Estimation of activation parameters for diffusion-controlled crystallization of barium tungstate from sodium tungstate melts by differential thermal analysis

The proximity (d₁₂) between a diffusing species and its host crystal necessary for a successful diffusion for diffusion-controlled crystallization of barium tungstate from sodium tungstate melts in platinum crucibles was estimated. These distances increased with increased cooling rates (R_T) and crystallization temperatures (T₀). Energy (E), enthalpy (ΔH_a), entropy (ΔS_a) and free-energy (ΔG_a) of activation and the pre-exponential factor (k₀) were evaluated using an ordinary Arrhenius equation k_D1 = k₀e^−E/RT, where k_D1 was the diffusion rate-constant. These parameters were virtually unaffected by the changes in T₀ and R_T.     

Proximity between reacting partners for diffusion-controlled growth of barium tungstate crystals from sodium tungstate melts

The separation distance (d₁₂) between a diffusing particle and its host necessary for a successful diffusion was estimated for diffusion-controlled crystal growth of BaWO₄ from Na₂WO₄ melts. Such distances slightly increased with increased cooling rates (R_T) and crystallization temperatures (T₀). The energy (E), enthalpy (ΔH_a), entropy (ΔS_a) and free-energy (ΔG_a) of activation, and the probability factor (P) were also estimated. These parameters did not change with the changes in R_T and T₀.     

Differential Thermal Analysis Studies on the Crystallization of Strontium Tungstate from Sodium Tungstate Melts Thermodynamic and Kinetic Parameters

From the estimated diffusion rate-constants (k_D1) of strontium tungstate crystal growth from sodium tungstate melts in platinum crucibles, energy (E), enthalpy (ΔH_a), entropy (ΔS_a) and free-energy (ΔG_a) of activation and the pre-exponential factor (k₀) for the process were estimated using an ordinary Arrhenius equation k_Dl = k₀e^−E/RT. These thermodynamic parameters were virtually unaffected by the changes in crystallization temperatures (T₀) and cooling rates (R)_T. The distance (r₁₂), between a diffusing species and its host necesary for a successful diffusion, increased with T₀ and T_T but there was no direct correlation.     

Differential thermal analysis studies on the crystallization of strontium tungstate melts. Variation of rate constants with crystallization temperatures and cooling rates

Kinetics of strontium tungstate crystallization from sodium tungstate melts were studied in platinum crucibles (by DTA) by continuous cooling from initial crystallization temperatures T₀ = 800° to 1000° to below the eutectic temperature at cooling rates R_T = 0.67° to 3.3° min⁻¹. Heterogeneous nuclei first formed slowly onto metal platinate particles within the solution during induction periods (t ); the main crystal growth then started after the development of some exces solute concentration (ΔC ) at the induction temperature (T ). The actual growth after t was diffusion rate-controlled. The diffusion rate-constants (k_Dt) for growth after the induction periods along the major axis were estimated; the increased with T₀ and R_T. These values were higher than those for diffusion-controlled crystal growth of strontium tungstate from sodium tungstate melts in alumina crucibles but much smaller than the real diffusion rate-constants (k_Dl)_real.     

Induction periods and mechanism and kinetics of nucleation of barium tungstate crystal growth from sodium tungstate melts in platinum crucibles

Induction periods (t) and mechanism and kinetics of nucleation in barium tungstate crystallization from sodium tungstate melts in platinum crucibles were studied. A theoretical relation has been developed to express the dependence of t on the cooling rates (R_T) and the rate (R_c) of development of excess solute concentration. At any crystallization temperature the average rate-constant (k_n) for heterogeneous nucleation was related to R_c by (k_n/p)^1/(p+1) = 1/(tR_c^γ), where γ is a constant and p is the average number of particles in the critical nuclei. The critical temperature (T), critical supersaturation (S) and γ values were estimated.     

A novel self‐consistent Nývlt‐like equation for metastable zone width determined by the polythermal method

