A complete analysis of one or two unknowns using BRACKET-8 takes about 25 min for 16 runs. A faster sampler and a line printer might improve the situation somewhat, especially when there are many samples. Nevertheless, this system has been very reliable; and we have found that, when the computer is used in a closed-loop mode to control sampling, the tedious process of sample handling is eliminated and multiple runs are encouraged. Furthermore, when sampling is automatic and random, the effect of instrumental drift can be minimized by averaging many analyses. This technique combined with computer integration techniques results in a considerably improved system. A limited number of assembly language listings of these programs are available.
ACKNOWLEDGMENT The authors thank Roger Anderson for his many helpful programming suggestions, ~~~d~~ J~~~~for his work on software modification and noise reduction, L. B. Rogers for originally suggesting the Bracket-8 program, and Robert Lim for his work on the atomic absorption of trace platinum. RECEIVED for review March 31,1970. Accepted July 27,1970. This work was performed under the auspices of the U. S. Atomic Energy Commission. Reference to a company or product name does not imply approval or recommendation of the product by the University of California or the U. S. Atomic Energy Commission to the exclusion of others that may be suitable.
Correction Factors for Electron Probe Microanalysis of Silicates, Oxides, Carbonates, Phosphates, and Sulfates Arden L. Albee and Lily Ray Division of Geological Sciences, California Institute of Technology, Pasadena, Calif, 91 109
Calibration curves for electron probe microanalysis element A in the binary AO-BO relative to that of element of binary oxide systems can beclosely described by the A in the end member oxide AO, and ~ A A Bis a constant. A ~a~ A ~(1 ~- ~*AB)C*AB, linear expression C A * ~ / K = Values of the correction parameter, @*AB, greater than 1.0 where CAAB is the concentration of oxide A in oxide generally means that absorption dominates in the correction binary AB relative to pure oxide A and K*ABis the background corrected intensity of a characteristic radiafactor, whereas values less than 1.O indicate that fluorescence tion line of the cation in oxide A in the oxide binary AB dominates. relative to that of pure oxide A. The binary correction The correction factor for a given composition in a multiparameter, A AB, can be extended to multicomponent component system, relative to the pure end member, which systems by using the concentration-weighted average is most convenient for most applications, is defined as of the binary parameters. Correction parameters have been calculated for 36 elements commonly ocP*ABC.. . n where: curring in natural silicates, oxides, carbonates, phosphates, and sulfates at 15 and 20 kV accelerating poCAABC . , .n tential and 52.5' and 38.5O take-off angle. P*ABc... n =
+
..n
THECORRECTION FACTORS introduced by Bence and Albee ( I ) are especially convenient for silicate mineral analysis and were used by at least four groups analyzing the Apollo XI lunar samples. Their use has been limited by the lack of factors for many common elements and by their restriction to an accelerating potential of 15 kV and a take-off angle of 52.5". This paper presents correction factors for the common elements of silicates, oxides, carbonates, phosphates, and sulfates and for several accelerating potentials and take-off angles. Details and tests of the technique are given in the original paper ( I ) .
and is calculated from the correction parameters by:
P.'ABc.. . CAABC . . .n a A A A CAABC..
=
@*AB
+ (1 -
@*AB)
C*AB
(1)
where C*ABis the concentration of oxide A 0 in binary AO-BO relative to the end member oxide AO, KAAB is the background-corrected intensity of a characteristic radiation of (1) A. E. Bence and A. L. Albee, J. Geol., 76, 382-403 (1968). 1408
e
naAAB
.
+
.CnABC . . .n e A A n
+ PABC . . . + . ..C'ABC... n
n
(3) Hence, the correction factor has a linear dependence on the concentration of all elements in the sample. The basic equation for converting observed counts to actual concentration is:
ANALYTICAL FORM OF CORRECTION PARAMETER Typical oxide binaries show a nearly linear relationship for C / K us. C :
+ CBABC.. .
(4)
where the subscripts u and ws refer to unknown and working standard, respectively, k*, and k4wsrefer to observed counts for the unknown and working standard, respectively, and P A w s is the correction factor for the working standard. In practice the calculation of p"uis iterated using a matrix of @values in Equation 3 and using K ? , as the first approximation of C.ku; each successive value of CA, and the final value are calculated from Equation 4 using the successive and final values of P% [see example in (I)].
ANALYTICAL CHEMISTRY, VOL. 42, NO. 12, OCTOBER 1970
CALCULATION OF CORRECTION PARAMETERS Correction parameters, relative to the simple oxides, were calculated for K,, La, or M, lines of the elements most commonly encountered in the electron microanalysis of natural silicates, oxides, phosphates, carbonates, and sulfates. A FORTRAN program was written, based in part on the MAGIC program of Colby (2), that calculates corrections for almost any number or combination of elements (K,, Lia U92; K,, Nelo U B ; La, L,, Cazo U92; Ma, A+, La6, + Ndso, Sne2-+ Big3,Thgo Ug,). Our program uses the generation factor of Duncumb and Reed (3), the absorption correction of Philibert (4,as modified by Duncumb and Shields (5) and Heinrich (6), and the characteristic fluorescence correction of Reed (7). These corrections are essentially those used and discussed in detail by Colby (2), Goldstein and Comella (8),and Sweatman and Long (9). Using this basic correction program as a sub-routine, correction factors relative to the pure elements (fE) were calculated for a characteristic emission line of each of 36 elements in all the simple oxides and in all molecular 1 :1 combinations of the simple oxides. Correction factors for the 1 : 1 combinations relative to the simple oxides ( p - 4 A : B) were calculated by :
-
-
-
-+
1 .oo
C/ K 0.90
0.84, CALCULATED FROM
0.80
0.72, CALCULATED FOR NiO 0.70
NiO
20
40
I 80
60
FeO
C( WT. O h ) Figure 1. Calculated correction factors for the NiOFeO system, which exhibits pronounced deviation from linearity of CFeO/KFe us. CFeO
1.7
1I -f.67,
The correlation parameters (@,“AB) for the binaries were then calculated using the linear relationship of Equation 1.
