Kinetics of Materials - R Balluff S Allen W Carter (Wiley 2005) WW Part 10 ppt
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 ... the total grain-boundary free energy decreases. This process is also competitive and often produces unwanted coarse-grained structures. 15.1 COARSENING OF A DISTRIBUTION OF PARTICLES 15.1.1 ... others, *Statistical self-similarity holds when the normalized grain-size distribution and the number -of- sides distribution remain constant during growth. A grain structure at a later time...
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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]. ... therefore demonstrates the role of microscopic reversibility in the symmetry of the Onsager coefficients. More demonstrations of the Onsager principle are described in Lifshitz and Pitaerskii ... Kirkendall effect was observed with inert markers in polymer-solvent systems where the large polymer molecules diffused more slowly than the small solvent molecules [15]. Figure 3.5 shows an...
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Kinetics of Materials - R. Balluff S. Allen W. Carter (Wiley 2005) WW Part 4 ppt
... ENT SYSTEMS In earlier chapters we examined systems with one or two types of diffusing chem- ical species. For binary solutions, a single interdiffusivity, 5, suffices to describe composition ... 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'= ... sum over Bessel functions. For diffusion with spherical symmetry, trigonomet- ric functions apply. All such solutions can be obtained by the separation -of- variables method, which is described...
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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...
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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 ... INTERFACES AS SOURCES AND SINKS FOR ATOMIC FLUXES The basic mechanisms by which various types of interfaces are able to move non- conservatively are now considered, followed by discussion of whether...
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Kinetics of Materials - R. Balluff S. Allen W. Carter (Wiley 2005) WW Part 11 pptx
... 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 ... process is called Coble creep. Grain boundaries serve as both sources and sinks in polycrystalline materials- those grain boundaries with larger normal tensile loads are sinks for atoms trans- ... 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
... 519 phase transformations, 419 See also growth of phases, martensitic transformations, nucleation, nucleation with concurrent growth kinetics, order-disorder transformations, precipitation, ... growth spirals on surfaces, 291 climb of, 266 379, 478 Bardeen-Herring source/sink for climb force due to stress, 255 diffusion-limited kinetics, 267 dislocations as sinks for excess ... maps for, 405 of pipe, 412 of pores in grain boundary, 414 of powders, 401 scaling laws, 40 3-4 04 systems of simple geometry, 403 bundle of parallel wires, 391 two spherical particles,...
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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 ... - 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 ... when Onsager presented a uni- fied approach to irreversible processes [4]. In this book we explore some of On- sager&apos ;s ideas, but it is worth remarking that his theory applies to systems...
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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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