The interstitial concentration and temperature dependence of the diffusion coefficient ratio D12/D11 in ternary austenites containing silicon or manganese has been experimentally determined using diffusion couples based on the concept of "transient equilibrium". The results are compared with values predicted theoretically from statistical and thermodynamic considerations. </p> <p> The kinetics of the growth of proeutectoid ferrite in binary and ternary austenites have been determined, using two-phase diffusion couples. The results are consistent with the premise that carbon diffusion controls the rate of interface migration. It is demonstrated, theoretically and experimentally, that the ternary results fall into two classes - one in which local equilibrium may be assumed, and one in which "constrained local equilibrium" may be postulated. / Thesis / Doctor of Philosophy (PhD)

<p> Rate of adsorption data for gases on molecular sieve·s and coals have been interpreted using equations for unsteady state diffusion derived from Fick's law for spheres usually, ignoring the amount adsorbed and the shape of the adsorption isotherm. These inappropriate equations result in calculated diffusivities that are too low and activation energies that are too large. </p> <p> Numerical. solutions of Fick's law were made for diffusion and adsorption in a porous sphere of radius R by finite difference methods for the following conditions: a. Diffusion is the rate-controlling step, and the diffusivity, D, is constant. b. Within an increment of the particle the total amount of adsorbate per unit volume, T is related to the "effective" concentration, c, by a Langmuir-like isotherm T = abC/(1 + bC). c. At zero tine the particle containing no adsomate is surrounded by adsozbate of concentration, Co, which remains constant throughout the rate process, and d. Equilibrium is established immediately at the periphery of the sphere. </p> <p> The solutions are obtained in terms of Z = Q/Q and T=(DCo/QR^2) t = kt, where t is time, k is a constant equal to the term within the brackets, and Q and Q are the amounts adsorbed per unit volume at time t and at equilibrium. The quantity within brackets is also a valid expression for linear and Freundlich-like adsorption isotherms and probably holds for other isotherms. Plots of z as a function of T shift systematically as the parameter B = bCo increased from 0, corresponding to a linear adsorption isotherm, to large values; the value of Z at a given T increasing with increasing values of B. For B = 0 the numerical solution is identical with analytical solution for the linear adsorption isotherm which for values of z <0.87 is given by kt = (2/π) { (-1 - πZ/6) - (1 ~πZ/3) ^1/2 } where k = DCo/R^2Q. For large values of B the numerical solutions approach as a limit the parabolic law kt = (1/2) {(1- 2Z/3) - (1- Z) } The value of (1/k~) o.zidt~ at short times increases fran 3.385 for B = 0 to 4 .. 243 for very large values of B.. From experimental data the value of k derived using the equation for B = 0 is 1.56 larger than for the parabolic equation. Hence the values of D obtained from the initial linear portions of t.he rate curve change by only a factor of 1.56 when the type of isotherm is changed from linear to rectangular. </p> <p> Rates of adsorption and the adsorption isotherm were determined for N2 , CH4, co2 , and C2H6 on samples of Linde 4A molecular sieve at several temperatures from -78° to +50°C in a manostatic volumetric aborption apparatus. The Langmuir equation satisfactorily approximatedthe isotherms and the values of B were moderately large at the lower temperatures of each series of experiments, eg., for N2 at -78°C, 10.6; for CH4 at -78°C, 7.3; for co2 at 0°C, 64; for Ci!6 at 0° and 30°C, 37 and 10.3. </p> <p> The rate data plotted as Z against t^1/2 were not linear at short times but curved upward initially before becoming linear. The initial (, nonlinear portion persisted significantly longer than the brief uncertain period at the beginning of the experiment. This phenomena could result from the equilibration at the periphecy of the particles requiring a finite time rather than being instantaneous. </p> <p> An equation based on the parabolic law model and a first order equilibration process was derived, which fits. the experimental data for 0.05 < Z < 0.95. This equation is appropriate only to data with a large value of B, but is probably a reasonable approximation for other rate data. </p> <p> The rates of adsorption for different molecules were co2 > N2 > CH4 > c2H6 · The activation energies for the diffusivity were found to be 4.1 and 6.0 kcal./nole for methane and ethane. The _heats of adsorption were found to be 7.2 and 8.3 kcal/mole for methane and ethane. </p> / Thesis / Master of Engineering (MEngr)

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21123号 / 工博第4487号 / 新制||工||1697(附属図書館) / 京都大学大学院工学研究科分子工学専攻 / (主査)教授 佐藤 啓文, 教授 関 修平, 教授 山本 量一 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

