Solute embrittlement of SiC

Abstract

The energies and stresses associated with the decohesion of β-SiC in the presence of mobile Pd and Ag impurities are studied from first principles. Density functional theory calculations are parameterized with a generalized cohesive zone model and are analyzed within a thermodynamic framework that accounts for realistic boundary conditions in the presence of mobile impurities. We find that Pd impurities will embrittle SiC when Pd is in equilibrium with metallic Pd precipitates. Our thermodynamic analysis predicts that Pd embrittles SiC by substantially reducing the maximum stress of decohesion as a result of a phase transition between decohering planes involving an influx of Pd atoms. The methods presented in this work can be applied to study the thermodynamics of decohesion of SiC in other aggressive environments containing oxygen and water, for example, and yield environment dependent cohesive zone models for use in continuum approaches to study crack propagation and fracture.

Intergranular fracture of tungsten containing phosphorus impurities: A first principles investigation

“…For modelling brittle fracture of grain boundaries in solids, it is beneficial to consider the interface as a cohesive zone embedded in an elastic medium. This encourages the employment of excess properties such as proposed by Gibbs for describing interfaces [44][45][46][47]. Through this approach the excess properties can be used to represent inhomogeneities such as interfaces and grain boundaries in the material.…”

“…This becomes important when the crack growth occurs much slower than the impurity motion and to account for it, the modelling needs to be performed at constant chemical potential. To ensure chemical equilibrium it is necessary that the chemical potential of impurities within the cohesive zone matches that of the impurity reservoir from which the diffusing impurity atoms emanate [46]. Through Legendre transforms the grand force potential to be minimised can be defined as…”

“…where S is the entropy, µ is the chemical potential, θ is the impurity concentration and the stress is represented by σ = ∂φ/∂δ [46,48]. Typically, to compute the effects of temperature it is necessary to resort to statistical mechanical approaches, such as cluster expansion techniques [49][50][51], to account for configurational entropic contributions.…”

“…For the decohesion, the property of particular interest is the excess energy curve, which can be used to evaluate cohesive zone properties associated with grain boundaries, including the peak stress and the Griffith work of fracture. To extract such properties we adopt the strategy outlined by Van der Ven and co-workers [44,46]. In this approach the grain boundary is seen as an anomaly from the otherwise homogeneous crystalline material.…”

“…For this purpose we perform relaxed ab initio tensile simulations of a perfect crystal strained in the [310]-direction. In the literature [44,46] it is well documented that such simulations have more than one potential equilibrium state, depending on whether the initial state supercell is subjected to an evenly distributed strain or if the strain is localised between two atomic planes. In the present work both possibilities are accounted for by probing the energy vs. displacement for both tensile strategies and then for each strain increment it is assumed that the prevailing ground state configuration is that which exhibits the lowest energy.…”