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.     

The crystallisation of alkaline-earth metal tungstates from sodium tungstate melts

This paper presents studies on the crystallisation of alkaline-earth metal tungstates by slow cooling of saturated solutions in sodium tungstate melts at 700 to 1000 °C. Solubility-temperature diagrams were prepared for this temperature range. The effects of variation in the initial crystallisation temperature, cooling rate and metal salt structure on crystal number and size were investigated. Final crystal lengths increased with increase in the initial crystallisation temperature and decreased with increasing rate of cooling. Crystals grown from sodium tungstate melts at any temperature were generally smaller than those grown from lithium chloride melts (at the same temperature): they were similar in size to crystals grown from the metal chloride melts but crystallised at temperatures 150 ° to 250 °C lower.     

The crystallisation of alkaline-earth metal metasilicates from metal chloride melts: Preliminary experimental studies

The crystallisation of alcaline-earth metal metalsilicates was studied by slow cooling of saturated solutions in the metal chloride melts at T₀ = 830° to 1300°C, down to ambient temperature; cooling rates were varied from 20° to 200°C hr⁻¹. Calcium metasilicate crystallised as β-CaSiO₃ prisms, strontium metasilicate as α-SrSiO₃ platelets and barium metasilicate as α-BaSiO₃ platelets. Final crystal lengths increased with reduction in cooling rate and with increase in initial crystallisation temperature.     

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.     

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 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.     

Thermodynamic analysis of solute-solvent interactions in the solubility-temperature relations of alkaline-earth metal tungstates and sodium tungstate

This paper presents a study of thermodynamic analysis of the solubility-temperature phase diagrams for solutions of calcium, strontium and barium tungstate in sodium tungstate melts in the temperature range 660 to 1200 °C. At temperatures 1000 °C and above, the solutions were ideal but below 1000 °C the solutions became non-ideal and the non-ideality increased with decreasing temperature. At any mole fraction concentration of the solute the excess free energies of mixing and the activity coefficients increased in the order CaWO₄ > SrWO₄ > BaWO₄, whereas the excess chemical potentials decreased in the order CaWO₄ < SrWO₄ < BaWO₄.     

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.     

The annealing of alkaline-earth metal polymetaphosphate powders (I). Crystallisation and sintering processes

Amorphous barium, strontium, calcium and magnesium polymetaphosphate powders (MP₂O₆)_n, n = 20 were prepared by dehydration of the corresponding polymetaphosphate hydrate precipitates. These powders were annealed by different continuous and isothermal heat treatments over the temperature range 450° to 700 °C, the glass transition temperatures T_g to above (T_g + 120) °C. The morphologies at different degrees of crystallisation were studied by scanning electron microscopy. For the main crystallisation process (ten to sixty-seventy percent crystallisation), the powder particles retained their original pea-pod form; then after seventy percent crystallisation, these crystallised particles sintered laterally to lozenge-shaped twin-hexagonal crystals of lengths 0.5 to 3 μm. Differential thermal analysis confirmed that a markedly exothermic crystallisation process (overall enthalpy changes from about 30 to 45 kJ mol⁻¹) was occurring within the powder particles. Crystallisation rates varied from < 0.005 min⁻¹ at temperatures near T_g to > 0.5 min⁻¹ at higher temperatures; the activation energies for this process varied from 360 to 560 kJ mol⁻¹. The completely annealed crystals were studied by scanning electron microscopy, X-ray diffraction and further differential thermal analysis to 1000 °C. The X-ray diffraction d value patterns, the fusion temperatures and the enthalpies of fusion were all in close agreement with the literature values for the corresponding beta alkaline-earth metal polymetaphosphates prepared by melt crystallisation.     

The crystallisation of alkaline-earth metal molybdates and tungstates from lithium chloride melts by continuous cooling. Nucleation mechanism and kinetics and induction periods

Calcium, strontium and barium molybdate (and tungstate) solutions in lithium chloride melts were crystallised in alumina and in platinum crucibles; saturated solutions were cooled from initial temperatures 700° to 800°C down to room temperature at cooling rates 40° to 200°C hr⁻¹. The nucleation and early crystal growth were investigated by chemical and differential thermal analysis and by optical microscopy studies. Crystallisation occurred through heterogeneous nucleation at low supersaturations. Heterogeneous nuclei formed slowly onto metal aluminate (and platinate) particles within the solution during induction periods from < 0.2 to 14 hr. The main growth surge then started and few new nuclei were formed. The nucleation probably terminated at times just after the times for maximum rate of formation of nuclei. Then, at any temperature, the induction periods (t ) varied inversely with cooling rate and with the rate (R_c) of development of excess solute concentration according to the relation, The parameters k₁ were related to the rate constants (k_n) for the heterogeneous nucleation. These constants in turn probably dependend on the free energy for formation of critical heterogeneous nuclei and thence on some nucleator vs solute surface energy ‘wetting’ function. The k₁ and k_n values at any temperature decreased in the order : they increased from 2 to 4 times for 100°C rise in temperature.     

