Kinetic theory of crystallization of amorphous materials

Careful analysis of the Avrami equation [x = 1 ?exp(?Atⁿ)] shows that an activation energy for crystallization (E_c) for amorphous materials can be defined over a selected range of temperatures. This activation energy can be determined experimentally using non-isothermal differential scanning calorimetry (DSC) by determining the crystallization temperature (T_c) as a function of heating rate (φ). A plot of (ln(φ/T_c) has a slope equal to E_c/n. The activation energy for the crystallization of amorphous arsenic obtained by this non-isothermal method is found to be in fair agreement with that obtained from an isothermal DSC experiment.     

Complex primary crystallization kinetics of amorphous Finemet alloy

The complex primary crystallization kinetics of the amorphous Finemet soft magnetic alloys has been analyzed by non-isothermal DSC measurements. The local activation energies E_c(α) were determined by an isoconversional method without assuming the kinetic model function and its average value was about 383 kJ/mol. The nucleation activation energy E_n and growth activation energy E_g were 425 and 333 kJ/mol, respectively. And the apparent local activation energies E_c can be expressed by E_n and E_g as follows: E_c = aE_n + bE_g. The local Avrami exponents lies between 1 and 2 in a wide range of 0.2 < α < 0.9, and it indicates that dominating crystallization mechanism in the non-isothermal primary crystallization of amorphous Finemet alloy is one dimensional growth at a near-zero nucleation rate for surface crystallization. The significant variation of local Avrami exponent and local activation energy for primary crystallization with crystallized volume fraction demonstrates that the primary crystallization kinetics of amorphous Finemet alloy varies at different stages. In addition, the variable local activation energies E_c(α) and local Avrami exponents n(α) are applicable and correct in describing the primary crystallization process of the amorphous Finemet alloy according to the theoretical DSC curve simulation.     

Electrical conductivity of CsCuCl<Subscript>3</Subscript> crystals at structural phase transition

The electrical conductivity σ of CsCuCl₃ single crystals synthesized by the crystallization method from aqueous solutions in the ternary CsCl–CuCl₂–H₂O system has been studied. The σ measurements for CsCuCl₃ crystals have been carried out in the temperature range of 397–455 K, which covers the structural phase transition from the low-temperature (sp. gr. P6₁22, Z = 6) to the high-temperature (sp. gr. P6₃mc, Z = 2) modification at T _tr = 423 ± 8 K. A jump of σ by a factor of ~3 is observed on the σ(T) dependence in the region of the structural transition, which indicates the existence of first-order phase transition. The electric transfer activation enthalpies ΔHσ are found to be 1.0 ± 0.1 eV at T > T _tr and 0.8 ± 0.1 eV at T < T _tr. The σ value for CsCuC_l3 crystals amounts to 7 × 10^–6 S/cm at 455 K.     

Kinetics of non-isothermal crystallization and glass transition phenomena in Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses by DSC

The crystallization process affects solid properties through the crystal structure and morphology established during the transition process. An important aspect of the crystallization process is its kinetics, both from the fundamental point of view of amorphous material as well as the modeling and phase transition. In the present research work, non-isothermal crystallization data in the form of heat flow vs. temperature curves has been studied by using some well known models for amorphous Ga₁₀Se₈₇Pb₃ and Ga₁₀Se₈₄Pb₆ chalcogenide glasses, prepared by the melt quenching technique. The glass transition phenomena and crystallization of these glasses have been studied by using non-isothermal differential scanning calorimetery (DSC) measurements at constant heating rates of 5, 10, 15, 20, 25 and 30 K/min. The glass transition temperature (T_g), crystallization temperature (T_c), and melting temperature (T_m) were determined from DSC thermograms. The dependence of T_g and T_c on the heating rate was used to determine different crystallization parameters such as the order parameter (n), the glass transition energy (ΔE_g) and the crystallization activation energy (ΔE_c). The results of crystallization were discussed on the basis of different models such as Kissinger's approach and the modification for non-isothermal crystallization in addition to Johnson, Mehl, Ozawa and Avrami.     

