Determination of activation energies for nucleation and growth from isothermal differential scanning calorimetry data

Differential scanning calorimetry (DSC) is usually adopted to analyze solid-state phase transformation incorporating nucleation, growth and impingement. Then, for isothermal transformation, time-dependent Avrami exponent and overall effective activation energy can always be deduced using recipes, which are derived from an analytical phase transformation model. On this basis, a concise and reliable approach to determine time-independent activation energies for nucleation and growth is proposed. Numerical calculations have demonstrated that the new approach is sufficiently precise under different conditions of transformation (e.g. nucleation: mixed nucleation and Avrami nucleation; growth: interface-controlled growth and diffusion-controlled growth; impingement: randomly nuclei dispersed, anisotropic growth and non-random nuclei distributions). Application of the approach in crystallization of Zr₅₅Cu₃₀Al₁₀Ni₅, Zr₅₀Al₁₀Ni₄₀ and Cu₄₆Zr₄₅Al₇Y₂ bulk amorphous alloys as measured by isothermal DSC was performed.     

Isothermal and non-isothermal crystallization kinetics in amorphous Ni45.6Ti49.3Al5.1 thin films

The crystallization kinetics in Ni_45.6Ti_49.3Al_5.1 film were studied by differential scanning calorimetry through isothermal and non-isothermal approaches. The activation energy for crystallization was determined to be 374 and 280 kJ/mol by the Kissinger and the Augis & Bennett method, respectively, in non-isothermal methods. In the isothermal annealing study, the Avrami exponents were in the range of 2.78-3.80 between 793 and 823 K, suggesting that the isothermal annealing was governed by three dimensional diffusion-controlled growth for Ni_45.6Ti_49.3Al_5.1 thin films, in which the activation energy of nucleation is higher than that of growth. In addition, the transformation rate curves of Ni_45.6Ti_49.3Al_5.1 film were also constructed by isothermal methods. The crystallization kinetics of amorphous Ni_45.6Ti_49.3Al_5.1 film can thus be appreciated and the transformation rate also can be employed to control the degree of crystallization.     

Crystallization kinetics of the Zr61Al7.5Cu17.5Ni10Si4 alloy using isothermal DSC and TEM observation

The crystallization behavior and microstructure development of the Zr₆₁Al_7.5Cu_17.5Ni₁₀Si₄ alloy during annealing were investigated by isothermal differential scanning calorimetry, X-ray diffractometry and transmission electron microscopy. During isothermal annealing of the Zr₆₁Al_7.5Cu_17.5Ni₁₀Si₄ alloy at 703 K, Zr₂Cu crystals with an average size of about 5 nm were first observed during the early stages (30% crystallization) of crystallization by TEM. The Zr₂Cu crystal size increased with annealing time and attained an average size of 20 nm corresponding to the stage of 80% crystallization. In addition, the change in particle size with increasing annealing time exhibited a linear relationship between grain growth time and the cube of the particle size for the Zr₂Cu type crystalline phase. This indicates that the crystal growth of the Zr₆₁Al_7.5Cu_17.5Ni₁₀Si₄ alloy belongs to a thermal activated process of the Arrhenius type. The activation energy for the grain growth of Zr₂Cu is 155 ± 20 kJ/mol in the Zr₆₁Al_7.5Cu_17.5Ni₁₀Si₄ amorphous alloy. The lower activation energy for grain growth in compared to that for crystallization in Zr₆₅Cu₃₅ 440 kJ/mol crystal corresponds to the rearrangement of smaller atoms in the metallic glass, Al or Si (compare to Zr).     

Kinetics of crystallization of titanium based binary and ternary amorphous alloys

Metallic glasses are kinetically metastable materials. These amorphous materials can be transformed into a crystalline state by both isothermal and isochronal methods. The study of this transformation, and hence the thermal stability of metallic glasses, are important from an application view-point. In the present work, the non-isothermal crystallization kinetics of two titanium-based amorphous alloys namely, Cu₅₀Ti₅₀ and Ti₅₀Ni₃₀Cu₂₀, are reported. The activation energies for crystallization, E_c for both the systems have been evaluated using different non-isothermal methods viz. derived through Kissinger, Augis and Bennet and Ozawa. The values of E_c obtained using these methods are consistent for both the metallic glasses and it is found that E_c for the ternary metallic glass is considerably higher than the binary metallic glass. The increase in the activation energy on the substitution of Ni in the Cu–Ti metallic glass suggests the increase in the thermal stability.     

