Investigating the vortex melting phenomenon in BSCCO crystals using magneto-optical imaging technique

Using a novel differential magneto-optical imaging technique we investigate the phenomenon of vortex lattice melting in crystals of Bi₂Sr₂CaCu₂O₈ (BSCCO). The images of melting reveal complex patterns in the formation and evolution of the vortex solid-liquid interface with varying field (H)/temperature (T). We believe that the complex melting patterns are due to a random distribution of material disorder/inhomogeneities across the sample, which create fluctuations in the local melting temperature or field value. To study the fluctuations in the local melting temperature/field, we have constructed maps of the melting landscape T _m(H, r), viz., the melting temperature (T _m) at a given location (r) in the sample at a given field (H). A study of these melting landscapes reveals an unexpected feature: the melting landscape is not fixed, but changes rather dramatically with varying field and temperature along the melting line. It is concluded that the changes in both the scale and shape of the landscape result from the competing contributions of different types of quenched disorder which have opposite effects on the local melting transition.     

Molecular dynamics simulation of the melting of a twist Σ=5 grain boundary

The existence of a possible grain boundary disordering transition of the melting type in a =5 (001) twist boundary of aluminium bicrystal below the melting temperature was investigated using a constant pressure molecular dynamics simulation. The calculated melting temperature T _cm of the bulk Al is about 960 K. The total internal energy, the structure factor, and the pair distribution function were calculated at different layers across the grain boundary. The mean atomic volume, the grain boundary energy, and the thermal expansion coefficients were also calculated using the same simulation method. This simulation also allows us to image the grain boundary structure at different temperatures. The equilibrium grain boundary structure at 300 K retains the periodicity of the coincident site lattice, so that the lowest energy structure corresponds to the coincident site arrangement of the two ideal crystals. With increasing temperature, the total internal energy of the atoms for both the perfect crystal and the grain boundary increases, as do the number of layers in the grain boundary. The grain boundary core exists and the perfect crystal structure still exists outside the grain boundary at 0.9375 T _cm. However, two atomic layers of the equilibrium grain boundary structure at 0.9375 T _cm lose the coincident site lattice periodicity and attain a structure with liquid-like disorder. Therefore, partial melting of the grain boundary has occurred at the temperature above 0.9375 T _cm which is in agreement with the experimental results.     

On the surface configuration of solids in relation to the surface free enthalpy excess and its consequences in phase transitions

Summary In previous studies the average number of neighbors (n _avrg) of an atom in the surface phase was found to increase by about (5÷20)% between 0 K and the melting temperature for all solid chemical elements in the periodic table. This increment makes the solid surface “geometrically impossible” to exist at the melting temperature. The latter results in the collapse of crystal structure, beginning with the formation of liquid in the surface layers. Ratio of critical and melting temperature is also discussed.     

Study of Crystal Structure of Polypropylene/Mg2B2O5 Whisker Composite

The effects of whisker content, sample holding time, and differential scanning calorimetry (DSC) analysis of the crystal structure of polypropylene/Mg ₂ B ₂ O ₅ whisker composites were investigated. DSC shows a double melting peak, T ₁ at about 151°C and T ₂ at about 166°C. Detailed analysis of wide angle X-ray diffraction (WAXD) shows that a γ phase may exist in the polypropylene/Mg ₂ B ₂ O ₅ composite. The experimental results also show that the crystal structure according to MPLT (melting peak at low temperature) was more perfect and the crystallinity according to MPLT increased with increasing whisker content. The sample holding time at room temperature following injection molding had a significant effect on the number of γ -crystal nuclei.     

Surface energy and pressure of diamond and silicon nanocrystals

Based on the pair potential of interatomic interaction, we study the dependence of various properties of diamond and silicon nanocrystals with a free surface on size, surface shape, and temperature. A model nanocrystal has the form of a parallelepiped faceted by {100} planes with a square base. The number of atoms N in the nanocrystals is varied from 5 to infinity. The Debye temperature, Gruneisen parameter, specific surface energy, isochoric derivative of specific surface energy with respect to temperature, and surface pressure are calculated as a function of the size and shape of diamond and silicon nanocrystals at temperatures ranging from 20 K to the melting point. The surface pressure P _sf(N) ∼ N ^−1/3 is much lower than the pressure calculated by the Laplace formula for similar nanocrystals for given values of density, temperature, and number of atoms. As the temperature increases from 20 K to the melting point, the isotherm P _sf(N) lowers and changes the shape of the dependence on N; at high temperatures, it goes to the region of extension of small nanocrystals of diamond and silicon.     