The Precipitation of Strontium and Lead Sulphates from Aqueous Solution. Kinetics of the Crystal Growth

The precipitation of strontium and lead sulphates from well-stirred supersaturated aqueous solutions, of initial solute concentrations C₀ = 0.001 to 0.020 M and C₀ = 0.0002 to 0.003 M respectively, was studied at 20° and 40°C by chemical analysis and optical microscopy. Nucleation occurred during induction periods and continuous regular growth then took place onto the nuclei formed during these periods. Crystallisation was complete after 4 to 48 hr. The crystal growth was rate-controlled by the rate of deposition of metal salt ions onto the growing crystal surfaces. This rate (dC/dt), at any growth time, then depended on both the overall surface area (A_t) and on the residual excess solute concentration (ΔC_t) in solution according to the relation while the growth rate (dα/dt), expressed in terms of degree of crystallisation, was . The rate constants (k_α) for the crystal growth of strontium and lead sulphates at 20°C were 22 and 4200 sec⁻¹ M⁻² respectively — that is, greatest for the salt with least cation hydration –; these constants increased 4 to 6 times for 20°C temperature rise. The rate-determining process for the metal salt deposition was probably the ion dehydration.     

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.     

The precipitation of barium-, strontium- and calcium molybdates from aqueous solution: Kinetics of the crystal growth

The kinetics of precipitation of barium, strontium and calcium molybdates, from supersaturated aqueous solutions of initial solute concentrations C₀ = 0.0004 to 0.003 M, C₀ = 0.002 to 0.015 M and C₀ = 0.1 to 0.06 M, respectively, were studied at 25° by conductivity measurements and chemical analysis. Nucleation occurred during induction periods and continuous crystal growth then took place onto the crystallites formed during the induction periods. The growth rates at any time were expressed, in terms of degree of crystallisation, by the relation . The rate constants (kα) for the crystal growth of barium, strontium and calcium molybdates at 25° were 7700, 200, and 8.7 sec⁻¹ M⁻², respectively.     

The precipitation of barium chromate from aqueous solution (with rapid mixing): Kinetics of the crystal growth

The kinetics of precipitation of barium chromate from well-stirred aqueous solutions of initial solute concentrations C₀ = 0.0001 to 0.0010 M (supersaturations 8 to 80) was studied at 25 °C by conductivity measurements and chemical analysis. Nucleation occurred during induction periods and regular crystal growth then took place onto the crystallites formed during the induction periods. The crystal growth was rate-controlled, in this range, by the rate of deposition of metal salt ions onto the growing crystal surfaces. This rate, at any time, then depended on both the overall surface area (A_t) and on the residual excess solute concentration (ΔC_t) in solution according to the relation, the growth rate expressed in terms of degree of crystallisation was then The rate constant (K_α) for the crystallisation of barium chromate at 25 °C was 1.5 10⁶ sec⁻¹ M⁻².     

The crystallisation of chromite-magnesiochromite spinels from a calcium magnesium aluminosilicate glass: Nucleation,crystal growth and final crystal sizes

The crystallisation of chromite-magnesiochromite spinels was studied from a calcium magnesium aluminosilicate glass (a simulated slag) containing 3 to 12 percent total iron oxides and 0.3 to 1.5 percent chromium(III) oxide, at temperatures from 1400° to 700 °C. – Spinel crystallisation occurred in glasses with 3–7 percent FeO and 0.7–1.1 percent Cr₂O₃. At temperatures 1100 °C and above, the nucleation was rapid and crystal numbers very high, at FeO contents above 3 percent and Cr₂O₃ contents above 0.7 percent; at 1056° and 1000 °C however, the crystal numbers reached some optimum values but then decreased as clinopyroxene crystals grew onto and enveloped the spinel microcrystals. In these glasses, the crystal lengths varied with growth time according to the relation, l_t = 2 k_g t^α = R_g1 t^α, where α = 0.7–1.0: this time dependence was a compromise between a relation for dendritic growth and one for facetted growth. The growth rates generally increased about five to seven times for 160 °C temperature rise: the energy of activation for the spinel crystal growth was then estimated as 180 ± 60 kJ mole⁻¹. – No spinel crystals were observed in glasses with more than 7 percent FeO content, only clinopyroxene crystals. Probably, these latter had nucleated rapidly and grown onto spinel microcrystals, while the spinel microcrystals were still of < 0.1 μm size.     

