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. This paper is based on a presentation delivered at the symposium “Activated and Liquid Phase Sintering of Refractory Metals and Their Compounds” held at the annual meeting of the AIME in Atlanta, Georgia on March 9, 1983, under the sponsorship of the TMS Refractory Metals Committee of AIME.     

Modeling of supersolidus liquid phase sintering: I. Capillary force

Prealloyed powders subjected to supersolidus liquid phase sintering (SLPS) exhibit partial melting. A liquid phase forms along the grain boundaries, at the interparticle neck region, or on the particle surface. Densification involves an increase in the liquid volume fraction along with simultaneous coalescence of the particles. A two-particle model is developed that takes into account an increasing liquid content with coalescence, as well as a shape change of the merging particles (initially spher-ical). The variation in capillary force with processing parameters such as temperature and liquid volume fraction give improved predictions over prior models. The model predicts that the capillary force is affected strongly by the amount of liquid phase, wetting angle, and the shape of the coa-lescing particles.     

The critical grain size for liquid flow into pores during liquid phase sintering

A model of grain-liquid mixture containing a spherical pore is analyzed to describe the pore filling during liquid phase sintering. Since the radius of liquid menisci around a pore increases linearly with the grain size, the menisci form a spherical bubble at a critical grain size and the pore is rapidly filled with liquid flowing from numerous menisci at the specimen surface. The values of the critical grain size for pore filling are calculated for various dihedral angles, wetting angles, and liquid contents. Although the predicted critical grain size is subject to errors because of assumptions in the models, the values agree in an order of magnitude with some experimental results. The effect of entrapped gas on pore filling and the expected behavior of irregular pores are also briefly discussed.     

Hysteresis of Capillary Stress in Unsaturated Granular Soil

Constitutive relationships among water content, matric suction, and capillary stress in unsaturated granular soils are modeled using a theoretical approach based on the changing geometry of interparticle pore water menisci. A series of equations is developed to describe the net force among particles attributable to the combined effects of negative pore water pressure and surface tension for spherical grains arranged in simple-cubic or tetrahedral packing order. The contact angle at the liquid–solid interface is considered as a variable to evaluate hysteretic behavior in the soil–water characteristic curve, the effective stress parameter χ, and capillary stress. Varying the contact angle from 0 to 40° to simulate drying and wetting processes, respectively, is shown to have an appreciable impact on hysteresis in the constitutive behavior of the modeled soils. A boundary between regimes of positive and negative pore water pressure is identified as a function of water content and contact angle. Results from the analysis are of practical importance in understanding the behavior of unsaturated soils undergoing natural wetting and drying processes, such as infiltration, drainage, and evaporation.     

Rearrangement densification in liquid-phase sintering

Grain rearrangement has a significant role in sintering densification when a liquid phase forms. Although grains may change shape, bringing the grain centers closer to each other and producing overall densification, this contribution is slow and localized to the grain contacts regions. On the other hand, the movement of individual grains through capillary force effects can provide a burst of rapid densification. To describe the spatial grain arrangement quantitatively, a new parameter is proposed, termed the grain-arrangement factor. An increase in the grain-arrangement factor indicates the microstructure is packing to a higher density. Analysis of the relations between this factor and other microstructure parameters provides an indirect method to measure the state of grain arrangement in liquid-phase sintering. Experiments performed on a tungsten heavy alloy show that the grain-arrangement factor mainly depends on the solid volume fraction and the dihedral angle.     

A theoretical analysis of solution-precipitation controlled densification during liquid phase sintering

Models for solution-precipitation controlled, intermediate stage liquid phase sintering (LPS) have been derived by assuming a tetrakaidecahedron grain geometry with cylindrical pore channels along the grain edges and incorporating the liquid content and dihedral angle by adapting Wray's two phase grain model. The stress distribution of a thin liquid film between the grains is modelled as a hydrostatic squeeze film. The model predicts that a thin viscous liquid film is stable and suppors the normal stress arising from the Laplacian force at the liquid-vapor interface. The derived equations for both diffusion and interface reaction controlled liquid phase sintering show significant differences with respects to Kingery's LPS models, but are in good agreement with those based on liquid phase controlled creep models. Comparative analyses of the derived models indicate that the rate controlling mechanism during solution-precipitation shifts from diffusion to interface reaction control or vice versa as a function of particle size and/ or grain growth.     