Equilibrium melting temperature as a result of induction time measurements: Isotactic polypropylene

A method for the determination of equilibrium melting temperature from induction time measurements is suggested. Theory of the induction time, t _i (most probable period from the beginning of isothermal crystallization to the instant when a stable crystal nucleus starts growing) involves parameters that influence the nucleation-crystallization process, such as specific interfacial free-energy parameter, specific surface energies of a growing nucleus, enthalpy of crystal melting, diffusion activation energy, undercooling and the equilibrium melting temperature, T_m°. An extrapolation method exploiting the aspect of the induction time that it increases to infinity, that is, 1/t _i decreases to zero at the equilibrium melting temperature, cannot be used to calculate the equilibrium melting temperature. High- or low-temperature approximations of the basic equation yield some simplifications that make it possible to find its parameters via the best fit of the equation with experimental data. This procedure can yield also the value of the equilibrium melting temperature if the measured data are sufficiently precise. Applying that procedure to crystallization data of isotactic polypropylene, we obtained the values of the equilibrium melting temperatures 199.5°C (high-temperature approximation) and 212.7°C (low-temperature approximation). A more detailed discussion of the procedure suggests that from both these reasonable values, the higher one is more justified. This result agrees well with higher T_m° data reported in the literature.     

Effect of EPDM Content on Melt Flow,Microstructures and Fracture Behavior of Dynamically Vulcanized PP/EPDM Blends

Polypropylene (PP)/Ethylene‐propylene‐diene terpolymer (EPDM) blends were dynamically vulcanized with dicumyl peroxide (DCP), using a two‐step method of even dispersion of DCP in EPDM at first and then cross‐linking at elevated temperature. The results showed that though both chain scission and cross‐linking occurred, the cross‐linking reaction predominated in this process and the number of EPDM particles was increased, accompanied with a reduction in particle size and uniform dispersion. Differential scanning calorimetry (DSC) results indicated the existence of PP/EPDM graft copolymer. The essential work of fracture (EWF) results showed that both the specific essential work of fracture (w _e ) and the specific plastic work (w _p ) increased with increasing EPDM content, the fracture toughness and plastic energy consumption (βw _p ) could be improved simultaneously and the ratio of w _e and βw _p could be controlled by adjusting EPDM and DCP content.     

Calorimetric study of Te15(Se100− x Bi x )85 glassy alloys using differential thermal analysis

A calorimetric study of Te₁₅(Se_{100? x} Bi _x )₈₅ glassy alloys (x = 0, 1, 2, 3 and 4 at. %) is reported. Differential thermal analysis (DTA) was performed at heating rates of 10, 15, 20 and 25 K/min. The spectra were used to determine the glass transition temperature, T_g , the crystallisation temperature, T_c and the melting temperature, T_m . All these parameters shift to higher values with increasing heating rate, β. The glass transition temperature and the melting temperature increase, and the crystallisation temperature decreases, with increase in the Bi content, x. The activation energy of the glass transition, E_g , was evaluated using the Moynihan and Kissinger methods. The activation energy of crystallisation, E_c , was calculated using modified Kissinger and Matusita approaches. The thermal stability of these glasses has been studied and found to decrease with increase in Bi content. The results obtained are explained on the basis of a chemically ordered network model and an average coordination number.     

Thermal Cross‐Linking of Poly(Vinyl Methyl Ether). I. Effect of Cross‐Linking Process on the Viscoelastic Properties

Abstract

Thermal cross‐linking of poly(vinyl methyl ether) (PVME) in the absence of cross‐linking agent, was detected rheologically. The linear viscoelastic properties of PVME were found to be greatly changed by the onset of the cross‐linking process. The viscoelastic material functions, such as dynamic shear moduli, G′ and G″, complex shear viscosity, η*, and loss tangent, tan δ, were found to be sensitive to the structure changes during the cross‐linking process and the formation of a three‐dimensional polymer network. At the onset temperature of the cross‐linking process, an abrupt increase in G′, G″, and η* (several orders of magnitude) during dynamic temperature ramps (2°C/min heating rate) was observed with some frequency dependence. The temperature dependence of tan δ was found to be frequency independent at the gel‐point, T _gel, that is, the crossover in tan δ regardless of the value of frequency can be taken as an accurate method for determination of T _gel. The coincidence of G′ and G″ at the gel‐point cannot be considered a general method for evaluation of T _gel due to its high frequency dependence, that is, T _gel determined from the crossover of G′ and G″ in the dynamic temperature ramp at 1 rad/sec is about 20°C less than at 100 rad/sec. Furthermore, a dramatic increase in η₀ above the minimum (“v” shape) was observed at T = T _gel in agreement with the value obtained from tan δ vs. T (190°C). The time–temperature‐superposition principle was found to be valid only for temperatures lower than the T _gel (190°C); the principle failed at T ≥ 190°C. This was clearly seen in the low‐frequency region as a deviation from the terminal slope in the G′ curve. Similar behavior was observed in the modified Cole–Cole analyses (G″ vs. G′) that is, the curves start to deviate at 190°C.     

