Towards a microscopic theory of the modulus of elasticity in crystalline covalent materials and a survey of potential superhard materials

The present report is an account of the generalization of the dynamic elasticity theory earlier proposed by Bucknum et al. and applied to the cubic diamond and tetragonal glitter lattices. It describes a theory of elasticity in which the elasticity moduli are based upon the microscopic constants of the various structure-types. Such microscopic constants include the force constants of the chemical bonds in the unit of pattern of the material, its associated lattice parameters, and the elastic chemical bond deformation parameters of the material. In developing the outward features of the dynamic elasticity model, it is shown that an integral over the force density in the unit cell of a given material; where the force is modeled based upon the elastic deformation forces of the chemical bonds in the unit of pattern of the material, and the volume is written as a function of the deformations taking place inside the unit cell of the material; generates the terms for calculating its modulus of elasticity at pressure, in components, that are directed along the principal axes of the unit cell. Several potential solutions to the problem of superhardness are discussed and illustrated.     

A DFT study on the electronic structure for iridium nitride under high pressure

We present density functionary theory (DFT) calculations on the structural parameters and electronic structure for iridium nitride by using the generalized gradient approximation (GGA) and the Perdew–Burke–Ernserhof (PBE) exchange-correlation functional. The lattice parameters and bulk modulus (B ₀) for the ground state are obtained, and the energy band structure and electron densities of states (DOS) of IrN₂ are presented. It is found that IrN₂ has a very close indirect energy gap. There is a strong covalent bond between the two nearest N atoms. This gives rise to a very high elastic modulus of IrN₂ and reveals the quasimolecular nature of the N₂ in IrN₂ crystal. Lattice parameters, bulk modulus, and the electronic structure of IrN₂ under high pressure have also been investigated based on DFT. The compressibility along three cell vectors is very close to each other. The band gap increases a little with the pressure even when the pressure is up to 100 Gpa.     

Ab initio calculation of structural,lattice dynamical,and thermal properties of cubic silicon carbide

We present first-principles calculations of the structural, lattice dynamical, and thermal properties as well as Raman results for cubic silicon carbide (3C SiC). The plane-wave pseudopotential approach to density functional theory (DFT ) in the local density approximation has been used to calculate the equilibrium properties of 3C SiC, i.e., the ground-state energy, the band structure, the valence electron density, the lattice constant, the bulk modulus, its pressure derivative, and the ionicity factor of the chemical bonds. The linear-response theory within DFT has been used to obtain the phonon frequencies, the eigenvectors, and the mean-square atomic displacements. Furthermore, we calculated the mode Grueisen parameters, the internal-strain parameter, the elastic constants, the Born effective charge, and the high-frequency dielectric constant. The specific heat at constant volume and at constant pressure, the thermal expansion coefficient, the temperature dependence of the lattice constant, and that of the isothermal and adiabatic bulk modulus have been derived within the quasi-harmonic approximation. Finally, the second-order Raman spectrum of 3C SiC has been calculated using phenomenological polarizability coefficients and ab initio frequencies and eigenvectors. © 1995 John Wiley & Sons, Inc.     

First principles investigation on the ultra‐incompressible and hard TaN

The structural, electronic, and mechanical properties of TaN were investigated by use of the density functional theory (DFT). Eight structures were considered, i.e., hexagonal WC, TaN, NiAs, wurtzite, and CoSn structures, cubic NaCl, zinc‐blende and CsCl structures. The results indicate that TaN in TaN‐type structure is the most stable at ambient conditions among the considered structures. Above 5 GPa, TaN in WC‐type structure becomes energetically the most stable phase. They are also stable both thermodynamically and mechanically. TaN in WC‐type has the largest shear modulus 243 GPa and large bulk modulus 337 GPa among the considered structures. The volume compressibility is slightly larger than diamond, but smaller than c‐BN at pressures from 0 to 100 GPa. The compressibility along the c axis is smaller than the linear compressibility of both diamond and c‐BN. The estimated hardness is 34 GPa. Thus, TaN in WC‐type structure is a potential candidate to be ultra‐incompressible and hard. The unique mechanical properties of TaN in WC‐type structure would make it suitable for applications under extreme conditions. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Low-compressibility and hard material carbon nitride imide C2N2(NH): First principles calculations