Kinetic analysis of the isochronal crystallization of Ti40Zr25Ni8Cu9Be18 metallic glass

The isochronal crystallization kinetics of the Ti₄₀Zr₂₅Ni₈Cu₉Be₁₈ metallic glass has been investigated by differential scanning calorimetry (DSC). Results indicate that the two crystallization events of this metallic glass cannot be well-described by the classic Johnson-Mehl-Avrami (JMA) kinetic equation. The kinetic equation considering the impingement effect has been found more applicable for describing the isochronal crystallization kinetics of this amorphous alloy. Accurate values of kinetic parameters were determined by fitting the theoretical DSC data to experimental curves. The kinetic parameters change in different crystallization stages and show strong heating rate dependence. Reasons of the deviation from the JMA kinetics for the isochronal crystallization of Ti₄₀Zr₂₅Ni₈Cu₉Be₁₈ metallic glass were discussed.     

Isochronal crystallization kinetics of Cu60Zr20Ti20 bulk metallic glass

Isochronal crystallization kinetics of Cu₆₀Zr₂₀Ti₂₀ bulk metallic glass has been investigated by differential scanning calorimetry. By means of the Kissinger, Ozawa, Kempen, Matusita and Gao methods, average effective activation energies for the first and second crystallization reactions in Cu₆₀Zr₂₀Ti₂₀ are calculated to be about 375 ± 9 and 312 ± 11 kJ mol⁻¹, respectively, which are smaller than the values deduced from isothermal experiments. Meanwhile, average Avrami exponents, 3.0 ± 0.1 and 3.4 ± 0.2, for two crystallization reactions in isochronal anneals, differ from the value about 2.0 in isothermal anneals. The nonidentity of the Avrami exponents and effective activation energies may be contributed to different crystallization mechanisms and the nature of non-isokinetic between isochronal and isothermal experiments. The values of frequency factor k₀ for the first and second crystallization reactions of Cu₆₀Zr₂₀Ti₂₀ are (1.7 ± 0.3) × 10²⁴ and (7.0 ± 0.8) × 10¹⁸ s⁻¹, respectively, and the large value of k₀ has been discussed in terms of the atomic configuration and interaction.     

Thermal stability and crystallization phenomena of low cost Ti-based bulk metallic glass

The thermal stability, kinetics of crystallization, and glass forming ability of a Ti₄₈Ni₃₂Cu₈Si₈Sn₄ bulk amorphous alloy have been studied by differential scanning calorimetry using both isothermal and non-isothermal experiments. The activation energy, frequency factor, and reaction rate for the crystallization cascade were determined via the Kissinger method. X-ray diffractometry and transmission electron microscopy studies revealed that crystallization starts with the primary precipitation of Ti(Ni,Cu), followed by the nucleation of Cu₃Ti from the amorphous precursor. The kinetics of nucleation of the primary crystalline phase was also investigated using the Johnson–Mehl-Avrami method and the Avrami exponent, n, was determined. This new alloy possesses a significantly larger supercooled liquid region than any other non beryllium- or non rare earth – containing titanium-based bulk metallic glass to date.     

Study on crystallization kinetics of Al65Cu20Ti15 amorphous alloy

The crystallization behavior and thermal stability of amorphous phases of Al₆₅Cu₂₀Ti₁₅ alloy obtained by mechanical alloying were investigated by using in-situ X-ray diffraction and differential scanning calorimetry (DSC) under non isothermal and isothermal conditions. The result of a Kissinger analysis shows that the activation energy for crystallization is 1131 kJ/mol. The higher stability against crystallization of Al₆₅Cu₂₀Ti₁₅ amorphous alloy is attributed to the stronger interaction of atoms in the Al-Cu-Ti system and formed of complicated compound like Al₅CuTi₂ and Al₄Cu₉ as primary phases. The isothermal crystallization was modeled by using the Johnson-Mehl-Avrami (JMA) equation. The Avarami exponents suggest that the isothermal crystallization is governed by a three-dimensional diffusion-controlled growth.     

