rabbit, an electron microprobe data ... an electron microprobe data-reduction program using...
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RABBIT, AN ELECTRON MICROPROBE DATA-REDUCTION
PROGRAM USING EMPIRICAL CORRECTIONS
by
Fraser E. Goff
U.S. Geological Survey
Menlo Park, CA 94025
U.S. Geological Survey OPEN FILE REPORT 77-351
This report is preliminary and has not been edited or reviewed for conformity with Geological Survey standards.
ABSTRACT
RABBIT is a FORTRAN IV computer program that uses Bence-Albee empirical
corrections for the reduction of electron microprobe data of silicates, oxides,
sulphates, carbonates, and phosphates. RABBIT efficiently reduces large
volumes of data collected on 3-11 channel microprobes.
INTRODUCTION
RABBIT is a high volume computer program written in FORTRAN IV that
is designed to reduce electron microprobe data in counts to quantitative
chemical analyses in weight-percent. Refinements correct the data for
instrumental drift, deadtime, and background. RABBIT uses empirical
correction schemes (Bence and Albee, 1968; Albee and Ray, 1970) for matrix
corrections of silicates, oxides, sulphates, carbonates, and phosphates.
Data sets may contain 150 individual analyses, and any number of data sets
can be processed back to back. Optional routines: 1) calculate cations/unit
cell; 2) normalize any three elements in terms of their atomic proportions;
and 3) print tables of analyses. RABBIT was designed to be convenient,
flexible, and capable of handling large amounts of data.
METHODS
Data Handling. A flow chart (Figure 1) will aid in the following discussions,
and Table 1 defines unfamiliar terms. RABBIT can reduce data sets containing
as many as 150 analyses and can reduce any number of data sets back to back.
Space is allocated in RABBIT for 11 elements, but more could easily be
accomodated. Up to 40 counts per unknown make up the count set for each
analysis. The standard deviation of the counting statistics is computed from
n (^
i=l n ~ l
where a = standard deviation
K = average counts of count set
K^= the value of the ith count
n = number of counts in count set,
Figure 1: Flow chart for program RABBIT,
rRead alpha factors
Read title, date, and other parameters
Data averaging
Standard deviation
Deadtime correction
Read beginning standards and backgrounds
Read and store unknown data
Read final standards and backgrounds
Print all standard data
Process unknown data
Drift correction
Bence-Albee correction
Compute error in counting statistics
Additional calculations
I Print unknown data
~Get new data |
End
Table 1: Definition of terms
channel - the X-ray energy for each element is detected on a separate channel,
counting interval - the length of time (in sec.) that X-ray energy is counted,
counts - the energy counted during one counting interval,
count set - all the counts accumulated for each unknown; the data for one
unknown makes up a count set.
data set - all the count sets accumulated for the run; the data for all the
unknowns being analyzed in the run make up a data set.
run - all the data for the job; includes standard, background, and unknown
data.
Deadtime. Averaged counts are next corrected for deadtime. This correction
will vary from probe to probe depending on the equipment and the operating
parameters in use. RABBIT is designed to function with three wavelength
dispersive (WDS) channels and eight energy dispersive (EDS) channels. No
deadtime correction is presently made to the three WDS channels. Counts from
the EDS system are corrected for deadtime relative to the total energy stimu
lating the EDS detector, as measured on a ninth EDS channel. The routine
that follows is adapted form Beaman and others (1972). Let
X, « - (2) 1 t
x? = I (exp C-X.d)) (3) t A
where E = average counts from EDS system
if = average counting interval in seo.
d = deadtime of detector in sec.
For ease of manipulation we have
v = I Y - x I f 41A.- I *. ^1 I V^V
Y = Y 7 (*>} A4 - A^L {$)
where Z = upper limit of convergence in sec
If X, jl X., we make X = X and substitute this new value of X into Equation (3)
for iteration. The routine rapidly converges until X- < X.. The counts for
each individual channel are then deadtime corrected by letting
(6)
where 1C - deadtime corrected*%
average counts/sec.
Values of d and Z currently built into RABBIT are 7.5 x 10" sec. and-5 -8
1.0 x 10" respectively when using specimen currents less than 3.0 x 10 amp.,
but these values should be modified for individual needs.
Standards and Backgrounds. Standard and background data are read into the
program before and after the unknown data just as they are collected on
the probe. Standard and background data are averaged and deadtime corrected
in the same manner as unknown data but no counting statistics are computed
for backgrounds. The program reads number flags from the data cards to
differentiate standards from backgrounds. Backgrounds are treated as standards
which contain 0% of the unknown elements, thus background data does not need
any special editing. RABBIT allows a maximum of 20 standards plus backgrounds
to be used per run.
Instrument Drift and Background Corrections: Instrument drift is assumed to
be linear with time. Standard and background counts are drift corrected by
linear equations to the time of observation of each unknown. The standard
counts are background corrected by subtracting the background counts. The
unknown counts are then compared to the corrected standard counts and equated
to values of weight percent. These corrections are repeated for each element
to produce a raw analysis.
Bence-Albee Corrections. Because of their simplicity empirical correction
schemes are used for interelement matrix effects which reduce programing costs
and computer time. RABBIT incorporates the measured alpha-factors of Bence
and Albee (1968) and uses the computer generated alpha-factors of Albee and
Ray (1970) where measured values are not available (Table 2). The alpha-
factors for 36 elements are read into the program as data and stored as a
36 x 36 matrix. The alpha factors listed in Appendix II are for probes with
a take-off angle of 52.5° and operating voltages of 15 KV. Alpha factors
for other take-off angles and operating voltages may be obtained from Albee
and Ray (1970). and Amli and Griffin (1975) .
Beta-factors are computed from the standards using a computer routine
adapted from Eq. (3) of Albee and Ray (1970). The program allows compensation
to be made for elements present in the standard which are not to be analyzed
in the run. For example, if benitoite (BaTiSi^Og) is used as a titanium
standard, the beta-factors from benitoite must take into account the matrix
effects of barium even though barium may not be included in the analysis.
Raw analyses are corrected using a computer routing following Bence and
Albee (1968, p. 402) which iterates through the calculations twice.
Error in Counting Statistics. Once corrected oxide values are computed, the
overall error in counting statistics is calculated from the standard deviations
of counts in both standards and unknowns using partial differential equations.
We have the basic relationshipC S
U = (7)cs
where U = Unknown weight percent
S = Standard weight percent
C = Counts of unknown u
C = Counts of standard s
Because the total uncertainty of U is a function of the standard deviations
of the counts for both unknown and standard, W and W (ignoring the backgrounds),
the solution for the uncertainty, WT , is obtained with partial differential
equations (for example, Holman (1966), p, 38). We have
Wrp
6U £6C <= C u
«u w(8)
(9)
6U C S
ssc=- u (10)
S W Cs Wu (11)
The final equation is used to solve for the total standard deviation.