I
I
I
I
CALCULATED FOR MgO FROM Mg0:AIzO: 4.563, MEASURED FROM
4.5
where C A A : is the oxide weight concentration for the molecular 1:1 combination of oxides A and B. In the original paper ( I ) a A A B was evaluated at the end member concentration since C A A B I K A A B a - 4 A B as C A A B -+ zero. However, as illustrated in Figures 1 and 2, evaluation of QAAB from the 1 :1 composition reduces the error due to any deviation from linearity in the compositional range of most interest, Le., where oxide A is less than 50 molecular per cent. The strong fluorescence of F e by Ni results in a pronounced deviation from linearity in the FeO-NiO system (Figure l), but al’eFeO-NiO extrapolated from the 1 :1 composition, is a reasonable value for FeO less than 50 molecular per cent, particularly in complex samples. Figure 2 shows a smaller, and more typical, deviation from linearity in the Mg0-Al2O3 system. In this case the deviation from linearity is very small in the range of composition of natural samples.
-
DISCUSSION Tables I-IV present correction factors for 36 elements relative to their simple oxides for acceleration potentials of 15 kV and 20 kV for take-of€ angles of 52.5” (A.R.L.) and 38.5” (M.A.C. and Hitachi). Others can be provided upon (2) J. W. Colby, Adoatt. X-Ray Anal., 11, 287-305 (1968). (3) P. Duncumb and S. J. B. Reed, Nat. Bur. Stand. (U.SJ, Spec. Publ. 298, 133 (1968). (4) J. Philibert, “X-Ray Optics and X-Ray Microanalysis,” Academic Press, New York, N. Y., 1963, p 379. (5) P. Duncumb and P. K. Shields, “The Electron Microprobe,” John Wiley, New York, N. Y.,1966, p. 284. (6) K. F. J. Heinrich, ibid., p 296. (7) S. J. B. Reed, Brit. J. Appl. Phys., 16, 913 (1965). (8) J. I. Goldstein and P. A. Comella, Goddard Space Flight Center, X-642-69-115. (9) T. R. Sweatman and J. V. P. Long, J. Petrology, 10, 332 (1969).
C/K
1.4 L
1.3
1.2
1.I
.io . .-
CALC. 1.03 2.1.023 MEAS:
Figure 2. Calculated and measured correction factors for the Mg0-A1203 system
request. It should be emphasized that the use of suitable corrections permits electron microanalysis using a small suite of carefully-characterized natural minerals or synthetic simple crystalline phases as standards. The advantages of these parameters is that the calculation procedure is much simpler and can be performed by desk calculator or by the small computers coming into general laboratory use. In contrast the program used to calculate these factors required a core memory of 120,000 bytes on an IBM 360-75. Bence and Albee ( I ) , Knowles et al. (IO), and the experience
(10) C. R. Knowles, J. V. Smith, A. E. Bence, and A. L. Albee, J . Geol.,66,439 (1969).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 12, OCTOBER 1970
1409
Table I. Correction Factors for 15 kV Accelerating Potential and 52.5" Take-Off Angle (A.R.L. Microprobe). K, for C to Zn, L, for Rb to Hf, M, for Th and U. Factors in the First Column Are for Both 0 and H 2 0
____ 0 C F NA MG AL S I P S -_ CL K
C02
1 . 1 5 -13131.20 1.18 1.21 1.18 174-1-1:60 1.69 1.74 1.33__1.51__1.59__1~63 1.27 1.42 1.48 1.51 1.13 1.18 1.18
__
-
-
___ __
~
OX I O - N O R M A L I LEO A-F AC TORS
T l 0 2 C R 2 ~ 0 3 MNO 9.36 1.67 1.86 5.25 3.12 4.18 9.74 7.20 8.70 2.39 1.65 1.83 2.14 1.26 1.34 1.50 1.63 1.14--1.18 1.28 1.37 1 ~ 1 ~ 0 01.06--1.121 . 0 5 -l-21 1.21 1.24l~Z5-1~28-1~00--1.01 1.06 1.04 1.03 1.09 1.12 1.11 1.13 1.13 1.15 1.26
0 1.00 1.15 5.73
__
-~
___-__
mmt
TAKE O F F Miu a i L 5 1 5 K E V s K A FOR C TO ZNILA FOR RE TO H F t M A FOR T H L U
3.24 4.87 1.48
1.15 1.07 ~ 9 0.98 0.95 1.00
CAO 8.14 3.10 5.75
FEO
COO
2.04 6.07 2.32 2.62 1.76
2.1: 2.43 6.96 8.17 2.34 2.50 2.86 3.18 l T - 2 3 7 1.53 1.651.27 1.35 1-16 1.22 1-05 1.10' 1.05 1.10 0.96 0.99
1.46
1.23 1.13 1.04 1.05
0.96
NIO
