ANALYST, JANUARY 1993, VOL. 118 79 Microanalysis of Bismuth Indium Selenide Thermoelectronic Materials by X-ray Fluorescence Spectrometry With Reference Assays of Indium Stanislav Kotrly, Jitka Sramkova and Radko Chadima Department of Analytical Chemistry, University of Chemical Technology, 532 10 Pardubice, Czechoslovakia Josef Cerma k Computing Centre, University of Chemical Technology, 532 10 Pardubice, Czechoslovakia Screening of a small area on the natural cleavage face of a layered single crystal was used for X-ray fluorescence spectrometric (XRF) assays. A precise determination of indium (within the range I-8% m/m) in Bi2-,ln,Se3 single crystals was based on the calibration of the net intensity of the In Ka1,2 line with the use of the results of extraction-photometric analysis after decomposition of the crystal chips exposed to X-rays.In acetate buffer medium (pH = 4.0, V,, = 40 cm3) and with an adequate excess of quinolin-8-01 and thiosulfate (masking of bismuth), the tris(quinolin-8-olato)indium(i1i) chelate was completely transferred into 10 cm3 of chloroform. The absorbance of the chloroform extract was measured at 400 nm against a blank extract. For calibration of the X-ray spectrometer a computer program was written using a simplified least-squares method of linear regression for both variables subject t o experimental error. The XRF method allows the selection of a piece of crystal suitable for measurements of physical parameters. Keywords: Bismuth indium selenide; X-ray fluorescence analysis; single crystal reference samples; indium assay; quinolin-8-01 extraction A growing need for the microanalysis of semiconducting materials with regard to their physical parameters has presented the analyst with challenging new problems.Some interesting approaches to the microanalysis of semiconducting crystals have been explored mainly with the use of atomic absorption spectrometry. 1-3 Bismuth and indium have been determined in 100 mg samples of Bi-In-Te thermoelectronic material by visual ethylenediaminetetraacetic acid (EDTA) titrations.4 Controlled-potential coulometry has been applied for the precise and accurate determination of the components in thin films of copper indium selenide.5 In studies of semiconducting materials, considerable atten- tion has been devoted to the AyBY' compounds of tetradymite structure (where the main components A = Bi, Sb and B = Se, Te), which find promising applications in thermoelectronic devices.Single crystals doped with atoms of another element (e.g., In) can be grown by a modified Bridgman method to obtain a crystal cone of layered structure;6 however, there is always a certain concentration gradient of the added com- ponent within the crystal. For the interpretation of the nature of point defects due to the substitution of indium atoms for bismuth in the lattice of an AZBY' crystal, it is necessary to compare the changes in free carrier concentration, as deter- mined from the transport coefficient and reflectivity measure- ments, with the real content of indium. Thus an exact assay of the built-in component should be carried out on actual samples taken for the measurement of physical properties. X-ray fluorescence spectrometry (XRF), as a non-destruc- tive analytical method, is useful in this field.Previous experience with quantitative XRF microanalysis of semicon- ducting materials has been summarized in a critical review,7 but no further major contributions to this field have been published recently. In this paper, statistical analysis of numerous experimental data is used to assess the applicability of XRF measurements on a small area of a natural crystal face. The problems of XRF calibration based on an accurate chemical determination of indium8 are also discussed in detail. Experimental Apparatus For the X-ray measurements an ARL 8420+ XRF sequen- tional spectrometer equipped with a DEC PDP-11/73 com- puter was used.The In Kal,2, Se Kal.2 and background intensities were measured with a rhodium-target X-ray tube operated at 60 kV and 40 mA, with a lithium fluoride (200) crystal, a fine collimator and a scintillation detector. The counting time was 10 s unless stated otherwise. A screening mask was made of phosphor bronze with a 2 x 12 mm cut-out in the centre to define a selected area on the crystal face for the XRF measurement (Fig. 1). The crystal chip was placed on the rear side of the mask and fixed with adhesive tape. Along the circumference of the opening the chosen area of