Grain Growth Kinetics Research Articles

Cellular automata simulation for high temperature austenite grain growth based on thermal activation theory and curvature-driven mechanism

Based on the thermal activation theory and curvature-driven mechanism, a 2D cellular automaton model with different state transition rules was built. Validity of the model was proved by the shrinking of circular grains. Grain growth of high temperature austenite was simulated by this model; the morphology, grain size distribution, topological aspects, and local kinetics of austenite grain growth were analyzed under different simulation time. Among the grains with different sides, the 6-sided grains are the most common and 5-sided grains are the second most common. The grains with more than six sides will grow and grains with less than six sides will shrink, while the 6-sided grains will neither grow nor shrink. The kinetics of normal grain growth follows the Burke equation and the growth exponent at different temperatures and activation energies has been researched.

Arresting bubble coarsening: A two-bubble experiment to investigate grain growth in the presence of surface elasticity

Many two-phase materials suffer from grain growth due to the energy cost which is associated with the interface that separates both phases. While our understanding of the driving forces and the dynamics of grain growth in different materials is well advanced by now, current research efforts address the question of how this process may be slowed down, or, ideally, arrested. We use a model system of two bubbles to explore how the presence of a finite surface elasticity may interfere with the coarsening process and the final grain size distribution. Combining experiments and modelling in the analysis of the evolution of two bubbles, we show that clear relationships can be predicted between the surface tension, the surface elasticity and the initial/final size ratio of the bubbles. We rationalise these relationships by the introduction of a modified Gibbs criterion. Besides their general interest, the present results have direct implications for our understanding of foam stability.

Kinetics of Austenite Grain Growth During Heating and Its Influence on Hot Deformation of LZ50 Steel

Grain growth behaviors of LZ50 have been systematically investigated for various temperatures and holding times. Quantitative evaluations of the grain growth kinetics over a wide range of temperature (950-1200 °C) and holding time (10-180 min) have been performed. With the holding time kept constant, the average austenite grain size has an exponential relationship with the heating temperature, while with the heating temperature kept constant, the relationship between the austenite average grain size and holding time is a parabolic curve approximately. The holding time dependence of average austenite grain size obeys the Beck’s equation. As the heating temperature increases, the time exponent for grain growth n increases from 0.21 to 0.39. On the basis of previous models and experimental results, taking the initial grain size into account, the mathematical model for austenite grain growth of LZ50 during isothermal heating and non-isothermal heating is proposed. The effects of initial austenite grain size on hot deformation behavior of LZ50 are analyzed through true stress-strain curves under different deformation conditions. Initial grain size has a slight effect on peak stress.

Kinetics of densification and grain growth in ultrafine WC-Co composites

Dilatometer densification measurements were performed on WC-Co composites containing 2, 5 and 10wt% Co. The runs were carried out under a flow of 10% H2-Ar up to 800°C followed by vacuum up to 1400°C. Analysis of diffusional densification kinetics suggest an initial solid state densification from 800 to about 1190°C attributed mainly to grain growth-densification indicated by acceptable fittings to a modified Coble intermediate stage model. This behavior was confirmed by grain growth analysis (range 820 to 1400°C) measured in fractures surfaces of partially densified pellets. It was detected either a softening solid state stage or eventually liquid formation at ~1150–1200°C and a kind of viscous flow densification behavior operating prior to apparently the solution-precipitation liquid phase sintering. The densification model for diffusional liquid phase sintering applied well in the 1260–1400°C range with 105–150kcalmole−1 activation energy depending on Co content. The standard rearrangement stage was also valid partially within the temperature range 1320 to 1400°C. Certain fittings of present densification data using phenomenological continuous mechanics approach were carried out, obtaining activation energies ranging between 6 and 35kcalmole−1. Although no clear assignments of such values to probable matter diffusion processes could be made, it is noted the latter value (35kcalmole−1) is close to the 25–36kcalmole−1 values obtained for the classical liquid rearrangement stage.

Kinetics of grain growth in La-doped ultrapure Al2O3

Kinetics of grain growth was measured in dense polycrystalline ultrapure alumina doped with 100 ppm of lanthanum. The evolution of grain size followed cubic kinetics, which can be attributed to the influence of solutes. Based on the increase of Gibbsian excess of segregating dopants with increase in the average grain size, it can be approximated that boundary velocity scales as inverse-square of grain size, leading to cubic grain growth kinetics. The activation energy of grain growth was found to be 418 ± 22 kJ mol−1 for La-doped alumina; comparable to that of undoped ultrapure alumina, and much lower than the activation energy of creep in La-doped alumina. The grain boundary mobility was found to be almost an order of magnitude lower than that of undoped ultrapure alumina, which can be attributed to the drag of oversized dopants segregated to the grain boundary core. These findings provide a basic understanding of the effects of segregating dopants on grain growth, and can be exploited in the production of coarsening resistant nanograined materials.