Using a power‐law relation between three‐dimensional nucleation rate J and dimensionless supersaturation ratio S, and the theory of regular solutions to describe the temperature dependence of solubility, a novel Nývlt‐like equation of metastable zone width of solution relating maximum supercooling ΔT_max with cooling rate R is proposed in the form: ln(ΔT_max/T₀) = Φ + β lnR, with intercept Φ = {(1–m)/m }ln(ΔH_s/R_GT_lim) + (1/m)ln(f/KT₀) and slope β = 1/m. Here T₀ is the initial saturation temperature of solution in a cooling experiment, ΔH_s is the heat of dissolution, R_G is the gas constant, T_lim is the temperature of appearance of first nuclei, m is the nucleation order, and K is a new nucleation constant connected with the factor f defined as the number of particles per unit volume. It was found that the value of the term Φ for a system at saturation temperature T₀ is essentially determined by the constant m and the factor f. The value of the factor f for a solute–solvent system at initial saturation temperature T₀ is determined by solute concentration c₀. Analysis of the experiment data for four different solute‐water systems according to the above equation revealed that: (1) the values of Φ and m for a system at a given temperature depend on the method of detection of metstable zone width, and (2) the value of slope β = 1/m for a system is practically a temperature‐independent constant characteristic of the system, but the value of Φ increases with an increase in saturation temperature T₀, following an Arrhenius‐type equation with an activation energy E_sat. The results showed, among others, that solubility of a solute is an important factor that determines the value of the nucleation order m and the activation energy E_sat for diffusion. In general, the lower the solubility of a solute in a given solvent, the higher is the value of m and lower is the value of E_sat. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of metastable zone width and induction time for a seeded aqueous solution of potassium sulfate

The metastable zone width (MSZW, ΔT_m) and induction time (t_ind) were determined with computer simulation for seeded batch crystallization of potassium sulfate from aqueous solution. The MSZW and induction time determined with simulation showed the same behavior as experimental values reported in the literature; log (ΔT_m) increased linearly with an increase in log R (R: cooling rate) and t_ind decreases in proportion to (ΔT)⁻ⁿ (ΔT: supercooling, n: nucleation order in the secondary rate expression of B=k_n(ΔT)ⁿ). The secondary nucleation parameters (k_n and n) were deduced both from the simulated MSZW and induction times by using the previously proposed model [J. Cryst. Growth, 2010, 312, 548–554]. The secondary nucleation rate calculated with the deduced parameters was in agreement with that calculated with the parameters input for simulation.     

Elasticity and Orientational Order in Some trans-p-n-Alkoxy-α-methyl Cyanophenyl Cinnamates

The splay (k ₁₁), twist (k ₂₂) and bend (k ₃₃) elastic constants determined by the Freedericksz method and the orientational order parameters (s) derived from optical measurements in the nematic phase of six homologues of trans-p-n-alkoxy-α-methyl cyanophenyl cinnamates (n OMCPC) are reported. The data close to the nematic-isotropic transition point (T _NI) are compared with T _NI and the heats of transition (ΔH). The temperature-variation of elastic constants is discussed in terms of existing theories. The pretransitional increase in the twist and bend constants near the nematic-smectic A transition point (T _NA ) of 10 OMCPC has also been analysed.     

Thermodynamic characteristics of Ti-based glass-forming alloys

Based on thermodynamic characteristics of the stable metallic liquid at melting temperature and the supercooled liquid, the present work calculated the mixing enthalpy ΔH^mix, the mixing entropy ΔS^mix and the Gibbs free energy difference between the supercooled liquid and the resulting crystalline phases ΔG of typical Ti-based amorphous alloys. The results show that for the case of larger ΔS^mix, moderate ΔH^mix for the stable liquid and smaller ΔG for the supercooled liquid, Ti-based alloys tend to achieve high glass-forming ability (GFA). A new parameter, β, defined as (T_g ? T_k)/(T_l ? T_g), has been introduced to evaluate the GFA of Ti-based bulk amorphous alloys (wherein T_g, T_l, and T_k represent the glass transition temperature, the liquidus temperature, and the Kauzmann temperature, respectively). Experimental data imply that the larger the β, the better the GFA for Ti-based amorphous alloys.     

Kinetics of crystal growth of strontium tungstate from solutions in sodium tungstate melts by continuous cooling

The crystallisation kinetics of strontium tungstate from unstirred saturated solutions in sodium tungstate melts was studied by continuous cooling from initial crystallisation temperatures T₀ = 1000° to 800°C to room temperature at cooling rates R_T = 0.67° to 3.3°C min⁻¹. The main crystal growth was diffusion rate-controlled; the final crystal growth was rate-controlled by the development rate of excess solute concentration. The estimated diffusion rate constant (k_D) values increased with cooling rates and initial crystallisation temperatures. They are higher than the rate constants for diffusion-controlled growth of calcium tungstate from sodium tungstate melts, but very much smaller than those for strontium tungstate from lithium chloride melts.     

