Parabolic Grain Research Articles

Effect of Ti addition on the thermal stability of nanocrystalline AZ61 Mg alloy

Nanostructured alloys possess exceptional desirable properties but suffer from low thermal stability, as a consequence of a high content of grain boundaries where the atoms are in non-equilibrium lattice positions. Here nanocrystalline Ti/AZ61 magnesium matrix composite (AZ61Mg-Ti) was annealed isothermally between 573 K and 723 K. Subsequently, the thermal stability was analyzed, taking nanocrystalline AZ61 alloy as the comparative object. After annealing at 723 K for 600 min, the average grain size of AZ61Mg-Ti was approximately 95 nm, much less than that for the annealed AZ61 alloy (~450 nm). And Ti particles with size of ~410 nm and nano scale Ti3Al particles with size of ~ 8 nm were uniformly distributed in magnesium matrix. The kinetics of magnesium grain growth for nanocrystalline AZ61Mg-Ti, was well interpreted by generalized parabolic grain growth model, D8−D08=kt. The activation energy (Eg) for grain growth was calculated to be 134 kJ/mol, being 42 kJ/mol higher than that for pure Mg. For Eg, the contribution rates of drag effect and pinning effect to improve thermal stability were calculated to be 62% and 38%, respectively. Hardness evolution of annealed samples was studied and with raising annealing temperature the downtrend for AZ61Mg-Ti was more gradual than for AZ61 alloy due to the effect of the non-thermal sensitive Ti particles and the restricted Mg grain growth. After annealing treatment at 723 K for 600 min, the hardness was 1.27 GPa, higher than that for the annealed AZ61 (1.13 GPa).

Study of Grain Growth in a Ni-Based Superalloy by Experiments and Cellular Automaton Model.

The grain growth behavior in a typical Ni-based superalloy was investigated using isothermal heat treatment experiments over a holding temperature range of 1353–1473 K. The experimental results showed that the grain structure continuously coarsened as the holding time and holding temperature increased during heat treatment. A classical parabolic grain growth model was used to explore the mechanism of grain growth under experimental conditions. The grain growth exponent was found to be slightly above 2. This indicates that the current grain growth in the studied superalloy is mainly governed by grain boundary migration with a minor pinning effect from the precipitates. Then, the grain growth in the studied superalloy during isothermal heat treatment was modelled by a cellular automaton (CA) with deterministic state switch rules. The microscale kinetics of grain growth is described by the correlation between the moving velocity and curvature of the grain boundary. The local grain boundary curvature is well evaluated by a template disk method. The grain boundary mobility was found to increase with increasing temperature. The relationship between the grain boundary mobility and temperature has been established. The developed CA model is capable of capturing the dependence of the grain size on the holding time under different holding temperatures.

Pressureless two-step sintering of ultrafine-grained tungsten

The challenge of producing dense ultrafine-grained (UFG) tungsten is hereby addressed by a simple pressureless two-step sintering method. It provides a uniform microstructure with ~99% theoretical density and ~700 nm grain size, which is among the best sintering practice of pure tungsten reported in the literature. Benefitting from the finer and more uniform microstructures, two-step sintered samples show better mechanical properties in bending strength and hardness. While parabolic grain growth kinetics is verified, a transition in the nominal grain boundary mobility was observed at 1400 °C, above which the effective activation enthalpy is ~6.1 eV, below which grain boundary motion is rapidly frozen with unusually large activation enthalpy of ~12.9 eV. Such highly nonlinear behavior in activation parameters with respect to temperature suggests that activation entropy and maybe collective behavior play a role in grain growth. We believe the as-reported two-step sintering method should also be applicable to other refractory metals and alloys, and may be generalized to multi-step or continuous-cooling sintering design using machine learning.

Effect of Intercritical Annealing Conditions on Grain Growth Kinetics of Dual Phase Steel

The study of grain coarsening and its kinetics during intercritical annealing is of vital importance for the production of dual phase (DP) steels with appropriate microstructure and properties required for industrial applications. In the present work, the kinetics of grain growth in the two-phase austenite plus ferrite region was studied based on the parabolic grain growth law. It was revealed that the thermally-activated grain growth of ferrite depends on the soaking temperature and the presence of austenite islands, where these two factors compete with each other. As a result, by increasing the temperature, initially the rate of growth increases and the activation energy of grain growth (Q) was determined as 615 kJ/mol, which indicates the high-temperature dependency. However, after the formation of a certain amount of austenite and the formation of chain-network morphology of austenite, the increase of temperature results in a decreased growth rate with the Q value of − 258 kJ/mol. This suggests that the pinning effect counteracts the temperature effect in this stage. The effect of grain size on mechanical properties and work-hardening behavior was also discussed. Higher work-hardening rate was observed for the fine-grained DP microstructures, which was found to be responsible for the better strength–ductility trade off.

