Grain Growth Rate Research Articles

Effect of growth restricting factor on grain refinement of aluminum alloys

Grain structure is an important and readily observable feature in aluminum alloy castings. Depending on the constitutional and heat-flow conditions in a solidified aluminum alloy, various morphologies are possible. Grain refining is one of the predominant techniques in controlling the quality of castings. It plays a vital role in improving metallurgical characteristics and mechanical properties of aluminum alloys. Fine equiaxed grains ensure remarkable benefits. There are a number of techniques to achieve fine equiaxed grain structure, but grain refinement by the addition of grain refiners referred to as inoculation is the most popular due to its simplicity. Grain refinement has been studied extensively by researchers for several decades, not only for developing efficient grain refiners but also for achieving an understanding of the mechanism of grain refinement. In spite of its commercial importance, benefits and numerous scientific studies in this area, the grain refinement of aluminum and its alloys is still a controversial subject. Solute elements like titanium segregate to the inoculants/melt interface affecting the dendrites and also affect the constitutional undercooling at the solid–liquid interface. This segregating power of an element is quantified by the growth restricting factor (GRF). In the present investigation, the effect of GRF on grain refinement of aluminum-silicon alloys was studied by the addition of Al-5Ti-1B master alloy. It is evident from this investigation that the growth rate of grains is inversely proportional to the GRF.

Formation of Homo-Template Grains in Bi0.5Na0.5TiO3Prepared by the Reactive-Templated Grain Growth Process

The effects of chemical composition on texture development have been examined for Bi0.5Na0.5TiO3 prepared by the reactive-templated grain growth method, using stoichiometric, Na-excess, and Na-deficient specimens. The highly textured material is obtained by heating the stoichiometric specimen at about 1100°C. Texture development is enhanced in the Na-excess specimen, and the highly textured specimen is hardly obtained for the Na-deficient specimen. The chemical composition affects the formation and growth stages of homo-template grains. Large homo-template grains form in the Na-excess specimen and grow at the expense of small matrix grains. These conditions of the preferential growth of homo-template grains are lost in the Na-deficient specimen because of the small size of homo-template grains and a high growth rate of matrix grains. The dependence of microstructure development on chemical composition is discussed based on the structure of the grain surface on an atomic scale.

Structure, electrical properties and temperature characteristics of Bi0.5Na0.5TiO3–Bi0.5K0.5TiO3–Bi0.5Li0.5TiO3 lead-free piezoelectric ceramics

(1−x−y)Bi0.5Na0.5TiO3–xBi0.5K0.5TiO3– yBi0.5Li0.5TiO3 lead-free piezoelectric ceramics have been prepared by an ordinary sintering technique, and their structure, electrical properties, and temperature characteristics have been studied systematically. The ceramics can be well-sintered at 1050–1150 °C. The increase in K+ concentration decreases the grain-growth rate and promotes the formation of grains with a cubic shape, while the addition of Li+ decreases greatly the sintering temperature and assists in the densification of BNT-based ceramics. The results of XRD diffraction show that K+ and Li+ diffuse into the Bi0.5Na0.5TiO3 lattices to form a solid solution with a pure perovskite structure. As x increases from 0.05 to 0.50, the ceramics transform gradually from rhombohedral phase to tetragonal phase and consequently a morphotropic phase boundary (MPB) is formed at 0.15≤x≤0.25. The concentration y of Li+ has no obvious influence on the crystal structure of the ceramics. Compared with pure Bi0.5Na0.5TiO3, the partial substitution of K+ and Li+ for Na+ lowers greatly the coercive field Ec and increases the remanent polarization Pr of the ceramics. Because of the MPB, lower Ec and large Pr, the piezoelectricity of the ceramics is improved significantly. For the ceramics with the compositions near the MPB (x=0.15–0.25 and y=0.05–0.10), the piezoelectric properties become optimum: piezoelectric coefficient d33=147–231 pC/N and planar electromechanical coupling factor kP=20.2–41.0%. In addition, the ceramics exhibit relaxor characteristic, which probably results from the cation disordering in the 12-fold coordination sites. The depolarization temperature Td shows a strong dependence on the concentration x of K+ and reaches the lowest values at the MPB. The temperature dependences of the ferroelectric and dielectric properties at high temperatures may imply that the ceramics may contain both the polar and non-polar regions at temperatures above Td.

