Softening Of Velocity Research Articles

Sound velocity softening in body-centered cubic niobium under shock compression

Our understanding of pressure-induced anomalies in the physical and mechanical properties of Nb with a simple body-centered cubic structure remains limited both experimentally and theoretically. In this work we experimentally investigate the sound velocity of the compressional, bulk, and shear waves of Nb up to about 69 GPa and 1100 K under shock compression. These measurements reveal a significant softening in both the compressional and shear wave sound velocities in Nb compressed at 50 to 60 GPa. First-principles computations indicate that this anomalous behavior is most likely due to a pressure-induced Lifshitz-type electronic topological transition at 50 to 60 GPa. This study thus indicates that high-order phase transformations associated with the changes of electronic structures play an important role in the physical modification of transition metals.

Acoustic velocities, elasticity, and pressure-induced elastic softening in compressed neodymium

For the first time, the acoustic velocities and elasticity of double hexagonal close-packed neodymium (Nd) were measured at high pressure using ultrasonic interferometry in conjunction with synchrotron X-ray techniques. Both the compressional and shear wave velocities increased with an increase in pressure of up to ~5.4 GPa before they exhibited almost constant values upon further compression. This pressure-induced elastic wave velocity softening can be attributed to the structural instability in dhcp-Nd. From the current sound velocities and density data, we obtained new bulk and shear moduli as well as their pressure dependence for polycrystalline dhcp-Nd, yielding B0 = 33.2(9) GPa, G0 = 14.1(5) GPa, ∂B/∂P=3.6(4), and ∂G/∂P=1.3(2), while other elasticity-related/mechanical properties, including Young's modulus, Debye temperature, Poisson's ratio, and Grüneisen parameter, which are important parameters for the application of Nd in extreme environments, were also derived.

Pressure-induced velocity softening in natural orthopyroxene at mantle temperature

AbstractIn this study, we have measured the compressional and shear wave velocities of (Mg1.77Fe0.22Ca0.01)Si2O6 natural orthopyroxene up to 13.5 GPa and 873 K using ultrasonic interferometry in conjunction with in situ synchrotron X-ray diffraction and imaging techniques. Previous acoustic experiments on orthoenstatite (OEn) MgSiO3 indicated that both compressional and shear velocities (VP and VS) of OEn undergo continuous velocity softening above 9 GPa at room temperature, which has been attributed to the phase transition from OEn to the metastable, high-pressure clinoenstatite HPCEn2. For the first time, our results suggest that pressure-induced velocity softening can occur in natural orthopyroxene at high-temperature conditions relevant to the Earth's cold subduction zones. Estimates of the impedance and velocity contrasts between orthopyroxene (Opx) and high-pressure clinopyroxene (HPCpx) have been calculated, and the possibility of this phase transformation being a plausible candidate for seismic X-discontinuities at depth around 250–350 km is re-evaluated.

Softening of sound velocity and Hugoniot parameter measurement for shocked bismuth in the solid-liquid mixing pressure zone

Polymorphic phase transformation and melting under shock wave loading are important for studying the material dynamic mechanical behavior and equation of state in condensed matter physics. In this paper, the accurate Hugoniot parameter and sound velocity of shocked pure bismuth (Bi) in a pressure range of 17.3-28.3 GPa are obtained by using flyer impact method and rarefaction overtaking technique, respectively, and the sound velocity softening trend in shock-induced melting zone and the melting kinetics of Bi are then analyzed. In each experiment, six Bi samples with different thickness values are affected by oxygen-free-high-conducticity copper flyer fired through power gun. Shock wave velocity and particle velocity in Bi are experimentally determined through measuring the impact velocity and shock wave time in the thickest sample by photon Doppler velocimetry (PDV) technique. The velocity profiles on each interface between Bi and lithium fluoride (LiF) window are measured by displacement interferometer system of any reflector (DISAR), and then the sound velocity of shocked Bi is determined using the rarefaction overtaking method. The analyses of our results show that the softening of sound velocity of Bi approximatively satisfies the linear relation of Cs=3.682-0.015 p in the solid-liquid coexistence zone, and the pressure zone of the solid-liquid coexistence phase is further affirmed to be in a range of 18-27.4 GPa. Additionally, the obtained Hugoniot data for Bi in this paper supply a gap in the pressure zone of solid-liquid mixing phase. The quadratic equation with the expression of Ds=0.401+ 3.879 up-0.876 up2 can better demonstrate the relation between shock wave velocity and particle velocity than a linear one when the particle velocity lies in a range of 0.5-1.0 km/s, and this non-linear property maybe has a relationship with the shock-induced melting of Bi. Finally, our wave profile measurement of the Bi/LiF interface shows peculiar ramp characteristics in the expected velocity plateau zone in the pressure zone of solid-liquid coexistence phase, which may be associated with both the nonhomogeneous melting kinetics and the long time scale of melting for bismuth.