Mo对钨基重合金液相定向迁移规律的影响

将93W-4.9Ni-2.1Fe压坯和95(93W-4.9Ni-2.1Fe)-5Mo压坯叠加,在1 500℃下烧结,利用光学金相显微镜观察界面附近的晶粒组织,利用能谱仪(EDAX)进行线扫描分析。结果表明,钼能够细化钨晶粒,但在液相中不是十分稳定,会向不含Mo的样品中迁移,Ni、Fe液相也有向Mo含量高的区域迁移的现象,并且随保温时间延长,迁移现象越明显。将W-Mo-49Ni-21Fe混合粉末铺放在纯钨板上,于1 500℃下烧结,利用数字显微镜测定和观察烧结样品二面角和液相侵入钨板的深度。结果表明,固-液界面张力引起液相向钨板的定向迁移,导致液相中W、Ni、Fe的含量均减少。钼含量越高,体系的二面角越小,固-液界面张力越小,因而定向迁移现象越明显,液相侵入钨-钨晶界越深,同时液相中W、Ni、Fe的含量更低。     

Shrinkage and splitting of microcracks under pressure simulated by the finite-element method

The two-dimensional finite-element method is applied to analyze the shrinkage and splitting of microcracks regularly arranged on or perpendicular to a grain boundary under pressure. Grain-boundary and surface diffusions are coupled by the boundary conditions at the triple point of the microcrack surface and the grain boundary. The shrinkage and splitting processes for the two kinds of microcracks are revealed by detailed finite-element analyses. For the microcrack lying on a grain boundary, it first shrinks to a small void shape, then the void is split by the grain boundary and the two split voids assume a cylindrical shape under the capillary force of the surface. For the microcrack perpendicular to the grain boundary, it is split into two segments by the grain boundary during the early stage of shrinkage. Then, the split microcracks stop shrinking and evolve into two cylindrical channels with a circular section by the capillary force of the surface. These evolution processes are controlled by the applied pressure, microcrack spacing, ratio of grain-boundary diffusion to surface diffusion, and equilibrium dihedral angle, defined by surface and grain-boundary tensions. The influences of these controlled parameters on the evolution processes are numerically clarified based on a great number of finite-element analyses.     

The effect of elastic anisotropy on the migration of intergranular liquid films and the precipitation of a liquid phase in a CoCu alloy

When a Co20Cu (wt%) alloy prepared by liquid phase sintering at 1300°C is heat-treated at 1150°C, the intergranular liquid films and grain boundaries migrate, leaving behind a new solid solution with reduced Cu content. The phenomenon is identical to that observed previously in MoNi. The calculated driving force for the migration is almost equal to the coherency strain energy in the solute diffusion zone ahead of the migrating boundaries. The migrating liquid films show faceting with curved planes and edges. Their shape closely resembles the growth shapes predicted on the basis of the coherency strain energy with anisotropic elastic constants. During the heat-treatment, liquid precipitates form within grains and at grain boundaries, and they also show faceting, which is consistent with orientation dependent coherency strain energy in the diffusion zone around the precipitates.     

Grain boundary migration with precipitation and dissolution of a liquid phase in MoNi alloy

When 85Mo15Ni (by weight) alloys prepared by liquid phase sintering at 1380°C are heat-treated at 1520°C, the grain boundaries and liquid films between the grains migrate, leaving behind them a new MoNi solid solution with Ni content higher than that in the initial solid formed during the liquid phase sintering treatment. The grain boundaries migrating during this discontinuous dissolution of the liquid phase have a flat shape. When the temperature change is reversed by first sintering at 1520°C and subsequently heat-treating at 1380°C, the grain boundaries and liquid films again migrate, with the composition change of the solid reversed. Liquid precipitates form at grain boundaries and migrate with them, their size and total volume increasing during the migration. The grain boundaries have a curved shape and their initial migration rate is considerably higher than that during the discontinuous dissolution. This contrasting migration behaviour between the discontinuous dissolution and precipitation is attributed to the coherency strain energy operating locally on both grain boundary segments and liquid droplets, and to the high mobility of fine liquid droplets.     

