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.     

Effect of entrapped inert gas on pore filling during liquid phase sintering

The effect of an inert gas entrapped in isolated pores on liquid flow into them during liquid phase sintering has been studied. An analysis of the balance between the capillary pressure of the liquid menisci and the gas pressure shows that the entrapped gas delays the pore filling and produces bubbles. If the gas pressure exceeds a critical level, the pores remain intact and the critical point for their filling will never be reached. These predictions are confirmed by experimental observations on large spherical pores produced artificially in an Fe-Cu alloy. Argon gas is trapped in the pore by first sintering in Ar-H₂ mixture gas and then in H₂ after the isolated pores are formed. The entrapped inert gas of even low pressure is thus shown to cause a substantial porosity in liquid phase sintered specimens. Formerly a Doctoral Student at the Korea Advanced Institute of Science and Technology.     

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.     

Microstructural change during liquid phase sintering of W−Ni−Fe alloy

The changes of bulk density and microstructures during heating and liquid phase sintering of 98W-1Ni-1Fe compacts prepared from 1 and 5 μm W powders have been observed in order to characterize the densification behavior. The compact prepared from a fine (1 μm) W powder begins to densify rapidly at about 1200°C in the solid state during heating, attaining about 95 pct density upon reaching the liquid phase sintering temperature of 1460°C. The compact prepared from a coarse (5 μm) W powder begins to densify rapidly at about 1400°C in the solid state, attaining about 87 pct density upon reaching the liquid phase sintering temperature. Thus, the skeleton of grains is already formed prior to liquid formation. During the isothermal liquid phase sintering, substantial grain growth occurs, and the liquid flows into both open and closed pores, filling them sequentially from the regions with small cross-sections. The grains subsequently grow, into, the liquid pockets which have been formed at the pore sites. The sequential pore filling by first liquid thus is shown to be the dominant densification process during the liquid phase sintering of this alloy, as has been demonstrated earlier with spherical model pores and as predicted theoretically.     

Coarsening of cobalt grains dispersed in liquid copper matrix

Coarsening of spherical Co-rich grains dispersed in Cu-rich liquid matrix is investigated. The specimen compositions are 50 pct Co-50 pct Cu, 40 pct Co-60 pct Cu, and 30 pct Co-70 pct Cu by weight. The annealing temperatures have been varied between 1150 and 1300 °C. The specimens have been prepared by usual powder metallurgy technique from fine Co and Cu powders. Due to the equal density of Co and Cu, the Co-rich grains remain uniformly dispersed in the liquid matrix. The increase of average grain size with annealing time,t, follows closely thet ^1/3 law predicted for diffusion controlled mechanism by Lifshitz, Slyozov, Wagner (LSW) and Ardell. The observed increase of the growth rate with increasing solid grain fraction is a clear evidence for diffusion controlled mechanism. The linear intercept distribution of the grains agrees closely with the predictions for reaction controlled growth in LSW theory, but the result is also consistent with Ardell’s prediction that when the grains grow with small inter-grain distance under diffusion control, the grain size distribution is almost identical to that of the reaction controlled growth in LSW theory. The estimated values of the diffusion constant and its activation energy agree in order of magnitude with the typical values for diffusion in liquid metal. Formerly a student in the Department of Materials Science at the Korea Advanced Institute of Science     

The contiguity of liquid phase sintered microstructures

Contiguity is a measure of the dispersed phase contact area in a composite microstructure and is particularly important to the properties of liquid phase sintered materials. For an assumed spherical geometry, the contiguity is calculated for various interfacial energies, grain size ratios, and volume fractions of solid phase. The volume fraction solid is linked to the dihedral angle to indicate conditions where grain shape accommodation is necessary. The effect of a distribution in solid phase grain sizes is to lower slightly the contiguity from the monosized grain value. Coalescence is linked to the occurrence of curved boundaries at intergrain contacts involving differing grain sizes. The results are correlated to prior observations on cemented carbides.     

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.     

