On the size dependence of melting parameters for silicon

Using the dependences of melting point T_m and crystallization point T_c on the number of atoms (N) in a spherical silicon crystal that were calculated elsewhere [6] by the method of molecular dynamics, (i) the number of atoms at which the latent heat of the solid–liquid phase transition disappears and (ii) temperature T₀ = T_m(N₀) = _Tc(N₀) below which solidifying nanoclusters remain noncrystalline are estimated. These values are found to be N₀ = 22.8156 and T₀ = 400.851 K. The N dependences for silicon melting parameters, namely, a jump of entropy of melting, latent melting heat, slope of the melting line, and jumps in the surface energy and volume, are derived.     

Thermodynamical properties of Zr-based bulk metallic glasses

The temperature dependence of Gibb's free energy difference (ΔG), entropy difference (ΔS) and enthalpy difference (ΔH) between the undercooled melt and the corresponding equilibrium solid phases of bulk metallic glass (BMG) forming melts has been proved to be very useful in the study of their thermodynamical behavior. The present study is made by calculating ΔG, ΔS and ΔH in the entire temperature range T_m (melting temperature) to T_g (glass transition temperature) for three Zr-based samples of BMGs: Zr₅₇Cu_15.4Ni_12.6Al₁₀Nb₅, Zr_41.2Ti_13.8Ni₁₀Cu_12.5Be_22.5 and Zr_58.5Cu_15.6Ni_12.8Al_10.3Nb_2.8. The study is made on the basis of Taylor's series expansion and a comparative study is also performed between the present result and the result obtained in the framework of expansions proposed by earlier workers, and also with the experimental results. An attempt has also been made to study the glass forming ability for BMGs.     

Field dependent susceptibility of the 2D ferromagnet (CH3NH3)2CuCl4 in the paramagnetic phase

The temperature dependence of the ac susceptibility (χ) at constant applied magnetic field was investigated in the paramagnetic region of the quasi-2D ferromagnet (CH₃NH₃)₂CuCl₄. Above the Curie temperature (T_C=8.85 K) a maximum in the χ(T,H) curves was observed at T_m(H). The temperature at the maximum increases with increasing applied field. This anomaly is related to short range fluctuations close the order transition. The behavior of T_m(H) is governed by the gap exponent of the scaling function (Δ=γ+β). We found Δ=2.2±0.1 in very good agreement with the previously known values of γ and β.     

An equation of state for alkali metals

Semi-empirical equations of state based on Lindemann's law have been developed to determine the pressure (P) dependence of the melting temperature (T_m) of Li, K, Rb and Cs. The basic inputs are Grüneisen parameter and the bulk modulus. T_m–P variations exhibit maximum melting temperature with concave downwards. The maximum in T_m for Cs is found to occur at pressure of 2.2 GPa whereas for Li, K and Rb it falls in the range of 7–9.5 GPa. The predicted values of T_m as a function of pressure, based on the present empirical relation, fit quite well with the available experimental data. The empirical relation can also be used to extrapolate T_m at higher pressure from the values available at lower pressures.     

Melting and elastic shear instability of alkali halides

Ultrasonic data for the elastic moduli c_ij as functions of pressure and temperature are used to calculate critical temperatures T_cr(P = 0) and their initial pressure derivatives (?T_cr/?P)_P=0 for the elastic stability of the alkali halides with the rocksalt and CsCl structures. The stability criteria used for the two structures are c′ = ½(c₁₁ ? c₁₂) = 0 and c₄₄ = 0, respectively. The critical parameters T_cr(P = 0) and (?T_cr/?P)_P=0 exhibit remarkable correlations with the melting temperatures T_m(P = 0) and their initial pressure derivatives (?T_m/?P)_P=0, offering strong support to the existence of a connexion between shear instability and melting, as postulated by previous investigators. Critical parameters for the rocksalt oxides MgO, CaO, and SrO compare favourably with the critical and melting parameters for their fluoride analogues LiF, NaF and KF respectively.     

