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In the potential energy landscape theory of liquids, the energetic configurational landscape of a liquid is modeled using a potential energy function comprising a population of stable potential energy minima called inherent states, which represent the stable atomic configurations of the liquid. These configurations are separated by saddle points that represent barriers for configurational hopping between the inherent states. In this article, we survey recent progress in understanding metallic glass-forming liquids from a potential energy landscape perspective. Flow is modeled as activated hopping between inherent states across energy barriers that are assumed to be, on average, sinusoidal. This treatment gives rise to a functional relation between viscosity and isoconfigurational shear modulus, leading to rheological laws describing the Newtonian and non-Newtonian viscosity of metallic glass-forming liquids over a broad range of rheological behavior. High-frequency ultrasonic data gathered within the supercooled-liquid region are shown to correlate well with rheological data, thus confirming the validity of the proposed treatment. Variations in shear modulus induced either by thermal excitation or mechanical deformation can be correlated to variations in the measured stored enthalpy or equivalently to the configurational potential energy of the liquid. This shows that the elastic and rheological properties of a liquid or glass are uniquely related to the average potential energy of the occupied inherent states.

The configurational properties associated with the transition from anelasticity to plasticity in a transiently deforming metallic glass-forming liquid are studied. The data reveal that the underlying transition kinetics for flow can be separated into reversible and irreversible configurational hopping across the liquid energy landscape, identified with beta and alpha relaxation processes, respectively. A critical stress characterizing the transition is recognized as an effective Eshelby "backstress," revealing a link between the apparent anelasticity and the "confinement stress" of the elastic matrix surrounding the plastic core of a shear transformation zone.

A rheological law based on the concept of cooperatively sheared flow zones is presented, in which the effective thermodynamic state variable controlling flow is identified to be the isoconfigurational shear modulus of the liquid. The law captures Newtonian as well as non-Newtonian viscosity data for glass-forming metallic liquids over a broad range of fragility. Acoustic measurements on specimens deformed at a constant strain rate correlate well with the measured steady-state viscosities, hence verifying that viscosity has a unique functional relationship with the isoconfigurational shear modulus.

The equilibrium and nonequilibrium viscosity and isoconfigurational shear modulus of Pt57.5Ni5.3Cu14.7P22.5 supercooled liquid are evaluated using continuous–strain-rate compression experiments and ultrasonic measurements. By means of a thermodynamically-consistent cooperative shear model, variations in viscosity with both temperature and strain rate are uniquely correlated to the variations in isoconfigurational shear modulus, which leads to an accurate prediction of the liquid fragility and to a good description of the liquid strain-rate sensitivity.