First principles calculations are performed to investigate the structural, mechanical, and electronic properties of C₂N₂(NH). Our calculated lattice parameters are in good agreement with the experimental data and previous theoretical values. Orthorhombic C₂N₂(NH) phase is found to be mechanically stable at an ambient pressure. Based on the calculated bulk modulus and shear modulus of polycrystalline aggregate, C₂N₂(NH) can be regarded as a potential candidate of ultra-incompressible and hard material. Furthermore, the elastic anisotropy and Debye temperatures are also discussed by investigating the elastic constants and moduli. Density of states and electronic localization function analysis show that the strong C-N covalent bond in CN₄ tetrahedron is the main driving force for the high bulk and shear moduli as well as small Poisson's ratio of C₂N₂(NH).     

Electronic,elastic and thermal properties of lutetium intermetallic compounds

The electronic, structural, elastic, thermal and mechanical properties of Lutetium intermetallic compounds LuX (X = Mg, Cu, Ag, Au, Zn, Cd and Hg) have been studied using ab-initio full potential linear augmented plane wave (FP-LAPW) with the generalized gradient approximation (GGA) in their non magnetic phase. The ground state properties such as lattice constant, bulk modulus, pressure derivatives of bulk modulus are reported in CsCl-(B₂ phase) structure. We also report the band structure and density of states at equilibrium lattice constant. The calculated band structures indicate that these intermetallics are metallic in nature. The second order elastic constants of these compounds are also predicted for the first time. The ductility of these compounds is determined by calculating the bulk to shear ratio B/G_H.     

Ab initio Predictions of Structural and Thermodynamic Properties of Zr2AlC Under High Pressure and High Temperature

The structural and thermodynamic properties of Zr₂AlC at high pressure and high temperature are investigated by first principles density functional theory method. The calculated lattice parameters of Zr₂AlC are in good agreement with the available theoretical data. The pressure dependences of the elastic constants, bulk modulus, shear modulus, Young's modulus, and Vickers hardness of Zr₂AlC are successfully obtained. The elastic anisotropy is examined through the computation of the direction dependence of Young's modulus. By using the quasiharmonic Debye model, the thermodynamic properties including the Debye temperature, heat capacity, volume thermal expansion coefficient, and Grüneisen parameter at high pressure and temperature are predicted for the first time.     

First principles prediction of the elastic,electronic, and optical properties of Sb2S3 and Sb2Se3 compounds

We have performed a first principles study of structural, mechanical, electronic, and optical properties of orthorhombic Sb₂S₃ and Sb₂Se₃ compounds using the density functional theory within the local density approximation. The lattice parameters, bulk modulus, and its pressure derivatives of these compounds have been obtained. The second-order elastic constants have been calculated, and the other related quantities such as the Young's modulus, shear modulus, Poisson's ratio, anisotropy factor, sound velocities, Debye temperature, and hardness have also been estimated in the present work. The linear photon-energy dependent dielectric functions and some optical properties such as the energy-loss function, the effective number of valence electrons and the effective optical dielectric constant are calculated. Our structural estimation and some other results are in agreement with the available experimental and theoretical data.     

Pressure-volume relationships for CeSe and CeBe13 up to 25 GPa

The variations in the volumes of CeSe and CeBe₁₃ have been determined by powder X-ray diffraction in a diamond anvil cell up to 25 GPa at room temperature. In each case, the bulk modulus and its first pressure derivative have been determined. They do not indicate the presence of any negative contribution due to a Kondo volume-dependent interaction or a pressureinduced valence change. A crystallographic phase transformation to a cubic CsCl-type structure has been evidenced for CeSe above 18 GPa.     

Theoretical prediction of the structural,elastic, electronic,optical and thermal properties of the cubic perovskites CsXF3 (X = Ca,Sr and Hg) under pressure effect

Some physical properties of the cubic perovskites CsXF₃ (X = Ca, Sr and Hg) have been investigated using pseudopotential plane-wave method based on the density functional theory. The calculated lattice parameters within GGA and LDA agree reasonably with the available experimental data. The elastic constants and their pressure derivatives are predicted using the static finite strain technique. We derived the bulk and shear moduli, Young's modulus, Poisson's ratio and Lamé’s constants for ideal polycrystalline aggregates. The analysis of B/G ratio indicates that CsXF₃ (X = Ca, Sr and Hg) are ductile materials. The thermal effect on the volume, bulk modulus, heat capacity and Debye temperature was predicted.     