Static and dynamic crystallization in Mg–Cu–Y bulk metallic glass

The static and dynamic crystallization behavior of Mg₆₅Cu₂₅Y₁₀ bulk metallic glass was investigated by X-ray diffraction, differential scanning calorimetry and transmission electron microscopy. It was found that the kinetics of both anisothermal and isothermal crystallization were adequately represented by the Kissinger and KJMA relations, respectively. The apparent activation energy for crystallization was calculated to be 139 kJ/mol; this value is close to the self diffusion of Mg in both a crystalline and non-crystalline matrix. The Avrami exponent was found to vary from 2.2 to 2.5 with increasing annealing temperature which implies that, at high annealing temperatures, nucleation occurs at a constant rate accompanied by diffusion-controlled growth of spherical grains. Tensile straining in the supercooled liquid region indicated that crystallization is slightly accelerated compared with static crystallization; this phenomenon was found to adversely affect the ductility of the alloy.     

Glass formation and non-isothermal crystallization of Zr62.5Al12.1Cu7.95Ni17.45 bulk metallic glass

Glass forming ability (GFA) and non-isothermal crystallization kinetics of Zr_62.5Al_12.1Cu_7.95Ni_17.45 bulk metallic glass were investigated. Its critical dimension is up to 7.5 mm and its critical cooling rate is less than 40 K s⁻¹, indicating its better GFA. It manifests two crystallization procedures and the second crystallization peak is more sensitive to heating rate than the first crystallization peak. The glass transition and crystallization both have remarkable kinetics effects. The apparent activation energies derived from the Kissinger plots are 175.24 ± 27.59 KJ mol⁻¹ for glass transition E_g, 212.84 ± 15.84 KJ mol⁻¹ for onset crystallization E_x, 230.51 ± 23.85 KJ mol⁻¹ for the first crystallization peak E_p1 and 124.85 ± 15.15 KJ mol⁻¹ for the second crystallization peak E_p2.     

Non-isothermal crystallization kinetics of La2CaB10O19 from glass

The non-isothermal crystallization kinetics of La₂CaB₁₀O₁₉ (LCB) from a La₂O₃-CaO-B₂O₃ glass was studied. Differential thermal analysis methods were performed on three glass powders to obtain the kinetic parameters of LCB crystallization mechanism. The activation energies for overall crystallization (E), obtained by the methods of Kissinger and Ozawa, were in the range of 479-569 kJ/mol. Multiple (five) analysis methods were used to estimate the Avrami exponent (n), which could consequently be reduced into the single value of n = 3.1 ± 0.3. The growth morphology index (m) of LCB was corroborated by microscopy (optical and electron) images, which revealed a three dimensional growth. Energy dispersive spectroscopy confirmed that LCB is the crystallizing phase from the glass by an interface controlled mechanism. The parameters of the Johnson-Mehl-Avrami kinetic model for the analysis of LCB crystallization from glass were found to be n = m = 3.     

Fabrication and characterization of metallic glasses with a specific microstructure for micro-electro-mechanical system applications

Metallic glass microstructures with high aspect ratios for micro-electro-mechanical system applications have been fabricated by micro-electro-discharge machining and selective electrochemical dissolution methods. Micro-holes and three-dimensional microstructures machined on the La₆₂Al₁₄Ni₁₂Cu₁₂, Zr₅₅Al₁₀Ni₅Cu₃₀ and Cu₄₆Zr₄₄Al₇Y₃ bulk metallic glasses by micro-electro-discharge machining are evaluated by using X-ray diffraction, scanning electron microscopy, and nanoindentation. The experimental results demonstrate that the machined samples kept their amorphous structure without devitrification, and their machining characteristics are related to the thermo-physical properties of the alloys and the electrode diameters. Porous, single-pore and thin-walled Zr-based metallic glass tubes with micro-pore structures can be prepared by selective electrochemical dissolution method. The high aspect ratio microstructures fabricated by the two methods have the potential applications as micro-nozzles, polymer micro-injection molding tools, micro-channels or micro-flow meters in micro-electro-mechanical system devices.     

