Soft Acoustic Mode Research Articles

A density functional study of the pressure induced phase transition inLiYF4

An investigation of the pressure induced phase transition from the scheelite phase(I41/a,Z = 4) to thefergusonite-like phase (I 2/a,Z = 4) and to the LaTaO4 phase (P 21/c,Z = 4) of LiYF4 is presented. Employing density functional theory (DFT) within the generalized gradientapproximation, the structures were relaxed for a pressure range of 0–20 GPa without imposedsymmetry. The influence of pressure on the lattice vibrational spectrum of the scheelite phase(I41/a,Z = 4) was evaluated using the direct approach, i.e. using force constants calculated from atomicdisplacements. This work tends to confirm the transformations . At 20 GPa, a P 21/c structure with a pentacoordinated lithium cation is found to be the moststable phase. This structure is compatible with a transition driven by aBg zone-centre soft optic mode linked to a soft acoustic mode along the [] direction as observed from the evolution of the phonon dispersion curves as a function ofpressure.

Elastic constants of bcc austenite and 2H orthorhombic martensite in CuAlNi shape memory alloy

Elastic constants of cubic austenite and orthorhombic 2H martensite phases in the Cu–Al–Ni shape memory alloy were determined by ultrasonic pulse-echo technique using multiple single crystal specimens and a novel optimization based evaluation method that minimizes the uncertainty stemming from experimental errors as well as experimental effort. Multiple martensitic single crystals were prepared from the austenite crystal by a dedicated deformation technique. Taking advantage of the fact that the elastic constants of the austenite and 2H martensite phase were evaluated on the same piece of material, soft acoustic modes and elastic properties of both phases were compared taking into account the lattice correspondence. It is found that the 2H martensite crystal partially inherits the soft acoustic modes of the austenite and hence its elastic properties.

Prediction study of elastic properties under pressure effect for zincblende BN, AlN, GaN and InN

We have performed a first-principles full-potential augmented-plane wave plus local orbitals (FP-APW+lo) calculations with density functional theory in local density approximation, in aim to determine and predict the pressure dependence of elastic constants of BN, AlN, GaN and InN compounds. From our results, we sustain the idea of no evidence that the soft acoustic mode is responsible for the phase transition.

Ultrasonic study of the temperature and pressure dependences of the elastic properties of ceramic dimolybdenum carbide ( -Mo2C)

Pulse-echo overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of ceramic samples of dimolybdenum carbide (α-Mo2C) as functions of temperature in the range 130–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. The temperature dependences of the shear elastic stiffness (μ) and Young's modulus (E) show normal behaviour and can be approximated by a conventional model for vibrational anharmonicity. The longitudinal elastic stiffness (CL) increases with decreasing temperature and shows a knee at about 200 K; the decrease in slope below the knee indicates longitudinal acoustic-mode softening. The adiabatic bulk modulus (BS) is also affected by the mode softening below 200 K. The values obtained for the acoustic Debye temperature (ΘD) for ceramic α-Mo2C agree well with the thermal Debye temperature determined previously from heat capacity measurements. The velocities of both the longitudinal and shear ultrasonic waves in ceramic α-Mo2C increase approximately linearly with pressure: both the long-wavelength longitudinal and shear acoustic modes stiffen under pressure. The values determined at room temperature for the hydrostatic-pressure derivative (∂μ/∂P)P=0 of the shear stiffness is similar to those found for ceramic TiC and TaC; while (∂CL/∂P)P=0 and (∂BS/∂P)P=0 have large values, possibly due to the defect microstructure of ceramic α-Mo2C.

Novel phase transition in orthoenstatite

Single-crystal Brillouin scattering measurements on natural orthoenstatite [OEN] to 1350 °C at 1 atm show significant softening of the elastic moduli C 33 and C 55 ahead of a phase transition. To our knowledge, these are the first observations of acoustic mode-softening in orthoenstatite at high temperature and room pressure and could have important implications for Earth's mantle. The phase transition is rapid and shows some hysteresis in the observed transition temperature, T tr . Experiments performed on increasing and decreasing temperature bracket the transition temperature between 1090(10) °C ≤ T tr ≤ 1175(10) °C, and pronounced acoustic mode-softening is evident at temperatures above 900 °C. Backscattering measurements to T = 1350 °C show no evidence for additional transitions. OEN was recovered at room temperature. Our results are interpreted in terms of elastic softening ahead of a displacive phase transition. Before the displacive transition can occur, however, the elastic softening appears to trigger the observed reconstructive transition to the more-stable protoenstatite (or high clinoenstatite) structure. We suggest that the displacive phase transition would lead to a previously unreported pyroxene structure with Cmca symmetry.

