X-ray scattering and theα-α′ phase transition in coherent metal-hydrogen systems

Metallic singlet ground state systems have often anomalous elastic properties which result from the coupling of the phonons to the crystal field energy levels of the rare earth ions. It is shown that structural and magnetic phase transitions should occur in the same way in those systems. They are caused by a sufficiently strong electron-ion interaction. While the orbital part of this interaction is responsible for possible structural phase transitions, the spin dependent part is responsible for magnetic phase transitions. This is demonstrated in detail by considering as an example the aspherical Coulomb charge scattering and the isotropic exchange interaction. We calculate the sound velocity, the sound attenuation and the excitations in the presence of the aspherical Coulomb charge scattering. Furthermore we discuss the mutual coupling of structural and magnetic phase transitions. This includes a consideration of other types of coupling than aspherical Coulomb scattering and isotropic exchange.     

Reorientation phase transition in temperature in a two- and three-dimensional ferromagnet with the account of magnetoelastic coupling

In the paper, we have investigated reorientation phase transitions in a two-dimensional ferromagnet. It is shown that the account of magnetoelastic coupling results in the appearance of an angular phase, and the phase transitions are of the first order. The temperature interval of the angular phase existence is determined mainly by elastic and magnetoelastic parameters of the system. For a three-dimensional system the observable effect disappears. The obtained results are consistent with experimental data.     

Elastic and Thermodynamic Properties of CdSe from First-Principles Calculations

The lattice parameters, bulk modulus, phase transition pressure, and temperature dependencies of the elastic constants c_ij of CdSe are investigated by using the Cambridge Serial Total Energy Package (CASTEP) program in the frame of Density Functional Theory (DFT). It is found that the phase transitions from the ZB structure to the RS structure and from WZ structure to RS structure are 2.2 GPa and 2.8 GPa, respectively. Our results agree well with the available experimental data and other theoretical results. The aggregate elastic modulus (B, G, E, A), the Poisson's ratio (υ), the Grüneisen parameter (γ), the Debye temperature Θ_D on pressure and temperature are also successfully obtained.     

Electroelastic field of a sphere located in the vicinity of a plane piezoelectric surface

The electric field generated by a scanning probe microscope is determined. Analytical expressions for the electroelastic field in a piezoelectric sample and the external electric field are derived for a spherical probe. It is demonstrated that the coupling of elastic and electrostatic fields in the piezoelectric material leads to energy redistribution between such fields. This circumstance causes variations in the normal component of the electric field strength at the interface and the capacitance of a probe.     

Elastic phase transitions in metals at high pressures

The elastic phase transitions of cubic metals at high pressures are investigated within the framework of Landau theory. It is shown that at pressures comparable with the magnitude of the bulk modulus the phase transition is connected with the loss of stability relative to uniform deformation of the crystalline lattice. Discontinuity of the order parameter at the transition point and its equilibrium value are expressed through the second-?to fourth-order elastic constants. The second-,third-?and fourth-order elastic constants and phonon dispersion curves of vanadium under hydrostatic pressure are obtained by first-principles calculations. Structural transformation in vanadium under pressure is studied using the obtained results. It is shown that the experimentally observed at P?≈?69?GPa phase transition in vanadium is the first-order phase transition close to a second-order phase transition.     

Calculation of the electroelastic Green’s function of the hexagonal infinite medium

The electroelastic 4 × 4 Green’s function of a piezoelectric hexagonal (transversely isotropic) infinitely extended medium is calculated explicitly in closed compact form ((73) ff. and (88) ff., respectively) by using residue calculation. The results can also be derived from Fredholm’s method [2]. In the case of vanishing piezoelectric coupling the derived Green’s function coincides with two well known results: Kröner’s expressions for the elastic Green’s function tensor [4] is reproduced and the electric part then coincides with the electric potential (solution of Poisson equation) which is caused by a unit point charge. The obtained electroelastic Green’s function is useful for the calculation of the electroelastic Eshelby tensor [16].     

Structural phase transition induced by the Jahn-Teller effect. Antiferrodistortive ordering

We study the phase transitions induced by the Jahn-Teller effect ofE-doublet ions in a cubic crystal with antiferrodistortive interactions. AnS=1 pseudospin model is constructed which takes the three lowest vibronic levels of the Jahn-Teller complexes into account. We find a second-order phase transition to a tetragonal phase with two inequivalent sublattices. The transitions between the vibronic levels give rise to bands of collective vibronic excitations with strongly temperature-dependent frequencies. The nature of the various modes is analyzed in detail. We also study the coupling to the elastic displacement field of the crystal. For a sufficiently large coupling constant, this coupling stabilizes a different low-temperature tetragonal phase with two equivalent sublattices. In a certain region of coupling constants, a transition occurs between the two tetragonal phases by second-order transitions to an intermediate phase of lower symmetry. The influence of the coupling on the dynamic behaviour is discussed.     

