Energetics of intrinsic point defects and hydrogen in tungsten borides: a first-principles study

Abstract

To understand the irradiation resistance and hydrogen (H) behavior in tungsten borides (WxBy) in a burning plasma fusion environment, the energetics of intrinsic point defects and hydrogen (H) in six stable ground state W borides, including W2B, WB, WB2, W2B5, WB3 and WB4, have been investigated using first-principles density functional theory (DFT) calculations. The results show that the formation energies of interstitials and vacancies do not directly depend on the W and B content in W borides. However, the interaction between vacancies of a stoichiometric vacancy (SV) cluster in WxBy is related to the atomic ratio of B to W (y/x). The vacancies of a minimum-size SV cluster in WxBy are energetically repulsive for y/x  1, while the vacancies energetically bind together for y/x larger than 1. The formation energy of B Frenkel pairs in each W boride is lower than that of W Frenkel pairs. Among the six evaluated WxBy compositions, WB has the highest and the lowest formation energy of H interstitials and H-vacancy complexes, respectively; however, these two energies in WB2 are in reverse order. The average H binding energies to single vacancies in WB and WB4 are comparable with that in W, while this binding energy in WB3 and WB2 is obviously higher or lower than in W, respectively. The diffusion activation energy of H in W borides is anisotropic. One dimensional (1D) diffusion of H in W2B, as well as 1D/2D diffusion in WB, W2B5, WB3 and WB4 are preferred at relatively low temperatures; however, 3D diffusion of H is predicted in WB2. The diffusion activation energy of H generally increases with B content in W borides due to the increasing local charge deficit caused by strong B-B covalent bonds. This study is useful for evaluating the performance of W borides in a fusion environment.

Surface stability and H adsorption and diffusion near surfaces of W borides: a first-principles study

“…The optimized lattice parameters for WB a 1 = b 1 = 3.138 Å and c 1 = 16.957 Å; for WB 2 a 2 = b 2 = 2.926 Å, c 2 = 7.747 Å, and for W 2 B a 3 =b 3 = 5.579 Å and c 3 = 4.753 Å. The structures of these three W borides are available in previous work [31,38].…”

“…N W and N B are the number of W and B atoms. µ W and µ B are the chemical potential of W and B in W x B y , respectively, which are available in [38]. A is the surface area.…”

“…The ground-state bulk WB 2 with the lowest formation enthalpy has a structure of ReB 2 with a space group of P6 3 /mmc [31,38]. The surface structures of the (0001) orientation with different terminations and the (2 11 0) surface of P6 3 /mmc-hP6-WB 2 are shown in figure 3.…”

“…Previous studies have revealed that WB has the lowest average formation enthalpy in W boride compounds [30,31] and single-phase WB was observed to form near W surfaces after pure W was boronized in experiments [21], we therefore focus on the surface stability of low-index WB surfaces, in addition to the H adsorption and diffusion behavior near these WB surfaces. The energetics of intrinsic point defects and H in six ground-state W borides with various stoichiometries, such as W 2 B, WB, WB 2 , W 2 B 5 , WB 3 and WB 4 , have been studied using density function theory (DFT) in our previous work [38] and it was found that the H behavior in bulk P6 3 /mmc-hP6-WB 2 is significantly different from I4 1 /amd-WB. In addition to the second lowest average formation enthalpy and a relatively high formation energy of Frenkel pairs, P6 3 /mmc-hP6-WB 2 has the lowest H formation energy and the lowest H binding energy to single vacancies, as well as nearly isotropic H diffusion among the six evaluated W borides [38].…”

“…The energetics of intrinsic point defects and H in six ground-state W borides with various stoichiometries, such as W 2 B, WB, WB 2 , W 2 B 5 , WB 3 and WB 4 , have been studied using density function theory (DFT) in our previous work [38] and it was found that the H behavior in bulk P6 3 /mmc-hP6-WB 2 is significantly different from I4 1 /amd-WB. In addition to the second lowest average formation enthalpy and a relatively high formation energy of Frenkel pairs, P6 3 /mmc-hP6-WB 2 has the lowest H formation energy and the lowest H binding energy to single vacancies, as well as nearly isotropic H diffusion among the six evaluated W borides [38]. In consideration of these outstanding properties of WB 2 and the presence of W 2 B as W is coated by low B content [24], we also studied the stability of low-index surfaces of ground-state WB 2 and W 2 B, as well as H behavior near the relatively stable surfaces of these two W borides.…”