Thermoelectric and morphological effects of peltier pulsing on directional solidification of eutectic Bi-Mn
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I.
INTRODUCTION
D U E to the importance of heat and mass transfer during crystal growth, considerable attention has focused on the fundamental aspects of directional solidification.~-4 The Bi/MnBi eutectic is considered a useful model system to study, because its microstructure and magnetic properties are strongly dependent on the solidification parameters and it is compatible with Peltier Interface Demarcation. 5-8 One method of studying the dynamics of crystal growth by directional solidification is through the use of Peltier Interface Demarcation (PID).~'2'8'9 This technique utilizes a current pulse passing through the directionally solidifying sample to create a rapid thermal perturbation at the solid/liquid interface due to the Peltier effect. ~0This perturbation results in a morphological anomaly or demarcation corresponding to the solid/liquid interface shape at the instant of the current pulse. Although PID has been of considerable usefulness in studying, for example, interface breakdown, ~ interface curvature, and micro- and macro-transients in growth velocity] '7 there has been little research into the fundamental aspects of PID. The purpose of the work reported here is to correlate the morphological effects of PID with pulsing conditions and measured thermal transients, and to investigate other possible influences of P1D-induced thermoelectric effects on the solidification process. In this study we have directly measured the thermal transients induced by Peltier pulsing in eutectic Bi/MnBi, and have identified the contributions of the Thomson, Peltier, and Joule heat fluxes. The experimental results obtained for eutectic Bi/MnBi in this study are in qualitative agreement with the effects predicted for pure Bi from published thermoelectric data. j~ II.
BACKGROUND
When a current is passed across the boundary between a solid and its melt, energy can be absorbed or released at the R.P. SILBERSTEIN, Senior Research Scientist, D.J. LARSON, Jr., Staff Scientist, and B. DRESSLER, Associate Research Engineer, are with Research and Development Center, Grumman Aerospace Corporation, Bethpage, NY 11714. This paper is based on a presentation made at the symposium "Fluid Flow at Solid-Liquid Interfaces" held at the fall meeting of the TMS-AIME in Philadelphia, PA on October 5, 1983 under the TMS-AIME Solidification Committee. METALLURGICAL TRANSACTIONS A
interface. 10 This Peltier effect is related to other thermoelectric effects and can occur simultaneously with them. For a current density J, the heat generated per unit area at the solid/liquid interface is given by Qp =- rrJ
[11
where rr is the Peltier coefficient for the material, At temperature T, in a thermal gradient d T / d x , the heat released per unit volume at a particular location is given by dT Or = rJ~-Tx,
r = -
T dS -dT
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where r is the Thomson coefficient and S is the Seebeck coefficient (or thermopower), both of which depend on T. The Joule heating per unit volume due to the resistivity, p, of the material is: Qj = j 2 p
[3]
The Peltier
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