Vladimir A. Mukhanov

The interrelation between hardness and compressibility of substances and their structure and thermodynamic properties

A strong correlation relationship has been established between the structure and specific Gibbs free energy of the substance atomization on the one hand, and the substance hardness and volume compressibility on the other. In the framework of the model proposed hardness is directly proportional to the specific Gibbs free energy per bond in isodesmic crystals. An application of a correction coefficient to the ionic component of chemical bonds allows one to evaluate the hardness of compounds having both the covalent (polar and nonpolar) and ion bonds. In the framework of the suggested approach we have been the first to correctly calculate the temperature dependence of the hardness by the example for diamond and cubic boron nitride.

Thermodynamic model of hardness: Particular case of boron-rich solids

A number of successful theoretical models of hardness have been developed recently. A thermodynamic model of hardness, which supposes the intrinsic character of correlation between hardness and thermodynamic properties of solids, allows one to predict hardness of known or even hypothetical solids from the data on Gibbs energy of atomization of the elements, which implicitly determine the energy density per chemical bonding. The only structural data needed is the coordination number of the atoms in a lattice. Using this approach, the hardness of known and hypothetical polymorphs of pure boron and a number of boron-rich solids has been calculated. The thermodynamic interpretation of the bonding energy allows one to predict the hardness as a function of thermodynamic parameters. In particular, the excellent agreement between experimental and calculated values has been observed not only for the room-temperature values of the Vickers hardness of stoichiometric compounds, but also for its temperature and concentration dependencies.

Thermodynamic aspects of materials’ hardness: prediction of novel superhard high-pressure phases

In the present work, we have proposed a method that allows one to easily estimate the hardness and bulk modulus of known or hypothetical solid phases from the data on Gibbs energy of atomization of the elements and corresponding covalent radii. It has been shown that hardness and bulk moduli of compounds strongly correlate with their thermodynamic and structural properties. The proposed method may be used for a large number of compounds with various types of chemical bonding and structures; moreover, the temperature dependence of hardness may be calculated, which has been performed for diamond and cubic boron nitride. The correctness of this approach has been shown for the recently synthesized superhard diamond-like BC5. It has been predicted that the hypothetical forms of B2O3, diamond-like boron, BC x and CO x , which could be synthesized at high pressures and temperatures, should have extreme hardness.

On melting of B4C boron carbide under pressure

The pressure dependence of melting temperatures for boron carbide and B4C-carbon eutectic has been studied up to 8 GPa, and it was found that in both cases the melting curves exhibit negative slope (−13 ± 6 K/GPa), that is indicative of higher density of the melt as compared to the solid phase.

Hardness of materials at high temperature and high pressure

The intrinsic character of the correlation between hardness and thermodynamic properties of solids has been established. The proposed thermodynamic model of hardness allows one to easily estimate hardness and bulk moduli of known or even hypothetical solids from the data on Gibbs energy of atomization of the elements or on the enthalpy at the melting point. The correctness of this approach is illustrated by an example of the recently synthesized superhard diamond-like BC5 and orthorhombic modification of boron, γ-B28. The pressure and/or temperature dependences of hardness were calculated for a number of hard and superhard phases, i.e. diamond, cBN, B6O, B4C, SiC, Al2O3, β-B2O3 and β-rh boron. Excellent agreement between experimental and calculated values is observed for temperature dependences of Vickers and Knoop hardness. In addition, the model predicts that some materials can become harder than diamond at pressures in the megabar range.

Self-propagating high-temperature synthesis of boron phosphide

A new method of producing boron phosphide (BP) submicron powders by a self-propagating high-temperature reaction between boron phosphate and magnesium in the presence of an inert diluent (sodium chloride) has been proposed. Bulk polycrystalline BP with microhardness of HV = 28(2) GPa has been prepared by sintering the above powders at 7.7 GPa and 2600 K.

On melting of silicon carbide under pressure

The melting of silicon carbide has been studied at pressures 5–8 GPa and temperatures up to 3300 K. It has been found that SiC melts congruently, and its melting curve has negative slope of −44 ± 4 K/GPa.

Self-propagating high-temperature synthesis of boron subphosphide B12P2

Two new methods to produce nanopowders of B12P2 boron subphosphide by self-propagating high-temperature synthesis have been proposed. Bulk polycrystalline B12P2 with microhardness of HV = 35(3) GPa and stability in air up to 1300 K has been prepared by sintering these powders at 5.2 GPa and 2500 K.

On Electrical Conductivity of Melts of Boron and Its Compounds under Pressure

The electrical conductivity of melts of boron and its carbide (B4C), nitride (BN), and phosphide (BP) has been studied at pressures to 7.7 GPa and temperatures to 3500 K. It has been shown that these melts are good conductors with specific electrical conductivity values comparable with that of iron melt at ambient pressure.

On melting of boron subnitride

Melting of rhombohedral boron subnitride B13N2 has been studied in situ at pressures to 8 GPa using synchrotron X-ray diffraction and electrical resistivity measurements. It has been found that above 2.6 GPa B13N2 melts incongruently, and the melting curve exhibits positive slope of 31(3) K/GPa that points to a lower density of the melt as compared to the solid phase.