The Shape of the Moving Grain Boundary in the Reversed-Capillary Technique Under Consideration of the Drag Effect

The shape of the curved part of the migrating grain boundary driven by capillary forces was studied for the reversed-capillary bicrystal technique. A comparison of experimentally observed and theoretically calculated shapes showed good agreement when the drag effect by mobile obstacles was taken into account. So far previous studies dealing with the reversed-capillary technique have not considered the drag effect. Consequently, they assume a scaling behavior of the shape of the moving grain boundary. In this study it is shown that this assumption generally is not possible for the reversed-capillary technique. Furthermore, it is shown that the geometry factor used for determination of the driving force is dependent on the displacement. Problems specific to the reversed-capillary technique due to the drag effect are discussed. The analysis of the boundary shape is presented as a tool to distinguish free and dragged motion.     

Effect of Grain Boundary Segregation and Migration on Diffusion Profiles: Analysis and Experiments

In many experimental studies, curved penetration profiles are observed for grain boundary diffusion performed in the B kinetics regime in contrast to the shape expected from the solutions of the second Fick's equation. To explain these curvatures the effects of grain boundary structure, grain boundary migration, and grain boundary segregation have been successively proposed in the literature. Using previous data for Cu–Ag and Cu–Ni and new ones on Cu–Fe and Cu–Zn systems we will show how it is possible to separate all these possible contributions and how, knowing the true origin of the curvature, one can deduce much quantitative information impossible (or very difficult) to obtain by other techniques.     

Grain Boundary Motion during Ag and Cu Grain Boundary Diffusion in Cu Polycrystals

Grain boundary (GB) motion in high-purity Cu material (5N8 and 5N Cu) is investigated using the results of radiotracer GB diffusion measurements with tracers exhibiting fundamental differences in the solute-matrix atom interactions. The results on GB solute diffusion of Ag (revealing a miscibility gap in the Ag-Cu phase diagram) and Au (forming intermetallic compounds with Cu) in Cu and on Cu self-diffusion are analyzed.The initial parts of the Ag and Cu penetration profiles turned out to be substantially curved. The profile curvature is explained via the effect of GB motion during ^110m Ag and ⁶⁴Cu GB penetration. The activation enthalpies of GB motion in these two independent measurements occurred to be very close, 95 and 103 kJ/mol, respectively. Moreover, these values turn out to be close, but still somewhat larger than the activation enthalpy of Cu GB self-diffusion in Cu material of the same very high purity, Q ^Cu _gb = 72 kJ/mol. Although tracer diffusion measurements of Au GB diffusion in Cu yielded only limited information on GB motion, the absolute values of GB velocities are consistent with those calculated from the Ag and Cu GB diffusion data.     

Grain Boundary Migration in Metals: Recent Developments

Current research on grain boundary migration in metals is reviewed. For individual grain boundaries the dependence of grain boundary migration on misorientation and impurity content are addressed. Impurity drag theory, extended to include the interaction of adsorbed impurities in the boundary, reasonably accounts quantitatively for the observed concentration dependence of grain boundary mobility. For the first time an experimental study of triple junction motion is presented. The kinetics are quantitatively discussed in terms of a triple junction mobility. Their impact on the kinetics of microstructure evolution during grain growth is outlined.     

Grain Boundary Migration in Ceramics

During ceramic fabrication, densification processes compete with coarsening processes to determine the path of microstructural evolution. Grain growth is a key coarsening process. This paper examines grain boundary migration in ceramics, and discusses the effects of solutes, pores, and liquid phases on grain boundary migration rates. An effort is made to highlight work in the past decade that has contributed to and advanced our understanding of solute drag effects, pore-boundary interactions, and the role of liquid phases in grain growth and microstructural evolution. Anisotropy of the grain boundary mobility, and its role in the development of anisotropic (anisometric) microstructures is discussed as it is a central issue in recent efforts to produce ceramic materials with new combinations of properties and functionality.     

Grain Boundary Diffusion and Linear and Non-Linear Segregation of Ag in Cu

Ag grain boundary (GB) diffusion was measured in the Cu-0.2at%Ag alloy in a wide temperature range from 473 to 970 K. The direct measurements of Ag GB diffusivity D ^alloy _gb under conditions of the Harrison C regime revealed that D ^alloy _gb is almost identical to D ^pure _gb determined earlier for Ag diffusion in high-purity Cu (Divinski, Lohmann, and Herzig, 2001). The penetration profiles determined in the Harrison B regime showed a complex, multi-stage shape. This diffusion behavior can be rationalized assuming that besides GBs significantly covered by segregated Ag atoms, some fraction of GBs remains almost free from Ag atoms in the studied temperature interval. The total amount of pure GBs drastically decreases with decreasing temperature. This hypothesis was proven by measurements of Ag GB diffusion in Cu near 5 bicrystals, which allowed us to analyze in detail the non-linear segregation of Ag in Cu GBs.     