<p> This investigation is concerned with the development of a general ternary diffusion analysis for the diffusion-controlled oxidation of binary alloys based on the concept of local equilibrium and phenomenological diffusion theory and its application to appropriate experimental systems. </p> <p> The theoretical analysis is in two parts. In the first part diffusion equations for the alloy and oxide phases are obtained and tested against experiments for Ni-10.9% Co alloy at 1000°C. In the second part phenomena observed in binary alloy oxidation such as supersaturation, internal oxidation and morphological instability are qualitatively discussed and the concept ot the stationary diffusion path on the isotherm is applied to binary alloy oxidation. In general the ternary diffusion analysis satisfactorily accounts for the diffusion-controlled oxidation properties of several binary alloys. </p> <p> An experimental investigation of the oxidation of nickel-iron alloys at 1000°C is described. In the first part of the experimental investigation, thermodynamics of the ternary iron-nickel-oxygen system at 1000°C has been investigated in support of the oxidation studies. The second part is comprised of a detailed kinetic and metallographic study of nickel-iron alloys containing upto 25% iron exposed to oxygen atmospheres at 1000°C and determination of the metal concentration profiles in the oxide and alloy phases. The experimental results for these alloys are in good agreement with the theoretical calculations. </p> / Thesis / Doctor of Philosophy (PhD)

The A15-based Nb3Sn and V3Ga superconducting compounds are an integral part of synchrotrons and magnetic fusion reactor technology, especially where a magnetic field higher than 10 T is required, which lies beyond the limit of conventional Nb-Ti superconductors (~8 T). These brittle intermetallic compounds are difficult to manufacture in the form of wires, required for the application purpose, using the traditional wire-drawing process. Hence, bronze technique is adopted to fabricate such filamentary wires. This is based on the solid-state diffusion where A3B compound (A=Nb or V, B=Sn or Ga) forms during the interaction of Cu(B) and A. The operation of pure superconducting wires gets restricted to the field of 12 T, however, the ever-increasing demands for an improved efficiency have promoted the development of these A15 wires with the addition of alloying elements such as Ti and Zr. Many important physical and mechanical properties of such wires depend on the growth behaviour of these compounds. Therefore, understanding the growth of such compounds necessitates an in-depth analysis on diffusion behaviour of various elements in both bronze-based solid solutions as well as A15-intermetallics. Estimation of diffusion parameters makes use of the most commonly used diffusion couple technique. There are mainly three methods available for the estimation of the interdiffusion coefficients, proposed by Matano-Boltzmann (MB), Den Broeder (dB), same as Sauer-Freise (SF) and Wagner. Among these three, MB treatment is known to be the least accurate method, especially when there is a deviation of molar volume in a system from the ideality. At the same time molar volume might affect the estimation process differently for dB and Wagner’s approach. MB method is still being used neglecting the actual molar volume variation. On the other hand, the implementation of dB or Wagner’s approach for the estimation remains to be random. For the first time, we have critically examined the role of molar volume on estimated diffusion parameters and indicated the more accurate approach. Similar analysis for the estimation of the intrinsic diffusion coefficient is conducted considering Heumann and van Loo’s methods. Furthermore, the discussion is extended to the estimations of various diffusion parameters considering the measured composition profile in the V-Ga system. A detailed diffusion study has been conducted on Cu(Ga) and Cu(Sn) solid solutions to examine the role of the vacancy wind effect on interdiffusion. The interdiffusion, intrinsic and impurity diffusion coefficients are determined to facilitate the discussion. It is found that Ga and Sn are the faster diffusing species in the respective systems. The trend of the interdiffusion coefficients is explained with the help of the driving force. Following that, the tracer diffusion coefficients of the species are calculated with and without consideration of the vacancy wind effect. We found that the role of the vacancy wind is negligible on the minor element in a dilute solid solution, which is the faster diffusing species in this system and controls the interdiffusion process. However, consideration of this effect is important to understand the diffusion rate of the major element, which is the slower diffusing species in this system. Major drawback of studying diffusion in multi-component systems is the lack of suitable techniques to estimate the diffusion parameters. In this study, a generalized treatment to determine the intrinsic diffusion coefficients in multi-component systems is developed utilizing the concept of pseudo-binary approach. This is explained with the help of experimentally developed diffusion profile in the Cu(Sn, Ga) solid solution. Based on an interdiffusion study using an incremental diffusion couple in the V-Ga binary system, we have shown that V diffuses via lattice, whereas Ga does so via grain boundaries for the growth of the V3Ga phase. We could estimate the contributions from two different mechanisms, which are, usually, difficult to delineate in an interdiffusion study. Available tracer diffusion studies and the atomic arrangement in the crystal structure have been considered for a discussion on the diffusion mechanisms. Diffusion–controlled growth rate of V3Ga at the Cu(Ga)/V changes dramatically because of a small change in Ga content in Cu(Ga). One atomic percent increase in Ga leads to more than double the product phase layer thickness and a significant decrease in activation energy. Kirkendall marker experiment indicates that V3Ga grows because of diffusion of Ga. Role of different factors influencing the diffusion rate of Ga and high growth rate of V3Ga are discussed. The growth of Nb3Sn by bronze technique on two different single crystals and deformed Nb is studied. The grain boundary diffusion-controlled growth rate is found to be different for each of these three specimens. The difference is explained on the basis of the grain size of Nb3Sn. Elemental additions such as Ti and Zr to either bronze or metal are found to improve the superconducting properties. We have examined their effects on the growth rates of A15-phase formed in Cu(B,x)/A and Cu(B)/(A,x), where x is Ti or Zr. In either cases Ti and Zr-additions result in an improved growth rate of the product phase and reduces activation energy with increase in alloying addition; however few precipitates are formed in the interdiffusion zone for Cu(B,x)/A. Wavelength dispersive spectrometry (WDS)-mapping reveals these to be x-rich. Scanning transmission electron microscopy (STEM)-analysis suggests having composition gradient inside a single precipitate. TEM-diffraction demonstrates these to be Ti(A) solid solution crystallizing as BCC-structure for Cu(B,Ti)/A. These are located on grain boundaries of A15-phase. Electron back-scattered diffraction (EBSD)-analysis demonstrates grain morphology of product phase and found the average grain size to exhibit a decreasing trend with increasing x content. Columnar grains, on Ti and Zr addition tend to form as equiaxed ones. Based on the morphology and grain size pattern, the role of grain boundary diffusion is speculated to have a dominant effect with increase in elemental additions. The texture evolution of the product phase is also investigated and found the product phase to grow as a strongly textured one with the elemental additions. A peculiar pattern is observed for the texture of the product phase and its adjacent A or A(x) grains.

