Generalized Nearest-Neighbor Broken-Bond Analysis of Randomly Oriented Coherent Interfaces in Multicomponent Fcc and Bcc Structures

Abstract

In this article, a model for the estimation of matrix/precipitate interfacial energies is developed. The classic nearest-neighbor broken-bond (NNBB) model is taken as a basis and further developed, to (1) take into account atomic bindings over an arbitrary number of neighboring shells and (2) account for general, multicomponent solid solutions. The model is sufficiently simple and yet reliable for providing estimates of interfacial energies in applications in complex, time-consuming computer simulations of a microstructure/precipitate evolution in which more sophisticated approaches cannot be used. As an example, the model is applied to randomly oriented interfaces in fcc and bcc crystal structures. It is shown that both kinds of crystal interfaces, fcc and bcc, exhibit roughly the same mean interfacial energies, as long as a sufficient number of nearest-neighbor shells is taken into account. A comparison with published experimental and theoretical data on interfacial energies shows good agreement.

In situ measurement and modelling of austenite grain growth in a Ti/Nb microalloyed steel

“…(6) l ki is the chemical potential of component i in precipitate k, c ki is the mean concentration of element i in precipitate k, q k is the radius of precipitate k, and c k is the interfacial energy of the precipitate-matrix interface. These interfacial energies are obtained from a nearest neighbour broken bond model [54]. The Gibbs free energies are calculated using the standard CALPHAD method and the associated thermodynamic database [55].…”

An analytical approach to the β-phase coarsening behaviour in a thermally sprayed CoNiCrAlY bond coat alloy

“…But σ can also be mathematically achieved by considering it as a function of a chemical component in the alloy system [52]. In its basic form, the interfacial energy is directly proportional to the enthalpy of the alloy, which can be expressed as [65],…”

“…It has been found by Sonderegger et al. that z*/z = 0.329 in fcc and bcc structures based on the nearest-neighbour broken-bond analysis [65]. N* is the number of cross bonds per atom at the interface and can be determined using the relation of * = 4 2/3 / 2 (11) where is the effective lattice constant, taken as = ( + )/2.…”

Simulation of Precipitation Kinetics and Precipitation Strengthening of B2-precipitates in Martensitic PH 13–8 Mo Steel

“…The mobility data used in the simulations are compiled from the assessments of Jönsson 15) and Liu et al 16) The generalized broken-bond model 17) is used for calculation of the interfacial energy γ0 between matrix and precipitates. A radius-dependent size-correction is used for the small, coherent B2 precipitates.…”