the crystal face was marked with a steel needle. The mask with the fixed crystal was then placed on a poly(tetrafluoroethy1ene) (PTFE) spacer and fastened with a spring to the sample holder of the spectrometer cassette.The effective layer thickness, tef, for the crystal chips was calculated for an intensity ratio RJR, = 0.999 of the In Kal,z line (51.4 pm). Interpolation with the use of tabulated mass absorption coefficients for the elements Se, In and Bi at Ag K a and Mo K a lines was carried out with the Bragg-Pierce law; hence using relevant mass coefficients and assuming additivity, the mass absorption coefficients p/p for the pure matrix of Bi2Se3 and Bil,7Tno.3Se3 and Bil ~51no.5Se3 crystals were calculated as 47.1, 44.1 and 42.0 cmz g-1, respectively. Then, with the use of our experimental density values of 7.69, 7.47 and 7.33 g cm-3 and using an approximate expression (e.g., ref.9), t,f = 460 (p/p)-l p-1 pm, the effective layer Sample for physical measurements Fig. 1 Selection of a sample from a single crystal chip80 ANALYST, JANUARY 1993, VOL. 118 thickness was calculated to be 127, 140 and 149 pm, respectively. The spectrophotometer arrangement and the equipment used for the extraction-photometric determination of indium were described previously.8 Reagents and Solutions All reagents were of analytical-reagent or semiconductor grade. The solutions necessary for the extraction-photometric procedure were described previously.8 Standard indium(1ii) solution, 5 x 10-4 rnol dm-3 in approximately 10-3 mol dm-3 HN03, was prepared by exact dilution of a 0.01 mol dm-3 stock solution made by dissolving pure indium metal in dilute nitric acid.The concentration of indium in the two standard solutions was determined by photometric EDTA microtitration using Xylenol Orange as indicator (pH = 2.9, 540 nm), which proved to be an exact standardization procedure. Decomposition of Samples Single crystals of bismuth selenide are difficult to dissolve in mineral acids. The following procedure allows indium(ir1) nitrate solution to be obtained in the presence of an excess of bismuth(iii) and selenic acid in a medium of approximately 0.3 mol dm-3 nitric acid. As the decomposition procedure is to be modified with respect to the amount of indium present in the final solution (1-20 pg cm-3), the following procedure is given here for a sample mass of up to 30 mg and a final volume of 100 cm3. Add 5 cm3 of reversed (Lcfort) aqua regia [nitric acid- hydrochloric acid (3 + l ) ] to a sample (1-8% In) in an evaporating dish and heat on a steam-bath. If oxidation of the sample is not complete, add another 5 cm3 portion of the Lefort mixture and evaporate to dryness.A white residue should be obtained. Rinse the covering watch-glass with 5 x 10-3 rnol dm-3 nitric acid and evaporate again. Use 10 cm3 of dilute nitric acid (1 + 4) to dissolve the residue and then use 20 cm3 of 0.2 mol dm-3 nitric acid to transfer the solution into a 100 cm3 calibrated flask and finally 5 X 10-3 mol dm-3 nitric acid for washings and dilution to the mark. The resulting concentration of nitric acid should be about 0.3 mol dm-3. Extraction-Photometric Determination of Indium Transfer the following reagents into a 100 cm3 separating funnel: 10 cm3 of 0.22 rnol dm-3 sodium acetate, 5 cm3 of a 0.25% solution of quinolin-8-01 in redistilled water acidified with acetic acid and 5 cm3 of 2% sodium thiosulfate solution. Mix well, add a 5 cm3 aliquot of the sample solution and dilute the aqueous phase to about 40 cm3.Extract with 10 cm3 of chloroform by shaking for 4 min. Discard first a small portion of the extract and then transfer the chloroform phase through a filter-tube fitted with small dried filter-paper into a 10 mm glass cell. Use a cell with a longer inner length if the content of indium is below 1%. Cover the cell with a well fitting PTFE cap and measure the absorbance at 400 nm against a blank extract as reference, obtained with the use of a solution containing a corresponding amount of dissolved pure Bi2Se3.For washing, the cells and glassware were also rinsed with dilute nitric acid (1 + 10). Burettes and pipettes were calibrated by weighing measured volumes of distilled water. Regression Analysis of the XRF Calibration Data The calibration experiments (cf., Table 1) showed that the errors of the extraction-photometric method were more or less comparable to those of the X-ray intensity measurements. Therefore, it was not possible to assume, as is commonly done in