EFFICIENCY OF β-NUCLEATING AGENTS IN PROPYLENE/α-OLEFIN COPOLYMERS

Crystallization and melting behavior of β-nucleated propylene/1-pentene random copolymers were studied. Samples with different comonomer content were nucleated with the calcium salt of suberic acid. The WAXS, differential scanning calorimetry (DSC), and polarized light microscopy (PLM) measurements showed that morphological behavior of the β-nucleated copolymers is similar to that of the homopolymer, but the rate of crystallization and the characteristic temperatures decrease with increasing pentene content. Crystallization at low temperatures and lower chain regularity lead to the formation of imperfect crystal structures with high instability, which enables the study of structural perfection processes like ββ′- or βα-recrystallization during partial melting. The PLM studies proved that the critical crossover temperature T(βα) decreases with increasing pentene content. The effect of comonomer content on the critical recooling temperature ( T _R ^* ), as well as on the equilibrium melting point of the β-form ( T _m ⁰) was also investigated. However, in our case, the linear Hoffman–Weeks method proved to be unsuitable for the accurate determination of T _m ⁰.     

On the criterion of the crystal-liquid phase transition

A localization criterion is proposed for the crystal-liquid phase transition (PT). According to this criterion, the PT begins when the E _d/k _b T ratio reaches a boundary value E _d(s)/k _b T _m such that a solid phase is present above it and a liquid phase is present below it in a phase diagram. Here, E _d is the energy of atom delocalization, k _b is the Boltzmann constant, T is the temperature, and E _d(s) is the delocalization energy for a solid phase at melting point T _m. This criterion is shown to generalize the Lindemann criterion of melting to the case of crystallization and the Löven criterion of crystallization to the case of melting. This localization criterion is found to be applicable for both normally melting substances and substances that melt with a decrease in the specific volume upon the transition into a liquid phase. The relation of the localization criterion to the vacancy and diffusional criteria of the crystal-liquid PT has been studied. The inequality T _N < T _m, where T _N is the temperature of the onset of crystallization, is explained using the localization criterion. The calculated values of the T _N /T _m ratio coincide well with the experimental estimates. The maximum value of T _N /T _m is likely to be most probable in crystals with a bcc structure and a small value of the Grüneisen parameter. The T _N /T _m ratio is analyzed at the points in the PT where no change in the specific volume occurs and an entropy jump is nonzero.     

Surface energies of metals in both liquid and solid states

Although during the last years one has seen a number of systematic studies of the surface energies of metals, the aim and the scientific meaning of this research is to establish a simple and a straightforward theoretical model to calculate accurately the mechanical and the thermodynamic properties of metal surfaces due to their important application in materials processes and in the understanding of a wide range of surface phenomena. Through extensive theoretical calculations of the surface tension of most of the liquid metals, we found that the fraction of broken bonds in liquid metals (f) is constant which is equal to 0.287. Using our estimated f value, the surface tension (γ_m), surface energy (γ_SV), surface excess entropy (−dγ/dT), surface excess enthalpy (H_s), coefficient of thermal expansion (α_m and α_b), sound velocity (c_m) and its temperature coefficient (−dc/dT) have been calculated for more than sixty metals. The results of the calculated quantities agree well with available experimental data.     

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.     

Thermodynamic approach to the size dependence of the melting temperatures of films

The size dependence of melting temperature T _m of metallic films (tin and copper) on different substrates, including amorphous carbon and another refractory metal (i.e., the dependence of T _m on film thickness h) is investigated. It is found that the effect of the interfacial boundary can result in the growth of T _m for thin metallic films on carbon substrates with a reduction in film thickness h. For a system with a metallic film on a metallic substrate, the size dependence of T _m is less pronounced and T _m falls with a reduction in h.     

Properties of the superconducting state in molecular metallic hydrogen under pressure at 347 GPa

The thermodynamic properties of the superconducting state induced in metallic molecular hydrogen under the influence of pressure 347 GPa were determined. In particular, it has been shown that the critical temperature (T_C) changes in the range from 120 to 90 K for μ^?∈〈0.08,0.15〉, where μ^? is the value of the Coulomb pseudopotential. Next, the energy gap near the temperature of zero Kelvin (2Δ(0)) was calculated. It has been stated, that the dimensionless ratio 2Δ(0)/k_BT_C slightly decreases with the increase of μ^? from 3.98 to 3.84. In the last step, the ratio of effective electron mass (m^?_e) to the bare electron mass (m_e)) was determined. It has been proved that m^?_e/m_e takes its highest value equal to 1.96 for T=T_C.     