-1.12-1.13-1~08-1.10 l . l 2 ~ _ l . 0 ~ ~ _ 1 ~ 0 6 ~ 1 . 0 3 1.04 0.98 1.00 1.17 1-18 1.13 1.14 1.16 1.11 1.09 1.07 1.08 1.06 1.04 1.18 1.19 1.13 1.14 1.17 1.11 1.09 1.06 1.07 1.05 1.08 RB 1.41 1.30 1.27 1.32 1.18 1.261731.32 1.38 1.40 1.47 1.51 1-60 ___._ SR 1.34 -1.24--1.21-_1.25 1.13 1.20 1.26 1.25 1.30 1.32 1.38 1.41 1.49V 1-28 1.23 1.56 1-18 1.21 1.09 1.16 1.21 1.19 1.23 1.24 1.29 1.31 1.38 ZR 1.24 1.19-1~.23___136__1.42_-_1.~4-~.49-1.~5 1.17 1.07 1.12 1.18-1~151.~18-_1.19 1.23 1.25 1.31 EA 1.46 1.42 1.39 1.42 1.47 1.42 1.46 1.42-1~.~4~5~--~1~43-1.461.49 1.29 1.21 1.19 1.21 1.19 1.23 LA 1.42 1.39 1.36 1.40---_1~44 1.40 1.43 1.39 1.42 1.39 1.41 1.45 1.27 1.23 1.16 1.18 1.16 1.20 CE 1.42 1.39 1.36 1.40 1.43 1.39 1.42 1.39 1.41 1.38 1.40 1.43 1.27 fZZ3-Tl6l.l~m15 1 19 -P R 1.42 1.39_1-.._3 5_-1.3 9. - 1 ~ 4 3 - -1 ._39-__1.42_ -1238 1m 4 1 1.36 1.3 8 1.42 1 51.23---1 y18- -1a-I 71.14---1.18 NO 1-44 1.41 1.37 1.41 1.45 1.41 1.44 1.40 1.43 1.37 1.39 1.43 1.36 1.25 1.20 1.18 1.16 lF19SH 1 . 4 7 1 ~ 4 4 _ _ _ 1 ~ 4 1 - 1 > ~ 4 4 _ -1.-48 1.441.47 1.43 1.46 1.40 1.41 1.45 1.38 1.28 1.24 1.25 1.18 l.2iG - 01 -5:-2 1-49 1.45 1.49 1.52 1T48 1.51--1-;47 1.50 1.42 1.44-1~~48-?~40-1~~39~--1;28'1.29 -1725-1724 OV 1.54 1.51 1.48 1.51 1.55-1.51 1.53 1.50 1.52 1.44 1.46 1.49 1.42 1.40 1.30 1.32 1.29 1.31 ER 1.57 1.54 1.50 1.53 1.57 1.53 1.56 1.52 1.54 1.46 1.*71.511.43-.411.37 1.3L 1.31 1.34 HF 1*_58--1.-55--1.51_ 1.54 - 1 2 5 8 1.54 1.56-1.52 1.55 1.46 1.47 1.51 1.43 1.40_-1137-1.38 1.36 1.35 TH 1.63 1.57 1.56 1.60 1.67 -1.61-1.66 1.61 1.67 1.77 1.43 1.50 1.41 1.37 1.35 1.38 1.35 1.41 U 1.65 1.58 1.5_7-_116_1_ 1.67 1.60 1.66 1.60 1.66 1.74 &44 1.51 1.42 1.37 1.35 1.38 1.35 1.40 CU ZN
1.19 1.19
1.17 1.18 1.34 1.27
1.14
1.15
1.141.19 1.20
A4R.L. PRGSE TAKE C F F bNGLE OF 5 2 . 5 DEGREES 1 5 K E V v K A FOR C TO Z N ~ ~ ~ ~ ~ F O R ~ R B - T O - HFFO~R~ Tf iHA C U
-___
~
CUO O -p26:0-
_C ~ F NA
MG
9.50 _
2.51
2.98 2.18
...
O X I D E -NORMALIZE0
~
A-FACTORS ~__~______-.___
ZN_q__RB_ZO S R J J203 -LRK2 -8AO2;56--i* L A Z O5 37 Z .CkE62- 0- 3 -2.86 5.72--6.26 6.49 7.01 1_1 . 1 1_L l A 8 2 18.14 14.66 16.34 7.38--7.07 7.44 2.62 3.514.06--4~454r62.12 2.27 2.32 2~45--1._20 -1.32 1.38 1.48 -1.95 1.96 -2.-10 2.36 0.93 1.00 1.05 1.11 1-72 1.74 1.58
of the labs using the Bence-Albee factors have indicated that results with 1-2% error are readily attainable. Most of this error is attributable to factors other than the correction procedure when standards reasonably close in composition to the sample are used, i.e., silicate standards for silicates, and phosphate standards for major elements of phosphates, etc. With such a choice of standards, most of the effect of 1410
0
____
~-
~
~
PR203 -.- -NG2J03 SH203 GO203 OYZJ03 E R Z 0 3 HF02 THO2 UOZ 2.76 2.832.-99--3.183. 35--3:5-lp4T03 7.57 8.23 7.04 8.21 8.97-9.98 10.82 11.68 14.99 35.33 39.59 2.38 2.40 2.46 2.53 2.60 2.68 3.05 4.84 5.17 2.19 2.26__ 1 ~ 0 0 ~ 1 ~ 0 1 ~ ~ _ 1 ~ 1.14 0 3 ~ ~1 -16 5 ~ 0 1.73 4 l.b4 1.52 1.60 1.69 0.83 0.84 0.89 1.20 1.25
any errors in the correction factors cancels out. Table V compares measured and calculated values of @factors for selected elements. The measured values are based on the data used for the original Bence-Albee factors plus two to five additional sets of measurements made since then. The phases used are listed in Table V. Factors for the Mg0-A1203-Si02 and Ca0-AlZO3-SiOZ ternaries were calcu-
ANALYTICAL CHEMISTRY, VOL. 42, NO. 12, OCTOBER 1970
Table 11. Correction Factors for 20 kV Accelerating Potential and 52.5' Take-Off Angle (A.R.L. Microprobe). K, for C to Zn, L, for Rb to Hf, M, for Th and U. Factors in the First Column Are for Both 0 and HzO __
A.R.L. PROBE TAKE OFF ANGLE 0F 52.5 n E G L i E L . - 2OKEVsKA F O R C T O ZNtLA FOR R8 T O HFtMA F O R TH G U
~
-
@Xl@E-NORMALIZ.~O-~F~CTOR_S_~ 0
C
F NA
MG AL
SI P S CL K CA TI CR MN FE CO NI CU ZN R8
SR Y
F
0 1.00 1-18 8.97 1.98 1-46 1.24