A possible role of the surface free enthalpy excess of solid chemical elements in their melting and critical temperature

A 5–20% increase in the average number of neighbors of an atom (n_avrg) in the surface phase between 0 K and melting temperature T_m makes the solid surface “geometrically impossible” to exist at some temperature called the melting temperature. The latter results in the collapse of crystal structure, beginning with the formation of surface layers of liquid a few atoms thick, in agreement with recently published studies. The critical temperature of solid chemical elements is also discussed. The derivation yields expressions for the heat of melting (ΔH_m), entropy of melting (ΔS_m), melting temperature (T_m) and critical temperature (T_c) in case of pure metals.     

Void formation in Nickel during high temperature proton irradiation

Pure Ni foils, doped with He from 0 to 28 appm, were irradiated with protons at temperatures in the range 0.3–0.6 T_m (T_m = melting point in °K) and void formation was studied. The influence of He doping, irradiation temperature and alloying were investigated. For constant He content and proton fluence, void number density and swelling are maximum at about 400°C, while the void size increases with temperature. Most voids are octahedral in shape with no sign of truncation. Helium is required to nucleate voids, and lowering the stacking fault energy by alloying suppresses void formation completely. Present results suggest that void nucleation is inhomogeneous. Some implications of these findings are discussed.     

Melting temperature variation with concentration of alkali halides in mixed crystal systems

Diffusion-vibration theory of melting (Sharmaet al 1991) has been extended to study the variation in the melting temperature of mixed ionic crystals with concentration. The melting temperature varies non-linearly with concentration in the KCl _x Br_1−x , RbCl _x Br_1−x , K _x Rb_1−x Br and NaCl _x Br_1−x mixed alkali halides and shows a sharp increase in melting temperature for values ofx>0.5 which is in good agreement with the experimental values. This behaviour has been explained on the basis of present propounded theory.     

Solid-liquid phase transition in small water clusters: a molecular dynamics simulation study

Water clusters, (H₂O) _n , of varying sizes (n = 8, 12, 16, 20, 24, 28, 32, 36, and 40) have been studied at different temperatures from 0 to 200 K using molecular dynamics simulations. Transitions between solid and liquid phases were investigated to estimate the melting temperature of the clusters. Although the melting temperatures showed non-monotonic behaviour as a function of cluster size, their general tendency follows the classical relationship T _m ∝ n ^?1/3 to the cluster size n. Moreover, it was observed that the liquid-solid surface tension decreased with the cluster size in a similar way to the liquid-vapour surface tension in bulk water. Upon cooling, ice-like crystals were formed from the smaller clusters with n up to 20, while the larger clusters were transformed to glassy structures. The decrease in the glass transition temperature with the cluster size was observed to be much less than the corresponding melting temperature. The mutual order of the melting and glass-transition temperatures were found to be reversed compared with that observed for bulk water.     

The melting mechanism in binary Pd0.25Ni0.75 nanoparticles: molecular dynamics simulations

The melting mechanism for Pd_0.25Ni_0.75 alloy nanoparticles (NPs) was investigated using molecular dynamics (MD) simulations with quantum Sutton-Chen many-body potentials. NPs of six different sizes ranging from 682 to 22,242 atoms were studied to observe the effect of size on the melting point. The melting temperatures of the NPs were estimated by following the changes in both the thermodynamic and structural quantities such as the total energy, heat capacity and Lindemann index. We also used a thermodynamics model to better estimate the melting point and to check the accuracy of MD simulations. We observed that the melting points of the NPs decreased as their sizes decreased. Although the MD simulations for the bulk system yielded higher melting temperatures because of the lack of a seed for the liquid phase, the melting temperatures determined for both the bulk material and the NPs are in good agreement with those predicted from the thermodynamics model. The melting mechanism proceeds in two steps: firstly, a liquid-like shell is formed in the outer regions of the NP with increasing temperature. The thickness of the liquid-like shell increases with increasing temperature until the shell reaches a critical thickness. Then, the entire Pd–Ni NP including core-related solid-like regions melts at once.     

High P–T Brillouin scattering study of H2O melting to 26 GPa

The properties of solid and liquid phases of H₂O at high pressure and temperature remain an active area of research. In this study, Brillouin spectroscopy has been used to determine the temperature dependence of sound velocities in H₂O as a function of pressure up to 26 GPa through the phase field of ice VII and into the liquid to a maximum temperature of 1200 K. The Brillouin shift of the quasi-longitudinal acoustic mode moves to lower frequencies upon melting at each pressure. As a test of the method, measurements of the melting of Ar by Brillouin scattering at several pressures show a similar behavior for the acoustic mode, and measured melting points are consistent with previous results. The results of H₂O melting are consistent with previously reported melting curves below 20 GPa. The data at higher pressure indicate that ice melts at a higher temperature than a number of previous studies have indicated.     