Crystallization kinetic studies on Bi1.75Pb0.25Sr2Ca2Cu3-xSnxOδ glass-ceramic by using non-isothermal technique

The Sn substituted Bi_1.75Pb_0.25Sr₂Ca₂Cu_3-xSnxO_δ glass ceramic (where x = 0, 0.1, 0.3, and 0.5) samples were prepared by the melt-quenching method. Crystallization kinetic studies of the samples were conducted using the differential thermal analysis (DTA). The oxidation behavior of the samples was also analyzed using the thermogravimetry analysis (TG). The DTA curves were registered with different heating rates (5, 10, 15, and 20 Kmin^? 1) up to 1200 ± 0.5 K. The crystallization results were analyzed, and activation energy of crystallization process as well as the crystallization mechanisms and the effect of Sn substitution on powder glass ceramic were characterized. The glass transition temperature (T_g), the first crystallization peak temperature (T_x1) and the second crystallization peak temperature (T_x2) values were obtained as 713.0 ± 0.5–746.6 ± 0.5, 731.0 ± 0.5–760.8 ± 0.5 and 789.0 ± 0.5–820.1 ± 0.5 K, respectively. The activation energy (E_a) of crystallization was estimated from DTA results to be about 332.8 ± 0.1, 358.0 ± 0.1, 353.1 ± 0.1 and 348.9 ± 0.1 kJ/mol for x = 0, 0.1, 0.3 and 0.5, respectively, by using the Kissinger method. The Avrami parameter (n) values calculated at different Sn ratio from DTA results were found to be between 1.70 ± 0.01 and 2.57 ± 0.01, results reflect the growth of small particle with a decreasing nucleation rate.     

Kinetics of non-isothermal crystallization of chalcogenide glasses from the Sb32As5S48I15 system

The work considers the kinetics of non-isothermal crystallization, especially from the point of view of the possibility of applying the Augis–Bennett method for the determination of activation energy. The necessity of introducing the usual approximation T ≫ T₀ was analyzed. It was shown that the method can be applied not only in the cases when T ≫ T₀, but also when T > T₀ that is, when the two temperatures differ only by about 10%. We show also that the application of the Augis–Bennett formula in such cases is more accurate the higher the value of the Avrami index n is. The method was applied to study the crystallization kinetics of the glass Sb₃₂As₅S₄₈I₁₅. The results obtained by differential scanning calorimetry (DSC) under non-isothermal conditions were also analyzed using the Kissinger and Matusita method. In the process of glass heating, a single peak is observed for glass transformation and a double peak for glass crystallization. The activation energies of glass transition (E_g) and crystallization (E_c) were determined, as well as the value of the Avrami index n for the second crystallization process. The obtained values for n and m indicate that the crystallization phase involves three-dimensional nucleation and growth. On the other hand, in agreement with the obtained results of the theoretical analysis, such n value justifies the application of the Augis–Bennett method for the investigated glass for which T and T₀ do not differ significantly.     

Crystallization kinetics of electro-deposited amorphous CoP alloys

The crystallization characteristics of amorphous Co-15.2 at.% P and Co-18.4 at.% P alloys were studied by means of a differential scanning calorimeter (DSC) and a transmission electron microscope (TEM). The analysis of DSC data obtained in the isothermal operation was performed by means of the Johnson-Mehl-Avrami (J-M-A) rate equation. The values of the J-M-A time index, n, for the crystallization of Co-15.2 at.% P and Co-18.4 at.% P alloys were 3.3 ± 0.1 and 2.2±0.1, respectively. It has been revealed through these experimental results and TEM observation during the crystallization process of the amorphous alloys that the crystallization of the former alloy results in interface-controlled three-dimensional spherical growth (n = 3) of Co₂P crystal, whereas the crystallization of the latter alloy results in two-dimensional growth (n = 2) of Co₂P disks having constant thickness. It has also been found that the apparent activation energy for the crystallization is 195 kJ/mol. and 190 kJ/mol. for Co-15.2 at.% P and Co-18.4 at.% P alloys, respectively.     

