Microstructural evolution during liquid phase sintering: Part II. Microstructural coarsening

During liquid phase sintering, microstructural coarsening takes place. One mechanism by which this occurs is Ostwald ripening. Alternatively, particle coalescence also leads to a concomitant reduction in the solid particle surface area per unit volume. In isolated structures in which particle-particle contacts are made, the rate of coarsening by coalescence is limited by the time between particle contacts, for this is long compared to the time to fuse two particles together. In skeletal structures the “coalescence time” limits coarsening by coalescence since this is long in comparison to the time between contacts. Expressions for the rate of particle coarsening are developed for the different mechanisms and different particle morphologies. The results of these calculations are combined with the microstructure maps developed in Part I of this paper to refine these maps so that they predict both the morphology developed and the dominant mechanism of coarsening in liquid phase sintered systems.     

A reanalysis of the kinetics of neck growth during liquid phase sintering

During liquid phase sintering, solid particles make contact and can subsequently coalesce into one particle. This coalescence phenomena can affect the type of microstructure formed and its subsequent coarsening behavior during liquid phase sintering. The mechanism of particle coalescence is assumed to be the liquid state analog of the evaporation-condensation mechanism of sintering. In this work, a detailed study of the geometry appropriate for analysis of the coalescence phenomena during liquid phase sintering is made. It is found that in the early stages of particle coalescence, the neck between the particles acts as a geometrical barrier to diffusion and the neck between the particles grows approximately ast ^1/5,i.e., the same kinetics appropriate for solid state sintering are obtained. At longer times, the neck area no longer restricts diffusive flow and at ^1/6 dependency of neck growth is obtained. The use of numerical techniques also allows the analysis to be carried out with fewer geometrical restrictions than in the original analysis of the evaporation-condensation mechanism.     

An analysis for estimating the probability of particle coalescence in liquid phase sintered systems

During liquid phase sintering solid particles move about within the liquid and make contact with each other. Microstructural examination of liquid phase sintered alloys clearly indicates that some of these contacts lead to particle coalescence even in systems in which wetting of the solid by the liquid is presumed to occur. Under these circumstances, the grain boundary formed by the particles must have a rather low energy and hence, misorientation. In this study, attention is directed at the problem of calculating the probability of a collision between particles that lead to the formation of a low angle grain boundary and hence, coalescence. By making simple but physically plausible assumptions about the nature of low angle grain boundaries, the coalescence probabilityp _c can be determined as a function of a parameterθ where θ = withγ _SL =solid-liquid surface energy,γ _ss = average solid-solid grain boundary energy and У is the angular extent of the energy cusp associated with a low angle grain boundary. A simple analytical expression ofp _c ,p _c = 0.1θ (1-cosθ) is derived and found to be in excellent agreement with other techniques for calculatingp _c for values ofθ ≲ 10 deg, the range most probable for liquid phase sintered alloys. Some discussion of the accuracy and assumptions of the present model is also given.     

Kinetics of interparticle contact formation during the laser sintering of two-component powders

The kinetics of interparticle contacts formation during the liquid-phase sintering of unlike materials under the action of laser irradiation was investigated. Trios of particles arranged in a row according to the schemes glass—polymer glass, metal—polymer—metal, and metal—glass—metal were sintered. The processes of particle approach and liquid neck formation between particles were studied. Possibilities for the manufacture of powder components with polymer and glass binders by the use of selective laser sintering followed by heat treatment are considered]. Institute of Technical Acoustics, Academy of Sciences of Belarus', Vitebsk. Translated from Poroshkovaya Metallurgiya, Nos. 5–6(407), pp. 37–41, May–June, 1999.     

Particle growth by coalescence during liquid phase sintering of Fe-Cu

Particle growth during liquid phase sintering of Fe-30 wt% Cu and Fe-60 wt% Cu was measured and compared with a recently developed coalescence theory. Measured normalized particle size distribution, time-dependence of average particle size and dependence of growth rate on solid phase volume fraction agree well with calculations based on the assumption of a diffusion-controlled coalescence process where all component particles are assumed to have equal coalescence frequency. Slight discrepancies can be explained as the results of nonspherical particle shape and of favored coalescence opportunity for larger particles.     