C02 2.17 1-00 8.26 1.76 1.29 1.14 la?? 1.05 1.09 1.03 1.04 1.0U 1.12 1.04 1.06 1.04 1.03 1.01 1.07 1-05 1.09 1-07 1.12 1.11 1.11 1-09 1.14 1.12 1.11 1-09 1.14 1.16 1.15. 1.17 1.36 1.28 1.29 1.21 1.24 1.18 1.20 1.14 1.37 1.39 1.34 1. 3 1 1.33 1.30 1.33 1.30 1-31. 1.31 1.ql 1.34 l.*l1.38 1.44 1-61 1.46 1.43 1.47 1-44 1.56 1-40 1.56 1.50
1.09 1.55 1-00 2.52 1.62 1.35 1.18 1.12 t.05
1-11 1.04
1.00 1-04 1-05
1.08 1.07 1.05 1.07 1.12 1-12 1.38 1.31 1.25 1.2;
-____________ZR RA LA CE PR
_
NO SH GD
DY ER
HF TH
U
_
_
tun
_
1.31
_
1s 2 P 1.27 1.27 1.Ze 1.3: 1.35 1.37 1.39 1-41 1.49 1.49 _
0
3.68
ZNO 4.12
QR20 9.56
F .NA
5.57 1.L6 1.09
HN
3.77 3.57 3.?? 4.18 2.94 3.23 2.38 2.20 1.82 1.70 1.55 1-47 1.26 1.32 I.?? 1.26 1.04 1.06 0.070.90 0.95 0.95 0.91 0.92 0.90 0.92
FE
0.86
0.88
CO NI CU ZN RB SR Y ZR
0.84 0.02 1.00 1.00 1.81 1.68 1.54 1.45 1.14 1-11 1-10 1.09 1-10
0.66 0.80 0.55
1.11 1.13 1-14 1-20 1.22 1.35 1.33
1.11 1-13 1.14 1.15 1.20 1.38 1.35
NA20 1.59 3.42 3.02 1.00 2.27 1.75 :.46 1.31 1.20 1.23 1.10 1.05 1.08 1-08
----
SI02 P2O5 S0_3---CL K2O CAO T!O2 CP203 H-NO _-FEO -_C@O--_NIO2.01 2.57 2.96 3.34 9.30 12.62 13.43 16.01 2.08 2.42 2.70 2.95 3.35 4.92 7.62 10.32 11.89 47.06 3_1_9 3.78 3.88 5.44 6.97 9.55 11.35 4.43 6.23 7.05 7.61 4.68 7.62 9.20 12.17 15.24 17.22 3.21 3.27 3.52 1.26 1.51 1.59_-1.69 1.30-_1.~3_-_1~9?__2.29 2.R1 3.18_-3.56-_3,9.6 -4.461.00 1.15 1.18 1.24 1.00 1.25 1.40 1.56 1.82 2.03 2.24 2.45 2.72 1.92 1.05 1.07lr_11-0.94--1.12 1.22 1.31 1.48__1_162__1.76-_1.89__2.07. l.58 1.00 1.00 1.03 0.90 1.02 1.10 1.15 1.25 1.34 1.43 1.51 1.64 1.40 1.53 1.00 1-02 0.91 -1.00 1.06 1.08 1.161.21 1.28 1.33 1.43 1.27 1.36 1.40 1.00 0.89 0.96 1.01 1.02 1.07 1.10 1.15 1.18 1.25 1.29 1,36___1239_ 1.431.00 1 ~ 0 3 _ ~ 1 . 0 8 ~ 1 , 0 7 ~ ~ 1 ~ 1 0 ~ 11. 1. 51_ _1_~1 . 1 7 1.23, 1.15 1.18 1.18 1.21 1.44 1.00 t.00 0.98 0.99 0.99 1.01 1.02 1.06 1.09 1.12- -lL12 __1214 - 1 . 2 C 1.35_,.OO 0.93 0.94-0.93-0.Q6-_-0,95 --0.99 !.11 1.11 1-13 1.12 1.13 1.19 1.23 1.26 1.00 0.92 0.91 0.94 0.94 0.97 1.12 1-10 ?.12 1.11 1.12 1.13 1.16 1.18 1.14 1.00 0.95 0.90 0.90 0.03 1.11 1.lh 1.13 ~ - 1 5 1.13 1.14 1.13 1.16 1.18 1.14 1.03 1.00 0.99 0.89 0.92 1.10 1.13 1.12 1.13 1 . ~ ~ ~ ~ 1 2 ~ 3 ~ 1 1 1 01.15 ~ l . 11.11 3 1.13-0.99 1_.00-__0.95 0.88 1.12 1.15 1.14 1-15 1.13 1.14 !.il 1.13 1.16 1.11 1.12 1.11-1.02 1;00---0;99' 1.09 ?.12 1-11 1.12-_1.10 1.11_-_1.-081.09 1.12 1-07 l.08___-1206--l.08 0.98---1_.001-14 1.17 1.15 1.17 1.15 1-16 1.11 1.13 1.16 1.11 1.11 1.09 1.11 1-10 1.04, 1.14 1.17 1.16 1-17 1.15 1.16 1.11 1.13 1.15 1.10 1.10 1.08 1.10 1.08 1.121.64 1.76 1.86 1-21 1.19 1-24 1.07 A.19 1.28 1.31 1.42 1.47 1.56 1.63 1-76 1.54 1.65 1.73-1.?6_-1.14 1 . 1 8 _ _ 1 ~ 0 3 _ ~ ~ 1 ~ 1 4 ~ - 1 ~ 2 2 ~ 1 ~ 2 ~8 3.1~- _ 1 _ , __1_.46-__1._52 33_ __ 1.631.44 1-53 1.F 2.66 1-11 1.15 1.01 1.10 1.17 1-16 1.25 1.29 1.36 1.41 1.51 1.38 ;.46_l.5?___l158_1_.P9_ _1.1?--OL99 -1.07-1.14 1.14__1~20_11223~~1.~O__1.34~~~443~ 1.33 1-39 1.35 i.39 1.35 1.38 1.41 1.45 1.49 1.21 1-16 1.14 1.16 1.15 1.19 1.3 1 1 .3 6 1.33p1.361y3 -3 113 5 ~ ~ 1 ~ 3 ~ ~ ~ 1 ~ 0 ~ --12 ~ 1_2_? 1 ~1-6- 1 ~ 1.30 L.35 1.32 1.35 1.32 1.35 1.34 1.38 1.41 1.19 1.16 1.11 1.13 1.11 1.15 1.25 1.34 1.3: -1-.34--7.31-1 . 3 3 --1.32 1.35 1239 1.33__?.1~_1.12~_1.12 1.1-Op___l.131.3i 1.36 1.33 1.36 1.32 1.35 1.33 1.35 1.39 1.33 r.17 1.14 1.13 1.10 1.14 1.33_i.38-_1135___1.38_ 1.341.37-_1.?3 _1.36-_1.39 __1.33 -_1_.20-1.17 - 1.18- - 1.12 --1.161.37 1.42 1.38 1-42 1.37 1.40 1.35 1.37 1.41 1.35 1.36 1.20 1.22 1.18 1.18 1.39 1-44 1-41 1.4' 1.40 1.42 1.36 1.38 1.42 1.35 1.36 1.22 1.24 1.21 lL24 1.41 1.46 1.43 1.46 1.41 1.44 1-57 1.39 1.43 1.36 1.36 1.34 1.25 1.23 1.26 1.42 :.47 1.43-1.46---12_42 1.45--1..37-__1239 ____1.43--,lL36-1.341.32._-1.?4.1.33. 1.28 1.53 1.61 Le57 1.63 1.59 1.65 1.86 1.34 1.41 1.34 1.32 1.32 1.35 1.34 1.40 1.52 1.60 Z.55 1.61 1.56 k.62 1.79 ..-la34 1-42 1.34 1.31 1.31 . 1.34.-1.3_2 __!.38_
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p
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Y203 10.69 '.9$ 7.22 7.69
.
