Kapteijns Geert, Richard David, Lerner Edan
Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands.
Department of Physics, Syracuse University, Syracuse, New York 13244, USA.
Phys Rev E. 2020 Mar;101(3-1):032130. doi: 10.1103/PhysRevE.101.032130.
Structural glasses formed by quenching a melt possess a population of soft quasilocalized excitations-often called "soft spots"-that are believed to play a key role in various thermodynamic, transport, and mechanical phenomena. Under a narrow set of circumstances, quasilocalized excitations assume the form of vibrational (normal) modes, that are readily obtained by a harmonic analysis of the multidimensional potential energy. In general, however, direct access to the population of quasilocalized modes via harmonic analysis is hindered by hybridizations with other low-energy excitations, e.g., phonons. In this series of papers we reintroduce and investigate the statistical-mechanical properties of a class of low-energy quasilocalized modes-coined here nonlinear quasilocalized excitations (NQEs)-that are defined via an anharmonic (nonlinear) analysis of the potential-energy landscape of a glass, and do not hybridize with other low-energy excitations. In this paper, we review the theoretical framework that embeds a micromechanical definition of NQEs. We demonstrate how harmonic quasilocalized modes hybridize with other soft excitations, whereas NQEs properly represent soft spots without hybridization. We show that NQEs' energies converge to the energies of the softest, nonhybridized harmonic quasilocalized modes, cementing their status as true representatives of soft spots in structural glasses. Finally, we perform a statistical analysis of the mechanical properties of NQEs, which results in a prediction for the distribution of potential-energy barriers that surround typical inherent states of structural glasses, as well as a prediction for the distribution of local strain thresholds to plastic instability.
通过骤冷熔体形成的结构玻璃具有大量软准局域激发——通常称为“软点”——据信它们在各种热力学、输运和力学现象中起关键作用。在一组狭窄的情况下，准局域激发呈现为振动（正常）模式的形式，这些模式可通过对多维势能进行谐波分析轻松获得。然而，一般来说，通过谐波分析直接获取准局域模式的数量会受到与其他低能激发（例如声子）的杂化的阻碍。在这一系列论文中，我们重新引入并研究了一类低能准局域模式——这里称为非线性准局域激发（NQEs）——的统计力学性质，这些模式是通过对玻璃势能面进行非谐（非线性）分析定义的，并且不会与其他低能激发杂化。在本文中，我们回顾了嵌入NQEs微观力学定义的理论框架。我们展示了谐波准局域模式如何与其他软激发杂化，而NQEs恰当地代表了软点且不发生杂化。我们表明NQEs的能量收敛到最软的、非杂化的谐波准局域模式的能量，巩固了它们作为结构玻璃中软点的真正代表的地位。最后，我们对NQEs的力学性质进行了统计分析，这导致了对围绕结构玻璃典型固有状态的势能垒分布的预测，以及对塑性失稳的局部应变阈值分布的预测。
