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.     

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.     

Thermodynamic properties of strontium tungstate crystal growth from sodium tungstate melts

Energy (E), enthalpy (ΔH_a), entropy (ΔS_a) and free-energy (ΔG_a) of activation and the pre-exponential factor (k₀) of the ordinary Arrhenius equation k_Dl = k₀e–E/RT were estimated for diffusion-controlled crystal growth of SrWO₄ from Na₂WO₄ melts. E increased slightly with increased cooling rates (R_T). k₀ was parallel to k_Dl and increased with increasing R_T. ΔH_a, ΔS_a, and ΔG_a did not change with the changes in R_T and crystallization temperature (T₀). The distance (d₁₂), between a diffusing particle and its host necessary for a successful diffusion, was estimated. Such distances slightly increased with T₀ and R_T.     

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.     

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.     

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.     

Effect of buffer layers on the dislocation structure of heteroepitaxial systems

Transmission electron microscopy (TEM) as well as X-ray topography (XRT) and X-ray diffractometry have been used for investigation of the structure of the LPE heteroepitaxial system In_0.05Ga_0.95As-In_yGa_1−yAs_1−xP_x-GaAs(111) A. A critical value of the lattice misfit has been shown to exist at the metallurgical boundary ((Δa/a)* ≈ 10⁻³) which results in the change of the film nucleation and growth mechanism as well as the change of misfit dislocations (MDs) generation mechanism. With (Δa/a)₀ > (Δa/a)* the nucleation and growth mechanism is mixed: island growth at the first stages of growth and layer-by-layer growth at large thicknesses. MDs are created in an “island film” developing a non-ordered dislocation network. The density of threading dislocations (N_d) is ∼ 10⁸ cm⁻². With (Δa/a)₀ < (Δa/a)* there is layer-by-layer mechanism of film's nucleation and growth from the very first stages of crystallization. MDs are injected into continuous layer along the inclined slip planes {111}, thus forming a regular three-dimensional grid of MDs. N_d is less than 10⁶ cm⁻² in the case. A model of dislocation structure formation in heterolayers has been proposed. Within the frame of this model the two critical values of phosphorus concentration in the quaternary melt have been quantitatively determined. These are corresponding to the change of MD generation mechanism. The expected values of N_d for (Δa/a)₀ > (Δa/a)* and (Δa/a)₀ < (Δa/a)* have been theoretically determined.     

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.     

The Crystallisation of Calcium Molybdate and Tungstate from Lithium Chloride Melts by Continuous Cooling. The Kinetics of Crystal Growth in Alumina Crucibles

The kinetics of crystallisation of calcium molybdate and tungstate from unstirred supersaturated solutions in lithium chloride melts — in alumina crucibles — was studied by continuous cooling from initial temperature T₀ = 800°C down to room temperature at cooling rates R_T = 20° to 200°C hr⁻¹. The solutions were analysed chemically and the crystals were examined by optical microscopy. Crystal growth started practically immediately after the onset of cooling: at first, the amount of material deposited onto crystals was far less than the amount of excess solute developed within the supersaturated solutions but crystallisation rates then increased as the crystal sizes increased. Then, after some time t* (at about seventy percent crystallisation), all excess solute was deposited onto growing crystals.     

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.     

Kinetic investigations within the transition region from polyhedral to skeletal growth mode (III). Growth kinetics of the basal face of zinc single crystals and its edge under diffusion conditions

The growth kinetics of the basal face and its edge of zinc single crystals grown from zinc vapours in the presence of argon at pressures 5 – 250 Torr has been investigated simultaneously. The alterations of the crystal size R and the length of the basal edge a with time t have been measured at constant temperature and supersaturation. It is shown that the R²(t) and a²(t) dependences change their initial shape into linear at one and the same moment. It is established that the transition from a kinetic to a diffusion regime can be determined both by the kinetic critical size R_k and by the kinetic critical size a_k. It is found also that in the kinetic regime the lateral growth rate of the basal edge is higher than the normal growth rate of the {0001} face. During the growth in a diffusion regime the R²(t) and a²(t) curves of a given single crystal become parallel, due to the isotropic character of the transport processes of the material. The rate determining role of the diffusion in the parent phase on the growth of the basal face and its edge is demonstrated.     

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.     

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)     

Crystal structures of four dibromomethylene-functionalized cage compounds

Crystal structures of four dibromomethylene-functionalized hexa- and heptacyclotetradecane cages are reported. 7-(Dibromomethylene)heptacyclo[6.6.0.0^2,6.0^3,13.0^4,11.0^5,9.0^10,14]tetradecane (3): orthorhombic, Pnma, a = 14.744(1), b = 11.237(1), c = 7.4625(7) Å Z = 4; R = 0.0531 for 504 observed reflections. 7,12-Bis(dibromomethylene)heptacyclo[6.6.0.0^2,6.0^3,13-0^4,11 .0^5,9.0^10,14]tetradecane (4): monoclinic, I2/a, a = 11.257(1), b = 9.5844(8), c = 13.884(2) Å, = 92.254(8)° Z = 4; R = 0.0413 for 663 observed reflections. 10,14-bis(dibromomethylene)hexacyclo[6.6.0.0^2,6.0^3,13.0^4,11.0^5,9]tetradecane (6): monoclinic, P2₁/n, a = 8.118(1), b = 15.273(4), c = 12.826(3) Å, = 104.20(1)° Z = 4; R = 0.0384 for 1392 observed reflections. 14-(dibromomethylene)hexacyclo[6.6.0.0^2,6.0^3,13.0^4,11.0^5,9]tetradecan-10-one (7): monoclinic, P2₁/n, a = 8.2879(7), b = 15.273(1), c = 10.0565(9) Å, = 92.271(8)° Z = 4; R = 0.0320 for 1402 observed reflections. The functional groups lead to slight shortening of bond lengths.     