Additional and Optional Calculations. The atom weight-percent of the elements
is determined from the oxides by letting
(W f ) v o a
..9994
:.o
(12)
where W = atom weight-percent of element a
W = oxide weight-percent of element a
f = atomic weight of element a a
V = valence of element a a
Cations/unit cell (mineral norms) are calculated for all unknowns in
a given data set on the same basis. Therefore, this option is best used for
runs in which all the unknowns have the same structural formula (e.g., all
pyroxenes, all feldspars, etc.). We have
Tox - To - Ta
115.9994 N ^"
ox
where T = total weight-percent oxygen
T = total oxide weight-percent
C = cations/unit cell
N = number of oxygens/unit cell
RABBIT will calculate the normalized atomic proportions of any three pre-
chosen elements for each analysis. This option is convenient for later construction
of ternary plots and is most effective when a run consists of all feldspars or
all pyroxenes, etc.
Each analysis is printed with complete information on raw counts, counting
statistics, raw analysis, corrected analysis, and atomic proportions. A final
option prints a table of all analyses with the calculated cations/unit cell
underneath .
DECK SET-UP
A ready-to-run deck is shown diagramatically in Figure 2. Note that
the data consists of two parts: 1) the Bence-Albee alpha factors (listed
in Appendix II) and 2) the parameter cards and count data which are described
in the following sections (an example is listed in the second half of Appendix II)
10
Figure 2:
Deck set-up
for program RABBIT.
AL
PH
A
FA
CT
OR
S
/
FIN
AL
JC
L
CA
R
w*
D
RA
ME
JER
C
AR
DS
A
ND
C
OU
NT
>RS
ING
D
AT
A
DA
TA
^ XS
xXX
PR
OG
RA
M
RA
BB
IT
JOB
C
AR
D
AN
D
JCL
C
AR
DS
Table 2: Matrix numbers and valences of oxides and elements which can be
analyzed by RABBIT (adapted from Albee and Ray, 1970).
Matrix Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Oxide or Element
0
co2
F
Na20
MgO
A1203
Si02
P2°5
so3
Cl
K20
CaO
Ti02
Cr203
MnO
FeO
CoO
NiO
Valence
2
2
1
1
2
3
4
5
2
1
1
2
4
3
2
2
2
2
Matrix Number
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Oxide or Element
CuO
ZnO
Rb20
SrO
Y2°3
Zr02
BaO
La2°3
Ce2°3
Pr2°3
Nd2°3
Sm2°3
Gd2°3
Dy2o3
Er203
Hf02
Th02
U00
Valei
2
2
1
2
3
4
2
3
3
3
3
3
3
3
3
4
4
4
12
PARAMETER CARD FORMATS
Columns Name Format Description
Card 1
1-80
Card 2
1-2
3-4
5-7
LABEL
3-2-13
14-15
0,5-0,7
0,8^9
2.0-2J,
M
N
OX
MSTD
NORM(l)
NORM(2)
NORM (3)
ITAB
20A4
12
12
13
F4.1
12
12
12
12
12
Title, any characters may be used
Number of standards plus backgrounds, maximum = 20
Number of elements to be analyzedj maximum =11
Number of unknowns to be analyzed, maximum - 150
Number of oxygens/unit cell (for example, 8.0 for feldspars); use 1.0 if option is ignored
Number of standard elements (for beta- factor calculations); maximum = 11
First element to be normalized for ternary plot; elements are identified by their channel number; program will accept numbers 1-11; use 0 in space 14 if option is ignored
Second element to be normalized for ternary plot
Third element to be normalized for ternary plot
Option to print analyses in tabular form; blank means no y 1 means yes
Card 3
1-8 ROW(1),ATWT(1) A2,F6.3 Element label and atomic weight for element in first caannel (for example, FE55.847); an additional card must be used for elements in eleventh channel
13
Columns Name Format
9-16,..., ROW(2),ATWT(2), A2,F6.3
73-80 .ROW(IO),ATWT(10)
Card 4
1-8 ROW(11),ATWT(11) A2,F6.3
Card 5
1-2 MFLAG(l) 12
21-22
Card 6
1-2
MFLAG(2),..., 12
MFLAG(ll)
VAL(l) 12
3-4,..., VAL(2),..., 12
21-22 VAL(ll)
Card 7
1-16 OXID2(1),OXID1(1) A8,A8
17-32,..., OXID2(2),OXID1(2), A8,A8
65-80 ...,OXID2(5),OXID1(5)
Description
Second channel - 'tenth channel
Eleventh channel; remove this card if 10 or less elements are analyzed
Bence-Albee matrix number (from Table 1); numbers must be in same order as data are taken from microprobe. There must be as many matrix numbers as standard elements (item 5, card 2)
Second matrix number - eleventh matrix number
Valences (from Table 1); must be in same order as data a.re taken from microprobe
Second valence - eleventh valence
Oxide and element headings to be used for table (for example; FEO FE ); must be in same order as data are ta^en from microprobe; last pair of headings must read TOTAL TOTAL; maximum number of heading pairs = 12; remove cards 7-9 if ITAB = 0 (item 9, card 2)
Second pair - fifth pair of headings
14
Columns Name Format Description
Card 8
1-16,..., OXID2(6),OXID1(6), A8,A8
65-80 .-. .,OXID2(10),OXID1(10)
Card 9
1-16, OXID2(11),OXID1(11) A8,A8
17-32 OXID2(12),OXID1(12)
Sixth pair - tenth pair of headings
Eleventh and twelfth pairs of headings
STANDARD CARD FORMATS
Card 1
1-52
53-54
55-56,...,
57-58
Card 2
1-6
7-12,...,
61-66
HEAD
WT(J,1)
WT(J,2),,,»
WT(J,11)
A52
12
12
F6.3
F6.3
Title of standard or background; any characters may be used
Flag for first channel that declareshow data are to be used in calculations; 0 = channel is ignored, 1 = channel is used for background, 2 = channel used for standard
Flags for second - eleventh channels
Oxide weight-percent of element in first channel
Second - eleventh channels
15
Columns Name Format Description
Card S (Data card; must be re-formated for different microprobes)
1-6 DATA(NUM,1) 16 Count data for first channel
7-8 Blank
9-14 DATA(NUM,2) 16 Count data for second channel
15-16 Blank
17-22 DATA(NUM,3) 16 Count data for third channel
23-24 Blank
25-30 JTIME 16 Counting interval (in 10~3 sec)
31-32 Blank
33-38 ITIME 16 Total beam current energy in counts
Card 4 (Data card; must be re-formated for different microprobes)
1-6 DATA(NUM,4) 16 Count data for fourth channel
7-8, Blank
»
57-62 DATA(NUM,11) 16 Count data for eleventh channel
63-64 Blank
65-70 DATA(NUM,12) 16 Total energy in counts for energy- dispersive system (for deadtime
corrections) Cards 3 and 4 are repeated for each count; maximum » 40 counts
Cards 5 and 6 Two blank cards end the count data for the first standard orbackground. Repeat cards 1-6 for each additional standard or background; maximum =20
16
UNKNOWN CARD FORMATS
Columns Name Format Description
Card 1
1-52 NAME(J,I) 13A4 Title of unknown; any characters maybe used
Cards 2 and 3 Data cards; same format as cards 3 and 4 in Standard Card Formats above
Cards 4 and 5 Blank cards; same procedure as cards 5 and 6 in Standard Card Formatsabove
17
STANDARD CARD FORMATS
(End of Run)
All standards and backgrounds are arranged in the same order before and
after the unknowns; card format is the same as in Standard Card Formats above;
the last pair of data cards ends with 4 blank cards.
