231 CONTINUE ... 89 24 PRINT 29,RA'v.<AV 90 LINE:S»LINES-N-3 __ 9:
IF(l INES,LT.0(25.26 92 25. LINE.S»47__ 93
PK.NT 205 94 PRINT._Z^L .. .^95..-..
CALL HEADING 96 26 CONTINUE 97
GO TO 3$ 98 33 PRINTJ4 99 34 FORMAT(19H ISOTOPE NOT LISTED) 100 I F ( I .EG.NO RiJNS)35.36 . JJJl 2 7 F0RMÄT(3X»A2.4X.E10.3.2X.F8.4.3X.A3.A1,2X.R3.5(2X.F5.l).5X.F6.3, 102 C6X,E10,3.2X,F6A3.^X,F5..2.2X.E8.1 ) 103
28 F0RMATi43X.R3.5(2'x.F5,l ) . 5X . F6. 3 »6X ,E 1 0. 3 .1 7X .E8. 1 ) 104 29 FORMAT(e2X»4HRAV=.F6.3.2X,4HKAV=,tl0.3.//) 105
2C5 FORMAT(IHlI 106 2^6 FORMAT(55H ) 107 3u FORMAT!1X.I4.10X.Ell.4r2X.F10,4) 108 31 FORMAT(1X.F4.1.9X.F7.2.1CX.I2.10X.A8.A1.7X.F5.2) 109 32 FOPMAT(A8.rX-.F8.4,2(2X.F8.41 ."3X.E10.3) 110 36 IF(J,EO.N)26.37 111
_3J. J£liJ±J — — UJ- DO 38' JE.JE1.N 113 READ 32tlD( JE).TLr;(JtJ_i_liiLJUxIiAT(J£J.tl(a£l . 1.14
i BEY AND ALLARD
I i
38 CONTINUC 115 GOL T 1- 6 m 35 r'.NTINUE 117
LHQ. _ n» SUBROUTINE HEADING 119 PRINT 1 .
1 FORMAT(/lX.6HSYMBOI,.6)'.3HPPM«5X.9HDET i. IM IT ^ 3X ♦8HCOMMENTS.2X t 121 -S.hmAi2L*2A*3hlLhxte.iJ>JAhjSiUiUlLSAT .4X^HTL .fcx.^HTi Mtflx. IHB.IJJU—_U2-
ClH|C»9X,2HMF,6X.lHS.8Xt2HEI/) t23 END . ._ ._ ^ ii.4- SUBROUTINE CAUC IC( R.Tl. tTSAT tEl .AI ,HX ) 125 TYPE KEAL KX .. 126 1F(R,GT.1,25)1,2 127
_J_RXl = Uüia*25 128 GO TO 5 129
2 JF(R.U..UÖ)3i4 UXL 3 RX1«1,0 131
GO TO 5 . . 132 ^ RXl=l,ü/R 133
._5, JUS« U lVV«^-TLl/( TL-TSATn««RXl/lAI«£Il , L34- END 135 SUBROUTINE CAk£_ TiMifiAJUttcLAliAT .ILW1 . . _L3.t- tF(R,GT,1,25)1,2 137
L RX-i,25 . _ _ 138 RX1«1/1.25 139
aQ_TS_l UP 2 I7X-R 141
RXl».,c/R 142 3 TS1««djÜ,^-TLfa)/(TLB-TSAT))«»RXl/2,0 145
TS2=((100,ü-rB)/(Tb-TSAT))««RXl/2,0 _ __^1**_ TS3»(TS1+TS2)«»RX 1A5 TLWxl10C.0+TSAT«TS3i;(l,ü+TS?) 146 END 147 SUBROUTINE CALC TLTM-Bf TB.TSAT ,TL) 148._ TS«aoe.O-tLE")/«TLe-T5ATi-<XOO,Ö-TÖ)/(TB-TSAT) ' r*9 _TL« < 1 o:,0*TSAT»TS)/a,{HTS) 150 END 151 SUBROUTINE CALC ? ( TH,TL2,AE1,AE2 ,TSAT 1 ,TSAT2,R I 152 R«LOGF(ll0u,0-TLl)/lTLl-rSATl)*(TL2-TSAT2l/(100,0-TL2))/ 153
CLOGF « AE1/AE2J 154 END 155
Appendix B
SAMPLE PROGRAM OUTPUT
10 BEY AND ALLARD
ru n •H e O)« oj n i*n >o « e e o -^r or e> o a e e a o e o a o>> O G> oe e e ♦ ♦ • ♦ * 4 * * * * ♦ ♦ e e o o o o e o a e e o
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nion« nn« mm«« om« ^«40% or^«4 «« r^ IOMM
■ ■■«■■ > > -« « K X X
Nnin oo« K >v r- »wn P>I*K r. r-K m ■> m -< ^ w nnn ir. mm KM*\ •* Knn MMN «««
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_i cv »~ « « r- -in
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in ui >- u
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Appendix C
DATA CODING FORM
11
12 BEY AND ALLARD
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UNCLASSIFIED Sgcurily Clagsificaiion
DOCUMENT CONTROL D4TA R&D iSecurity clmiticatton ol tHI*. body ot mbttrmct and ttnhlttng annotation mwl b* •ntitrfti *fh»n th* os*rMll report it ctmiUmd)
t ORIGINATING ACTIVITY (Corporal» author)
Naval Research Laboratory Washington, D. C. 20390
2«. REPORT SECUHITV C L ASStFlC * T ION
Unclassified 2b. CROUP
3 REPORT TITLE
A COMPUTER PROGRAM FOR THE QUANTITATIVE INTERPRETATION OF MASS SPECTROGRAPHIC PHOTOPLATES
4 oEscmPTivE NOTES fTyp. of r.por(.r><(inciu.(v.<(.t..j This is a. final report on the Computer program for determining impurity concentration in solids.
s AUTHORI3I ff/nf .-i«m«. middle initial, lm»t n9m9}
Paul P. Bey and James G. Aliard
« REPORT OATE
April 8, 1968 7m. TOTAL NO. OF PACES
16 70. NO OF RCFS
9* CONTRACT OR GRANT NO.
NRL Problem P03-07A 6. PROJECT NO
ARPA Order Number 418
9a. ORIGINATOR'S REPORT NUMBERISI
NRL Report 6655
tb. OTHER REPORT NOIS) (Any other number* thml mm? bm mttifnmd thim rmport)
10. orlTRIBUTION ITATEMCNT
This document has been approved for public release and sale; its distribution is unlimited.
11. SUPP'.CMCNTART NQT-J 12. SPONSORING MILITARY ACTIVITV
Advanced Research Projecfs Agency Washington, D. C. 20301
To determine impurity concentrations in solids using mass spectographs, ion- sensitive emulsions are used. The principal problem in obtaining quantitative re- sults from a mass spectrum recorded on a photographic plate is determining the characteristic respon&e curve. Calculations required to determine the parameters in an empirical function which accurately represents the response curve of Ilford Q2 emulsions are programmed in FORTRAN laniuage. The program input data consists of the impurity-ion mass, line density, and exposure; the impurity-ion con- centration and the detection limit are calculated and printed as output.
DD.'r..i473 (PAGE,,
S/N oioi-807.eeoi 13 UNCLASSIFIED ' Security CUttincation
UNCLASSIFIED Security CtassJication
KEY WONOt
Mass spectrographic computer program Impurity analysis Mass spectrographic data processing Analysis of solids
HOLE WT 1— —
DD/r..1473 BACK, (PAGE 2) 14
UNCLASSIFIED Security Claiiirication