The magnetoelastic contribution to thermal expansion of rare-earth metal scheelites RLiF<Subscript>4</Subscript> (R = Tb-Yb)

The paper presents systematic experimental and theoretical studies of thermal expansion for rare-earth metal scheelites RLiF₄ (R = Tb-Ho, Tm, and Lu). Pronounced thermal expansion anomalies were observed. The magnetoelastic contributions were determined taking into account corrections for changes in the phonon contribution in the RLiF₄ series according to the Debye thermal expansion model. The calculated multipole moments of various orders for various rare-earth metal ions were compared to analyze the applicability of the quadrupole approximation to totally symmetric modes in the scheelite structure. For some ions (Ho and Tm), the magnetoelastic contributions to thermal expansion could not be described by the temperature dependences of their quadrupole moments, that is, multipole moments made considerable contributions. The totally symmetric magnetoelastic coefficients for the scheelite structure were determined from the experimental data on magnetoelastic contributions. These coefficients were compared with those for the zircon structure.     

Magnetoelastic contribution to the thermal expansion of the rare-earth phosphates TbPO4 and TmPO4

The thermal expansion of the rare-earth phosphates TbPO₄ and TmPO₄ having zircon structure has been investigated experimentally and theoretically. Significant magnetoelastic anomalies of the thermal expansion have been identified and the magnetoelastic contributions have been isolated allowing for corrections to the variation of the phonon contribution along the rare-earth ion series. It is shown that the magnetoelastic contribution to the thermal expansion of terbium and thulium phosphate is well described by the temperature dependence of the quadrupole moments of the rare-earth ions. The fully symmetric magnetoelastic coefficients for Tb³⁺ and Tm³⁺ are determined and a comparison is made of the magnetoelastic anomalies of the thermal expansion and the magnetoelastic coefficients of rare-earth phosphates and vanadates allowing for the differences in the crystal fields of the two isomorphic groups of zircons. Fiz. Tverd. Tela (St. Petersburg) 39, 106–111 (January 1997)     

Anomalies in thermal expansion of DyVO4 induced by quadrupolar ordering

The thermal expansion of the DyVO₄ crystal has been experimentally and theoretically investigated in the range of the Jahn-Teller structural phase transition. The manifestation of totally symmetric magnetoelastic interactions upon this transition has been studied for the first time. It is found that the temperature dependences of the unit-cell and thermal expansion parameters along the nonactive Jahn-Teller direction in the basal plane for the DyVO₄ crystal exhibit characteristic magnetoelastic anomalies at T<T _c due to the ordering of quadrupole moments of Dy³⁺ ions. The magnetoelastic contributions of the totally symmetric ε^α1 and ε^α2 and symmetry-lowering ε^γ modes to the thermal expansion are calculated within the general crystal-field formalism. The total quadrupolar coefficient G ^γ and magnetoelastic coefficient B ^γ are determined from the spectroscopic and spontaneous deformation data. It is demonstrated that the thermal expansion of the DyVO₄ crystal in the tetragonal and orthorhombic phases is well described in the framework of the unified model using a common set of interaction parameters for both phases.     

Anomalies in the Young modulus at structural phase transitions in rare-earth cobaltites RBaCo<Subscript>4</Subscript>O<Subscript>7</Subscript> (R = Y,Tm-Lu)

The elastic properties of rare-earth cobaltites RBaCo₄O₇ (R = Y, Tm-Lu) have been experimentally studied in the temperature range of 80–300 K. The strong softening of the Young modulus ΔE(T)/E ₀ ≈ −(0.1–0.2) of cobaltites with Lu and Yb ions has been revealed, which is due to the instability of the crystal structure upon cooling and is accompanied by an inverse jump at the second-order structural phase transition. The softening of the Young modulus and the jump at the phase transition decrease by an order of magnitude and the transition temperature T _s and hysteresis ΔT _s increase from a compound with Lu to that with Tm. A large softening of the Young modulus at the structural transition in Lu- and Yb cobaltites indicates that the corresponding elastic constant goes to zero, whereas this constant in Tm cobaltite is not a “soft” mode of the phase transition. It has been found that the structural phase transition in Lu- and Yb cobaltites is accompanied by a large absorption maximum at the phase transition point and an additional maximum in the low-temperature phase and absorption anomalies in Tm cobaltite is an order of magnitude smaller.     