Crystallization kinetics and optical band gap studies of Se96In4 glass before and after slow neutron irradiation

Results of differential scanning calorimetry (DSC) under non-isothermal condition on Se₉₆In₄ semiconducting chalcogenide glass before and after slow neutron irradiation, for different exposure times, have been reported and discussed. Some of Sn atoms have been injected into the glass by nuclear transmutation processes and the binary glass is converted into a ternary. This is accompanied by an increase in the activation energy of crystallization, E_c, and in the glass transition temperature, T_g and a decrease in the glass transition activation energy, E_t, in the onset crystallization temperature, T_c and in the peak temperature of crystallization T_p. Optical band gap measurements have also been carried out, before and after irradiation, on identical thin pellets of Se₉₆In₄ glass. The energy band gap, E_g, is found to decrease upon irradiation. These effects have been attributed to a structural change upon doping and to irradiation induced defects.     

Thermal analysis of bulk amorphous arsenic triselenide

Through the use of differential scanning calorimetry, the heat capacity and crystallization parameters of amorphous As₂Se₃ have been studied. It is found that the heat capacity above the glass transition temperature (T_g) exceeds, by a factor of 1.6, the Dulong-Petit limiting value found below T_g. The crystallization process is found to obey first-order kinetics with an activation enthalpy of 1.24 eV and an enthalpy of crystallization of 0.36 eV · molecule^?1. The effect of sample age on the rate constant is also reported.     

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.     

Diffusion in bulk-metallic glass-forming Pd–Cu–Ni–P alloys: From the glass to the equilibrium melt

Since the discovery of bulk-metallic glasses there has been considerable research effort on these systems, in particular with respect to mass transport. Now the undercooled melt between the melting temperature and the caloric glass transition temperature, which has not been accessible before due to the rapid onset of crystallization, can be investigated and theories can be tested. Here we report on radiotracer diffusion measurements in metallic bulk-glass-forming Pd–Cu–Ni–P alloys. Serial sectioning was performed by grinding and ion-beam sputtering. The time, temperature as well as the mass dependence, expressed in terms of the isotope effect E, of Co-diffusion were investigated. In the glassy state as well as in the deeply supercooled state below the critical temperature T_c, where the mode coupling theory predicts a freezing-in of liquid-like motion, the experimentally determined very small isotope effects indicate a highly collective hopping mechanism involving some ten atoms. Below T_c the temperature dependence shows Arrhenius-type behavior with an effective activation enthalpy of 3.2 eV. Above T_c the onset of liquid-like motion is evidenced by a gradual drop of the effective activation energy and by the validity of the Stokes–Einstein equation, which is found to break down below T_c. This strongly supports the mode coupling scenario. The Stokes–Einstein equation is presently tested for other constituents of the alloy. The Co isotope effect measurements, which have never been carried out near T_c in any material, show atomic transport up to the equilibrium melt to be far away from the hydrodynamic regime of uncorrelated binary collisions.     

Structural transformation on Se0.8Te0.2 chalcogenide glass

Using X-ray diffraction and differential scanning calorimetry (DSC), the structure and the crystallization mechanism of Se_0.8Te_0.2 chalcogenide glass has been studied. The structure of the crystalline phase has been refined using the Rietveld technique. The crystal structure is hexagonal with lattice parameter a = 0.443 nm and c = 0.511 nm. The average crystallite size obtained using Scherrer equation is equal 16.2 nm, so it lies in the nano-range. From the radial distribution function, the short range order (SRO) of the amorphous phase has been discussed. The structure unit of the SRO is regular tetrahedron with (r₂/r₁) = 1.61. The Se_0.8Te_0.2 glassy sample obeys the chemical order network model, CONM. Some amorphous structural parameters have been deduced. The crystallization mechanism of the amorphous phase is one-dimensional growth. The calculated value of the glass transition activation energy (E_g) and the crystallization activation energy (E_c) are 159.8 ± 0.3 and 104.3 ± 0.51 kJ/mol, respectively.     