Dielectric characteristics of neodymium heptamolybdate crystals grown by gel encapsulation technique

Results obtained from the dielectric studies of neodymium heptamolybdate crystals grown in the system Nd(NO₃)₃ –MoO₃ –NH₄OH– HNO₃ —Na₂SiO₃ by gel encapsulation technique are presented. The variation of dielectric constant (ε′), dielectric loss (tanδ) and conductivity (σ) with frequency at different temperatures is studied. The dielectric constant of the material increases sharply, attains a peak value and then decreases rapidly, as material's temperature rises from room temperature to higher degrees. The temperature at which the peak value is attained is the transition temperature of the material. Dielectric loss (tan δ) follows almost a similar behaviour. The conductivity (σ) is also found to be temperature-and frequency-dependent. This sharp rise in ε′ is attributed to the contribution from space charge polarization. Theoretically obtained data using the expression ε′ = a₀ + a₁ T² and —In σ = a + b(T — T₀)² for T < T₀) fits very well with the experimentally obtained data indicating that space charge polarization increases as some power of temperature larger than one.     

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.     

Stereochemistry of 1,2-oxaphospholanes. Part X. Synthesis,X-ray structure and NMR spectroscopy of (2S*,3R*,5R*)-2-methoxy-3,5-dimethyl-2-oxo-1,2-oxaphospholan-3-ol

The title compound (4a) was synthesized from a phosphite compound obtained from 4-hydroxy-2-pentanone and dimethylphosphorochloridite, after addition of an equivalent of water. Thecis-configuration of the P=O and C3-OH groups was established based on³¹P NMR chemical shifts. In chloroform, as well as in benzene solution, the most favorable conformations of the title compound are ₄ ⁵ T,⁴ E, and ₄ ⁵ T. The crystal and molecular structure of4a has been determined by single-crystal X-ray diffraction data, and refined toR=0.056. The five-membered ring has an envelope⁴ E (C₅) conformation, with the asymmetry parameter C ₅(4)=3.5°. Both the C5-CH₃ and the C3-CH₃ groups are equatorial. In the solid state, the molecules form dimers with hydrogen bonding between the hydroxyl groups and the phosphoryl oxygen atom of an adjacent molecule. A quantitative comparison of the structure of 4a with the structure of the related 2-mcthoxy-3,5,5-trimethyl-2-oxo-1,2-oxaphosphospholan-3-ol is given.     

Barrier to crystal nucleation in anorthite

The kinetics of crystal nucleation in anorthite (CaAl₂Si₂O₈) have been determined over the range of undercooling between 475 and 600°C. The plot of In(I_vη) versus (ΔT_|staggered|r²T_|staggered|r³)^?1 is a straight line of negative slope over the temperature range investigated. The slope of this relation indicates a free energy barrier to crystal nucleation of about 82 kT1 (where $\text{T1 = 0.8T}{}_{\mathrm{E}}$). The intercept at (ΔT_|staggered|r²T_staggered|r³)^?1 = 0 is approximately 10²⁷ cm^?3 s^?1P. Samples of anorthite glass were also analyzed by differential thermal analysis, with the temperature of maximum crystallization rate being determined as a function of heating rate. From this variation, a nucleation barrier of about 80 kT1 was estimated. The combined results are in good agreement with predictions of the classical theory of homogeneous nucleation.     

The thermodynamic equilibrium of the formation process of High-Tc superconducting phase YBa2Cu3O7−x

Analysing the equilibrium state of the formation reaction of the high-T_c superconducting phase 1:2:3 (YBa₂Cu₃O_7−x) on the base of the pressure-temperature-oxygen content (P-T−x) correlation research and using the Van't-Hoff equation, the Gibbs free energy (ΔG_m) of the reaction has been calculated for the first time. It is seen that the absolute value of ΔG_m is not large and of the order of 2.5 kcal · mole⁻¹. This leads to an instability of the 1:2:3 phase. Also, from the calculated values of ΔG_m relative stability regions of the 1:2:3 phase are determined for different values of x. Combinatively analysing the relation lg P = A−B/T (where A – the x-dependent constant, and value of B was determined to be equal to 10518 atm. K) and the value of ΔG_m, we come to the conclusion that the synthesis of YBa₂Cu₃O_{7 − x} when x → 0 must be carried out under high oxygen pressure and low temperature for a lasting time, because the reaction rate is limited by slow diffusion in the solid phase.