Investigation on the existence of a ‘Hillert regime’ in normal grain growth

The existence of a ‘Hillert regime’ in 3D normal grain growth, where the grain size distributions (GSDs) at different time-steps match the Hillert distribution during parabolic grain growth, is investigated for different initial GSDs using large-scale phase-field simulations. The short-lived ‘Hillert regime’ was present in the early-stage only in few cases. The GSDs obtained at a later-stage for all cases are self-similar over long period; independent of the initial GSDs; and wider than the Hillert distribution. Also, the topological properties in the ‘Hillert regime’ were different from that in the later-stage self-similar regime.

Effect of temperature and grain size on the stability of the microstructure of Ag films during annealing

Grain growth in thin silver films is investigated experimentally. It is shown that the duration of the incubation period preceding linear or parabolic grain growth depends on the annealing temperature and average grain size. It is found that the lower the isothermal annealing temperature and the smaller the grain size, the longer the period of incubation, i.e., the longer the period of microstructure stability.

Formation mechanism, crystallite growth and electrical conductivity of nano-crystalline CuxFe3−xO4 (0.75 ≤ x ≤ 1.25) spinels prepared by glycine-nitrate process

The CuxFe3−xO4 (0.75≤x≤1.25) nano-crystalline powders were prepared by an optimized glycine-nitrate process (GNP) followed by calcination. Thermal analysis and X-ray diffraction (XRD) data revealed that formation of CuFe2O4 takes place in three steps. In the first step, iron and copper nitrates decompose to Fe2O3 and Cu, respectively. Then, Cu changes to CuO and finally CuO reacts with Fe2O3 to form CuFe2O4. The optimized GNP process was then applied on CuxFe3−xO4 spinels to find the optimum x value representing a single phase product with the best conductivity. Electrical measurements in air at 650–800°C showed that the highest electrical conductivity, among CuxFe3−xO4 spinels, belonged to stoichiometric CuFe2O4 compound (7.6Scm−1 with 1.5% uncertainty at 800°C). The results of annealing exhibited that the resulting CuFe2O4 spinel is thermally stable and its crystallite growth behavior can be explained by the parabolic grain growth law. The activation energy of the crystallite growth was calculated as 363kJmol−1 with 4% uncertainty.

Nanocrystalline yttria: Grain growth depression by thermal annealing in air

Nanocrystalline yttria was prepared by mechanical processing. A fraction was annealed in air at 473 K. Annealed and non-annealed powders were treated in Ar at temperatures between 700 and 1000 K, which induced a parabolic grain growth kinetics with an Arrhenius-like dependence on temperature. Grain growth is significantly slower in annealed powders with respect to non-annealed ones. This is related to oxygen chemical absorption during annealing in air and the consequent decrease of oxygen vacancies originally present in powders.

Nanoscale Grain Growth Behaviour of CoAl Intermetallic Synthesized by Mechanical Alloying

Grain growth behaviour of the nanocrystalline CoAl intermetallic compound synthesized by mechanical alloying has been studied by isothermal annealing at different temperatures and durations. X-ray diffraction method was employed to investigate structural evolutions during mechanical alloying and annealing processes. The disordered CoAl phase with the grain size of about 6 nm was formed via a gradual reaction during mechanical alloying. The results of isothermal annealing showed that the grain growth behaviour can be explained by the parabolic grain growth law. The grains were at nanometric scale after isothermal annealing up to 0·7 T m. The grain growth exponent remained constant above 873 K indicating that grain growth mechanism does not change at high temperatures. The calculated activation energy indicated that the grain growth mechanism in the disordered CoAl phase at high temperatures was diffusing Co and Al atoms in two separate sublattices. Furthermore, an equation has been suggested to describe the grain growth kinetics of nanocrystalline CoAl under isothermal annealing at temperatures above 873 K (T/T m ≥ 0·5).

Grain growth studies on nanocrystalline Ni powder

The microstructure of nanocrystalline Ni powder produced by ball-milling and its thermal stability were investigated by applying different methods of X-ray diffraction line-profile analysis: single-line analysis, whole powder-pattern modelling and the (modified) Warren–Averbach method were employed. The kinetics of grain growth were investigated by both ex-situ and in-situ X-ray diffraction measurements. With increasing milling time, the grain-size reduction is accompanied by a considerable narrowing of the size distribution and an increase in the microstrain. Upon annealing, initial, rapid grain growth occurs, accompanied by the (almost complete) annihilation of microstrain. For longer annealing times, the grain-growth kinetics depend on the initial microstructure: a smaller microstrain with a broad grain-size distribution leads to linear grain growth, followed by parabolic grain growth, whereas a larger microstrain with a narrow grain-size distribution leads to incessant linear grain growth. These effects have been shown to be incompatible with grain-boundary curvature driven growth. The observed kinetics are ascribed to the role of excess free volume at the grain boundaries of nanocrystalline material and the prevalence of an “abnormal grain-growth” mechanism.