3C-SiC的结构和热力学性质

利用第一性原理平面波模守恒赝势密度泛函理论研究了3C-SiC的结构, 其零温(0 K)零压下的晶格常数、体弹模量及其对压强的一阶导数、弹性常数的计算结果与实验值和其它理论计算结果相符合. 通过准谐德拜模型, 得到了不同温度不同压强下的热容和德拜温度, 发现热容随着压强增加而减小, 德拜温度随压强增加而增加, 并成功地获得了相对晶格常数、相对体积、体弹模量、热膨胀系数与温度和压强的关系.     

Exploring the structural,mechanical and thermodynamic properties of Ti-V solid solutions

Although Ti-V based high-temperature alloys are used in aerospace engine, rocket engine and hot sections, the structure and mechanical properties of Ti-V alloys remains controversy. To explore the correlation between structural and mechanical properties, we apply employed the DFT method to study the phases stability, mechanical and thermodynamic properties of Ti-V solid solution. Two Ti-V solid solutions: Ti(V)_ss solid solution and V(Ti)_ss solid solution are discussed. Two Ti-V solid solutions are thermodynamic stability. In particular, the Ti-V solid solution prefers to form V(Ti)_ss solid solution, in while the V(Ti)_ss solid solution remains cubic structure. Furthermore, the Ti(V)_ss solid solution is a mechanical instability. However, the V(Ti)_ss solid solution is a mechanical stability. Here, the bulk modulus, shear modulus and Young's modulus of V(Ti)_ss solid solution are 136.9, 23.5 and 66.7 GPa. In particular, the bulk modulus of V(Ti)_ss solid solution is higher than the bulk modulus of the pure Ti. In addition, the V(Ti)_ss solid solution shows better ductility compared to the pure Ti and V. Naturally, the stability and mechanical properties of V(Ti) solid solution is related to the Ti-V metallic bond because of the localized hybridization between the Ti(3d) and V(3d).     

First-principles study of structural and electronic properties of gallium based nanowires

Structural stability and electronic properties of GaX (X = N, P, As and Sb) nanowires have been investigated using first-principles based density function theory approach. Out of linear, zigzag, square and hexagon shaped configuration, the square shaped geometry is energetically most stable. The computation of lattice parameters, bulk modulus and pressure derivatives for these Ga based nanowires observes the highest bulk modulus for hexagonal shaped GaN nanowire amongst all, suggest the mechanical strength of this geometry. Electronic band structures analysis shows the semiconducting as well as metallic behavior of these nanowires.     

Evaluation of the degree of cross-linking of cellulose-based superabsorbent hydrogels: a comparison between different techniques

Three different techniques have been applied to the evaluation of the degree of cross-linking of superabsorbent cellulose-based hydrogels obtained from water solutions of carboxymethylcellulose sodium salt (CMCNa) and hydroxyethylcellulose (HEC), chemically cross-linked with divinyl sulfone. These polyelectrolyte hydrogels are biodegradable and have the same sorption capacity as acrylate-based superabsorbents on the market. A ¹³C solid state NMR analysis was carried out on dry samples of hydrogel to obtain the degree of cross-linking, an important parameter that affects the swelling and mechanical properties of a hydrogel. Dynamic mechanical analysis was performed during the hydrogel cross-linking using a parallel plate rheometer under oscillatory deformations in order to monitor the evolution of the hydrogel viscoelastic properties during the synthesis. The value of |G*| and the slope of the stress-deformation ratio plots from uniaxial compression tests were used to evaluate the elastically effective degree of cross-linking according to classical rubber elasticity theory. Moreover, a dynamic mechanical analysis was carried out on cross-linked hydrogels at different degrees of swelling in order to investigate the influence of the swelling on the mechanical properties and the application of rubber elasticity theory to swollen hydrogels.     