ZRO: H& . O _ _ L A 2 0 3 - _ C E 2 0 3 - PR?O'__ND?O3 SM2C3-GD_Z03-~OY203-E4_20?-HF02 -TH22 ---.UO2 11.78 7.74 3.77 3.94 4.12 4.26 4.57 4.96 5.29 5.62 6.60 12.71 14.03 4.40 '0.L5 10.04 10.65 11.30 11.92 13.21 14.92 16.35 17.80 23.25 55.01 62.26_ 8.10 3.05 3.31 2.41 3.52 3.58 3.71 9-88 4-03 6-19 4.89 7-86 8.51 1.83 2.63 -2..672.90. 3.06 _3.20__1.J9-1.22p 1.26-1.29 1.45 - 2 . 1 3 2-26. 1.70 1.2~ 2.31 2.34 2.08 2.19 2.00 2.16 2.33 0.96 0.98 1.06 1.47 1.55 !.07-_1L13-2.12p 2.11 2.21 2.05 -_2.13-1.97 :.E6 1.99-2.13-_. 0.99_-1.33 -_1.40 0.96 1.OC 1.61 1.61 1.68 1.75 1.81 1.93 1.83 1-68 1.60 1.86 1.11 1.16 0.94 0.97 1.43 1.42 -?247--1.53 - 1.57 1.66 1.67 1.75 1.77 1.61 1-08 1.12 1.73 1-80 1.i9 1.19 1.23 1.27 1.29 1.35 1.40 1.47 1.54 1.41 0.95 0.98 1.69-_1..73 -1.12 1-14 1-17 1-20 1.22 l . ? 5 - _ 1 ~ 2 F __1.33 1 - 3 8 -_1.51 0.94. 0.96 0.98 0.99 1.02 1.03 1-05 1.77 1.30 0.95 0.06 1.00 1.08 1-15 0.95 0.87 0.Q; 0.91 0.92 0.03 _ O S o 4 _ 0.961.13 1.16-0.86__-0.68 0.89 -1.01 1.'1_-0.91 0.68 0.85 0.660.97 0.88 1.06 1.07 0.88 0.87 0.86 0.89 0.52 1.03 1.06 1.00 1.01 3.01 0.88 0.88 0.89 0.85 0.80 0.81 0.89 0.82 0.85 1-02 1.011.00 1.01 i.03 1.05 1.00 0.90 0.89 0.89 0.84 0.86 0.79 0.82 0.96 0.99 0.96 -o-..99-iLoi-:-.c2 1.01 0.97. 0.97_-_0.87 -0~850 ~ 8 1 o,81 0.78 -0.91 0.930.98 0.99 0.95 1.00 1.01 1-03 1.00 0.95 0.86 0.e5 0.80 0.75 0.90 0.91 0.95 O.P_6_9OZ54- 0._95__ 0.960.97 0.97 0.94 -_0.90-_ 0.83 ____0.82 0.78 0.85-_0.R6 0.98 0.99 0.95 0.97 0.97 0.98 0.98 0.98 0.95 0.91 0.85 0.78 0.86 0.88 0.98 0.19 0.91 OSo5 0.96 0.97 0.96 0.96 0.94 0.9? 0.89 0.84 0.85 0.861.08 1.12 1.73 1-70 1.87 1.95 2.01 1.92 2.04 1.89 1.80 1.23 1.23 1.28 1.04 ?.07_1Z57__-!2~63__1.69_~_1.~6 - 1 . 8 1 - 1.931.9_3 1.70-_1.-62 -1.81 __l-.14--lm191.00 1.02 1.46 1-50 1.56 1.62 1.66 1.76 1.86 1.77 1.65 1.67 1.10 1.14 0.9e 1.jO--l .36-_iL40_ 1-..44--1_.50_ -1.53 12.61-lr69_-_l.t61 - lL7_01-.-52-_ __1.05 -1.08 1.22 1.23 1.00 1.03 1.02 1.04 1.03 1.01 1.00 1-01 1.02 1.04 1.15 1.19 l.l@ 1.19 0.97 1.00 1.01 1.00 1-00 0.98 0.07 0.98 0.98 1-01 1.11 1.15 1-16 1.17 0.97 0.99 1.00 1.01 1.01 0.98 0.96 0.96 0.96 0.98 1.14 1.11 1.14 1.15 0 ~ 9 6 ~ ~ 0 ~ 9 8 ~ ~ 0 . 9 9 ~ ~ ~ 1 .0-97-_0+94~_0.~94__0_._94__0.96 0 0 ~ ~ ~ i . 0 0 -_1.1-0--1.08 1-16 1.15 0.96 0.99 1-00 1.01 1-00 0.99 0.97 0.94 0.94 0.96 1.13 1.12 1-16 1-16 1-16 1.12 12011.02-1.01 1.00 c.99 0.9.6__0.94__0.95_1.09 1.12 1-16 1.17 1-16 1.17 1.13 1.14 1.03 1-02 1-00 0.97 0.97 0.95 1.07 1.10 1-16 1-16 1.16 1.19 1.17 1.18 1.13 1.03 1-01 1.00 0.97 0.94 1.05 1.07 1.17 1.18 1.14 1.!7 1.18 1.19 1.17 1.11 1.02 1.01 1.00 0.97 1.04 1.05 1.18 1.19 1.12 1.14 1_.1.5--1.-1~___~..161.15 1.09 1.08 l . 0 1 ~ 1 2 0 0 ~ ~ ~ l ~ O ~ l ~ 1 . 0 3 1.61 1.63 1.16 1-20 1.22 1-26 1.25 1.27 1.29 1.32 1.35 1.42 1.00 1.02 1-53 1.56 1-13 1.17 1.19 1.21 1.21 1.23 1.24 1.26 1.29 1.35 0.98 1-00
5< MG ,AL
SI P S CL
K CA T I CR
BA
L A CE PR
NO
SM GO
@I ER HF TH
.LL
1-00 l.q2 1.77 1.62 1.52 1.15 1.12 1.11 1.10 1.10
0.57
6.52 1.61 1.15 1.04
0.89
0.04
2.10 1.84 1.6' 1.23
2.1C 1.92 1-66 1.26 i.12 1.05 0.99 0.99
:.lo
1.03 0.98
0.07 0.05 0.95
0.95
0.0'
0.94
0.95
0.97 0.97 1.04 1-00 0.56 2.0n 1.19 1.15 1.14 i.12 1.12 1-12 is13
O.SE 1.00
1.93 2.18 1.99 1.18 1.13 1.?2 1.10 1-10 1.10 1.12 1.12 1.;3 1.13 1.53 1.47
0.97
1.14 1.15 1.10 1.56 1.49
~
__
-