18
ALPHA (36,36)
ATPRO(12)
ATWT(12)
AVE(12)
BETAC12)
DATA(40,12)
DEV(150,12)
DIFFC40,12)
DV(12)
ENERGY
FLAG
HEAD (13)
IFLAG
INORM
ITAB
ITIME
JFLAG
JTIME
KK
KR(12)
KX
LABEL
L
LI
VARIABLE DESCRIPTIONS
matrix for storage of alpha-factors (element, oxide) listed in Appendix II
atomic proportions of elements in an unknown
atomic weight of elements to be analyzed
average counts for each channel
beta-factors calculated for each element in an unknown
counts for each channel; 40 counts per channel
standard deviation of unknown data for each channel; maximum = 150 unknowns; values in weight percent
difference between the average counts and the individual counts; used in standard deviation calculation, maximum = 40
total standard deviation for each element used in Error in Counting Statistics routine
total counts stimulating EDS system; used for deadtime correction
counter used to limit the number of iterations through Bence- Albee correction routine
heading for standard and background identification; field is 13(A4) or 52 characters wide
holds information in intermediate storage for calculation in Bence-Albee routine
holds information in intermediate storage for calculation in ternary ratio routine
option variable to print data in tabular form-3
counting interval in 1 x 10
holds information in intermediate storage for calculation in Bence-Albee routine
absolute time in 1 x 10" 3 sec for use in drift correction
counter to control entry into various routines
final Bence-Albee corrected weight percent for each element
counter to control the total number of unknowns printed in final output table
title of job being run
number of standards plus backgrounds
counter used to calculate standard data at beginning and end of run; LI = 1 at beginning; LI = L + 1 at end
19
M
MF
MFLAG(12)
MG
MSTD
MZ
Ml(20,12)
M2
N
NAME(150,13)
NORM(3)
MUM
number of elements (channels) to be analyzed
counter used to print final output table
Bence-Albee matrix number (from Table 1)
counter used to print final output table
number of standard elements; used for beta-factor calculation
number of elements plus one; MZ = M + 1
flags that control whether data will be used as standard, background, or ignored; standard = 2, background = 1, ignored = 0
counter to control entry into routine that calculates unknown data
number of unknowns to be analyzed
title of unknown data; maximum = 150; field width = 13(A4)
three cations to be normalized for ternary plot (in mol-percent)
counter whose maximum value equals the number of counts per unknown analysis
OX
OXID1(12)
OXID2(12)
R
ROW(12)
S
SBETA(12)
SDEV(20,12)
SLOPE(12)
STD(20,12)
STIME(20)
SUM(12)
T
TAB1(150,12)
TAB2(150,12)
number of oxygens per unit cell
oxide labels used in final output table
element labels used in final output table
counts in energy dispersive system during one counting interval; used for deadtime correction
element headings for each channel; used to label output
average counting interval in 1 x 10" 3 sec
standard beta factors for each element
standard deviation of standard data for each element (channel); values in weight percent
slope determined by linear equation which measures change of standard value from beginning to end of run; used for drift correction; calculated for each element (channel)
standard value in counts for each element
absolute time when standard data was read from microprobe
standard deviation of count data
average absolute time when data was read from microprobe
element values in weight percent to be printed in final output table
element values in cations per unit cell to be printed in final output table
20
THOLD
TIME(150)
TNORM
TOT
TOTKR
TOTOX
TOTWT
Tl
UNKNWN(150,12)
UKWT(13)
VAL(12)
WT(20,12)
XI,...,X4
XR(12)
- average absolute time of first data read from microprobe; used for drift correction
- average absolute time of all unknown data
- total of three cations in mol-percent for use in calculation of ternary plots
- total atom weight percent
- total oxide weight percent
- total oxygen in weight percent for an unknown
- total oxide weight percent for standards and backgrounds
- counter to control THOLD
- average unknown count data for each element; maximum =150 unknowns
- average unknown data in weight percent for each element; Bence-Albee corrected
- valences of elements for each channel
- oxide weight percent of each element for every standard and background
- used for calculating deadtime correction
- first Bence-Albee corrected values in weight percent for each element of an unknown; stored for final Bence-Albee correction on last iteration
21
ACKNOWLEDGEMENTS
RABBIT was conceived after much urging from G. K. Czamanske. C. R. Bacon
and Julie M. Donnelly encouraged adoption of empirical corrections. Mel Beeson,
C. R. Bacon, and Vie Adams reviewed the manuscript. Sue Kendall kindly typed
the manuscript.
22
REFERENCES
Albee, A. L., and Ray, L. 1970, Correction factors for electron probe
microanalysis of silicates, oxides, carbonates, phosphates, and
sulfates, Analytical Chemistry, 42, pp. 1408-1414.
Amli, R., and Griffin, W. L., 1975, Microprobe analysis of REE minerals
using empirical correction factors: Amer. Mineral., vol. 60, p. 599-606,
Beaman, D. R., Isasi, J. A., Birnbaum, H. K., and Lewis, R., 1972, The
source and nature of deadtime in X-ray counting systems used in
electron microprobe analysis, Journal of Physics E, _5, pp. 767-776.
Bence, A. E., and Albee, A. L., 1968, Empirical correction factors for the
electron microanalysis of silicates and oxides, Journal of Geology,
76, pp. 382-403.
Holman, J. P., 1966, Experimental Methods for Engineers, McGraw-Hill, Inc.,
New York, 412 pp.
23
APPENDIX I: PROGRAM LISTING
/ RELAY
PRINT HEMOTE*
MGfl536 MENLO PAHK
J 3 578
//MG9513FG JOB <971000303«C923«6«20>,'CZAMZNSKE *CLASS«F
//
EXEC FORTGCLG,REGION.GOMSOK
//FORT.SYSIN 00 *
CC PROGRAM »RABHIT» BY FWASER E.
