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 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.     

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.     

Thermodynamics of the penetration of a liquid phase into sintered composites

Conclusions An investigation was carried out into the process of penetration of a metallic melt into three-phase sintered composites. A condition is proposed for the migration of a liquid along solid/solid interfacial boundaries. The feasibility is demonstrated in principle of producing titanium-tungsten hard alloys of progressively varying cobalt content.Translated from Poroshkovaya Metallurgiya, No. 10 (142), pp. 69–73, October, 1974.     

颗粒在液相中溶解-析出过程的蒙特卡罗模拟

利用蒙特卡罗方法,通过建立合理的模拟规则,对单个圆形颗粒在液相中被溶解并形成溶质、溶质扩散、以及溶质析出等过程进行模拟。模拟结果表明:颗粒溶解度随模拟时间延长而逐渐增加,液相中的溶质浓度相应趋于饱和;升高模拟温度会加快颗粒的溶解速率,使溶质在液相中达到饱和所需要的时间缩短,饱和浓度值相应增加;尺寸越小的颗粒表现出越高的溶解活性,通过对不同初始尺寸的颗粒在液相中达到溶解平衡过程的模拟,所得平衡尺寸及饱和浓度之间的关联性与Gibbs-Thomson关系较为吻合。上述模拟结果均与实际溶解情况较一致。     

Interphase boundary precipitation in liquid phase sintered W-Ni-Fe and W-Ni-Cu alloys

The microstructure of liquid-phase sintered, tungsten-based heavy alloys comprises a continuous network of spheroidal tungsten single crystals embedded in a ductile, fcc matrix phase, and the integrity of the tungsten-matrix interphase boundaries established during processing is of major importance in determining the resultant mechanical properties. A serious potential source of embrittlement in these systems involves the precipitation of a brittle third phase along these boundaries. In the present work the techniques of selected area and convergent beam electron diffraction, energy dispersive X-ray microanalysis, and scanning Auger electron spectroscopy have been used to identify the embrittling interphase boundary precipitate formed in a commercial W-4.5 wt pct Ni-4.5 wt pct Fe alloy. The interphase boundary precipitation of an intermetallic phase in a W-7.2 wt pct Ni-2.4 wt pct Cu alloy under controlled conditions of heat treatment has also been confirmed. The precipitate phase observed in the W-Ni-Fe alloy in the as-sintered furnace-cooled condition has been found to be an eta carbide with a diamond cubic crystal structure (space group Fd3m,a ₀ = 1.092 ± 0.005 nm) and a tentative composition of the form (Ni,Fe)₆W₆C, where the Ni:Fe atom ratio is approximately 2:3. Neither the carbide nor any evidence of an intermetallic phase was observed in the as-sintered, furnace-cooled W-Ni-Cu alloy, but a continuous interphase boundary film of intermetallic precipitate could be induced in specimens solution treated at 1350°C, water quenched, and aged isothermally in the temperature range 600 to 900°C. Selected area electron diffraction indicated that the phase was isomorphous with the intermetallic Ni₄W of the binary Ni-W system. 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. Formerly with Department of Mechanical and Industrial Engineering and Materials Research Laboratory, University of Illinois at Urbana-Champaign     

The effect of transformation stresses on the devitrification kinetics of a minory phase in liquid phase sintered ceramics

The crystallization of minory amorphous constituents in liquid phase sintered ceramics, for example in Si₃N₄, is usually accompanied by a volume change. The resulting mismatch between crystallizing second phase inclusions and the surrounding matrix of the primary phase leads to the formation of transformation stresses. The strain energy stored in the stress field reduces the thermodynamic driving force of crystallization. The coupling of crystallization, stress formation and relaxation is modelled. The extended duration of the crystallization process due to an intermediate stress induced decrease of the crystallization rate is assessed. The properties of amorphous grain boundary films are discussed with respect to stress relaxation and creep resistance at high temperatures.     

An atomistic study of solid/liquid interfaces and phase equilibrium in binary systems

A semiempirical Lennard-Jones/Embedded Atom Method model is used to capture real materials’ behavior through the introduction of many-body forces. By means of molecular dynamics (MD) calculations, the model is used to study the dependence of the solid/liquid interface velocity on temperature and composition. Based on the MD results, the free energies and the chemical potentials in the solid and liquid phases are calculated to produce the phase diagrams. These calculations illustrate the consequences of differences in energy and size between the components on the phase diagrams. An asymmetry in velocity between solidification and melting is found. Slowing of the interface velocity by solutes during solidification is demonstrated. This article is based on a presentation given in the symposium “Fundamentals of Solidification” which occurred at the TMS Fall meeting in Indianapolis, Indiana, November 4–8, 2001, under the auspices of the TMS Solidification Committee.     

Effect of strain rate on the flow stress of three liquid phase sintered tungsten alloys

Stress/strain tests were carried out in compression on three liquid phase sintered tungsten alloys, with tungsten contents of 90, 95, and 97.4 wt pct, in the strain rate range 10⁻³ s⁻¹ to 10³ s⁻¹. Each alloy shows a gradual increase of flow stress with strain rate, and evidence of work softening is observed when the strain rate is of the order of 2 s⁻¹ or greater. The work softening effect is shown to result from a temperature rise due to the plastic deformation and partly masks the strain rate effect at strains greater than 0.1. The 97.4 pct tungsten alloy also shows variable behavior due to cracking associated with the presence of a brittle phase at the tungsten particle/matrix interface.     

Influencing mechanism of Al2O3 on sintered liquid phase of iron ore fines based on thermal and kinetic analysis

The sintering behaviour of ore fines under different Al₂O₃ content and different alkalinity was studied by DSC–TG method. The reaction kinetics of the sintering process was calculated. Simultaneously, the experimental products were analysed by microscopic analysis. The effects of different content of Al₂O₃ and alkalinity on the sintered liquid phase were investigated. The results show that the increase of Al₂O₃’s content promoted the formation of calcium ferrite and the increase of liquid phase's formation in a certain range. When the content of Al₂O₃ is 2.5%, that is, A/S?=?0.42, the heat flux is the largest, correspondingly, the maximum amount of liquid phase is formed under this condition. The liquid phase's formation during the reaction under high alkalinity conditions is greater than that under low alkalinity conditions. The influencing mechanism of Al₂O₃ and alkalinity on the liquid phase of sintering is verified by the kinetic analysis.     

An assessment of the Fe-S system using a two-sublattice model for the liquid phase

The strong variation in thermodynamic properties of the liquid phase in some systems is often accounted for by hypothesizing the existence of molecular-like aggregates. It is now suggested that it could also be accounted for in terms of a two-sublattice model. This model is applied to the Fe-S system. A good agreement is obtained with experimental information on the sulfur activity and phase equilibria. The assessment of the Fe-S system was carried out using a computer-operated optimization procedure and the phase equilibria were calculated with a rather general computer program. A. Fernandez Guillermet is, at present he is on leave for studies at the Dept. of Metallurgy, Royal Inst. of Technology, S-10044 Stockholm.     

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.     

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.