ratio greater than 10 to 1. This fact is attributed to the absorption of trichloroborane a t 5.35 microns, which in this case becomes larger than the absorption of diborane which is being measured. It is suggested that for samples containing small amounts of diborane (6) in the presence of large quantities of trichloroborane the wave length of 6.15 microns be used. Even though this band is pressure sensitive, quantitative work can be accomplished by always maintaining a constant pressure in the cell with nitrogen and operating above 200-mm. total pressure. I n samples containing diborane (6)to-trichloroborane ratios of 2.5 to 1, a shift in the infrared absorption a t 10.24 microns occurs with the appearance of a small shoulder a t 10.25 microns. I n this instance, a small loss of accuracy is experienced. It has been
the practice with such samples to take measurements at the shoulder. These values are no better than k5Y0 with respect to the trichloroborane. General interference with the analysis can be expected by the presence of compounds containing boron-hydrogen and/or boron-chlorine linkages. ACKNOWLEDGMENT
The authors extend sincere appreciation and thanks to Arthur D. Bliss and Robert East for many helpful discussions and interest during the course of this work and t o Sidney Siggia for his interest and advice in the preparation of this manuscript. LITERATURE CITED
(1) Anderson, W. E., Backer, E. F., J . Chem. Phys. 18,698 (1950).
Causes and Control of Matrix Effects Spectrographic Discharges
( 2 ) Gillam, A.,
Stern, E. S., Jones, E. R. H., “Introduction to Electronic Absorption Spectroscopy in Organic Chemistry,” pp. 185-6; fiee also “Absorption Spectrophotometry,” p. 25, Lothian, Hilger, London, 1949. (3) McCarty, L. V., Smith, G. C., McDonald, It. S., ANAL. CHEM.26, 1027 (1954). (4) Nadeau, H. G., Olin hiathieson Chemical Corp., Kew Haven, Conn., unpublished mork, 1958. ( 5 ) Onak, T., Landesman, H. L Shapiro, I., J . Phys. Chem. 62, 1605 (1958). (6) Price, R. C., J . Chem. Phys. 16, 894 (1948). ( i )Wartik, T., Abstracts of Papers, Division of Inorganic Chemistry, 133rd Meeting, ACS, San Francisco, Calif., -4pril 1958. RECEIVED for review Kovember 23, 1959. Accepted July 18, 1960. This work was part of an Air Force contract for the Wright Air Develo ment Center. Research project confucted under supervision of J. F. Haller.
in
A. J. FRISQUE Research and Development Deparfment, Sfandard O i l Co. (Indiana), Whiting, lnd.
b In quantitative spectrographic analysis, changes in sample matrix can change analytical intensity ratios independent of element concentrations and cause large errors. Changes in the discharge temperatures that result from matrix changes were measured and found to explain the observed ratio changes. A new equation accounts for these temperature changes and defines new minimum requirements for matching line pairs. Interpretation of results based on this equation shows that changes in intensity ratio with matrix are a natural consequence of a poor choice of internal standard, that the best choice can b e made only b y deliberately varying the discharge temperature, and that when a choice less than perfect i s necessary, a temperature correction improves results. Matrix effects due to collisions of the second kind, which would not be corrected for, were not observed for the sensitive lines used.