GOFF IS
A FAST, HIGH VOLUME PROGRAM THAT
C REDUCES ELECTRON MIcROPROBE DATA FROM *A« SCALER COUNTS TO
C ELEMENTAL COMPOSITIONS IN
WEIGHT PERCENT.
CC THIS IS
A HENCE-ALBEE VERSION FOR OXIDES* SILICATES, CARBONATES,
C
SULFATES, AND PHOSPHATES.
CC OUTPUT CONSISTS OF
(1> AVERAGED COUNTS CORRECTED FOR BACKGROUND,
C DEADTIME, AND DRIFT,
(2) OXIDE WEIGHT PERCENT,
(3) BENCE-ALBEE
C CORRECTED OXIDE PERCENT,
(4) STD DEVIATION OF ALL COUNTING STATISTICS
C <5)
ATOM WT
PERCENT (6)
ATOMIC PROPORTIONS (71CATIONS/UNJT CELL
C
(8) NORMALIZED CATIONS FOR TERNARY PLOT
CCCDIMENSION UKWT(13>,UNKNWN(ISO*12),STD(20,12).SLOPE(20*12)(ROW(12),
1NAME<150*13) ,HEAD(13) *WT(20»12) OATA(40*12) «AVb(12> *ATWTU2) *
2LABEL(20>,KR(12)*COUNT(2),WAIT(2).STIHE(20),TIME(150)*ATPRO(12),
30IFF(40«12)*SUM(12)*DEV(150*12),DV(12),VAL(12)*M1(20*1?),BETA(12)*
4SBETA(12> ,SDEV(20»12) .MFLAGU2) ,NORM(3> t A
LPHA (36,36) ,XH(12)
DIMENSION TAB1(150*12)*TAB2(1SO*12),0X101(12).0X102(12)
INTEGER DATA*VAL,RREAL'8 KW,OXID1.0XID2
CC
READ IN BENCE-ALBEE ALPHA FACTORS
CDO 4443 J»l,36
READ 4444,(ALPHA(I,J)*I«1,9)
READ 4444*(ALPHA!I,J),I«10»1B>
READ 4444*(ALPHA(ItJ)*I»19,27)
READ 4444*(ALPHA(I,J),1-28,36)
4444 FORMAT(6X,9(F6.3,1X))
4443 CONTINUE
Cc READ IN PARAMETERS AND PROBE DATA
c501
READ 299.LABEL
299
FORMAT (20A4)
READ 300.L.M.N.OX.MSTO.(NORM(I).I«l,3>tITAB
300
FORMAT (212.13.F4.1.512)
IF (L)
500,500,502
502
READ 302.<ROW(I),ATWT(I)»I*1»MSTO)
302
FORMAT (12(A2.F6.3))
READ 506.(MFLAG(I).I.l.MSTD)
506 FORMAT (1212)
READ 305*(VAL(I),I«1,M)
305
FORMAT (1212)
MZ-M+1
IF (ITAB) 303,303*716
716
READ 701. (0X102(1) .OXIOUI) .I«1.MZ>
701
FORMAT (30A8)
303
PRINT 298,LABEL,LtM.N.MSTO.OX
298
FORMAT (iHl,20A4,//.5X,9HNO. STDS«, I2*5A,9HNO. ELEMs*I2i5X*
113HNO. UNKNOWNS-,13.5X.13HNO. STD ELEM»,I2*5X*12HNO* OXYGENS'.
2F4.1,//)
PRINT 297
297
FORMAT (1H .32HSTANOARO COUNTS AND COMPOSITIONS./)
TlaO
Ll»l
M2»0
KK»-1
10 00 5 J"LitL
CC READ STANDARDS AND BACKGROUNDS
CREAD 6tHEAD.(Ml(J.I).I»1»MSTO)
6
FORMAT (13A4.12I2)
READ 301*(WT(JfI).I-l.MSTD)
301
FORMAT (12F6.3)
CC
COMPUTf STANDARD BETA FACTORS
CIF
(KK> 419.104.104
419
00 422 I»1.MSTU
IF (Ml(J.I)-l) 422»4?2»423
423
JFLAG »
MFLAG(I)
SBETA(I)- 0*0
TOTWT »
0.0
00 424 KM.MSTD
IFLAGa MFLAG(K)
SBETA(I)" WT(JiK)
ALPHA(JFLAG*IFLAG)
* SBETA(I)
TOTWT. TOTWT
* WT(J.K)
424
CONTINUE
S8ETA(I)» SBETA(I>/TOTWT
422
CONTINUE
CC
AVERAGING SECTION
C104
00 105 I»!*12
AVE (I)"0,0
SUM(I)«0.0
105
CONTINUE
ENERGY»0
S»0
T»0
NUMaO
109
NUM-NUM*!
READ 110»(DATA(NUM.I).Ial,3>»JTIME.ITIME
110
FORMAT (I6«4(2X«I6)>
READ 111.(DATA(NUM.1).I»4.11).R
111 FORMAT (I6«8(2X«I6)>
IF (DATA(NUM.D)
500*112.113
113
00 114 1-1.12
AVE(I)-AVE(I)*DATA(NUM.I)
114
CONTINUE
S»S*ITIME
tNt«GY"ENERGY*R
T»T*JTIME
GO TO 109
112
NUMmNUM-1
00 115 1-1.12
AVE(I)aAVE(I)/NUM
115
CONTINUE
T»T/NUM
ENERGY-ENERGY/NUM
S«(S/NUM)*0.001
C COMPUTE STANDARD DEVIATION OF COUNTS
CIF
(NUM-1) 63t63.62
62
00 69 K*1.NUM
00 68 I«1.M
DIFF(NUM.I)«<AVE(I)-r)ATA(NUM,n) (AVE(I>-DATA(NUM.I))
' SUM(I)*SUM(I)*OIFF(NUMtI)
68
CONTINUE
69
CONTINUE
00 67 I«1.M
SUM(I)*SORT(SUM(I)/(NUM-1))
67
CONTINUE
GO TO 61
63
00 66 I«1»M
SUM(I)« 0.0
66
CONTINUE
61
IF (Tl>
38t38t39
38 THOLD-T
39
Tl«Tl*l
CC
APPLY OEAOTIME CORRECTION TO ENERGY OISPFUSIVE SYSTEM
C00 160 I»1.M
IF (1-3)
160tl60tl61
161 X1«ENERGY/S
165
X2»(ENERGY/S)»EXP<-X1«7.5E-05)
X3»ABS<X2-X1)
X4»X2»1.0£-05
IF <X3«X4) I62.163tl63
163
X1-X2
GO TO 165
162
AVE(I)"AVE(I) ((ENERGY/S)/X2)
160
CONTINUE
IF (KK)
