Experimental investigation and theoretical analysis of the structural relaxation in amorphous Fe40Ni40B20.
Amorphous metallic alloys are produced by a variety of techniques some of which involve rapid solidification of the alloying constituents. In these methods the solidification occurs so rapidly that the atoms are frozen-in and partially retain their liquid configuration. There are clear structural and other indications from their various properties that amorphous metallic alloys possess short range order but lack long range order. In general, amorphous alloys are not in a thermodynamic equilibrium state and, therefore, relax structurally whenever atoms attain an appreciable mobility. Associated with structural relaxation, many physical properties change; some significantly and others only slightly. Relaxation experiments in amorphous metallic alloys often display approximate In(t) kinetics which can be understood in terms of various models. In the present work the model by Primak (1955), for which the kinetic behaviour of a system depends on processes that are distributed over a range of activation energies, is used as a basis for further development. The Primak model allows, in principle, for the identification of the order of the relaxation reaction and for the determination of an initial activation energy spectrum Po(Єo), where Єo is a characteristic activation energy. Although the model provides for a qualitative explanation of the In(t) law, it has no predictive power as to the quantitative changes accompanying the various relaxing properties. Furthermore, an estimation of Po( Єo), inferred from various isothermal annealing procedures, reveals the approximate shape but does not fix its location on the activation energy axis. These shortfalls are attributed to complications in the frequency factor v, inherent to the Primak model. Also, the Primak model does not include consideration of the entropy involved in a 'configurational jump' of any particular atom during the relaxation process. Inclusion of the configurational entropy through the frequency factor v, in the present treatment, leads to a 'relaxation equation'. Structural relaxation measurements of density (in practice length - from which density can be approximately inferred) and electrical resistivity, in an Fe4oNi40B20 alloy, have been obtained and fitted to this relaxation equation. The fitting parameters are found, within experimental error, to be the same for both length and resistivity relaxation. The initial activation energy spectrum Po(Єo), as inferred from the fits, over the energy range 1.4 to 2.0 eV, reveals roughly three regimes, namely below 1.5 eV, from 1.5 to 1.8 eV, and above 1.8 eV, respectively, over which the initial activation energy spectrum Po( Єo) assumes different approximately constant values. Previous treatments have, however, implicitly assumed that Po( Єo) is constant throughout a temperature range over which In(t) kinetics is observed. The behaviour observed in this work is associated with the intrinsic relaxation mechanism involving consecutive diffusion of the metallic and metalloid atoms, respectively. A configurational entropy change inferred from this work is found to be negative as a consequence of contraction of the spread-out free volume resulting from thermal fluctuations. Within the framework of the 'present model', other related behaviour of amorphous metallic alloys, including the glass transition, crystallization and diffusion, are discussed. Where direct comparison between theory and experiment is possible for the various observed phenomena, the agreement is good and shows an overall consistency in our approach. Finally, the analysis considered here gives an expression which can be easily used to make quantitative predictions about the experimental relaxation behaviour. An immediate understanding of some of the main features of experimental data on relaxation can, therefore, be obtained through application of the present model.