Criteria for the Occurrence of the Diffusion-Induced Grain Boundary Migration

Recent experimental data on diffusion-induced grain boundary migration (DIGM) are reviewed. For the case of the coherency strain driving force, quantitative criteria for the occurrence of DIGM are suggested, which establish the relationship between the net driving force for grain boundary migration, the diffusivity in the vicinity of the grain boundary, the enthalpy of the grain boundary segregation, the misfit parameter for the solute atoms in the matrix and the solubility of the diffusing element in the matrix. It is shown that an upper limit for the grain boundary velocity during DIGM exists due to the solute drag effect.     

Correlation of Grain Boundary Character with Wetting Behavior

Wetting of 975 grain boundaries (GB's) by liquid Cu in an iron-based alloy has been studied as a function of the five macroscopic degrees of freedom (DoF's) of grain boundary character. In addition, models of GB energy in terms of all five DoF's, and of anisotropic solid-liquid interfacial energy have been developed. The experimentally observed wetting behavior is interpreted in terms of the model, and it is shown that reasonable overall agreement is obtained between experimental results and model predictions.     

Segregation Effects at a High-Angle Twist Boundary in ZnO

Ab initio density functional plane-wave pseudopotential calculations were performed for a = 7 ( = 21.79°) [0001] twist boundary in ZnO with and without the presence of Sb impurities. The segregation energies revealed a significant driving force for segregation and it was shown that the formation of an Sb monolayer was favoured. Decreased coordination in the boundary core suggested a trend towards the formation of an intergranular phase. The impurity states caused by the monolayer were located within the band gap and higher in energy relative to the state produced by a single impurity. Charge transfer to the Sb monolayer was observed indicating a possible enhancement of the grain boundary potential barrier.     

Solute segregation at grain boundaries

This feature article summarizes the present art and science of grain boundary segregation from the viewpoint of the authors activities in this field. In the part on equilibrium segregation, fundamental effects on grain boundary segregation are discussed such as the nature of the solute/matrix binary system, presence of additional elements, temperature, grain boundary orientation and type of interface. In addition, the predictive capabilities of grain boundary segregation diagrams are outlined. The present models of segregation kinetics are reviewed and discussed in connection with recent experiments. The last part of the paper is focussed on the most important consequences of grain boundary segregation, i.e., grain boundary cohesion and fracture.     

The Effect of Triple Junctions on Grain Boundary Motion and Grain Microstructure Evolution

The theory of steady state motion of grain boundary sytems with triple junctions and the main features of such systems are considered. A special technique of in-situ observations and recording of triple junction motion is introduced, and the results of experimental measurements on Zn tricrystals are discussed. It is shown, in particular, that the described method makes it possible to measure the triple junction mobility. It was found that the measured shape of a moving half-loop with a triple junction agrees with theoretical predictions. A transition from triple junction kinetics to grain boundary kinetics was observed. This means that triple junctions can drag boundary motion. It is demonstrated that the microstructural (granular) evolution is slowed down by triple junction drag for any n-sided grain. The second consequence pertains to six-sided grains. For a boundary system with dragging triple junctions there is no unique dividing line between vanishing and growing grains with respect to their topological class anymore, like n = 6 in the Von Neumann-Mullins relation.     

Grain Boundary Diffusion and Segregation in Interstitial Solid Solutions Based on BCC Transition Metals: Carbon in Niobium

Bulk and grain boundary (GB) diffusion of ¹⁴C in Nb has been studied by the radiotracer serial sectioning technique. B and C kinetic regimes were realized for GB diffusion in the temperature range from 800 to 1173 K. The values of P = sD _gb, D _gb and s follow the Arrhenius dependencies: P = 5.15 × 10^–15 exp[–(83.1 kJ/mol)/RT] m³/s (973–1173 K), D _gb = 2.3 × 10^–6 exp[–(133.0 kJ/mol)/RT] m²/s (800–950 K), and s = 4.7 exp[(49.9 kJ/mol)/RT].The increase in the GB diffusion compared with self-diffusion is very large despite the probable retardation effect due to the strong segregation.The results for GB diffusion of C in Nb as well as for other interstitial solutes (P, S) in bcc transition metals (- Fe, Mo) are discussed in the framework of the transition state theory. It is assumed that GB segregation decreases the energy of the ground state whereas the change in the diffusion mechanism (e.g. from vacancy to interstitial) leads to a strong decrease of the transition state energy. This change in the diffusion mechanism results in a fast GB diffusion of interstitial solutes in spite of their large tendency to segregate to GBs.     

