Phase Transformation Theory Research Articles

Energy variation in diffusive void nucleation induced by electromigration

An energy approach is proposed to describe electromigration induced void nucleation based on phase transformation theory. The chemical potential for an individual migrated atom is predicted by diffusion induced back stress equivalent principle. After determining the chemical potential for the diffusing atoms, the Gibbs free energy controlling the void nucleation can be determined and the mass diffusion process is considered. The critical void radius and nucleation time are determined analytically when the Gibbs free energy approaches the extreme value. The theoretical predictions are compared with the experimental results from literatures and show good accuracy. The proposed model can also be applied to other diffusion induced damage processes such as thermomigration and stress migration.

Three-dimensional domain patterns in tetragonal-to-monoclinic Bi4Ti3O12 ceramics: Nonlinear analysis and piezoresponse force microscopy imaging

Tetragonal-to-monoclinic Bi4Ti3O12 (BIT) exhibits complicated domain patterns thanks to its two independently switchable spontaneous polarizations that lie in the ac plane of the monoclinic unit cell. Utilizing the nonlinear theory of ferroelectric phase transformation based on the deformation gradient tensor and spontaneous polarization, we systematically analyzed domain patterns in BIT, classifying its domain walls (DWs) into five different classes. Three-dimensional piezoresponse force microscopy (3D PFM) was then adopted to characterize the ceramic BIT, revealing intriguing domain patterns in planar, lateral, as well as tilted grains. Guided by the nonlinear theoretical analysis, 3D polarization distributions were successfully reconstructed, wherein 9°-, 90°-, 91°-, and 180°-DWs were observed along with 171°-charged DWs. The nonlinear analysis is thus confirmed by 3D PFM characterizations, and the combined theoretical analysis and experimental investigation contribute to our understanding on the 3D tetragonal-to-monoclinic ferroelectric domain patterns.

First-principles phonon-based model and theory of martensitic phase transformation in NiTi shape memory alloy

Remarkable shape memory property of Nitinol (NiTi) originates from a diffusion-free reversible phase transition it exhibits upon cooling from the cubic austenite to a low-symmetry martensite structure. Atomistic mechanisms of this martensitic transformation (MT) and consequent emergence of its various low-symmetry structures are not understood yet. Starting with first-principles density functional theoretical calculations, we present here a phonon-based model and its statistical mechanical analysis to obtain atomistic insights into martensitic phases and transformation in NiTi. We uncover seven order parameters that are relevant to the MT in NiTi. From Monte Carlo simulations of an effective model Hamiltonian derived to capture its low energy landscape, we determine its soft phonons and establish the cell-doubling M5′ mode as the primary order parameter. Using Landau theoretical analysis, we show that relative strengths of its third-order coupling with secondary order parameters (e.g. strain) determine the symmetry of low-T structures emerging at its MT. These couplings can be used as the descriptors of stability of martensitic phases that will guide the strategies to improve the shape memory of NiTi through substitutional alloying.

Towards the theory of phase transformations in metastable liquids. Analytical solutions and stability analysis

The process of ongoing nucleation and evolution of particles in a metastable liquid caused by external mass sources and crystal withdrawal mechanism is considered. The steady-state and unsteady-state analytical solutions are found analytically. The crystal-size distribution function, as well as the standard Cauchy problem for the liquid supersaturation, are derived. The linear dynamic stability theory of steady-state solutions is developed. The neutral stability surface as a function of system parameters is determined.

Crystallization kinetics and role of stress in Al induced layer exchange crystallization process of amorphous SiGe thin film on glass

The present study reports Al induced crystallization of amorphous (a)-SiGe in the Al-Ge-Si ternary system with the a-SiGe/Al bilayer structure on glass at low temperature ∼350 °C. The origin of the Al induced layer exchange (ALILE) mechanism that occurs in the a-SiGe/Al system is investigated by studying the crystallization kinetics as well as the evolution of stress in the Al layer during the crystallization process. The growth kinetics was analyzed using Avrami's theory of phase transformation as the crystallization occurs under isothermal condition. It shows that initial growth of the polycrystalline (poly)-SiGe phase follows a 3D mode, characterized by n ∼ 3, where n is the Avrami constant. It then switched over to a 2D mode through an intermediate explosive growth as the crystallization fraction increases. The stress was evaluated using X-ray diffraction analysis based on multi-hkl sin2 ψ formalism. A corroboration of the growth kinetics with stress analysis shows that nucleation and growth of the poly-SiGe phase inside the Al layer at 350 °C leads to buildup of compressive strain in the Al layer. The increase in strain energy due to compression in the Al layer at elevated temperature is the driving force that initiates the layer exchange process.

