Theory Of Grain Growth Research Articles

Transmission electron microscopy detection of microtexture variations and their effects on thin film stability

We have studied grain growth and the development of preferred orientation in thin gold films using transmission electron microscopy conical dark field imaging. The technique is capable of detecting texture variations characterized by mean orientation differences smaller than 5°. We have observed microscopic regions with distinct 〈111〉 fiber textures that differ, primarily, in the mean azimuthal deviation from the fiber axis. For one texture, the 〈111〉 axes of individual grains are found to have an average deviation of 1.5° from the foil normal, a second is characterized by a mean deviation of 5°, and a third is more nearly random with only a slight 〈111〉 orientation preference. The shapes of the differently oriented regions depend on the preparation of the sodium chloride substrate before deposition. We have studied the dependence of preferential orientation development on substrate surface topography and the evolution of microstructure in differently textured regions. Hillock growth, observed only in nearly randomly oriented regions of the films, cannot be explained by current theories of grain growth or hillock formation.

On a stochastic theory of grain growth—IV

The stochastic theory of grain growth proposed previously [C. S. Pande, Acta metall. 35, 2671 (1987)] is developed further, in this paper. It is shown that in addition to lognormality and power law kinetics, dynamic scaling (self similarity) can also be derived from the model. Effects of an arbitrary initial grain size distribution and specimen size are also examined. Finally the question of volume conservation is re-examined in the light of recent criticsms.

On the theory of normal grain growth

Abstract The theory of normal grain growth that invokes random walk is further extended by allowing for biases in step direction. It is concluded that the predictions of this theory are in overall quantitative accord with experiment. However, the degree of agreement between theory and experiment as to the exact form of the grain size distribution function remains in doubt because of a lack of precision in the definition and measurement of grain size. Possibly, this difficulty may be surmounted by replacing measurements of grain size by those of the lengths of grain boundary edges as found in planar sections of polycrystals.

A general theory of secondary recrystallization in grain oriented Fe-Si: Metallurgical parameters controlling the microstructural evolution

The secondary recrystallization (SR) process and the related effects on the magnetic properties of silicon-iron are discussed in the framework of the general statistical theory of grain growth including texture and Zener drag influence. It has been shown that SR in silicon-iron is related to a selective growth process experienced by Goss grains due to specific grain boundary conditions generated by the surrounding grains (texture). In this paper some examples showing the specific role of various microstructural parameters influencing the selectivity of SR (such as Zener drag intensity and its drop rate, initial grain size, etc.), are discussed and related to the magnetic properties, which are mainly controlled by the final average grain size and orientation.

The thermal instability of nanocrystalline NiP materials with different grain sizes

Nanocrystalline (NC) NiP materials with average grain sizes ranging from 7 to 48 nm were synthesized by crystallization of amorphous alloys. The thermal instabilities of these samples, which are characterized by the nanometer-sized grain growth, were studied by using a differential scanning calorimeter (DSC). Experimental evidences indicate that with a decrease of the grain size, the starting temperature, the peak temperature, and the activation energy for the grain growth process increase significantly. The tendency of a decreasing instability in the smaller grain-sized sample is contradictory to the classical theory of grain growth in conventional polycrystalline materials. The anomalous instability was analyzed following an experimental fact that the excess energy and the excess volume of the interfaces in the NC materials are decreased with a reduction of the grain size.

Ba(Ti, Zr)O3 Ceramics Sintered with Lead Borate Glass

The sintering of Ba(Ti, Zr)O3 ceramics is significantly influenced by the addition of 4PbO·B2O3. The eutectic temperature of 4PbO·B2O3 is around 500°C, so it exists as a liquid phase during the sintering process. Grain growth in Ba(TiyZr1-y)O3 exhibits a peculiar phenomenon. The liquid has high surface tension which aids solubility and penetration. As a consequence, the spreading liquid can penetrate solid-solid interfaces. Penetration leads to disintegration of the solid and subsequent rearrangement of fragments. The theory of grain growth in the presence of a liquid phase is examined in terms of the equation Rn=k*t. The grain growth kinetic exponent, n, has an inverse relationship with the rate of grain growth. With suitable amounts of glass frit and sintering temperature, the density of the ceramics was enhanced and the dielectric and piezoelectric properties were improved.