lated using a least-square program to make full use of synthetic phases interior to these systems. The linearity of CjK us. C was checked by calculating the entire set of factors from both the 1 :1 molecular composition and from the end member composition. The deviation is pronounced only for large differences in molecular weight, arising from the quadratic term involving the mass absorption
coefficients in the absorption correction
[ 5,
C i p A L ] 2(as
n=a
in Figure 2), and for large characteristic fluorescence corrections for closely adjacent elements (as in Figure 1). Factors were also calculated using options suggested by various authors, i.e., constant cs. variable ionization potential, J , and
ANALYTICAL CHEMISTRY, VOL. 42, NO. 12, OCTOBER 1970
1411
~
Table IV. Correction Factors for 20 kV Accelerating Potential and 38.5 O Take-Off Angle (M.A.C. and Hitachi Microprobes). K, for C to Zn, La for Rb to Hf, M a for Th and U. Factors in the First Column Are for Both 0 and HzO
F NA2O HGO~ALZ03_~102._-~205 SO3 CL K2O CAO TI02 CR203 N !-O FEO COO-_-NIO1.11 1.73 2.23 2.56 2.93 3.45--'-3.9i-'ii.74 16.30 17.37 2i;os 2.35 2;77--3.12-3.45 3.94 13.82 56.48 9.36 3.75 5.48 7.34 8.68 11.97 4.40 4.16 1.61 4.29 6.13 7.92 11.00 13.14 5.70 5.37 6.81 7.80 8.96 9.70 9.67 11.80 1-00 3.55 16.0-032 23.02 3.81 3.89 4.2T 2.57 1-00 1.3_0--1.45-1.60 _1.70-1.81--1.36_-1.873 - 1 5 -2.55 - 3.20 - 3 . 6 6 4.12 4-63 5.24 1.74 2.55 1.00 1.08 1.17 1.22 1.29 1-01 1-31 1.48 1.68 2.01 2.27 ' 2.52-2.7P'-3.111.43 1.92 2.10--1.00 1.06--1.09--l:~~-1.27 1.39 lt60 1.78 1.94 2.10 2.32 -1.44 -1.55---1.65 1.80 1.23 1.57-1;71 1.83--1.00 1.00 1.04 1.13-1;191.33 1.15 1.38 1.49 1.56 1.64~_-1.00___1.@2~-0.90 1-01 1.08 1.12 1.21 1.29 1.37 1.44-1.55 1.08 1.25 1.33 1.38 1.44 1.50 1.00 0.88 0.97 1.02 1.04 1.10 1.15 i.zi-i;25 1.13 1.27--1._)_4-_-1~38__1.43_- 1 - 4 5 . . 1.52--_1.00_ -1.04 -_1.09-1~-09--_1.14 - -1.15 -1.201.23 1.30. 1-04 1.12 1.17 1.18 1.21 1.22 1.25 1.55 1.00 1.01 0.99 1-01 1-01 1-04 1.04 1.09 1 - 0 0_ - 1 . 0 6 - - l . l _ l ~ - l . l l -1.14_1.14_-1.16 1.38 --l.45p-l.00 0.94 0 . 9 5 _ - 0.94 F.97 0.97 1.32 1.04 1.08 1.12 1.11 1-11 1.13 1.151.24 1-19 1.3T-11.00--0.93 0.92 0.95 0.95 --0.99 1.05 1.08 1.12 1.11 1.13--1.-11 1.13 1.15 1.19 1.21 1.17 1.00 0.96 0.91 0.910.94 1.08 1.11 1.14 1.13 1.15 1.13 ~ ~ 1 ~ 1 5 ~ ~ 1 ~ 1 5 ~ 1 ~ 1 ~ ~ 7.n ~ 1 1.07 1.10 1.:3 1.12 1.13 1.12 1.13 1.12 1.14 1.17 1.13 1.15 0.99 1.00 0.96 0.88 ~ 0 ° 1 ~ 1 3 ~ 1 ~ ~ ~ 1 ~ ~ - 1~* 1 31- - 1~. 1 5 -1 2 ~ 1.13 ~ ~ 1 . 1 5~- 1 1.12 ~ 1.15-1~17-~~.12~~~1.141.14 - 1 . 6 2 l.OO"0.99 1.11 1.09 1.06 1.09 1.12 1.11 1.12 1-10 1.11 1.08 1.10 1.13 1.08 1.09 1.09 - 1.11 0.97 1-00 -N I 1.11 1.13 -1.12 1-04 CU 1.16 1.14 1~11--1~14--1~~17-~ 1.15 1.17 1.15 -1.161.12 1.14--1.16 --1.12 1;12ZN 1-16 1.15 1-12 :a17 I . l b - - l ~ l ~ _1.15 - _ 1.16 1.12 1.13 1-16 1.11 1.11 1.09 1.11 1-10 1.13 RB 1.38 1.29 1.42 .8 5 1-q-9 8 1.2 1 1.1 9- - 1s 2 4-- 1 F6 -1 . ~ 9 - ~ - 1 - ; 3 ~ - - - ~ ~ 3 ~ 1 ~ 3 4 7 6-5--T.7 4 1 -; 83SR 1.30 1-21 1.33 1.61 1.73--1.84-_1.14_ 1.12 1.17 1.01 1.13 1.22 1.26 1.38 1.441.53 1.61 1.74 Y 1.24 1.17 1 ~ ~ - 1 . 4 9 -1.59 1.67 1-74 1.10 ' 1 ~ 1 4 ~ " ~ 0 ~ 9 8 " ~ 1 ~ O B ~ 1 T 1 7 ~ 1.28'' ~ 1 ~ 1.33 1 9 -1.42- - - l a 4 8 1.59 ZR 1.20 1.13 1.21 1.42 1.52_-_1.58 1.65 1.07 1.10 0.97 1-06 1.13 1-15 1.23 1.27 1.35 1-40 1.50 8A 1 ~ 3 6 ~ 1 ~ 3 1 ~ ~ 1 ~ 3 0 ~ 1 ~ 1.343 2 ~ -1.38' - 1 ~ 3- 18. 