Kinetics of Materials - R Balluff S Allen W Carter (Wiley 2005) Episode 3 doc

kinetics of materials r balluff s allen w carter wiley 2005 potx

... Crystal Growth from a Supersaturated Vapor 12.2 .3 Surfaces as Sinks for Supersaturated Lattice Vacancies 12 .3. 1 Structure of Crystal/Liquid Interfaces 12 .3. 2 Crystal Growth from an Undercooled ... - 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 ... vectors). Linear transformations-such as rotations, reflections, and affine distortions- can be performed on vector forces and responses by matrix multiplication to describe force-response relations...

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 ... m, c~ij Stress, stress tensor, component Pa = Jm -3 Ir Rate of entropy production per J m -3 s- l K-' 7- Characteristic time S of stress tensor unit volume @i Diffusion potential...

Kinetics of Materials - R. Balluff S. Allen W. Carter (Wiley 2005) WW Part 2 ppt

... interface curvature; when interfaces possessing regions of different curvatures are present, differences in diffusion potential will drive diffusional transport between these regions in a direction ... 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]. ... constant temperature and pressure. 0 The surroundings may be regarded as a reservoir at constant temperature and pressure. 0 It may be necessary to transfer a quantity of heat, dQ, from...

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 ... mobility should 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- ... 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,...

Kinetics of Materials - R. Balluff S. Allen W. Carter (Wiley 2005) WW Part 4 ppt

... 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. ... everywhere except where its argument is zero, where it has an infinite singularity. It has the property s j(F')6(F- Fo)dr'= f (r& apos;0); so it also follows that s6 (F- Fo)dr'= ... 4.2 .3. When the boundaries are planar orthonormal surfaces, solutions to the diffusion equation have the form of trigonometric series. For diffusion in a cylinder, the trigonometric series is...

Kinetics of Materials - R. Balluff S. Allen W. Carter (Wiley 2005) WW Part 6 ppt

... the ratio of strain over stress) is then El .E2 - 1- -_ - (~1 - 2~2) eiWt S( W) = uo eiWt uo go (8.71) Because the strain lags behind the stress, the stress-strain curve for each ... 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...

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 ... 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] ... temperatures where the required diffusion can 0ccur.l Defects such as dislocations can be sources or sinks for atoms or for vacancies. Whether such point entities are created or destroyed...

Kinetics of Materials - R. Balluff S. Allen W. Carter (Wiley 2005) WW Part 9 ppt

... 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 ... 33 6 local mean curvature. Such capillary forces are especially influential in fine-scale microstructures containing interfaces with large curvatures where pressure differences can ... phenomena associated with both isotropic and anisotropic surfaces. The kinetics of surface smoothing, the formation of surface grooves on free surfaces at intersections with grain boundaries, and...

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 ... 3Geometrical constructions for describing anisotropic surfaces are reviewed in Section C .3. 1. Some Geometrical Aspects of Anisotropic Surfaces EXERCISES 35 5 14.2 Assume that self-diffusion ... Fraction of grains possessing N sides. Figures compare Marder&apos ;s theoretical results with experimental measurements of bubble growth in soap froths made by Glazier et al. From Marder...

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 ... two-component systems [3] . The methods of constructing homogeneous molar free energies for phase dia- grams can also be used to construct first-order approximations of free-energy den- sities when...

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