Primary crystallization in Fe 65Nb 10B 25 metallic glass

The kinetic analysis of primary crystallization under heat treatment of Fe 65Nb 10B 25 metallic glass is obtained from quantitative microstructural data in combination with calorimetric data. The mathematical description is grounded on the Kolmogorov–Johnson–Mehl–Avrami model generalized to account for the compositional changes of the parent phase, responsible for the decreasing of both the nucleation frequency and the growth rate of the primary grains. The modeling and calculation of the transformation rate has been performed to determine the optimum range of values of the viscosity, driving force for crystallization and interfacial energy, leading to a reasonable agreement with the experimental kinetic data. It is shown that the indicated modeling procedure is quite suitable to obtain an indirect evaluation of the interfacial energy between Fe 23B 6-type nanocrystals and a disordered matrix with global Fe 65Nb 10B 25 composition.

Influence of alloying elements on grain-growth in Zr(Fe) and Cu(Fe) thin-films under in situ ion-irradiation

Thin-films of Zr(Fe) and Cu(Fe) were ion-irradiated in situ in a transmission electron microscope to study the influence of alloying elements on grain-growth. These two systems are different in that Zr–Fe has a negative heat of mixing and Cu–Fe a positive heat of mixing. Irradiations conducted at temperatures of 20–573 K showed precipitation in Zr(Fe) but not in Cu(Fe). The grain sizes increased monotonically with fluence and in both cases the pure metal exhibited more grain-growth than the alloy. A more drastic reduction of grain-growth rate was observed in Zr(Fe) (where precipitate drag occurred) than in Cu–Fe (where only solute drag was available). Zr(Fe) samples were also subjected to 1 MeV electron irradiation but no grain-growth was observed. The results are discussed in terms of the mechanisms of grain-growth under irradiation.

Ordering of Cylindrical Domain of Block Copolymers under Moving Temperature Gradient: Effects of Moving Rate

In a previous paper (Macromolecules 2007, 40, 5923), we reported that a zone heating method, which imposes the moving temperature-gradient (∇T) field on ordering process of various melts in general, enabled to control a macroscopic orientation of hexagonally packed cylindrical microdomain structures (hex-cyl) of block copolymer (bcp) bulk. In this report, we have investigated how the variation of the moving rate of ∇T affects the macroscopic orientation by using two kinds of polystyrene-block-polyisoprene bcps having different mobility. We found that the upper limit of the moving rate required to induce the unique texture and orientation of hex-cyl became large with increasing the mobility of the bcps. These results indicate that the moving rate should be smaller than the intrinsic growth rate of the hex-cyl grains in the undercooled disordered melt.

Microstructure evolution upon annealing of accumulative roll bonding (ARB) 1100 Al sheet materials: evolution of interface microstructures

The microstructure evolution upon annealing of 1100 aluminum samples that were accumulative roll bonding (ARB) processed were studied with the use of transmission electron microscopy. It was found that the ultra-fine microstructure resulted from the ARB process was not stable. Specifically, a two-stage grain growth behavior was observed, in which a relatively slower rate of grain growth was followed by a more rapid grain growth rate at higher annealing temperature. The bonding interfaces that were unique to the roll bonding process were found to have a significant influence on the grain growth behavior when the grain size of the material was of similar dimension as the bonding interface separation. Discontinuous pockets consisting of smaller grains were found to have formed upon annealing. These pockets represented the remnants of the heavily deformed layer from wire brushing.