Ab initio all-electron periodic Hartree-Fock study of hydrostatic compression of pentaerythritol tetranitrate

We present a computational study of hydrostatic compression effects on the pentaerythritol tetranitrate (PETN) energetic material up to 22.7 GPa by means of the ab initio all-electron periodic Hartree-Fock quantum mechanical method with the STO-3G Gaussian basis set. We fitted the calculated volume-energy relation to the energy SJEOS polynomial function from which we obtained the compression dependence of the pressure (P), the bulk modulus (B), and its pressure derivative (B'). We also fitted the experimental volume-pressure relation to the pressure SJEOS polynomial function, which allowed us to calculate the experimental bulk modulus (B(exp)) and its pressure derivative (). Our calculated values, B = 6.73 GPa and B' = 24.63, are in reasonable agreement with the values B(exp) = 8.48 GPa and = 14.42 from our fit to the experimental X-ray data and with the value B(exp) = 9.8 GPa that was derived from the experimental elastic constants. In addition, we present a discussion on how the lattice vectors and the internal coordinates (i.e., bond lengths, bond angles, and torsion angles) of the C(CH(2)ONO(2))(4) molecules in the PETN lattice change during hydrostatic compression of the crystal. Our calculated results suggest that the C(CH(2)ONO(2))(4) molecules cannot be considered as being rigid but are in fact flexible, accommodating lattice compression through torsions, bendings in their bond angles, and contractions in their bond lengths. At pressures higher than about 8 GPa, however, both the C(CH(2)ONO(2))(4) molecules and the c lattice vector seem to stiffen somewhat. The a lattice vector does not exhibit this stiffening. As a consequence, the pressure dependence of the c/a ratio shows a minimum at about 8 GPa.     

Theoretical study of the pressure-induced B3–B1 phase transition in Cd1−xMnxTe

The high pressure phase transition in Cd_1−xMn_xTe (0 ≤ x ≤ 0.5), which is from the cubic zinc-blende structure (B3) to the NaCl structure (B1), is investigated by using first principles spin-polarized LCAO calculations based on the density functional theory (DFT) formalism. The calculations indicate that the transition pressure of the B3-to-B1 structural phase transformation depends on the Mn content of the sample. This result is consistent with the expectation that the substitution of Cd by Mn in CdTe tends to perturb the tetrahedral coordination geometry and thereby to destabilize the B3 structure. Several structural properties (equilibrium lattice constant, bulk modulus, transition pressure, etc.) of Cd_1−xMn_xTe (x = 0.0, 0.25 and 0.5) CdTe have been calculated, which are in agreement with the previous results.     

The Zeolitic Imidazolate Framework ZIF‐4 under Low Hydrostatic Pressures

The zeolitic imidazolate framework ZIF‐4 has recently been shown to exhibit large structural flexibility as a response to hydrostatic pressures, going from an open pore phase ( ZIF ‐ 4 ( Zn )‐ op ) to a closed pore phase ( ZIF ‐ 4 ( Zn )‐ cp ). The use of diamond anvil cell (DAC) setups has so far restricted thorough experimental insight into the evolution of lattice parameters at pressures below p < 0.1 GPa. Here we revisit the high‐pressure properties of ZIF‐4(Zn) by applying a new high‐pressure powder X‐ray diffraction setup that allows for tracking the evolution of lattice parameters in pressure increments as small as Δp = 0.005 GPa in the pressure range p = ambient – 0.4 GPa; a pressure resolution that cannot be achieved by using traditional DACs. We find ZIF‐4(Zn) has a bulk modulus of K( ZIF ‐ 4 ( Zn )‐ op ) = 2.01 ± 0.05 GPa and K( ZIF ‐ 4 ( Zn )‐ cp ) = 4.39 ± 0.20 GPa, clarifying and confirming some ambiguous results that have been reported previously.     

Structural, elastic constant, and vibrational properties of wurtzite gallium nitride: a first-principles approach

Perdew-Wang proposed generalized gradient approximation (GGA) is used in conjunction with ultrasoft pseudopotential to investigate the structural, elastic constant, and vibrational properties of wurtzite GaN. The equilibrium lattice parameters, axial ratio, internal parameter, bulk modulus, and its pressure derivative are calculated. The effect of pressure on equilibrium lattice parameters, axial ratio, internal parameter (u), relative volume, and bond lengths parallel and perpendicular to the c-axis are discussed. At 52 GPa, the relative volume change is observed to be 17.8%, with an abrupt change in bond length. The calculated elastic constants are used to calculate the shear wave speeds in the [100] and [001] planes. The finite displacement method is employed to calculate phonon frequencies and the phonon density of states. The first- and second-order pressure derivative and volume dependent Gruneisen parameter (γ(j)) of zone-center phonon frequencies are discussed. These phonon calculations calculated at theoretical lattice constants agree well with existing literature.     