Effect of laser irradiation on thermal and optical properties of selenium–tellurium alloy

The crystallization parameters such as glass transition temperature (T_g), onset crystallization temperature (T_c), peak crystallization temperature (T_p) and enthalpy released (ΔH_C) of the bulk Se–Te chalcogenide glass has been studied by using Differential Scanning Calorimeter (DSC), under non-isothermal condition at a heating rate of 20 K/min. The values of T_g, T_c, T_p and ΔH_C with and without laser irradiation for different exposure time have been studied. The optical absorption of pristine and laser irradiated thermally evaporated Se–Te films has been measured. The films shows indirect allowed interband transition that is influenced by the laser irradiation. The optical energy gap has been found to decrease from 1.61 to 1.38 eV with increasing irradiation time from 5 to 20 min. The results have been analyzed on the basis of laser irradiation-induced defects in the film.     

Thermal and electric transport properties of (60−x)V2O5–xAs2O3–20Fe2O3–10CaO–10Li2O unconventional glassy system

This paper presents the results of kinematical studies of glass transition and crystallization in the unconventional glassy system (60?x)V₂O₅–xAs₂O₃–20Fe₂O₃–10CaO–10Li₂O (x = 0, 10, 20, 30, 40 mol%) using differential scanning calorimetry (DSC). The glass transition temperatures (T_g), the onset crystallization temperatures (T_c), and the peak temperatures of crystallization (T_p) were found to be dependent on the compositions and the heating rates. From the dependence on heating rates of (T_g) and (T_p) the activation energy for glass transition (E_g) and the activation energy for crystallization (E_c) are calculated. The thermal stability of (60?x)V₂O₅–xAs₂O₃–20Fe₂O₃–10CaO–10Li₂O was evaluated in term of, criteria ΔT = T_c ? T_g. All the results confirm that the thermal stability increase with increasing As₂O₃ contents. From the electric–dielectric measurements it was found that, σ_dc, σ_ac(ω) and θ_D/2 decrease with increasing As₂O₃ contents. It is also observed that the dielectric constant (ε₁(ω)) and the loss factor (tan δ) decrease with increasing As₂O₃ contents in this glass system.     

NMR and infrared study of cation motion in vitreous and polycrystalline TlPO3

The activation energy for Tl⁺ conduction in TlPO₃ glass is obtained from analysis of temperature-dependent motional narrowing for Tl²⁰⁵ NMR spectra and determinations of the localized far infrared (FIR) vibrational frequency for Tl⁺. Use is made of the phenomenological equation of Hendrickson and Bray to analyze the NMR data, yielding E_a = 1.19 eV; the measured FIR Tl⁺ vibrational frequency of 80 cm^?1 yields E_a = 1.09 eV. No significant ionic conduction is observed in polycrystalline TlPO₃. Differential scanning calorimeter measurements yield a glass transition temperature T_g of 96°C and the onset of crystallization temperature of 132°C. Measurements of the Tl²⁰⁵ chemical shift interaction as a function of frequency indicate that (1) the Tl⁺ sites in both polycrystalline and glassy TlPO₃ are ionic, the sites in the polycrystal being slightly more ionic than in the glass; (2) the chemical shift interaction is anisotropic in the glass and isotropic in the polycrystal; and (3) distributions in the values of the principal components of the chemical shift tensor exist in the glass, corresponding to a variety of TlO bond lengths and bond strengths.     

Effect of Neutron Irradiation and Annealing on the Intensity of the Copper Related 1.01 eV Emission Band in n-type GaAs

Effect of neutron irradiation (E = 2 MeV, ϕ ≤ 10¹⁵ n/cm²) and subsequent annealing (T ≤ 700 °C, t = 30 min) on the intensity of the copper-related peaked at hvm =1.01 eV emission band in n-type GaAs (n₀ = 2 × 10¹⁸ cm⁻³) is studied. A strong irradiation-induced increase of the above emission intensity was observed testifying about the irradiation-stimulated growth in the concentration of copper-related 1.01 eV radiative centres (Cu_GaV_As pairs). A model is presented to explain this effect.     