applications of simple regressions, that the independent variable, i.e., the analyte content, is virtually free from errors. This was confirmed by computations using both a linear and a quadratic fit to the calibration XRF data and assuming that the mean values for the reference assays were sufficiently precise.The results were not satisfactory and similar conclusions were obtained for inverse approaches. A relatively simple least-squares method for a linear relationship if both variables are subject to experimental errorl03l1 was modified for our situation of asymmetric sets of data and used to write a program for a personal computer. For each sample of the monocrystal the number of repeated intensity measurements [corrected for the background, R(In), y l ] was ny = 12, whereas the number of parallel assays of indium (xl, In %) was rz, = 4. Thus, for six calibration samples the total number of points was 6nynx = 288. The computation procedure is briefly outlined below. First, a regression y ( x ) , i. e., line 1 y = a l + hlx (1) is calculated under the assumption that only the dependent variable y is subject to experimental error.Then, for an inverse regression x(y), error-free values of y are assumed to yield a regression line x = a; + b h , which is rearranged as line 2 y = a2 + b2x (2) This inverse regression need not be carried out at all, because the correlation coefficient rxy for the whole set of data can be expressed in terms of the slope values of both regression lines: (3) where the common symbols denote the sample values of the covariance sxy. and the standard deviations s,, sy. The regression lines 1 and 2 have a common intercept at x = X and y = j i . The angle a between these lines can be calculated from the values of the line slopes bl and b2: (4) The line representing the best fit lies between the two regression lines and its position is given by an angle LO with respect to line 1.The method under consideration10 is based on the idea that this angle is affected by the statistical weights p , and p y , Their ratio can be expressed by the inverse ratio of particular variances: pJpx = s$/s;. The angle o is then defined as P y P x + PJ o = a x If the errors of the two variables are approximately compar- able, as here, then px- = p y and o = a/2. The slope for the best fit is then defined as b1 + t a n o 1 - bl t a n o 63 = and this value is then used to calculate the intercept a3 using the sums of all experimental y and x data. Computation of the calibration set presented in Table 1 gave the following equation: y = -0.03215 + 0.22945~ (7) where y is the net intensity in counts s-1 x 103 andx represents In (% m/m).For computation of a quadratic fit to the calibration data on consideration of both variables subject to experimental error, the minimum for weighted sums of the squares of deviations for both variables was found with the use of theANALYST, JANUARY 1993, VOL. 118 81 Brent optimization method. The following regression equa- tion was obtained: y = -9.225 X 10-3 + 0.22313 x + 7.4925 x 1 0 - 4 ~ 2 (8) For statistical tests and the calculation of confidence intervals, a probability level of 95% was assumed. Results and Discussion Samples of Layered Monocrystals The single crystal of Bi2-,In,Se3 prepared by a modified Bridgman method was obtained in the form of an elongated cone (length 50-60 mm and diameter about 9 mm), which could easily be cleaved into thin slices parallel to the cone axis.The cleavage faces had a smooth and mirror-bright surface. For physical measurements a small rectangle (approximately 2 X 12 mm or less) was cut out from a chosen area of the crystal slice (Fig. 1). As there is always a certain concentration gradient of the doped element in the directions parallel and perpendicular to the crystal axis, each crystal segment taken for the measure- ments represents an individual sample. As found by electron microprobe analysis, the indium content does not change significantly within such a crystal chip (cf., ref. 6). The total mass of the crystal sample may vary from less than 1 to about 40 mg depending on its size and thickness (0.1-0.5 mm).The advantage of non-destructive XRF analysis is obvious, as the whole crystal chip has to be decomposed if chemical analysis is required. The reliability of the chosen method must be adequate to provide safe results that can be correlated with the physical parameters. Extraction-Photometric Determination of Indium As a chemical reference method, the