Texture evolution and the role of grain boundaries in skeletal formation during coarsening in solid-liquid mixtures

During coarsening of high-volume-fraction solid-liquid mixtures, a solid skeleton is formed. Electron back-scattered diffraction (EBSD) analysis of Sn particles in a liquid Pb-Sn eutectic is employed to yield quantitative evidence for the mechanisms that are operative during skeletal formation. We find that the grain boundaries (GBs) play a substantial role in setting the skeletal structure; however, they do not alter the mechanisms for skeletal coarsening. Particles do not rotate into low-energy configurations to minimize the GB energy in the solid-liquid mixture. Thus, there is no particle rotation-induced coalescence. We find that coalescence is not prevalent; Ostwald ripening is the primary mechanism for coarsening in this system. Our data suggest a model for skeletal formation and the origin of the skeletal stability. This model indicates that the primary factor in determining skeletal stability is the number of GB contacts. We recommend two methods to tailor the number of GBs and to engineer the properties of these solid-liquid mixtures.     

Settling in solid-liquid systems with specific application to liquid phase sintering

The evolution of microstructure in liquid phase sintered (LPS) alloys as it occurs in a gravity environment is discussed. If the solid phase volume fraction (V_p) is initially sufficiently low, a dispersion of isolated solid particles within the liquid develops first. These isolated particles settle at a velocity approximately equal to the Stokes' velocity and, in a finite container, the settling leads to the formation of a solid skeleton when V_p reaches a critical value. This value is ca. 0.20 for Fe-Cu LPS alloys and because the transition to the skeleton structure is dictated by morphological considerations, we expect this critical value of V_p is system independent. Once formed, a skeletal structure can continue to settle. The settling mechanism is controlled by “extrication” of solid particles from the skeleton and their subsequent directional flow within the liquid as a result of the differing solid and liquid densities. Since particle extrication is a relatively slow process, the “skeletal” settling rate is much reduced in comparison to free settling rates. Particle extrication times are system dependent; they are much less in W-(Fe-Ni-Cu) alloys than in Fe-Cu alloys. The differences are believed related to the variations in average neck size to average particle size ratio between the two materials. Both settling velocities in isolated and skeletal structures and the parameters defining the transitional behavior are discussed in terms of system physiochemistry and morphology.     

Spark plasma sintering of a nanocrystalline Al-Cu-Mg-Fe-Ni-Sc alloy

The microstructure and aging behavior of a nanocrystalline Al-Cu-Mg-Fe-Ni-Sc alloy was studied. The nanocrystalline powders were produced by milling at liquid nitrogen temperature and then consolidated using spark plasma sintering (SPS). The microstructure after SPS consisted of a bimodal aluminum grain structure (coarse-grained and fine-grained regions), along with Al₉FeNi and Al₂CuMg particles dispersed throughout. The microstructure observed in the as-consolidated sample is rationalized on the basis of high current densities that are generated during sintering. Solution treatment and aging of the SPS Al-Cu-Mg-Fe-Ni-Sc sample resulted in softening instead of hardening. This observation can be explained by the reduced amount of Cu, Mg, and Si in solid solution available to form S′ Al₂CuMg due to the precipitation of Al₇FeCu₂ and Si-rich particles, and by the fact that rodlike S′ Al₂CuMg particles could only precipitate out in the coarse-grained regions, greatly decreasing their influence on the hardness. This lack of precipitation in the fine-grained region is argued to represent a new physical observation and is rationalized on the basis of physical and thermodynamic effects. The nanocrystalline SPS Al-Cu-Mg-Fe-Ni-Sc sample was also extremely thermally stable, retaining a fine-grained structure even after solution treatment at 530°C for 5 h. The observed thermal stability is rationalized on the basis of solute drag and Zener pinning caused by the impurities introduced during the cryomilling process.     

Some Features of Coalescence Processes and Mechanisms in Systems of Nonmetallic Crystalline Particles

The influence of particle size, presence of soluble impurities, and the development of solid-state polytype transitions in systems of nonmetallic crystalline particles on coalescence mechanisms during sintering is considered. The following cases that have not been studied previously are discussed. Coalescence is activated by oxygen during sintering fine plasma chemical powders of AlN, TiC, and TiN. Its mechanism may be considered as alloy formation realized by movement of a boundary between areas differing in oxygen concentration. Development of this coalescence governs the formation of collective grain growth centers. Polytype transitions in self-bonded SiC give rise to the occurrence of Ostwald coalescence accomplished as recrystallization by the grain in grain type. Polytype transitions in SiC and AlN may cause the growth of fine monopolytype grains at the expense of coarse grains consisting of a collection of multilayer polytypes. On the example of silicon-bonded SiC it is shown that during liquid-phase sintering of ceramic materials with solubility of solid phase in the liquid phase three types of Ostwald coalescence may be realized differing in the mass-transfer mechanisms: reprecipitation through the liquid phase (solution of carbon in silicon); joining of two or more single original SiC particles by a single-crystal shell forming as a result of crystallization of the condensed phase from the melt-solution; combined reprecipitation through a liquid phase and recrystallization by migration of boundaries between particles.     