Crystallization Kinetics of Lamellar Crystals Confined in Polymer Thin Films

We used dynamic Monte Carlo simulations to investigate the crystallization kinetics of flat-on lamellar polymer crystals in variable thickness films. We found that the growth rates linearly reduced with decreasing film thickness for the films thinner than a transition thickness d_t , while they were constant for the films thicker than d_t . Moreover, the mean stem lengths (crystal thickness) we calculated decreased with film thickness in a similar way to the growth rates, and the intramolecular crystallinities we calculated confirmed the film thickness dependence of the crytsal thickness. Besides, the crystal melting rates in thin films were calculated and increased with decreasing film thickness. We proposed a new interpretation on the film thickness dependence of the crystal growth rate in thin films, suggesting that it is dominated by the crystal thickness in terms of the driving force term (l–l _min) expressed by Sadler, rather than the chain mobility based on experiments. The crystal thickness can determine whether a crystal grows or melts in a thin film at a fixed temperature, indicating the reversibility between the crystal growth and melting.     

Evidence of maximum in the melting curve of hydrogen at megabar pressures

Hydrogen at high pressures of ∼400 GPa might be in a zero-temperature liquid ground state (N. Ashcroft, J. Phys.: Condens. Matter A 12, 129 (2000), E. G. Brovrnan et al., Sov. Phys. JETP 35, 783 (1972)). If metallic hydrogen is liquid, the melting T _melt(P) line should possess a maximum. Here we report on the experimental evaluation of the melting curve of hydrogen in the megabar pressure range. The melting curve of hydrogen has been shown to reach a maximum with T _melt = 1050 ± 60 K at P = 106 GPa and the melting temperature of hydrogen decreases at higher pressures so that T _melt = 880 ± 50 K at P = 146 GPa. The data were acquired with the aid of a laser heating technique where diamond anvils were not deteriorated by the hot hydrogen. Our experimental observations are in agreement with the theoretical prediction of unusual behavior of the melted hydrogen [S. Bonev et al., Nature 481, 669 (2004)]. The article is published in the original.     

Mechanisms of bulk diffusion at “high” and “low” temperatures

A phenomenological model has been proposed for bulk self-diffusion and diffusion of interstitial atoms in the ranges of high (T > T _D) and low (T < T _D) temperatures (where T _D is Debye temperature). It has been shown that the mechanisms of diffusion at high and low temperatures differ significantly. In the high-temperature range, the diffusion is provided by fluctuations, which can be described in terms of local melting, i.e., the formation of a “liquid diffusion channel.” In the low-temperature range, when melting for some reasons is hindered, the diffusion is due to the fluctuation formation of a “hollow diffusion channel.” The calculation of the activation energies of these processes in the case of self-diffusion agrees well with the experiment in the temperature range T > T _D and has demonstrated that the activation energy increases significantly at T < T _D. The calculation of the activation energy for diffusion of interstitial atoms in bcc metals agrees well with the experiment in the entire temperature range and provides an explanation of the decrease in the activation energy of diffusion at low temperatures.     

Pore size distribution in porous glass: fractal dimension obtained by calorimetry

By differential Scanning Calorimetry (DSC), at low heating rate and using a technique of fractionation, we have measured the equilibrium DSC signal (heat flow) J _q ⁰ of two families of porous glass saturated with water. The shape of the DSC peak obtained by these techniques is dependent on the sizes distribution of the pores. For porous glass with large pore size distribution, obtained by sol-gel technology, we show that in the domain of ice melting, the heat flow J_q is related to the melting temperature depression of the solvent, ΔT _m , by the scaling law: J _q ⁰∼ΔT _m ^{- (1 + D)}. We suggest that the exponent D is of the order of the fractal dimension of the backbone of the pore network and we discuss the influence of the variation of the melting enthalpy with the temperature on the value of this exponent. Similar D values were obtained from small angle neutron scattering and electronic energy transfer measurements on similar porous glass. The proposed scaling law is explained if one assumes that the pore size distribution is self similar. In porous glass obtained from mesomorphic copolymers, the pore size distribution is very sharp and therefore this law is not observed. One concludes that DSC, at low heating rate ( q? 2^°C/min) is the most rapid and less expensive method for determining the pore distribution and the fractal exponent of a porous material. Received 23 July 1999 and Received in final form 16 February 2001     

Multiple order parameter theory of surface melting: A van der Waals approach

We describe a van der Waals approach with multiple order parameter for surface melting near the triple pointT _T which is based on density functional theory for bulk freezing. The occurrence of surface-induced melting, non-melting or blocked (incomplete) melting is governed by the specific form of the long-ranged tail in the interparticle potential. In the case of melting, the residual crystallinity at the vapor side of the quasi-liquid layer is shown to decay with a stretched exponential (power) law inT _T -T for long-(short-) ranged interparticle forces