General 2.5 power law of metallic glasses

Metallic glass (MG) is an important new category of materials, but very few rigorous laws are currently known for defining its “disordered” structure. Recently we found that under compression, the volume (V) of an MG changes precisely to the 2.5 power of its principal diffraction peak position (1/q₁). In the present study, we find that this 2.5 power law holds even through the first-order polyamorphic transition of a Ce₆₈Al₁₀Cu₂₀Co₂ MG. This transition is, in effect, the equivalent of a continuous “composition” change of 4f-localized “big Ce” to 4f-itinerant “small Ce,” indicating the 2.5 power law is general for tuning with composition. The exactness and universality imply that the 2.5 power law may be a general rule defining the structure of MGs.Metallic glasses (MGs) possess many unique and superior properties, such as extremely high strength, hardness, and corrosion resistance, etc., making them promising metallic materials with widespread applications (1, 2). Thousands of MGs with a wide range of compositions and properties have been synthesized over the past decades. However, so far the development of MGs is mainly based on tedious composition mapping in multicomponent space to pinpoint the combination of elements with optimized glass-forming ability (GFA). This method for development of MGs is a time- and resource-intensive strategy of trial and error which highlights the need for the guidance of a general theory (2, 3). Intensive research effort has been devoted to finding general rules in various MGs to understand the fundamentals and to guide the development of new MGs (4, 5). Quantitative correlations between their properties have been observed. For instance, compressive yield strength and elastic moduli of MGs are found to be intimately connected with their glass transition temperature T_g (6–10), and the ductility, fragility (11, 12), and Poisson’s ratio of MGs are closely related (13–16). The extensive correlations in properties suggest that the disordered MGs may share general rules in their structure. To clarify this scenario, detailed and accurate structural information spanning short range to long range is required. However, the current experimental probes and theories are limited to local structure in MGs (17). Therefore, understanding how the atoms efficiently fill up the 3D space and how this controls the bulk properties of MGs remains a long-standing theoretical challenge (18–23). To date, few general and exact rules regarding structure–property relationships have been established in MGs (23).Encouraging progress on understanding structure–property relationships in MGs has recently been made through the discoveries of the noncubic (2.3 or 2.5) power laws that correlate the principal diffraction peak (PDP) position q₁ with the bulk density ρ or average atomic volume, V_a, i.e., ρ∝(q₁)^D or V_a∝(1/q₁)^D, where D equals ∼2.3 with varying the composition of MGs at ambient pressure (19) or ∼2.5 for tuning the density of MGs with pressure (22, 24). Whereas composition and pressure show similar exponents in the power laws in MGs, composition and pressure are two independent variables for controlling the density (volume) of materials; they usually have dramatically different effects on MGs. For example, pressure is thought to cause only elastic densification in MGs without obvious structural change because of their already densely packed structure; the structure and properties of MGs are very sensitive to even minor compositional variations (25, 26). In addition, to achieve composition change, different samples usually have to be synthesized. And, many other variables are thought to be inevitably involved, making the compositional change complex (23). Therefore, some basic questions have been perplexing to the glass community: Why do “complex” compositional and “simple” pressure power laws show similar exponents? Is there any connection between them? These questions remain unanswered and have been the major obstacle in understanding the nature of these noncubic power laws.To address these questions, a systematic study in the 2D pressure-composition space seems to be required. However, the consistency of the data in this kind of study will be questionable. Alternatively, in the present study, we choose the polyamorphous Ce₆₈Al₁₀Cu₂₀Co₂ MG as a model system. It is well known that Ce-based MG systems show a polyamorphic transition between ∼2 GPa and ∼5 GPa caused by the pressure-induced 4f electron localized-to-itinerant transition (27, 28). During this polyamorphic transition, both the atomic size and the electronegativity of Ce are significantly changed (29). Composition tuning in MGs mainly means the variation of atomic size and electronegativity of components, which controls the formation of MGs (30). Therefore, although nothing changes in the nucleus, for MGs this pressure-induced polyamorphic transition is equivalent to a continuous “composition” change with the 4f-localized “big Ce” gradually substituted by 4f-itinerant “small Ce.” As a result, we are able to vary both pressure and composition of a MG in a well-controlled way for the first time, to our knowledge.