Study of bainitic transformation kinetics in SAE 52100 steel

The objective of this research was to investigate the bainitic formation in austempered SAE 52100 steel. The original microstructure of SAE 52100 steel consisted of spheroidized pearlite. In the formation of bainite, SAE 52100 steel samples were austenitized at a temperature of 849 °C for 20 min, and then quickly quenched to the isothermal temperatures between 232 °C and 427 °C for various holding times from 20 s to 120 min. The hardness and microstructure of austempered SAE 52100 samples were analyzed using a Rockwell C hardness tester and metallurgical optical microscope. In addition, the bainitic formation in SAE 52100 steel was characterized using the theory of kinetic phase transformation. The activation energies of lower bainite and upper bainite microstructure were found to be 4.72 × 104 J/mol and 6.07 × 104 J/mol with frequency factors of 23.03 (1/s) and 273.65 (1/s), respectively.

Crystal plasticity model to predict fatigue crack nucleation based on the phase transformation theory

A crystal plasticity model is developed to predict the fatigue crack nucleation of polycrystalline materials, in which the accumulated dislocation dipoles are considered to be the origin of damage. To describe the overall softening behavior under cyclic loading, a slip system-level dislocation density-related damage model is proposed and implemented in the finite element analysis with Voronoi tessellation. The numerical model is applied to calibrate the stress–strain relationship at different cycles before fatigue crack nucleation. The parameters determined from the numerical analysis are substituted into a modified phase transformation model to predict the critical fatigue crack nucleation cycle. Comparing with the experimental results of Sn–3.0Ag–0.5Cu (SAC305) alloy and P91 steel, the proposed method can describe the constitutive behavior and predict the fatigue crack nucleation accurately.

Determining Coalbed Methane Content Structure

The study provides experimental evidence of scientific ideas that are important for developing the phenomenological basis of the theory of phase transformations in the ‘coal – methane’ system accompanying the formation of gas-dynamic processes in coal beds when their initial stress-strain state and temperature background are disturbed during mining. Residual gas content of coal was determined versus the time after its recovery from coal beds and the weighted mean particle size; the effect of the pore structure of natural coals on the gas-dynamic activity of coal beds was estimated. It was shown that the major part of volatile compounds (mostly methane) is dissolved in the bulk of carbon layers.

Design of high-strength and damage-resistant carbide-free fine bainitic steels for railway crossing applications

A novel high-strength steel design is proposed, with a fine bainitic microstructure free from inter-lath carbides, for railway crossings applications. The design is based on the phase transformation theory and avoids microstructural constituents like martensite, cementite and large blocky retained austenite islands in the microstructure which are considered to be responsible for strain partitioning and damage initiation. The designed steel consists of fine bainitic ferrite, thin film austenite and a minor fraction of blocky austenite which contribute to its high strength, appreciable toughness and damage resistance. Atom probe tomography and dilatometry results are used to study the deviation of carbon partitioning in retained austenite and bainitic ferrite fractions from the T0/T0ʹ predictions. A high carbon concentration of 7.9 at.% (1.8 wt%) was measured in thin film austenite, which governs its mechanical stability. Various strengthening mechanisms such as effect of grain size, nano-sized cementite precipitation and Cottrell atmosphere at dislocations within bainitic ferrite are discussed. Mechanical properties of the designed steel are found to be superior to those of conventional steels used in railway crossings. The designed steel also offers controlled crack growth under the impact fatigue, which is the main cause of failure in crossings. In-situ testing using micro digital image correlation is carried out to study the micromechanical response of the designed microstructure. The results show uniform strain distribution with low standard deviation of 1.5% from the mean local strain value of 7.7% at 8% global strain.

Slip transmission assisted by Shockley partials across [formula omitted] interfaces in Ti-alloys

Slip transmission across α/β interfaces is of great significance in understanding the strength of Ti-alloys, but currently a detailed mechanistic understanding of the process is still lacking. Here we develop a microscopic phase-field framework that incorporates the generalized stacking fault energy and the interface crystallography, which are, respectively, calculated by atomistic methods and revealed by crystallographic theories of phase transformations and experimental characterization. The model is then applied to studying the transmission of a constant flux of discrete dislocations across multiple α/β interfaces at micron-scale. The simulations predict interesting slip transmission mechanisms that have not been reported before, wherein Shockley partials play a critical role in assisting the dislocation transfer across the interfaces. The dislocation configurations generated by these mechanisms seem to agree well with experimental characterizations. Spatial cross-over between full dislocations in α is also seen from the simulations, which is again attributed to a reaction mechanism involving Shockley partials. A parametric study further reveals that stacking fault energy can influence the slip transmission in terms of transmitted dislocation types, transmission rate, and the residual dislocation content, suggesting a new strengthening strategy at the α/β interface level. This work offers new understanding of the complex slip transmission process in Ti-alloys and demonstrates a new computational tool complementary to advanced electron microscopy analysis of plastic deformation.

