Volume-dependence of the melting temperature with Debye's model for Si and Ge

Lindeman's criterion for melting of covalent crystals is formulated using Debye's model. The contribution of the acoustical, especially transverse-like acoustical phonon modes to the total mean-square displacement is predominant at higher temperatures and essential to the melting scheme. Using the volume-dependence of the transverse-like Grüneisen constant at higher temperatures, the volume effect on the melting temperature of Si and Ge is studied by Lindeman's melting law. The obtained melting curve decreases as function of the compressed volume, and is qualitatively in agreement with the observed tendency for Si and Ge.     

Liquid Madelung energy and Schottky defect energy related to liquid structure and melting temperature for alkali halides

Motivated by the work of Reiss et al in which the melting temperature T_m of alkali halides is correlated with Coulomb energy, we consider the cohesive energy W of ionic melts and Schottky defect energy E_s in the hot crystal, relative to the thermal energy k_BT_m It is shown here that W is accurately approximated by the liquid Madelung energy and hence that Wk_BT_m relates to the charge-charge direct correlation function c_QQ(r) at r = 0 The existence of a “Madelung constant” for the liquid at T_m is thereby demonstrated through the alkali halide series An estimate of the ratio E_s/k_BT_m then considered, the basic additional ingredient being argued to be the static dielectric constant of the solid The BarrDawson-Lidiard empirical correlation between E_s, and k_BT_m can be understood in this way.     

On the mechanical stability of bcc transition elements and alloys

A volume independent and a volume dependent lattice energy function involving short-range interatomic potentials were able to be fitted to the elastic constants, cohesive energy, lattice parameter and for the latter function to the vacancy formation energy and bcc-fcc lattice stability energy, as well, for fcc metals and bcc alkali metals, but not to the cohesive energy and C' elastic constant of bcc transition metals. The assumption that directional, but partial, covalent bonds exist between nearest-neighbors in the bcc transition elements provides an explanation for the latter results and in addition explains the identical dependence of C' and the bcc-fcc lattice stability upon N_d, where N_d is the average number of d electrons, for the bcc transition metals and alloys. Both the mechanical and thermodynamic stability of the bcc structure for transition metals and all transition metal alloys disappears for 5 ? N_d > 2 and <?1.     

Melting of lead and zinc to 60 kbar

The melting curves for lead and zinc were determined to 60 kbar. Our melting data for lead is in good agreement with that of Millet up to 22 kbar, beyond which Millet's values are significantly higher than ours. The melting curve for zinc is almost linear to 60 kbar and our values are lower than the values reported by other workers. The melting relationship proposed by Kennedy as well as the Lindemann law have been examined in the light of the new melting data for these two metals. A straight line can be fitted through the T_m vs ΔV/V₀ plots for zinc within the limits of experimental precision, but the data for lead shows a departure from the straight line fit. The lead melting curve is concave toward the T_m axis, as predicted by the Lindermann law and, in this respect, resembles previously studied Van der Waals solids.     

Ionic conduction in KBr-KI mixed crystals

Ionic conductivity of KBr_1?xI_x (0 ? x ? 0.5) mixed crystals has been studied as a function of temperature in the range of 2 ionic conductivity and lowers the activation energy appreciably which is consistent with our earlier results on AgBr-AgI mixed crystals, and proposal that the purely elastic displacements (lattice strain) caused by the very “wrong size” of the substituent ions is primarily responsible for the behavior. The strain thus produced is expected to cause “lattice loosening” and hence lowering of the melting points (T_m) or the enthalpy of formation of the Schottky defects (H_s). A semiquantitative calculation shows this to be the case.     

Defect characterization in CeO2−x at elevated temperatures—I: X-Ray diffraction

The atomic defect structure of nonstoichiometric ceria was studied by means of X-ray diffraction. Polycrystalline samples of CeO_2?x (0?x?0.21) have been examined at 900 and 1000°C, with the stoichiometry controlled by adjusting the oxygen partial pressure between 1 and 10^?21 atm. It was observed that the lattice expands as a function of increasing defect concentration and exhibits only fluorite-like diffraction peaks. The integrated intensities of the Bragg reflections were analyzed for CeO₂ and CeO_1.91, at 900°C by difference electron-density techniques. It was concluded that the cation sublattice is essentially intact, and that the oxygen sublattice must be defective in nonstoichiometric ceria. Least-squares analyses on CeO_2?x (0?x? 0.21) at 900 and 1000°C supported the electron-density results and also showed that the temperature factors of both cations and anions increase with an increase in defect concentration, implying greater mean-square displacement of the atoms from their equilibrium positions.     

