Crystal Elastic Constants Research Articles

An Improved Artificial Neural Network Elastic Constant Prediction Method Based on Particle Swarm Optimization

As machine learning methods keep developing in materials science, using machine learning to mine novel materials has become a research hotspot. For microscopic crystals, the first-principles calculation of elastic constants has always been a conventional research method. However, the first-principles calculation method is time-consuming and laborious, which limits the development of materials. In order to achieve efficient discovery of new materials, this paper proposed an improved artificial neural network (ANN) method to predict the elastic modulus of crystals improved by particle swarm optimization (PSO), which build the PSO-ANN model in use of structures and elastic constants of crystals. Experiments show that the root mean square error (RMSE) can reach within 1GPa. To verify the accuracy of the method for other crystal predictions, the MgZn2 crystal is modelled and calculated by using the first-principles calculation method. Comparing with the prediction method proposed, the average error of the predicted elastic constants is within the range 5.6%.

К расчету упругих постоянных третьего порядка кристаллов сплава на основе TiNi с памятью формы

К расчету упругих постоянных третьего порядка кристаллов сплава на основе TiNi с памятью формы

Elastic constants of colloidal crystals with body-centered cubic lattice and constant potential on the particles

The model of charge-stabilized colloidal crystals with a monatomic body-centered cubic crystal lattice is proposed to determine elastic constants of the first and the second order. The crystals are described based on the Poisson-Boltzmann nonlinear differential equation. Electric behavior of the colloidal particles obeys the constant potential model. Elastic constants of the crystals are derived from the stress-strain dependencies obtained by means of computational simulation. Elastic constants were obtained for a broad range of lattice parameters. Stability of the crystals and the presence of the many-body effective interactions in them are briefly discussed.

Anomalous thermodynamic properties and phase stability of δ−Pu1−xMx (M=GaandAl) alloys from first-principles calculations

The composition-dependent crystal structure, volume, elastic constants, and electronic structure of $\ensuremath{\delta}\text{\ensuremath{-}}{\mathrm{Pu}}_{1\ensuremath{-}x}{M}_{x}$ $(M=\text{Ga and Al},0\ensuremath{\le}x\ensuremath{\le}0.1)$ alloys are systematically studied by using first-principles EMTO-CPA calculations. It is shown that the fcc and $L{1}_{2}$ structures co-exist in the alloys with $x\ensuremath{\le}0.04$ whereas for $xg0.04$, the $L{1}_{2}$ structure is more and more preferable and around $x=0.1$, it tends to be stabilized alone. The evaluated $V\ensuremath{\sim}x$ of the $L{1}_{2}$ structure, being negative deviation from Vegard's law, turns out to be in good agreement with the experimental result. For $x\ensuremath{\le}0.04$, the estimated $E$, $G$, $\ensuremath{\nu}$, and $\mathrm{\ensuremath{\Theta}}$ of both the fcc and $L{1}_{2}$ structures are in line with the measured data, whereas when $xg0.04$, only those of the $L{1}_{2}$ structure are close to the experimental results. The electronic hybridization between Pu and $M$ atoms is dominated by Pu for the $s,d$, and $f$ states but $M$ for the $p$ state. The strong interactions between Pu and $M$ atoms in the same site of the $L{1}_{2}$ structure should be responsible for its relative stability in the alloys with $xg0.04$. The electron-phonon coupling further decreases the phase stability of $\ensuremath{\delta}\text{\ensuremath{-}}{\mathrm{Pu}}_{1\ensuremath{-}x}{M}_{x}$ with increasing $x$.

Computer Simulation: A Tool for Researching the Basic Physical Properties of NiAl and Ni<sub>3</sub>Al

The crystal structures, lattice parameters, volumes, elastic constants, bulk moduli and shear moduli of the binary NiAl and Ni3Al alloys have been predicted by taking the first-principles plane-wave method in combination with ultra-soft pseudo-potentials. Also the pressure dependence ofCij,BandGare described and quantitatively discussed. The calculated results agree with the experimental data. The elastic constants obtained from our calculations meet their mechanical stability criteria. The DOS results show that the strong Ni-Al interaction plays an important role in the chemical bond of the Ni-Al alloys. Our predictions should be testified by the experimental investigations.

Macroscopic elastic constants of pure metal based on the interactions between microscopic particles

The research activities of the calculation of the elastic constants of metal are mainly focused on the elastic constants of crystal at the micro level. To the calculation of the macroscopic elastic constants of metal, although molecular dynamics method and quasicontinuum method can be used, but there are shortcomings in them, such as a large amount of computation and that the spatial scale of the study model is limited. Therefore, with a pure metal thin plate composed of a single layer of microscopic particles as research object, a new mechanical model is established after the interactions between microscopic particles of the thin plate are applied on the continuum mechanics model of the thin plate. According to this model, the calculation formulas for the microscopic elastic constants, which are the elastic constants of any triangle region in the model, are obtained. After the concept of the ideal micro structure is presented, the calculation formulas for the macroscopic elastic constants, the elastic modulus and the Poisson’s ratio of pure metal are obtained, where the Poisson’s ratio is the constant that is equal to 1–3. As an example, the elastic constants and the elastic modulus of pure copper are solved, where c 11 is 175.811 GPa, c 12 is 58.604 GPa, c 33 is 58.604 GPa and E is 156.277 GPa, the rationality and the correctness of the model are verified. The model presented fully embodies the discreteness of the microstructure of solid, is a development to the continuum model, and is more suitable to reality, more simplified and more new to the study of the macroscopic elastic constants of pure metal.

