kinetics of materials r balluff s allen w carter wiley 2005

... X 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 Samuel M Allen Robert W Balluffi W Craig Carter W i t h Editorial Assistance from Rachel A Kemper Department of Materials Science and Engineering Massachusetts Institute ... knowledge of kinetics is valuable because it leads to prediction of the rates of materials processes of practical importance Analyses of the kinetics of such processes are included here as an...

Ngày tải lên: 27/06/2014, 23:20

... X 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 Samuel M Allen Robert W Balluffi W Craig Carter W i t h Editorial Assistance from Rachel A Kemper Department of Materials Science and Engineering Massachusetts Institute ... knowledge of kinetics is valuable because it leads to prediction of the rates of materials processes of practical importance Analyses of the kinetics of such processes are included here as an...

Ngày tải lên: 11/08/2014, 10:22

... as the system approaches equilibrium Assume that Kinetics of Materials By Robert W Balluffi, Samuel M Allen, and W Craig Carter Copyright @ 2005 John Wiley & Sons, Inc 23 24 CHAPTER : IRREVERSIBLE ... the stress and strain tensors), which can be further separated into j hydrostatic and deviatoric terms as dw = P d v 6ij d z i j (where and t are the deviatoric stress and strain tensors, respectively) ... first and second laws of thermodynamics Onsager s principle supplements these postulates and follows from the statistical theory of reversible fluctuations [5] Onsager s principle states that when...

Ngày tải lên: 11/08/2014, 10:22

... applied stress establishes different diffusion potentials at various sources and sinks for atoms in the material Diffusion currents between these sources and sinks are then generated which transport ... representative of single-crystal graphite, where the basal plane is parallel to the layers shown In general, the properties of crystals and other types of materials, such as composites, vary with ... anisotropic materials is discussed in Section 4.5 62 CHAPTER 3: DRIVING FORCES AND FLUXES FOR DIFFUSION jumping process (see Chapter 7) When stress is present, the work, W , must be added to this energy...

Ngày tải lên: 11/08/2014, 10:22

... trigonometric series For diffusion in a cylinder, the trigonometric series is replaced by a sum over Bessel functions For diffusion with spherical symmetry, trigonometric functions apply All such ... diffusion results in linear systems of diffusion equations A linear transformation of the concentrations produces a simplified system of uncoupled linear diffusion equations for which general solutions ... composition variables Analysis of such diffusion is complex because multiple cross terms and particleparticle chemical interaction terms appear The cross terms result in N independent interdiffusivities...

Ngày tải lên: 11/08/2014, 10:22

... fashion as the interstitials regain their random distribution t Stress applied Stress oo removed Time, t Figure 8.16: Strain vs time for an anelastic solid during a stress cycle in which stress ... unstressed crystal Show that when stress is suddenly applied to an unstressed crystal, the relaxation time for the randomly distributed C atoms to assume the nonrandom distribution characteristic ... is paid to grainboundary transport in this chapter However, briefer discussions of diffusion along dislocations and free surfaces are also presented To describe the effects of grain-boundary structure...

Ngày tải lên: 11/08/2014, 10:22

... 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 u r discussion follows reviews by of Shewmon [18] and ... the transverse direction Solution The transverse diffusion rate is controlled by the relatively slow crystal diffusion rate because the diffusing atoms must traverse the patches of perfect crystal...

Ngày tải lên: 11/08/2014, 10:22

... The dislocations will therefore form crystal growth or dissolution spirals in the boundary similar to the growth spirals that form on crystal free surfaces at points where lattice dislocations impinge ... is the integral of the flux 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) ... its morphology-its external macroscopic shape and its internal microstructure-when suitable driving forces exist As always, these driving forces result from differential decreases in total free...

Ngày tải lên: 11/08/2014, 10:22

... away from 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 ... faces The shape that the crystal assumes depends upon the number and rate at which ledges move across its surfaces When one of the surfaces consists of a series of straight parallel ledges of ... Number of sides (b) (a) Figure 15.14: (a) Average area of grains vs time (b) Fraction of grains possessing N sides Figures compare Marder 's theoretical results with experimental measurements of...

Ngày tải lên: 11/08/2014, 10:22

... low temperatures, ordered structures result in which the nearest-neighbors of A atoms are + 'In this section, the terms ordered structures, order parameters, and ordering transformations appear ... the surface ss .s ~~~~~ ~~ Surface Surface Surface diffusion Nondensifying Atoms diffuse along the surface from larger-curvature surface regions to lowercurvature 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...

Ngày tải lên: 11/08/2014, 10:22

... this range, clusters will therefore grow (“move”) in cluster space by a random-walk process just as during the mass diffusion of particles Well away from N,, drift arising from the force field of ... characteristic of the reference structure (usually taken as the crystal structure of the matrix in the case of phase transformations) is absent and the interface s core structure consists of all ... with screw dislocations are generally considerably weaker, but can be important for transformation strains with a large shear component Determinations of the various strain energies use Eshelby’s...