In situ investigations on the amorphous to crystalline phase transformation of precursors for methanol synthesis catalysts

Two in situ methods are presented to study phase transformations in the synthesis of Cu/Zn hydroxycarbonates as catalyst precursors for industrial methanol production. In contrast to the well-established application of in situ FTIR probes in the detection of liquid phase concentrations, we evaluated spectra arising from the structural changes in the solid phase during the transformation of amorphous georgeite to nanocrystalline zincian malachite. Further, a novel microreaction system is employed to gain statistical insight on the scattering of the reaction time as a function of various process parameters. The obtained transformation kinetics during aging are described by a model based on the theory of solvent-mediated phase transformations showing excellent agreement with experimental results. The quantitative impact of temperature, concentration and zinc content on dissolution, nucleation and growth of the respective phases is discussed.

An original unified approach for the description of phase transformations in steel during cooling: first application to binary Fe–C

Exploiting Landau’s theory of phase transformations, defining an original order parameter and using the phenomenological transformation temperatures, it is reported that it is possible to describe in a global approach the conditions for the formation of each constituent (ferrite, bainite, martensite) from austenite during cooling in steel. It allowed to propose a new rigorous classification of the different thermodynamic conditions controlling each phase transformation. In a second step, the approach predicts naturally the effect of cooling rate on the bainite start temperature. Finally, perspectives are assessed to extend the approach in order to take into account the effect of an external field such as applied stress.

Three-Dimensional Domain Patterns in Tetragonal-to-Monoclinic Bi 4ti 3O 12 Ceramics: Nonlinear Analysis and Piezoresponse Force Microscopy Imaging

Tetragonal-to-monoclinic Bi4ti3O12 (BIT) exhibits complicated domain patterns thanks to its two independently switchable spontaneous polarizations that lie in the ac plane of the monoclinic unit cell. Utilizing the nonlinear theory of ferroelectric phase transformation based on the deformation gradient tensor and spontaneous polarization, we systematically analyzed domain patterns in BIT, classifying its domain walls (DWs) into five different classes. Three-dimensional piezoresponse force microscopy (3D PFM) was then adopted to characterize the ceramic BIT, revealing intriguing domain patterns in planar, lateral, as well as tilted grains. Guided by the nonlinear theoretical analysis, 3D polarization distributions were successfully reconstructed, wherein 9°-, 90°-, 91°-, and 180°-DWs were observed along with 171°-charged DWs. The nonlinear analysis is thus confirmed by 3D PFM characterizations, and the combined theoretical analysis and experimental investigation contribute to our understanding on the 3D tetragonal-to-monoclinic ferroelectric domain patterns.

Model of Forming Isotropic and Anisotropic Graphite Under High Temperatures and Fluences Neutron Irradiation

A model is proposed for describing the shape change of isotropic and anisotropic graphite under the influence of high temperatures and high neutron radiation fluences. The model is based on a new approach, which uses the following provisions: description of the near-pore neighborhood in graphite as a solid solution using the theory of phase transformations of the first kind; consideration of a new phase as a spheroidal pore of small eccentricity, flattened along the direction of greatest stress; taking into account the clustering of carbon atoms at fluences of more than . The graphite non-isotropy is characterized by different pore sizes, different diffusion coefficients, the lengths of the paths of graphite atoms along and across volume of the sample, which in turn depend on the temperature of the sample. It is proposed that the initial element on the basis of which a new phase will be formed is the spheroidal pore of small eccentricity, flattened along the direction of the highest tension. A kinetic equation that describes the diffusion of pores under the influence of high temperatures and intense neutron fluxes is obtained. Initially, the pores are in a field of predetermined stresses oriented along and across the sample. The contribution of diffusion processes is due to the term proportional to the pore distribution function in the sample, and the effect of the neutron flux is described by an additional term in the kinetic equation. The obtained kinetic equation for anisotropic graphite can be transformed for isotropic graphite. For isotropic and anisotropic graphite, model solutions have been obtained that characterize the change in its volume with time under the influence of a neutron flux and high temperature. It is shown that the magnitude of the change in the relative volume of reactor graphite for isotropic graphite exceeds a similar value for anisotropic graphite. Theoretical confirmation of the laws governing the swelling of anisotropic graphites under the influence of large neutron fluences and in the high-temperature field, previously obtained by other authors, is obtained: longitudinal compression of anisotropic graphite samples corresponds to a change in the linear dimensions of isotropic graphites; the transverse compression of anisotropic graphite samples is less than the change in the longitudinal linear dimensions of isotropic graphites.

