Thermo Basics
The auxiliary function used as a criterion for equilibrium under known temperature and pressure, given in differential form as -Sdt+Vdp+sum(muidni).
What is the Gibbs free energy?
The transformation process whereby the number of particles of a new phase is observed to increase with time.
What is nucleation?
A common measure of transformation driving force, which increases with departure from the equilibrium temperature, owing to its proportionality to the Gibbs free energy change.
What is undercooling or superheat?
Both are simply termed "delta-T", in reference to the equilibrium temperature. Note also that, at least for relatively small delta-T, the Gibbs free energy change driving a transformation is well described by delta-S * delta-T, since -dG/dT=S.
The mechanism that controls the growth kinetics of a particle in a single-component crystal (e.g. fcc-Cu) growing from its melt (e.g. liquid-Cu), also comprised of the single component.
What is atomic attachment at the interface?
The interface mobility in this case is limited only by the ability of atoms to attain the spatial registration associated with the growing crystal. (There is a ready supply of Cu atoms at the interface.)
A basic relationship, stated as a zeroth order premise for describing kinetics as a response.
What is the assertion that "the rate is proportional to driving force."
This premise is evident in basic relationships such as the familiar Ohm's law, I=cV, where the current (rate) is related to the potential drop (driving force) through a proportionality constant, the conductance.
The portion of solution free energy associated with mixing that is different from that which would arise from ideal mixing behavior.
What is the excess free energy?
The transformation process whereby the average particle size increases with time, while nV and SV decrease and VV remain constant.
What is particle coarsening or "Ostwald ripening"?
The contributing source of Gibbs free energy that is quantified by the mixing behavior represented on a Gibbs free energy curve, where G is plotted vs composition.
What is the bulk chemical Gibbs free energy?
The G-X curves include the thermal (SdT), mechanical (VdP) and chemical (mudn) contributions of the bulk free energy. Interface and strain effects associated with heterogeneous (multiphase) states are not included.
The mechanisms required for the motion of grain boundaries, as observed during the transformation known as grain growth.
What are atomic detachment and attachment?
Grain growth required motion (a.k.a. migration) of grain boundaries. As a minimum, motion of a clean grain boundary (with no excess solutes, etc.) requires detachment of atoms from one grain and attachment of atoms to the adjacent grain. This simple picture may be altered by the diffusion of vacancies to/from the moving boundary, which may serve as a sink/source for vacancies.
A transition for which the rate depends on the frequency with which an activation barrier is overcome.
What is an activated process?
Generally, the activation is thermal, where the activated fraction varies as exp(-1/kT). Transformations that depend on thermal activation are known as "thermally activated" and can generally be described by an Arrhenius equation.
A portion of a molar thermodynamic quantity that can be attributed to a particular component in a solution (i.e. mixture). It is a part of the mole-fraction weighted sum.
What is a partial molar quantity?
A phenomenon where one phase fraction increases with time, independent from the number of particles, nV.
What is particle growth?
The driving force for the transformation known as "Ostwald ripening," which involves the coarsening of discrete particles of one or more phases within another continuous phase.
What is the reduction of phase boundary interfacial free energy?
The reduction in interfacial free energy arises from the reduction of total phase boundary area. Additional reductions may arise as a result of changes in the orientation distribution of interfaces.
The mechanism through which particles of a new phase are formed within a parent phase.
What is nucleation?
Nucleation can be considered a mechanism, as we have described by considering a particular mechanistic path and associated barrier. Nucleation can also be considered to be a type of transformation, observable in bulk.
The size above which a spherical embryo is stable and will spontaneously increase in size, according to a classical nucleation theory.
What is the critical radius?
The critical radius (r*) is given by the condition dG/dr=0 and can be considered to be the radius above which an increase in embryo size decreases the free energy of the system more than the positive free energy change resulting from the associated increase in interfacial area.
A thermodynamic state function, given by -(dG/dT)P and also by the integral of CpdT.
What is the entropy?
A transformation in which a single-phase polycrystalline material evolves to reduce the grain boundary area per unit volume.
What is grain growth?
The thermo-chemical driving force for a nucleation-based transformation is effectively reduced by these forces, associated with the free energy rquired to create new interfaces and the dependence of this energy on interface curvature.
What are capillary forces?
The influence of capillary forces is described by the Gibbs-Thomson equation, which we will consider in more detail in a subsequent unit.
A limiting mechanism in many types of transformations where a phase forms and grows with a different composition from that of the parent phase (i.e. with chemical partitioning).
What is chemical diffusion?
Indeed, chemical diffusion is a limiting mechanism that controls the kinetics observed in many types of transformations. Diffusivity of different species in different solutes may vary greatly, and transport over microstructural distances may become the rate-limiting step. We will discuss this in detail.
The units with which nucleation rate can be describes.
What are units of 1/m3s.
Nucleation rate is typically expressed as the number of new particles formed per second within a given volume of material.
The state with the lowest free energy of any possible state accessible to the system.
What is the equilibrium state?
A common form of plot, representing the temperature dependence of isothermal transformation kinetics and typically comprised of iso-completion curves that indicate the observable start and finish of the transformation.
What is a TTT or IT diagram?
A material state described by a local free energy minimum but not a global minimum.
What is a metastable state?
Metastable states are stable with respect to small perturbations, within the domain described by the local minimum. These states are not at equilibrium, however, and large perturbations may initiate spontaneous transformation toward a global minimum.
A mechanism that enables recovery and recrystallization transformations, where the relaxation of dislocation structures and the growth of strain free domains requires atomic motion and reconfiguration.
What is vacancy diffusion?
The diffusion of vacancies is very important in facilitating the atomic reconfiguration necessary for recovery and recrystallization.
The effect on the indicated rate that results from increasing the value of k in the JMA model,
f(t)=1-exp(-(kt)^n).
What is a decrease in the transformation time?
Note that the product kt within the model shows that an increase in one requires a reciprocal decrease in the other to observe the same fraction for a given time. An increase in k requires a decrease in t for the same fraction. A decrease in t indicates an increase in transformation rate.