Universal Fractional Noncubic Power Law for Density of Metallic Glasses Qiaoshi Zeng, 1,2,4,5,* Yoshio Kono, 3 Yu Lin, 1 Zhidan Zeng, 1,2,4,5 Junyue Wang, 4,5 Stanislav V. Sinogeikin, 3 Changyong Park, 3 Yue Meng, 3 Wenge Yang, 4,5 Ho-Kwang Mao, 4,5 and Wendy L. Mao 1,2 1 Geological and Environmental Sciences, Stanford University, Stanford, California 94305, USA 2 Photon Science and Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA 3 HPCAT, Geophysical Laboratory, Carnegie Institution of Washington, 9700 South Cass Avenue, Argonne, Illinois 60439, USA 4 HPSynC, Geophysical Laboratory, Carnegie Institution of Washington, 9700 South Cass Avenue, Argonne, Illinois 60439, USA 5 Center for High Pressure Science and Technology Advanced Research (HPSTAR), 1690 Cailun Road, Pudong, Shanghai 201203, People’s Republic of China (Received 21 March 2014; published 8 May 2014) As a fundamental property of a material, density is controlled by the interatomic distances and the packing of microscopic constituents. The most prominent atomistic feature in a metallic glass (MG) that can be measured is its principal diffraction peak position (q 1 ) observable by x-ray, electron, or neutron diffraction, which is closely associated with the average interatomic distance in the first shell. Density (and volume) would naturally be expected to vary under compression in proportion to the cube of the one- dimensional interatomic distance. However, by using high pressure as a clean tuning parameter and high- resolution in situ techniques developed specifically for probing the density of amorphous materials, we surprisingly found that the density of a MG varies with the 5=2 power of q 1 , instead of the expected cubic relationship. Further studies of MGs of different compositions repeatedly produced the same fractional power law of 5=2 in all three MGs we investigated, suggesting a universal feature in MG. DOI: 10.1103/PhysRevLett.112.185502 PACS numbers: 81.05.Kf, 61.05.cp, 62.50.-p The macroscopic properties of materials are intimately linked to their microscopic structure. For crystals, their natural regular shapes (polyhedrons with faceted surfaces) reflect the strict atomic level packing symmetry in unit cells. Detailed unit cell information can be uncovered by diffraction techniques, which shows sharp Bragg peaks as a direct consequence of their long-range periodic arrange- ment of atoms. Microscopic length scale changes in a unit cell directly reflect its global three-dimensional (3D) density or volume change. In contrast, no such relationship has been established in glasses. Because of the lack of long- range translational periodicity, diffraction of glasses only yields a few broad peaks (haloes) rather than sharp Bragg peaks. Few constraints on the glass atomic packing have been discovered. A theoretical description of their atomic structure is very difficult and can only be done statistically since it requires a “unit cell” containing an infinitely large number of atoms. Thus, determining how the local atomic packing scales up to fill 3D space in glasses remains mysterious, which severely hinders our effort to establish the relationships connecting the microscopic atomic struc- ture and the global properties of glasses [1–4]. Constraints from experiments are critical for the theoretical effort to resolve these problems. Because of the removal of the constraints of charge neutrality and bond angles, metallic glasses (MGs) [5–7] are believed to have very dense and efficient packing of atoms and/or clusters [1,2,8]. In addition, no matter how different their pair distribution functions look in real space (different specific atomic structure), their diffraction pat- terns in reciprocal space are usually quite similar, with a well-defined and symmetrical principal diffraction peak (PDP), typically located at q 1 ¼ 2 to 3 Å -1 (2π=q 1 falls into the range of the first neighbor atomic distance). While limited, this provides direct structural information at the atomic level and is expected to include the statistical information of average interatomic spacing (d) according to the well-known Ehrenfest relationship [9], i.e., d ∝ ð1=q 1 Þ. The strong correlation between q 1 and d has been extensively observed [10–12] in MGs and was recently directly confirmed by a subnano beam trans- mission electron microscopy (TEM) study [13]. A cubic power law scaling, V a ∝ ð1=q 1 Þ D , where the power D equals 3, and V a is the average atomic volume, is expected for a macroscopic isotropic, disordered system. Based on these relationships, the easily measurable PDP position q 1 has been broadly employed to characterize the global strain [10,12] or density change [11,14] in various glasses. However, the nominally “disordered” glasses actually have been found to exhibit a very complex “ordered” atomic structure beyond short range order [1,2,15–20]. Thus, the use of those relationships for the complex glass structure is far from rigorous and thus has been controversial [4,21–24], which challenges the validity of many practical measurements and our basic understanding of glassy materials as well. Pressure is a powerful and clean parameter which can simply increase the density (decrease the volume) of a MG PRL 112, 185502 (2014) PHYSICAL REVIEW LETTERS week ending 9 MAY 2014 0031-9007=14=112(18)=185502(5) 185502-1 © 2014 American Physical Society