USD 539.53
A. R. Oganov (New York, USA; Moscow, Russia) A. O. Lyakhov (New York, USA)
Towards the theory of hardness of materials
Recent studies have shown that hardness, a complex property, can be calculated using very simple approaches or even analytical formulae. These form the basis for evaluating controversial experimental results (as we illustrate for TiO2-cotunnite) and enable a systematic search for novel hard materials, for instance, using global optimization algorithms (as we show on the example of SiO2 polymorphs).
Keywords: evolutionary prediction of crystal structure, TiO2-cotunnite, SiO2 polymorphs, computational design of superhard materials.
Recent studies have shown that hardness, a physically complex property, can be calculated using simple approaches and even analytical formulae. These approaches provide clarity in situations where experimental results are questionable (as shown for the case of pseudo-hard TiO2 with the cotunnite structure) and open the way to a systematic search for new hard materials, in particular, using global optimization methods (as shown by the authors for the example of SiO2 polymorphs).
Keywords: evolutionary algorithm for crystal structure prediction, TiO2 cotunnite, SiO2 polymorphs, computer design of superhard materials.
USD 539.53
F. M. Gao, L. H. Gao (Qinhuangdao, China)
Microscopic models of hardness
Recent developments in the field of microscopic hardness models have been reviewed. In these models, the theoretical hardness is described as a function of the bond density and bond strength. The bond strength may be characterized by energy gap, reference potential, electron-holding energy or Gibbs free energy, and different expressions of bond strength may lead to different hardness models. In particular, the hardness model based on the chemical bond theory of complex crystals has been introduced in detail. Examples of the hardness calculations of typical crystals, such as spinel Si3N4, stishovite SiO2, B12O2, ReB2, OsB2, RuB2, and PtN2, are presented. These microscopic models of hardness would play an important role in the search for new hard materials.
Keywords: hardness, bulk modulus, shear modulus, ionicity, superhard materials.
A review of recent developments in the field of microscopic hardness models is given. In these models, the theoretical hardness is described as a function of bond density and bond strength. Bond strength can be characterized by the band gap, the reference potential, the electron holding energy, or the Gibbs free energy. Therefore, different expressions of bond strength will lead to different hardness models. In particular, a hardness model based on the chemical bond theory of complex crystals is described in detail. Examples of hardness calculations for typical crystals such as spinel S3N4, stishovite SiO2, B12O2, ReB2, OsB2, RuB2 and PtN2 are given. These micromodels of hardness will play an important role in the search for new hard materials.
Keywords: hardness, bulk modulus, shear modulus, ionicity, superhard materials.
USD 621.921.34; 666.233.004.14
V. A. Mukhanov (Villetaneuse, France) O. O. Kurakevych (Paris, France) V. L. Solozhenko (Villetaneuse, France)
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.
Keywords: superhard materials, boron, theory of hardness.
Recently, a number of successful theoretical models of hardness have been proposed. The thermodynamic model of hardness, based on the correlation between hardness and thermodynamic properties of solids, makes it possible to predict the hardness of known or even hypothetical solids based on data on the Gibbs energy of atomization of elements, which indirectly determine the energy characteristics of chemical bonds. In this case, the only necessary structural characteristic is the coordination number of atoms in the lattice. Within the framework of this approach, the hardness of known and hypothetical modes was calculated of elemental boron and a number of compounds based on it. Thermodynamic interpretation of the energy characteristics of chemical bonds allows calculating the hardness of the phases as a function of their thermodynamic parameters. In particular, good agreement between the experimental and calculated values of Vickers hardness was observed not only for stoichiometric compounds at room temperature, but also for the temperature and concentration dependences of hardness.
Keywords: superhard materials, boron, hardness theory.
USD 539.53
J. S. Tse (Saskatoon, Saskatchewan, Canada)
Intrinsic hardness of crystalline solids
The current status of various theoretical approaches to the prediction of material hardness has been reviewed. It is shown that the simple empirical correlation with the shear moduli generally provide very good estimates of the Vickers hardness. Semi-empirical models based solely on the strength of the chemical bonds, although performed as well, are theoretically incomplete. First-principles calculations of the ideal stress and shear strength are perhaps the most reliable and theoretically sound approach available to compare theoretical predictions with experiment.Keywords: hardness, crystalline solids, shear moduli, strength of the chemical bonds, ideal stress, shear strength.
The current state of various theoretical approaches to predicting the hardness of materials is considered. It is shown that a simple empirical correlation with the shear modulus usually gives a very good estimate of the Vickers hardness. Also developed semi-empirical models based solely on the strength of chemical bonds are theoretically incomplete. First-principles calculations of the ideal stress and shear strength are perhaps the most reliable and theoretically sound approach to comparing theoretical predictions with experimental results.