I
N QUASTITATIVE SPECTROGRAPHIC AN.~LYSIS, line intensities that are
used to measure element concentrations are affected profoundly by the sample matrix. Differences in composition between standards and samples can produce large errors usually attributed to matrix, interelement, or extraneous element effects. Composition differences
1484
ANALYTICAL CHEMISTRY
in the matrix cause the intensities of the minor constituent lines to change independently of concentration, and the intensities of different lines to be affected differently. Intensity ratios are likewise adversely affected. To avoid these effects, samples must resemble calibration standards. Similar compositions are obtained by preparing calibration standards to match each sample, which takes time, or by heavy dilution of both standards and samples, which reduces sensitivity. Maximum sensitivity without time-consuming calibrations has not been possible. h spectrochemical series (6), electrodes of modified shape (I), and a total-arcing method (19) have been used in attempts to overcome matrix effects. A temperature correction that had been used successfully for other purposes was also suggested (I,d), but it was claimed to be unnecessary with stable sources (3)presumably with a constant matrix The complexity of the problem is illustrated by dhrens’ list of composition-dependent factors that can influence line intensities ( 2 ) . The problem is simplified, however, for an idealized combination of sample and discharge source, In such a system, the matrix is important only insofar as i t regulates the discharge temperature. Although the matrix effects predicted for such a system are minimum effects,
they must be examined first before other factors can be assessed. THEORETICAL
I n an ideal sample, the partial pressure of each constituent depends on its concentration in the condensed phase and the vapor pressure of the pure constituent. I n an ideal source, the sample and discharge are a closed system a t a single temperature, and all phases and energy states are in equilibrium. For thermal excitation in an idealized system, the discharge temperature determines the concentration of an excited state, according to the Boltzmann equation: p*
=
p,exp
- E/kT,
Under constant source conditions, the temperature is determined by the effective ionization potential of the discharge gases (3). Therefore, the matrix determines temDerature. T,, and hence, p * , the concetkration of particles in the excited state. From Henry’s or Raoult’s laF, p , = f.Po,and, from the Clausius-Clapeyron equation, Po = B exp - A H / k T ,
Hence, p * = j B exp
- (AH
+ E)/kT,
Upon substituting for p* in the basic equation I = Agvp*, it becomes
Z
=
A g d f exp
-
(AH
+ E)/kT,
z =K. We
(2 1
From Equation 1,on the other hand, the intensity ratio is I'
=
K.W, exp
I 8
-
[ ( A H , - AH,)
+
(E, - Es)l/kTm
(3)
Equation 2 adequately measures W , only under conditions in which the exponential term of Equation 3 is constant. For this purpose, the relatively constant T , values of invariant matrices are sufficient, but, with variable T, values, Equation 3 shows that the intensity ratio will change with temperature:
(4) Then Equation 2 is adequate only when d(lnI,/IJ/dTm is zero or when (AH,AH,) ( E , - E.) is zero. Variable matrices preclude constant T, values and thereby necessitate perfect matching of line pairs. If standard and sample are mismatched by 1 electron volt, Equation 3 shows that a 400" change in temperature a t 7500" K. can change the intensity ratio by 10%; a 2000" change, by 75%.
+
/
(1)
where I and T , are the time-integrated quantities. I n practice, the temperature a t the sample surface from which vaporization occurs should be intermediate between that of the discharge directly above it and that of the bulk sample and electrode directly beneath it. Therefore, the temperature of vaporization, which should properly be used in the Clausius equation, is lower than T,. However, to the extent that this surface temperature depends on T , and, since the discharge is the common energy source for all processes, is defined by T,, the form of Equation 1is not affected. The two energy terms, AH and E, express the dual volatilization-excitation role of the discharge for an idealized system where a single temperature applies. Only excitation is accounted for by the more conventional idealized equation ( I S ) , I-KN exp E / k T , where K is the transition probability, N is the number of atoms per unit volume Le., pressure-and E is the energy difference between the initial and final (ground) state. I n measuring concentration conventionally by intensity ratios, an internal standard corrects for sample entrainment and is intended to correct for temperature variations. For the simplest case of a unit-slope Forking curve, the empirical equation is
"
a
/I0
/'
/
TI
T2
Figure 1 . Calibration for analysis with Equation 6 C
The smaller change is within experimental error; the larger, outside it. Matrix changes can change the discharge temperature by several thousand degrees ( 3 ) . Equation 4 shows that, unless all of the energy terms to be matched are known, the discharge temperature must be deliberately varied to choose an internal standard properly. Temperature must also be varied for real samples, with their additional energy terms, if such additional terms are constant. Matrix changes directly provide the necessary temperature variations to test for matching, and the moving plate technique (4) sometimes indirectly provides them. A line pair that gives the same intensity ratio in a cool alkali metal arc, as in a hot carbon arc, is a matched pair. A pair that gives the same intensity ratio throughout the discharge interval may be a matched pair if elements of different ionization potential and volatility are present. Such elements cause the temperature t b vary during the discharge interval, and ratios that are constant under these conditions have shown temperature immunity. Practically, perfect matching may not be possible. Because the internal standard must be an element that is determined infrequently, the choice may be limited. If an internal standard that gives the same intensity ratio a t different temperatures cannot be found, a temperature correction can be applied. Either absolute or relative T, values can be inserted into Equation 3 to make this correction. Absolute values require measurement of intensity ratios and knowledge of the constants Kl,2 and A E 1 . 2 , whereas relative values require measurement of ratios only.