20t20t21
, CC
PRINT STANDARD INFORMATION
C20
DO 32
I«ltMIF
(MKJtD) 30*30t31
31 STO (JtD»AVE(I>
SOEV(JtI)B(SUH(I)*WT(JtI))/STD(J*I)
GO TO 32
30
STO(JtI)*0.0
SOEV(J.I). 0.0
32
CONTINUE
STIME(J)"T«.THOLD
IF (KK)
46t47t47
46
PRINT 45
45
FORMAT (iHOtSXtSHSTART)
GO TO 48
47
PRINT 49
49
FORMAT (1H0.5X.6HFINISH)
48
PRINT 25»HEAO.STIME(J)
25
FORMAT (1HO«/*5X»13A4*5HTIME**F9.3*/)
PRINT 2?0*(ROW(I)*I«1*MSTO)
220
FORMAT (In
*17X*12(A4*6X))
PRINT 28*(STO(J»I)tlslfM)
28
FORMAT (1H0.11HAVE COUNTSs.12(F10.3))
PRINT 26t(WT(J*I)*I*1fMSTO)
26
FORMAT (1H
.11HWT PERCENT*.i2(F10.3))
PRINT 65»(SOEV(J,I)»I*1.M)
65
FORMAT (IN
illH STO OEV»t12(F10.3))
5 CONTINUE
CC READ IN
UNKNOWN DATA
CKKal
IF <M2>
36i36t37
36
00 42 Jrl.N
READ <»0i <NAME<J«I) il»iii3)40
FORMAT (13A4)
GO TO
104 21
00 41
Irl.M
UNKNWN(JtI)*AVE<I)
OEV(J,I)»SUM(I)
41 CONTINUE
TIME (J)aT-THOLD
42
CONTINUE
KK«0
M2»l
L1»L»1
L»2«L
GO TO
10 37
L»L/2
PRINT 8
8 FORMAT <1H1*21HSTANDARO BETA FACTORSi/)
PRINT 4t (
SBETAU) .IM.MSTD)
4 FORMAT (1H0.11H BETA FACTr,12(F10.3),////)
CC CALCULATE DRIFT IN
STOS BY LINEAR EQUATIONS
C00 215 J«ltL
00 216 I»1.M
IF (STO(Jtl)) 217t2l7*218
00 218
SLOPE(J.I)»<STO(J»L.I)-STD(J.I))/(STIME(J*L)-STIME(J))
^GO TO
216
217
SLOPE(J*I)aO.O
216
CONTINUE
21S
CONTINUE
CC INTERPOLATE BETWEEN STO AND BKGO VALUE.
. CALCULATE RAW COMPOSITIONS
CPHINT 257
257
FORMAT (1HO»31HUNKNOWN COUNTS AND COMPOSITIONSt/)
00 280 K»ltN
00 265 I»1»M
N2al
00 266 J«ltL
IF <SLOPE(J»I>>
267«266t267
267
COUNT(N2)«SLOPE(JtU« TIME<KJ
»STO( J. I) -SLOPE < J. I )
«STIME < J)
WAIT(N2)«WT<JtI>
N2«N2*1
266
CONTINUE
SLOP»(COUNT(2)-COUNT(1))/(WAIT(2)-WAIT(1))
UKWT(I)*
((UNKNKN(K.I)-COUNT(1)*SLOP«WAlT(1))/SLOP)
IF (UKWT(I))
3.265i265
3 UKWTIpr 0.0
265
CONTINUE
CC COMPUTE BENCE-ALBEE CORRECTED COMPOSITIONS
CTOTKRr 0.0
1)0 440 1*1.*
KRU)s (UKMT(D/SHETA(I»
XH(I)» KK(I)
TOTKR* KR(I)
* TOTKR
440
CONTINUE
FLAG" 0.0
444
00 445 1*1»M
BETAU>» 0.0
445
CONTINUE
00 441 J»1,M
JFLAG« MFLAG(J)
00 442 I»1.M
IFLAG» MFLAG(I)
BE
TA
U)"
K
R(I)»
A
LP
HA
UF
LA
G.IF
LA
G)
* 8
ET
A(J
) 4
42
C
ON
TIN
UE
447
8ETA(J)« 8ETA(J)/TOTK«
441
CONTINUE
TOTKR»0.0
00 443 J»1.M
KR(J>« RETA(J)
* XR(J)
TAB!(KfJ)» KR(J)
TOTKRa KR(J)
* TOTKR
443
CONTINUE
TABKK»M*1>» TOTKR
FLAG* FLAG *
1.0
IF (FLAG-2.0) 444«444t446
CC PRINT ANALYSES
C446
PRINT 268i(NAHE(KiJJ)iJJali!3>iTIHE(K)
268
FORMAT (lHOi/i3X
t13A4i2X
( 5HTIME»»F9.3»/)
PRINT 258,(ROW(I>tl»l*M>
258
FORMAT <1H t17Xil2(A4i6X))
PRINT 269i(UNKNWN(Kif).I«liM)
269
FORMAT (iHOtllHAVE COUNTS*.12(F10,3))
PRINT 270*(UKWT(I>ilaliM)
270
FORMAT <1H tllH OXIDE PER»i12(F10.3))
PRINT 292i(BETA(I>tIal*M)
292
FORMAT <1H tllH BETA FACT*i12(F10.3)>
PRINT 408i(KR(I)tl'ltM)
408
FORMAT <1H tllH
B-A CORR.t12(F10.3))
PRINT 272.TOTKR
272
FORMAT (1H
.11HTOT WT PER«iF10.3)
CC COMPUTE TOTAL STO DEVIATION W/ PARTIAL DIFFERENTIALS
C00 64 JaliL
00 431 IMtM
IF (MKJiI)-l) 432*432,433
432
GO TO
431433
DV(I)» <(MT(JtI) * OEV(K.I))/STO(JiI))«»?.0
* ((
UNKNWN(KiI)
1
WT(J,I) SDEV(J.D) /(STO(J»I)
STO(Jtl))) »»2.0
OV(I)« SQRT(DV(I»
431
CONTINUE
64
CONTINUE
PRINT 271,(
nV(D,1=1.M)
271
FORMAT (1H0.11H
STO OEV«,12(FlO.3))
CC COMPUTE ATOM-WT PERCENT, ATOM PROPOR., CATIONS/UNIT CELL (OPTIONAL)
CTOT«0.0
00 409 I«1»M
UKWT(I)* KR(I>
UKWT(I)= <UKWT(I)»ATWTU) >/(ATWT(I)*( ( V
AL ( I > »
IS.9994) /?. 0) )
ATPRO(I)' <UKWT(I)/ATWT(I))
TOTsTOT»UKWT<I)
409
CONTINUE
PRINT 276*(UKWT(I)*I«1*M)
276
FORMAT (1H
»11H AT
WT PER«.12(F10.3))
PRINT 277,TOT
277
FORMAT (1H
»11HTOT ATOMPC«»F10.3)
