Duk N. Yoon

Effect of dihedral angle on the morphology of grains in a matrix phase

Minimum interface energy configurations of a uniformly intermixed grain-matrix aggregate are determined for various dihedral angles and matrix contents by numerical analysis of a model which consists of a rhombic dodecahedron grain in contact with matrix at its curved surfaces along truncated edges and corners. For dihedral angles, Φ, greater than 90 deg, the total interface energy,E, increases monotonically with the matrix volume fraction,Vm. For Φ= 0 deg,E decreases withVm until the grains become spherical atVm = 26 pct. For 0 deg Φ ≤ 75 deg,E vs Vm curves show the minima which represent the stable configurations to be obtained whenVm can be freely varied. For Φ ≤ 60 deg, the matrix is always continuous along the grain edges. For Φ 75 deg, the matrix becomes separated at the grain corners below certain critical values ofVm. The contiguity decreases monotonically withVm. The slope ofE vs Vm curve is shown to be an effective pressure on the specimen surface, which represents the driving force for changing the grain configuration with a corresponding change ofVm while keeping the grain volume constant. The implications of these results on solid state sintering, liquid phase sintering, and the penetration of liquid into liquid phase sintered alloys are discussed. Finally, the results of a previous analysis by Beere are shown to disagree with the present work for systems with low dihedral angles apparently because of inaccuracy in his calculation.

Coarsening of tungsten grains in liquid nickel-tungsten matrix

In sintered W-Ni alloys with 1,7, and 30 wt pct Ni the tungsten grain growth in liquid matrix at 1540°C was investigated. The observed grain size distributions and growth rate are compared with the theoretical predictions of Wagner, Lifshitz and Slyozov, Lay, and Ardell. In the 70 pct W-30 pct Ni alloy the tungsten particles settled to the bottom of the specimens immediately upon melting of the matrix, but the spherical grain shape is maintained during the initial stage of annealing. In these specimens the linear intercept distribution of the grains agrees with the prediction of the LSW (Lifshitz, Slyozov, and Wagner) theory for the reaction controlled growth mechanism. On the other hand the growth rate appears to follow the t1/3 law predicted for the diffusion controlled mechanism. These results are consistent with Lay and Ardells theory in which the concentration gradient around grains is inversely proportional to the average grain size in the limit of small matrix fraction. In the alloys with 1 and 7 pct Ni a meaningful comparison of the observed linear intercept distribution of the grains with theoretical predictions is difficult because of grain contact flattening due to densification. The grain growth is larger with less matrix fraction in the specimens and this result provides an evidence for the diffusion controlled grain growth during the liquid phase sintering of this alloy.

Kinetics of grain coarsening during sintering of Co-Cu and Fe-Cu Alloys with low liquid contents

The coarsening of grains immersed in varying amount of liquid matrix is investigated in Fe-Cu and Co-Cu alloys at the liquid phase sintering temperatures. Specimens containing 20, 30, and 50 wt pct Cu have been prepared by compacting and sintering mixtures of fine powders. With 50 wt pct of Cu, spherical grains are dispersed in the liquid matrix. With 20 wt pct of Cu, anhedral grains are in contact with the neighbors across grain boundaries or thin liquid films, and the liquid matrix forms continuous prisms along the three grain contacts. The form of the rate law for grain coarsening at all compositions agrees with predictions of the diffusion controlled Ostwald ripening theories of Lifshitz, Slyozov, Wagner, and others. The coarsening rate also increases with decreasing matrix content. The activation energy for grain coarsening does not vary with specimen composition. Therefore, the rate controlling mechanism for coarsening of the anhedral grains in contact with each other appears to be the solution and reprecipitation of solute atoms by diffusion through the liquid matrix.

A critical test for the coherency strain effect on liquid film and grain boundary migration in MoNi(CoSn) alloy

Abstract A critical experiment has been performed to test the coherency strain hypothesis for the chemically induced migration of liquid films and grain boundaries. The liquid films and grain boundaries in liquid phase sintered 95Mo-5Ni alloys migrate when Co is added to the liquid matrix. Behind the migrating boundaries form MoNiCo solid solutions. The migration also occurs when Sn is added to the liquid matrix. Because of the diluting effect of Sn, the Ni concentration in the solid formed behind the migrating boundaries is lower than that in the initial MoNi alloy. By adding both Co and Sn to the liquid matrix at different ratios, the coherency strain in the diffusion zone ahead of the moving boundaries can be varied from negative to positive. When the coherency strain is 0, the migration velocity becomes 0, although the free energy of mixing is finite. The results show definitively that the driving force for the liquid film and grain boundary migration is the coherency strain energy as proposed by Hillert.

Pore filling process in liquid phase sintering

Models for liquid flow into isolated pores during liquid phase sintering are described qualitatively. The grains are assumed to maintain an equilibrium shape determined by a balance between their tendency to become spherical and a negative capillary pressure in the liquid due to menisci at the specimen surface and the pore. With an increase of grain size, the grain sphering force decreases while the radius of liquid menisci increases to maintain the force equilibrium. When grain growth reaches a critical point, the liquid menisci around a pore become spherical and the driving force for filling the pore rapidly increases as liquid flows into it. The critical grain size required for filling a pore increases linearly with pore size. Experimentally, filling of isolated pores has been investigated in Fe-Cu powder mixture after liquid phase sintering treatment and after dipping into a molten matrix alloy. The observed pore filling behaviors agree with the qualitative predictions based on the models. In Fe-Cu alloy, pore filling is terminated by gas bubbles formed in liquid pockets.