Abnormal growth of faceted (WC) grains in a (Co) liquid matrix

If the grains dispersed in a liquid matrix are spherical, their surface atomic structure is expected to be rough (diffuse), and their coarsening has been observed to be controlled by diffusion in the matrix. They do not, furthermore, undergo abnormal growth. On the other hand, in some compound material systems, the grains in liquid matrices are faceted and often show abnormal coarsening behavior. Their faceted surface planes are expected to be singular (atomically flat) and therefore grow by a defect-assisted process and two-dimensional (2-D) nucleation. Contrary to the usual coarsening the-ories, their growth velocity is not linearly dependent on the driving force arising from the grain size difference. If the growth of the faceted grains occurs by 2-D nucleation, the rate is expected to increase abruptly at a critical supersaturation, as has been observed in crystal growth in melts and solutions. It is proposed that this growth mechanism leads to the abnormal grain coarsening. The 2-D nucleation theory predicts that there is a threshold initial grain size for the abnormal grain growth (AGG), and the propensity for AGG will increase with the heat-treatment temperature. The AGG behavior will also vary with the defects in the grains. These predictions are qualitatively confirmed in the sintered WC-Co alloy prepared from fine (0.85-Μm) and coarse (5.48-Μm) WC powders and their mixtures. The observed dependence of the AGG behavior on the sintering temperature and the milling of the WC powder is also qualitatively consistent with the predicted behavior.     

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 t^1/3 law predicted for the diffusion controlled mechanism. These results are consistent with Lay and Ardell's 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. Formerly a student in the Department of Materials Science at the Korea Advanced Institute of Science, Seoul, Korea. On leave at the Max-Planck-Institut für Metallforschung in Stuttgart, West Germany.     

The role of pore evolution during supersolidus liquid phase sintering of prealloyed brass powder

ABSTRACT

The aim of this research is to study the pore structure as well as to assess the liquid phase sintering behaviour of Cu-28Zn powder specimens at different green density levels and temperatures. For this purpose, samples were compacted to obtain six different green densities and then sintered at 870°C, 890°C and in part at 930°C for 30?min. The results revealed that the spherical pores which are formed inside the grains can be swept by grain boundaries due to grain growth and join to primary pores so that secondary intragranular pores are eliminated and intergranular pores enlarged at higher temperatures. Also, the pores move upwards to the top of sample due to buoyancy forces. The role of pore structure in distortion is more tangible at higher temperatures (930°C) so that O-shape and X-shape distortions were observed at high and low green density samples, respectively.     

细粒级铁矿粉对烧结液相和矿结构的影响

利用基础烧结设备检测了细粒级铁矿粉同化速度、流动能力,并通过微型烧结杯模拟料层下部单元点烧结过程的方法来研究配加15%细粒级矿粉的烧结矿结构变化,有效分析了3种细粒级矿粉在烧结时的液相行为及对烧结矿结构和性能的影响。通过比较生产用混匀矿与配加质量分数为15%的A、B、C粉的烧结矿结构表明:A粉有利于减少烧结矿内部孔洞的尺寸,减少核颗粒和液相间较大孔洞的数量,并能促进针铁矿发展;B粉会增加烧结矿内部大孔洞,增加柱状或片状铁酸钙的生成;C粉同化速度慢,液相流动能力差,粘结效果差,会使液相与核颗粒间孔洞尺寸和数量增加。烧结杯试验结果表明:在生产用混匀矿中使用质量分数为15%的A粉,烧结矿的转鼓指数提高2.94%,低温还原粉化指数(RDI)降低3.37%。     

Quantitative characterization of microstructures of liquid-phase-sintered two-phase materials

Many powder metallurgy materials have a common microstructure character—spherical or equiaxed particles embedded in a matrix. This article presents an analytical approach that establishes relationships between a broad range of three-dimensional (3-D) microstructure parameters and two-dimensional (2-D) measurements for these materials. Specifically, the grain coordination number, measured dihedral angle, connectivity, and contiguity are directly related to the solid volume fraction, interfacial energies (equilibrium dihedral angle), and grain size. The volume fraction, the equilibrium dihedral angle, and the grain sizes are treated as independent variables. Other microstructural parameters can be expressed as functions of these independent variables. Results show that when the mean grain size is smaller than a critical value, these microstructure parameters change rapidly as the grain grows during processing at high temperatures. When the mean grain size is larger than a critical value, these microstructure measurements approach corresponding stable values.     

Molecular dynamics and order of microconfined liquid crystals

A new technique based on the dipolar-correlation effect was applied in combination with field-cycling-relaxometry to study ordering effects and slow director fluctuations in a nematic liquid crystal confined in porous glasses. Both methods demonstrate a strong influence of geometrical confinements on the distribution of director fluctuation modes. The mean-squared fluctuation estimated from the dipolar-correlation effect decreases exponentially with decreasing pore diameter. The critical mean pore size for the onset of bulk behaviour was found to be of the order of 120 nm. Frequency dependences of spin-lattice relaxation times exhibit sudden sharp deviations from the square root law at frequencies below the MHz-range. These changes are assumed to reflect the lack of long wavelength fluctuations in the spectrum of director fluctuation modes due to finite pore sizes.     