PRINT 283*(ATPRO(I)*lBltM)
283
FORMAT (1H
tllHATOMlC PRO«.12(F10.5))
IF (OX)
280*280*274
274
TOTOX. <TOTKR.TOT)/(15.9994»OX)
TAB2(K*M«1)« 0.0
DO 291
I«ltM
UKWT(I>« ATPRO(I)/TOTOX
TAB2(K*P« UKWT(D
TAB2(K*M»1)« TAB2(KtM*l)
* UKWT(I)
291 CONTINUE
PRINT 412*<UKWT(I).I«1.M)
412
FORMAT (1H
t11HATOMS/CELL«t12(F10.5))
CC NORMALIZE THREE ELEMFNTS FOR TERNARY DIAGRAMS
CIF
<NORM(1» 280*280*464
O
464
TNORM«0.0
, CO
DO 460 IMt3
INORMB NORM(I)
TNORM. TNORM
* UKWT(lNORM)
460
CONTINUE
IF (TNORM)
280*280*465
465
DO 461
I«l*3
INORMB NORM(I)
UKWT(JNORM) (UKWT(INORM) »
100.0)/TNORM
461 CONTINUE
PRINT 462*( ROW(I)*UKWT(NORM(D) ,I«1,3)
462
FORMAT (1H0.52HNORMALIZED ATOM RATIOS FOR TERNARY PLOT OF ELEMENTS
lt*A2*lH**F5.1*6X,A2*lH«,F5.1*6X*A2*lH**F5.1>
280
CONTINUE
IF (ITAB)
720*720*721
720 60 TO
501 CC
PRINT DATA IN
TABULAR FORM
C721
MG«0
MF« -11
KX« N
710 IF
(KX-12) 708*708.709
708
MF« MF*12
MG« N
GO TO
711709
MF« MF»12
MG« MG*12
711
PRINT 700
700
FORMAT (iHlt//////)
PRINT 718t((NAME(K.JJ)*JJ«1,2).K.MF.MQ)
718
FORMAT (11X*12(2X*2A4))
00 71? I»1.MZ
PRINT 713t 0X101(I).(TAH1(K.I)*K«MFtMG>
713
FORMAT (1H *lXtAMtl2(F10,3))
712
CONTINUE
PHINT 714.OX
714 FORMAT (1HO./.1X.26HCATIONS/UNIT CELLI OXYGFN*.F4.1t//)
00 715 I«1»M2
PRINT 713.
OXI02<I)t<TAB2<K.I)tK»MFtMG)
715
CONTINUE
IF (KX-12)
501.501.717
717
KX. KX-12
GO TO
710 500
STOP
END
/ //oo.srsiN no *
APPENDIX II: SAMPLE DATA LISTING
The following data consist of 1) alpha factors (as described in text
above) and 2) microprobe data. This example is for a run of five unknown
pyroxenes using three standards and one background (assembled from several
compounds as noted on title-card below). The elements were compared against
the standards as follows:
Ca, Mg, Si -- Diopside CPX-1
Fe, Mn Hedenbergite C-9
Al, Ti Amphibole 52-4
Calculated beta factors for amphibole 52-4 included compensation for Na and K.
The elements were read off the microprobe in the order Fe, Ca, Mg, Si, Al, Mn, Ti,
32
ee
oooooooaooo^oooinooooooo-^ooo
oooocoooooooooocooooooooooo
o ooeoooooooooeoooooon
o oooocoooooooooocoo
OO3O9O3OOO939OOO3O3OOOOOOOOO OOO3OOO9OO3OOO3OO
>\>
oooooocooooooooooooooooooooooooo oooooooooooooooo
»>M>M *>»-^- .-Ul »- fc- * *- »-fc- * -
OOOOOGOOOOOOOOOOOO OOOOOOOOOOOGOGOOOOOO
oooooooooooooooooooooooooooooooooooooooooooo
OOOOOOOOOOOO3OOOOOOOOOOOOOOO3O9OOOOOOOOOOOOOOOOOOOO3OOOOOOOOO
oooooooooooooooooooooooooooooooooooooooooooruooooooooooooooooo
OOOO3OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO<COOOOOOOOOOOOOO3OO
ooooooooooooooooooooooooooooooooooo oooooooooooooooooooo
moo UI OB(XIOU)> tjorv <c r\j
34
«-4 «- O - .-4 OO « O.-4 O -* O *+
OOOCOOOOOOOOOOOOOOOOOOOOO
OOOCOOOOOOOOOOOOOOOCOOOOO-*>?O3!
^4 r> ^ -» -i-.«o-H-« n
ooooooooooooooooooooooooooooooooooooooooooooooooooooa3 i
oooooooooooooocooooocooeooooooooocooooocooeceooeococr>
o a: r^ in M MQ. -J- UJ -C (VI
FtMN
FFO
HMO
CATl
CAO
TI02
MGTOTAL
MGO
TOTAL
DIOPSIDE CPX-1
2.92 24
000813
005122
000760
005180
000809
005254
000833
005222
000815
005243
000799
005319
000756
005161
000790
005284
000784
005109
000762
005265
.56 16
011196
OOOH14
011302
OOOR47
0 1 H 34
000828
0 1 1 ) 46
000792
011113
000838
011196
000799
01U27
000795
011034
000828
011250
000810
011122
000837
HEDCNBERGITE
24.29 21
006589
004751
006462
004763
006092
004831
006452
004652
006036
004732
006509
004782
006260
004797
006684
004695
006370
004698
006337
004540
005899
004711
006298
004643
006440
004662
.30 1.