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.     

Laser Sintering of SiO2 Powder Compacts

Regularities of sintering compacted SiO₂ powder under the action of a CO₂-laser are studied by experiment. Features are considered for rebuilding the structure of a powder body (particle regrouping, formation of interparticle contacts, joining of particles into conglomerates, evolution of the porous structure) in different stages of sintering (with different laser irradiation duration). Sintering is accomplished by a liquid-phase mechanism (by melting particles and joining solid unmelted cores by the liquid phase formed). The results obtained may be used for developing laser sintering methods for ceramic powders.     

Analysis of particle growth by coalescence during liquid phase sintering

A statistical approach has been applied to particle coarsening during liquid phase sintering assuming direct particle coalescence as basic growth mechanism instead of Ostwald ripening. The coalescence process controlled by diffusion through the melt results in an increase of the average particle size proportional to the cube root of sintering time. After a short initial sintering interval the particle size distribution approaches a unique normalized form which is considerably broader than forms predicted by Ostwald ripening theories. The effect of preferred coalescence possibilities for definite particle size ranges and the effect of concurrent coalescence and Ostwald ripening are treated and discussed.     

The effect of Mo addition on the liquid-phase sintering of W heavy alloy

The morphological and compositional changes of grains have been investigated in the initial stage of liquid-phase sintering of W-Mo-Ni-Fe powder compacts. Both large (5.4-μm) and small (1.3-μm) W powders have been used to vary their time of dissolution in the liquid matrix. When 8OW-10M0-7Ni-3Fe (wt pct) compacts of fine (about 1- to 2-μm) Mo, Ni, and Fe and coarse (5.4-μm) W powders are liquid-phase sintered at 1500 °C, the Mo powder and a fraction of the W powder rapidly dissolve in the Ni-Fe liquid matrix. The W-Mo grains (containing small amounts of Ni and Fe) nucleate in the matrix and grow while the W particles slowly dissolve. In this transient initial stage of the liquid-phase sintering, duplex structures of coarse W-Mo grains and fine W particles are obtained. As the W particles dissolve in the liquid matrix during the sintering, the W content in the precipitated solid phase also increases. The dissolution of the small W particles is assessed to be driven partially by the coherency strain produced by Mo diffusion at the surface. During sintering, the W particles continuously dissolve while the W-Mo grains grow. When the compacts are prepared from a fine (1.3-μm) W powder, the W grains dissolve more rapidly, in about 1 hour, and only W-Mo grains remain. These observations show that the morphological evolution of grains during liquid-phase sintering can be strongly influenced by the chemical equilibrium process. formerly Graduate Student, Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology     

Effect of size and shape of tungsten particles on dynamic torsional properties in tungsten heavy alloys

The effect of the size and shape of tungsten particles on dynamic torsional properties in tungsten heavy alloys was investigated. Dynamic torsional tests were conducted on seven tungsten alloy specimens, four of which were fabricated by repeated sintering, using a torsional Kolsky bar, and then the test results were compared via microstructure, mechanical properties, adiabatic shear banding, and deformation and fracture mode. The size of tungsten particles and their hardness were increased as sintering temperature and time were increased, thereby deteriorating fracture toughness. The dynamic torsional test results indicated that in the specimens whose tungsten particles were coarse and irregularly shaped, cleavage fracture occurred predominantly with little shear deformation, whereas shear deformation was concentrated into the center of the gage section in the conventionally fabricated specimens. The deformation and fracture behavior of the specimens having coarse tungsten particles correlated well with the observation of the in situ fracture test results, i.e., cleavage crack initiation and propagation. These findings suggested that there would be an appropriate tungsten particle size because the cleavage fracture mode would be beneficial for the “self-sharpening” of the tungsten heavy alloys.     

