Phenomena
The broad class of transformation characterized by an overall reduction in the energy associated with interfaces, curvatures, and interface junctions.
What is coarsening?
The interaction energy that governs whether a system will tend to exhibit chemical clustering or chemical ordering at low temperature and governs the critical temperatures for these behaviors.
What is the enthalpy of mixing?
Regarding atomic diffusive transport, it is the ratio between the local chemical potential gradient and the drift velocity.
What is the atomic mobility?
v_B=-beta_B((delmu_B)/(delx))
Know as "the diffusion equation" - in a diffusing system, it is the equation to which any solute profile must be a solution.
What is Fick's second law?
An interfacial property that describes the proportionality between the driving force for migration and the migration velocity.
What is the interface mobility?
A transformation that involves a distribution of particles of one phase within a continuous second phase, where the mean particle size increases while the number of particles decreases, all with no change in the volume fraction of the phases.
What is particle coarsening or Ostwald ripening?
G_i^0+RTlnX_i+RTlngamma_i
What is the partial molar Gibbs free energy.
The broad class of transformation associated with the increase in the amount of one or more phases, forming from one or more parent phases - generally serving to reduce the chemical/lattice free energy.
What is precipitation?
The driving force for relaxation processes, such as recovery and recrystallization.
What is stored strain energy?
A companion transport mechanism required to enable substitutional diffusion.
What is vacancy motion?
An experimental configuration involving two specimens - different compositions of the same phase - joined together and permitted to relax at some temperature - used to measure the interdiffusion coefficient.
What is a diffusion couple?
A local property of an interface, describing the spatial variation (along the surface) of the interface normal.
What is interface curvature?
A thermally activated relaxation transformation involving vacancy diffusion and the reconfiguration of high-energy dislocation entanglements into lower energy structures - sometimes involving the formation of low-angle boundaries and dislocation cell structures.
What is recovery?
A fundamental transport equation, based on conservation of mass, given in one dimension as:
{dc}/{dt} =del/{delx}(D(x){delc}/{delx})
What is Fick's second law?
Non-driven diffusive transport of particles in which the net distance traveled is proportional to t1/2.
What is a random walk or "Brownian" motion?
The underlying orientation-dependent description of free energy that gives rise to the equilibrium shape of a crystal (i.e. the "Wulff shape").
What is the "gamma plot"?
gamma(theta) or gamma(n)
A mechanism by which long-chain molecules can exhibit long-range diffusive motion, even though they are highly entangled and constrained.
What is reptation?
The general mathematical temperature dependence observed in thermally activated processes, of which diffusion is an example.
What is the Arrhenius behavior?
Rate prop exp({-E_A}/{kT})
The quantity denoted by K in the expression:
DeltaT=GammaK = gamma/ {Delta S}K
What is the interface curvature?
A condition that can be applied to a moving interface during growth involving chemical partitioning to relate the velocity of the interface to the local chemical gradient.
What is a flux balance?
vDeltac=-D((delc)/(delx))
An equation describing the conditions of mechanical equilibrium at a grain boundary junction, given in simple form as:
(sum gamma_ibar(t_i)=0)
What is Young's equation?
A condition whereby a migrating planar interface tends to become nonplanar to gain some local kinetic advantage - typically involving a balance between interfacial properties and transport phenomena.
What is morphological instability?
The term for the activation barrier for nucleation - given for the spherical case in simple form as (16 pi)/3 (gamma^3)/(Delta g_v^2)
What is delta-G-star?
(DeltaG^*)
The mechanism responsible for enhanced transport associated with the general disorder at a high angle grain boundary.
What is grain boundary diffusion?
J=Dgradc
What is Fick's first law?
A consequence of mass conservation that can be applied to relate interface motion to chemical partitioning and diffusive transport.
What is the principle of a flux balance?
A diagram that provides a quantitative summary of transformation kinetics by showing nominal "start" and "finish" times at various temperatures.
What is a TTT or IT diagram?
(time-temperature-transformation)
(isothermal transformation)
The thermodynamic potential given in differential form as
-SdT+VdP+sumn_idmu_i
What is the Gibbs free energy?
A phenomenon that slows the rate of transformation, because of the interaction between long-range diffusion fields around growing particles.
What is soft impingement?
Defined as the work required to create a unit area of an interface, it arises because of the increased energy associated with non-uniformities and/or discontinuities in structural/chemical order across some mathematically describable surface.
What is interfacial energy?
The net transport of electric charge that may accompany chemical diffusion in an ionic crystal.
What is ionic conduction?
Regarding diffusion, the parameter given by:
(1+{del ln gamma_i}/{del ln X_i})
What is the thermodynamic factor?
A 1-D microstructural feature, associated with contact between three grains.
What is a grain tri-junction?
A transformation involving chemical separation or clustering at low temperature within a single phase structure - occurs within a region of the phase diagram indicated by a miscibility gap.
What is spinodal decomposition?
A general model that is useful for characterizing f(t) for transformations involving nucleation and growth, given in general form as:
f(t)=1-exp(-kt^n)
What is the Johnson-Mehl-Avrami (JMA) model?
The process of compositional separation that occurs at a moving interface as a phase grows with a solute content that is different from the parent phase.
What is chemical partitioning?
For a component in a solution, it is the ratio of the chemical activity to the mole fraction of the component.
This is an indicator of the degree of non-ideality with regard to the mixing behavior of the component as a solute with a particular solvent in a particular structure.
What is the activity coefficient?
A mechanism often associated with high temperature deformation but which also may enable creation or elimination of vacancies, thus serving as a source or sink for lattice motion during substitutional diffusion.
What is dislocation climb?
A phenomenon that involves motion of the lattice - associated with net vacancy migration - during substitutional diffusion.
What is the Kirkendall effect?
v=(D_A-D_B)(delX_B)/(delx)
The interface between ordered domains across which there is a mismatch in site occupancy.
What is an antiphase boundary?
A transformation that proceeds by collective and cooperative short-range atomic motion that changes the crystal structure through lattice distortion, with no requirement for long-range diffusion.
What is a martensitic transformation?
The measurable transport quantity given by:
(X_AD_B+X_BD_A)(1+{dellngamma_A}/{dellnX_A})
What is the interdiffusion coefficient?
(This is known as Darken's equation, describing substitutional diffusion in a binary solution).
The formation of dislocation defects at the interface of a growing particle - serving to relieve misfit strain.
What is coherency loss?
The fundamental energetic relationship defining the conditions (e.g. T, P, Xi) for equilibrium in a multiphase multicomponent system. It is the basis for the "Gibbs phase rule".
What is the Gibbs-Duhem relation.
SdT-VdP+summu_idn_i=0
The formation of a new particle of a precipitating phase on a preferred or "catalytic" site within the parent structure.
What is heterogeneous nucleation?
The relationship that can be used to determine the composition-dependent effective diffusivity in a binary solution, given by:
tildeD(c)={intxdc}/{-2t{dc}/{dx}
What is the Boltzmann-Matano relation?
A surface of a crystal that exhibits terraces, ledges, and steps - associated with the orientation of the surface with respect to the crystal structure and atomic packing.
What is a vicinal surface?
The boundary defining the region on a phase diagram where we expect to observe barrier-less chemical separation within a miscibility gap.
What is the coherent spinodal?
An equation that describes the fundamental relationship between diffusivity and viscosity.
etaD=(kT)/(6pir)
What is the Stokes-Einstein equation?