extraction-photometric determination of indium with quinolin-8-ols was chosen, because its reliability was well tested in previous assays of telluride monocrystals. It was realized, however, that decom- position of selenide crystals was difficult. It was necessary to use Lefort aqua regia to achieve a complete dissolution. As bismuth is easily hydrolysed in the presence of chloride ions, the sample solution was evaporated to dryness and the residue dissolved in nitric acid (cf., Experimental). In this way selenium was oxidized to selenic acid and a sample solution of indium(i1i) with an excess of bismuth(rr1) and a defined hydrogen ion concentration was obtained.A 5 cm3 aliquot was then taken for the extraction-photo- metric analysis. From the aqueous phase (Vaq = 40 cm3) buffered with acetate to pH 3.6-4.2, indium(ii1) was trans- ferred to the chloroform phase (Vorg = 10 cm3) in a single quantitative extraction step as the tris(quino1in-8-olato)- indium(ii1) chelate. Bismuth was masked effectively with thiosulfate. The absorbance of the chloroform extract was measured at 400 nm against a blank extract which was carried out simultaneously.For calibration of the procedure a standard 5 x 10-4 mol dm-3 solution of indium nitrate was prepared and checked with the use of a precise photometric EDTA microtitration with Xylenol Orange as indicator. To a solution obtained by dissolving pure Bi2Se3 (20-60 mg in 100 cm3) a certain volume of the standard indium(ri1) solution was added to obtain, after appropriate acidification and dilution to 100 cm3, the same nitric acid concentration as in a sample solution. Thus, for a lower concentration range of indium(ii1) (3-9 pg in a 5 cm3 aliquot), the chloroform extracts were measured with SO mm glass cells against corresponding blanks and the following regression line ( n = 14, sxv = 0.0054) was obtained: A X lo3 = -12.3 k 7.7 + (33.31 k 1.31) ml, (9) where mI, i s the amount of indium(m) in micrograms per aliquot of the sample solution.For higher concentrations of indium(ii1) (up to 110 pg per aliquot), it was necessary to measure the absorbance of chloroform extracts in 10 mm cells. The calibration measure- Table 1 Calibration data for the assay of indium in samples of Bi2-,In,Se3 layered monocrystals X-ray fluorescence- X-ray intensity, R(1n Kcx,.~) In found? Sample Coefficient x Calculated* Average/counts s-l In (YO) (ny = 12) RSD (Yo) In (YO) A h (YO) No. for In I 0.01 2 0.1 3 0.2 4 0.3 5 0.4 6 0.5 Extraction spectrophotometry- Samplc No. 1 2 3 4 5 6 0.176 33.8 7.45 0.287 f 0.005" 0.193 k 0.007b 1.78 322,6 1.14 1.546 k 0.007" 3.61 651.1 0.87 2.98 f 0.012a 5.50 1169.4 0.48 5.24 f 0.011" 7.44 1626.7 0.40 7.23 k 0.013" 9.45 2248.3 0.31 9.94 ?c 0.014" 9.80 f 0.019b +0.111 +0.017 -0.23 -0.63 -0.26 -0.21 +0.49 +0.35 In found Absorbance9 Takent/mg (n, = 4) RSD (Yo) mI"/Pg Assay (%) 69.762' 0.160' 5.43 5.55 0.160 t 0.014 27.72d 0.27 If 0.83 43.15 I .57 * 0.02 41.374" 0.401t 2.15 63.87 3.11 k 0.11 25.569" 0.426f 1.22 67.92 5.34 k 0.11 22.15ZC 0.490" 0.17 78.05 7.09 * 0.02 9.92 2 0.04 17.699' 0.548f 0.26 87.29 * From masses of the reactants if homogeneity of the crystal is assumed. t With the use of regression equations: a cqn. (7) or (1l);b eqn. (8). AIn = difference with respect to the calculated composition. $ Total volume of thc sample solution: 5 Average of four parallel extractions; measured against the relevant blank extract: e 50 mm and f 10 mm cell. Confidence intervals arc givcn with the means.100 and 50 cm3.82 ANALYST, JANUARY 1993, VOL. 118 1400 Table 2 Assay values for some samples of layered monocrystals 1120 I v) v) Extraction In found spectrophotometry 4- 5 840 Coefficient x by XRF* Sample for In (Yo) mass t/mg y1 In found (YO) AIn (%)$ 0 5.11b -0.15 4- C > . 4- 0.1 1.522" 28.262d 6 1.534 k 0.007 -0.011 0.3 5.15" 31.03% 8 5.26k0.04 -0.11 .gj 560 0.4 7.63" 21.727C 8 7.79 k 0.07 -0.16 - 280 0.5 9.23" 17.155~ 6 8.90 k-0.07 +0.33 9.11b +0.21 0 In Ka1.2 I - ,..'I?, ,I*. 