Crystal structure and elastic properties of betaine fumarate and of betaine maleate, two isomers of ((CH3)3NCH2COOH . OOC(CH)2COOH

Abstract X-ray structure analyses of orthorhombic betaine fumarate and monoclinic betaine maleate yielded space group Pnma, a 1=26.510(5) Å, a 2=6.684(1)Å, a 3=6.376(1)Å, Z=4, ρ calc=1.371g cm-3, ρ obs=1.370 g cm-3 and, respectively, space group P21/n, a 1=6.132(1)Å, a 2=10.823(2)Å, a 3=17.246(3)Å, α 2=92.87(3)°, Z=4, ρ calc=1.355 g cm-3, ρ obs=1.351 g cm-3. In both compounds the hydrogen betaine cations are joined to the corresponding anions by strong H-bonds with O···O distances of about 2.48Å. Large single crystals of optical quality of betaine maleate have been grown from aqueous solutions. Further, we determined their coefficients of thermal expansion and their elastic and thermoelastic constants. In comparison to the pronounced anisotropy of the mechanical properties of betaine fumarate, the elastic constants of betaine, maleate appear only slightly anisotropic. Between 80 K and 305 K no phase transision could be detected in betaine maleate. However, softening of certain acoustic modes at temperatures below about 160 K might be a hint at structural instabilities at even lower temperatures.

Magnetostriction in ferromagnetic shape memory alloys

There is intense interest in the development of new magnetostrictive materials having large strains. Recent experiments [1,2] showed that the ferromagnetic shape memory alloys (SMA) have some perspectives to generate significant magnetic-field-induced deformations. Taking into account the high mobility of the martensite crystal lattice variants, the corresponding magnetic measurements were performed by using the SMA Ni–Mn–Ga and Fe–Pd. It is concluded that the condensation of the soft acoustic phonon mode TA2 q= 1 3 〈 1 1 0 〉 takes place at T= T i> M s in Ni–Mn–Ga alloy ( M s—martensite start temperature). Magnetic property anomalies accompany this phase transition which can be interpreted as a transition to an intermediate phase. The characteristic temperatures M s and T i are close in some alloys. The simultaneous action of the lattice instabilities connected with the formation of martensite and intermediate phases produces the essential decreasing of the elastic constants and as a result the strong growth of the high temperature phase magnetostriction nearly at T= M s. The behavior of the martensitic phases in magnetic field is also discussed.

Ultrasonic study of the temperature and pressure dependences of the elastic properties of β-silicon nitride ceramic

Ultrasonic wave velocity measurements have been used to determine the elastic stiffness moduli and related elastic properties of high-purity, dense β-Si3N4 ceramic samples as functions of temperature in the range 150–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. Due to its covalently bonded, rigid structural framework β-Si3N4 is an elastically stiff material; the elastic stiffness moduli of the ceramic at 295 K are: CL = 396 GPa, μ = 119 GPa, BS = 238 GPa, E = 306 GPa, Poisson's ratio σ = 0.285. The longitudinal elastic stiffness CL increases with decreasing temperature and shows a knee at about 235 K; the decrease in slope below the knee indicates mode softening. The shear elastic stiffness μ shows mode softening which results in a plateau centred at about 235 K and an anomalous decrease with further reduction in temperature. The hydrostatic-pressure derivatives of elastic stiffnesses at 295 K are (∂CL/∂P)P=0 = 4.5 ± 0.1, (∂BS/∂P)P=0 = 4.3 ± 0.1 and (∂μ/∂P)P=0 = 0.17 ± 0.02 (pressure < 0.12 GPa). An interesting feature of the nonlinear acoustic behaviour of this ceramic is that, in the pressure range above 0.12 GPa, the values obtained for (∂μ/∂P)P=0 and the shear mode Gruneisen parameter (γS) are small and negative, indicating acoustic-mode softening under these higher pressures. Both the anomalous temperature and pressure dependences of the shear elastic stiffness indicate incipient lattice shear instability. The shear γS(=0.005) is much smaller than the longitudinal γL(=1.18) accounting for the thermal Gruneisen parameter γth(=1.09): since the acoustic Debye temperature ΘD(=923 ± 5 K) is so high, the shear modes play an important role in acoustic phonon population at room temperature. Hence knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic β-Si3N4.

