Prediction of Novel Ultrahard Phases in the B–C–N System from First Principles: Progress and Problems

Abstract

The modern synthesis of superhard and, especially, ultrahard phases is a fascinating area of research that could lead to the design of new, industrially important materials. Computational methods built within the well-established quantum mechanics framework of density functional theory (DFT) play an important role in the search for these advanced materials and the prediction of their properties. The close relationship between the physical properties of carbon and boron nitride has led to particular interest in the B–C–N ternary system, characterized by the small radii of the elements, resulting in short interatomic distances and reduced volumes—the parameters being ‘recipes’ for very high hardness in three-dimensional structures. The purpose of this review is to provide a brief outline of recent developments and problems in predicting novel ultrahard carbon allotropes as well as binary and ternary compounds of the B–C–N system with particular emphasis on the analysis of the models used to evaluate the hardness of the theoretically predicted structures.

Crystal chemistry and ab initio investigations of new hard tetragonal C9 and C12 allotropes with edge- and corner-sharing C4 tetrahedra and diamond-related properties

“…Table 4 shows the hardness values calculated using other models in addition to the thermodynamic model. As in the case of other ultrahard phases [25], the Lyakhov-Oganov model gives underestimated hardness values, while both empirical models do not work properly in the case of C 9 and C 12 , which are characterized by low (0.82 and 0.71) values of the Pugh's modulus ratio (G/B).…”

“…Four modern theoretical models [20][21][22][23] have been used to predict (H V ). It has been previously reported that the thermodynamic (T) model [20], which is based on thermodynamic properties and crystal structure, shows surprising agreement with available experimental data [24] and is therefore recommended for hardness evaluation of superhard and ultrahard phases [25]. The Lyakhov-Oganov (LO) model [21] takes into account the topology of the crystal structure, the strength of covalent bonding, the degree of ionicity and directionality; however, in the case of ultrahard phases of light elements, this model gives underestimated hardness values [24,25].…”

Prospective view of nitride material synthesis

“…With the advent of the ability to separate the constituents of air and produce oxygen‐free atmospheres (either in vacuum or inert), it has become commonplace to enable the formation of materials from techniques such as vapor deposition/reaction, melt growth, and solution growth to create materials that can be stable at standard temperatures and pressures even though they are not found in nature. Of these many materials, the nitrides continue to be of particular interest in a number of applications, from high hardness materials 1,2 to high oxygen resistance thermal materials 3 to strong catalysts 4–7 . As single crystals, many of the nitrides have favorable properties for opto‐electronic use, including (ultra‐)wide band gaps 8,9 and high reverse bias diode breakdown voltages 10,11 .…”

Novel superhard tetragonal BCN from crystal chemistry and first principles

“…They were early synthesized to replace expensive diamond, unstable at elevated temperatures, in mechanical applications (cf. review paper [4]). The research efforts to identify new chemical systems call for structure prediction programs like CALYPSO [5] and USPEX [6] and more recently machine learning crystallography code CrystalMELA [7].…”

“…In the present paper, we further develop the topic of novel compounds based on light elements within the B-C-N diagram [4] by focusing on original carbon nitrides. Firstly, we propose a novel cohesive carbon allotrope; hexagonal C 5 through crystal chemistry schematics going from two dimensional 2D carbon to three-dimensional 3D carbon through rationalized C insertion; the 3D allotrope C 5 was found to belong alike Lonsdaleite to lon topology (3D lon-C 5 ).…”