Kinetics of Materials - R Balluff S Allen W Carter (Wiley 2005) WW Part 4 ppt
Kinetics of Materials - R. Balluff S. Allen W. Carter (Wiley 2005) WW Part 4 ppt
... 2Carslaw and Jaeger s treatise on heat flow is a primary source [3]. 3Estimates of times required for “nearly steady-state’’ conditions are addressed in Section 5.2.6. EXERCISES 125 ... the form of trigonometric series. For diffusion in a cylinder, the trigonometric series is replaced by a sum over Bessel functions. For diffusion with spherical symmetry, trigonomet- ric functions ... forces-such as thermal gradients or electric fields- 'Such defects, if present, will be assumed to be in local thermal equilibrium at very small concen- trations. Kinetics of Materials. ...
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Kinetics of Materials - R. Balluff S. Allen W. Carter (Wiley 2005) WW Part 2 ppt
... follow from statements of the first and second laws of thermodynamics. Onsager s principle supplements these postulates and follows from the statisti- cal theory of reversible fluctuations [5]. ... for anisotropic materials in Chapter 4. Table 2.1 presents corresponding well-known empirical force-flux laws that apply under certain conditions. These are Fourier s law of heat flow, ... metals [4] . 34 CHAPTER 2 IRREVERSIBLE THERMODYNAMICS COUPLED FORCES AND FLUXES The statistical-mechanics derivation of Onsager&apos ;s symmetry principle is based on microscopic reversibility...
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Kinetics of Materials - R. Balluff S. Allen W. Carter (Wiley 2005) WW Part 6 ppt
... mechanical response of anelastic materials. Scalar forces in the spring and dashpot model become analogs for a more complex stress tensor in materials. To enforce this analogy, we use the terms stress ... nearest-neighbors). 0 Assume a simple ball-and-spring model in which the atoms are replaced by balls of mass m, which are coupled by nearest-neighbor bonds rep- resented by linear springs having a restoring ... level of stress, such a material responds immediately with a unique value of the strain. How- ever, in many real materials, stress-induced diffusional processes cause additional time-dependent...
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Kinetics of Materials - R. Balluff S. Allen W. Carter (Wiley 2005) WW Part 9 ppt
... mean curvature. Such capillary forces are especially influential in fine-scale microstructures containing interfaces with large curvatures where pressure differ- ences can become correspondingly ... boundary with isotropic surface energy yB intersects a free surface with isotropic surface energy ysl a grain-boundary groove forms in order to achieve a capillary-force balance, as illustrated ... over the surface enclosing each surface site. Representing each surface site as a box with a square base of area l/cs (where cs is the number of surface sites per area) and height 6, the particle...
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Kinetics of Materials - R. Balluff S. Allen W. Carter (Wiley 2005) WW Part 10 ppt
... the grain center. The pressure due to this curvature therefore induces growth. Grains with fewer than six sides show the opposite behavior, whereas grains with six sides possess flat sides and ... class consists of grains with the same number of sides, N, and grains with the same number of sides grow at the same rate. The (N-6)-rule&apos ;s derivation is simple because there are no ... of grains vs. time. (b) Fraction of grains possessing N sides. Figures compare Marder&apos ;s theoretical results with experimental measurements of bubble growth in soap froths made...
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Kinetics of Materials - R. Balluff S. Allen W. Carter (Wiley 2005) WW Part 11 pptx
... ss .s Surface Surface Surface diffusion Nondensifying Atoms diffuse along the surface from larger-curvature surface regions to lower- curvature surface regions. ss.v Surface Surface Vapor ... transport Nondensifying Atoms are transported through the vapor phase from larger-curvature surface regions to lower-curvature surface regions. VF - - Viscous flow Either Atoms are transported ... 16.3.1 Sintering Mechanisms Neck growth can occur by any mass transport mechanism. However, processes that permit shrinkage by pore removal must transport mass from the interior of the particles...
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Kinetics of Materials - R. Balluff S. Allen W. Carter (Wiley 2005) WW Part 17 ppt
... 645 maps for, 40 5 of pipe, 41 2 of pores in grain boundary, 41 4 of powders, 40 1 scaling laws, 40 3 -4 04 systems of simple geometry, 40 3 bundle of parallel wires, 391 two spherical particles, ... order-disorder transformations Allen- Cahn equation, 44 1 antiphase boundaries, 44 2, 44 5 critical wavelengths, 44 4 CsCl (B2) structure, 42 4 diffuse interface, 43 7, 44 5 free energy of inhomogeneous system, ... vs. djscontinuous free-energy changes during, 42 8 Landau expansion of free energy, 42 0 order of a phase transformation, 42 0 order parameters, 42 0 conserved vs. non-conserved, 42 8 phase-field...
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Kinetics of Materials - R. Balluff S. Allen W. Carter (Wiley 2005) WW Part 1 pot
... CONTENTS 12.2 Motion of Crystal/Vapor Interfaces 12.2.1 Structure of Crystal/Vapor Surfaces 12.2.2 Crystal Growth from a Supersaturated Vapor 12.2.3 Surfaces as Sinks for Supersaturated Lattice ... Kinetics of Materials is the study of the rates at which various processes occur in materials- knowledge of which is fundamental to materials science and engineer- ing. Many processes ... - Anew-rOld new old-rnew This pattern-a rank-one tensor is transformed by a single matrix multiplication and a rank-two tensor is transformed by two matrix multiplications-holds for tensors...
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Kinetics of Materials - R. Balluff S. Allen W. Carter (Wiley 2005) WW Part 3 potx
... distortions in the fixed stress field, so different amounts of work, W, must be done against the stress field during these jumps. The rate of a particular jump in the absence of stress is proportional ... vary linearly with stress and be expressible as a tensor in the very general linear form (3.78) kl where the stress-dependent terms in the sum are relatively small. Similar consider- ations ... proportional to the exponential factor exp[-Gm/(lcT)], where G" is the free-energy barrier to the 16When the stress is nonuniform and stress gradients exist, the stress will exert a force,...
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Kinetics of Materials - R. Balluff S. Allen W. Carter (Wiley 2005) WW Part 7 pot
... diffusion on most surfaces is anisotropic because of their low two-dimensional symmetry. When the surface structure consists of parallel rows of closely spaced atoms, separated by somewhat larger ... GLASSY POLYMERS 239 with p arises from the successive saturation of the lower-energy sites as the concen- tration is increased. This causes a progressive decrease of the activation energy ... somewhat larger inter-row distances, diffusion is usually easier parallel to the dense rows than across them. In some cases, it appears that the 60ur discussion follows reviews by of Shewmon [18]...
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