3 4 1.38-'-1.44 1.49 - 1-.52---1.2T---1.14 1.13 1.15---1.14-1.18 1.11 1.15 LA 1.32 1.29 1.26 1.30 1.35 1.32 1.35 1.32 1.35 1.38 1.43 1.46 1.18 1.15 1.10 1.12 CE 1.32 1.29 1.26 1.2-.~4-1.3~--1.35 - 1 . 3 1 - 1.34 - 1.36rc40 1.43 T. ~ - T . T 3 - T . T - - L T 2 - - I - , ~ i - ~ -PR 1.31 1 - 2 8 1.25 1.28 1.33 1.30 1.33 1.30 1.33 1.34 1.37 1.41 1.36 1.15 1.11 1.11 1-09 1.13 NO 1.33 1.-30--1.27--1.301.35-1.32 1.35 -1.31 1.34 1.34 1.371.41-1.35 - - l e 1 6 - 1.13 1.121.10' 1.14 -SM--l.36 1.33 1-30 1.32 1.37 1.33 1.37 1.34 1.36 1.34 1.37 1.41 1.35 1.18 1.16 1.17 1.11 1.15 GO 1.40--1.37--1.34-1.361.41 - - l a 3 8 1.41' 1.37-. 1.39" 1.36 1.38---1-.42 1.36 -Tm3E---'.19. 1.20 '-1.17 1.17 DI 1.43 1.40 1.36 1.38 1.43 1.39 1.43 1-40 1.41 1.36 1.39 1.42 1.36 1.37 1.21 1.23 1-20 1.23 ER 1.45 1.42 1 38 l L - 4 T - 1 < 7 5 - -1-;4T-..1 4 5 -1.41--I -33-1 .T-T.m-T. 43 1YT6- T;sT--l , ~ - - r . Z * - - - I 2 2 - - 7 X HF 1.47 1.43 1.40--1.42 1.46 1.43 1.46 1.41 1.44 1.37 1.39 1.43 1.36 1.35 1.33 1.35 1.34 1.27 fF1.54T-17-7-. 47 1. S;i- 1m6- 1 -1.56 ---I. 631.60 -1 6 6 ' -1 94- -1 .Tl-----l JQ - 1 ; JZ---l; 3 6 -* 1.30' ' I;34 1.33 ' ' 1.40u 1.54 1-47 ~.47-5_1_1.59.__?r55--~~~1-. -1-j-3 ~LL. 1 - 3 9 r.!_2__-!.._~~_.__??2?.--1.33_ .i..??, *.i:3?. C02 0 o 1.00 2.44 C 1.20 1-00 F 11.38 10.59 NA 2.16 1.90 MG 1.52 1.35 _AL_ _ _ _ 1.29 _ 1.17 SI 1.15 1-06 P 1.10 1-04 s 1.05 1.00 CL 1.13 1.09 K 1.061.03 _ CA _ 1.03 1-00 T I 1.07 1.05 CR 1.09 1-07 MN 1.12 1-10 FE 1.11 1.09
&lJ--l.J5--
.
::;;
.
.
-__
-
.
--
-
-___
ZN R8
_SR_ _ Y
-ZR_ BA LA CE -PR
NO SH GO
DY ER HF
1-00 1.96 1.80 1.64 1.53 1.14 1.11 1.10 1.09 1.09 1.10 1.12 1.13 1.19 1.21 1.36 1.33
___-TH ___ U
1.00 2.09 1.92 1.74 1.62 1.15 1.12 1-11 1.09 1.10 1.11 1.12 1.13 1.14 1.20 1.39 1.35
____!*.v.___
0.96 0.97 0.99 1-00 0.95 0.97 -0? .8-09 ,9 0.98 0.98 0.97 1-00 1.05 1-10 1.14 1.88 1.96 2.05 2.15 2.23 2.12 2.27 2.13 1.00 1.04-1.08-1,71__ 1*77-1.85-_ 1.93 2.00-2.14 2.03 2.44 0.96 1.00 1.03 1.58 1.62 1.69 1.76 1.82 1:94---2.0-62.22_2.27--~0.97-_1.00__ 1.46_-1.50_ 1 . 5 6 - -1.62 _1.66--1.76--1.87_1.78 1.20 1.22 1.24 1-26 1.00 1.03 1.03 1.04 1.04 1-02 1.02 1.15 1.17 1-20 1.21 0.97 1.00 1.01 1.01 1-01 0.99 6.99 1.13 1.15 1.17 1.19 0 ~ 9 6 0 . 9 9 - - - - 1.00 ~ - - - - 1.01 1.01 0.99 0.97 1.11 1.13 1.15--1.17_-0.95 0.98 0.99--1.93 1.00-0.980.95 1.11 1.13 1.15 1.16 0.96---0.-98--0.99 1.00 -O ;l O 0.99 0;97-'-0795 1.11 1.13 1.15 1.~6---1.21-1.15---1.00 1-01 1-01 1.03 0.99 1.12 1.14 1.16 1.17 1 ~ 2 2 1.21 i.i5--i . i 6 - - 1 ~ 0 ~ - - i ~ ~ ~ 1 . 0 1.12 1.14 1.16 1.18 1.19 1.22 1.20 1.22 1.15 1.02 1.01 1.13 1.15 1.17 1.18 1-17 1.19 l ; ~ l - l ~ l . l 9 1.13 1.01 1*-13-1-15 1.18 1~1~~~1.13__1~16_-1.17 1 . 1 8 1 . 1 8 1 . 1 8 1-13 1.60 1.63 1.69 1.70 i;i7 1.21 i.Z4"'-1~27 i ~ z e ixi-i.33--1.3i lmY2 1.55 1.60 1-62 1.14 1.1-8-->-.2-01.23 1.23 1.26 1.27
well be due to the lack of adequate theory and of accurate measured constants for the lighter elements, especially oxygen. For this reason it is desirable t o use standards not too different in composition, including oxygen concentration, from the standards, but still not abandoning the concept of fewer, well-known standards. For silicates we use the simplest silicates as standards, i.e., Na(A1Si30g), MgZSiO,, Al?SiOs,
..
