{'fraction_non_alphanumeric': 0.029586636466591168, 'fraction_numerical': 0.013023782559456399, 'mean_word_length': 4.819604612850083, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Intrinsic features of an ideal glass

In order to understand the long-standing problem of the nature of glass states, we performed intensive simulations on the thermodynamic properties and potential energy surface of an ideal glass. We found that the atoms of an ideal glass manifest cooperative diffusion, and show clearly different behavior from the liquid state. By determining the potential energy surface, we demonstrated that the glass state has a flat potential landscape, which is the critical intrinsic feature of ideal glasses. When this potential region is accessible through any thermal or kinetic process, the glass state can be formed and a glass transition will occur, regardless of any special structural character. With this picture, the glass transition can be interpreted by the emergence of configurational entropies, as a consequence of flat potential landscapes.

The nature of glassy states (GS) is one of the most compelling puzzles and questions facing scientists today. [1] The significance of GS not only lies in the importance of their various applications, but also stems from the challenge to current theories in condensed matter physics and thermodynamics. [2,3] Until now, it is probably safe to say that, both GS and the glass transition (GT) are within a dark area in the field of materials science and condensed matter physics. Given that a glass is neither a normal liquid nor a standard solid, GS are quite often not described in any detail by standard textbooks. [4] Although the problems have been recognized for over a century and great efforts have been made on various aspects of GS and GT, from disordered structures to kinetic fragility, from dynamic heterogeneity to thermodynamic models, [4][5][6][7][8] the debate on essential issues is still quite lively.
One of most crucial issues regarding GS is that below the Kauzmann temperature T K the entropy of a supercooled liquid by extrapolation becomes lower than the crystal entropy. [9] This constitutes the so-called Kauzmann paradox, which thermodynamic models face. To avoid the paradox, an unusual state of matter, namely an ideal glass, was proposed. [10][11][12][13] It is defined as a glass state with zero configurational entropy. For more than half a century, the ideal glass remained a conjecture, as its existence has been doubtful in real materials. [14] In 1998, two of the present authors (DY and XG) demonstrated that an Al 43 cluster in its most stable configuration shows a typical glass transition character, [15] which can be identified as an ideal glass. [16] Ten years later, the ideal glass was found experimentally in that system. [17] To our knowledge, the Al 43 cluster may be the first ideal glass theoretically predicted in real materials. It thus provides an ideal system to study the nature of the GS and GT at the atomic level. In this letter, we report the results of molecular dynamics (MD) simulations and stochastic surface walking (SSW) [18,19] studies of the thermodynamic properties of the ideal glass Al 43 . For comparison, the symmetric Al 55 with I h symmetry and Al 40 with D 6h symmetry were also studied. [20] The SSW algorithm was recently developed by Shang and Liu and has been proven to be an efficient tool to explore the potential landscape of both clusters and periodic systems. [21,22] An automated climbing mechanism is implemented in the SSW algorithm to manipulate a structural configuration from a local minimum to a high-energy configuration along one random mode direction. We found that the intrinsic nature of an ideal glass is closely associated with a flat potential landscape. We adopted the glue potential to described the atomic interaction of Al. This potential can correctly reproduce many basic properties of aluminum in crystalline and non-crystalline phases. [23] The constant-temperature MD method without any boundary conditions was used in the calculations, and any global motion of clusters was carefully eliminated. To obtain a reliable result, the simulation spanned the sub-microsecond scale in sub-picosecond steps. To characterize the shape of a cluster, the principal radii of gyration were calculated.
In the present calculations, the heat capacity was based on a constant-temperature ensemble, and the volume of clusters was calculated based on the Wigner-Seitz primitive cell approximation.
[24] Diffusion constants, which are an important thermodynamic quantity for identifying phases, were obtained by calculating the mean-square displacement of each atom. To characterize a cooperative motion among atoms, we define the time-dependent with ∆t = 5 ps.
Here we also provided the direct potential landscape from an SSW calculation. For each cluster, we performed 10 parallel SSW runs and collected 105 minima. To identify cluster structures, a distance-weighted Steinhardt-type order parameter[25] was used to distinguish distinct minima. the specific heat has a small jump. Meanwhile the shape of clusters begins to change, as indicated by the principal radii of gyration (right panel of Fig. 1). Since the system is in a well-defined liquid state above 550 K (see below), the GT range can be defined from 350 K to 550 K. In the following we will focus on this temperature range.
We found that, before melting to a normal liquid state, atoms in GS display a remarkable cooperative diffusion, which is intrinsically different from that exhibited by liquid states. Fig.   2   This is typical behavior for atomic diffusion of liquids due to less cooperation among atoms.
On the other hand, at 460 K in the GS, R c (t) shows a remarkable variation with time, with some periods essentially as for 200 K and others consistent with 600 K. This indicates that atom diffusion is induced by a cooperative motion in a short time, i.e., a solid-solid transition. It should be noted that the cooperative motion in ideal GS is different from that reported in supercooled molecular liquids, which display a non-Arrhenius character. [5,26] The above results suggest that the GT being associated with solid-solid structure tran- With the increase of temperature, the ideal glass can visit more and more configurations, consequently the configurational entropy keeps increasing until the melting temperature (T m in Fig. 5) is reached. Here the free energy curves show a crossover between the ideal GS and liquid state, because the ideal glass is a distinct state rather than a frozen-in supercooled liquid. On the contrary, for GS with a frozen-in supercooled liquid, [3,28,29] the free energy curves will merge into that of liquid state near T m , rather than a crossover.
In summary, we have demonstrated that, an ideal glass state is a distinct state rather than a frozen-in supercooled liquid. The intrinsic feature of an ideal glass is a flat potential landscape. The glass transition of an ideal glass can be viewed as the process of gaining more and more configurational entropy. We believed that the glass transition only depends on the special potential landscape not the structural details.