010696
000705
010771
000715
010980
000694
010772
000711
010293
000713
010469
000693
010900
000698
010851
000691
009904
000812
010618
000827
010481
000751
010283
000761
010508
000799
.93 53.93
007520
000138
007618
000160
007592
000152
007445
000146
007564
000139
007734
000155
007530
000150
007460
000140
007752
000145
007749
000131
C-9
06
48.34
000585
000242
000674
000281
000707
000297
000665
000261
000708
000364
000688
000261
000588
000320
000682
000?77
000543
000225
000514
000255
000761
000297
000418
000253
000464
000252
0.66
119230
000339
119243
000313
119258
000310
119271
000311
119287
000295
119299
000304
119314
000354
119329
000320
119342
000312
119358
000310
0.3
3119418
000322
119432
000337
119444
000334
119456
000323
119469
000335
119485
000321
119498
000340
119511
000335
119528
000328
119543
000336
119557
000343
119570
000383
119582
0003b2
0.0 0.23
010061
ooonoo010061
000000
010055
000000
009995
000000
010014
oooooo010021
OOOOOO
009996
OOOOOO
010023
OOOOOO
010055
OOOOOO
010010
OOOOOO
.70 0.0
010044
OOOOOO
010091
000000
010077
OOOOOO
010071
OOOOOO
010071
OOOOOO
010064
OOOOOO
010028
OOOOOO
010072
OOOOOO
010046
OOOOOO
010056
OOOOOO
010025
OOOOOO
010043
OOOOOO
010026
OOOOOO
0.22
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
0.14
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
000000
OOOOOO
si
00.22
OOOOOO
OOOOOO
oooooo
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO2
0.0
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
SI02
2220
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
0000
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
OOOOOO
oooooo
OOOOOO
OOOOOO
AL
0000
021534
021505
021638
021673
021*77
021846
021445
021776
021532
021538
2000
021703
021766
021572
021598
021677
021569
021784
021670
021380
021345
021623
021383
021579
AL203
CO
AMPHIdULF 52-4
26.28 10.50 4.29
39.50 10.10 0.56
3.08
2.24
006889
00494)
001794
119609
010125
004100
001351
000192
000485
000000
OOOOOU
007016
005167
001810
119621
010088
000020?22
1.4
5
00
00
00
000000
02
01
44
004055
006948
00^057
006973
004036
006735
003905
006993
004012
00716]
004035
006980
003978
007040
003978
006803
003966
00117*.005010
001143
005047
001132
005137
001142
005139
0012B9
005217
001300
005024
001357
005020
001420
005142
001325
000197
001882
000201
001905
000185
001748
000167
001724
000190
001913
000212
001842
0001*5
001752
000214
001795
000168
000429
119A34
000449
119646
000464
119659
000502
119671000463
119684
000419
119696
000464
119709
000456
119721000492
000000
010067
000000
01004:i000000
010038
000000
009990
000000
010021
000000
010034
000000
010023
000000
010059
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
oooooo000000
oooooooooooooooooooooooooooooooooooooooooo
020154
020199
020129
019863
020066
019945
020197
020056
020053
BACKGROUNDS OFF Ai_203.
si02* AND C
PX-I 0*0
o.o o.o
o.o o.o
o.o o.o
51 118
59 119800
100235
48
8
22
146
296
o.o o.o
11
11
11
11
10
.0
20100
CR2SI BEGIN ANALYSES OF
SECOND GROUP OF PYROXENES
003507
004727
003462
004594
003420
004721
003438
004791
66004027
004836
004235
004877
004113
004934
004277
004824
67003557
004836
003571
004699
68003621
004797
003751
004809
003747
004771
008773
000929
008858
000961
008734
000910
008690
000904
008470
000886
008105
000900
008093
000828
008080
000838
008529
000905
008451
000873
008704
000861
008109
000902
008414
000975
005273
000153
005254
000172
005487
000176
005397
000161
005324
000164
005275
000179
005310
000172
005182
000160
005655
000161
005655
000142
005575
000171
005692
000188
005612
000179
119818
000398
119831
000405
119843
000354
119856
000419
119875
000359
119889
000352
119903
000385
11Q916
000369
119940'000387
119955
000415
120022
000400
120036
000390
120048
000394
010135
OOOOOO
010050
OOOOOO
010123
OOOOOO
010109
OOOOOO
010081
OOOOOO
010088
OOOOOO
010098
OOOOOO
010091
OOOOOO
010081
OOOOOO
010089
OOOOOO
010057
OOOOOO
010060
OOOOOO
010021
OOOOOO
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oooooooooooo
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oooooooooooooooooooooooo
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oooooooooooooooooo
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oooooooooooooooooooooooo
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oooooooooooooooooo
oooooo
oooooooooooooooooooooooo
oooooooooooo
oooooooooooooooooo
020645
020741
020506
020945
020946
020775
021026
020B13
020657
020549
020643
020741
020819
r-.en
U>
00
C051
20
6*5120 *
26C120
2£9120
£*9120
£99120
199180
625120
02£120
£9C120
0002
BBC 120
2S9I20
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2o
e*ST20
6SOI20
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£05120
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APPENDIX III: SAMPLE OUTPUT LISTING
40
PYROXENES OF
15 DEC 751
15 KV .03 MA
SECOND BATCH
NO. STOS« 4
NO. ELEMa 7
NO. UNKNOWNS*
5
STANDARD COUNTS AND COMPOSITIONS
START
NO. STU ELEMs 9
NO. OXYGENS* 6.0
DIOPSIPE CPX-1FE
AVC COUNTS"
0.0 NT PERCENT-
2.920
STD DEV»
0.0
START
HEDENBEHGITE C-9
FE
AVE COUNTS*
6340.613
NT PERCENT*
24.290
STD DEV«
0.396
START
AMPHIBOLE 53-4FE
AVE COUNTS*
0.0 NT PERCENT*
26.260
STD OEV*
0.0
CA
11162.000
24.560
0.093
CA
0.0 21.300
0.0CA
0.0 10.500
0.0
MG
7596.398
16.930
0.358
MG
0.0 1.060 0.0
MG
0.0 4.290
0.0
SI
6001.824
53.930
0.465
SI
0.0 48.340
0.0SI
0.0 39.500
0.0
TIMK»
AL
0.0 0.660
0.0
TIME*
AL
0.0
0.300
0.0
TIME*
AL
1532.412
10.100
0.130
0.0MN
0.0 0.0
0.0
206.375
MN
317.207
3.700
0.289
371.938
MN
0.0
0.560
0.0
TT NA
0.0 0.230
0.220
0.0TI NA
0.0 0.0
0.140
0.0TI
NA
527. ?26
3.080
2.240
0.183
K
0.2?0
K
0.0K1.450
START
BACKGROUNDS OFF AL203. SI 02,
AVE COUNTS*
NT PERCENT*
STD DEV*
FINISH
OIOPS10E
AVE COUNTS*
UT PERCENT*
FE
51.000
0.0 0.0
CPX-1FE
0.0 2.920
CA
118.000
0.0 0.0C
A
11161.250
24.560
AND CPX-1
MG
59.000
0.0 0.0MG
7550.414
16.930
SI
625.219
0.0 0.0SI
599?. 934
53.930
TIME"
AL
937. 8?9
0.0 0.0
TIMF*
AL
0.0 0.660
506.938
MN
166.573
0.0
0.0
2801.063
MN
0.0 0.0
TI
339.991
0.0 0.0TI
0.0 0.230
NA
K
0.0
0.0
NA
K
0.220
0.220
sin DEV«
FINISH
0.0
0.2^0
0.102
0.4810.0
0.0
FINISH
0.0
HEDEN8FRGITE C-9
FE
AVE COUNTS*
6402.426
MT PERCENT*
24.290
STO DEV«
0.1 OS
FINISH
AHPHIBOLE
AVE COUNTS*
WT PERCENT*
STO OEV*
52-4FE
0.0 26.280
0.0
CA
0.0 21.300
0.0CA
0.0 10.500
0.0
MG
0.0 1.060
0.0MG
0.0 4.290
0.0
SI
0.0 48.340
0.0SI
0.0 39.500
0.0
TIME*
AL
0.0 0.300
0.0
TIME*
AL
1531.033
10.100
0.125
3015.813
MN
324.486
3.700
0.66S
3196.000
MN
0.0 0.560
0.0
TI
0.0
0.0 0.0TI
527.721
3.080
0.171
NA
0.140
0.0
NA
3.340
1.450
BACKGROUNDS OFF AL203i SI02.
