Part X - Communications - Computer Program System for Analysis of Electron Microbeam Probe Data

QUANTITATIVE applications of the electron micro-beam probe frequently involve the evaluation of complex mathematical expressions and/or the analysis of large amounts of experimental data. The purpose of this communication is to describe briefly a versatile and useful computer program system that is applicable to analyze rapidly a wide variety of practical microprobe problems. This system consists of a group of ten FORTRAN programs that can be stored on tape, cards, or in the memory disc of the computer. These programs, or links, can be run individually or in any prespecified sequence without interrupting the operation of the computer or without destroying information which is being transfered from one link to another. For the program system described here a GE-235 computer with disc storage was used, so that the DCHAIN method of program linking was employed. Included in the library are programs to: 1) initiate analysis of a new set of data and transfer control between all other programs in any predetermined manner; 2) generate theoretical calibration curves of composition vs relative intensity; 3) generate empirical deviation parameters from least-square fits of experimental calibration data from standards of known composition; 4) convert raw X-ray data to corrected composition; 5) determine inter diffusion coefficients by Matano analysis of con centrat ion -distance data on a uniaxial diffusion couple; 6) determine activation energies and frequency factors of temperature-activated processes such as diffusion; and 7) generate calibration curves for determination of the thickness of thin films using microanalysis. A detailed description of these computer programs and their underlying principles is available on request from the authors."' The first program to generate theoretical calibration curves of corrected relative intensities vs composition uses the Poole and Thomas atomic number correction' and the Philibert absorption factor' with a voltage-dependent mass absorption coefficient for electrons in the alloy. A modified Castaing fluores- cence correction is also used which includes the effects of both Ka and KO radiation and over voltage.' Once the theoretical curves have been calculated in 1 wt pct intervals, these results are least-squares fit to obtain Ziebold deviation parameters' which are stored in COMMON in the computer memory. The net discrepancies between the original theoretical calibration curve and the regenerated curve using the Ziebold parameter are computed. Although this link is explicitly written for K-K fluorescent interactions, it can be applied to K-L, L-K, and L-L interactions as previously disc~ssed."~ Similar programs have also been written to utilize the Wittry fluorescence correction, Birks combined corrections, and various other corrections.' These modified programs have proved to be quite useful for quantitative comparisons of the results of the various theories. The program for conversion of raw X-ray data to corrected composition includes corrections for drift, backround, and instrumental dead time. The corrected intensities are converted to composition by use of the Ziebold equation"2 and parameter obtained from the program system. The results can be obtained for either atom or weight fractions. In addition to accurately computing interdiffusion coefficients the Matano analysis program calculates least-square smoothed values of concentration, concentration gradient, and curvature for each point on the raw input concentration profile. In order to obtain high accuracies a unique method of performing a least-square polynomial fit to incrementally advancing profile segments which overlap is used.' This program has been successfully modified for use in ternary diffusion problems3 and can readily be modified to handle analysis of diffusion profiles which include phase boundary discontinuities. This link is generally applicable to analysis of interdiffusion data obtained by other techniques as well as by the microprobe. The primary function of the next program is to least-squares fit experimental diffusion data to the normal Arrhenius function: D = Doexp(-Q/RT), to obtain values of Do and Q. In addition the probable error and one, two, and three u statistical confidence limits of DO, Q, and log D are evaluated. This program is also directly useful for analysis of any other simple temperature-activated processes including conductivity, and certain deformation and chemical processes. The program to generate calibration curves for film-thickness determination using the microprobe is based on a numerical integration of the equation derived by Cockett and ~avis.' Values of film thickness obtained by this program for copper on various substrates are in good agreement with measurements made by other techniques. Versions of the above program system have been prepared for use with or without a remote teletype connection to the computer for processing on either a real-time or time-share basis. The instrumentation coupling a microprobe to a teletype for automatic data collection and analysis by the presently described program system has been reported elsewhere by the authors.' If teletype equipment is not used to communicate with the computer, standard methods of card reading and tape reading can be used. In either