Manifestation of quantum statistics in vibrational dynamics of poly(ethylene) crystals

The temperature dependences of the transverse expansion ?_⊥(T) and the longitudinal contraction ?_‖(T) (with respect to the axes of chain molecules) in large-sized poly(ethylene) (PE) crystal grains (100×60×60 nm) are measured using x-ray diffraction in the temperature range 5–380 K. The temperature dependence of the elongation of the molecular skeleton ?_C(T) is obtained by Raman spectroscopy. It is found that the dependences ?_⊥(T), ?_‖(T), and ?_C(T) exhibit a similar specific nonlinear behavior. Analysis of these dependences indicates that the nonlinearity is associated with the quantum statistics of transverse vibrations. The energies and amplitudes of zero-point (at T=0) transverse (torsional and bending) vibrations and the relevant zero-point components ?_‖(0) and ?_C(0) are estimated. It is revealed that the zero-point components make a considerable contribution to the dynamics of the PE crystal up to the melting temperature (～400 K).     

Surface self-diffusion studied by microscopic measurements of crystallite profile evolutions

Dendritic gold crystallites on graphite are heated in ultra high vacuum up to less than 0.5 of the melting point (T_m). Electron microscopy shows that the gold crystallites change their shapes by surface self-diffusion. The dendritic contours round off while the crystallite remains very flat (20 to 40 Å). The increase with time of the radii of dendrite tips is measured statistically. Such an evolution can be described by analogy to the blunting of either metal tips (Nichols and Mullins) or monoatomic cleavage tips (Höche and Bethge). Using this result, a new technique to measure surface self-diffusion coefficients (D) is proposed. Test measurements have shown that this is an interesting, very sensitive method to measure D (down to 10^?13 cm^?2 s^?1) which enables measurements to be made in an unusual low temperature range (0.25 T_m < T < 0.5T_m). In special cases the dendrites are split by the surface self-diffusion which is qualitatively in agreement wih the theory.     

Magnetic properties and magnetocaloric effect of Sr-doped Pr0.7Ca0.3MnO3 compounds

In this work, we pointed out that Sr substitution for Ca leads to modify the magnetic and magnetocaloric properties of Pr_0.7Ca_0.3-xSr_xMnO₃ compounds. Analyzing temperature dependence of magnetization, M(T), proves that the Curie temperature (T_C) increased with increasing Sr content (x); T_C value is found to be 130–260 K for x = 0.0–0.3, respectively. Using the phenomenological model and M(T,H) data measured at several applied magnetic field, the magnetocaloric effect of Pr_0.7Ca_0.3-xSr_xMnO₃ compounds has been investigated through their temperature and magnetic field dependences of magnetic entropy change ΔS_m(T,H) and the change of the specific heat change ΔC_P(T,H). Under an applied magnetic field change of 10 kOe, the maximum value of -ΔS_m is found to be about 3 J/kg·K, and the maximum and minimum values of ΔC_P(T) calculated to be about ±60 J/kg·K for x = 0.3 sample. Additionally, the critical behaviors of Pr_0.7Ca_0.3-xSr_xMnO₃ compounds around their T_C have been also analyzed. Results suggested a coexistence of the ferromagnetic short- and long-range interactions in samples. Moreover, Sr-doping favors establishing the short-range interactions.     

Superconducting critical temperature, Tc, and phase equilibrium diagram of A3B β-W) type compounds

A correlation between the superconducting critical temperature, T_c, and solid solution range (SSR) appearing in the phase equilibrium diagram of A₃B (β-W) type compounds has been observed. Among the compounds of incongruent melting (peritectic or peritectoid) type, the T_c is directly proportional to the solid solution range. Further, in the low temperature range, the solid solution range invariably is found on the A element-rich side of the stoichiometric composition (75 at. % A: 25 at. % B), suggesting a fundamental importance in the “A-chain integrity,” viz., an A element can substitute for a B element which is not a part of the chain, but a B element cannot replace an A element which forms a part of the chain) which is believed to be a key to superconductivity.     