Influence of Carbon Equivalent Content on Phase Transformation During Inter-critical Heating of Dual Phase Steels Using Discrete Micro-scale Cellular Automata Model

In this paper, a cellular automata method based model is proposed for simulating phase transformation kinetics of inter-critical heating of dual phase (DP) steel. This developed model deals with the kinetics of pearlite dissolution, ferrite transformation and austenite grain growth based on carbon diffusion process. Diffusion equation is discretized and solved by finite difference method whereas austenite grain growth is controlled by transition rules applied in cellular automata algorithm. The model is operated in the temperature range of 730–890 °C for four different specimens of DP steel. This model predicts appropriately the microstructure and volume fraction of formed austenite during inter-critical heating of DP steel. In addition, this study shows that the presence of carbon and alloying elements enhances carbon equivalent of DP steel, helps in austenite formation.

Thermal stability of nanocrystalline Mg-based alloys prepared via mechanical alloying

The thermal stability and the kinetics of grain growth of nanocrystalline Mg–6Al–1Zn and Mg–6Al–1Zn–1Si alloys prepared via mechanical alloying were investigated. It started with elemental powders, using a variety of analytical techniques including differential scanning calorimetry (DSC), X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM) and energy dispersive spectrometry. The kinetics of grain growth in isothermal annealing was investigated. The XRD results show that, although the grain sizes of both material systems increase as the annealing temperature rises, the Si-containing system displays a relatively smaller grain size, i.e., 60 nm compared with 72 nm in Mg–6Al–1Zn system, after being exposed to 350 °C for 1 h. The second-phase intermetallic particle Mg2Si formed during the isothermal annealing of Mg–6Al–1Zn–1Si system could influence not only the activation energy but also the exponent of kinetic equation. Higher hardness values obtained in the Si-containing system would be due to the formation of Mg2Si intermetallic phase.

Grain growth during annealing of cryogenically-rolled Cu–30Zn brass

The grain-growth behavior of cryogenically-rolled Cu–30Zn brass during isothermal annealing at 900 °C was examined. The observed microstructure coarsening was interpreted in terms of normal grain growth with a grain-growth exponent of ∼4. The relatively slow grain-growth kinetics was attributed to the formation of precipitates at the grain boundaries and the interaction of texture and grain growth. The development of a moderate-strength {110}<uvw> α fiber texture (∼4 times random) as well as the presence of a limited number of twin variants within the grains suggested the occurrence of variant selection during annealing.

Assessment of solid state and liquid phase sintering models by comparison of isothermal densification kinetics in W and W-Cu systems

The role of liquid phase and grain growth during the intermediate stage of sintering is investigated by comparing the isothermal densification rate of the tungsten skeleton in two systems: solid-state sintered W and liquid-phase sintered W-10wt%Cu. Densification curves at 1380 °C, i.e. well after completion of capillary rearrangement in W-Cu, are confronted to the predictions of a model that considers a single representative grain size with quasi-equilibrium interfaces and a monotonic increase in grain size and coordination with density. In both systems, the densification mechanism is taken to be governed by W diffusion along grain boundaries. For system W-Cu, a phenomenological law is proposed to allow accounting for the decrease in liquid surface curvature during funicular filling of the pores by the liquid-phase. The kinetics of grain growth is described via current literature model. Good agreement is demonstrated between experimental measurements and model predictions when relying on material parameter values given in literature. In system W-Cu, the detrimental effect of the decrease in dihedral angle is, at the beginning of the funicular stage, compensated by the contribution to sintering stress brought about by the concave curvature of liquid/vapour interface. The sensitivity of computational results to model hypotheses and material parameters is assessed. The most influential parameters are diffusivities along W grain boundaries and along W/vapour and W/Cu interfaces.

Grain-growth Kinetics of Olivine Using in-situ 2D X-ray Diffraction

Grain-growth Kinetics of Olivine Using in-situ 2D X-ray Diffraction

Shedding some light on the early grain growth regime: About the effect of the initial microstructure on normal grain growth

In the present paper the effect of the initial microstructure on the coarsening kinetics of normal grain growth is investigated. To that aim, two microstructures characterized by two distinctively different grain size distributions—one following a normal and the other one following a bimodal distribution—are analyzed as they undergo coarsening by means of Monte Carlo Potts model simulations showing different behaviors at early relaxation times but reaching the same quasi-stationary self-similar growth regime for long-time annealing.

