Hardness of covalent and ionic crystals: first-principle calculations

A new concept, the strength of bond, and a new form expressing the hardness of covalent and ionic crystals are presented. Hardness is expressed by means of quantities inherently coupled to the atomistic structure of matter, and, therefore, hardness can be determined by first-principles calculations. Good agreement between theory and experiment is observed in the range of 2 orders of magnitude. It is shown that a lower coordination number of atoms results in higher hardness, contrary to common opinion presented in general literature.     

Superconductivity in crystals with covalent bonds

Novel types of ground states associated with properties of heavy fermion systems are derived for crystals with covalent bonds generated by short-range exchange forces between valence electrons of atoms localized at lattice sites. It is shown that the short-range exchange forces can give rise to a narrow energy band in which electrons can exhibit an enormous effective mass. The same exchange forces provide the microscopic mechanism for spin-singlet pairing of electrons into Cooper pairs which are responsible for superconductivity in these systems. This superconductivity exhibits several different anisotropic superconducting states. The effective mass, Fermi energy, specific heat, Pauli susceptibility, critical temperatures and critical magnetic field of heavy fermion systems are calculated and compared with experimental data.The authors thank Dr. . Jano for discussions.     

Lattice dynamics of ionic and covalent crystals

Lattice dynamics has some claim to being the oldest branch of solid state physics. Planck's Theory of Radiation and the Theory of Specific Heat was published by Einstein in 1907, On Vibrations in Space Lattices by Born and von Karman in 1912, and On the Theory of Specific Heat by Debye in the same year. Other early papers on lattice dynamics included those by Debye and by Waller on the effect of temperature op the scattering of x-rays by a crystal. In the 1920's Peierls made fundamental contributions to the theory of thermal conductivity and of electrical conductivity involving lattice dynamics, and in the 1930's Blackman brought to an end the acceptance of the complete validity of the Debye theory of specific heat and also contributed the first papers on anharmonic effects in the absorption of infrared radiation by ionic crystals. The work we have mentioned used the formal theory of lattice dynamics to account for the thermal and other properties of crystals. It was not until 1940 that Kellermann made the first moderately successful attempt to predict the dynamical properties of a crystal—sodium chloride—from something approaching first principles, and it was in the late 1950's that the development of the technique of neutron inelastic scattering made it possible for the first time t o acquire detailed knowledge of the spectrum of lattice vibrations of a crystal. The development of this experimental technique, pioneered by Brockhouse, was possibly the main impetus for the greatly increased activity in the subject at the present time. The formal theory of lattice dynamics in the harmonic approximation is now on a firm foundation, largely provided by the work of Born and his collaborators, and was recently reviewed by Maradudin, Montroll and Weiss.¹ Much recent work has been concerned with anharmonic effects and their influence on the thermal, dielectric, and radiation-scattering properties of crystals, and on the theory of the dynamics of imperfect crystals. The subject has become comparatively wide-ranging. In this review we shall concentrate on work where the ultimate objective is to understand the dynamical properties of a crystal in terms of the interaction between electrons and nuclei or, more realistically, between ‘ion cores’ interacting directly and through the valence electrons. This objective has been most nearly achieved for the alkali metals because of their relatively simple electronic structure, but we largely exclude metals from consideration since the subject, Lattice Dynamics of Metals, has recently been reviewed by Joshi and Rajagopal.² Kellermann's theory³ of the dynamics of sodium chloride involved interactions between point charges representing the ions, Born having already shown⁴ that the cohesive energy of alkali halides could be understood on this basis. The theory of the cohesive energy of ionic crystals has recently been reviewed by Tosi.⁵ We begin at this point in the development of the theory for nonmetallic crystals since many of the concepts in more recent work can be expressed in terms of those which apply to the simple point ion model of an ionic crystal. The dielectric and dynamical properties of ionic crystals are so intimately connected that we also briefly discuss the former.     

Dislocation dynamics in solid solutions of covalent crystals

The dislocation mechanism of solid solution strengthening of covalent semiconductor crystals has been studied. The change in the regularities of dislocation dynamics in solid solutions from those in the components of the solution is connected with the manifestation of the nonlinear drift of dislocation kinks. The theory developed suggests an explanation of specificities of the dislocation mobility in a Ge_1–cSi_c solid solution.     

Hardness and slip systems of orthorhombic hen egg-white lysozyme crystals

Hardness and slip systems by an indentation method were investigated on different habit planes of orthorhombic hen egg-white lysozyme (O-HEWL) crystals containing water. A dependence of the hardness on the water-evaporation time exhibits three stages as incubation, transition and saturated ones, as tetragonal (T)-HEWL crystals reported previously. The hardness values of (1 1 0), (0 1 0) and (0 1 1) habit planes of O-HEWL in the incubation stage or wet condition exhibits 6, 8 and 10 MPa, respectively. The hardness depends on indented planes but it is independent of the air-humidity and crystal volumes. These values correspond to the intrinsic hardness for O-HEWL crystals containing water. In the incubation stage, the slip traces are clearly observed around the indentation mark and the corresponding six kinds of slip systems are identified to be {0 1 1}<1 0 0>, {1 1 0}<1 1 0>, {0 1 1}<0 1 1>, {1 1 0}<0 0 1>, {1 0 0}<0 0 1> and {0 1 0}<0 0 1>.     

Screening of the electric field in covalent crystals containing point defects

An expression is derived within the framework of the Debye-Hückel approximation for the screening length of a field in a p-type semiconductor taking into account the energy spread of immobile acceptor levels and the density of states tail of the valence band. It is shown that the screening length depends additively on the product of the carrier density and their diffusion coefficient ratio (for free holes and holes hopping via acceptors).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 41–43, November, 1984.     

