Segregation and morphological instability due to double-diffusive convection in rotational directional solidification
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I. INTRODUCTION
DIRECTIONAL solidification is an important technique to grow alloys or single crystals, with desired compositions, for many technological applications. In addition to the compositional uniformity, morphological stability of the solidification front is crucial to the alloy’s quality. The classic constitutional supercooling[1] gives an upper stability boundary for a planar interface. Beyond this boundary, the interface may break down into cellular or dendritic structures. The pioneering work by Mullins and Sekerka[2] gave a rigorous foundation for the onset of morphological instability by considering the interfacial energy and the wavelength of the unstable modes. Although the theory assumes a fixed concentration at the interface and no convection, it provides a first approach to control the planar interface. In short, to prevent the interface from breakdown, solute concentration needs to be lower than the critical value. For the vertical situation having the melt at the top, e.g., the Bridgman configuration, the stabilized thermal condition is ideal for the theory. However, in reality, because of interface deformation and radial heat flow, which are often caused by the release of heat of fusion, thermal buoyancy flow is present. Solute segregation (both radial and axial) can further introduce solutal buoyancy, and this is particularly significant when a rejected solute is lighter than the melt. The interaction of both, or the so-called double-diffusive convection, causes uneven solute distribution at the interface. The local solute accumulation further leads to an earlier onset of morphological instability.[3,4] A well-known example is the directional solidification of succinonitrile (SCN) containing ethanol in a glass ampoule.[3] Schaefer and Coriell observed a smooth concave interface for a pure sample. However, when the ethanol concentration reached a critical value, a depression or pit was observed at the interface center C.W. LAN, Professor, Y.W. YANG, H.Z. CHEN, and I.F. LEE are Master Students with the Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617, Republic of China. Contact e-mail: [email protected] Manuscript submitted November 12, 2001. METALLURGICAL AND MATERIALS TRANSACTIONS A
before the morphological breakdown. Lan and Tu[4] further carried out numerical simulation and showed that the pit formation is due to double-diffusive convection. Singh et al.[5] observed a similar pit formation, but much deeper, for the growth of PbBr2 containing AgBr (5000 ppm). The deeper pit was believed to be the cause of the large interfacial energy that can sustain high supercooling inside the pit. When the solute content increases, the local depression or pit becomes obvious. Once the pit is formed, the solute inside is trapped, accelerating the morphological instability. Reducing local solute accumulation is a simple way to avoid pit formation, and the control of double-diffusive convection is, thus, important. Beside radial-solute distribution, axial segregation is
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