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 and 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. DOI: 10.1103/PhysRevLett.99.135502 PACS numbers: 61.43.Dq, 62.10.+s, 62.20.Dc, 62.40.+i Some of the earliest efforts to describe the mechanics of deformation and flow of metallic glasses and liquids were carried out by Argon [1]. Inspired by the deformation of soap bubble rafts [2], Argon proposed that these materials deform by plastic rearrangements of atomic regions involving tens of atoms, termed shear transformation zones (STZ's). Argon further recognized that these plastically rearranging regions were not free but confined within an elastic medium [3]. Using Eshelby's insightful analysis [4], he estimated the effect of elastic matrix confinement on the energy barrier separating the initial and transformed state of the STZ. He further argued that the elastic matrix confinement of an isolated transformed STZ would lead to reversible elastic energy storage in the STZ-matrix system, implying that transformed STZ's have a memory of their original untransformed state. Interestingly, Argon's concept was recently studied in a deforming metallic glass foam, where buckled membranes and their accommodating stress fields were observed to behave like elastically confined STZ's [5].As recognized by Johari and Goldstein [6], the underlying relaxation mechanisms of liquids and glasses are governed by two kinetic processes: a fast process, termed the process, viewed as a locally initiated and reversible process, and a slow process, termed the process, viewed as a large scale irreversible rearrangement of the material. From a potential energy landscape perspective, Debenedetti and Stillinger [7] have identified the transitions as stochastically activated hopping events across ''subbasins'' confined within the inherent ''megabasin'' (intrabasin hopping) and the transitions as irreversible hopping events extending across different landscape megabasins (interbasin hopping). A 1D section of a potential energy landscape illustrating this concept is presented schematically in Fig. 1. Johnson and Samwer [8] have recently shown that, by employing a sinusoidal function to describe the megabasin potential energy density, a scaling law for the yield strength of a frozen-in configuration arises in terms of the curvature of the potential energy density function (i.e., the isoconfigurational shear modulus), revealing a universal shear strain limit of c 0:036. More recently, Demetriou ...

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.

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 glassforming 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. DOI: 10.1103/PhysRevLett.97.065502 PACS numbers: 61.43.Fs, 61.66.Dk Over the last three decades, several phenomenological theories have been proposed to explain flow in metallic glasses, most of which were founded on two hypothetical flow mechanisms: dilatation [1] and cooperative shear [2]. By analogy to granular materials, metallic glasses were thought to flow by deformation-induced dilatation, which results in the creation of a microstructural ''free volume'' leading to flow localization and consequent softening [1]. Owing to their ability to effectively capture the flow characteristics of metallic glasses, free volume models have been regarded as good phenomenological flow models and have been widely embraced. Even though experimental assessment of excess molar volume provided certain evidence of deformation-induced dilatation [3,4], it has not been possible to quantitatively link measurable free volume to flow as predicted by free volume models. To some extent, this can be attributed to the lack of a fundamental thermodynamic definition of ''free volume'' leading to constitutive models that possibly lack thermodynamic consistency. In an alternative approach [2], flow in amorphous metals was thought to be accommodated by cooperative shearing of atomic clusters, referred to as ''shear transformation zones.'' In a recent study [5], it has been shown that plastic yielding in metallic glasses can be effectively accounted for by adopting a cooperative yielding analysis for these flow zones similar to the one developed by Frenkel [6] for dislocation-free crystals. In the present study, we employ such cooperative shear flow analysis to investigate the rheology of metallic glass-forming liquids.Following [5], a periodic energy density versus strain can be formulated as = 0 sin 2 =4 c , where 0 is the barrier energy density, and c is a critical shear strain limit shown to be a universal scale for metallic glasses. Considering that the shear modulus is given by the curvature of the energy density function, i.e., G d 2 =d 2 j 0 , a linear relationship between barrier energy density and shear modulus can be formulated as 0 8= 2 2 c G. Multiplying by an effective zone volume , the total energy barrier for configurational hopping between inherent states, which can be regarded as the activation barrier for shear flow, can be expressed as W 8= 2 2 c G . Acknowledging that the variables contributing to barrier softening are G an...

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The equilibrium and nonequilibrium viscosity and isoconfigurational shear modulus of Pt 57.5 Ni 5.3 Cu 14.7 P 22.5 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. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2732822͔The Pt-Ni-Cu-P bulk-glass forming system 1 is known to form one of the toughest bulk metallic glasses to date, 2-4 characterized by a fracture toughness value of ϳ80 MPa m 1/2 . The inherent toughness of this system is shown to be a consequence of its tendency to undergo extensive shear-band networking prior to fracture. 2 This tendency has been primarily attributed to its high Poisson's ratio ͑ϳ0.42͒, which designates that the material favors accommodation of stress by shear. Interestingly, Poisson's ratios of metallic glasses were recently shown to be directly correlated to the rheology of their undercooled liquid state, and specifically to the liquid fragility. 5 In a recent rheological study 6 it is demonstrated that Pt-based liquid is indeed one of the most fragile metallic glass-forming liquids, which to some extent explains its inherently tough nature. In the present study we employ continuous-strain-rate compression experiments and acoustic measurements in conjunction with a recently developed cooperative shear model 7-9 to assess the rheology and ultrasonic properties of Pt 57.5 Ni 5.3 Cu 14.7 P 22.5 liquid under equilibrium and nonequilibrium conditions.The rheology of the supercooled liquid was assessed using the continuous-strain-rate compression setup described in a previous study. 10 The alloy ingot was prepared by first prealloying Pt ͑99.9 mass %͒, Ni ͑99.9 mass %͒, and Cu ͑99.99 mass %͒ by induction melting, and then alloying P ͑99.999 mass %͒ by stepwise furnace heating. The specimens were prepared by first fluxing the alloy with B 2 O 3 , and subsequently casting it into 4 mm diameter rods, whose amorphous nature was verified by thermal analysis. The rods were cut and polished to produce 4 mm tall cylindrical specimens. The typical 2:1 geometric ratio was not adopted here, as the 1:1 ratio was found more appropriate for geometrically constraining the specimens against unusually excessive barreling ͑possibly related to a high Poisson's ratio͒. The compression experiments were performed for an adequate duration to ensure that a steady-state flow stress had been attained. The strain-rate dependent viscosity measured in the temperature range of 473 to 523 K is presented in Fig. 1. The strain-rate dependence exhibits the typical trend observed in other glass forming systems: in the low strain rate limit, viscosity is stabilized at the Newtonian limit characterized by a strainrate se...