C.S. Pande

Yield stress of fine grained materials

Abstract A model is proposed for the yield stress of ultra-fine grained materials based upon Coble creep. Using Coble creep with a threshold stress for finer grains and conventional Hall–Petch strengthening for larger grains, an analytical relation is derived for the yield stress as a function of grain size for a range from very large to very small. A grain size distribution is incorporated into the analysis to account for a distribution of grain sizes occurring in most specimens. This result is compared with experimental data from Cu and NiP and shown to be in good agreement.

Formation of annealing twins in f.c.c. crystals

A microscopic model for the formation of annealing twins in f.c.c. crystals is proposed. It is argued that Shockley partial loops nucleate on consecutive {111} planes by growth accidents occurring on migrating {111} steps associated with a moving grain boundary. The higher the velocity of the boundary, the higher the twin density. The absence of twins in high stacking fault energy materials and the influence of temperature on twin density can be rationalized in terms of the model. Additional supporting, circumstantial evidence has been developed by examining the influence of deformation damage on the incidence of twinning in copper and the effect of boron in reducing twin density in annealed nickel.

Yield stress of nanocrystalline materials: role of grain- boundary dislocations, triple junctions and Coble creep

A theoretical model is suggested which describes the strengthening of nanocrystalline materials due to the effects of triple junctions of grain boundaries as obstacles for grain-boundary sliding. In the framework of the model, a dependence of the yield stress characterizing grain-boundary sliding on grain size and triple-junction angles is revealed. With this dependence we have found that, in as-fabricated nanocrystalline materials, the yield stress depends upon a competition between conventional dislocation slip and grain-boundary sliding. On the other hand, yield stress dependence on grain size in heat-treated nanocrystalline materials is described as that caused by a competition between conventional dislocation slip and Coble creep. Grain-size and triple-junction angle distributions are incorporated into the consideration to account for distributions of grain size and triple-junction angles, occurring in real specimens. The results of the model are compared with experimental data from as-fabricated and heat-treated nanocrystalline materials and shown to be in good agreement.

Uniqueness and self similarity of size distributions in grain growth and coarsening

Abstract The late stage statistical self-similarity or scaling observed in normal grain growth and coarsening are derived from a model for their evolution using a Fokker–Planck equation obtained from stochastic considerations. Using a suitably generalized H-theorem, it is shown that there is indeed a unique state (self-similar state) evolving from an arbitrary initial state. The time dependence of the appropriate average sizes in normal grain growth, bubble growth, and coarsening are deduced from this model. Multiple self-similar states in some previous models based on mean field treatment do not appear in the present analysis.

Analysis of Cu-Ni diffusion in a spherical geometry for excess vacancy production

Abstract Darken’s equations are formulated for a spherical geometry and used to examine excess vacancy formation for a Cu–Ni binary system. A subsequent numerical analysis is performed to solve for the excess (above the local thermodynamic equilibrium) vacancies. The results indicate a propensity for pore formation due to the presence of supersaturated vacancies.

Stochastic analysis of two-dimensional grain growth

Abstract Consideration of the physics and topology of the two-dimensional grain growth suggests that a stochastic expression is required for individual grain growth rates. Two sources for the stochastic behaviour are topological switching events and the average linear correlation between grain size and topological class. A size-based continuum stochastic formulation is presented on the basis of topological correlation. This analysis leads to a Fokker–Planck equation for the size distribution, which yields a unique self similar asymptotic state that is reached from arbitrary initial states. Grain size distributions obtained from these considerations are in good agreement with experimental observations.

A synthesis of mechanisms for initiation of the cellular (or discontinuous precipitation) reaction

Abstract To provide a basis for understanding mechanisms for initiation of the cellular reaction, the junction of an incoherent grain boundary with microfaceted interfaces at both the rationally and the irrationally oriented interfaces of grain boundary allotriomorphs is examined with the Cahn–Hoffman formalism. When relative values of the three ξ vectors are appropriate, the angle between the grain boundary and a facet at the allotriomorph edge can vary from 0 to 90° and still be in equilibrium throughout this range. Also, the same vector applies everywhere on a given planar facet. With the aid of DIGM, these considerations can permit a grain boundary to migrate part way along the broad face of an allotriomorph to initiate the cellular reaction via the Tu–Turnbull mechanism, or migrate to the allotriomorph end and isolate it a la Hillert–Lagneborg, or entirely fail migration, thereby allowing operation of the Fournelle–Clark mechanism, depending upon relative values of the ξ vector components.

Analytical form of the sweep constant in grain growth

Abstract The sweep constant in grain growth, θ*, is defined as the number of grains that disappear when the grain boundaries sweep through a total volume equal to that of the average grain. An analytical derivation is presented that expresses θ* for self-similar grain growth solely in terms of the self-similar size distribution. Specific applications of this analysis are presented, and the implications of these results with respect to grain growth kinetics are discussed.

The analytical modeling of normal grain growth

A fundamental understanding of grain-growth phenomena provides a means to predict and control many of the observed material properties. This article reviews the development and present state of analytical theories of grain growth. The major geometric, dynamic, and statistical factors that must be considered in a rigorous formulation of grain dynamics are outlined.

Room-temperature optical inspection reliably indicates

A recently discovered phenomenon can be used to easily evaluate whether a cuprate contains superconducting grains. Quite simply, the room-temperature color of the microstructure, when viewed through crossed polarizers, indicates the presence or absence of superconducting phases. Regardless of the composition or desired product of processing, optical examination indicates the grains that are superconducting. Because the technique depends on reflectivity, automated detection of superconductivity is possible. The optical technique described also sheds light on the commonality and origin of superconductivity in the hisjh-temperature superconductors.