Thermal behavior of gamma-irradiated low-density polyethylene/paraffin wax blend

The thermal properties of low-density polyethylene (LDPE)/paraffin wax blends were studied using differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) and melt flow index (MFI). Blends of LDPE/wax in ratios of 100/0, 98/2, 96/4, 94/6, 92/8, 90/10 and 85/15 (w/w) were prepared by melt-mixing at the temperature of 150°C. It was found that increasing the wax content more than 15% leads to phase separation. DSC results showed that for all blends both the melting temperature (T_m) and the melting enthalpy (ΔH_m) decrease linearly with an increase in wax content. TGA analysis showed that the thermal stability of all blends decreases linearly with increasing wax content. No clear correlation was observed between the melting point and thermal stability. Horowitz and Metzger method was used to determine the thermal activation energy (E_a). MFI increased exponentially by increasing the wax content. The effect of gamma irradiation on the thermal behavior of the blends was also investigated at different gamma irradiation doses. Significant correlations were found between the thermal parameters (T_m, ΔH_m, T₅%, E_a and MFI) and the amount of wax content and gamma irradiation.     

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.     

Predominant factors affecting the dielectric and piezoelectric properties of bismuth-containing complex perovskite solid solution

To study the factors affecting the dielectric and piezoelectric properties of bismuth-containing complex perovskites, the solid solution (1−x)Pb(Mg_1/3Nb_2/3)O₃-xBi(Mg_2/3Nb_1/3)O₃ was prepared by the solid state reaction method and its dielectric and piezoelectric properties were investigated. It is found that (1) at room temperature, the nonlinearity of the DE-loop for Pb(Mg_1/3Nb_2/3)O₃ is completely suppressed at a rather low x (<5%); (2) dielectric constant versus temperature curves deviate from the Curie-Weiss law at a temperature T_d much higher than the dielectric constant peak temperature T_m and T_m−T_d decreases considerably with increasing x; and (3) frequency dispersion ΔT_m=T_m (1 MHz)−T_m (10 kHz) increases with increasing x. Possible factors responsible for the variation of the dielectric and piezoelectric properties with x are discussed.     

Development of nanocrystalline Mn-Zn ferrites for high frequency transformer applications

Microwave-Hydrothermal (M-H) method has been successfully used for the synthesis of nanocrystalline Mn-Zn ferrites which are used for high-frequency applications. As synthesized powders were characterized using X-ray diffraction (XRD) and transmission electron microscopy (TEM). The nanopowders were annealed at 600 °C/20 min using the microwave sintering method. The frequency dependence of dielectric constant (ε′) was measured in the range of 10 Hz-1.3 GHz and initial permeability (μ_i) was measured in the range of 10 Hz-1 MHz. The total power loss (P_t) was measured on the annealed samples at 100 kHz and 200 mT condition. Conductor-embedded-ferrite transformers were fabricated and output power (P_o), efficiency (η) and temperature rise (ΔT) were measured at sinusoidal voltage of 25 V at 1 MHz. The transformer efficiency (η) was found to be high and surface rise of temperature (ΔT) is very low.     

Surface free energies of solid metals: Estimation from liquid surface tension measurements

An equation is derived on semi-theoretical grounds which expresses the solid-vapour surface free energy as a function of the liquid surface tension and the solid-liquid interfacial free energy. A means of calculating reliable values for the solid-liquid energy is presented, which then allows an accurate estimate of solid surface energy at the melting temperature, T_m, to be made for the large number of elements for which dependable liquid surface tension data exist. A method of estimating surface entropy is presented, and has been used to calculate the energies typical of “average”, high-index surfaces at temperatures ranging from 0 K to T_m. It is felt that this paper describes the most accurate method presently available for the calculation of the surface energy of solids in the absence of direct experimental measurement.