Keywords: hardness, crystal, shear modulus, strength of chemical bonds, ideal stress, shear strength.
USD 548.3
Q. Li, H. Wang, Y. M. Ma (Changchun, China)
Predicting New Superhard Phases
The search for new superhard materials is of great importance in view of their major roles played for the fundamental science and the industrial applications. Recent experimental synthesis has made several great successes, but the synthetic difficulty in general remains. Materials design technique is highly desirable as a request to assist experiment. In this paper, two rational theoretical methods of design of superhard materials have been reviewed: (i) substitutional method, which is successful in some cases, but limited to the known chemically related phases, and (ii) global free energy minimization method, which can be applied to large scale of materials with the only information of chemical compositions. The successful applications have been described and the main principles are summarized.
Keywords: superhard materials, crystal structure prediction, substitutional method, free energy minimization method, first-principles.
The search for new superhard materials is very important both for their role in fundamental science and for industrial applications. Several very successful synthesis experiments have been carried out recently, but difficulties in synthesis in general remain. Material design techniques are needed to assist in the experiments. In this paper, two rational theoretical methods for the design of superhard materials are reviewed: (1) the substitution method, which is successful in some cases but is limited to known chemically related phases, and (2) the global free energy minimization method, which can be applied to a large number of materials with only information on their chemical compositions.
Keywords: superhard materials, crystal structure prediction, substitution method, free energy minimization method, first principles.
USD 544.225:546.27
K. Shirai (Mihogaoka, Ibaraki, Osaka, Japan)
Electronic structures and mechanical properties of boron and boron-rich crystals (Part I)
Boron and boron-rich crystals are hard materials, which have unique properties compared with other hard materials, such as diamond. Various ways of the arrangement of icosahedra yield many complicated crystal polymorphs and their derivatives. Although the crystals are basically hard, these are internally flexible for the mechanical and chemical properties. This flexibility is a consequence of conspiracy between the soft part and the hard part of the structure. The soft part is conveyed by the icosahedral unit, and the hard part is by the bonds connecting icosahedra. This article attempts to provide a consistent description for the unique characters of boron and boron-rich solids from the electronic-structure calculations. Recent developments of the first-principles calculation provide significant contributions to our understanding of the unusual properties of this class of materials. In particular, a combination of high-pressure experiment is successful in providing convincing evidence for our understanding, while it gives rise to unforeseen developments, such as discovery of superconductivity. Throughout analyzes of many properties of boron solids, care is repeated for the effects of special arrangement of atoms and atom relaxation for those of complicated structures, which otherwise would mislead our intuitive interpretations. Special emphasis is placed on the phase stability and phase transitions at high pressure, because of recent successful discoveries of novel hard materials, such as γ-orthorhombic boron and diamond-like BC5 compound. The first part of this review describes the ground state of boron and boron-rich crystals. The energy gap, native defects, and phonon properties are discussed.
Keywords: rhombohedral boron, boron-rich crystals, first-principles calculation, icosahedron-based structure, native defects, electronic structure.
Boron and boron-rich crystals are hard materials whose unique properties are comparable to those of other hard materials such as diamond. The different arrangements of the icosahedra give rise to many complex crystalline modifications and their derivatives. Although the crystals are essentially hard, their mechanical and chemical properties are intrinsically compliant. This ductility results from the agreement between the soft and hard parts of the structure. The soft part is provided by the icosahedral node and the hard part by the bonds connecting the icosahedra. This paper is an attempt to give a consistent description of the unique properties of boron and boron-rich solids based on electron structure calculations. Recent developments in first-principles calculations have made important contributions to our understanding of the unusual properties of this class of materials. In particular, the combination of high-pressure experiments has been successful in providing compelling evidence for our understanding and has led to unexpected developments such as the discovery of superconductivity. Analyses of many properties of solid boron highlight the need for caution in determining the influence of specific atomic arrangements and relaxation for these complex structures, which might otherwise mislead our intuitive interpretations. Particular attention is paid to phase stability and phase transitions at high pressures because of the recent successive discoveries of new solid materials such as γ-orthorhombic boron and the diamond-like compound BC5. In the first part of this review, the ground state of boron and boron-rich crystals is described. Band gaps, intrinsic defects, and phonon properties are discussed.
Keywords: rhombohedral boron, boron-rich crystals, first-principles calculations, icosahedra-based structure, intrinsic defects, electronic structure.