The intensity ratio of an atom-atom or ion-ion pair from the same element is related to T , by the equation: -1 I2 1 2.3= (log - - log K1.2) AEi12
ZI
Expressing Equation 3 logarithmically and eliminating - 1/2.3kT, between Equation 3 and 5 gives a working-curve equation that includes a relative temperature term: log
Z
_"
1.
log K,' f log W , f
Kd
I log -2 11
(6)
Equation 6 is equivalent €6 Equation 2 except for the term Kd log (I~/II). Kd measures the extent of mismatching of the I J I , pair; log (Iz/I1)measures the changes in T, as the matrix is varied. Wheh K d is zero, the I J I . pair is perfectly matched and not affected by changes in I2/Il. When K d is not zero, I J I , will change as 12/11changes, and values for W , will be erroneous if the conventional equation that omits the R dlog (I*/Il)term is used. If an atom-atom or ion-ion pair with a wide AEl.a value is not available for T , measurement, an ion-atom pair can be used. For such a pair, AE1.2 will be large-comparable to the ionization potential of the element. I n this case, the need to consider atom-ion-electron equilibrium according to the Saha equation complicates the expression (5, 8 , 16, 16). The relationship between intensity ratio and temperature for such a pair has been given ( I d ) by
-1 = 2.3 kT,
(log 12
ZI
- log K1,2 -
This equation, which implies constant VOL. 32, NO. 1 1 , OCTOBER 1960
1485
electrpn density, differs from the atomat'oin or ion-ion equation by the value 5/2 log IcT,. However, log T , changes only slightly in comparison to T , and, within experimental error, can be incorporated into the log K l , 2term; then Equations 5 and 7 are equivalent. T o determine by Equation ti, the must be measured values I J 1 8 and 12/11 and K d and K," must be known. To determine K d , the analysis element W e is held constant and the matrix 12/11 is varied. T o determine K,", the matrix 12,'11 is held constant and TI', is varied. These relationships are s h o w scheniaticall\- in Figure 1. Figure l a shons log (Z.
Fa 3 0 2 l A .
4.0 E
V SI84 A . GI 2589 A .
I.Ot
- e Il
8
2.0
D
-
rI 3242A.. la
0 E
0.6
6.0
3.0
V 3184A.. GI 2589A
0a 3072 A . Ge 2 5 8 9 A .
P 2S35A.
Ge 2589A.
lo-
N I 30041
0
612589 A 7
WE
S12881A
6
-
w
-02
--.
-0 I
Q3
0 3-
e
'
8
0 0 3072 A .
f
V3104 A .
I
I
I
3.0
6.0
3.0
1
6.0
1
12.C
/-
I
3.0
I
6.0
I
12.0
S I
3.0
s40
s Sn 2 8 4 0 A
Y o 3170A
--2o
2n3345A
P253S A .
S I 2932 A .
S I 293241.
lo06 --\
I
6.0
-I n
0 3I
12.0
I
3.0 I
6.0 I
12.0 I
I
31. 0
6.0 I
12.0 1
ISr l l 3464A. 'Sr
P= Additional
61;NoCI.