Crystallization of amorphous Cu60Zr40 prepared by magnetron sputter deposition

The crystallization of amorphous Cu₆₀Zr₄₀ prepared by magnetron sputter deposition was studied by differential scanning calorimetry, X-ray diffraction and transmission electron microscopy. Calorimetric results were similar to those reported in the literature for liquid-quenched Cu₆₀Zr₄₀, including the manifestation of a glass transition. Crystallization above and below the glass transition temperature, T_g, occurred by nucleation and growth of the equilibrium phase, Cu₁₀Zr₇. This phase was characterized by convergent beam electron diffraction. With isothermal annealing below T_g, the time scale for crystallization indicated that the vapor-quenched alloy was kinetically more stable than the liquid-quenched alloy. This was interpreted as a difference in the quenched-in structures, produced by the different synthesis methods. During longer anneals, TEM analysis indicated that the structure was being contaminated by oxygen.     

Investigation of viscosity and crystallization in supercooled-liquid region of Zr-based glassy alloys

Using viscosity measurement method and in-situ heating synchrotron radiation, the viscosity of the (Zr_0.55Al_0.1Ni_0.05Cu_0.3)_100 ? xY_x (x = 0, 0.5, 1, 2) bulk metallic glasses (BMGs) in their supercooled liquid regions (SLRs) and the in-situ heating nucleation were investigated, respectively. In the SLR, the (Zr_0.55Al_0.1Ni_0.05Cu_0.3)₉₉Y₁ metallic glass which shows distinct plastic strain in compression exhibits higher viscosity than the other three BMGs, however their Poisson's ratios are almost the same. The synchrotron diffraction results show that crystallization happened in the SLR of the (Zr_0.55Al_0.1Ni_0.05Cu_0.3)₉₉Y₁ glassy alloy, which could be the reason for the higher viscosity and larger plastic strain in compression compared to the other three alloys. The fracture surfaces of the glassy alloys were observed and analyzed.     

Studies on the formability of Al-based metallic glasses/nanocomposites based on isochronal DSC analysis

The Al₈₆Si_0.5Ni_4.06Co_2.94Y₆Sc_0.5 metallic glass of highly improved glass-forming ability (GFA) has been investigated by isochronal differential scanning calorimetry measurements, as well as the Al₈₅Ni₅Co₂Y₈ for comparison. The experimental results indicate that the Al₈₆Si_0.5Ni_4.06Co_2.94Y₆Sc_0.5 exhibits enlarged temperature interval between the first and second crystallization onsets (termed as primary fcc-Al/glass region), as well as enlarged second activation energy (E_p2) against the nucleation and the growth of intermetallic compounds besides fcc-Al. The variation of the Avrami exponent demonstrates that the primary crystallization process is a rapid two- and three-dimensional diffusion-controlled nucleation and growth mechanism initially, and the whole process is strongly controlled by the growth of fcc-Al crystals. According to the analysis on the basis of atomic mobility of alloy components, it demonstrates that the enlarged primary fcc-Al/glass region obtained through proper coexistence of dissimilar and similar elements would be in favor of preparing Al-based metallic glasses or nanocomposites in greater size.     

Phase transformation and crystallization kinetics of melt-spun Ni60Nb20Zr20 amorphous alloy

The glass transition and crystallization kinetics of melt-spun Ni₆₀Nb₂₀Zr₂₀ amorphous alloy ribbons have been studied under non-isothermal and isothermal conditions using differential scanning calorimetry (DSC). The dependence of glass transition and crystallization temperatures on heating rates was analyzed by Lasocka's relationship. The activation energies of crystallization, E_x, were determined to be 499.5 kJ/mol and 488.6 kJ/mol using the Kissinger and Ozawa equations, respectively. The Johnson–Mehl–Avrami equation has also been applied to the isothermal kinetics and the Avrami exponents are in the range of 1.92–2.47 indicating a diffusion-controlled three-dimensional growth mechanism. The activation energy obtained from the Arrhenius equation in the isothermal process was calculated to be E_x = 419.5 kJ/mol. The corresponding three dimensional (3D) time–temperature–transformation (TTT) diagram of crystallization for the alloy has been drawn which provides the information about transformation at a particular temperature. In addition, the intermetallic phases and morphology after thermal treatment have been identified by X-ray diffraction (XRD) and scanning electron microscope (SEM).     