The crystallisation of alkaline-earth metal oxides from metal chloride melts: Solubility-temperature phase diagram analyses and preliminary experimental studies

The solubility v temperature phase diagrams for magnesium, calcium, strontium and barium oxide solutions, in lithium, sodium and potassium chloride melts and in the alkaline earth metal chloride melts, have been analysed. The solutions in the alkali metal chlorides are pseudo-binary reciprocal ternary mixtures; the more soluble barium and strontium oxides showed small deviations, calcium oxide showed larger deviations while the extremely sparingly-soluble magnesium oxide showed extensive deviations from ideality. These deviations were related to electrostatic interactions in solution, that depended in turn on some function of reciprocal solute and solvent caiton radii. The solutions in the alkalineearth metal chlorides are binary mixtures with MO · 4 MCl₂ solvate formation. — Some preliminary crystallisation experiments were carried out, by slow cooling of saturated solutions in the metal chloride melts: calcium and strontium oxide crystallisation from lithium chloride melts and barium oxide crystallisation from all three alkali metal chloride melts would be worth further investigation.     

The crystallisation of alkaline-earth metal tungstates (molybdates,chromates, and sulphates) from metal chloride melts

This paper presents studies on the crystallisation of alkaline-earth metal tungstates, molybdates, chromates and sulphates by slow cooling of solutions in lithium chloride and alkaline-earth metal chloride melts at 600° to 1100°C. Solubility — temperature diagrams were prepared for this temperature range. The effects of solute — solvent interaction, crystallisation temperature range and rate of cooling on crystal form and size were investigated. Final crystal size increases with reduced rate of cooling and with increasing crystallisation temperature; barium sulphate crystallisation from lithium chloride melt is anomalous.     

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.     

Cooling crystallization of aluminum sulfate in pure water modulated by sodium dodecylbenzenesulfonate

This study investigated the cooling crystallization of aluminum sulfate to explore the basic data for the recovery of aluminum resources from coal spoil. Cooling crystallization process of aluminum sulfate with sodium dodecylbenzenesulfonate (SDBS) was investigated experimentally. The effects of operating conditions, namely rotate speed and cooling rate on the crystal size (Median diameter, D_0.5) were studied. Based on single factor experimental results, the response surface method (RSM) with a Box–Behnken design (BBD) was used to determine the key operating conditions, from which a predictive equation was established to quantitatively describe the relationships of D_0.5 and there relative parameters. The optimum operating conditions for cooling crystallization of aluminum sulfate were as follows: rotate speed of 200–300 rpm, cooling rate of 4–5 °C /min and n (SDBS)/n (Al₂(SO₄)₃) of around 5E‐4. Molecular dynamics (MD) results reveal that SDBS decreases the diffusion coefficient (D) of Al³⁺ molecules, which inhibits nucleation and promotes crystal growth.     

Effect of supersaturation on the crystallization of phenylbutazone polymorphs

The article describes the effect of degree of supersaturation, σ, on the crystallization of specific polymorphs of phenylbutazone from its methanolic solution at 20 °C. At low initial supersaturation, σ ≤ 2.0, the fraction of the metastable α polymorph in the crystallized product exceeds that of the δ polymorph, while at σ ≥ 5.0, the fraction of the stable δ polymorph increases in the crystallized product. The results are explained by the effect of supersaturation on the relative rates of nucleation and crystal growth of the polymorphs. Furthermore, the mechanism of nucleation and crystal growth also change with supersaturation. Supersaturated methanolic solutions of phenylbutazone exhibit a critical temperature at which the nucleation rates of the polymorphs decrease drastically. This effect is partly explained by the decreased mobility of phenylbutazone molecules at lower temperatures. Nucleation is most rapid when the crystallization temperature is close to the transition temperature, T_t(α ⟷ δ), between the polymorphs, α and δ. The nucleation rate decreases as the temperature difference between T_t(α ⟷ δ) and the crystallization temperature increases. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)