Investigations on the growth kinetics of GP zones and a′R-precipitates in Al-Zn alloys

X-ray small-angle scattering (XSAS) and resistivity (R) measurements were particularly done with an Al-Zn (15 at·,%) alloy in rather wide ranges of both the ageing time t_a and ageing temperature T_a, in order to obtain information on the dependence of the growth exponent m of the l = β₀t^m growth law and the activation energy E_act on t_a and T_a. The XSAS-measurements yielded that within the range of the GUINIER radius r_G between 1 nm and 2 nm the growth is essentially retarded (m < 0.1) and for r_G > 2 nm m depends on T_a ranging from 0.15 to 0.23 with a maximum at 175°C. Reasons for these effects are discussed. The differences between the m-values obtained by means of XSAS-and TEM-measurements are explained by the distinctions of the two methods applied. The E_act taken from XSAS- and R-measurements show a remarkable increase with t_a. At the beginning of the decomposition E_act = (0.49 ± 0.05) eV holds well explainable by the migration of quenched-in VZn pairs, but at the end E_act = (1.05 ± 0.07) eV was found. This value was also obtained from TEM-investigations (growth of the length). It fits well the E_act of ZnV pairs in thermal equilibrium at T_a.     

A new criterion for the glass-forming ability of liquids

Based on theoretical calculations using the fragility concept and the nucleation theory for a model glass-forming system, we propose a dimensionless criterion, ?, expressed by T_rg(ΔT_x/T_g)^a, with T_rg, the reduced glass-transition temperature, ΔT_x, the width of the supercooled liquid region when heating a glass, T_g, the glass transition temperature, and a, the exponent. The application of this simple criterion to various glasses, including network, metallic, and molecular glasses (except pure water), indicates an excellent correlation between the critical cooling rate R_c and ? in a Log R_c-? single master plot with a = 0.143.     

On the effect of impurities on the metastable zone width of phosphoric acid

The experimental data published in the literature on the metastable zone width, as determined by the maximum supercooling ΔT_max using the conventional polythermal method, of phosphoric acid aqueous solutions containing impurities were analyzed to understand an increase in ΔT_max/T₀ with an increase in saturation temperature T₀ of solute–solvent system and the effect of impurities on the metastable zone width. For the analysis the following relations were used: ln(ΔT_max/T₀)=Φ+βln R (K. Sangwal, Cryst. Res. Technol. 44, 2009, 231−247) and (T₀/ΔT_max)²=F(1−Zln R) (K. Sangwal, Cryst. Growth Des. 9, 2009, 942−950; J. Cryst. Growth 311, 2009, 4050−4061), where Φ, β, F and Z are constants. Analysis of the experimental data revealed that: (1) the parameters Φ and F strongly depend on saturation temperature T₀ and concentration c_i of impurities, but the constants β and Z are independent of T₀ and depend on c_i, (2) the dependence of the parameters Φ and F on T₀ follows an Arrhenius-type equation with activation energy E_sat, (3) the activation energy E_sat for diffusion of ions/molecules of phosphoric acid containing impurity ions is equal to the differential heat of adsorption Q_diff for these impurities, (4) the effectiveness of an impurity is directly connected with the values of their differential heat of adsorption Q_diff; the lower the values of Q_diff for an impurity, the lower is its effectiveness in promoting nucleation, (5) the activation energy E_sat is not related with its heat of dissolution ΔH_s and (6) the increase in ΔT_max/T₀ with an increase in T₀ for phosphoric acid is associated with the activation energy E_sat for diffusion of solute molecules in the solution such that E_sat<0.     

Relaxation behavior of supra-molecular hydrogen-bonded liquid crystal phase structures: SA:11OBA

Low-frequency (20 Hz–10 MHz) dielectric response in liquid crystalline (LC) phases of hydrogen-bonded (HB) complex, SA:11OBA, is studied. Synthesis of SA:11OBA with non-mesogenic succinic acid (SA) and mesogenic p-n-undecyloxy benzoic acid (11OBA) and its spectroscopic confirmation are detailed. Phase transition temperatures (T_C) involving nematic, smectic-C (SmC), and smectic-G (SmG) phases by capacitance C(T) and loss tanΔ(T) anomaly agree with the microscopy (polarizing optical microscope) and calorimetry (differential scanning calorimetry) results. Low-frequency dispersion infers two types of reorientation processes, viz. higher frequency (～MHz) and lower frequency (kHz) processes. Distinct time scale mechanism are presented. Arrhenius behavior infers influence of HB on activation energy (E_a). Off-centered dispersion, viz. ?′(ω) with ?″(ω), analyzed through the Cole–Cole plots in N, SmC, and SmG phases infers a strong temperature trend for dielectric strength (Δ?) and distribution (α) parameters. Temperature dependence of α-parameter reveals on LC phases increasing fixture of molecular dipole in LC phase structure. Results are discussed in the wake of the body of data reported in LC phases exhibited by other LC compounds.     

