Emergence of Crystal-like Atomic Dynamics in Glasses at the Nanometer Scale

Abstract

The vibrational dynamics of a permanently densified silica glass is compared to the one of an -quartz polycrystal, the silica polymorph of the same density and local structure. The combined use of inelastic x-ray scattering experiments and ab initio numerical calculations provides compelling evidence of a transition, in the glass, from the isotropic elastic response at long wavelengths to a microscopic regime as the wavelength decreases below a characteristic length of a few nanometers, corresponding to about 20 interatomic distances. In the microscopic regime the glass vibrations closely resemble those of the polycrystal, with excitations related to the acoustic and optic modes of the crystal. A coherent description of the experimental results is obtained assuming that the elastic modulus of the glass presents spatial heterogeneities of an average size a $ =2. DOI: 10.1103/PhysRevLett.110.185503 PACS numbers: 63.50.Lm, 62.30.+d, 62.65.+k, 64.70.ph Amorphous solids lack the long-range translational periodicity of crystalline materials. Nevertheless, their structure presents a residual order on the short and medium ranges [1]. At short distances the structure can be characterized in terms of interatomic distances and bond-angles distribution. The medium-range order extends typically over a length D $ 2=ÁQ 0 of a few ($ 5) interatomic distances, as indicated by the width ÁQ 0 of the first sharp diffraction peak in the static structure factor, SðQÞ. The length scale of the nanometer is believed to be the relevant one to understand the phenomenology of the glass transition. In fact, close to the dynamical arrest, the atomic motion of a supercooled liquid is characterized by nanometer-sized regions where the molecules move cooperatively [2][3][4][5][6][7]. Recent numerical simulation studies [8][9][10] have also given some evidence of the presence of static correlation lengths of a size comparable to the dynamical correlations, by investigating either subtle structural order parameters [8] or point to set correlations [9,10]. However these quantities are not easily accessible experimentally, because they are not revealed by standard two-points correlation functions, such as the SðQÞ. Thereby a detailed description of the medium-range order in glasses is still missing.Only recently, the development of new experimental probes has given some evidence of the presence of atomic regions of nanometric size in a few amorphous materials. Local symmetries in a colloidal suspension have been detected by means of a cross correlation analysis using coherent x rays [11]. Subnanoscale-ordered regions originating from atomic polyhedra have also been detected in a metallic glass employing an electron nanoprobe supported by an ab initio molecular dynamics simulation [12]. On a similar glass a wide spatial distribution of the elastic modulus, on the length scale of the nanometer, has been detected by means of atomic force acoustic microscopy [13]. Here we employ an alternative way to gather information on the structure of the canon...

Thermal conductivity accumulation in amorphous silica and amorphous silicon

“…This large concave-up dispersion has been observed in experimental measurements and numerical models of amorphous materials including a-SiO 2 [18,41,42,63,64]. We note that at frequencies lower than 10 12 rads/s, experimental measurements of a-SiO 2 recover a linear dispersion [18,26,28,63,67]. This frequency range is not accessible with the a-SiO 2 models studied in this work.…”

“…While experiments on a-SiO 2 show that there is a crossover region for the low-frequency lifetime scaling from ω −2 to ω −4 [25] and then back to ω −2 [25][26][27][28], our present model is not large enough to investigate the mode properties in this crossover region. Because experiments are limited for a-Si thin films [24], we also consider an ω −4 scaling for Eq.…”

“…To evaluate expressions and models for the low-frequency mode lifetimes requires knowledge of how the lifetimes scale with frequency. The scaling for a-SiO 2 has only recently been measured, with evidence of ω −2 , ω −4 , and a second ω −2 regime as the mode frequency ω increases from 3.14 to 6.28 ×10 12 rads/s [25][26][27][28]. For a-Si, the scaling is not well understood, with temperature-dependent and film thickness-varying measurements suggesting both ω −2 and ω −4 scalings [4][5][6][7][8][9]23,24,[29][30][31][32][33][34].…”

“…By using a constant sound speed, the lifetime and diffusivity frequency scalings will be the same. For amorphous materials, the scaling exponent n has been found experimentally and numerically to be between two and four [6][7][8][9][25][26][27][28][41][42][43]. A value of two corresponds to anharmonic scattering [44], while a value of four corresponds to Rayleightype scattering from point defects [45].…”

“…This approach has been previously used to predict effective dispersion curves of disordered and amorphous materials experimentally [18,26,28,63] and numerically [41,42,[64][65][66]. The structure factor at a wave vector κ κ κ is defined as [2] …”