O=CaC03
0; Z n O
e = A1203
Q =
Sb204
A = Si02
0 ;Pb(N03),
@= PbO
Ul = Na2C0,
0 = Co304
8 = MgO
0
0' F e 2 0 3
0=
Figure 3.
Sonunit slopes for both equations are accounted for by plotting the calibration data in logarithmic form in the conventional manner. The deviation of the average values for the uncorrected results is 59yc ; for the corrected results, i t is 11%. Uncorrected results are low for positive values of K d and high for negative values. CONCLUSION
I n spite of an\- effect of the matrix on electrode temperatures which, if independent of discharge temperature. would affect vaporization, a correction factor based only on the discharge temperature provides a qignificant improvement in analytical accuracy. Large changes in inteniity ratio n i t h
I 2932A.
Graphite
D = K2CO3
= Li2C03
Sn 0,
Intensity ratios
(/e//8)
vs. temperature index
matrix under conventional source conditions correlate kvell with the discharge temperature associated with the matrix rather than the matrix proper. This observation has implications of immediate practical importance in analysis, as well as for future studies of matrix effects. Practically, an internal standard that gives IJZ8 values immune to matrix changes can be found only by varying the discharge temperature by an amount at least equal t o that which might be encountered in practice. Future studies of matrix effects that are assumed to be matrix-specific effects must take into account these nonspecific temperature effects. Matrix-specific effects, such as those due to collisions of the second kind, would appear as points well outside the normal limits of pre-
cision in plots such as Figures 3 and 4. Evidence for such matrix-specific effects from the vanadium/germanium pair in the zinc oxide and aluminum oxide matrices in Figure 3 was absent when similar data m r e obtained for the calibrations of Figure 4. Such evidence would presumably have been obtained n ith longer-lived, less-sensitive lines (2). K h e n I , originates from different salts or solids, the total energy leading to the excited state of the I , line will vary. Such effects are not accounted for by Equation 6. I n the present experiment, use of single compounds as the source of each element assured constant energy requirements for each line. Anion effects and those of crystal structure a ere therefore absent. VOL. 32, NO. 1 1 , OCTOBER 1960
1487
Table II. Analysis Results for Different Matrices, P.P.M.
v
Test samples
Fe 22
22
Elements, Known Ti Si 22 22 22
Mn 22
blg 26
Mo
P 1020
Baa 940
Sn 26
Zn 160
A1 3.1
Based on Conventional Equation 33 6.4 16 3.7 220 37 34 1500 51 35 0.8 66 36 4.5 47 26 17 3.6 210 1400 54 33 0.6 BaC03 25 26 8.0 28 29 13 11.0 200 1300 36 28 2.3 39 29 6.4 32 37 15 20.0 430 1400 33 65 2.1 Li2C0, 28 28 7.4 27 43 13 10.0 150 1200 43 20 1.8 30 31 7.2 21 46 13 9.5 150 1500 48 23 2.1 Av., found 39 31 6.6 32 36 15 9.6 230 1400 45 34 1.6 Kd -0.64 -0.29 $0.67 -0.36 -0.28 +0.19 +0.83 $0.72 -0.18 -0.25 -0.93 $0.58 Deviation of the av., yo 77 41 61 45 64 32 63 77 51 73 79 48 Based on Kew Equation KC1 20 24 19 24 24 22 1500 940 24 170 2.6 30 l8 18 20 23 18 25 21 1400 920 24 160 2.4 BaCOt 15 19 19 20 23 17 21 900 930 25 100 3.7 19 18 20 29 26 22 32 1300 1000 23 200 3.4 Li2C03 15 19 19 13 32 17 33 800 910 26 65 4.4 14 19 21 13 33 19 30 610 1100 26 75 5.6 Av., found 19 19 20 19 26 21 26 1090 980 25 130 3.7 Deviation of the av., % 14 14 9 14 18 5 0 7 5 4 19 19 a MgO substituted for BaC03 matrix. KC1
48
LITERATURE CITED
6 0.02 8 m g .