Microstructural evolution and grain growth kinetics of GZ31 magnesium alloy

Grain growth behavior of Mg–3Gd–1Zn (GZ31) magnesium alloy was studied in a wide range of annealing time and temperature to clarify the kinetics of grain growth, microstructural evolution and related metallurgical phenomena. This material exhibited typical normal grain growth mode under annealing conditions with annealing temperature of lower than 300°C and soaking time of lower than 240min. However, the abnormality in grain growth was also evident at annealing temperature of 400°C and 500°C. The dependence of abnormal grain growth (AGG) at mentioned annealing temperatures upon microstructural features such as dispersed precipitates, which were rich in Zn and Gd, was investigated by optical micrographs, X-ray diffraction patterns, scanning electron microscopy images, and energy dispersive X-ray analysis spectra. The bimodality in grain-size distribution histograms also signified the occurrence of AGG. Based on the experimental data on grain growth obtained by annealing treatments, the grain growth exponent and the activation energy were also figured out.

Angular-dependent interatomic potential for the Cu–Ta system and its application to structural stability of nano-crystalline alloys

Abstract Atomistic computer simulations are capable of providing insights into physical mechanisms responsible for the extraordinary structural stability and strength of immiscible Cu–Ta alloys. To enable reliable simulations of these alloys, we have developed an angular-dependent potential (ADP) for the Cu–Ta system by fitting to a large database of first-principles and experimental data. This, in turn, required the development of a new ADP potential for elemental Ta, which accurately reproduces a wide range of properties of Ta and is transferable to severely deformed states and diverse atomic environments. The new Cu–Ta potential is applied for studying the kinetics of grain growth in nano-crystalline Cu–Ta alloys with different chemical compositions. Ta atoms form nanometer-scale clusters preferentially located at grain boundaries (GBs) and triple junctions. These clusters pin some of the GBs in place and cause a drastic decrease in grain growth by the Zener pinning mechanism. The results of the simulations are well consistent with experimental observations and suggest possible mechanisms of the stabilization effect of Ta.

Two-Step Grain-Growth Kinetics of Sub-7 nm SnO2 Nanocrystal under Hydrothermal Condition

In this work, the grain growth kinetics of SnO2 quantum dots under hydrothermal conditions was investigated. By varying the reaction temperature and duration, SnO2 particle sizes were tuned from 2 ...

Modelling and Prediction of the Deformation during Co-Sintering of a High Temperature Dual Membrane Fuel Cell

In the frame of a FP7 project (FET-Energy “IDEAL-Cell”, 2008-2011), we have developed with a European consortium a new type of high temperature fuel cell based on a dual membrane with mixed proton and oxygen ions conductivity. This dual conductivity porous membrane, made of a proton conducting phase (BCY15) and of an oxygen conducting phase (YDC15) was sandwiched between a dense BCY15 electrolyte and a dense YDC15 second electrolyte, forming a tri-layer itself sandwiched by a cathode (LSCF48) and an anode (BCY15 + Ni). In this configuration, water is formed neither at the cathode nor at the anode, minimizing electrodes concentration overpotentials, but rather within the dual membrane which interconnected porosity ensures water evacuation. The IDEAL-Cell project i) proved the concept, ii) showed that this new fuel cell was performing better at 750°C than PCFCs and SOFCs having equivalent thickness, iii) showed that the concept was fully reversible with a high dynamic when shifting from the fuel cell regime to the electrolyzer regime, iv) showed that BCY15 was also an excellent oxygen ions conductor when fed with oxygen, and then demonstrated that the cell could be fabricated by using solely BCY15 (replacing YDC15 in the dual membrane and for the oxygen electrolyte), leading to a drastic simplification of the concept, hence of the shaping process. Today, this simplified cell is fabricated at the laboratory scale by a sequence of successive steps (1/ cold pressing, rolling and sintering of the porous dual membrane at 1350°C, 2/ deposition of both electrolytes by dip coating, and sintering at 1350°C, 3/ deposition of both cathode and anode by bar-coating, and sintering at 1150°C), which is hardly cost effective in view of stacking and further development. The present work proposes to demonstrate that co-sintering of the whole cell in a single step is possible, and to determine under what conditions of geometry, starting materials and sintering cycle a flat and stress-free cell in view of stacking, efficiency and durability can be produced via this simplified process. The research described in this paper was based on the thermomechanical modelling of the multilayer deformation occurring during sintering via a finite element numerical simulation, in which debinding, elastic and irreversible deformations, kinetics of grain growth and pores shrinkage are integrated. The thermomechanical parameters were obtained on a differential CTE measurement set-up, and the microstructural ones by image analysis on SEM images.