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The electro–mechanical connection between under bump metallization (UBM) and solder in flip–chip bonding is achieved by the formation of brittle intermetallic compounds (IMCs) during the soldering process. These IMCs continue to grow in the solid–state during storage at room temperature and service at an elevated temperature leading to degradation of the contacts. In this thesis, the diffusion–controlled growth mechanism of the phases and the formation of the Kirkendall voids at the interface of UBM (Cu, Ni, Au, Pd, Pt) and Sn (bulk/electroplated) are studied extensively. Based on the microstructural analysis in SEM and TEM, the presence of bifurcation of the Kirkendall marker plane, a very special phenomenon discovered recently, is found in the Cu–Sn system. The estimated diffusion coefficients at these marker planes indicate one of the reasons for the growth of the Kirkendall voids, which is one of the major reliability concerns in a microelectronic component. Systematic experiments using different purity of Cu are conducted to understand the effect of impurities on the growth of the Kirkendall voids. It is conclusively shown that increase in impurity enhances the growth of voids. The growth rates of the interdiffusion zone are found to be comparable in the Cu–Sn and the Ni–Sn systems. EPMA and TEM analyses indicate the growth of a metastable phase in the Ni–Sn system in the low temperature range. Following, the role of Ni addition in Cu on the growth of IMCs in the Cu–Sn system is studied based on the quantitative diffusion analysis. The analysis of thermodynamic driving forces, microstructure and crystal structure of Cu6Sn5 shed light on the atomic mechanism of diffusion. It does not change the crystal structure of phases; however, the microstructural evolution, the diffusion rates of components and the growth of the Kirkendall voids are strongly influenced in the presence of Ni. Considering microstructure of the product phases in various Cu/Sn and Cu(Ni)/Sn diffusion couples, it has been observed that (i) phases have smaller grains and nucleate repeatedly, when they grow from Cu or Cu(Ni) alloy, and (ii) the same phases have elongated grains, when they grow from another phase. A difference in growth rate of the phases is found in bulk and electroplated diffusion couples in the Au–Sn system. The is explained in AuSn4 based on the estimated tracer diffusion coefficients, homologous temperature of the experiments, grain size distribution and crystal structure of the phase. The growth rates of the phases in the Au–Sn system are compared with the Pd–Sn and the Pt–Sn systems. Similar to the Au–Sn system, the growth rate of the interdiffusion zone is found to be parabolic in the Pd–Sn system; however, it is linear in the Pt–Sn system. Following, the effect of addition of Au, Pd and Pt in Cu is studied on growth rate of the phases. An analysis on the formation of the Kirkendall voids indicates that the addition of Pd or Pt is deleterious to the structure compared to the addition of Au. This study indicates that formation of voids is equally influenced by the presence of inorganic as well as organic impurities.