1 'i\ /I I ': - ; I 'Xi / I *%.I. I !? Background : I j I I I - , I i "%. ------ I 1 ---..' I I [ I $ AIn = In(XRF) - In(spectrophotometry). - Fig. 2 Scan of the In Kal.2 line (counting time, 10 s) ments were characterized by a regression line (n = 18, syx = 0.0075) passing through the origin: A x 103 = (6.276 k 0.041) mi, (10) The results of several series of parallel extraction-photometric determinations of indium in actual samples of layered monocrystals are summarized in Tables 1 and 2.As can be seen, the method yields precise data on which standardization of the XRF analysis can be based. Quantitative X-ray Fluorescence Analysis In preliminary experiments with solid solutions of tellurides and selenides, difficulties arose with sample preparation for XRF. The materials that were synthesized to yield a poly- crystalline bulk solid were apt to give a more or less homogeneous powder after prolonged grinding in an agate mortar, but in the grey-black powder so obtained there were always some microscopic silvery scales.Nevertheless, the surface of a briquette made from such powder was found to be adequate even for electron microprobe analysis. However, a large sample of the material was needed to make a briquette of adequate diameter. Effective grinding of layered selenide crystals was found to be even more difficult, so for milligram samples this procedure was not applicable. A fusion technique was also found to be impracticable [Caution: selenide and telluride materials affect gold alloy crucibles]. Layered monocrystals can easily be cleaved into thin slices. As their trigonal axis is always perpendicular to the pulling direction, i.e., to the axis of the crystal cone, the cleavage face obtained coincided with the (0001) crystal plane. This orientation was confirmed using the Laue back-reflection method.6 The natural face so obtained had in most instances the lustre of a metallic mirror and was found to be adequate for XRF measurements, This allowed a certain area on the crystal chip to be selected for the XRF analysis.In order to define such a chosen piece of the crystal, a screening mask with a rectangular opening was used. Hence it was possible to obtain the necessary analytical information before that piece of the crystal was cut out and taken for physical measure- ments. A relatively simple matrix of the Bi-In-Se crystal made the choice of the analytical lines easy. The channel Se Kal,z was measured for the main component of approximately constant content. For indium the channel In K c Y ~ , ~ was selected (Fig.2). The vicinity of these lines was scanned using a fine collimator and a 60 s count and so it was found that there were no interferences caused either by the matrix or the components of the bronze screening mask (Cu, Sn, P). In order to achieve a high sensitivity, the effect of the excitation voltage on the counts at the In Kal,Z channel was examined within the range 40-60 kV. The maximum voltage of 60 kV was then used for further measurements. The effect of the thickness of a crystal chip (see above) on the intensity measurements was tested experimentally. First, a chip from a Bil.51no.5Se3 crystal of thickness 0.60 mm was measured; then a layer 0.11 +_ 0.02 mm thick was splintered off and taken for a repeated measurement. The difference between the net counts at the indium channel was statistically insignificant.On consideration of the calculated effective layer thickness and the manipulation risks with thin, friable crystals, the samples for the XRF assays should be at least about 0.2 mm thick. The stability of the background close to the In K C Y ~ , ~ line was confirmed by scanning (60 s count) the crystal samples 1 and 6, which represent the minimum and maximum content of indium, respectively. For 12 measurements the standard deviation for the background was 1.0 counts s-1. 'The reproducibility of the net count rate corrected for the background is shown by the calibration data in Table 1. Each sample was measured 12 times. The pooled standard deviation for all 72 measurements If(degrees of freedom) = 661 was 5.4 counts s-1.Even for sample No. 1 with the lowest percentage of indium, the intensity at the channel In Ka1,2 was signifi- cantly above the background. Various approaches to quantitative evaluation of the XRF measurements of indium were investigated with respect to the results of extraction-photometric assays of monocrystal sam- ples that were cut out exactly from the area of the crystal exposed to the primary X-radiation. The radiation scattered and emitted from the screening mask is superimposed on the analytical lines of the sample and this fact has to be taken into account in considerations about appropriate calibration models. A calibration plot of log [R(In)/R(Se)] versus log [ C(In)/C(Se)] applicable for such a pseudo-binary system was found to be less reliable than a simple calibration of the In Kal,* intensity [corrected for the background in counts s- I , R(In)] against the indium content.As errors of the reference