Abnormal acoustic wave velocities in basaltic and (Fe,Al)‐bearing silicate glasses at high pressures

AbstractWe have measured acoustic VP and VS velocities of (Fe,Al)‐bearing MgSiO3 silicate glasses and an Icelandic basalt glass up to 25 GPa. The velocity profiles of the (Fe,Al)‐bearing and basaltic silicate glasses display decreased VP and VS with minima at approximately 5 and 2 GPa, respectively, which could be explained by the mode softening in the aluminosilicate networks. Our results represent the first observation of such velocity softening extending into the chemically complex basaltic glass at a relatively low transition pressure, which is likely due to its degree of polymerization, while the Fe and Al substitutions reduce sound velocities in MgSiO3 glass. If the velocity softening in the basaltic and silicate glasses can be used as analogs for understanding melts in Earth's interior, these observations suggest that the melt fraction needed to account for the velocity reduction in the upper mantle low‐velocity zone may be smaller than previously thought.

Ultrasonic investigation of the organic spin-liquid compoundEtMe3Sb[Pd(dmit)2]2

Ultrasonic measurements performed on the spin-liquid organic compound $\mathrm{Et}{\mathrm{Me}}_{3}\mathrm{Sb}[\mathrm{Pd}(\text{dmit}{)}_{2}{]}_{2}$ reveal an inhomogeneous elastic behavior above 40 K due to the rotational motion in the $\mathrm{Et}{\mathrm{Me}}_{3}\mathrm{Sb}$ cations. Two velocity softening anomalies and concomitant attenuation peaks at 40 K and 160 K are respectively attributed to the rotation of methyl and ethyl groups. At lower temperatures, the elastic character is homogeneous and an anomaly is observed below 2 K. A magnetic field study suggests that two kinds of excitations contribute to this anomaly. First, a softening of the velocity toward the lowest temperatures which is not dependent on magnetic field implies other degrees of freedom than spins. Second, spin excitations coupled to longitudinal acoustic phonons yield a velocity softening anomaly that completely disappears for field values higher than 7 T. Consistent attenuation anomalies are also observed for both contributions. These data suggest that only one kind of spin excitation exists in the spin-liquid ground state below 1.5 K. A spinon-phonon interaction likely explains the magnetic field dependent elastic anomalies. However, no spin-gap-like excitations related to a pairing instability of the spinons could be detected in this experiment.

Ultrasonic and microwave investigation of the structural and magnetic transitions inCaFe2As2andBaFe2As2single crystals

Pulsed ultrasonic experiments performed on the parent compounds of FeAs based superconductors $A$Fe${}_{2}$${\mathrm{As}}_{2}$ ($A=\text{Ba}$, Ca) revealed elastic anomalies that agree with a two-step process for the structural/magnetic transitions. Upon cooling, a pronounced velocity softening of longitudinal phonons propagating along the $\mathbit{c}$ axis is observed at the structural transition ${T}_{\mathrm{s}}$ due to a distortion of the lattice. Below a slightly lower temperature ${T}_{\mathrm{N}}$, a biquadratic coupling between the distortion and an antiferromagnetic order parameter produces a steep velocity stiffening upon further cooling, the stiffening being five times larger in ${\mathrm{CaFe}}_{2}$${\mathrm{As}}_{2}$ than in ${\mathrm{BaFe}}_{2}$${\mathrm{As}}_{2}$. Microwave resistivity measurements at 16.5 GHz suggest that, upon cooling, the lattice distortion at ${T}_{\mathrm{s}}$ is driven by magnetic fluctuations in ${\mathrm{BaFe}}_{2}$${\mathrm{As}}_{2}$, while it is rather due to lattice fluctuations in ${\mathrm{CaFe}}_{2}$${\mathrm{As}}_{2}$. This suggestion appears consistent with a second-order character of the transitions in ${\mathrm{BaFe}}_{2}$${\mathrm{As}}_{2}$ and a first-order one in ${\mathrm{CaFe}}_{2}$${\mathrm{As}}_{2}$.