The grain boundary migration induced by diffusional coherency strain in MoNi alloy

Abstract The hypothesis of coherency strain energy as the driving force for chemically induced grain boundary migration (CIGM) has been tested in an 85Mo-15Ni alloy prepared by liquid phase sintering. When Co and Sn is added to the liquid phase sintered specimens, CIGM occurs and a coherency strain is expected to be produced at the growing grains due to the solute diffusion from or to the grain boundaries. Under a constant driving force the average CIGM distance increases linearly with heattreatment time. When Co and Sn are simultaneously added at different ratios, the coherency strain δ0 is expected to vary from negative to positive, and the average CIGM rate is observed to vary nearly parabolically with the estimated coherency strain δ0, becoming 0 in the range where δ0 is 0. The result shows definitively that the coherency strain energy is the driving force. The conditions under which the coherency breaks and hence no CIGM occurs are displayed by a coherency map.

Coarsening behaviour of Mo grains dispersed in liquid matrix

Abstract In a 85Mo-13.5Ni-1.5Fe alloy by wt%, the etch boundaries formed during cyclic heattreatment at the liquid phase sintering temperature of 1430°C have revealed the growth pattern of individual grains. The isolated grains grow in a nearly concentric pattern in agreement with the solution-reprecipitation process through the liquid matrix, and the observed growth rates of the individual grains are also consistent with the theoretical predictions of Ostwald ripening. The grain boundaries between some grains in contact migrate to the direction of the smaller grains, and the rate is expected to be determined by the movement of the grooves formed at the junctions of die grains and the matrix, which is in turn dependent on solution-reprecipitation through the matrix. The overall coarsening process is thus shown to be determined by the solution-reprecipitation through the matrix.

Chemically induced migration of liquid film in W-Ni-Fe alloy

Abstract The rate of chemically induced migration of liquid films analogous to DIGM is shown to vary with the amount of the solute atom added. Molten Ni-Fe films between spherical W particles or W-Ni grains formed by liquid phase sintering have been observed to migrate during heat-treatment at 1550°C, and the migration rate increases with the amount of Fe added until the total Fe Ni ratio exceeds about 2 3 by weight. The result is attributed to increasing Fe concentration and, hence, increasing coherency strain energy in thin diffusion layer on the surface of retreating W or W-Ni grains. Upon prolonged heat-treatments, the curvature of liquid films increases sufficiently to cause a reversal of their migration.

An analysis of the surface menisci in a mixture of liquid and deformable grains

The capillary force due to liquid menisci at the surface of a mixture of deformable grains and a limited amount of liquid (exemplified by liquid phase sintered alloys) is analyzed. Geometrical models for the grains and the menisci at the specimen surface are described. The menisci curvature required to keep the grains in the anhedral (contact flattened) shape with limited liquid content is calculated from the condition that the capillary force is counterbalanced by the sphering force of the grains. The radius of the menisci at equilibrium increases with liquid content. Its dependence on the dihedral angle, on the wetting angle, and on the ratio of the interfacial energies between the liquid-vapor and solid-liquid phases is also described. The grain-meniscus system maintains a shape geometrically similar with respect to change of grain size; hence, the meniscus radius increases in proportion to the grain radius. It is proposed that the difference between the capillary force and the sphering force is the meaningful driving force for grain shape accommodation during liquid phase sintering. Finally, some experimental evidence supporting the results of these analyses is discussed.

The effect of curvature on the grain boundary migration induced by diffusional coherency strain in mo-ni alloy

Abstract When a liquid phase sintered Mo-Ni alloy is heat-treated at 1400°C after replacing the liquid matrix with a Cu melt, the grain boundaries between some grains migrate, producing a Ni depleted Mo-Ni solid solution behind them. The phenomenon is same as those commonly referred to as DIGM with the Cu melt acting as the sink for Ni atoms. When Fe of 1% by weight is added to the Cu melt, the grain boundaries do not migrate, because the compressive coherency strain produced by Ni diffusion from the lattice is exactly compensated by the tensile strain due to the Fe diffusion into it. The diffusional coherency strain energy is thus shown to be the driving force for the grain boundary migration. Because Mo is insoluble in liquid Cu, the grain boundaries are pinned at the grooved ends. The grain boundary curvature thus increases during the migration, causing a migration reversal and consequently an oscillatory motion. The observed critical curvature for the migration reversal falls closely into the range predicted on the basis of the generation of misfit dislocations when the migration velocity decreases to a critical value because of the curvature. The reversal of the grain boundary migration resulting in an oscillatory motion is thus shown to be a natural consequence of the coherency strain hypothesis for the driving force if the inhibiting effect of the grain boundary curvature is taken into account.