0.95 0.91 0.85 2.09 1.99 1.87 1.78 2.01 1.96-1.82 1.84 1.89. 1.67 1 - 0 3 -1.04 1-01 0.99 1-00 1-03 0.97 0- 9 8 . 0 1 0.95 0.96 0.98 --0.95'-0.970.97 0.95 0.96
-ma
.-
0.87 0.881.30 1.36 1.20-1.26 1.16 1.21 1.09 1.13 1.211-26. 1.16 1.21 1.20 1-17 1.16 1.13 1.19---1.17 1.14 1-17
0 - ~ ; 9-c;97-~ O.~~---LII---I.~~ 1-00 0.97 0.95 -1.08 1.11 1.01 1.00 0.98 1.06 1.08 ~.09__~.01__1.00__1.03 1.04 1.41 1750 1-;0~---~02 1.30 1.34 1.42 0.98-1.:0-
K(A1Si308), CaSiOs, MnSi03, FeSi03, etc. Thus, the correction factor relative to the standard is small and systematic errors in the @-f@ctorstend to cancel out. In addition, because of their importance in silicate analyses we use the empirical factors rather than the calculated factors for most of the @-factors in Table V. Tables of @-factors are provided for 15 kV and 20 kV.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 12, OCTOBER 1970
1413
~
~
~
~
In practice it is convenient t o reduce raw intensity data to K-values for a given accelerating potential before the corrections are calculated for the sample. Thus:
Table V. Calculated and Measured a-Factors for Selected Elements A.R.L. microprobe, 52.5 take-off angle, 15-kV acceleratingpotential Evaluated Evaluated at 1 : l at end molecular member oxide composition Measureda aE03
a$* aM.0 AI
%io*
G
O
aEgO aAi20J CaO
ago a%0 @io GP*03
a&* @EO*
1.03 1.09 1.67 1.04 1.13 1.40 1.44 1.05 1.20 1.39 0.90 1.07 1.08 1.14 1.20
1.03 1.09 1.62 1.04 1.14 1.39 1.43 1.05 1.23 1.45 0.92 1.06 1.08 1.15 1.20
(7) and:
1.023 1.102 1.563 1.036 1.172 1.320 1.346 1.029 1.19 1.33 0.924 1.123 1.188 1.16 1.27
(8) The correction program then only needs to contain a single matrix of &-factors and elements measured at various accelerating potentials can be handled together.
ACKNOWLEDGMENT The authors are indebted t o A. A. Chodos for the microprobe analyses and perceptive criticism.
aEo* a Measured using following simple phases, mostly synthetic crystalline phases: A1203, SOz, SiOz glass, AlzSiOj, Mg~SizOs, MgzSi04, MgAlzOa, Mg3A12(SiO+, 5 glasses between MgzSizOs and Mg3Alz(Si04)3, CaSiO3, CaS103 glass, Ca3A12(SiO4)3,Ca(Al2Si208),CaAI(AlSiO,), Fel-,O, FeZSiO4,FezSiz06,ZnO, Znz SO4, ZrSiOa.
RECEIVED for review May 18, 1970. Accepted July 10, 1970. This work was supported by NSF grant (GA-12867) and NASA contract (NAS-9-8074). Division of Geological Sciences Contribution number 1852.
Determination of Unsaturation by Analytical Hydrogenation and Null Point Pressuremetry D. J. Curran and James L. Driscolll Department of Chemistry, Uniwrsity of Massachusetts, Amherst, Mass. 01002 A multirange differential capacitive-type pressure transducer system has been used to follow pressure changes in a closed system during analytical hydrogenation of unsaturates and subsequent in situ regeneration of hydrogen gas by hydrolysis of sodium borohydride. A graphical treatment of the recorded data yields the volume of NaBH, needed to generate hydrogen equivalent to that consumed in the hydrogenation reaction. The method uses an experimentally determined correction to the data for the free space equivalent of the volume of solution and liquid added to the system. Precision and accuracy are a few parts per thousand for sample sizes corresponding to 0.1 millimole of unsaturation in favorable cases and as little as 1.2 micromoles of octene-1 have been determined with an accuracy of about 2 per cent relative.
As PART OF OUR STUDIES of applications of pressure transducers in chemical analysis, we have investigated the determination of unsaturation by following pressure changes in a close reactor. A number of procedures for low pressure analytical hydrogenation at atmospheric pressure are well known ( I ) . However, they often suffer from lack of high Present address, Rhode Island Hospital, Providence, R. I. (1) S. Siggia, “Quantitative Organic Analysis via Functional Groups,” 3rd ed., John Wiley and Sons, New York, N. Y., 1963, pp 318-341. 1414
ANALYTICAL CHEMISTRY, VOL. 42,
precision and accuracy and are frequently time-consuming. A notable exception is the recent work of H. C. Brown, C. A. Brown, and coworkers (2-12). Their apparatus and procedures feature in situ preparation of the catalyst and generation of hydrogen gas, and automatic restoration of the internal pressure of the system to the value prevailing prior t o the hydrogenation reaction. The former involve sodium borohydride reactions and the latter involves a self-sealing mercury valve. Precision and accuracy were in the range 0.5 to 1 . 5 % relative in most cases for a number of types of unsaturation for sample sizes ranging from 2 mmoles to 50 pmoles of (2) H. C. Brown and C. A. Brown, J. Amer. Chem. SOC.,84, 1493 (1962). (3) Ibid., p 1494. (4) Ibid., p 1495. (5) Ibid., p 2827. (6) H. C. Brown and K. Sivasankaran, ibid., p 2828. (7) C. A. Brown and H. C. Brown, ibid., p 2829. ( 8 ) H. C. Brown, K. Sivasankaran, and C. A. Brown, J . Urg. Chem., 28, 214 (1963). (9) .~ H. C. Brown and C. A. Brown, Tetrahedron.. Suool.. _ _ 8, . . Part I. 149 (1966). (10) C. A. Brown and H. C. Brown. J . Ora. Chem.,. 31,. 3989 ‘ (’1966). (11) C. A. Brown. S. C. Sethi. and H. C. Brown. ANAL.CHEM.. 39, 823 (1967). ’ (12) C. A. Brown, ibid., p 1882. I
~
NO. 12, OCTOBER 1970