High-resolution Brillouin scattering observation of ferroelastic soft phonon, using spherical Fabry–Pérot interferometer and computer controlled spectra accumulation

A high-resolution Brillouin scattering system has been developed for the purpose of observing and analysing the spectral shape of low frequency phonons down to ∼ 100 MHz . A spherical Fabry–Pérot interferometer with a resolution of about 10 8 is utilized. However, with such a high-resolution spectrometer, the frequency of a usual single-mode laser is not sufficiently stable. In order to avoid the influence of its drift, we developed a computer controlled procedure for spectra accumulation. The soft acoustic mode of the ferroelastic crystal KD 3(SeO 3) 2 has been observed by applying the present system. The Brillouin spectra are well adjusted by a damped harmonic oscillator. The temperature dependence of the damping constant shows no anomalies in contrast with that of the frequency.

Entropically Induced Euler Buckling Instabilities in Polymer Crystals

Molecular simulations show that heating crystalline polyethylene leads to an entropically induced Euler buckling instability, associated with the softening of the long wavelength transverse acoustic vibrational modes propagating along the chain axis. This entropic effect is augmented by axial compressive stress, leading to a decrease in the instability temperature with applied stress. For zero or low compressive stresses, the instability will occur above the melting temperature and impose a maximum temperature for the superheated crystal; for high compressive stresses, the instability will occur below the melting temperature and trigger a transition to another solid structure.

Ultrasonic study of the temperature and pressure dependences of the elastic properties of a single-crystal Heusler structure Cu41Mn20Al39 alloy

Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic-stiffness tensor components Cu and the adiabatic bulk modulus, BS, of a ferromagnetic Heusler structure Cu41Mn20Al39 at % alloy single crystal as functions of temperature in the range 14–300 K and hydrostatic pressure up to 0.2 GPa at room temperature. At 295 K the elastic stiffnesses are: C11=133 GPa, C44=92 GPa, C′ (=(C11−C12)/2)=17 GPa, C12=99 GPa, CL(=C11+C44−C′)=205 GPa, and BS (=C11−4C′/3)=106 GPa. Cu41Mn20Al39 is a comparatively soft material elastically because its elastic properties are influenced strongly by magnetoelastic effects. The results of measurements of the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to obtain the hydrostatic-pressure derivatives of the elastic – stiffness tensor components. At 295 K (∂C11/∂P)P=0, (∂C44/∂P)P=0, (∂C′/∂P)P=0, (∂C12/∂P)P=0, (∂CL/∂P)P=0, and (∂BS/∂P)P=0 are 5.0±0.1, 3.0±0.1, 1.0±0.2, 3.0±0.3, 7.7±0.4 and 3.7±0.4, respectively. Application of hydrostatic pressure does not induce acoustic-mode softening: the pressure derivatives (∂CIJ/∂P)P=0 and (∂BS/∂P)P=0 and the acoustic-mode Gruneisen parameters are positive. An interesting feature of the non-linear acoustic behaviour of this alloy is that the value obtained for (∂C′/∂P)P=0, associated with the softer shear mode propagated along the [1 1 0] direction and polarized along the [1 1 0] direction, is small in comparison with those of the other shear and longitudinal modes. The Gruneisen parameter of this mode, and hence its vibrational anharmonicity, is much larger than those of the other long-wavelength acoustic phonon modes. © 1998 Kluwer Academic Publishers

Elastic and nonlinear acoustic properties and thermal expansion of rare-earth metaphosphate glasses

Abstract The thermal expansions and the ultrasonic wave velocities and attenuations of (Sm2O3)0.234(P2O5)0.776 and (La2O3)0.222 (P2O5)0.778 and mixed (La2O3)x (Sm2O3)y(P2O5)0.75 (where x + y = 0.25) metaphosphate glasses have been measured as functions of temperature. The change in the ultrasonic wave velocity induced by application of hydrostatic pressure up to 0.16 GPa has also been measured at selected temperatures between room temperature and 375 K. The experimental results provide the temperature dependences of the adiabatic elastic stiffnesses C11 and C44 and related elastic properties and provide the hydrostatic-pressure derivatives (∂C 11/∂P)P=0 and (∂C 44/∂P)p=0 of the elastic stiffnesses and (∂B S/∂P)P=0 of the bulk modulus. The results obtained for C IJ and (∂C IJ/∂P)P=0 are used to determine the long-wavelength acoustic-mode Grüneisen parameters; these quantify the vibrational anharmonicity, which is essential information for developing the acoustic mode contribution to the thermal expansion of the glasses. Hence the ultrasonic velocity measurements in metaphosphate glasses modified with Sm3+ and La3+ ions enable separation of these acoustic-mode contributions from those due to the excess modes. Using the soft-potential model, it has been shown that, at low temperatures, the excess low-energy vibrational states provide negative contributions to the thermal expansion and to the nonlinear acoustic properties. For the mixed metaphosphate glasses of the type (La2O3)x(Sm2O3)y(P2O5)0.75, the acoustic-mode softening induced by Sin3+ is negated by the addition of La3+; as a result the acoustic-mode Grüneisen parameters and the thermal expansion are extremely small.