The analytical modeling of normal grain growth

A fundamental understanding of grain-growth phenomena provides a means to predict and control many of the observed material properties. This article reviews the development and present state of analytical theories of grain growth. The major geometric, dynamic, and statistical factors that must be considered in a rigorous formulation of grain dynamics are outlined.

The theory and inhibition of abnormal grain growth in steels

Abnormal grain growth results from the presence of a few grains of sufficient size advantage to overcome the pinning forces of a particulate array. When grain growth inhibition fails, the growth process is abnormal, and extremely large grains are produced. This article reviews the theoretical background for grain growth and particle pinning, and particular attention is drawn to the important effects of particle distribution (random or grain boundary precipitation) and the grain size distribution prior to coarsening. Attempts to produce complete inhibition of austenite grain growth are described.

A note on the stochastic theory of normal grain growth

The treatment of grain growth as a diffusion-drift process in time size space has recently received renewed attention. In the present paper we emphasize that the grains move in only one dimension in time-size space, while in the diffusion-drift model introduced by Pande and Dantsker [ Acta metall. mater. 38, 945 (1990)], the grains are allowed to move in 1, 2 and 3 dimensions. We also demonstrate that their theory predicts grain size distribution functions that do not satisfy all the requirements normally attributed to such functions.

Statistical theory of two-dimensional grain growth—I. The topological foundation

For designing a statistical theory of 2-dimensional grain growth the two-parametric topological distribution function ϕin describing the number of grains of a grain size class i (equivalent radius Ri) and of the number of sides n was investigated. Of special importance are the (statistical) relationships between Ri and n. It could be shown that many of such relationships proposed in literature did not satisfy the generally valid topological law n̄ = 6 and that the form of this relationship is not unique but depends on the nature of the microstructure. In the present paper mainly two special cases, the random (“Voronoi”) and, in particular, the equiaxed (“quasicircular”) microstructure, are considered. For the latter case which is the case being approximated during grain growth the here called “special linear relationship” n̄i = 3 + 3Ri/R̄ was found to be valid by measurements of Ri and n of a great number of grains. The “physical meaning” of this relationship was displayed by deriving it with the help of a simplified model of circular grains applying the principles of complete and of random surface covering. This relationship which will be very important for the theory of grain growth (Part II) was shown to be valid in the case of random distribution of equiaxed grains of different size. It was further shown that with the circular grain model and the above mentioned two principles also other topological relationships (e.g. the Aboav-Weaire equation) could be interpreted.

The scaling theory of normal grain growth: Beyond the mean-field approximation

Computer simulations of domain coarsening have given excellent agreement with patterns observed experimentally in grain-boundary networks. In contrast, the statistical distribution functions predic...

Statistical theory of two-dimensional grain growth—II. Kinetics of grain growth

A statistical theory of two-dimensional is derived from fiinciples. It describes the time evolution of the distribution function of the grain radii as a solution of a two-parametric continuity equation depending, besides on the time, on the radius R and on the number n of sides of the grains. Here beside the growth rate of an individual grain which is determined by the von Neumann-Mullins equation, also the changing rate of n (e.g. by neighbour switching) had to be evaluated. For solution of the continuity equation, additionally a topological relationship (mean number of sides as function of R) is required to be known. Since this relationship depends on the microstructure (see Part I), it causes a certain ambiguity in the final kinetic equations. For comparison, a simplified model using circular grains is treated which is based on heuristic assumptions but gives better insight into the “physical meaning” of the suppositions and results of the theory. The literature on this subject is thoroughly discussed. In particular, the physical of volume conservation during grain growth, which is connected with the fulfillment of the basic topological law n = 6, was shown for several investigations not to be satisfied on the level of the basis equations.

Theory of Grain Growth in the Presence of Second Phase Particles

Theory of Grain Growth in the Presence of Second Phase Particles

The influence of high pressure on the solidification of supercooled Se melt

Abstract Under pressures between 1.75 and 8 GPa a supercooling of Se melt and an average grain size of the samples quenched under pressure with constant cooling rate 100 K/s were measured. In framework of the classic theory of nucleation and grain growth the numerical evaluation of surface tension and activation energy of crystal growth was performed. The comparison of properties of supercooled Se melt to that of Pb and In reveals anomalies on the pressure dependences of Se melt properties. This circumstance is discussed in connection with the semiconductor-metal transition discovered earlier in Se melt.