Electrical properties of TiO2 thin films

The electrical properties of n-type titanium dioxide thin films deposited by magnetron-sputtering method have been investigated by temperature-dependent conductivity. We observed that the temperature dependence of the electrical conductivity of titanium dioxide films exhibits a crossover from T^?1/4 to T^?1/2 dependence in the temperature range between 80 and 110 K. Characteristic parameters describing conductivity, such as the characteristic temperature (T₀), hopping distance (R_hop), average hopping energy (Δ_hop), Coulomb gap (Δ_C), localization length (ξ) and density of states (N(E_F)), were determined, and their values were discussed within the models describing conductivity in TiO₂ thin films.     

Formation Volume of Vacancies in Elements and the Defect Formation Mechanism of Melting

The formation volume V_v of vacancies is given by V_v = (h_v/L) ΔV_f with h_v = 8L (formation enthalpy h_v of vacancies and heat L of fusion given in same units; ΔV_f = change of volume due to melting). If there are phase transitions within the solid, L and ΔV_f must be replaced by (L + Δ H_t) and by (ΔV_f + ΔV_t), respectively (Δ H_t and Δ V_t refer to the heat (s) of transition (s) and to the volume change(s) due to transition(s), resp.). The pressure dependence of the melting point is dT_m/dp = (T_mV_v)/h_v. Independent of the sign of V_v any increase of the vacancy concentration above the maximum concentration possible within the solid decreases the melting point thus resulting in the observed surface melting. The melting point is fixed by the characteristics of vacancy formation (h_v, S_v, V_v) and by the bulk modulus of the solid (S_v = formation entropy of vacancies).     

Nonisothermal crystallisation kinetics of amorphous selenium prepared by high-energy ball milling: A comparison with the melt-quenching and thin-film techniques

Differential scanning calorimetry (DSC) studies were performed under nonisothermal conditions at various heating rates for glassy Se made by high-energy ball milling. Comparisons were made between the ball-milling technique and the melt-quenching and thin-film techniques. Well-defined endothermic and exothermic peaks were observed at the glass-transition temperature, T_g, and the onset temperature of crystallisation, T_c. The isoconversional method of Vyazovkin was used to determine the variation in the activation energy for crystallisation with temperature, E_α(T). The value of E_α(T) was dependent on the sample preparation method. The thermal stability of the Se glasses was evaluated by calculation of the temperature difference (T_c ? T_g) and the S-parameter. In addition, the glass-forming ability was estimated by the criteria of reduced glass-transition temperature, T_rg, and the Hruby number, H_R. The structures of the Se samples that resulted from the DSC analysis were identified using an X-ray diffractometer. The glasses formed using the thin film technique were the most stable.     

Magnetic and Electric Birefringence in the Isotropic Phase of a Nematic of Large Positive Dielectric Anisotropy

Abstract

Magnetic (Δn_H ) and electric birefringence (Δn_E ) in the isotropic phase of strongly positive (Δ 8)trans-p-n-octyloxy α-methyl-p'-cyanophenyl cinnamate (8 OMCPC) have been measured. It is established that they both exhibit a (T - T*)^?1 dependence, T _NI - T* being 1.4 K. Also, the induced birefringence is found to be proportional to the square of the applied field, magnetic or electric.     

Unusual Glassy Smectic-G Liquid Crystal: Heat Capacity of N-p-n-Pentyloxybenzylidene-p'-n-butylaniline between 11 and 393 K

Abstract

The heat capacities of the title compound (C₃H₁₁,O—C₆H₄,- CH=N—C₆H₄,—C₄H₉, abbreviation 5O ? 4) with a purity of 99.92 mole percent have been measured with an adiabatic-type calorimeter between 11 and 393 K. The transition temperature and the enthalpy and entropy of phase transition for stable crystal → S_G, S_G → N and N → isotropic liquid were T _c = 299.69 K/ΔH = 22.68 kJ mol^?1/ΔS = 75.70 JK^?1 mol^?1, 325.72/7.11/21.79 and 342.48/1.78/5.22, respectively. The crystal which melts at 285.5 K is a metastable modification. The S_A phase hitherto reported in between S_G and N does not exist. The glassy So state was realized by rapid cooling of the specimen from the So phase. The molar enthalpy of the glassy S_G state at 0 K was by (10.1±0.1) kJ mol^?1 higher than that of the stable crystalline state and the residual entropy of the glassy state was (9.40±0.83) JK^?1 mol^?1. The relaxational heat-capacity anomaly was observed from as low as 100 K and double glass transition phenomenon occurred around 200 K; a quite unusual phenomenon which has never been observed for the glassy states of nematic and cholesteric liquid crystals. The present results give a fair evidence that the unusual glass transition phenomenon previously found for the S_G state of 6O?4 (a homologous compound) is not exceptional at all but common to the smectic glasses; at least common to the glassy S_G states. Two possible origins responsible for the double glass transitions have been discussed.