Comprehensive first-principles study of stable stacking faults in hcp metals

Abstract

The plastic deformation in hcp metals is complex, with the associated dislocation core structures and properties not well understood on many slip planes in most hcp metals. A first step in establishing the dislocation properties is to examine the stable stacking fault energy and its structure on relevant slip planes. However, this has been perplexing in the hcp structure due to additional in-plane displacements on both side of the slip plane. Here, density functional theory guided by crystal symmetry analysis is used to study all relevant stable stacking faults in 6 hcp metals (Mg, Ti, Zr, Re, Zn, Cd). Specially, the stable stacking fault energy, position, and structure on the Basal, Prism I and II, Pyramidal I and II planes are determined using all-periodic supercells with full atomic relaxation. All metals show similar stacking fault position and structure as dictated by crystal symmetry, but the associated stacking fault energy, being governed by the atomic bonding, differs significantly among them. Stacking faults on all the slip planes except the Basal plane show substantial out-of-plane displacements while stacking faults on the Prism II, Pyramidal I and II planes show additional in-plane displacements, all extending to multiple atom layers. The in-plane displacements are not captured in the standard computational approach for stacking faults, and significant differences are shown in the energies of such stacking faults between the standard approach and fully-relaxed case. The existence of well-defined stable stacking fault on the Pyramidal planes suggests zonal dislocations are unlikely. Calculations on the equilibrium partial separation further suggests c + a dissociation into three * Corresponding author Email address: zhaoxuan.wu@epfl.ch (Zhaoxuan Wu) Preprint submitted to Acta Materialia October 9, 2016This is a pre-print of the following article: Yin, Binglun; Wu, Zhaoxuan; Curtin, W.A. Acta Materialia 2017, 123, 223--234.. The formal publication is available at http://dx.doi.org/10.1016/j.actamat.2016.10.042 partials on the Pyramidal I plane is unlikely and c dissociation on Prism planes is unlikely to be stable against climb-dissociation onto the Basal planes in these metals.

Dislocation core properties ofβ-tin: a first-principles study

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Local volume effects in the generalized pseudopotential theory

“…In general, we find that there is agreement between the GPT and aGPT at the stable stacking fault. However, for the unstable stacking fault the aGPT improves upon the GPT relative to the DFT results of Yin et al 31…”

“…whereG αβ (ε) = γh γαhγβ is the strained metric tensor. If the strain is sufficiently small so as to vanish at quadratic order ε αβ = δε αβ , we may write G αβ (ε) = G αβ + 2 µν δε µν h µα h νβ (31) where G αβ is the metric tensor of the unstrained crystal. By denoting the second term as δG αβ and expanding Eq.29 about δG = 0, we find…”

Stacking faults and the -surface on first-order pyramidal planes in -titanium

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“…We will show that there is no stable stacking fault in α-Ti with a fault vector of ≈ 1 2 (c + a). Yin et al [13] used symmetry arguments and a hard sphere model to identify approximate translation vectors of possible stable stacking faults without calculating the full γ surfaces. They then carried out full relaxations of these faults using DFT for six hcp metals including Ti.…”