Theoretical study of thermal properties for SiGe system

Using our presented treatment with the volume effect on the force constants of the pure constituent, we study the thermal properties of Si-Ge solid solution from first principle in the electronic theory of solids. The specific heat at constant volume of Si_1−xGe_x solid solution is monotonous function of the concentration x and is approximately given by the linear interpolation of atomic fraction. The Grüneisen constant and the thermal expansion coefficient of Si_1−xGe_x system have the characteristic concentration dependence. The almost constant value at high temperatures and the negative minimum at low temperature of the Grüneisen constant are not monotonous as function of x, and show a maximum near x = 0.7 and a minimum near x = 0.2, respectively. Then, the linear thermal expansion coefficient at low and high temperatures deviate largely from the linear interpolation of the atomic fraction.     

Development of nanostructured magnetic materials based on high-purity rare-earth metals and study of their fundamental characteristics

The effect of the structural state on magnetic and hysteretic properties of compounds with high contents of a 3d transition metal, i.e., R ₂Fe_{14 ? x} Co _x B and RFe_{11 ? x} Co _x Ti (where R = Y, Sm; 0 ≤ x ≤ 8), was studied. Alloys were prepared using high-purity rare-earth metals by two different methods: induction melting and argon-arc melting. Severe plastic deformation and rapid melt-quenching allowed preparation of nanostructured samples. Structural studies of the samples were performed by X-ray powder diffraction and atomic-force microscopy methods. Magnetic hysteretic properties were studied using a PPMS magnetometer in the temperature range of 4.2–300 K in fields to 20 kOe. It was shown that the dependences of fundamental magnetic parameters (Curie temperature, saturation magnetization, and magnetocrystalline anisotropy constant) on the cobalt content exhibit a similarity for both systems. It was found that, depending on sample treatment, the grain size varies from 30 to 70 nm after severe plastic deformation and in wider ranges (from 10 to 100 nm) after rapid quenching, not exceeding the single-domain size. The interrelation between the microstructure and magnetic characteristics was investigated. It was revealed that the concentration dependence of the coercivity for both systems has a maximum at the same cobalt content, i.e., x = 2.     

Theory of melting,vacancy model

A theory of melting based on vacancy model is formulated. The polymer solution theory is used for derivation of the melting equation for a two-species model of melting solid. Under simplifying assumptions the analysis leads to a simple correlation betweenT _m and 〈v〉, the average energy of interaction between the vibrating atoms. Pseudopotential method is used for calculating 〈v〉 for the alkali metals lithium, sodium, potassium and rubidium at temperatureT _m. The calculated values ofT _m〈v〉 are in accord with those expected from our model. Application to the high pressure melting curves of solids is also discussed.     

Structural and Mössbauer spectroscopic studies of Fe0.7−xCrxAl0.3 alloys

Fe_0.7−xCr_xAl_0.3 alloys with x=0, 0.1, 0.2, 0.3 and 0.35 have been synthesized by arc melting and studied by X-ray diffraction and Mössbauer spectroscopy. All the samples studied were found to have single phase with body center cubic structure. The lattice parameter a, and hence the volume, were obtained from the X-ray diffraction patern and found to increase with increasing the chromium concentration. At room temperature Mössbauer studies show magnetic ordering for small values of x and paramagnetic behavior for large values of x under investigation. The Mössbauer spectra were analyzed considering a distribution of magnetic hyperfine fields for small values of x and two singlets were added for large values of x. During the fitting procedure, the relation between the hyperfine field and the isomer shift in the hyperfine field distribution was linear relation. The average hyperfine field and isomer shift as a function of chromium content x were found to decrease with increasing x. The results are explained in terms of local environmental effects on the hyperfine interactions.     

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.     

Lattice dynamics and debye temperature of AlCu,AlSi and AlGe alloy systems

The lattice dynamics and specific heat at constant volume for AlCu alloy system is studied using our previous treatment based on the microscopic electronic theory. Considering the volume and electron density effect on the dynamical matrix of the pure constituent, we obtain the band and local mode frequencies at the temperature-dependent specific heat in the Al_1−x Cu_x solid solution. Then, using the data about the mean elastic wave and the specific heat extrapolated to the absolute zero temperature, the Debye temperature is presented for the Al_1−xCu_x, Al_1−xSi_x and Al_1−xGe_x alloy systems. The Debye temperature decreases as a function of the Cu atomic fraction x for Al_1−xCu_x alloy, and remarkably for Al_1−xSi_x and Al_1−xGe_x solid solutions.     