On the unusual kinetics of the hydrogen uptake by Pd-coated Mg

Recent experiments show that the total hydrogen uptake by Pd-coated Mg decreases with increasing hydrogen pressure. It is demonstrated that this unusual feature of the hydrogen uptake kinetics can be explained in the framework of the standard theory of nucleation and grain growth assuming that the nucleation rate is represented in the power law form with a rather high exponent ( N≈22).

The effect of cold deformation on the structure, texture and properties of yttrium high temperature superconducting powders and strips

Cold deformation of YBa 2Cu 3O 7 − x (phase 123, T c = 88.5–92 K) powders and strips causes partial decomposition of the 123 phase, a reduction in the degree of orthorhombicity of the structure up to almost complete degradation, and a decrease in T c . When they are deformed, yttrium high temperature superconductors acquire basal (001) [110] texture with high pole density (13–15 arbitrary units), low scattering angle (±6°–7° from the normal direction), and a weak preference for a, b or a + b in the rolling direction; traces of (139) orientations may also be found. This texture is known to be favourable for increasing j k . The combined effect of cold deformation and a carbon-containing binder leads, however, to a complete loss of superconductivity at 77 K or above. Depending on the regime of subsequent annealing, the following effects may be observed: degradation of the orthorhombic structure with a decrease in T c ; restoration of the orthorhombic structure and T c of the 123 phase with complete or substantial loss of basal-type texture; change in texture type or retention of the basal texture ( p α = 0 (005) = 6–7 arbitrary units) with restoration of the orthorhombic lattice and T c of the 123 phase. The appearance of a set of orientations from (139) to (001) in the deformation texture is evidence for the process of recrystallization grain growth. This suggests the appearance of plastic deformation of the ceramics (most probably of the shear type). With long annealing and thermocycling, the basal texture changes in accordance with the theory of compromise recrystallization grain growth up to the restoration of basal texture.

On a stochastic theory of grain growth—III

The stochastic theory of grain growth proposed previously [C. S. Pande, Acta metall. 35, 2671 (1987)] is examined and discussed in the light of a recent criticism [N. Ryum and O. Hunderi, Acta metall. 37, 1375 (1989)]. We show that the theory is able to answer all major objections raised by Ryum and Hunderi. In particular we develop further the stochastic theory utilizing an N dimensional diffusion term, ( N = 1, 2, or 3 and show mathematically that for N = 3 the volume of the specimen is trictly conserved. The grain size distribution is obtained for three dimensions in closed analytical form and is found to be approximately lognormal, in good agreement with experiments.

Topological Foundation and Kinetics of Texture Controlled Grain Growth

In the present paper first a statistical theory of 2-dimensional grain growth for the textureless case based on first principles - the von Neumann - Mullins equation and the topological grain size - grain sides relationship - is described. Then it is shown that the latter relationship follows from two fundamental topological principles, the principles of complete and random surface covering, which are shown to be responsible also for other empirical topological 2-D and 3-D relationships (e.g. Weaire equation). Finally, textures are introduced into the topological discussion.

Model of Secondary Recrystallization in Silicon-Iron and Comparison With Experiments

A comparative analysis has been made of selective grain growth processes at different layers of a grain oriented silicon iron sheet. Shorter incubation time and best orientation selection during secondary recrystallization appear at 40 μm from the sheet surface. This has been linked to the presence of a relatively strong //RD fiber in the texture. The differences through the sheet thickness are assumed to be inherited from the hot band. Computer simulations in the framework of the statistical theory of grain growth support the proposed selection mechanisms.

On a stochastic theory of grain growth—II

The stochastic theory of grain growth proposed previously [C. S. Pande, Acta metall. 35, 2671 (1987)] is developed further in this paper. This theory leads to a Fokker-Planck equation for the grain size distribution. Two different “deterministic” terms for this equation, one proposed by Hillert and other by Pande, are compared. It is found that contrary to expectations Hillert's determistic term even with the addition of a “diffusion” like term does not lead to a grain size distribution which could be in agreement with experiments. The deterministic term proposed by Pande, leads to a grain size distribution which is similar to lognormal distribution, and closer to experimental results.