Bubble formation during horizontal gas injection into downward-flowing liquid

Bubble formation during gas injection into turbulent downward-flowing water is studied using high-speed videos and mathematical models. The bubble size is determined during the initial stages of injection and is very important to turbulent multiphase flow in molten-metal processes. The effects of liquid velocity, gas-injection flow rate, injection hole diameter, and gas composition on the initial bubble-formation behavior have been investigated. Specifically, the bubble-shape evolution, contact angles, size, size range, and formation mode are measured. The bubble size is found to increase with increasing gas-injection flow rate and decreasing liquid velocity and is relatively independent of the gas injection hole size and gas composition. Bubble formation occurs in one of four different modes, depending on the liquid velocity and gas flow rate. Uniform-sized spherical bubbles form and detach from the gas injection hole in mode I for a low liquid speed and small gas flow rate. Modes III and IV occur for high-velocity liquid flows, where the injected gas elongates down along the wall and breaks up into uneven-sized bubbles. An analytical two-stage model is developed to predict the average bubble size, based on realistic force balances, and shows good agreement with measurements. Preliminary results of numerical simulations of bubble formation using a volume-of-fluid (VOF) model qualitatively match experimental observations, but more work is needed to reach a quantitative match. The analytical model is then used to estimate the size of the argon bubbles expected in liquid steel in tundish nozzles for conditions typical of continuous casting with a slide gate. The average argon bubble sizes generated in liquid steel are predicted to be larger than air bubbles in water for the same flow conditions. However, the differences lessen with increasing liquid velocity.     

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.     

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     

Quantitative determination of topological and metric properties during sintering of copper

Quantitative paths of microstructural change, represented as a variation of topological and metric properties with pore volume fraction, were experimentally determined by applying quantitative microscopy to sequences of samples sintered without compaction from two size fractions of spherical copper powder, and one size fraction of dendritic copper powder. The two spherical size fractions followed paths of microstructural change during sintering that were identical except for a scale factor. The connectivity of the pore network first increased slightly, then decreased, reaching zero at a pore volume fraction (V _V ) of about 0.08. Isolated pores begin to appear atV _V = 0.20, and increased in number. The area of the pore-solid interface at first decreased slowly, then more rapidly and ultimately linearly with pore volume fraction, as has been reported in other systems. Total curvature of pore-solid interface decreased from the positive value characteristic of the loose powder stack to a negative value, passed through a minimum, and increased toward zero as full density is approached. The area of grain boundary initially increased slowly, as interparticle contacts grew; at aboutV _V = 0.15, grain growth set in, and the grain boundary area decreased, as the mean grain intercept rapidly increased with densification. The dendritic powder had a highly irregular surface shape, and consequently a loose stack structure containing more than 90 pct porosity. The path that it followed was qualitatively, but not quantitatively, similar to that observed for the spherical powders. These observations are discussed in terms of the unit geometric processes that dominate each of the three stages of loose stack sintering.     

Quantitative determination of topological and metric properties during sintering of copper

Quantitative paths of microstructural change, represented as a variation of topological and metric properties with pore volume fraction, were experimentally determined by applying quantitative microscopy to sequences of samples sintered without compaction from two size fractions of spherical copper powder, and one size fraction of dendritic copper powder. The two spherical size fractions followed paths of microstructural change during sintering that were identical except for a scale factor. The connectivity of the pore network first increased slightly, then decreased, reaching zero at a pore volume fraction (V _V ) of about 0.08. Isolated pores begin to appear atV _V = 0.20, and increased in number. The area of the pore-solid interface at first decreased slowly, then more rapidly and ultimately linearly with pore volume fraction, as has been reported in other systems. Total curvature of pore-solid interface decreased from the positive value characteristic of the loose powder stack to a negative value, passed through a minimum, and increased toward zero as full density is approached. The area of grain boundary initially increased slowly, as interparticle contacts grew; at aboutV _V = 0.15, grain growth set in, and the grain boundary area decreased, as the mean grain intercept rapidly increased with densification. The dendritic powder had a highly irregular surface shape, and consequently a loose stack structure containing more than 90 pct porosity. The path that it followed was qualitatively, but not quantitatively, similar to that observed for the spherical powders. These observations are discussed in terms of the unit geometric processes that dominate each of the three stages of loose stack sintering.     

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.     

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,V _m . For Φ= 0 deg,E decreases withV _m until the grains become spherical atV _m = 26 pct. For 0 deg Φ ≤ 75 deg,E vs V _m curves show the minima which represent the stable configurations to be obtained whenV _m 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 ofV _m . The contiguity decreases monotonically withV _m . The slope ofE vs V _m 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 ofV _m 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.