Ultrasonic study of the temperature and pressure dependences of the elastic propertiesof fcc Co-Mn alloy single crystals

To search for ramifications of magnetovolume effects in the magnetoelasticity of Co-Mn alloys, the elastic and nonlinear acoustic properties of single crystals with compositions ${\mathrm{Co}}_{75}$${\mathrm{Mn}}_{25}$, ${\mathrm{Co}}_{68}$${\mathrm{Mn}}_{32}$, ${\mathrm{Co}}_{52}$${\mathrm{Mn}}_{48}$, and ${\mathrm{Co}}_{46}$${\mathrm{Mn}}_{54}$, which have different magnetic configurations, have been determined ultrasonically. Pulse-echo-overlap measurements of the velocities of ultrasonic modes have been used to determine the three independent elastic-stiffness tensor components ${\mathrm{C}}_{\mathrm{IJ}}$ and the adiabatic bulk modulus ${\mathrm{B}}^{\mathrm{S}}$, as a function of temperature in the range from 4.2 up to about 800 K, and the pressure derivatives (\ensuremath{\partial}${\mathrm{C}}_{\mathrm{IJ}}$/\ensuremath{\partial}P${)}_{\mathrm{P}\mathrm{=}0}$ and (\ensuremath{\partial}${\mathrm{B}}^{\mathrm{S}}$/\ensuremath{\partial}P${)}_{\mathrm{P}\mathrm{=}0}$ at room temperature. These measurements of the elastic and nonlinear acoustic behavior of fcc Co-Mn alloys assist understanding of the structural and magnetic phase stability in this alloy system. Two of the alloys studied (${\mathrm{Co}}_{52}$${\mathrm{Mn}}_{48}$ and ${\mathrm{Co}}_{46}$${\mathrm{Mn}}_{54}$) are antiferromagnetic at room temperature; their elastic-stiffness tensor components and bulk moduli are affected by the onset of antiferromagnetic ordering and strong magnetoelastic coupling in the antiferromagnetic phase. The ${\mathrm{Co}}_{68}$${\mathrm{Mn}}_{32}$ alloy, with composition centered between the superantiferromagnetic and superparamagnetic regions in the phase diagram, does not undergo any transition. The temperature dependences of the elastic stiffnesses associated with the three independent ultrasonic modes propagated in the austenite and martensite phases of the ferromagnetic ${\mathrm{Co}}_{75}$${\mathrm{Mn}}_{25}$ alloy show that the \ensuremath{\epsilon}\ensuremath{\rightarrow}\ensuremath{\gamma} transition is strongly first order; the absence of long-wavelength acoustic-mode softening shows that its driving mechanism is not elastic in origin. Application of pressure does not induce acoustic mode softening for any of these alloys: the pressure derivatives (\ensuremath{\partial}${\mathrm{C}}_{\mathrm{IJ}}$/\ensuremath{\partial}P${)}_{\mathrm{P}\mathrm{=}0}$ and (\ensuremath{\partial}${\mathrm{B}}^{\mathrm{S}}$/\ensuremath{\partial}P${)}_{\mathrm{P}\mathrm{=}0}$ are positive. The long-wavelength longitudinal-acoustic-mode Gr\uneisen parameters of antiferromagnetic ${\mathrm{Co}}_{46}$${\mathrm{Mn}}_{54}$ show the unusual feature of being smaller than those for the shear waves: magnetovolume contributions to vibrational anharmonicity are stronger for longitudinal than for shear waves. The longitudinal-mode gamma ${\ensuremath{\gamma}}_{\mathrm{L}[110]}$ of this ${\mathrm{Co}}_{46}$${\mathrm{Mn}}_{54}$ alloy passes through a maximum value of 7.0 at 388 K: the vibrational anharmonicity of this mode is markedly enhanced in the vicinity of the N\'eel temperature.