Structural phase transition induced by the Jahn-Teller effect. Antiferrodistortive ordering

We study the phase transitions induced by the Jahn-Teller effect ofE-doublet ions in a cubic crystal with antiferrodistortive interactions. AnS=1 pseudospin model is constructed which takes the three lowest vibronic levels of the Jahn-Teller complexes into account. We find a second-order phase transition to a tetragonal phase with two inequivalent sublattices. The transitions between the vibronic levels give rise to bands of collective vibronic excitations with strongly temperature-dependent frequencies. The nature of the various modes is analyzed in detail. We also study the coupling to the elastic displacement field of the crystal. For a sufficiently large coupling constant, this coupling stabilizes a different low-temperature tetragonal phase with two equivalent sublattices. In a certain region of coupling constants, a transition occurs between the two tetragonal phases by second-order transitions to an intermediate phase of lower symmetry. The influence of the coupling on the dynamic behaviour is discussed.Supported by Schweizerischer Nationalfonds     

声波在一维易膨胀介质中传播的计算机模拟

建立了一种新的介质模型，其弹性模量在声波处于压缩状态时较大，而在膨胀状态时较小. 在这种介质中，纯的压缩或膨胀波的传播特性与一般弹性介质类似，只是它们分别以压缩声 速或膨胀声速传播.但当它们在某一区域中同时存在时，它们之间会相互耦合，产生非常强 的非线性效应.对这两种波在对行和追赶两种情况的耦合特性作了详细地模拟计算.结果显示 在两种情况下，压缩波和膨胀波的耦合均会造成体系的膨胀.体系的膨胀与压缩弹性模量和 膨胀弹性模量的相对差有关.此外，还对弹性模量随声波压力连续变化的体系进行了模拟计 算.结果证实由非连续变化的弹性模量所得的结论可由连续变化的弹性模量的极限情况得到. 关键词： 颗粒物质 声波 弹性介质     

Order-disorder structural phase transitions described by the three-states potts model

Orientational ordering of spontaneously distorted building blocks of a crystal is a mechanism for order-disorder structural phase transitions. We study as a model substance the case of a simple cubic array of tetragonally deformed octahedral complexes. The three equivalent tetragonal deformations along the cube axes are taken as the three states of the Potts model. We investigate the various structures which can appear depending on the type of interaction between the complexes. The phase diagram, the stability of the various phases, the type of transitions, and the temperature dependence of the order parameter are studied in mean-field approximation. We further show that piezodistortive coupling to the elastic strain may stabilize different low-temperature structures, and that it gives rise to a renormalization of elastic constants and to acoustic anomalies.Work supported by the Swiss National Science Foundation     

Mechanical spectra measurement to probe the magnetolattice coupling in cupric oxide

Mechanical spectra (complex Young's modulus Y*=Y′+iY″ versus frequency and temperature) of polycrystalline cupric oxide CuO were measured by vibrating reed method from liquid nitrogen temperature to room temperature at the kilohertz frequency. The abnormal behavior of internal friction and the change of slope of the real part of the complex Young's modulus versus temperature are observed around 213 and 230 K, where two successive magnetic transitions were established. At low temperatures, below 130 K, a higher internal friction platform with the decrease of temperature was clearly observed which might show a phase transition. Our study indicates that mechanical spectrum is an effective tool to detect subtle phase transitions and there is a strong magnetolattice coupling in CuO.     

Stoney formula for piezoelectric film/elastic substrate system

With the trends in miniaturization, and particularly the introduction of micro- and nano-electro-mechanical system,piezoelectric materials used in microelectronic devices are deposited usually in the form of thin film on elastic substrates.In this work, the bending of a bilayer comprising a piezoelectric film deposited on an elastic substrate, due to the mismatch,is investigated. An analytic formula relating the curvature of the bilayer to the mismatch, the electroelastic constants and the film thickness is obtained, and from this formula, a transverse piezoelectric constant d_31 can be estimated. Meanwhile the influence of electromechanical coupling coefficient on the curvature is discussed.     

Some aspects of the thermodynamic behaviour of ferroelastic and co-elastic phase transitions

Ferroelastic phase transitions and phase transitions involving coupling between the driving order parameter and elastic degrees of freedom (i.e. co-elastic phase transitions) follow empirically a Landau-type mean field behaviour over large temperature intervals. At temperatures close to the transition point the upper critical dimension is reduced to three if fluctuations are sufficiently constrained in reciprocal space. At low temperatures, the observed temperature independence of the order parameter in the saturation regime (S-regime) is correlated with the quantum limit of the dissipation-fluctuation theorem. The good agreement between experimental observations and the predictions of a Landau-type treatment of the excess Gibbs free energy even for large values of the order parameter leads to the conclusion that the convergency of the polynomial form of the Gibbs free energy is due to small energy coefficients rather than due to the order parameter being small.     

