Roughening of the interface between grains and liquid matrix in sintered TaC-20Ni
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ch alloys as W-Ni,[1] Co-Cu,[2] Fe-Cu,[3] Pb-Sn,[4] and MgO-CaMgSiO4[5] prepared by liquid-phase sintering with relatively large amounts of the liquid phases show nearly spherical grains. Such grain shapes indicate that the interfaces between the grains and their matrices are rough at the liquid-phase sintering temperatures. The grains show normal coarsening because the rough interfaces move continuously with their velocities determined by diffusion in the matrix. In other sintered materials such as WC-Co[6] and Al2O3SiO2-CaO,[7] the grains are polyhedral with flat interfaces between the grains and the liquid matrices. These flat interfaces must be singular corresponding to cusps in the polar (Wulff) plots of the interface energy against the orientation. The grains show abnormal coarsening because the singular interfaces move by the step mechanism, as proposed earlier.[8,9] It is possible that the rough or singular interfaces between the grains and the liquid phases in multicomponent systems depend on temperature, although the ranges of temperature where the solid and liquid phases coexist are usually limited. The roughening transitions of crystal surfaces in single component systems have been extensively examined both theoretically[10–17] and experimentally.[15,16,17] It was predicted that crystal surface would undergo roughening transition with its step free energy gradually decreasing to 0 at the roughening transition temperature,[18,19] and the observations in 4He agreed well with this prediction.[20] The crystal equilibrium shape changes were also shown to be related to surface roughening by Rottman and Wortis.[16,21,22] Using a lattice gas model, they showed that a crystal with cubic YOUNG KYU CHO, Research Associate, and DUK YONG YOON, Professor, are with the Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Daejon 305-701, Korea. DUK YONG YOON is also an Invited Scientist at the Korea Research Institute of Standard and Research, Daejon 305-340, Korea. Contact e-mail: [email protected] JUNG HOON CHOI, Graduate Student, is with the Department of Materials Science and Engineering, University of Wisconsin–Madison, Madison, WI 53706. Contact e-mail: sjhchoi@ hotmail.com. JONG KU PARK, Staff Researcher, is with the Korea Institute of Science and Technology, Seoul 136-791, Korea. Manuscript submitted November 13, 2004. METALLURGICAL AND MATERIALS TRANSACTIONS A
symmetry would have a cubic shape with flat surfaces and sharp edges at low temperatures. With temperature increase, the corners and edges became round until the flat low index surface areas disappeared at the roughening transition temperature TR. Because the size of the flat low index surface decreases linearly with the step free energy to 0 at TR,[15,16] it is possible to estimate the relative change of the surface step free energy with temperature from the shape change. The observations of the shape changes in 4He,[20] NaCl,[23] and -Ag2S[24] with temperature qualitatively agreed with this prediction. T
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