Localized valence states in the forbidden gap of non-crystalline tetracene

Employing the thermally stimulated current technique the existence of three distinct gaussian trap distributions in vapor-deposited tetracene layers has been established. In layers formed at T_f ? 130 K the valence band is split into a distribution of localized states, the width being σ ? 0.06 eV, and the density N_t equal to the molecular density. Upon increasing T_f from 130 to 180 K, both N_t and σ decrease, indicating a decrease of structural disorder. For $\text{T}{}_{\mathrm{<mtext>f</mtext>}}\text{? 180}\text{K}$ the center of the trap distribution is at E₀ = 0.07 eV above the valence band. At T_f = 180 K an optimum quasi amorphous structure is formed which still lacks long-range order, but in which short-range order is present to a degree that in local regions a narrow valence band can be established. Trap distributions centered near 0.4 and 0.7 eV with a width of 0.07 and 0.1 eV, respectively, and containing about 10¹⁵ states/cm^?3, are almost independent of film formation condition, and are probably also of structural origin.     

New experimental results on nucleation of Au on NaCl: Dependence on deposition rate and time

Systematic experiments have shown that saturation density, nucleation rate, and condensation coefficient are considerably smaller than previously reported. The low condensation coefficient and the linear deposition rate dependence of the nucleation rate show that the model usually applied for the theoretical explanation of the nucleation process needs some revision. From measured condensation coefficients we have estimated the diffusion length of adatoms, x_s = (14.4 ± 2.4) nm, and the difference between desorption and diffusion energy, E_a – E_sd = (0.31 ± 0.01) eV. Possible reasons for the deviation of the new results from the earlier ones are discussed.     

Effect of arsenic atom substitute with antimony on crystallization processes and thermal stability of the (Sb,As)-S-I system

Non-isothermal differential scanning calorimetry measurements of Sb_xAs_37-xS₄₈I₁₅ chalcogenide glasses for x = 0, 7, 12, 22, 32 and 37 at.% at different heating rates were applied for the analysis of the crystallization processes and thermal stability. The activation energies of glass transition (E_g) and crystallization (E_c) were obtained. Methods based on the temperature of peak and methods based on the shape of peak of crystallization were used for E_c calculations. The activation energies of glass crystallization were determined for the Sb₃₇S₄₈I₁₅ glass, as well as the value of the Avrami index n using the Matusita–Sakka theory. The analysis showed that the detected crystallization processes are characterized by the value n which indicates that volume nucleation and three-dimensional growth are involved. Depending on the model used, the values of this parameter for SbSI ranged from 122(14) to 133(14) kJ/mol, whereas for the structural unit Sb₂S₃, the values were in the range from 160(18) to 176(50) kJ/mol. Values of E_c for Sb₂S₃ structural unit, correspond to values which can be found in the literature. E_g values are in the range from 222(40) kJ/mol to 302(8) kJ/mol, depending on Sb content. Reducing of thermal stability against crystallization can be explained by the exchange of the elements from the same group of the Periodic Table (As and Sb) and similar nature of the analogous structural units, involving no change in the coordination number, whereas the share of the ionic bond in them is changed.     

Glass formation and crystallization in highly undercooled Te-Cu alloys

The large undercoolings required for glass formation have been achieved by the slow cooling (10-20°C/min) of liquid Te-Cu alloys in the form of a fine droplet emulsion. Within the region of glass formation, between 19 and 39 at.% Cu, DTA measurements indicate that the glass (T_g) and crystallization (T_c) temperatures during heating exhibit a broad maximum at the eutectic. During slow cooling of Te-rich alloy droplets, the maximum undercooling for nucleation increases from 213°C for pure Te to 264°C for Te-12.5 at.% Cu. An enhanced depression of the nucleation (T_n) temperature compared with the change of the liquidus develops in Te-rich alloys upon approaching the glass forming composition range and can be a useful feature in assessing the glass forming tendency. Thermal cycling experiments indicate that even at an undercooling of 181°C crystallization in an eutectic Te-29 at.% Cu alloy is limited by an inadequate nucleation rate in clean droplet samples. For a eutectic alloy, at undercoolings in excess of 200°C crystal nucleation does develop in the droplet samples, but complete crystallization is hindered by a rapidly rising liquid viscosity with increased undercooling.