Thermal evolution of the full three-dimensional magnetic excitations in the multiferroic BiFeO3

The idea of embedding and transmitting information within the fluctuations of the magnetic moments of spins (spin waves) has been recently proposed and experimentally tested. The coherence of spin waves, which describes how well defined these excitations are, is of course vital to this process, and themost significant factor that affects the spin-wave coherence is temperature. Here we present neutron inelastic scattering measurements of the full threedimensional spin-wave dispersion in BiFeO3, which is one of the most promising functional multiferroic material, for temperatures from 5K to 700K. Despite the presence of strong electromagnetic coupling, the magnetic excitations behave like conventional magnons over all parts of the Brillouin zone. At low temperature the spin-waves are well-defined coherent modes, described by a classical model for a G-type antiferromagnet. A spin-wave velocity softening is already present at room temperature, and more pronounced damping occurs as the magnetic ordering temperature TN \sim 640K is approached. In addition, a strong hybridization of the Fe 3d and O 2p states is found to modify the distribution of the spin-wave spectral weight significantly, which implies that the spins are not restricted to the Fe atomic sites as previously believed.

In situ ultrasonic velocity measurements across the olivine-spinel transformation in Fe2SiO4

Compressional (P) and shear (S) wave velocities across the olivine-spinel transformation in Fe{sub 2}SiO{sub 4} were investigated in situ using combined synchrotron X-ray diffraction, X-ray imaging, and ultrasonic interferometry up to 5.5 GPa along the 1173 K isotherm. The onset of the spinel to olivine transformation at 4.5 GPa and olivine to spinel transition for Fe{sub 2}SiO{sub 4} at 4.8 GPa was concurrently observed from X-ray diffraction, the amplitude of the ultrasonic signals, the calculated velocities, and the ratio of P and S wave velocities (v{sub P}/v{sub S}). No velocity softening was observed prior to the fayalite to spinel transition. The velocity contrasts across the Fe{sub 2}SiO{sub 4} spinel to fayalite phase transition are derived directly from the measured velocities, which are 13 and 12% for P and S waves, respectively, together with a density contrast of 9.4%. A comparison with literature data indicates that the changes in compressional-wave velocity and density across the olivine-spinel transformation in Fe{sub 2}SiO{sub 4} are comparable to those with different iron concentrations in the (Mg,Fe){sub 2}SiO{sub 4} solid solution, whereas the shear wave velocity contrast decreases slightly with increasing iron concentration.

Ultrasonic studies of the spin-state transition and the local distortion in LaCoO3

Temperature dependence of longitudinal and transverse ultrasonic velocities and attenuations of the single-phase polycrystalline LaCoO3 were presente d. A clear softening in the longitudinal ultrasonic velocity accompanied by a sharp peak in attenuation were observed near the spin-state transition temperature(≈90K), which did not appear in the transverse mode measurement. This anomalous ultraso nic behavior further demonstrates that the spin-state transition of Co3+ ions in LaCoO3 near 90K are more likely from a low spin state (LS,t62ge 0g) to an intermediate spin state (IS,t5 2ge1g ) than to a high s pin state (HS,t42ge2g ). A b ig attenuation peak accompanied by a slight softening in velocity was observed near 200K in both longitudinal and tr ansverse modes, which was probably caused by the relaxation of the local distort ions originating from Jahn-Teller effect of the randomly distributed IS state Co 3+ ions.

Brillouin scattering and x-ray photoelectron studies of germanium nanoclusters synthesized in SiO2 by ion implantation

Brillouin scattering and x-ray photoelectron spectroscopy (XPS) have been utilized to characterize Ge+-implanted thermal SiO2 layers on a Si substrate with subsequent annealing at 500°C and 1100°C. Sputtering depth profiling in conjunction with XPS studies have been applied to identify the chemical state of elemental Ge and GeO2 precipitations in the SiO2 matrices. The presence of a subsurface GeOx zone as predicted in kinetic 3-dimensional lattice simulations has been confirmed. It is concluded that the intermediate step of Ge oxide formation seems necessary for the creation of Ge nanoclusters. The Ge atomic concentrations obtained from XPS were used to compute the bulk and shear moduli, and consequently the surface acoustic wave (SAW) velocities, for the Ge∕GeO2∕SiO2 systems. These calculations confirm the character of SAW velocity softening as determined from the Brillouin scattering investigations.