Self-Limited to Parabolic Grain Growth Kinetics in Metal Oxide Thin Films

Distinctive microstructure engineering of amorphous to nanocrystalline electroceramic thin films is of high relevance for integration in low to high temperature operating MEMS-devices. Up to now, kinetic rules of nucleation, crystallization and grain growth of precipitation-based ceramic thin films are unknown. In this study, general rules for the crystallization and grain growth kinetics of a pure single-phase metal oxide thin film with only one kind of cation, i.e. ceria, made by spray pyrolysis from a precursor with one single organic solvent is discussed [1,. The near-and long range disorder is studied via Raman, DSC investigation of crystallization enthalpy, XRD, SEM and TEM for amorphous to fully crystalline state. These 400 nm thick-thin films were dense, crack-free and amorphous directly after deposition on a sapphire substrate. Briefly, above deposition temperature crystallization sets in with respect to temperature and persists over a broad temperature range from 400 to 950°C. In this regime, biphasic amorphous-crystallien films exist and grain growth proceeds simultaneously to crystallization. Isothermal grain growth studies showed that after short dwell times of 10-20h stable microstructures established following self-limited grain growth law [. In this state, driving force for the crystallization is the reduction of free enthalpy for phase transformation and interface diffusion prevails. A transition to classical grain curvature-driven parabolic grain growth kinetics appeared once the material reached the fully crystalline state for average grain sizes larger than 140 nm and higher annealing temperatures. Volume diffusion was then activated in addition to the interface diffusion. It was found that once crystallized the material shows independent on processing route equal XRD density and microstrain, as well as Raman characteristics. However, dependent on processing conditions i.e. choice of organic and, according, deposition temperature of the film amorphous states vary and affect strongly crystallization and grain growth history for the biphasic films.

Potts Model Simulation of Grain Boundary Junction Limited Grain Growth

The standard Monte Carlo (MC) Potts model is modified regarding the mobility of grain boundaries and their junctions allowing the simulation of a size effect observed in nanocrystalline grain growth. In large simulation studies different properties are measured. For initially very small grains the early growth regime corresponds to a separate coarsening state, which is characterised by an average growth law and a self-similar grain size distribution that both show strong deviations from the parabolic normal grain growth behaviour. The simulation results can be described by a theoretical model based on a statistical mean-field theory for nanocrystalline grain growth.

Flame spray deposition of La 0.6Sr 0.4CoO 3− δ thin films: Microstructural characterization, electrochemical performance and degradation

Thin films of La 0.6Sr 0.4CoO 3− δ (LSC) were deposited by flame spray deposition at a deposition temperature of 200 °C. The as-deposited LSC films were dense, particle-free and amorphous. Upon annealing above 600 °C, the films crystallized into the rhombohedral perovskite LSC phase. For isothermal annealing at higher temperatures parabolic grain growth kinetics occur in parallel to densification of the thin films. Electrochemical measurements on symmetrical cells with LSC films on CGO pellets showed lowest area specific resistance (ASR) of 0.96 Ω cm 2 at 600 °C for films of 38 nm in grain size annealed at 700 °C. Degradation of the ASR of the LSC films of 3.9% was found after 5 days operation at 550 °C in ambient air.

DENSIFICATION AND GRAIN GROWTH OF NANOCRYSTALLINE NIAL POWDER DURING PRESSURELESS SINTERING

Nanocrystalline NiAl powder was prepared by mechanical alloying. The prepared powder was cold compacted and sintered at different temperatures and times. The crystallite size of green and sintered compacts was estimated from X-Ray Diffraction peak profile analysis. Thereafter, the Generalized Parabolic Grain Growth model and Master Sintering Curve concept based on Combined Stage Sintering model were employed to investigate the grain growth and densification behavior of nanocrystalline NiAl powder during sintering, respectively. The results of modeling were in a very good agreement to that of experiment. Finally, by comparing the modeling results the sintering parameters were optimized.

Ultra grain refinement and hardening of IF-steel during accumulative roll-bonding

A strip of commercial Ti–IF-steel was processed by accumulative roll-bonding (ARB) up to three cycles. The mean grain size and hardness distribution profiles along the thickness were obtained using atomic force microscopy and instrumented indentation tests. The grain refinement occurred mainly at the subsurface regions where the shear strain is high. The stacking of the strips before the subsequent rolling passes places the ultra-fine grains in the center region, leading to a complete ultra grain refinement along the thickness after only three ARB cycles. A parabolic grain size distribution profile results along the thickness that is a direct consequence of the shear strain during ARB so that the number of superimposed parabolas is 2 n−1 , where n is the number of ARB cycles. For all samples the hardness distribution along the thickness bears a direct correspondence to the local grain size following the well-known Hall–Petch relation. It is concluded that there is a direct relationship among shear strain, grain refinement and hardening of ARB processed materials with the shear strain being the main instrument for grain refinement in the present process.

