Materials Science Research Lecture
Slowly-compressed nano-crystals, bulk metallic glasses, rocks, granular materials, and the earth all deform via intermittent slips or "quakes". We find that although these systems span 12 decades in length scale, they all show the same scaling behavior for their slip size distributions and other statistical properties. Remarkably, the size distributions follow the same power law multiplied with the same exponential cutoff. The cutoff grows with applied force for materials spanning length scales from nanometers to kilometers, indicating an underlying nonequilibrium phase transition. A simple mean field model for avalanches of slipping weak spots explains the agreement across scales. It predicts the observed slip-size distributions and the observed stress-dependent cutoff function. The analysis draws on tools from statistical physics and the renormalization group. The results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes. Connections to neuron avalanches in the brain and recent observations on stars will also be discussed, extending the range of scales to 16 decades in length.
[1] Jonathan T. Uhl, Shivesh Pathak, Danijel Schorlemmer, Xin Liu, Ryan Swindeman, Braden A.W. Brinkman,, Michael LeBlanc, Georgios Tsekenis, Nir Friedman, Robert Behringer, Dmitry Denisov, Peter Schall, Xiaojun Gu, Wendelin J. Wright, Todd Hufnagel, Andrew Jennings, Julia R. Greer, P.K. Liaw, Thorsten Becker, Georg Dresen, and Karin A. Dahmen, Universal Quake Statistics: From Compressed Nanocrystals to Earthquakes, Scientific Reports 5, 16493 (2015).
[2] N. Friedman, A. T. Jennings, G. Tsekenis, J.-Y. Kim, J. T. Uhl, J. R. Greer, and K. A. Dahmen. Statistics of dislocation slip-avalanches in nano-sized single crystals show tuned critical behavior predicted by a simple mean field model, Phys. Rev. Lett. 109, 095507 (2012).
[3] James Antonaglia, Wendelin J. Wright, Xiaojun Gu, Rachel R. Byer, Todd C. Hufnagel, Michael LeBlanc, Jonathan T. Uhl, and Karin A. Dahmen, Bulk Metallic Glasses Deform via Slip Avalanches, Physical Review Letters 112, 155501 (2014).
[4] N. Friedman, S. Ito, B.A.W. Brinkman, L. DeVille, K. Dahmen, J. Beggs, and T. Butler. Universal critical dynamics in high resolution neuronal avalanche data. Phys. Rev. Lett. 108, 208102 (2012).
[5] Mohammed A. Sheikh, Richard L. Weaver, and Karin A. Dahmen, Avalanche Statistics Identify Intrinsic Stellar Processes near Criticality in KIC 8462852, Phys. Rev. Lett. 117, 261101 (2016).