Rate of creep due to grain-boundary diffusion in polycrystalline solids with grain-size distribution

For steady-state deformation caused by grain-boundary diffusion, the macroscopic creep rate is analysed for a three-dimensional polycrystal consisting of space-filling grains, by taking into account the effects of diffusional interaction between grains, viscous grain-boundary sliding and grain-size distributions. For regular polyhedral grains, the grain–grain interactions increase the degree of symmetry of diffusional field, resulting in a decrease of the effective diffusion distance. Meanwhile, both the viscous grain-boundary sliding and the grain-size distribution are found to decrease the creep rate. At decreasing grain sizes, the influence of the viscous grain-boundary sliding becomes increasingly important, which explains the recent experimental observations that the creep rates of nanosized grains are much lower than those predicted by grain-boundary diffusion. On the effect of the grain-size distribution, the upper-bound and lower-bound creep rates are estimated.     

Grain-boundary sliding in elongated microstructures during diffusion creep

In diffusion creep, the contribution of grain-boundary sliding to the overall strain os can be evaluated in arbitrary polycrystals, if the angular distribution of grain boundaries is known. A os value of 0.5 is obtained for two-dimensional (2D) equiaxed microstructures consisting of regular hexagonal grains, equiaxed grains grown from a Voronoi structure or grains having a circular distribution of grain-boundary angles. The os value is also evaluated for uniaxially deformed 2D microstructures, both diffusionally and uniformly deformed. For the former, the deformed microstructure is obtained by the simulation of microstructural evolution in polycrystals with straight grain boundaries. The os value increases gradually with increasing or decreasing strain and is larger in the diffusionally deformed microstructures than in the uniformly deformed microstructures for a given grain aspect ratio. The os value for three-dimensional (3D) polycrystalline microstructures is also obtained from an ellipsoidal distribution of grain-boundary angles. The resultant os value is 0.60 for 3D equiaxed polycrystals and increases gradually with increasing strain.     

Measuring relative grain-boundary energies in block-copolymer microstructures

The (relative) energies of symmetric tilt grain boundaries in a strongly segregated lamellar block copolymer are determined by analysis of the dihedral angles at grain-boundary triple junctions. The analysis reveals two regimes: at low and intermediate misorientations (corresponding to a tilt-angle range 0≤θ≤85°) the grain-boundary energy is found to depend on the tilt angle as E(θ)～θ(x), with 2.5>x≥0. At large misorientations the grain-boundary energy is found to be independent (within the experimental uncertainty) of the angle of tilt. The transition between the two scaling regimes is accompanied by the transition of the grain-boundary structure from the chevron to the omega morphology. Grain-boundary energy and frequency are found to be inversely related, thus suggesting boundary energy to be an important parameter during grain coarsening in block-copolymer microstructures, as it is in inorganic polycrystalline microstructures.     

High-temperature creep of nickel under conditions of grain-boundary diffusion of impurities from the surface

Comparative investigations of the effect of diffusion streams of copper atoms (a weakly segregating impurity) and silver atoms (a strongly segregating impurity) from the surface in the high-temperature plastic deformation of nickel have been carried out. It has been established that in the high-temperature plastic deformation of nickel, when there are diffusion streams of copper and silver from the surface, there is a reduction in the creep resistance of nickel due to an increase in the contribution of grain-boundary slip to the overall deformation. Two stages, characterized by different values of the rate sensitivity factor m, are observed on the curve of the stress against the rate of deformation over a certain temperature range for each impurity. In the region of deformation rates of sec⁻¹, m≊0.2, and for sec⁻¹, m becomes less than 0.05. Institute of Physics of the Strength and Study of Materials. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 119–125, July, 1997.     