Controversy Over Elastic Constants Based on Interatomic Potentials

A controversy exists among literature reports of constraints on elastic constants. In particular, it has been reported that embedded atom method (EAM) potentials generally impose three constraints on elastic constants of crystals that are inconsistent with experiments. However, it can be shown that some EAM potentials do not impose such constraints at all. This paper first resolves this controversy by identifying the necessary condition when the constraints exist and demonstrating the condition is physically necessary. Furthermore, this paper reports that these three constraints are eliminated under all conditions, by using response EAM (R-EAM) potentials.

Dislocation – interphase boundary interaction in HCP bicrystals Zn-X, X = Be, Co, Hf

A dislocation near an interface between elastically anisotropic materials is subjected to an image force, attractive or repulsive, depending on the elastic constants of crystals on both sides of the interface and the geometry of the configuration studied. We study the effect of image force on dislocations for bicrystals composed of two hexagonal materials (Zn-X where X is Be, Co, or Hf). The elastic interaction energy is calculated using the theory of Barnett and Lothe. The configuration is: a dislocation parallel to the interface with the Burgers vector b=a/3 [-2110] and an interface which is defined by a rotation axis R = [0001] and rotation angles in the interval [0°, 90°]. The interaction energies obtained are summarized in isoenergy maps. For a dislocation located in the crystal 1, if the crystal 2 is harder than the crystal 1 (μ2 > μ1), the elastic interaction energy is positive, therefore the dislocation is submitted to a repulsive image force.

Stereographic projections of Poisson's ratio in auxetic crystals

AbstractAuxetic behavior (negative values of Poisson's ratio) in some cubic metals for a stretch along a cube‐face diagonal was investigated in detail by R. H. Baughman et al., F. Milstein, K. Huang, M. Jain, M. P. Verma. Directions with extreme values of Poisson's ratio in crystals for a stretch along a cube‐face diagonal and corresponding lateral strain along the orthogonal cube‐face diagonal and cube‐axis were considered by the authors. In this paper the stereographic projections of Poisson's ratio for a set of natural crystals with cubic, hexagonal and monoclinic symmetry were computed. From these stereographic projections the Poisson's ratio for any possible directions of stretch and lateral strain in the crystal were calculated and orientations of stretch and lateral strain with extreme values of Poisson's ratio were obtained. Crystals with auxetic behavior were revealed. Orientations of stretch directions and lateral strain directions with negative values of Poisson's ratio were determined. By analysis of the above results cuts with optimal negative values of Poisson's ratio were revealed in zinc, molybdenum sulfide, carbon, graphite, polypropylene, monoclinic natural minerals labradorite and augite, a complex silicate and in a set of cubic alloys. The exotic behavior of change of cross‐section of a cylindrical rod during stretching along the rod axis was revealed in the naturally‐occurring mineral SiO2 cristobalite – an example of a molecular auxetic. The elastic constants of crystals from the manual of Landolt–Börnstein were used in the calculations. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Using noise speckle pattern for the measurements of director reorientational relaxation time and diffusion length of aligned liquid crystals

A purely optical approach using noise as a perturbation source and speckle analysis is used to measure the diffusion length and the director reorientational relaxation time of an aligned nematic liquid crystal. This method gives a direct measure of the intrinsic director relaxation time without any voltage or optical driving nor nonlinear effects contrarily to previous approaches. The obtained values of the diffusion length and relaxation time are in excellent agreement with those calculated from the liquid crystal elastic and rotational viscosity constants.

Self-organization of (001) cubic crystal surfaces

Self-organization on crystal surface is studied as a two dimensional spinodal decomposition in presence of a surface stress. The elastic Green function is calculated for a $(001)$ cubic crystal surface taking into account the crystal anisotropy. Numerical calculations show that the phase separation is driven by the interplay between domain boundary energy and long range elastic interactions. At late stage of the phase separation process, a steady state appears with different nanometric patterns according to the surface coverage and the crystal elastic constants.

Determination of a transferable interatomic potential for alkali-metal perchlorates and its application to morphological modelling

The development of an interatomic potential for alkali-metal perchlorates is presented. The potential is fitted to orthorhombic sodium perchlorate and transferred to the perchlorates of caesium, potassium and rubidium. The derived potential data provide a consistent fit to the known crystal structures and elastic constants. Transferability of the potential to the cubic phase of sodium perchlorate leads to a poorer match to experimental data, which perhaps reflects the fact that this phase only stabilises at a high temperature. Unrelaxed and relaxed surface and attachment energies for the low-index crystal planes are calculated for potassium perchlorate, from which crystal morphologies are predicted. The simulations provide a good match to experimental growth morphologies using the Hartman–Perdok attachment energy model, but a poorer one using the more classical Gibbs–Wulff surface-energy model. Potential growth mechanisms, based on these observations, are discussed.