Compressibility of Gas Hydrates

Experimental data on the pressure dependence of unit cell parameters for the gas hydrates of ethane (cubic structure I, pressure range 0–2 GPa), xenon (cubic structure I, pressure range 0–1.5 GPa) and the double hydrate of tetrahydrofuran+xenon (cubic structure II, pressure range 0–3 GPa) are presented. Approximation of the data using the cubic Birch–Murnaghan equation, P=1.5B₀[(V₀/V)^7/3?(V₀/V)^5/3], gave the following results: for ethane hydrate V₀=1781 ų, B₀=11.2 GPa; for xenon hydrate V₀=1726 ų, B₀=9.3 GPa; for the double hydrate of tetrahydrofuran+xenon V₀=5323 ų, B₀=8.8 GPa. In the last case, the approximation was performed within the pressure range 0–1.5 GPa; it is impossible to describe the results within a broader pressure range using the cubic Birch–Murnaghan equation. At the maximum pressure of the existence of the double hydrate of tetrahydrofuran+xenon (3.1 GPa), the unit cell volume was 86 % of the unit cell volume at zero pressure. Analysis of the experimental data obtained by us and data available from the literature showed that 1) the bulk modulus of gas hydrates with classical polyhedral structures, in most cases, are close to each other and 2) the bulk modulus is mainly determined by the elasticity of the hydrogen‐bonded water framework. Variable filling of the cavities with guest molecules also has a substantial effect on the bulk modulus. On the basis of the obtained results, we concluded that the bulk modulus of gas hydrates with classical polyhedral structures and existing at pressures up to 1.5 GPa was equal to (9±2) GPa. In cases when data on the equations of state for the hydrates were unavailable, the indicated values may be recommended as the most probable ones.     

A New Molecular Theory of Non‐Linear Viscoelasticity for Vitrifiable (or Crystallizable) Thermoplastic Polyurethane Elastomers

The molecular theory of non‐linear viscoelasticity for vitrifiable thermoplastic polyurethane elastomers (VTPUE) is a refinement and extension of viscoelastic theory of thermoplastic elastomers and polyurethanes to glassy transition, a structural model and a mechanism of vitrification for glassy polymers were proposed. Five kinds of constituent chains with Nagai chain constraint consisting of soft‐domains, hard‐domains, and entanglements are used as the elementary structural and statistical ensemble units for the correlation of molecular and phase‐domain structures to the static and dynamic mechanical behaviors. So the influences of non‐Gaussian in character, the phase separation of domain, the network topology of structure, the affined deformation of constituent chains, and the thermal history are all taken into account in the constituent chains of the theory. Free energies of deformation for the VTPUE segment copolymer were calculated by the statistical mechanics with the probability distribution functions of the sizes for the five kinds of constituent chains. Then the static constitutive equations and modulus of four types of deformation and the dynamic shear viscosity, modulus and loss tangent of VTPUE are derived from the proposed theory. The theory is successful in relating the molecular chain parameters C₁₀₀, C₀₂₀, and C₂₀₀ to the constitutive equations and modulus under large deformations and the micro‐domain structure to the complex shear viscosity and modulus and the loss tangent. The dynamic shear modulus and loss tangent of VTPUE are related to the domain structures through the fraction of hard segments (W_h), the molecular weight of soft segment (M_ns), and the growth dimensional parameters of hard and soft domains (β). Two series of linear VTPUE copolymers (ES and ET) with different fractions(W_h) of hard segments and molecular weight (M_ns) of soft segments were prepared. Their static and dynamic mechanical properties were studied by uni‐axial extension and dynamic analysis tests. Then the constitutive equation at uni‐axial extension and the expressions of shear modulus and loss tangent are verified by these experimental data, and excellent agreement between the theory and experiments is achieved. It is shown, that the proposed theory can predict the viscoelastic behavior of vitrifiable thermoplastic polyurethanes.