Field-dependent elastic modulus and damping in pure iron, nickel and cobalt

Measurements of the ΔE-effect and magnetomechanical damping are reported for crystalline pure iron, nickel and cobalt bars. An automatic experimental system for measuring both magnitudes simultaneously has been used, taking advantage of its improved features which make it possible to include stress-dependence and path-dependence (due to magnetic hysteresis loop) studies in this work. Our results not only provide a useful qualitative comparison among the magnetoelastic behaviour of these three classic ferromagnetic materials, but also show a useful set of quantitative ΔE-effect and magnetomechanical damping values.     

Elasticity and inelasticity of silicon nitride/boron nitride fibrous monoliths

A study is reported on the effect of temperature and elastic vibration amplitude on Young’s modulus E and internal friction in Si₃N₄ and BN ceramic samples and Si₃N₄/BN monoliths obtained by hot pressing of BN-coated Si₃N₄ fibers. The fibers were arranged along, across, or both along and across the specimen axis. The E measurements were carried out under thermal cycling within the 20–600°C range. It was found that high-modulus silicon-nitride specimens possess a high thermal stability; the E(T) dependences obtained under heating and cooling coincide well with one another. The low-modulus BN ceramic exhibits a considerable hysteresis, thus indicating evolution of the defect structure under the action of thermoelastic (internal) stresses. Monoliths demonstrate a qualitatively similar behavior (with hysteresis). This behavior of the elastic modulus is possible under microplastic deformation initiated by internal stresses. The presence of microplastic shear in all the materials studied is supported by the character of the amplitude dependences of internal friction and the Young’s modulus. The experimental data obtained are discussed in terms of a model in which the temperature dependences of the elastic modulus and their features are accounted for by both microplastic deformation and nonlinear lattice-atom vibrations, which depend on internal stresses.     

Thermal expansion anomalies in TbVO4 due to the cooperative Jahn-Teller effect

The thermal expansion anomalies in TbVO₄ due to the cooperative Jahn-Teller effect were studied experimentally and theoretically. Characteristic magnetoelastic anomalies were observed in the curves of Δa/a and Δc/c of the cell parameters at T<T _c. Calculations of the magnetoelastic contribution to Δa/a and Δc/c from fully symmetric and and low-symmetry ɛ^δ modes were performed using the general crystal-field formalism, and the values of the magnetoelastic coefficient B ^δ were obtained from spectroscopic and spontaneous-deformation data. It is shown that the thermal expansion of TbVO₄ in both the tetragonal and orthorhombic phases can be described well on the basis of a general model based on a single set of interaction parameters. Fiz. Tverd. Tela (St. Petersburg) 40, 1663–1666 (September 1998)     

Temperature compensating Elinvar character in Fe-Mn-Si alloys

Young's modulus-temperature and thermal expansion curves were measured in γ-Fe-31Mn-(0.25-8.67) Si-0.77C (at%) alloys by dynamic audio resonance method and in a light dilatometer. The results show that the anomalies in Young's modulus and thermal expansion appear near the Néel temperature. The temperature coefficient of Young's modulus, (1/E_p)(dE_p/dT), is controlled by Si content below the Néel temperature. When Si content increases to 5.31 at%, (1/E_p)(dE_p/dT) is close to zero in temperature range from 260 to 335 K, i.e. the Fe-31Mn-5.31Si-0.67C (at%) alloy shows Elinvar character. The temperature range in which the Elinvar character appears is wider than that of γ-Fe-Mn Elinvar alloys. The change in exchange energy and the ΔE effect result from the effect of Si on the antiferromagnetic behavior in γ-Fe-Mn alloys since it induces or enhances localized magnetic moment. When the increase in normal Young's modulus due to lowering temperature is compensated by the ΔE effect caused by the antiferromagnetic ordering, Elinvar character appears.     

Influence of internal stresses on field-dependent elastic modulus and damping in pure nickel

Measurements of the ΔE-effect and magnetomechanical damping are reported for crystalline pure nickel under several states of internal stresses. The different internal stresses are obtained by means of a wide variety of heat treatments and studied via microscopic examination and measurement. The influence of the heating temperature, the heating time and the cooling method on the magnetoelastic properties is studied. Our results make it possible to select the most suitable heat treatment for each application and to optimize the magnetoelastic response of nickel. Relative variations from 2% to 13% can be obtained in the ΔE-effect, whereas relative variations from 40.0% to 99.9% are possible in magnetomechanical damping, in terms of specific damping capacity.     