Grain size distribution in two dimensions in the long time limit

It is shown that the inclusion of a “noise” term in the growth rate of individual grains leads to a stochastic model that provides a more realistic description of grain growth phenomenon. The resulting Fokker–Planck equation for the grain size distribution is solved numerically due to the difficulties in obtaining an analytical solution. The analysis is limited to two dimensions and assumes quasi-stationary distributions in the long time limit. The resulting grain size distribution is shown to be in agreement with that obtained from computer simulations, indicating the validity of the stochastic approach.

Numerical simulation of microstructural evolution of ceramic tool materials

The preparation of ceramic tool materials includes powdering, forming, hot-press fabrication and machining process, and the sintering is a key process, which governs the mechanical properties of the ceramic tool materials as well as the components and content. However, the sintering is a very complicated process. With the rapid development of the computer simulation technology and the computational material science, modeling and numerical simulation of ceramic sintering process become a novel way to investigate the sintering process on the micro- or macro-scale. Monte Carlo Potts’ model is widely applied to simulate the solid-phase sintering process of ceramics. Because of no assumption of the particle shape, the model can be properly used to simulate the mass-transport mechanisms. In this paper, a new Monte Carlo Potts’ model is proposed to investigate the single- and two-phase material systems, which is based on the Potts’ model of the description of the single-phase sintering without the presence of pores. The new simulation algorithm has been utilized to simulate the microstructural evolution in the single- and two-phase ceramic tool material sintering process with considering the presence of pores. Different types of interface, different types of grain boundary energy, initial grain size, the composition content, the initial pore size and the content of pore are considered in the new simulation algorithm. It is found from simulation results that the pore and the phase-two can pin the matrix phase and decrease the growth rate of matrix phase during the microstructural evolution, which has been invalidated by the experiment. The second-phase particle is useful for the refinement of matrix grain. The high rate of grain growth is disadvantage of the pore exhalation. The simulation results are consistent with the experiment results.

Grain Growth Behavior of Bi2O3‐Doped ZnO Grains in a Multilayer Varistor

A novel bismuth‐doped zinc oxide (ZnO) laminated structure is prepared in the present study. Seven layers with thickness ranging from 20 to 140 μm are laminated together with platinum (Pt) inner electrodes. The growth of Bi2O3‐doped ZnO grains within a very limited space between Pt electrodes is investigated. The grain growth behavior outside the confinement of electrodes is also studied for comparison purposes. At the beginning of sintering, a similar grain growth behavior is observed at different locations of the laminated structure. However, as sintering proceeds, the rate of grain growth within the Pt inner electrodes is decreased because of the decrease of available transportation paths. The grains between the electrodes then develop into a columnar shape as they make contact with the electrodes above and below them. Both the grain size and its distribution decrease with decreasing layer thickness.

Grain-growth kinetics of ferropericlase at high-pressure

Grain-growth kinetics of (Mg 0.85Fe 0.15)O ferropericlase was investigated at pressures of 5 and 10 GPa and temperatures of 1673–1873 K using a Kawai-type multi-anvil apparatus. Presintered ferropericlase aggregate with an average grain size of 4.0 μm was used as starting material of grain-growth annealing experiments. The grain-growth kinetics of ferropericlase is described by G n − G 0 n = k 0 t exp [ − ( E * + P V * ) / R T ] , where G is the average grain size at annealing time t, G 0 the initial average grain size, P the pressure, R the gas constant and T is the absolute temperature, with n = 2.6 ± 0.4, log 10 k 0 = −7.5 ± 1.7 m 2.6/s, E * = 262 ± 30 kJ/mol, V * = 4.7 ± 0.7 cm 3/mol. Compared at same pressure and temperature, grain-growth rate of ferropericlase is similar to olivine and faster than those of wadsleyite and ringwoodite. The present results show that, at the top of the lower mantle ( P = 25 GPa and T = 1773 K) grain size of ferropericlase in single phase system evolves to ∼2 × 10 −2 m after significant geological time (10 My) while a previous study predicts that grain size of MgO in two-phase system is as small as ∼8 × 10 −6 m at same condition.

