Rigidity and intermediate phases in glasses driven by speciation

Abstract

The rigid to floppy transitions and the associated intermediate phase in glasses are studied in the case where the local structure is not fully determined from the macroscopic concentration. The approach uses size increasing cluster approximations and constraint counting algorithms. It is shown that the location and the width of the intermediate phase and the corresponding structural, mechanical and energetical properties of the network depend crucially on the way local structures are selected at a given concentration. The broadening of the intermediate phase is obtained for networks combining a large amount of flexible local structural units and a high rate of medium range order.PACS numbers: 61.43. Concepts from mean-field rigidity in networks found their origin from Lagrangian constraint counting in mechanics [1] and have been applied with great success in glass science for several decades [2]. Bonds in a glass network can indeed be considered as constraints arising from interatomic stretching and bending forces. The connectivity or cross-link density (best quantified by the network mean coordination numberr) plays therefore a key role. In highly cross-linked networks wherer is large, there are more constraints than degrees of freedom per atom on average and the structure is stressed rigid (hyperstatic or overconstrained). At low connectivity, one has a flexible (hypostatic or underconstrained) structure that contains more degrees of freedom than constraints. Thorpe [3] analyzed the vibrational behaviour of such kind of networks and identified a mean-field (MF) floppy to rigid transition when the mean coordination number equalsr =r c = 2.38, a result that agrees with global (Maxwell) constraint counting as enunciated by Phillips [4] from the enumeration n c of bond stretching and bond bending forces.The underlying nature of this peculiar transition has been deeply reinvestigated recently because two transitions atr c(1) andr c(2) have been found [5] experimentally in a variety of glasses. These define an intervening region (or intermediate phase, (IP)) between the floppy and the stressed rigid phase. In the IP, glasses display some remarkable properties such as absence of ageing [6] or stress [7], selection of isostatically rigid local structures [5] or weak birefringence [8]. The two boundaries have been characterized from numerical calculations [9] and cluster analysis [10] on self-organized networks and identified as being a rigidity transition at lowr and a stress transition at highr. In the mean-field approach or in random networks where self-organization does not take place, both transitions coalesce into a single one. Moreover, links between IP and protein folding [11], high-temperature superconductors [12] or computational phase transitions [13] have been stressed that go much beyond simple analogies. The understanding of the IP is therefore of general interest. It has become clear that stress avoidance in the network is responsable for the width ∆r =r c(2) −r c(1) and the location of the intermed...

Fast-ion conduction and flexibility and rigidity of solid electrolyte glasses

“…Both (present work and ref 34 ) models incorporate the idea first invoked by Anderson and Stuart 37 that activation energy for ionic conduction (E A ) is made of two terms-an electrostatic energy (E c ) to create an ion and which determines the free carrier concentration n L , and a network stress energy (E s ) that facilitates migration of ions and determines carrier mobility µ. We, therefore, concentrate our efforts on estimating the energies, E c and E s , as they can be directly related to the statistics of clusters and the enumeration of constraints via statistical mechanics averages.…”

Concepts and applications of rigidity in non-crystalline solids: a review on new developments and directions

“…Physical ingredients (structure, dynamics, interactions, …) leading to the IP are still being debated in the literature, and its experimental characterization can be achieved from a variety of probes (thermal, calorimetric, optical, structural). In this respect, realistic MD simulations on glasses and supercooled liquids may provide an additional and insightful information [89][90][91], and it is interesting to note that thermal effects initially absent in theories of the intermediate phase [45,84,85,88], are now taken into account explicitly [86,87] which should permit to better understand how fluctuations, constraints, elasticity behave with temperature, and how such quantities are coupled to glassy relaxation.…”

“…Broadly speaking, these models can be put into two main categories. Some studies emphasize the central role of fluctuations [45,[84][85][86] in the emergence of a double threshold/transition that defines an IP between the flexible and the stressed rigid phase, and these features bear similarities with ordinary phase transitions given that fluctuations in coordination number will induce corresponding fluctuations in the order parameter (). Alternatively, mean-field aspects of jamming have been considered, and here fluctuations in coordinations are thought to be limited, but atoms are coupled spatially via elasticity [87,88] and can organise locally into distinct configurations that may promote an IP.…”

Crucial effect of melt homogenization on the fragility of non-stoichiometric chalcogenides

“…8a, similarly to previous findings 24 , and to other chalcogenides 4,[15][16][17]19,20 . The nearly vanishing of ∆H nr which defines a reversibility window, is usually correlated with the existence of an adaptative intermediate phase [38][39][40] that is found between the chalcogen-rich flexible phase, and the As-rich stressed rigid phase. The existence the reversibility window is, in fact, a direct consequence of the formation of an isostatic (stress-free) glass network that minimizes both stress (present at high As content) and the floppy modes (present at low As content) which would serve as impetus for relaxation.…”