Crystal field and quadrupole interaction effects in YbXO4 Zircons (X = V, P)

The magnetic and magnetoelastic properties of YbPO₄ and YbVO₄ crystals are investigated experimentally and theoretically; the crystal field parameters are determined, as well as the magnetoelastic coefficients B ^μ and total quadrupole coupling constants G ^μ for all symmetry modes. It is found that, for H ∥ [100], γ-symmetric quadrupole interactions predominate and are responsible for a significant contribution to the third-order susceptibility, magnetization, magnetostriction, and elastic constant. It is demonstrated that, in the absence of an external field, these interactions do not lead to quadrupole ordering, because the respective deformation susceptibility χ_γ is several times less than the critical value of 1/G ^γ. The influence of an external magnetic field along different symmetry axes on the quadrupole effects and quadrupole interactions in Yb zircons is investigated. It is demonstrated that, for H ∥ [110], the susceptibility χ_γ increases with the field, so that in a fairly strong field in the investigated crystals one can expect a γ-symmetric stimulated phase transition.     

Structure-mediated transition in the behavior of elastic and inelastic properties of beach tree bio-carbon

Microstructural characteristics and amplitude dependences of the Young modulus E and of internal friction (logarithmic decrement δ) of bio-carbon matrices prepared from beech tree wood at different carbonization temperatures T _carb ranging from 600 to 1600°C have been studied. The dependences E(T _carb) and δ(T _carb) thus obtained revealed two linear regions of increase of the Young modulus and of decrease of the decrement with increasing carbonization temperature, namely, ΔE ～ AΔT _carb and Δδ ～ BΔT _carb, with A ≈ 13.4 MPa/K and B ≈ ?2.2 × 10^?6 K^?1 for T _carb < 1000°C and A ≈ 2.5 MPa/K and B ≈ ?3.0 × 10^?7 K^?1 for T _carb > 1000°C. The transition observed in the behavior of E(T _carb) and δ(T _carb) at T _carb = 900–1000°C can be assigned to a change of sample microstructure, more specifically, a change in the ratio of the fractions of the amorphous matrix and of the nanocrystalline phase. For T _carb < 1000°C, the elastic properties are governed primarily by the amorphous matrix, whereas for T _carb > 1000°C the nanocrystalline phase plays the dominant part. The structurally induced transition in the behavior of the elastic and microplastic characteristics at a temperature close to 1000°C correlates with the variation of the physical properties, such as electrical conductivity, thermal conductivity, and thermopower, reported in the literature.     

Crystal field effects in rare-earth ferroborates RFe3(BO3)4 with R = Nd, Tb, Dy, or Er

Crystal field effects in rare-earth ferroborates RFe₃(BO₃)₄ with various rare-earth elements are studied theoretically. The rare-earth magnetoelastic interaction Hamiltonian is written in a multipole approximation. The field and temperature dependences of the multipole moments and strain susceptibilities of rare-earth ions in the ferroborate structure are calculated. A comparative analysis of anomalies in the thermal expansion and elastic constants of rare-earth ferroborates with Tb and Dy ions having identical magnetic structure but differing in the degree of anisotropy of the rare-earth ion is performed.     

Jahn-Teller transitions in Yb<Emphasis Type="Italic">X</Emphasis>O<Subscript>4</Subscript> (<Emphasis Type="Italic">X</Emphasis>=V,P) stimulated by a strong magnetic field

The effect of an external magnetic field directed along various symmetry axes of a crystal on Jahn-Teller-type structural phase transitions (quadrupole ordering) is studied in YbPO₄ and YbVO₄ crystals with zircon structure. In the absence of a magnetic field, the crystals are in a precritical state and do not exhibit a spontaneous quadrupole ordering. It is shown that, in a field H ∥ [110], the strain susceptibility χ_γ increases with the field and, at a sufficiently high field strength, an orthorhombic lattice deformation along the [100] axis arises in the crystals under study; i.e., a stimulated Jahn-Teller phase transition of γ symmetry occurs. Using interaction constants determined from independent experiments, we calculated phase diagrams and anomalies in the magnetic and magnetoelastic properties of the YbPO₄ and YbVO₄ crystals near the stimulated phase transitions, investigated the effect of various pairwise interactions on them, and analyzed possible experimental observations of the predicted effects.     