Supercube grains leading to a strong cube texture and a broad grain size distribution after recrystallization

This work revisits the classical subject of recrystallization of cold-rolled copper. Two characterization techniques are combined: three-dimensional X-ray diffraction using synchrotron X-rays, which is used to measure the growth kinetics of individual grains in situ, and electron backscatter diffraction, which is used for statistical analysis of the microstructural evolution. As the most striking result, the strong cube texture after recrystallization is found to be related to a few super large cube grains, which were named supercube grains. These few supercube grains become large due to higher growth rates. However, most other cube grains do not grow preferentially. Because of the few supercube grains, the grain size distribution after recrystallization is broad. Reasons for the higher growth rates of supercube grains are discussed, and are related to the local deformed microstructure.

The kinetics of grain growth in near-micrometre grain size copper produced by spark plasma sintering

Samples of copper with a grain size in the near-micrometre regime and in a nearly fully recrystallized condition have been prepared by a spark plasma sintering (SPS) process. The thermal stability of these samples in the temperature range from 950 to 1050 °C has been investigated by an analysis of the kinetics of grain growth, based on microstructural measurements using electron backscatter diffraction. In the temperature range from 950 to 1000 °C the activation energy for grain growth is approx. 300 kJ mol-1, corresponding to a value one and a half times the activation energy for self-diffusion in pure copper. In the temperature range from 1000 to 1050 °C the activation energy for grain growth is found to decrease, although annealing in this temperature range additionally results in non-uniform grain growth. For preparation of samples with a desired uniform grain size at present the best method appears to be via control of the temperature during the SPS process.

Studying the influence of triple junction energy and mobility on annealing processes

The kinetics of grain growth in nanocrystalline two-dimensional polycrystals and thin films can be controlled by the triple junctions of the microstructure. In the present work the influence of energy and mobility of grain boundaries and their junctions on annealing is investigated by analytic theories and modified Monte Carlo Potts model simulations. To that aim each structural feature of a polygonal grain is assigned its own specific energy and finite mobility, which results in four different limiting cases of self-similar growth kinetics each characterized by its own metrical and topological properties.

Phase field modeling for grain growth in porous solids

Concurrent evolution of grain size and porosity in solids is a technically important problem involving curvature-driven motion of grain boundaries and the pore motion by surface diffusion. A phase field approach comprising a system of Cahn–Hilliard and Allen–Cahn equations has been developed recently to tackle this problem. Through a formal asymptotic analysis, the current work demonstrates that the phase field model recovers the corresponding sharp-interface dynamics of the co-evolution of grain boundaries and pores; this analysis also fixes the model kinetic parameters in terms of real materials properties. As a case study, the model was used to investigate the effect of porosity on the kinetics of grain growth in CeO2 in 3D. It is shown that the model captures the phenomenon of pore breakaway often observed in experiments. Pores on three- and four-grain junctions were found to move along with the migrating boundary, while edge pores (on the boundary between two grains) were found to easily separate from the boundary. The simulations showed that pore breakaway leads to abnormal grain growth. The simulations also showed that grain growth kinetics in CeO2 changes from boundary controlled to pore controlled as the amount of porosity increases. The kinetic growth parameters such as the growth exponent and the rate constant (or equivalently the activation energy) were found to depend strongly on the precise amount and distribution of porosity, which reconciles the different experimental results reported for grain growth in CeO2.

Influence of Nb-Microalloying on the Formation of Nano/Ultrafine-Grained Microstructure and Mechanical Properties During Martensite Reversion Process in a 201-Type Austenitic Stainless Steel

In this study, influence of Nb-microalloying on formation of nano/ultrafined grain microstructure and mechanical properties during martensite reversion process in a 201-type austenitic stainless steel microalloyed with Nb was investigated. For this purpose, the 90 pct cold-rolled samples with almost fully martensitic microstructure were reversion annealed at 1023 K to 1173 K (750 °C to 900 °C) for 5 to 1800 seconds. The microstructural evolution was characterized using X-ray diffractometer, Ferritescope, optical microscope, scanning, and transmission electron microscopes. Mechanical properties were evaluated using hardness and tensile tests. The reversion mechanism was found to be diffusion controlled. In comparison with other types of 201 steel, the kinetics of grain growth at 1173 K (900 °C) was much slower in the Nb-bearing steel, being related to the rapid precipitation of nano-sized Nb-rich carbonitrides during reversion process. At this temperature, the finest austenitic microstructure was achieved in the specimen reversion annealed for 60 seconds, possessing a microstructure composed of nano and ultrafined grains with an average grain size of 93 nm. This specimen exhibited an excellent combination of ultrahigh strength (yield strength of 1 GPa and tensile strength of 1.5 GPa) and good ductility (tensile elongation of 35 pct).