Modeling of grain growth characteristics in three-dimensional domains and two-dimensional cross sections

In the modeling of grain growth of isotropic, single-phase materials using three-dimensional (3-D) Monte Carlo (MC) Potts algorithm, the theoretically expected grain growth exponent was obtained only in the late simulation stages. This article addresses the grain growth simulated by a modified MC Potts model using simple cubic lattices. The grain growth kinetics was analyzed both for the 3-D domain and for two-dimensional (2-D) cross sections. Regression analyses of the grain size data averaged over time, multiple simulations runs, and three cross sections showed that both the Louat function and the log-normal function can be fitted to the data. It was clearly observed that the lognormal function allows a better fit to the 3-D simulation data, while the Louat function is more suited to the cross-sectional data. Furthermore, parabolic grain growth kinetics was obtained both for the 3-D domain and for the cross sections, but the grain growth rates calculated for these cross sections were smaller than that obtained for the 3-D domain.

Three-dimensional grain growth modeling with a Monte Carlo algorithm

Power-law kinetics was obtained previously from grain growth simulations in isotropic, single-phase materials using three-dimensional (3D) Monte Carlo (MC) Potts models but the theoretically expected grain growth exponent was obtained only in the late simulation stages. This paper addresses the grain growth simulated by a modified 3D MC algorithm using 200×200×200 cubic lattices. The grain growth kinetics is analyzed both for the 3D domain and for two-dimensional (2D) cross-sections thereof. The 3D grain growth exponent obtained is found to be in agreement with theoretical predictions for the entire time domain. While the parabolic grain growth kinetics is also obtained for the cross-sections, the grain growth rates calculated for these cross-sections are smaller than that obtained for the 3D domain. A time-invariant grain size distribution is obtained both for the 3D domain and the cross-sections. The grain shape distribution obtained for the cross-sections is time-invariant but the distribution of grain facet numbers changes with time and appears to evolve toward a steady state in the later simulation stages.

A Monte Carlo algorithm for single phase normal grain growth with improved accuracy and efficiency

A modified two-dimensional Monte Carlo algorithm for single phase normal grain growth is proposed, which was inspired by physical grain growth mechanisms and was designed using object-oriented techniques. It leads to improved agreement of the simulation results with theoretical grain growth models, exhibits a significantly higher computational efficiency and reduces the influence of the seed on the simulation results. It was previously believed that the numerical finite size effects, which cause a lower grain growth exponent in the small grain size regime, are likely to dominate in the early stages of Monte Carlo simulations. In contrast to this conclusion, the modified algorithm proposed here correctly reproduces the theoretical predictions even in the small grain size regime and thus strongly supports the theoretical work on the relationship between self-similarity and grain growth kinetics. It can therefore be concluded that the grain boundary movement mechanism as modeled using the Monte Carlo technique inherently results in parabolic grain growth kinetics.

Effect of heating rate on properties of non-oriented electrical steel containing 0.4% Si

As the heating rate of the cold rolled sheets increases in the 0.4% Si electrical steel containing ultra-low carbon, the core loss decreases mainly due to the parabolic grain growth and the magnetic flux density also decreases because of the weakness of the 〈1 0 0〉 orientation.

Grain Growth in CeO2: Dopant Effects, Defect Mechanism, and Solute Drag

The effects of the dopants, Mg2+, Ca2+, Sr2+, Sc3+, Yb3+, Y3+, Gd3+, La3+, Ti4+, Zr4+, and Nb5+, on the grain boundary mobility of dense CeO2 have been investigated from 1270° to 1420°C. Parabolic grain growth has been observed in all instances. Together with atmospheric effects, the results support the mechanism of cation interstitial transport being the rate‐limiting step. A strong solute drag effect has been demonstrated for diffusion‐enhancing dopants such as Mg2+ and Ca2+, which, at high concentrations, can nevertheless suppress grain boundary mobility. Severely undersized dopants (Mg, Sc, Ti, and Nb) have a tendency to markedly enhance grain boundary mobility, probably due to the large distortion of the surrounding lattice that apparently facilitates defect migration. Overall, the most effective grain growth inhibitor at 1.0 % doping is Y3+, while the most potent grain growth promoter is either Mg2+ (e.g., 0.1%) or Sc3+ at high concentration (greater than 1.0%).