力和扩散机理下外延形貌的演化分析

本文提出了一个新的基于扩散界面的相场模型来描述外延生长中岛的形核、生长及熟化过程. 该模型同时考虑了弹性场、表面能、沉积、扩散、解吸和能量势垒等热力学及动力学过程对表面纳米形貌的影响. 采用经典的BCF模型来描述生长中的扩散形核过程, 而采用一个新的包含弹性应变能的自由能函数, 通过变分得到一个描述多层岛生长的相场方程, 该方法可以有效地描述外延生长中复杂的外延形貌. 采用有限差分格式对非线性耦合方程组进行求解. 数值结果显示, 该模型可以真实地再现外延生长中多层岛结构(即山丘状形貌)的演化过程, 模拟结果与已有实验结果一致. 同时模拟了生长过程中随外延形貌演化而形成的复杂生长应力, 研究表明, 在生长过程中, 岛中存在着复杂的应力分布, 且在岛边界处应力达到局部最大, 这与实验结果定性一致. 此外, 本文的重要发现是, 外延生长中的应力演化明显地影响原子的扩散过程, 当应力存在时, 外延结构变化较无弹性场时变快. 该项研究对理解外延生长中各物理机理的协同作用有重要的指导意义.     

Grain boundary sliding during ambient-temperature creep in hexagonal close-packed metals

Even at ambient temperature or less, below their 0.2% proof stresses all hexagonal close-packed metals and alloys show creep behaviour because they have dislocation arrays lying on a single slip system with no tangled dislocation inside each grain. In this case, lattice dislocations move without obstacles and pile-up in front of a grain boundary. Then these dislocations must be accommodated at the grain boundary to continue creep deformation. Atomic force microscopy revealed the occurrence of grain boundary sliding (GBS) in the ambient-temperature creep region. Lattice rotation of 5° was observed near grain boundaries by electron backscatter diffraction pattern analyses. Because of an extra low apparent activation energy of 20 kJ/mol, conventional diffusion processes are not activated. To accommodate these piled-up dislocations without diffusion processes, lattice dislocations must be absorbed by grain boundaries through a slip-induced GBS mechanism.     

Investigation of grain-boundary diffusion of nickel in molybdenum by auger electron spectroscopy

The dependence of the grain-boundary diffusion coefficient of nickel in molybdenum on annealing temperature was investigated. Possible causes are analyzed for differences in the values of the grain-boundary diffusion coefficients and the activation energies for this process from those obtained by earlier researchers.Institute of the Physics of Strength and Materials Science, Siberian Branch, Russian Academy of Sciences (SO RAN). Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 28–31, July, 1992.     

Anomalous diffusion in two-dimensional potentials with hexagonal symmetry

The diffusion process in a Hamiltonian dynamical system describing the motion of a particle in a two-dimensional (2D) potential with hexagonal symmetry is studied. It is shown that, depending on the energy of the particle, various transport processes can exist: normal (Brownian) diffusion, anomalous diffusion, and ballistic transport. The relationship between these transport processes and the underlying structure of the phase space of the Hamiltonian dynamical system is investigated. The anomalous transport is studied in detail in two particular cases: in the first case, inside the chaotic sea there exist self-similar structures with fractal properties while in the second case the transport takes place in the presence of multilayered structures. It is demonstrated that structures of the second type can lead to a physical situation in which the transport becomes ballistic. Also, it is shown that for all cases in which the diffusive transport is anomalous the trajectories of the diffusing particles contain long segments of regular motion, the length of these segments being described by Levy probability density functions. Finally, the numerical values of the parameters which describe the diffusion processes are compared with those predicted by existing theoretical models. (c) 2000 American Institute of Physics.     

Self-correlation functions for impurity diffusion in hexagonal lattices

Long-range diffusion of the substitutional impurity in the otherwise monoatomic hcp-like lattices (H1 type) via the monovacancy mechanism has been considered within the encounter approximation. A five-frequency model (valid for cubic lattices) extends here naturally into a sixteen-frequency model, leaving fourteen normalized frequencies, the latter describing an anisotropic part of the self-correlation function. Two simplified cases can be distinguished: a self-diffusion being described by a single normalized frequency and a true hcp lattice, where only three normalized frequencies remain independent of each other. A general formalism is discussed and a few examples are evaluated numerically.     

Influence of grain-boundary dynamics on shear and rotational deformation components in the creep of polycrystals

The as-a-whole motion of polycrystal grains with migrating and stationary boundaries is investigated during the creep of lead and lead-based alloys. It is shown that boundary migration promotes grain-boundary slip and fragmentation of regions along the boundaries, and that the effect is not related to differing orientations of the migrating and stationary boundaries. Migrating and stationary boundaries of equal slope were formed in aging alloys as a result of intermittent segregation and coalescence of phases. V. D. Kuznetsov Siberian Physicotechnical Institute, Tomsk State University. Tomsk Branch, Institute of Structural Macrokinetics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 40–45, June, 1998.     