Elastic Constants of Crystals from X‐ray Coherent Scattering Data. Dedicated to Professor Hermann NEELS on the occasion of his 80th birthday

AbstractThe X‐ray diffraction method for determining the elastic constants Cij and their temperature dependence using the Bragg reflection intensity is discussed.

Determination of the dielectric, piezoelectric, and elastic constants of crystals in class 32.

A new approach employing only two differently oriented crystal plates to determine all the dielectric, piezoelectric, and elastic constants of crystals in class 32 has been put forward. Meanwhile, a method to improve the determination accuracy of the clamped dielectric constants of crystals in class 32 also has been suggested. For example, all the constants of \ensuremath{\alpha}-quartz have been measured by the approach. The experimental results of \ensuremath{\alpha}-quartz have shown that the approach is very efficient.

Lattice dynamics and inelastic neutron scattering from forsterite, Mg2SiO4: Phonon dispersion relation, density of states and specific heat

Magnesium-rich olivine (Mg0.9Fe0.1)2SiO4 is considered to be a major constituent of the Earth's upper mantle. Because of its major geophysical importance, the temperature and pressure dependence of its crystal structure, elastic and dielectric constants, long-wavelength phonon modes and specific heat have been measured using a variety of experimental techniques. Theoretical study of lattice dynamics provides a means of analyzing and understanding a host of such experimental data in a unified manner. A detailed study of the lattice dynamics of forsterite, Mg2SiO4, has been made using a crystal potential function consisting of Coulombic and short-range terms. Quasiharmonic lattice dynamical calculations based on a rigid molecular-ion model have provided theoretical estimates of elastic constants, long-wavelength modes, phonon dispersion relation for external modes along the three high symmetry directions in the Brillouin zone, total and partial density of states and inelastic neutron scattering cross-sections. The neutron cross-sections were used as guides for the coherent inelastic neutron scattering experiment on a large single crystal using a triple axis spectrometer in the constant Q mode. The observed and predicted phonon dispersion relation show excellent agreement. The inelastically scattered neutron spectra from a powder sample have been analyzed on the basis of a phonon density of states calculated from a rigid-ion model, which includes both external and internal modes. The experimental data from a powder sample show good agreement with the calculated spectra, which include a multiphonon contribution in the incoherent approximation. The computed phonon densities of states are used to calculate the specific heat as a function of temperature using both the rigid molecular-ion and rigid ion models. These results are in very good agreement with the calorimetric measurement of the specific heat. The interatomic potential developed here can be used with some confidence to study physical properties of forsterite as a function of pressure and temperature.

Elastic constants of crystals from linear-response theory.

We propose a new scheme to calculate the elastic constants of solids which is based on linear-response theory. Elastic constants are given directly by a single self-consistent calculation (i.e., they are not obtained by numerical differentiation of total energies or stresses). As an illustration, we apply our procedure to the determination of the equilibrium lattice constant, bulk modulus, and pressure derivative of the bulk modulus of silicon.

Brillouin Scattering Study on the single crystals ofl-arginine phosphate (LAP)

This is the first report representing Brillouin Scattering Studies on single crystals of monoclinic LAP, which is a new organic material very useful for secondary harmonic generation. The crystal elastic constants were evaluated from the measured data. The curves of the reciprocal velocity and the acoustic velocity as a function of temperature are given here.

Diamond force constant reconciliation with crystal elastic constants, Raman frequency, bulk compressibility, and neopentane group frequency assignments

Using the diagonal stretching force constant Kr as the independant variables and assuming its values in the range 4.0–7.0×105 dyn cm−1 the diamond Raman frequency Vr is calculated for each set of force constans. It is suggested that a value of Kr=5.5×105 dyn cm−1 be adopted. (AIP)

Elastic constants of a stressed crystal. III. Static method of defining isothermal elastic constants of third order

A theory is developed which may be the basis for the experimental static determination of the third order elastic constants of crystals of arbitrary symmetry. The application of this theory to cubic symmetry crystals is considered. [Russian Text Ignored].

Correlation of yield strength with internal coherency strains for age-hardened Cu−Ni−Fe alloys

The maximum yield strengths for a given aging temperature were measured for age-hardened Cu−Ni−Fe alloys. The yield strengths were found to be proportional to the difference in cubic lattice parameters of unstressed precipitating phases and independent of other factors such as precipitate particle size and precipitate volume fraction. The yield strength dependence on lattice parameter differences alone indicated coherency stresses controlled the yield strengths. An analysis of the yield strength based only on internal coherency strains and stresses subsequently led to the derivation of an equation for the yield strength,i.e., $${_{}^{} }$$ where $$m$$ is the Taylor factor for converting from single crystal shear stress to polycrystalline tensile stress results,C ijare single crystal elastic stiffness constants and Δa is the difference in, anda 0 the average of the cubic lattice parameters of the precipitating phases. The equation indicates the yield strength is dependent only on the internal coherency strains and independent of particle size and precipitate volume fraction, as observed. The correlation of the experimentally measured yield strengths with the equation was quite good.