Figure 4. Removal of temperature dependence from intensity ratio H
E
e
e e
Matrix I
2
e
P
symbols same Figure 3
as
in
P
I . I S r I I 3464A. ISr
I 2932 A. = mole fraction of element W = weight of element Subscripts e and s = analysis and internalstandard elements, respectively Subscripts 1 and 2 = low- and high-energy lines, respectively, from same element
The relationship of tempersture to matrix effects might suggest the increased use of buffers. Temperaturedepressing alkali buffers, honexw, can be present in a mixture only t o the extent that graphite and sample proper are absent. Too little graphite results in globule formation and “popping” of refractory samples; too little sample, in loss of sensitivity.
J”
g
= =
NOMENCLATURE
v
=
E
=
T,
=
k = p, =
p* =
Po = B
=
H
=
1488
excitation potential of an excited state capable of emission above the ground state absolute temperature defined by matrix Boltzmann constant partial pressure of an element in an electrode cup partial pressure of an excited state of element capable of emission pressure of pure element from electrode cup under similar conditions integration constant in ClausiusClapeyron equation heat of sublimation (fusion $ vaporization) of element ANALYTICAL CHEMISTRY
f. a E a‘ W. at constant W. f. w. A
line-transition robability statistical weiggt of state capable of emission frequency of line
I J I . = K i . W. conventional workingcurve (unit-slope) equation K , = concentration constant in conventional working-curve equation which for constant W , = l/W, when I J I # = 1 AELZ = difference between excitation potentials of lines l and 2 Kd = [(AHL AH.) -I- (E. - E.)]/ i U i , z J
K.“ = K . ’ / ( K I , Z ) ~ ~ (IJI.)/(IZ/I,)Kd = K,” W,, temperaturecorrected working-curve equation
-
(1) Addink, N. IV.H., Spectrochim. Acta 5,495 (1953). ( 2 ) Ah,yns, L. H., “Spectrochemical Analysis, pp. 110-20, Addison Wesley Press, Cambridge, Mass., 1950. (3) Ibid., pp. 21-8. (4) Ibid.. D. 68. (5) Bowians, P. W. J., Spectrochim. Acta Supp. 10, Proc. Colloq. Spectros. Int. VI, p. 151 (1957). (6) Brode, W. R., Timma, D. L., J . Opt. SOC.Am. 39,6 (1949). (7) Dikhoff, J. A. M., Spectrochim. Acta Supp. 10, Proc. Colloq. Spectros. Int. VI, p. 162. (8) Golling, E., Ibid., p. 128 (1957). (9) Grossman, H. H., Sawyer, R. A., Vincent, H. B., J . Opt. SOC.Am. 33, 185 (1943). (IO) Harvey, C. E., “Method of Semiquantitative Spectrographic Analysis,” Applied Research Laboratories, Glendale, Calif., 1942. (11) Harvey, C. E., “Gpectro-Chemical Procedures,” Applied Research Lsboratories, Glendale, Calif., 1951. (12) Ho, I-Djen, Chang, Kung Soo, Spectrochim. Acta Supp. 10, Proc. Colloq. Spectros. Int. VI, p. 207 (1957). (13) Jaycox, E. K., ANAL. CHEM. 27, 347 (1955). (14) Levy, S. J., Appl. Phys. 1 1 , 480 (1940). (15) Lobhte-Holtgreven, W., Spectrochim. Acta Supp. 10, Proc. Colloq. Spectros. Int. VI, p. 111(1957). (16) hlandelstam, S. L., Ibid., p. 250 (1957). (17) Schuttevaer, J. W., Smit, J. A., Physica 10,502 (1943). (18) Scribner, B. F., “Symp. on Spectroscopic Light Sources,’’ Spec. Tech. Pub. S o . 76, p. 2, Am. SOC.Testing Materials, Philadelphia, Pa., 1948. (19) Slavin, M. L., IND.ENG.CHEM., ANAL.ED.10, 407 (1938). RECEIVEDfor review January 11, 1960. Accepted August 1, 1960. Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Pittsburgh, Pa., March 1960.