Ngày tải lên: 11/08/2014, 10:22

... nucleation with concurrent growth kinetics, order-disorder transformations, precipitation, solidification, spinodal transformations phase transformations, general features of classification, ... dislocations in crystals, 253 association with growth spirals on surfaces, 291 climb of, 266 Bardeen-Herring source/sink for vacancies, 280 climb force due to stress, 255 diffusion-limited kinetics, ... continuous vs djscontinuous transformations, 420, 431 free-energy changes during, 428 Landau expansion of free energy, 420 order of a phase transformation, 420 order parameters, 420 conserved vs non-conserved,...

Ngày tải lên: 11/08/2014, 10:22

... X 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 Samuel M Allen Robert W Balluffi W Craig Carter W i t h Editorial Assistance from Rachel A Kemper Department of Materials Science and Engineering Massachusetts Institute ... knowledge of kinetics is valuable because it leads to prediction of the rates of materials processes of practical importance Analyses of the kinetics of such processes are included here as an...

Ngày tải lên: 13/08/2014, 05:20

... applied stress establishes different diffusion potentials at various sources and sinks for atoms in the material Diffusion currents between these sources and sinks are then generated which transport ... narrow diffusion zone compared to the extent of the specimen in the diffusion direction, compatibility stresses are pure shear stresses, and if the stresses exceed the crystal 's yield stress, ... first and second laws of thermodynamics Onsager s principle supplements these postulates and follows from the statistical theory of reversible fluctuations [5] Onsager s principle states that when...

Ngày tải lên: 13/08/2014, 05:20

... representative of single-crystal graphite, where the basal plane is parallel to the layers shown In general, the properties of crystals and other types of materials, such as composites, vary with ... 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, trigonometric functions apply ... distribution of sources, one simply superposes the solutions for the individual sources by integration, as in Section 4.2.3 When the boundaries are planar orthonormal surfaces, solutions to the diffusion...

Ngày tải lên: 13/08/2014, 05:20

... diffusion Furthermore, the results from random walks provide a basis for understanding nonrandom diffusive processes The distribution of positions is easily formulated for a random walker on ... Defects and Dzffusion Oxford University Press, Oxford, 1972 L A Girifalco Statistical Physics of Materials John Wiley & Sons, New York, 1973 J .W Christian The Theory of Transformations in Metals ... Exercise 6.3 provides an illustration 6.3 MEASUREMENTS AND INTERPRETATIONS OF DlFFUSlVlTlES There are extensive reviews of the many measurements of the E i j , particularly in ternary systems...

Ngày tải lên: 13/08/2014, 05:20

... ratio of strain over stress) is then S( W) = ( ~ - ~ eiWt ) uoeiWt - _l -E uo E2 - 1- g o (8.71) Because the strain lags behind the stress, the stress-strain curve for each cycle consists of a hysteresis ... of sites The overall response of the crystal t o such a stress cycle is shown in Fig 8.16 When the stress uo is applied suddenly, the crystal instantaneously undergoes an ideally elastic strain ... 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 and strain below, but we not treat them as tensors...

Ngày tải lên: 13/08/2014, 05:20

... 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 ... others free to vary as the system seeks a lower-energy state Small-angle grain boundaries have crystal misorientations less than about 15" and consist of regular arrays of discrete dislocations (Le., ... least for the grain boundary and dislocation curves, as discussed in Section 9.2.3 Dislocations, grain boundaries, and surfaces can possess widely differing structures, and these structural variations...

Ngày tải lên: 13/08/2014, 05:20

... inclinations close to those of singular surfaces and having energies lying on the sides of cusps are composed of discrete steps and terraces corresponding t o the structures of their nearby singular surfaces ... analysis of the growth kinetics shows that the v vs P - Peq curve appears as in Fig 12.4 [l] General Crystal Surfaces General surfaces possess a high density of sites where atoms from the vapor ... least two reasons First, the system is out of equilibrium (the transformations are not reversible) Second, because differences in normal component of mechanical stresses (pressures, in the hydrostatic...

Ngày tải lên: 13/08/2014, 05:20

... expressed as the sum of two parts: the first is that of the singular terraces, which is ys cose , where ys is the energy per unit area of the terraces; the second is that of the ledges, which is ... deformed matrix and that of the recrystallized grains.' Also, compatibility stresses are often generated in stressed polycrystals so Recrystallization occurs when a crystalline material is plastically ... The dislocations will therefore form crystal growth or dissolution spirals in the boundary similar to the growth spirals that form on crystal free surfaces at points where lattice dislocations impinge...

Ngày tải lên: 13/08/2014, 05:20