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. SU SOK KANG, formerly a student in the Department of Materials Science at the Korea Advanced Institute of Science and Technology     

An analysis of the capillary forces in liquid-phase sintering of spherical particles

The interparticle force due to capillary action of a liquid contact between two solid spheres is shown rigorously to have two contributions, one the surface tension force itself and the other due to the pressure difference caused by surface curvature. Numerical means are used to solve for the shape of the liquid surface and to evaluate this interparticle force as a function of contact angle, volume of liquid, size of sphere, and surface tension. The rigorous solution is then compared to the often-used circle approximation. We also evaluate the effect of neglecting one of the terms in the force equation, as is sometimes done in the literature. The general force relations are then used to draw several practical conclusions concerning liquid-phase sintering of spherical powders.     

Capillary interaction between inclusion particles on the 16Cr stainless steel melt surface

Both in situ observational and theoretical analyses were carried out for inclusion particle behavior on a 16Cr stainless steel melt surface by paying special attention to the phase classification of inclusions and to the differences in interaction due to the type of phase (solid, liquid, or complex). The interaction was attractive between pairs of particles of the same kind, such as between solid-solid, complex-complex, liquid-liquid, or solid-complex particles, but it was repulsive for pairs of particles of different kinds, such as between solid-liquid or complex-liquid particles. As a result, this reverse phenomenon leads to selective interaction among various inclusions. The origin of attraction or repulsion between inclusion particles is the capillary force. This capillary interaction is strongly influenced by the particle size and shape, and by the contact angle of a particle with steel melt; it is less influenced by the particle density and shape, and by the interfacial tension. In particular, the degree of attractive or repulsive force strongly depends on the contact angle of a particle. Thus, some chalcogen elements should strongly affect the interaction of particles.     

Microstructure effect on dihedral angle in liquid-phase sintering

Granular systems with a wetting liquid phase produce an attractive normal force between the solid grains and a radial force that promotes bonding via neck growth. The classic force balance in the neck region relates the energy ratio of the grain boundary and solid-liquid interfaces to the dihedral angle φ as 2γ _SL cos (φ/2)=γ _SS . This relation is only applicable when the neck diameter is much larger than the neck thickness. This article presents a detailed analysis of two grains during liquidphase sintering, refining the linkage between the underlying surface energies and the microstructure and apparent effect of grain size on the neck size.     

The instability of solid-liquid interface in MoNi alloy induced by diffusional coherency strain

In an alloy of 85Mo-15Ni by weight prepared by liquid phase sintering for a long time, the relatively large spherical MoNi grains are in chemical equilibrium with the surrounding liquid matrix and are separated from each other by bulk liquid. When the chemical equilibrium between the grain and the liquid is broken either by heat-treating at a temperature different from that of the sintering or by adding Fe to the liquid, some grain surface zones become convex by reprecipitation of a new equilibrium solid, while others become concave by dissolution of the initial solid solution. An instability of the grain-liquid interface in the form of an undulating structure thus develops. It is demonstrated that the driving force for this solution-reprecipitation process arises from the coherency strain energy in the solute diffusion zone at the dissolving grain surface.     

Analysis of orientation clustering in a directionally solidified nickel-based ingot

Orientation imaging microscopy was used to study the field of lattice orientations in a directionally solidified ingot of nickel-based alloy in order to understand the evolution of grain structure and microtexture as a function of distance from the chilled surface. The lattice field is organized into equiaxed and randomly oriented grains at the chill plane. However, with increasing distance away from the chill plane, the microstructure organizes into increasingly coarse and ramified grain clusters in the region of columnar growth. The clusters comprise sets of grains connected by small-angle grain boundaries. Thus, the clustering of neighboring dendrites reflects a sharing of low-angle misorientations owing to the development of a strong 〈100〉 fiber texture and its concomitant, a profound change in misorientation distribution. The absence of any preferred orientation within a single cluster suggests that the clusters consist of separate grains. The radius of gyration and the fractal dimension have been used to characterize clustering in the microstructure. Clustering was found to increase with distance from the chill plane as the strength of the fiber texture increases. A critical misorientation angle was found at which the largest cluster percolates the microstructure. This critical angle decreases with increasing strength of the fiber texture.     