Influence of outphase Cu50Ti50 amorphous alloy addition on microstructural evolution of mechanically alloyed Zr66.7Ni33.3 amorphous alloy

The influence of outphase Cu₅₀Ti₅₀ amorphous alloy addition on microstructural evolution of Zr_66.7Ni_33.3 amorphous alloy has been investigated using a mechanical alloying method. It has been found that the milling induced microstructural evolution is related to the change of peak positions of the first maximum on X-ray diffraction patterns of the as-obtained amorphous alloys. With increasing milling time, the 3 wt.% Cu₅₀Ti₅₀ addition can give rise to the cyclic amorphization transformation of the as-milled alloy. The mechanical stability of the mixing amorphous phase can be greatly enhanced with increasing Cu₅₀Ti₅₀ addition up to 10 wt.%. Moreover, the addition of outphase Cu₅₀Ti₅₀ amorphous alloy not only increases the onset crystallization temperature of Zr_66.7Ni_33.3 amorphous alloy but also alters its crystallization mode. The effect of outphase amorphous addition on the mechanical stability of the Zr_66.7Ni_33.3 amorphous phase has been discussed based upon the bond order theory.     

Crystallization processes in amorphous Zr54Cu46 alloy

The crystallization of amorphous Zr₅₄Cu₄₆ alloy was investigated by using X-ray diffraction (XRD), differential scanning calorimetry (DSC) and transmission electron microscopy (TEM) techniques. The experimental results show that an endothermic peak in DSC traces for amorphous Zr₅₄Cu₄₆ alloy exists at about 1006 K, indicating following eutectoid reaction occurs, namely, Cu₁₀Zr₇+CuZr₂↔CuZr in amorphous Zr₅₄Cu₄₆ alloy during heating. With increasing the heating rate, the glass transition temperature T_g and onset crystallization temperature T_x of amorphous Zr₅₄Cu₄₆ alloy increase in parallel, and the supercooled liquid region ΔT_x (=T_x−T_g) holds almost constant with an average value of 44 K. Both XRD and TEM results prove that Cu₁₀Zr₇ and CuZr₂ are main crystallization products for amorphous Zr₅₄Cu₄₆ alloy under continuous heating conditions. No CuZr phase is identified because of its small precipitation amount. Finally, the crystallization processes of amorphous Zr₅₄Cu₄₆ alloy were summarized.     

Consolidation and mechanical properties of Cu46Zr42Al7Y5 metallic glass by spark plasma sintering

Cu₄₆Zr₄₂Al₇Y₅ metallic glass with nearly 100% relative density was obtained by spark plasma sintering (SPS) with a diameter of 15 mm, which was larger than the largest size of 10 mm for the as-cast specimen. The fracture strength of the sintered specimen reached 2044 MPa, which was 15% higher than that of the as-cast Cu₄₆Zr₄₂Al₇Y₅ glassy specimen. The densification and compressive properties of the sintered specimens were related to sintering temperature. Structural changes of the specimens sintered at various sintering temperatures resulted in the difference of macro-mechanical properties.     

The formation and crystallization of amorphous Al65Fe20Zr15

Amorphous Al₆₅Fe₂₀Zr₁₅ alloy has been prepared by mechanical alloying. The as-milled powders were analyzed by XRD and DTA. The fully amorphous alloy was identified by the hallo rings of XRD pattern. The effective activation energy of crystallization was estimated with modified Kissinger’s plot and it is 321.0 kJ/mol evaluated from the peak temperature of crystallization. The product phases of crystallization composed of Al₃Zr, Al₈₂Fe₁₈, AlFeZr and an unidentified phase. The crystallization kinetics was also discussed by using the isochronal DTA scans and the values of corresponding kinetic parameters were determined.