Evolution of grain-boundary ensembles in nickel during boundary migration induced by copper diffusion

The effect of copper diffusion-induced grain-boundary migration on the structure and grain-boundary ensemble in nickel is studied to show that during migration, individual regions of random grain boundaries acquire misorientations corresponding to special boundaries of the Σ3 type. This leads to the formation in nickel of a grain-boundary ensemble with a content of special grain boundaries exceeding 70%.     

Effect of cyclic stresses on the microstructures of hexagonal close packed metals

Slip band extrusions are formed in cadmium, magnesium and titanium, but not in zinc. The extrusions form preferentially in untwinned crystals. Filamentary growths occur at {10¯12} and {11¯21} twin interfaces during cyclic twinning.Possible dislocation interactions at these twin interfaces are described. The dislocation debris produced during cyclic strain in the slip bands and by cyclic twinning is shown to be similar and composed of a high density of dipole loops. It is therefore concluded that the occurrence and distribution of slip band extrusions in metals and the formation of twin boundary filamentary growths can be accounted for by a model based upon the glide of interstitial type dipole loops. Vacancy type loops will then cause crack nucleation in slip bands and deformation twin boundary regions.Twin boundary debris can also cause the observed fragmentation of twins by acting as a barrier to twin boundary movement.The author is grateful to Dr. A. G. Crocker, University of Surrey, for many discussions on the twinning mode in h.c.p. metals and to P. J. E. Forsyth for his interest and encouragement. The paper is published by permission of the Controller, H. M. Stationery Office. Crown copyright is reserved.     

Anomalous hydrodynamic drag due to differential diffusion

The response of a stratified two-component fluid (for example, salt water) to the action of a localized vertical force is considered. If the transport coefficients of two substances (heat and salt) differ considerably, specific disturbances of the buoyancy that influence the hydrodynamic drag of the medium may arise.     

Temperature and orientation dependences of the grain-boundary diffusion coefficient of antimony in copper bicrystals

An investigation is made of the diffusion of antimony through the bulk and along grain boundaries in copper bicrystals containing a symmetric 〈100〉 misorientation boundary with misorientation angles from 20 to 37.2°. The bicrystals are grown by the method of horizontal zone recrystallization. The temperature range for these studies is 480–580 °C, where the solubility of Sb in Cu is about 6 atomic % and practically temperature-independent. The concentration profiles are obtained by x-ray spectral microanalysis, and the grain-boundary diffusion parameters are computed by the method of Whipple and Suzuoka. The orientation dependence of the triple product P=sδD _b (where s is the segregation coefficient, δ the width of the grain boundary, and D _b the grain-boundary diffusion coefficient) is nonmonotonic, with a maximum for the special ∑5 misorientation boundary (36.9°). The effective activation energy for grain-boundary diffusion ranges from ∼70 kJ/mol for ∑5 to140 kJ/mol for general boundaries. Fiz. Tverd. Tela (St. Petersburg) 39, 1153–1157 (July 1997)     

Laws of the deformation and failure of molybdenum in creep with grain-boundary activation by diffusional nickel fluxes

The diffusion of nickel from the surface of polycrystalline molybdenum influences the crack formation and plastic deformation in creep. Investigation shows that diffusional fluxes of nickel from the surface reduce the critical deformation at which the first cracks appear in molybdenum. The contribution of grain-boundary slip to the deformation of molybdenum in creep is considerably increased in the presence of nickel diffusion from the surface as a result of easier crack formation and grain-boundary activation.Institute of Strength Physics and Materials Science, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 16–21, July, 1992.     

Anomalously broad Raman scattering spectrum due to two-magnon excitation in hexagonal YMnO3

A strong and broad Raman scattering (RS) spectrum is observed from two-magnon processes in YMnO3. The spectrum is analyzed by taking account (i) the magnon-exciton interaction and (ii) the magnon-phonon coupling in the intermediate state. Anomalous broadening of the RS is attributed to the large superexchange interaction between manganite ions and subsequent modification of magnons under the presence of the exciton and phonons in the intermediate state.