Grain Boundary Grooving as an Indicator of Grain Boundary Phase Transformations

The atomic force microscopy (AFM) was used to study the grain boundary (GB) groove profiles far away from the melting temperature T _m. It is shown that AFM allows one to measure the temperature dependence of the GB energy in a rather broad temperature interval (from 0.85 T _m to T _m). The GB energy and GB segregation of Bi were measured at 1123 K in the interval of the Bi bulk concentration x ^v _Bi from 5 to 140 ppm Bi. The transition from monolayer to multilayer adsorption is observed for the 19a GB at 1123 K and x ^v _Bi = 60 at. ppm Bi. At the same point (1123 K and x ^v _Bi = 60 at. ppm Bi) a discontinuity of the first derivative of the GB energy is observed. These features were explained using the model of GB prewetting phase transformation developed previously.     

The Lattice Model for Addressing Phenomenological Diffusion Problems Associated with Grain Boundaries

Mapping a phenomenological diffusion problem onto a lattice permits lattice-based random walk theory to address the problem. The solution is generally carried out using Monte Carlo methods. This paper reviews the substantial progress that has been made with this method for tracer diffusion associated with grain boundaries.     

Correlation of Grain Boundary Character with Wetting Behavior

Wetting of grain boundaries (GB's) by liquid Cu in an Fe-30wt%Mn-10wt%Cu alloy has been studied as a function of the five macroscopic degrees of freedom (DoF's) of grain boundary character. These were chosen to consist of two grain boundary normals (or bounding planes) and a twist angle. The five DoF's of 975 GB's were determined by electron backscattering patterns and serial sectioning, after annealing at 1120°C, and each GB was categorized as being either wet, dry, or mixed (i.e. partly wet and partly dry). Interpretation of the wetting behavior by means of a model of GB energy, which includes consideration of the five macroscopic DoF's, led to correct predictions of wet and dry behavior in 80% of the GB's studied.     

Anisotropy of P Grain Boundary Segregation in a Rapidly Solidified Fe-0.6wt%P Alloy

P grain boundary segregation in an Fe-0.6wt%P alloy quenched from the melt was quantified by X-ray Mapping (XRM) in a Scanning Transmission Electron Microscope (STEM). The misorientation across the boundaries was determined by using ACT (Automatic Crystallography for TEM (Transmission Electron Microscopy)) and CBED (Convergent Beam Electron Diffraction). A significant range of the degree of P segregation to individual grain boundaries was found. Combination of chemical and structural studies provides evidence that P segregation to low-angle grain boundaries is reduced.     

Grain Boundary Wetting Statistic in Zn/Ga System and its Application to Grain Boundary Energy Spectrum Estimation

The grain boundary statistic in zinc polycrystals in contact with saturated Ga(Zn) melt has been studied. The misorientation angle distributions for zinc thin foil and zinc plates were obtained. The influence of the misorientation angle value on the wetting probability p of grain boundaries was observed. The grain boundary energy distribution parameters were obtained by using the p() relationship. The dihedral angles in triple lines of non-wetted zinc samples were also measured and their distribution was used to obtain the grain boundary energy distribution function. The parameters obtained by two different methods correspond to one other.     

Co-Segregation Effects on Boundary Migration

We analyze the effect of co-segregation on the mobility of grain boundaries within the framework of the impurity drag theory originally proposed by Cahn and Lücke and Stüwe for an ideal solution. The new derivation extends this model to the case where there are two types of impurities (or three components in the alloy). Since the resultant expression for the boundary mobility is complicated, numerical solutions were obtained for several cases to show how co-segregation affects the boundary mobility. Depending on the relative diffusivities of the two impurities which are both attracted to the boundary, the mobility may either increase or decrease with increasing concentration of one of the impurities. When one of the impurities is attracted to the boundary and the other repelled from the boundary, increasing the concentration of the attractive impurity can lead to a sharp decrease in the boundary mobility.