Solid-state contributions to densification during liquid-phase sintering

Densification via liquid-phase sintering generally requires transport of substantial amounts of dissolved solid through the liquid. However, in composite systems, such as W-Cu, solid solubility in the liquid is almost negligible, and densification is hindered by the low amount of total mass transport. In this case, solid-state sintering of the skeletal solid structure in the presence of the liquid is a significant densification mechanism. In this article, the relative contributions to densification of both liquid and solid mass transport mechanisms are considered. A computer simulation is constructed to predict the densification behavior and concurrent microstructural development of liquidphase sintered composites for realistic heating cycles. Governing differential equations for densification are derived from idealized models of the microstructure, considering grain size, diffusion distance from vacancy source to sink, pore size, and pore morphology. Temperature-dependent terms, including the diffusivity, solubility, and surface energy, govern densification and microstructural parameters, such as the grain size, dihedral angle, and contiguity. Predictions for the sintered density, grain size, and contiguity are compared to experimental results for the W-Cu and W-Cu-Ni systems with approximately 20 vol pct liquid. For W-Cu, which has almost no intersolubility, solid-state sintering of W in the presence of liquid Cu is the dominant densification mechanism. Nickel additions increase solid solubility in the liquid and improve typical liquid-phase sintering contributions to densification. Alternatively, high sintered densities can be achieved in the absence of solubility with a sufficiently small particle size due to the solid-state contribution.     

液相烧结过程中粉末粒径分布演化模拟研究

液相烧结过程中, 粉末颗粒的熟化长大和聚并同时发生。利用群体平衡模型定量预测了相邻颗粒聚并效应作用下的粒径分布演化规律, 提出了一种基于欧式范数的方法以确定液相烧结过程是否达到稳态, 研究了从瞬态到稳态的转变过程中的粒径上限及其变化率, 发现颗粒瞬态粗化之后将得到稳态粒径分布。模型计算得到的粒径分布和实验数据之间吻合良好, 表明本数值模型具备定量预测能力。通过引入布朗粗化频率描述液相烧结过程中的聚并现象, 模拟结果表明颗粒的聚并行为显著延缓了瞬态向稳态的转变过程, 甚至可能导致最终得到非稳态粒径分布。     

Numerical studies of the motion of particles in current-carrying liquid metals flowing in a circular pipe

A mathematical model has been developed to describe the motion of particles in current-carrying liquid metals flowing through a cylindrical pipe. The fluid velocity field was obtained by solving the Navier-Stokes equations, and the trajectories of particles were calculated using equations of motion for particles. These incorporate the drag, added mass, history, electromagnetic, and fluid acceleration forces. The results show that particle trajectories are affected by the magnetic pressure number R _H, the Reynolds number Re, the blockage ratio k, and the particle-fluid density ratio γ according to the relative importance of associated force terms. In the axial direction, the particles follow the fluid velocity closely and will move further axially before reaching the wall as the fluid velocity (Re) increases. In the radial direction, the outwardly directed electromagnetic force on the particle increases with radial distance from the axis, with increasing electric current (R _H), and increasing size (k) of particle. The competition between the electromagnetic force and the radial fluid acceleration force in the entrance region results in particle movement toward the central axis before moving toward the wall for small electric current (low R _H) and directly toward the wall for large current (high R _H). The low inertia (γ) bubbles move faster toward the wall than heavier particles do. The radial velocity of the particle movement as it approaches the wall is predicted to decrease due to wall effects. This model has been applied to the movement of inclusions within the electric sensing zone (ESZ) of the liquid metal cleanliness analyzer (LiMCA) system in molten aluminum, and it was proved that LiMCA system could be used in aluminum industries.     

Structure formation in (Ti,W)C-Co alloys

Conclusions In (Ti, W)C-Co alloys with binder contents of 30 and 8% the main carbide particle growth mechanism during liquid-phase sintering withing the limits of applicability of Wagner's theory is apparently recrystallization through the liquid phase. In the later stages of sintering an 8% Co alloy can probably exhibit also coalescence. The controlling stage of the recrystallization is diffusion through the liquid phase. In the range of liquid-phase sintering times investigated (1–10 h) the carbide particles in (Ti, W)C-30% Co and (Ti, W)C-8% Co alloys form well-developed skeletons. Small variations in the structure of these skeletons can be brought about by changes in grain size. Changes in the specific surfaces (contact, phase, and total surfaces) of these alloys are in good agrement with the findings of theoretical investigations into the effect of sintering on interfacial areas.Translated from Poroshkovaya Metallurgiya, No. 11(203), pp. 78–84, November, 1979.