Global Structural Optimization of Tungsten Borides

Abstract

Tungsten borides are among a distinct class of transition-metal light-element compounds with superior mechanical properties that rival those of traditional superhard materials. An in-depth understanding of these compounds, however, has been impeded by uncertainties regarding their complex crystal structures. Here, we examine a wide range of chemical compositions of tungsten borides using a recently developed global structural optimization approach. We establish thermodynamically stable structures and identify a large number of metastable phases. These results clarify and correct previous structural assignments and predict new structures for possible synthesis. Our findings provide crucial insights for understanding the rich and complex crystal structures of tungsten borides, which have broad implications for further exploration of this class of promising materials.

Crystal Structure of W1−x B3 and Phase Equilibria in the Boron-Rich Part of the Systems Mo-Rh-B and W-{Ru,Os,Rh,Ir,Ni,Pd,Pt}-B

“…[20][21][22][23][24][25][26] Zhang et al [24] reopened the question on the correct crystal structure of WB 4 or WB 3 , as the calculated indentation hardness of WB 4 is lower than that of ReB 2 in contrast to the experimental result and the calculated normalized c/a ratio of WB 3 exhibits a negative pressure dependence, inconsistent with the observed trend. Li et al [25] in their latest study presented new thermodynamically stable structures for WB 3 (R 3m-''6u'') and WB 4 (P6 3 /mmc-''2u''). However, the DFT stability calculations so far never considered nonstoichiometric W 1Àx B 3 with defects in metal atom sites.…”

“…However, more recent theoretical calculations of band structure and physical properties (density functional theory calculations DFT) of this compound have inferred some confusion on the true crystal structure of ''WB 4 ''. [20][21][22][23][24][25][26] Whereas the first studies by Chretien and Helgorsky [15] reported a tetragonal unit cell for ''WB 4 '' (a = 0.634 nm, c = 0.450 nm), Rudy et al [16] claimed a hexagonal cell (a = 0.3004 nm, c = 0.3174 nm) but proposed ''WB 12 '' as a more appropriate composition. A first structure model was derived by Romans and Krug [17] from x-ray powder data backed by single crystal Laue and precession photographs indexed on a hexagonal lattice (a = 0.5200 nm, c = 0.6340 nm).…”

“…The theoretical DFT studies on the structural assignment and stability of WB 4 or MoB 4 (WB 3 or MoB 3 ) [20][21][22][23][24][25][26] claimed that WB 3 (MoB 3 ) with a two-dimensional boron net is thermodynamically more stable than WB 4 (MoB 4 ) with a three-dimensional boron skeleton. [20][21][22][23][24][25][26] Zhang et al [24] reopened the question on the correct crystal structure of WB 4 or WB 3 , as the calculated indentation hardness of WB 4 is lower than that of ReB 2 in contrast to the experimental result and the calculated normalized c/a ratio of WB 3 exhibits a negative pressure dependence, inconsistent with the observed trend.…”

Influence of boron vacancies on phase stability, bonding and structure ofMB2(M = Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W) with AlB2type structure

“…For group VI, B0 of CrB2-x is close to constant for x < 0.167 after which it start to decrease whereas B0 of both MoB2-x and WB2-x decreases at small x, compared to x = 0, followed by a small increase up to x = 0.25 and 0.333, respectively, and then decreases at higher x. Recently, phonon calculations of WB2, with AlB2 structure, showed imaginary frequencies which indicates that it is dynamically unstable [41]. By modifying WB2, either through creation of puckered B-layers (R3 ̅ m or P63/mmc) or formation of B-vacancies, the imaginary frequencies are expected to disappear as well as stabilize the phase.…”

High-Energy Density and Superhard Nitrogen-Rich B-N Compounds

“…CALYPSO has been used to investigate a great variety of materials at high pressures [33][34][35][36][37][38]. Detailed information on the calculations is provided in the Supplemental Material [39].…”