assays had to be considered, regression methods for both variables subject to experimental errors were applied. For the main concentration range (about 1-8% m/m In) a straight-line fit was found to be adequate. The computation with the data in Table 1 (rxy = 0.9995, n = 288) gave a regression line that was used to calculate the content of indium from the corrected intensity R(In), in counts s--1 x 103, of the indium channel Ka1,2 in the following reverse form: In (YO) = 0.1401 + 4.358 R(1n) (11) The results are given in Table 1. Regression eqn. (8) obtained for a quadratic model provided a closer fit to the two outer standard samples 1 and 6; however, the results for the main region deviated on the same level or even more than those of the linear model.However, it was possible to use eqn. (8) for estimating the limit of determination (LD) based on a conventional assumption of a permissible 10% relative error. If only the counting errors for the peak and backgroundANALYST. JANUARY 1993, VOL. 118 83 intensities were considered, the net count R(In)LD was calculated with the use of well known expressions as 31 counts s-1, which corresponded to 0.18% In. With the use of a pooled standard deviation of experimental intensities a more realistic estimation of R(In)LD was 54 counts s-1 and hence an estimate of the LD of 0.28% In was obtained, which corresponded well with the statistical analysis of the actual XRF assays.For recalibration of the spectrometer, one crystal sample with composition Bi, ,51no.5Se3 (0.5 mm thick) was preserved for further measurements. For example, with one series of assays the correction factor for the average In Kal,Z net counts was R(calc.)lR(meas.) = 2248/2219 = 1.013. Applications in Routine Assays of Single Crystals After recalibration of the X-ray spectrometer, a series of samples were measured on their natural cleavage faces, marked crystal pieces were cut out, dissolved and taken for a reference extraction-photometric determination of indium. Table 2 gives results for this series of assays, which were evaluated with the use of the above-given calibration proce- dures. It is interesting that virtually the same results of the extraction-photometric assays were obtained if the average values of absorbance were taken for calculation with the use of the regression line given in previous work for 10 mm cells [cf., eqn.(1) in ref. 81. Thus, for the sample with x = 0.1 the result was 1.515% In, for x = 0.3 5.26% In, for x = 0.4 7.78% In and for x = 0.5 8.88% In. If it is taken into consideration that the extraction-photometric method was newly developed with all necessary calibrations, these results provide interesting evidence of the reproducibility and repeatability of this method. Thc main advantage of the XRF method is that it is able to provide sufficiently precise (about 1 % relative) analytical information prior to the preparation of actual samples for physical measurements, thus allowing screening and selection of the crystal chips. The results presented in this paper have also shown that despite all the problems involved in XRF measurements on a limited area of a natural cleavage face of a single crystal, it is possible to obtain data that are representa- tive of the actual sample of the crystal within the error of an independent reference assay. In this respect the approach explored in this paper may be useful for further applications. 1 2 3 4 5 6 7 8 9 10 1 1 References Yudclcvich, I. G., and Beizcl, N . F., Zzv. Sib. Otd. Akud. Nuuk SSSR, Ser. Khim. Nuuk, 1978, 94. Dittrich, K . , and Vogel, H., Tuluntu, 1979, 26, 737. Shelpakova. I. R., Shcherbakova, 0. I . , Yudelevich. I. G., Bcizel. N. F., Dittrich, K., and Mothes, W., Tuluntu, 1982, 29, 577. Danzaki, Y., Shoji, T., Sasc, M . , and Takeyama, S . , Runseki Kagaku, 1983,32, 89. Yang, M. H., Lee, M. L., Lin, Y. M., and Hwang, H. L., Thin Solid Films, 1987, 155, 317. LoStak, P., BcncS, L., CiviS, S . , and Sussmann, H., J . Muter. Sci., 1990. 25, 277. Herrington, C. R., J. Electron Microsc. Tech., 1985, 2, 471. Sramkova, J., Kotrly, S . , and Kalischova, Y., Collect. Czech. Chem. Commun., 1988. 53, 3029. Rontgen~uoreszenzunulyse, ed. Ehrhardt, H.. Deutscher Vcr- lag fur Grundstoffindustrie, Leipzig, 1981, p. 94. Nyvlt, J . , Chem. Prim., 1959, 9. 468. Mdritz, P., in Wilson and Wilson’s Comprehensive Analytical Chemistry, ed. Svehla, G., Elsevier, Amsterdam, 1981, vol. XI, p. 109. Puper 21037001 Received July 13, 1992 Accepted September 21, 1092