Mean-coordination number dependence of the fragility in Ge–Se–In glass-forming liquids

Abstract

Differential scanning calorimetry measurements have been performed on elemental Se as well as on Ge_xSe_94−xIn₆ (x=4, 8, and 11 at%) and on Ge_ySe_88−yIn₁₂ (y=5, 7, and 9 at%) chalcogenide glasses. From the cooling rate dependence of the fictive temperature, the apparent activation energies, Δh*, and the fragility indices, m, as defined in the strong–fragile glass-forming liquid concept, are determined. It is found that, in Ge–Se–In system, there is an evolution from strong (m=67) to fragile (m=116) glass-forming liquids. The dependence of ‘m’ on the mean-coordination number, Z, is also obtained. This dependence is rationalized by assuming that, in this glassy alloy system, there is a tendency for the formation of In₂Se₃ clusters.

Introduction

The study of structural relaxation in the glass transition region of glass-forming liquids is important from academic and technological points of view. Relaxation processes in glasses occur at temperatures lower than their glass transition temperatures, T_g. The glass transition temperature can be defined as the temperature at which the equilibrium liquid viscosity is of the order of 10¹² Pa s or as the temperature at which the average relaxation time in the equilibrium liquid is about 100 s [1]. From the variations of the viscosity, η, or relaxation time, τ, with the normalized reduced T_g/T quantity, a classification scheme of glass-forming liquids has been proposed. This scheme is well known as the ‘fragility concept’ or as strong–fragile glass-forming liquid concept [2], [3] and allows the definition of a fragility index, m [4]. This ‘m fragility’ or ‘steepness’ index is a measure of the rate at which the relaxation time τ (or related properties) decreases with increasing temperature around T_g and is given by [4]

$$m={\frac{\mathrm{d}{\log }_{10}(\tau )}{\mathrm{d}\left(\frac{T_{\mathrm{g}}}{T}\right)}|}_{T=T_{\mathrm{g}}}\text{.}$$

In this classification scheme, glass-forming liquids which exhibit an approximately Arrhenius temperature dependence of their τ's are defined as strong and are characterized with a low value of m ($m\approx 16$ [5]). Those whose τ's are fitted with a Vogel–Fulcher–Tammann (VFT) equation are referred to as fragile and are characterized by a high value of m ($m\approx 200$ [6]). It is well recognized that oxide glass formers such as GeO₂ and SiO₂ with well-formed tetrahedral network rigid structures and directional bonds belong to the category of strong forming liquids [3], [7], [8], [9], [10]. On the other hand, linear polymeric materials are fragile forming liquids [11]. Thus, the concept of fragility in supercooled liquids has often been used as a basis for organizing data on amorphous materials: inorganic glasses [12], thermoplastics [9], polymer networks [13], and liquid-crystalline polymers [11].

However, despite the extensive efforts expended in research on this ‘fragility’ concept, the factors that determine m for a given liquid or polymer remain poorly understood [14]. As the unpredictability of this property is a problem, because many aspects of the viscous liquid, such as aging behaviour and non-exponentiality of relaxation, are closely related to m, it is important to obtain new data on any liquid that can be vitrified to get a better understanding of the strong–fragile glass-forming liquid concept.

Because the addition of a third element as an impurity has a pronounced effect on the structural relaxation process, we propose in this paper to study the role played by metallic indium on the relaxation processes of covalently bonded Ge–Se glasses. Therefore, the purpose of this work is to obtain new m-data on Ge–Se–In glassy alloys, correlate it with their mean-coordination number which could be changed in a controlled way, compare the newly obtained results with those already existing on Ge_xSe_100−x vitreous system, and discuss them in terms of the strong and fragile behaviours.