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Browsing by Author "Unnam, Jalaiah"

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    Iterative approaches describing atomic diffusion in finite single‐ and two‐phase systems
    Houska, Charles R.; Unnam, Jalaiah (American Institute of Physics, 1976)
    Iterative solutions are given for planar one‐dimensional atomic diffusion in finite single‐ and two‐phase systems. They are usable for any continuous variation of the interdiffusion coefficient D (C) within each phase, and need not be fitted to special functions such as a power series or an exponential function. Modified integral functions similar to one first proposed by Boltzmann are used along with a conservation criterion to locate the interface position ξ. Computer time for the iterative solutions is about two to three magnitudes shorter than finite‐difference (F‐D) calculations because of the rapid convergence of the integral equations. The accuracy of these approximate forms is considered. Excellent agreement was obtained between F‐D calculations and the iterative approach for semi‐infinite single‐phase systems. Good agreement is also found for two‐phase systems; however, the accuracy varies with the solubility gap size C βα−Cαβ. The best results are obtained for gaps larger than 0.7 which includes most eutectic systems. Calculations of composition profiles which are based upon the maximum solid solubilities for the Cu‐Ag system are within 1% of the F‐D calculations.
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    X‐ray diffraction approach to grain boundary and volume diffusion
    Unnam, Jalaiah; Carpenter, Joseph A.; Houska, Charles R. (American Institute of Physics, 1973)
    A generalized two‐dimensional diffusionmodel has been developed which consists of an array of boundaries coupled to the free surface and to the substrate lattice. The model makes use of three nonlinear partial differential equations which describe lattice, grain boundary, and surfacediffusion. This two‐dimensional model has been programmed for the IBM 360 computer using a finite‐difference solution to give concentrations as a function of time. An x‐ray intensity simulation program is developed to give integrated diffracted intensity for a given concentration distribution. This simulated intensity is compared with experimental intensity. Data are presented from a sample containing 8 μ of Ni on a (111)‐oriented Cu crystal diffused for various times at 900°C and a similar sample with 6.5 μ of Ni diffused at 600°C. The simulations are in good agreement with experimental intensity bands. Activation energies and frequency factors are given for volume and grain boundarydiffusion which are in good agreement with those literature values that are available. After a diffusion treatment at 600°C, it was found that pipe diffusion makes an important contribution to the volume diffusion coefficient. At 900°C this does not appear to be true. The contribution from pipe diffusion correlates with rocking curve data except for compositions close to that of the free surface.
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    An x‐ray study of diffusion in the Cu‐Ag system
    Unnam, Jalaiah; Houska, Charles R. (American Institute of Physics, 1976)
    The interdiffusion coefficients for both solid phases of the Ag‐Cu system have been determined from x‐ray diffraction and electron microprobe data. Specimens containing 3.2 μm of Ag on a (111) ‐oriented Cu crystal were used for the x‐ray studies, while a 15‐μm deposit of Ag was used for the probe specimens. Composition profiles for each phase were obtained from the x‐ray intensity bands and a new iterative one‐dimensional model was applied to determine the composition‐dependent diffusion coefficients. The average diffusion coefficients for both phases are nearly equal at about 10−10 cm2/sec at 750 °C, the diffusion temperature. Also, the solubility for the Ag‐rich phase is about three times the solubility for the Cu‐rich phase. These conditions result in interface reversal, i.e., the interface first moves into the substrate and later moves toward the free surface.Structural damage resulting from atomic diffusion was found to be much smaller for the Ag‐Cu system than for other single‐phase Cu‐base specimens that have been examined. Both crystal misorientation (tilt) and subgrains are formed as a result of diffusion. The subgrain shape in the plating depends upon the ratio of the thickness to the initial grain size of the plating.