Phase transformations in perovskites TbBaCo2−x FexO5 + γ

The transport, magnetic, and elastic properties of TbBaCo_2?x Fe_xO_{5 + γ} are investigated. It is shown that these compounds exhibit first-order metal-insulator and antiferromagnet-weak ferromagnet transitions in the orthorhombic phase (x < 0.12), while these transitions are not observed in the tetragonal phase (x > 0.12). In the concentration range corresponding to the orthorhombic phase, doping with iron stabilizes the weakly ferromagnetic phase. However, the tetragonal phase is antiferromagnetic. Oxygen vacancies are assumed to be ordered in the orthorhombic case and disordered in the tetragonal phase. An analysis of Young’s modulus, magnetostriction, and effects of pressure and substitution of the O¹⁸ oxygen isotopes for O¹⁶ indicates a weak correlation between magnetic transformations and the crystal lattice.     

Tribological system in the boundary friction mode under a periodic external action

A mechanical analog of a tribological system in the boundary friction mode is studied. A thermodynamic model is used to analyze the first-order phase transition between liquidlike and solidlike structures of a lubricant. The time dependences of the friction force, the relative velocity of the interacting surfaces, and the elastic component of the shear stresses appearing in the lubricant are obtained. It is shown that, in the liquidlike state, the shear modulus of the lubricant and the elastic stresses become zero. The intermittent (stick-slip) friction mode detected experimentally is described. It is shown that, as the lubricant temperature increases, the frequency of phase transitions between the lubricant structural states decreases and the total friction force and elastic stress amplitudes lower. When the temperature or the elastic strain exceeds the corresponding critical value, the lubricant melts and a kinetic slip mode in which the elastic component of the friction force is zero takes place.     

Elasticity of a magnetic lattice near the magnetic critical point

The isothermal elastic constants and the coefficient of anomalous thermal expansion of a magnetic lattice are discussed. The spin system is described by the Ising model with an exchange coupling depending on lattice spacing. A behavior of the elastic constants and the coefficient of thermal expansion is found which is in qualitative agreement with experiments. The isothermal compressibility remains positive nearT _c and no thermo-mechanical instability occurs (which would lead to a first-order phase transitions), in contrast to earlier theories.     

Dynamical stability and phase transition of ZrC under pressure

A comprehensive first principles study of structural, elastic, electronic, and phonon properties of zirconium carbide (ZrC) is reported within the density functional theory scheme. The aim is to primarily focus on the vibrational properties of this transition metal carbide to understand the mechanism of phase transition. The ground state properties such as lattice constant, elastic constants, bulk modulus, shear modulus, electronic band structure, and phonon dispersion curves (PDC) of ZrC in rock-salt (RS) and high-pressure CsCl structures are determined. The pressure-dependent PDCs are also reported in NaCl phase. The phonon modes become softer and finally attain imaginary frequency with the increase of pressure. The lattice degree of freedom is used to explain the phase transition. Static calculations predict the RS to CsCl phase transition to occur at 308?GPa at 0?K. Dynamical calculations lower this pressure by about 40?GPa. The phonon density of states, electron–phonon interaction coefficient, and Eliashberg's function are also presented. The calculated electron–phonon coupling constant λ and superconducting transition temperature agree reasonably well with the available experimental data.     

Structural phase transition and elastic properties of Curium and Uranium monobismuthides under pressure effect

A density functional (DFT) calculations of the structural, elastic and high pressure properties of the cubic XBi (X=U,Cm) compounds, has been reported using the full potential linear muffin-tin orbital (FP-LMTO) method. In this approach the local density approximation (LDA) is used for the exchange-correlation (XC) potential. Results are given for lattice constant, bulk modulus and its pressure derivatives. The pressure transitions at which these compounds undergo structural phase transition from NaCl-type (B1) to CsCl-type (B2) phase were found to be in good agreement with the available theoretical results. We have determined the elastic constants C₁₁, C₁₂, C₄₄ and their pressure dependence which have not been established experimentally or theoretically.     

Elastic phase transitions in plutonium

The rich phase diagram of plutonium with a large number of different transitions in a narrow temperature interval has been puzzling scientists for decades. We offer a theoretical proof that most of the structural transformations in plutonium at temperatures exceeding the Debye temperature are the elastic phase transitions. The proof is given in the framework of the Landau theory of phase transitions and space group theory taking into account the anomalously small value of the elastic shear constants related to tetragonal and orthorhombic lattice deformations.     

Elastic properties of magnetic materials

This review discusses the theoretical aspects of magnetoelastic coupling with emphasis on the magnetic perturbation of elastic properties. The basic theory of magnetostriction is set out with application to ferromagnets, ferrimagnets and antiferromagnets, and is followed by a discussion of the physical origin of the magnetoelastic coupling coefficients in both localized and itinerant magnetic systems. Magnetic contributions to elastic compliance are then discussed and sound velocity anomalies near magnetic phase transitions investigated, including the cooperative Jahn-Teller limit for which the acoustic mode itself drives a structural transition even when magnetic ordering does not occur. The review concludes with discussion of magnetoelastic (or mixed magnon-phonon) waves in low temperature magnetically ordered phases and with a study of local striction phenomena in magnetically dilute materials. The latter leads to a recognition of internal rearrangement modes which may also be present in concentrated magnetic systems, and which may or may not couple significantly to bulk homogenous strain.