A DFT-Based Quantitative and Geometric Analysis of the Effect of Pressure on Boron Arsenate

Abstract

Boron arsenate, BAsO4, is a β-cristobalite-like crystal which has been reported to exhibit the rather unusual property of negative linear compressibility behaviour at elevated pressures, that is expanding rather than shrinking in a linear dimension when subjected to pressure. This work proposes a ‘geometry—deformation mechanism’-based mathematical model to aid the discernment of the manner how this anomalous pressure behaviour is achieved. The model makes use of data obtained from DFT simulations over an extended range of pressures, including extreme pressure conditions, and rigorously explains the macroscopic properties of this material in terms of the nanoscale deformations. More specifically, through this model, it was possible to decipher the different contributions to the deformation mechanism and compressibility properties of BAsO4. Moreover, for the first time, it was shown that a rule related to the sum of angles of tetrahedrally coordinated atoms is so robust that it applies at the extreme pressures studied here.

Boron Arsenate Scaled‐Up: An Enhanced Nano‐Mimicking Mechanical Metamaterial

“…As explained by Grima‐Cornish et al, [ 54 ] given these parameters, one may calculate the height of the AsO 4 and BO 4 tetrahedra, h a and h b respectively as and the dimensions of 2D projected squares, in terms of the lengths of the diagonals, which correspond to the lengths of the edges lying in the (001) plane, i.e., d a (for the square related to the AsO 4 tetrahedron) and d b (for the square related to the BO 4 tetrahedron) and the 2D angle between them, θ 2d , as follows …”

“…The same work [ 54 ] further explains that when this material is subjected to a pressure change (increase), there are two main types of deformation that are crucial to imparting on this material its observed compressibility properties, namely: 1) A deformation of the tetrahedra themselves, due to changes in OX bond lengths and OXO bond angles, where the tetrahedra are observed to become elongated with an increase in pressure within the pressure range from c. 5 to c. 50 GPa, while retaining their characteristic tetragonal disphenoidal shape (i.e., the length d gets shorter and their height increases). This feature gives rise to the observed negative linear compressibility (NLC) characteristics in the c direction at elevated pressures within the range of c. 5 to c. 50 GPa (range predicted by the simulations) and occurs since over this pressure range, changes in the OXO bond angles are more pronounced than changes in the OX bond lengths.…”

“…One of the materials which has been extensively studied in recent years in terms of its anomalous mechanical properties, including molecular‐level auxeticity, [ 49–54 ] is the beta‐cristobalite phase of boron arsenate ( symmetry), [ 55,56 ] a rather simple crystalline material made from just three types of atoms: boron (B), arsenic (As), and oxygen (O). The boron and arsenic atoms are sp 3 hybridized and located at the centers of tetrahedra having oxygens at the vertices, to form BO 4 and AsO 4 tetrahedral units.…”

“…A geometric investigation of boron arsenate based [ 54 ] on data obtained through density functional theory (DFT) based simulations suggests that the AsO 4 and BO 4 tetrahedral units, when subjected to a hydrostatic pressure (with no additional uniaxial or shear loads) adopt the shape of tetragonal disphenoids, i.e., tetrahedra having four congruent faces which are in the shape of isosceles triangles. This means that the tetrahedra are completely defined by just two geometric variables, which could be the length d of the base and the length of two‐equal sides of these isosceles triangles, where the tetrahedra would have two opposite edges corresponding to the base of such triangles, with the other four edges corresponding to the sides (see Figure 1c–ii, where the base edges are highlighted via dashed lines).…”

“…[1] It also led to some very interesting and novel publications which reported and analyzed various constructs which exhibit a negative Poisson's ratio due to their geometry and deformation mechanism. [43][44][45][46][47][48] One of the materials which has been extensively studied in recent years in terms of its anomalous mechanical properties, including molecular-level auxeticity, [49][50][51][52][53][54] is the beta-cristobalite phase of boron arsenate (I4 symmetry), [55,56] a rather simple crystalline material made from just three types of atoms: boron (B), arsenic (As), and oxygen (O). The boron and arsenic atoms are sp 3 hybridized and located at the centers of tetrahedra having oxygens at the vertices, to form BO 4 and AsO 4 tetrahedral units.…”