In situ chemical vapour co-deposition of Al and Si to form diffusion coatings on TZM

Multilayer alumino-silicide and silicide coatings were formed by in situ chemical vapour co-deposition of Al and Si on TZM (Mo–0.5Ti–0.1Zr–0.02C) alloy for improving its high-temperature oxidation resistance. MoSi 2 and Mo (Si, Al) 2 layers were formed in the inner and the outer layers, respectively in the case of alumino-silicide coating. Whereas silicide coating consisted of Mo 5Si 3 and MoSi 2 phases in the inner and the outer layers, respectively. 24–100-μm thick coatings were formed by optimizing the pack mixture of Al and or Si, NH 4F and Al 2O 3 powders and conducting the experiments at 1000 °C for 8–36 h. MoSi 2 layer showed a faster growth rate and presence of columnar grains. A small weight gain at the initial stages was observed during the oxidation tests of the coated samples under continuous or cyclic heating at 1300 °C in air. Neither cracks nor peeling of the coating layers were noticed after oxidation tests.

An experimentally quantifiable solute drag factor

An empirically determined measure of the solute drag force called the drag factor is derived and defined. The drag factor is the derivative of mobility with respect to grain size, and describes well the drag effect of solute in the six different aluminas measured. A normalized drag factor allows direct comparison of different dopants, and validation of theoretically predicted trends. This construction is used to verify that the role of magnesia and rare-earth dopants in reducing the grain-growth rate is due to solute drag from the intrinsic mobility. These dopants segregate to the core of the grain-boundary, which differs from classical solute drag models that derive the drag effect from solute in the near-boundary lattice. The solute drag factor is also used to understand the role of drag in grain-boundaries that have mobilities that are enhanced relative to the pure material. This new approach for analyzing grain-growth advances the understanding of microstructural evolution and its relationship to properties.

The effect of structural changes on magnetic permeability of amorphous powder Ni80Co20

The structural changes of Ni80Co20 amorphous powder were tested during heating. The alloy was obtained by electrolysis from ammonia solution sulfate of cobalt and nickel on the titanium cathode. The differential scanning calorimetry (DSC) method was used to detect that the crystallization process of powder occurred in two stages with crystallization peaks temperatures of the first stage at 690 K and of the second stage at 790 K. The effect of structural relaxation and crystallization of powder on magnetic properties was predicted by measurement of the relative magnetic permeability change in isothermal and nonisothermal conditions. On the basis of the time change of relative magnetic permeability at a defined temperature in the temperature range of the first and second crystallization peak on the thermogram, the kinetics of crystallization was defined. It was predicted, that in the initial time interval, in the range of the first crystallization peak, the rate of crystallization is determined by the rate of nucleation of the amorphous part of the powder. However, in the second time interval, the crystallization rate is determined by the rate of diffusion. In the range of the second peak, in the beginning the rate of crystal growth is determined by activation energy of the atom pass from smaller to bigger crystal grain. In second time interval, the rate of crystal grain growth is determined by the diffusion rate of atoms to the location of integration into bigger crystal grains. For all processes which determine the rate of crystallization in temperature ranges of both crystallization peaks, the Arrhenius temperature dependence of rate for those processes is obtained. The relative magnetic permeability of crystallized powder at 873 K, is smaller for about 30 % than the relative magnetic permeability of fresh powder at room temperature. However, structurally relaxed powder at 573 K has an about 22 % larger magnetic permeability than the same fresh powder at room temperature.

