From ELF to compressibility in solids

Abstract

Understanding the electronic nature of materials' compressibility has always been a major issue behind tabulation and rationalization of bulk moduli. This is especially because this understanding is one of the main approaches to the design and proposal of new materials with a desired (e.g., ultralow) compressibility. It is well recognized that the softest part of the solid will be the one responsible for its compression at the first place. In chemical terms, this means that the valence will suffer the main consequences of pressurization.It is desirable to understand this response to pressure in terms of the valence properties(charge, volume, etc.). One of the possible approaches is to consider models of electronic separability, such as the bond charge model (BCM), which provides insight into the cohesion of covalent crystals in analogy with the classical ionic model. However, this model relies on empirical parametrization of bond and lone pair properties. In this contribution, we have coupled electron localization function (ELF) ab initio data with the bond charge model developed by Parr in order to analyze solid state compressibility from first principles and moreover, to derive general trends and shed light upon superhard behavior.

Figure 1

Bond charge model for homonuclear (left) and heteronuclear (right) molecules, A₂ and AX, respectively. The meaning of the main parameters that are needed in each case is shown in the figures: q and R_B stand for neutral homonuclear molecules as q, δ, r₁/r₂ and R_B do for heteronuclear ones; B label stands for the bond (see text for more details). $r_1^{\prime }$ and $r_2^{\prime }$ are also shown for clarity.

Figure 2

Definition of length-related bond charge model parameters, [R_B, r₁/r₂], for a homonuclear molecule, N₂ (left), and a heteronuclear molecule, BN (right).

Figure 3

Experimental vs. non empirical new bond charge model (NEWBCM) bulk modulus (GPa).

Figure 4

Experimental (empty symbols) and NEWBCM (full symbols) bulk moduli (in GPa) for IV, III–V and II–VI compounds. Bulk moduli in GPa, charge in electrons, R in atomic units.

Figure 5

Evolution of the geometrical parameters, r₁, r₂ and R_B, upon compression of the interatomic distance R for BN (left) and BAs (right). Data relative to the corresponding equilibrium values denoted by a 0 superscript. All numbers in Å.