Dynamics of a creep-slip model of earthquake faults

Starting off from the relationship between time-dependent friction and velocity softening we present a generalization of the continuous, one-dimensional homogeneous Burridge–Knopoff (BK) model by allowing for displacements by plastic creep and rigid sliding. The evolution equations describe the coupled dynamics of an order parameter-like field variable (the sliding rate) and a control parameter field (the driving force). In addition to the velocity-softening instability and deterministic chaos known from the BK model, the model exhibits a velocity-strengthening regime at low displacement rates which is characterized by anomalous diffusion and which may be interpreted as a continuum analogue of self-organized criticality (SOC). The governing evolution equations for both regimes (a generalized time-dependent Ginzburg–Landau equation and a non-linear diffusion equation, respectively) are derived and implications with regard to fault dynamics and power-law scaling of event-size distributions are discussed. Since the model accounts for memory friction and since it combines features of deterministic chaos and SOC it displays interesting implications as to (i) material aspects of fault friction, (ii) the origin of scaling, (iii) questions related to precursor events, aftershocks and afterslip, and (iv) the problem of earthquake predictability. Moreover, by appropriate re-interpretation of the dynamical variables the model applies to other SOC systems, e.g. sandpiles.

Anomalous elastic behaviour of Bi-Pb-Ag composites

Bi-Pb and Bi-Pb-Ag superconducting composites have been prepared by the solid state reaction method. After the usual characterization, ultrasonic longitudinal velocity and attenuation studies have been undertaken over a temperature range 80–300 K by the pulse transmission technique. In contrast to normal solids, the ultrasonic velocities of both the samples in the temperature range 200-100 K are found to decrease with decreasing temperature (softening), followed by a velocity maximum. The samples are also found to exhibit longitudinal attenuation peaks at temperatures = 260, 160 and 120 K. An attempt has also been made to verify whether the Wachtman's equations can theoretically explain the low-temperature behaviour of the Young's modulus of these materials. A qualitative explanation for both the phenomena of softening of velocity as well as the occurrence of attenuation peaks is given.

Ultrasonic studies of some Bi-based high-Tc superconductors

A series of Bi2-xPbxSr2Ca2Cu3O10 (0 < x < 0.5) high-Tc superconductors has been prepared by the solid state reaction method. After characterization, ultrasonic longitudinal velocity and attenuation studies were undertaken over the temperature range 80-300 K using the pulse transmission technique. In contrast to normal solids, the ultrasonic velocities of all the samples in the temperature range 250-150 K are found to decrease with decreasing temperature (softening). It has also been observed that most of the samples are found to exhibit longitudinal attenuation peaks at temperatures approximately=250 K, approximately=170 K and approximately=100 K. A qualitative explanation for the softening of velocity and the attenuation peaks is given on the basis of microstructure and relaxation.

Acoustic anomalies in weak ferroelectric Li2Ge7O15

Abstract The acoustic anomalies at the ferroelectric phase transition in Li2Ge7O15 have been studied by the Brillouin scattering and ultrasonic methods. The qualitative display of weak ferroelectricity is discussed. Frequency dispersion of the fluctuation contribution to sound velocity softening was found near Tc.

Frequency-dependent ultrasonic attenuation of YBa2Cu3O7.

At temperatures near ${T}_{c}$, experimental measurements of temperature-dependent ultrasonic attenuation at three frequencies exhibit maxima, and velocity measurements display softening of the lattice. These attenuation maxima result from a relaxation process which occurs around the superconducting transition, and the softening of velocity around ${T}_{c}$ may evidence a structural instability of Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ at these temperatures.

Softening of surface phonons in the (100) plane of Nb 3Sn

The propagation of the surface acoustic mode in the (001) plane is investigated as a function of the temperature dependent elastic moduli of Nb 3Sn in the cubic phase. For the [100] and [110]-directions a softening of the surface mode velocity ν s is found to follow the softening of the velocity ν T2 of the bulk shear mode T 2 A. It is shown that for the [100]-direction the ratio ( ν s ν T2 ) tends to ✓2 at the structural phase transition. The question is discussed of whether the softening of the surface mode can be observed with Brillouin scattering from opaque surfaces.

Ultrasonic investigation of the phase transitions in NH4Cl1–xBrx Mixed Crystals

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