Growth and Migration of Solids in Evolving Protostellar Disks. I. Methods and Analytical Tests

This series of papers investigates the early stages of planet formation by modeling the evolution of the gas and solid content of protostellar disks from the early T Tauri phase until complete dispersal of the gas. In this first paper, I present a new set of simplified equations modeling the growth and migration of various species of grains in a gaseous protostellar disk evolving as a result of the combined effects of viscous accretion and photoevaporation from the central star. Using the assumption that the grain-size distribution function always maintains a power-law structure approximating the average outcome of the exact coagulation/shattering equation, the model focuses on the calculation of the growth rate of the largest grains only. The coupled evolution equations for the maximum grain size, the surface density of the gas, and the surface density of solids are then presented and solved self-consistently using a standard -->1 + 1 dimensional formalism. I show that the global evolution of solids is controlled by a leaky reservoir of small grains at large radii, and propose an empirically derived evolution equation for the total mass of solids, which can be used to estimate the total heavy-element retention efficiency in the planet formation paradigm. Detailed comparisons with SED observations are presented in a following paper.

Genotypic variation in linear rate of grain growth and contribution of stem reserves to grain yield in wheat

Grain growth in wheat depends on current photosynthesis and stem water-soluble carbohydrates (WSC). In semiarid regions with terminal drought, grain filling in wheat crops may depend more on stem WSC content than on current assimilates. Reduction in grain yield under drought is attributed to shorter duration of linear grain growth despite increased contribution of stem reserves to grain yield. The amount of stem reserves is measured either by changes in stem dry weight (indirect method) or by stem WSC content (direct method). Genotypic variation in the rate and duration of linear grain growth and in percent contribution of stem reserves to grain yield has not been evaluated in wheat. The objectives of this study were: (i) to quantify the relationship between the direct and indirect measurement of stem reserves during and across the grain-filling period and (ii) to measure the extent of genotypic variation in rate and duration of linear grain growth and in percent contribution of stem reserves to grain yield. Dry weight, WSC content and grain yield of the main stem were measured at 10-day intervals in 11 diverse wheat genotypes under well-watered and droughted-field conditions across 2 years. Drought reduced stem WSC content from 413 to 281 mg and grain yield from 4.6 to 2.5 t ha −1. Stem WSC content and dry weight were positively correlated. Genotypic differences in linear rate of grain growth were significant in well-watered (ranging from 48.9 to 72.4 mg spike −1 day −1) and in droughted-field (ranging from 33.2 to 59.9 mg spike −1 day −1) conditions. Drought, on average, reduced the linear rate and duration of grain growth by 20 and 50%, respectively. Reduction in linear rate ranged from 13 to 43%. The amount of current assimilates and stem reserves contributed to grain yield was reduced, respectively, by 54 and 11% under drought. Genotypic differences in percent contribution of stem reserves to grain yield were significant in well-watered (ranging from 19.1 to 53.6%) and in droughted-field (ranging from 36.6 to 65.4%) conditions. The wheat genotypes responded differently to drought. Main spike grain yield was reduced by 43% under drought due to 26 and 11% reduction in grain weight and number of grains, respectively. Grain yield was correlated with linear grain growth under well-watered ( r = 0.96) and droughted ( r = 0.83) conditions. The genotypic variation observed indicates that breeding for a higher rate of linear grain growth and greater contribution of stem reserves to grain yield should be possible in wheat to stabilize grain yield in stressful environments.

Heat-shock effects on photosynthesis and sink-source dynamics in wheat ( Triticum aestivum L.)