The nature of temperature dependence of energy gaps in layer semiconductors

The temperature dependences of direct and indirect energy gaps in layer semiconductors GaS, GaSe and GaS_xSe_1?x are investigated in the temperature range 5–150 K. The nonmonotonous behaviour of E_g(T) dependences is observed in these crystals. It is shown that the effect of thermal expansion cannot in itself explain the observed anomalies. A new model of electron-phonon interaction explaining the E_g(T) behaviour in layer crystals is proposed.     

Elastic,magnetic, and magnetoelectric properties of the CaBaCo<Subscript>4</Subscript>O<Subscript>7</Subscript> multiferroic

The structural, elastic, magnetic, and magnetoelectric properties of the CaBaCo₄O₇ multiferroic are experimentally studied and compared with the properties of the related YBaCo₄O₇ cobaltite, where Y³⁺ ions substitute for Ca²⁺ ions. Unlike the frustrated YBaCo₄O₇ magnet, the softening of Young’s modulus and the hysteresis in the ΔE(T)/E ₀ curve of ferrimagnetic CaBaCo₄O₇ in the paramagnetic region are weak, and the anomaly during the magnetic transition increases by almost an order of magnitude. This difference can point to different characters of the development of a long-range magnetic order in these two cobaltites. The distortion of the crystal structure that removes the frustrations of exchange interactions is found to correlate with the magnetic behavior of the cobaltites under study. The magnetization curves of the Ca cobaltite have two steps below 15 K, which can point to the presence of a metastable state in a high magnetic field. The study of the longitudinal and transverse magnetoelectric effects in a pulsed magnetic field demonstrates that their magnitudes are maximal near T _C and change their character from linear to quadratic during passage through this temperature.     

Investigation of the ferroelastic phase transition in the SrMgF4 pyroelectric crystal

A SrMgF₄ compound has been synthesized and a high optical-quality crystal has been grown. Optical-polarization observations, X-ray diffraction analysis, and the measurement of the birefringence Δn _i (t) in the SrMgF₄ crystal have been carried out in the temperature range of 90–1200 K. A second-order improper ferroelastic phase transition accompanied by birefringence anomalies and the symmetry change P112₁ (Z = 12) ? Cmc2₁ (Z = 4) has been discovered at T ₀ = 478 ± 1 K. The crystal remains pyroelectric in both phases. Considerable contributions of the fluctuations of the order parameter have been observed in the temperature ranges of (T ₀ ? T) < 15 K and (T ? T ₀) < 60 K.     

EPR studies of linewidth anomalies at phase transitions in [N(C2H5)4]2MnCl4

We have studied [N(C₂H₅)₄]₂MnCl₄ crystal by X-band CW EPR spectra in the temperature range 170-300 K. The angular dependences of linewidth ΔH were measured and described in the light of a double-layer system (2D) with exchange interactions. Two temperature anomalies of linewidth ΔH were found at T₁=225 K and T₂=192 K on cooling. Different behaviors of ΔH anomalies recorded for an external magnetic field parallel and perpendicular to the ab crystallographic plane indicate ordering/disordering of MnCl₄ groups in this plane and their displacement along the c-axis which occurs in the temperature of about 225 K.     

Study of temperature dependence of density, bulk modulus, shear modulus and thermal pressure for mantle minerals

The temperature dependence of different parameters i.e. density ρ(T), bulk modulus K_T(T), shear modulus G_T(T) and thermal pressure ΔP_th for mantle minerals i.e. X₂SiO₄ (X=Mg, Fe, Co, Mn) have been studied in high temperature range on the basis of semi-phenomenological isobaric equation of state. The calculated values of these parameters are showing good agreements with experimental value in case of each mantle minerals.     

The entropy change on melting of simple substances

It is shown that the volume independent component, R 1n 2, of the entropy of melting, ΔS_m, for argon persists, unchanged, some distance into the fluid phase as a configurational entropy. For argon, sodium, and caesium in its normal melting regime ΔS_m = Rln 2 + αB_TδV_m, where ΔV_m is the volume change on melting and αB_T is the temperature independent product of the thermal expansion coefficient and the isothermal bulk modulus.