Superheating systematics of crystalline solids

Systematics of superheating (theta= T/Tm–1) of crystalline solids as a function of heating rate (Q) are established as beta= A(Q)(theta+ 1)theta2, where the normalized energy barrier for homogeneous nucleation is beta= 16pigammasl3/(3kTmDeltaHm2), T is temperature, Tm melting temperature, A a Q-dependent parameter, gammasl interfacial energy, DeltaHm heat of fusion, and k Boltzmann's constant. For all elements and compounds investigated, beta varies between 0.2 and 8.2. At 1 and 10^12 K/s, A = 60 and 31, theta= 0.05–0.35 and 0.06–0.45, respectively. Significant superheating is achievable via ultrafast heating. We demonstrate that the degree of superheating achieved in shock-wave loading and intense laser irradiation as well as in molecular dynamics simulations (Q~10^12 K/s) agrees with the theta–beta–Q systematics

Melting at the Limit of Superheating

Theories on superheating-melting mostly involve vibrational and mechanical instabilities, catastrophes of entropy, volume and rigidity, and nucleation-based kinetic models. The maximum achievable superheating is dictated by nucleation process of melt in crystals, which in turn depends on material properties and heating rates. We have established the systematics for maximum superheating by incorporating a dimensionless nucleation barrier parameter and heating rate, with which systematic molecular dynamics simulations and dynamic experiments are consistent. Detailed microscopic investigation with large-scale molecular dynamics simulations of the superheating-melting process, and structure-resolved ultrafast dynamic experiments are necessary to establish the connection between the kinetic limit of superheating and vibrational and mechanical instabilities, and catastrophe theories

Polymorphism, superheating, and amorphization of silica upon shock wave loading and release

We present a detailed and quantitative examination of the thermodynamics and phase change mechanisms (including amorphization) that occur upon shock wave loading and unloading of silica. We apply Debye-Grüneisen theory to calculate both the Hugoniot of quartz and isentropic release paths. Quartz converts to stishovite (or a stishovite-like phase) between 15 and 46 GPa, and persistence of the solid phase above its liquidus (i.e., superheating) is confirmed between 77 and 110 GPa. Calculations compare favorably to measurements of shock and post-shock temperatures. For silica, the method of measuring post-shock temperature is insensitive to predicting whether phase transitions actually occur during release. Measurements of release states in pressure-particle velocity space are compared to computed frozen-phase release paths. This comparison suggests transformation of a stishovite-like phase to lower density phases including quartz, liquid, or dense amorphous glass. Transformations to liquid or glass occur upon release from peak pressure of 26 GPa and above. The isentropic release assumption appears to be approximately valid. A shock pressure-temperature scale relating metamorphism of silica in shock-loaded quartz is proposed. Neither recovery of coesite nor substantial quantities of crystalline stishovite-like phases upon shock loading of quartz is predicted. Trace amounts of crystalline stishovite-like phases from shock loading between 15 and 26 GPa are expected

A new Pachpatte type dynamic inequality on time scales

In this paper, using the comparison theorem, we investigate a new Pachpatte type dynamic inequality on time scales, which provides explicit bounds on unknown functions. Our result unifies and extends a continuous inequality and its corresponding discrete analogues

Shock wave loading and spallation of copper bicrystals with asymmetric Σ3〈110〉tilt grain boundaries

We investigate the effect of asymmetric grain boundaries (GBs) on the shock response of Cu bicrystals with molecular dynamics simulations. We choose a representative Σ3〈110〉tilt GB type, (110)_1/(114)_2, and a grain size of about 15 nm. The shock loading directions lie on the GB plane and are along [001] and [221] for the two constituent crystals. The bicrystal is characterized in terms of local structure, shear strain, displacement, stress and temperature during shock compression, and subsequent release and tension. The shock response of the bicrystal manifests pronounced deviation from planar loading as well as strong stress and strain concentrations, due to GBs and the strong anisotropy in elasticity and plasticity. We explore incipient to full spallation. Voids nucleate either at GBs or on GB-initiated shear planes, and the spall damage also depends on grain orientation

Direct shock wave loading of Stishovite to 235 GPa: Implications for perovskite stability relative to an oxide assemblage at lower mantle conditions

Pure stishovite and coesite samples with zero porosity and dimensions appropriate for planar shock wave experiments have been synthesized with multi-anvil high-pressure techniques. The equation of state of stishovite is obtained by direct shock wave loading up to 235 GPa: K_(0T) = 306 ± 5 GPa and K'_(0T) = 5.0 ± 0.2 where K_(0T) and K'_(0T) are ambient bulk modulus and its pressure derivative, respectively. The Hugoniots (shock equations of state) for stishovite, coesite and quartz achieve widely differing internal energy states at equal volume and therefore allow us to determine the Gruneisen parameter of stishovite. On the basis of the resulting P-V-T equation of state for stishovite and previous studies on other phases on the MgO-SiO_2 binary, the breakdown reaction of MgSiO_3-perovskite to MgO and SiO_2 was calculated. Our calculations show that perovskite is thermodynamically stable relative to the stishovite and periclase assemblage at lower mantle conditions. We obtain similar results for a range of models, despite the appreciable differences among these experiment-based thermodynamic parameters

Shock-compressed MgSiO_3 glass, enstatite, olivine, and quartz: Optical emission, temperatures, and melting

Optical emission of MgSiO_3 glass, enstatite, olivine, and quartz under shock wave compression was investigated with optical pyrometry at discrete wavelengths ranging from visible to near infrared. We develop a new analysis of optical emission that does not require a gray body assumption. Instead, at each wavelength, the optical linear absorption coefficients (α) and blackbody spectral radiances (L_(λb)) of shocked and unshocked materials were obtained by nonlinear fitting to the time-resolved radiance from the target assembly. The absorption spectra of unshocked samples corresponding to the measured values of α reproduce those from independent static optical spectroscopic measurements. The measured values of α (ranging from 7 to 56 mm^(−1)) for shocked samples indicate that shock-induced high-pressure phases (including melt) can be regarded essentially as black bodies in the optical range investigated, although starting phases such as enstatite and olivine have band-like spectra at ambient conditions. The effect of emission from the air gap at the driver sample interface on the recorded radiance can be resolved, but α and L_(λb) cannot be separated for this component of the signal. The shock velocity-particle velocity relationships of these silicates derived from radiance history are in accord with previous investigations using independent techniques. Given the limited amount of shock wave data, possible high-pressure melting curves of Mg-perovskite and its assemblage with periclase are deduced; their melting temperatures near the core-mantle boundary (CMB) being 6000 ± 500 K and 4000 ± 300 K, respectively. It is proposed that Mg-perovskite melts with density increase at the CMB pressure

Shock-induced melting of MgSiO_3 perovskite and implications for melts in Earth's lowermost mantle

New shock wave equation of state (EOS) data for enstatite and MgSiO_3 glass constrain the density change upon melting of Mg-silicate perovskite up to 200 GPa. The melt becomes denser than perovskite near the base of Earth's lower mantle. This inference is confirmed by shock temperature data suggesting a negative pressure-temperature slope along the melting curve at high pressure. Although melting of Earth's mantle involves multiple phases and chemical components, this implies that the partial melts invoked to explain anomalous seismic velocities in the lowermost mantle may be dynamically stable

The role of Chinese fisheries libraries in responsible fisheries

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