Exploration Of Order From Disorder:Characteristic Properties Of Amorphous Solids And Their Structural Origin

Amorphous materials, e.g., glasses and sand piles, are ubiquitous in our daily life. But their outstanding nature is still poorly understood and remains a major change of condensed matter physics. Despite decades of intense study, a coherent theoretical framework for these systems is still lacking, which in the case of crystals can be ob-tained by exploiting the periodicity of the crystalline structure. One major challenge lies in the characterization, and accordingly the control of the structural disorder. This difficulty precludes the clarification of when and how the disorder takes effect to deviate properties of a solid from the crystal. Moreover, it hampers the detailed investigations at specific strength of disorder to elucidate the role of structural disorder behind the characteristic nature of amorphous systems. Our present research mainly focuses on understanding the physical properties of amorphous solids from the underlying "hidden order" in the complex structure.In the introduction (Chapter 1), we first briefly review the background of the soft condensed matter. The key features of the soft condensed matter and the current de-velopment of researches on amorphous materials are reviewed. We then summarize the basic facts of the glass transition, including the dynamic and the thermodynamic feature of glass-forming liquids, and a series of theoretical frameworks. Finally, we introduce the Jamming phase diagram by discussing the role of three control parameters. Focusing on the idealized model of frictionless particles which interact with each other through finite-range repulsion, we further introduce the criticality of the Jamming transition and the vibrational properties of marginally jammed solids. The Jamming transition at finite temperature and its relation with the glass transition is the focus of current researches, which is also briefly discussed.We pay particular attention on the normal modes of vibration because they are important to understand the properties of amorphous solids. In Chapter 2, we introduce in detail how to obtain the normal modes of vibration and how they are characterized. After that, we turn to one of the most important features in the vibration of amorphous solids:the arising of the Boson peak. We show that several models of the Boson peak in the literature are not universal. The structural origin of the Boson peak is discussed with the strength of disorder as a control parameter.In Chapter 3, we construct a structural order parameter from the energy equiparti-tion of normal modes of vibration to quantify the structural heterogeneity in disordered solids. The order parameter exhibits strong spatial correlations with low-temperature dynamics and local structural entropy. To characterize the role of particles with the most defective local structures identified by the order parameter, we pin them and mea-sure the system response. It turns out that particles with the largest value of the order parameter are responsible for the quasilocalized low-frequency vibration, instability, softening, and nonaffinity of disordered solids. The order parameter thus crucially links the heterogeneous structure to low-temperature dynamics and mechanical properties of disordered solids.In Chapter 4, we report an order-disorder transition from crystals to disordered crystals for static packings of frictionless spheres. While the geometric indicators are mostly blind to the transition, disordered crystals already exhibit properties apart from crystals. The transition approaches the close packing of hard spheres, giving rise to the singularity of the close packing point. We evidence that both the transition and prop-erties of disordered crystals are jointly determined by the structural orders and density. Near the transition, the elastic moduli and coordination number of disordered crystals show particular pressure dependence distinct from both crystals and jammed solids. Our results indicate that our current understanding of solids is rather incomplete. Solids close to the boundary of order and disorder may contain much richer physics than ex-pected.At last we summarize in Chapter 5.