Nanoscale peculiarities of the thermally stimulated surface autosegregation of covalent crystals: Gallium arsenide

Nanoscale changes in the morphology and elemental composition of cleavage surfaces of gallium arsenide crystals, which arise due to thermally stimulated surface autosegregation, are investigated in detail and systematized. It is shown that, depending on the annealing conditions (temperature, duration, and evacuation), gallium arsenide dissociates, forming submicron nonstoichiometric layers on the surface or local phases of arsenic, gallium, and gallium oxide. The mechanism and nature of autosegregation are determined by the competing processes of arsenic sublimation and its surface diffusion with an activation energy of ～31 kJ/mol. The migration of arsenic atoms is described with the help of a crystallochemical model. The nanomorphology of the surface phases includes arsenic and gallium nanoparticles with sizes of 10-200 nm, their agglomerates, and gallium oxide nano- and microcrystallites combined in plate- and chainlike configurations.     

Effect of three-body interactions on electronic polarizabilities and photoelastic behaviour of partially covalent crystals

Summary We have investigated the effect of three-body interactions on the photoelastic behaviour and the electronic polarization of silver, thallium and copper halides, which are partially covalent in character and possess three different crystall structures. The cation, anion and molecular polarizabilities calculated in their crystalline state seem to be reliable as they follow a systematic trend. Our calculated values of the strain derivatives of the electronic dielectric constants are much closer to their experimental data than those obtained by earlier workers. To speed up publication, the authors of this paper have agreed to not rceive the proofs for correction.     

Some features of surface formation during brittle failure of covalent crystals with diamond-type lattice according to EPR data

The dependence was found of the intensity of “mechanical paramagnetic centres” EPR signals on the temperature of grinding of diamond, silicon carbide, silicon and germanium crystals. Signals intensity increase with grinding temperature lowering (up to 77 K) is related with formation of the materials' amorphous phase during their brittle failure as well as with specific features of the microcracks structure development.     

Inter-relationship between optical dielectric constant and interatomic separation of mixed crystals in ionic and covalent binary compound families

An ion dependent dielectric model is developed for mixed binary crystals. The interatomic separation (R) and optical dielectric constant (ε_∞) of the mixed crystals are computed from the measured values of R and ε_∞ of pure crystals. An empirical relation between ε_∞ and R is therefore found for mixed crystals by using the computed values. It is found that the dielectric behaviour of ionic mixed crystals is cation dependent while that of covalent mixed crystals is anion dependent. The prescribed theory can therefore be used to form different mixed crystals with particular values of ε_∞ required in any specific opto-electronic devices.     

Hardness of Wurtzite-Structured Semiconductors

rickets hardness calculations of eleven wurtzite-structured semiconductors are performed based on the microscopic hardness model. All the parameters are obtained from first-principles calculations. There are two types of chemical bonds in wurtzite-structured crystals. The overlap populations of the two types of chemical bonds in lonsdaleite are chosen as Pe for wurtzite structure. The calculated bond ionicity values of the wurtzite-structured semiconductors are in good agreement with the ionicities from the dielectric definition. When the hardness of wurtzite-structured crystal is higher than 20 GPa, our calculated rickets hardness is within 10% accuracy. Therefore, the hardness of novel wurtzite-structured crystal could be estimated from first-principles calculations.     

Feasibility of covalent quasicrystals

An algorithm for constructing a quasicrystalline structure based on atoms with tetrahederal coordination of covalent atomic bonds (the typical coordination for group IV atoms) is proposed. The algorithm is used to construct a computer model of a cluster with icosahedral symmetry. The model is used to estimate the energy parameters of the structure and the distributions of bonds over interatomic bond lengths and interbond angles. The distributions obtained correlate well with the analogous results for silicon glasses and do not impose any fundamental constraints on the implementation of such structures in practice. Zh. éksp. Teor. Fiz. 114, 2187–2193 (December 1998)     

Raman tensor of covalent semiconductors

The Raman cross section in covalent semiconductors is analysed by means of simple tight-binding models. The required dependence of the model Hamiltonian upon the ionic displacements is estimated from the variation of the electronic susceptibility of a crystal under hydrostatic pressure. Our results for the Raman tensor are in satisfactory agreement with both experimental data and previous computations. Some results for the optical deformation potentials are presented as well.     

Elastic properties of covalent glasses

The dependence of bulk moduli on compositions has been studied for chalcogenide glasses and a-Si:H films. The modulus is nearly constant when the average coordination number (Z) is smaller than 2.7, and increases drastically when Z ⪆ 2.7. This dependence differs from the theoretical result, which predicts the elastic phase transition at Z = 2.4. Origins of this disagreement are discussed.     

Hardness of microporous SiC ceramics

Samples of silicon carbide ceramics with variable microporosity and hardness are studied. By measuring the hardness of the ceramics as a function of the integral porosity, it is established that the hardness is proportional to the mean length of bridges connecting pores. Microporosity is found to influence the hardness via stress concentration at the bridges, as a result of which they break up. Indentation causes extensive breakup of the bridges. The mean stress coefficient as a function of the integral porosity of the ceramics is estimated. It is shown that the micromechanisms of quasi-static indentation and high-speed indentation (penetration of a striking bar) are in many ways similar to each other.     

Superconductivity in covalent semiconductors

This review covers recent advances in superconductivity of diamond, Si, SiC, group III–V and II–IV semiconductors, metal-intercalated graphite and fullerites. The results are critically analyzed and prospects are given for future research directions. In particular, it is argued that the highest transition temperatures of ∼9 K in diamond and 11.5 K in CaC₆ can further be enhanced and that no reliable evidence exists yet for superconductivity in III-V semiconductors.