The Effect of Solute on the Homogeneous Crystal Nucleation Frequency in Metallic Melts
- PDF / 472,803 Bytes
- 8 Pages / 414.72 x 648 pts Page_size
- 76 Downloads / 211 Views
603
THE EFFECT OF SOLUTE ON THE HOMOGENEOUS CRYSTAL NUCLEATION FREQUENCY IN METALLIC MELTS
C.V. THOMPSON AND F. SPAEPEN Division of Applied Sciences,
Harvard U4niversity,
Cambridge,
MA 02138,
USA
ABSTRACT We have made a complete calculation that extends the classical theory for crystal nucleation in pure melts to binary alloys. Using a regular solution model, we have developed approximate expressions for the free energy change upon crystallization as a function of solute concentration. They are used, together with model-based estimates of the interfacial tension, to calculate the nucleation frequency. The predictions of the theory for the maximum attainable undercooling are compared with existing experimental results for non-glass forming alloys. The theory is also applied to several easy glass-forming alloys (Pd-Si, Au-Si, Fe-B) for qualitative comparison with the present experimental experience on the ease of glass formation, and for assessment of the potential for formation of the glass in bulk.
INTRODUCTION The study of the kinetics of homogeneous crystal nucleation in the melt is crucial to the understanding of the formation of metallic glasses. The classical theory of crystal nucleation in pure metal melts has been available for many years and has been successfully tested by experiment [1,21. Since all metallic glasses are in fact alloys, extension of the theory to multicomponent systems seems desirable. A number of authors have outlined formalisms for this extension, based on either partly thermodynamic [3,4] or purely kinetic [5-7) approaches to nucleation theory, but so far none of these formalisms have been worked out specifically for comparison with experiments. We have therefore made a simple but complete calculation of the homogeneous nucleation frequency in binary systems, so that our results could be compared to existing data from nucleation experiments. The partly thermodynamic approach [1, 3,4] to nucleation theory, which we chose for its simplicity, required the introduction of a simple regular solution model for the solid and liquid phases in order to calculate the free energy of crystallization in the undercooled regime. THEORY We have derived approximations for the dependence of the free energy change of crystallization per unit volume of crystal, AGv, on the solute concentration. In this paper, these deviations will be outlined schematically, using free energy diagrams; the complete calcula'&ons will be published separately [8]. Figure la depicts the free energy depe. lence on composition of the solid (crystalline) and liquid phases, at a temperature TI, well above the melting temperatures of either of the pure components, T 'A and Tm , B, where there is no twophase equilibrium possible at any composition. 'p is the chemical potential of element A in a liquid of composition xi and can be found by constructing a tangent to the liquid free energy curve at xt. The point at which this tangent
604
t
Fig. 1. Schematic Free Energy-Composition Diagrams
1>
a)
G
b) c)
A
X1
above the L
Data Loading...