Investigation on bulk Nd–Fe–Al amorphous/nano-crystalline alloy

Cylindrical ingots of bulk amorphous Nd₇₀Fe₂₀Al₁₀ with a diameter of 8 mm were prepared by a copper mold casting method. It was proved experimentally with X-ray diffraction, scanning electron microscopy and differential scanning calorimetry that the as-prepared alloy samples consisted mainly of the amorphous phase with a minute amount of nano-crystalline phase. The onset crystallization temperature (T_x) and the melting temperature (T_m) of the samples were 743 and 823 K, respectively, from DSC results. The temperature interval between T_x and T_m, ΔT=T_m−T_x, is 80 K and the resulting ratio of T_x/T_m is 0.90. Both a high T_x/T_m ratio and a small ΔT are considered the reasons for the good glass-forming ability. The Curie temperature (T_c) of these samples was 525 K from magneto-thermal gravimetric analysis. This measured value is higher than the highest T_c among binary Nd–Fe amorphous alloys. Annealing treatments were carried out for the as-cast samples to obtain dual-phase samples with different volume fractions of nano-crystalline phase. Magnetic measurement results indicated that the hard magnetic behavior is weakest for samples with 40% of nano-crystalline phase. The curve of the measured hysteresis loop area versus the volume fraction of nano-crystalline phase concaves upward, which agrees with what we predicated in our previous simulation results.     

Theoretical and experimental IR spectra of binary rare earth tellurite glasses—1

The binary rare earth tellurite glasses (A_nO_m)_x-(TeO₂)_1−x, where x = 0.1 and A = Sm, Ce, La, were prepared by melting the oxides at 800°C for 1 h and quenched rapidly. The IR spectra has been measured in the frequency region 4000-200 cm⁻¹. The main absorption bands in these glasses related to the characteristics of TeO₂. The detected shift in these bands are found to be sensitive to the glass structure. The A-O bond vibration in the glasses has been calculated. The results were interpreted on the basis of stretching force constant of each bond.     

Effect of Li2O content on physical and structural properties of vanadyl doped alkali zinc borate glasses

The effect of Li₂O content in vanadyl doped 20ZnO+xLi₂O+(30−x)Na₂O+50B₂O₃ (5≤x≥25) glasses has been studied with respect to their physical and structural properties. The absence of sharp peaks in XRD spectra of these glass samples confirms the amorphous nature. The physical parameters like density, refractive index, ionic concentration and electronic polarizability vary non-linearly with x mol% depending on the diffusivities of alkali ions. EPR and optical absorption spectra reveal that the resonance signals are characteristics of VO²⁺ ions in tetragonally compressed octahedral site. Spin-Hamiltonian, crystal field, tetragonal field and bonding parameters are found to be in good agreement with the other reported glass systems. The tetragonal distortion (g_⊥-g_∥) and Dt reveals that their values vary non-linearly with Li₂O content and reaches a minimum at x=10 mol%. An anomaly of character has been observed in all the properties of vanadyl doped glass systems, which gives a clear indication of mixed alkali effect.     

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.     

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.     

Relaxation round vacancies in the alkali metals

The long-range ionic displacements round a vacancy are shown to come from both the elastic, long-wavelength, limit and from the Kohn anomaly. The effect of the topology of the Fermi surface is stressed.Attention is then focussed on the alkali metals with almost spherical Fermi surfaces, where it can reasonably be assumed that the elastic displacements dominate. Complete relaxation around a vacancy relates formation energy E_v, bulk modulus B and atomic volume Ω through E_v = αBΩ where α is a constant. The formation volume follows as a balance between a negative harmonic contribution and a positive and larger anharmonic term.     

Effects of the temperature and the pressure on the intermediate valence of Ce(In1−xSnx)3

The curve of the lattice constant of samples Ce(In_1-xSn_x)₃ plotted as a function of the composition x deviates from the linear Vegard's law; the deviation is found to be much more eminent at liquid N₂ temperature than at room temperature. Effects of the pressure on the electrical resistivity was found to be very large for a sample with a composition x = 0.5 which is near to the critical value of the occurence of the intermediate valence state of Ce atoms. The atomic volume of Ce atoms is seen to play an important role for the occurence of the intermediate valence state.