Microscopic Brillouin Scattering Study in TeO 2: Pressure Dependence of Acoustic Modes

The pressure-induced ferroelastic transition of TeO2 is investigated in detail using microscopic Brillouin scattering in the backward geometry as a function of pressure. Both the quasi-transverse mode (T') and the quasi-longitudinal mode (L') are measured from 1 atm. to 2 GPa (transition pressure P c=0.9 GPa), using a diamond anvil cell for various propagation directions of phonons, of which the deviations ψ from [110] are 2.3°, 4°, 7.6°, 25°, 35°, and 45°. The T'-mode frequency for 2.3° decreases to the lowest value of ∼1.37 GHz at P c. Experimental results are generally explained on the basis of the Landau theory of the ferroelastic transition under pressure. It is concluded that the phase transition of the TeO2 crystal is driven by a soft acoustic mode. However, for the mode at ψ=45° corresponding to the pure longitudinal mode C11, an elastic anomaly found in the neighborhood of P c is larger than that for other modes.

Successive phase transitions of hexagonal barium titanate: soft acoustic mode and coupled acoustic-soft optic mode

The successive phase transitions at T 0 (222 K) and T C (74 K) of hexagonal BaTiO 3 have been studied by Brillouin scattering. An intense central peak was found near T 0 and was identified as a result of scattering from the coupled soft optic and acoustic mode. The coupled mode model was employed in order to explain the observed spectral changes. The ω 0 2Γ 0 ratio of the soft optic mode frequency ω 0 and the damping constant Γ 0, and the square of bilinear coupling constant A show linear dependence on temperature difference T − T 0, indicating the mean field behavior. The clear softening of c 66 shear acoustic mode was found near T C. The square of frequency of c 66 mode depends linearly on T − T C around the transition temperature. The results conclusively show that the phase transition at T C is the proper ferroelastic transition with the order parameter strain s 6.

ChemInform Abstract: Neutron Scattering Studies of YBa2Cu3O6.6 and CuGeO3

AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

Soft modes at ferroelastic phase transitions

Abstract Ferroelastic transitions have been classified by Aizu according to the genuine source of their instability. Ferroelastics of the acoustic type display an intrinsic soft acoustic mode whereas ferroelastics of the optic type become elastically soft by a bilinear coupling between softening optic modes and strain. Some crystals undergoing transitions of the latter kind at the center of the Brillouin zone are surveyed. Various behaviours of Raman active soft modes are encountered in systems of different complexity. Implications for the elastic properties and for domain structures are demonstrated.

Soft acoustic plasmons in cuprate superconductors

The layered electron gas model is applied to the study of plasmons in the normal state of cuprate superconductors consisting of one and two CuO conducting layers per unit cell. It is found that the well-behaved plasmon modes can exist for a restricted range of wave-vectors. We further notice that soft acoustic plasma modes may not exist in these materials because of high value of damping parameter, resulting from the strong electron-impurity scattering. The calculated plasma energies of well-behaved modes appear to be too high to be useful for pairing within a BCS framework.

Brillouin scattering study of hexagonal BaTiO3

Abstract The successive phase transitions at T 0 (222 K) and T c (74 K) of hexagonal BaTiO3 have been studied by Brillouin scattering. The anomalous central peak was found near T 0, and drastic changes in spectral shape and intensity were observed below T 0. The coupled-mode model for a soft optic and acoustic mode was employed to fit the experimental data in order to explain the observed spectral changes. The ω2 0/Γ0 ratio of soft optic mode frequency ω0 and damping constant Γ0 and the square of bilinear coupling constant show linear dependence on T - T 0, indicating the mean-field behavior. The complete softening of c66 shear acoustic mode was found near T c . The square of the frequency of c66 shear acoustic mode depends linearly on the temperature T –- T c . The results suggest that the phase transition at T c is the proper ferroelastic transition with the order parameter strain s6.

Soft acoustic mode in the ferroelectric phase transition of hexagonal barium titanate.

A Brillouin scattering study of the hexagonal modification of barium titanate ( $h$-BaTi${\mathrm{O}}_{3}$) was done to elucidate the soft mode behavior in the ferroelectric phase transition at 74 K. Measurements were made in the temperature region $20&lt;T&lt;300$ K. A clear softening of the ${c}_{66}$ shear acoustic mode was found at the phase transition. The squared frequency of the ${c}_{66}$ mode exhibits a linear dependence on the temperature difference from ${T}_{c}$, both above and below ${T}_{c}$. We conclude from this that the phase transition at ${T}_{c}$ is the proper ferroelastic transition with order parameter the elastic strain ${s}_{6}$.