Cold-rolling performance of non-equilibrium martensitic stainless steel produced by laser-arc hybrid welding

The cold rolling with the reduction up to 75% of martensitic stainless steel (MSS) weld was achieved on the basis of the sound laser-arc hybrid weld. The evolutions in the microstructure and crystallographic characteristics of this non-equilibrium structure were studied, which focused on the lower part of the weld because it was the poorest area. With the increase of the rolling reduction, the unordered austenite transformed to the fibrous martensite paralleled to the rolling direction. It decreased the weld toughness and increased the risk of breakage during continuous rolling. The tensile strength of the rolled weld increased by a factor about 2 compared to the weld before rolling, while the tensile ductility decreased by a factor of 10. The microstructure transformation mechanism was illustrated according to the thermodynamic analysis, which was depended on the nucleation probability of martensite, and the stress concentration caused by dislocation multiplication. The work hardening behavior was discussed on the basis of the phase transformation theory and dislocation strengthening. The microstructure-mechanical properties-rolling reduction relationship was established according to the measured data.

Modeling the kinetics of deformation-induced martensitic transformation in AISI 316 metastable austenitic stainless steel

The formation of deformation-induced martensite was studied during cold rolling of an AISI 316 stainless steel. Based on X-ray diffraction (XRD) phase analysis and metallographic etching, it was demonstrated that by increasing the reduction in thickness, the amount of martensite increases and tends to a saturated value. The kinetics of martensitic transformation was studied by consideration of von Mises equivalent strain. The Olson-Cohen, Angel, Johnson-Mehl-Avrami-Kolmogorov (JMAK), and Shin et al. models were analyzed and discussed. It was shown that the Avrami exponent, which is related to the nucleation mode, can be successfully correlated to the established theories of phase transformations. By taking into consideration of critical strain and martensite saturation in the JMAK-type formula, the Shin et al. model was characterized as the appropriate kinetics model to describe the formation of martensite during cold rolling.

The mixed lithium-magnesium imide Li2Mg(NH)2 a promising and reliable hydrogen storage material

A statistical theory of the structural phase transformations of the imide Li2Mg(NH)2 has been developed, the formation of which is accompanied by the release of free hydrogen. The standard Gibbs free energy formation of the imide's three phases: α, β, γ are calculated. Their dependencies on composition, temperature, pressure, and energy are found. Plots of concentration dependences of the free energy values of these phases are constructed for different temperatures, according to which the imide state diagram is established. Isotherms, isobars and isoplets are investigated. The possibility of hysteresis effect for α and β phases is shown. The results of the calculations are compared with the experimental data.

EXPOENTE DE AVRAMI PELA EQUAÇÃO DE JMAK PARA MÉTODO NÃO-ISOTÉRMICO DE ANÁLISE TÉRMICA

This work reports a discussion about of the general theory for phase transformations of Melh-Johnson-Avrami-Kolmogorov in process involving non-isothermal crystallization. This model allows determine as occurs the mechanism of the nucleus formation and of growth of crystalline phases during the crystallization process. To demonstrate the validity this theory, the Avrami exponent ( n ) of the LiO 2 -TeO 2 -WO 3 vitreous system was determined from DSC non-isothermal measurements. The obtained results indicate that the nucleation process is volumetric with two-dimensional or three-dimensional crystal growth. DOI: http://dx.doi.org/10.30609/JETI.2018-2.5566

EXPOENTE DE AVRAMI PELA EQUAÇÃO DE JMAK PARA MÉTODO NÃO-ISOTÉRMICO DE ANÁLISE TÉRMICA

This work reports a discussion about of the general theory for phase transformations of Melh-Johnson-Avrami-Kolmogorov in process involving non-isothermal crystallization. This model allows determine as occurs the mechanism of the nucleus formation and of growth of crystalline phases during the crystallization process. To demonstrate the validity this theory, the Avrami exponent (n) of the LiO2-TeO2-WO3 vitreous system was determined from DSC non-isothermal measurements. The obtained results indicate that the nucleation process is volumetric with two-dimensional or three-dimensional crystal growth. DOI: http://dx.doi.org/10.30609/JETI.2018-2.5566

Hydrogen Sorption Properties of Potassium Alanate

Molecular kinetic representations were used to develop the statistical theory of phase transformations of thermal decomposition of KAlH4 potassium alanate with formation of a more complex K3AlH6 alanate and KH potassium hydride and subsequent dehydrogenation of the latter accompanied with free hydrogen, pure potassium and aluminum yield. Temperature dependence of the emitted free hydrogen was established. Isotherms and isopleths were built. The possibility of hysteresis effect manifestation was established. The results of calculations were compared to the experimental data.