To assess the mechanisms causing genotypic differences in heat tolerance of wheat ( Triticum aestivum L.), physiological responses to a heat shock in a vegetative (‘end of tillering’) or a reproductive (‘early grain filling’) stage were studied. Three cultivars — Lavett, Ciano-79 and Attila — differing in adaptation to heat were grown in a glasshouse at a day/night temperature regime of 15/10 °C and a 12-h daylength from sowing to ‘end of tillering’ and next at two day/night regimes of 25/20 and 18/13 °C under natural daylength. The heat-shock treatment consisted of an exposure of plants to temperatures raised gradually over a time-span of 12 hours to above 30 °C with a maximum of 38 °C during three hours at midday for three days either at the ‘end of tillering’ or at ‘grain filling’. A heat shock at the ‘end of tillering’ strongly reduced the rate of leaf photosynthesis. A similar heat shock during ‘grain filling’ decreased both rate of photosynthesis (source) and grain growth (sink). The rate of leaf photosynthesis was decreased by 40 to 70%, depending on cultivar and developmental stage. Photosynthesis fully recovered within 4 days after the heat-shock treatment was ended. The effects of the heat shock on biomass yield were more pronounced for treatments at ‘early grain filling’ than at ‘end of tillering’. However, the impact of a 3-day heat shock on biomass yield was less than the effects of the pre- and post-treatment growing temperature.

Modelling of the Dynamic Processes of Structure Formation by Macroscopic Parameters of Plastic Deformation

In this paper, the phenomenological approach which connects the recrystallization parameters with thermomechanical characteristics of deformation is implemented to simulation of structural transformations. Two cases were considered, when the growth rate of recrystallized volumes is damping fast, and when a weak growth of recrystallized grains is observed. A pattern of structural states was obtained among the models with fast decrease in growth rate of recrystallized grain and weak grain growth. The abatement of the sensibility to the intensity of grain growth with increasing of strain rate was established. The function of recrystallized volume has oscillating behaviour depending on time and coefficient of recrystallization intensity. These results were confirmed by experimental researches of rheological behaviour of steels at low strain rates and high temperatures.

Principles of Microstructural Design in Two-Phase Systems

When a polycrystal is in chemical equilibrium, the microstructure evolves as a result of grain growth under the capillary driving force arising from the interface curvature. As the growth rate of an individual grain is the product of the interface mobility and the driving force, the growth of the grain can be controlled by changing these two parameters. According to crystal growth theories, the growth of a crystal with a rough interface is governed by diffusion and its interface mobility is constant. In-contrast, the growth of a crystal with faceted interfaces is governed by the interface reaction and diffusion for driving forces below and above a critical value, respectively. As the growth rate is nonlinear for the regime of interface reaction control, the grain growth is nonstationary with annealing time. Calculations reveal that the types of nonstationary growth behavior including pseudo-normal, abnormal, and stationary are governed by the relative value of the maximum driving force, gmax, to the critical driving force for appreciable growth, gc. Recent experimental observations showing the effects of critical processing parameters on microstructural development also support the theoretical prediction. The principles of microstructural design are deduced in terms of the coupling effects of gmax and gc.

Computer Model of Recrystallization Texture in Aluminum Alloys

During recrystallization, frequency of occurrence of nuclei with certain orientation depends on the location of the nucleation site, the energy stored at that location and the rate of release of stored energy. A computer model of nucleation of recrystallization process in cold rolled aluminum is developed based on the analysis of misorientation distributions around the nuclei of different orientations and the measured orientation dependent elastic energy stored in the specimen. Comparison of selected locations of nucleation sites with experiment shows that Cube nuclei are located much more randomly in the cold rolled matrix than the rolling texture components, namely, copper, brass, and sulfur. A specific range of rate of release of stored energy increases the frequency of occurrence of the Cube nuclei. Information on the stored energy after cold deformation and stress relieving provides a great deal of understanding on the mechanism that controls the primary recrystallization in deformed metals. From the diffraction peaks that are measured using X-rays in 88% cold-rolled and stress-relieved can body aluminum alloy, stored energy as a function of crystal orientation is calculated. The rate of reduction of stored energy plays a major role in deciding the rate of nucleation of new grains with different orientations. The stored energy of deformation and unique misorientation distribution that cube grains have in the cold rolled matrix is responsible for the enhanced growth rate of the nucleated cube grains. The simulated results are compared with the experimental data. Agreement of these results suggests that in the development of the cube texture, both oriented nucleation and oriented growth play an important role. Software was developed to simulate texture and microstructure transformation during the annealing process.