Capillary forces between spheres during agglomeration and liquid phase sintering

The capillary force due to a wetting liquid between solid particles is responsible for agglomeration and the rearrangement stage of liquid phase sintering. The capillary force has been calculated for several situations using a numerical technique. Included in the calculations are variations in particle size, contact angle, liquid volume, and particle separation. The capillary force obtained from these calculations is more accurate than prior estimates using a circular profile for the interparticle liquid bridge. A large attractive force exists between particles with small contact angles, particle sizes, and liquid volumes. Rupture of the liquid bridge is predicted using an energy analysis. At large contact angles, a zero force condition exists at an intermediate particle separation.     

GCr15轴承钢连铸冷却速率下凝固原位观察

GCr15轴承钢在连铸凝固过程中的组织生长与溶质偏析是碳化物液析的重要诱因,成为产品质量提升的关键.为此,针对国内某钢厂240 mm×240 mm GCr15轴承钢的连铸过程,选取方坯表面下方40、80和120 mm位置处的坯样为研究对象,首先建立二维凝固传热模型,结合红外测温试验,求解它们在糊状区的平均冷却速率,然后...     

The discontinuous precipitation of a liquid phase in MoNi induced by diffusional coherency strain

When a liquid phase sintered MoNi alloy is heat-treated at a temperature lower than that used for sintering where the solid and liquid phases coexist, the liquid films and grain boundaries between the grains migrate, leaving behind a new solid solution somewhat depleted of Ni. Since some liquid is produced during this migration, it resembles a discontinuous precipitation of the liquid phase. It is demonstrated experimentally that the driving force for this discontinuous precipitation arises from the coherency strain produced by Ni atom diffusion out of the grains. When two solute atom species simultaneously diffuse into or out of crystals in a ternary system, the resulting coherency strain depends on the size and concentration of the diffusing atoms and can be varied independently of the free energy of mixing. In particular, the coherency strain can be reduced to zero when the strain effects of the two atomic species exactly cancel each other. In this study, series of 90Mo10Ni alloy (by wt%) have been prepared by liquid phase sintering at temperatures between 1400 and 1520°C in order to produce solid MoNi grains of varying Ni concentration that are in equilibrium with the surrounding liquid matrix. The migration of liquid films and grain boundaries in the sintered specimens is induced by heat-treating them at 1400°C after adding various amounts of Fe to the liquid matrix. The migration does not occur when the estimated coherency strain is close to 0, although the free energy of mixing is finite. This result is a definitive demonstration that the driving force for the steady state migration is the coherency strain energy. The evidence that the grain boundaries exist in the sintered specimens and remain as grain boundaries during the migration is discussed.     

The coalescence phenomenon in liquid-phase sintering in the systems tungsten-nickel-iron and tungsten-nickel-copper

Summary Metallographic studies of W-Ni-Fe and W-Ni-Cu alloys demonstrated that grain growth during the formation of these alloys is affected by two mechanisms: dissolution-deposition and coalescence of pairs and groups of tungsten grains. The rate of the process of merging by sintering, which is governed by the rate of surface diffusion of atoms, may be expected to be commensurate to the rate of particle growth as a result of material transport through the liquid phase.However, the role of the process of merging by sintering will depend on the system being sintered, in particular on the composition of the low-melting constituent and, consequently, on its melting point, the solubility of the solid in the liquid phase (degree of supersaturation), angle of wetting, etc. Naturally, by changing the arithmetic mean radius of particles in a system, the coalescence process may change the character of the relationship proposed by Greenwood. For this reason, the regularity of particle growth, particularly under conditions of equilibrium composition of the liquid-phase constituent systems, will require further thorough study.