AVE COUNTS*
WT PERCENT*
STO OEV*
FE
50.000
0.0 0.0
CA
120.000
0.0 0*0
AND CPX-1
MG
60.000
0.0 0.0
TIME* 3356.938
SI
627.501
0.0 0.0
AL
936.688
0.0 0.0
MN
167.714
0.0 0.0
TI
341.132
0.0 0.0
NA
0.0
0.0
CM
st
STANDARD BETA FACTORS
BETA FACT-
1.110 1.114
UNKNOWN COUNTS AND COMPOSITIONS
1.14S
1.070
1.2011.110
1.057
1.720
1.058
CR2SI BEGIN ANALYSES
AVE COUNTS'
OXIDE PER-
BETA FACT-
B-A CORR-
TOT WT
PER*
STO OEV-
AT WT
PER-
TOT ATOMPC*
ATOMIC PRO-
ATOMS/CELL*
NORMALIZED
66
AVE COUNTS-
OXIDE PER-
BETA FACT*
B-A CORR*
TOT WT
PER*
STO DEV-
AT WT PER» TOT ATOMPC-ATOMIC PRO-
ATOMS/CELL-
NORMALIZED
67
AVE COUNTS-
OXIDE PER-
BETA FACT-
B-A CORR-
TOT WT
PER*
STD DEV-
AT WT
PER-
TOT ATOMPC-
ATOMIC PHO»
FE
3456.750
13.137
1.130
13.37b
97.674
0.083
10.396
56.727
0.18616
0.43643
ATOM RATIOS
FE
4163.000
15.858
1.127
16.101
99.323
0.504
12.516
57.906
0.22411
0.51943
ATOM RATIOS
FE
3564.000
13.546
1.130
13.794
97.896
0.038
10.722
56.764
0.19199
OF SECOND
CA
8763.750
19.227
1.091
18.859
0.187
13.479
0.33630
0.78843
GHOUP OF
MG
5352.750
11.905
1.215
12.640
0.114
7.623
0.31356
0.73511
FOR TERNARY PLOT OF
CA
8187.000
17.944
1.091 17.579
0.272
12.564
0.31347
0.72657
MG
5272.750
11.726
1.230 12.597
0.234
7.598
0.31250
0.72431
FOR TERNARY PLOT OF
CA
8490.000
18.618
1.094
18.274
0.121
13.060
0.32586
MG
5655.000
12.587
1.215
13.360
0.001 8.058
0.33143
PYHOXENES
SI
5385.453
47.763
1.082
48.309
O.b59
22.58?
0.80401
1.88496
TIME-
AL
1059.190
2. 06? 1.192
2.047
0.167
1.083
0.04015
0.09412
ELEMENTSlFEt 22.3
SI
5574.625
49.663
1.081 50.186
0.454
23.459
0.83525
1.93592
TIME-
AL
988.321
0.858
1.200
0.857
0.190
0.4S4
0.01681
0.03897
ELEMENTSIFE. 26.4
SI
5451.141
48.425
1.082
48.963
0.870
22.887
0.81491
TIMF-
AL
1016.479
1.337
1.196
1.331
0.149
0.705
0.02611
543.938
MN
1H9.305
0.555
1.133
0.566
0.061 0.439
0.00798
0.01872
CA. 40
602.688
MN
193.?55
0.650
1.129
0.661
0.118
0.51?
0.00932
0.02161
CA. 36
654.438
MN
173.225
0.161 1.133
0.164
0.157
0.127
0.00231
TI
450.670
1.820
1.091 1.878
0.169
1.126
0.02350
0.05510
.2 MG.
37.5
TI
419.435
1.306
1.085
1.341
0.019
0.804
0.01678
0.03889
.9 MG.
36.8
TI
458.502
1.949
1.090
2.010
0.116
1.205
0.02515
CO si-
ATOMS/CELL"
0.44807
0.76050
0.77349
1.90186
0.06094
0*00540
0,05870
NORMALIZED ATOM RATIOS FOR TERNARY PLOT OF ELEMENTSIKEt 2*.6
CAt 38.4
MGt 39.0
68
AVE COUNTS"
OXIDE PER"
BETA FACT-
B-A CORR-
TOT WT
PER-
STD OEV-
AT WT
PtR-
TOT ATOMPC-
ATOMIC PRO-
ATOMS/CELL-
NORMALIZED
69
AVE COUNTS-
OXIDE PER-
BETA FACT-
8-A CORrt-
TOT WT PER-
STD OEV-
AT WT PER-
TOT ATOMPC-
ATOMIC PRO-
ATOMS/CELL-
FE
3706.333
14.090
I. 129 14.327
99.832
0.191
11.137
58.040
0.19942
0.45806
ATOM RATIOS
FE
3486.667
13.240
1.130
13.483
99.390
0.604
10.481
57.584
0.18767
0.43093
CA
8409.000
18.438
1.092
18.072
0.013
12.916
0.32226
0.74025
MG
5626.312
12.525
1.220
13.344
0.039
8.048
0.33103
0.76038
FOR TERNARY PLOT OF
CA
8750.000
19.196
1.094
18.843
0.798
13.467
0.33601
0.77157
MG5401.664
12.022
1.213
12.743
0.178
7.685
0.31611
0.72586
SI
5486.188
48.779
1.084
49.425
O.?3b
23.103
0.82258
1.88949
TIME-
AL
1044.807
1.819
1.197 1.813
0.503
0.959
0.03556
0.08167
ELEMENTSIFEt 23.4
SI
5480.316
48.722
1.083
49.305
0.008
23.047
0.82060
1.88428
TlMf.
AL
1086.362
2.526
1.190 2.502
0.117
1.324
0.04909
0.11271
742.250
MN
205.298
0.941
1.131 0.959
0.005
0.743
0.0135?
0.03105
CAt 37
812.563
MN
183.352
0.405
1.133
0.414
0.057
0.320
0.00583
0.01340
TI
451.808
' 1.838
1.088
1.891
0.005
1.134
0.02367
0.05437
.8 MGt
38.8
TI
463.728
2.034
1.091 2.099
0.219
1.258
0.02626
0.06031
NORMALIZED ATOM RATIOS FOR TERNARY PLOT OF ELEMENTSIFEt 22.3
CA* 40.0
MGt 37.6
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