Revisiting the Dependence of Poisson's Ratio on Liquid Fragility and Atomic Packing Density in Oxide Glasses

Abstract

Poisson's ratio (ν) defines a material's propensity to laterally expand upon compression, or laterally shrink upon tension for non-auxetic materials. This fundamental metric has traditionally, in some fields, been assumed to be a material-independent constant, but it is clear that it varies with composition across glasses, ceramics, metals, and polymers. The intrinsically elastic metric has also been suggested to control a range of properties, even beyond the linear-elastic regime. Notably, metallic glasses show a striking brittle-to-ductile (BTD) transition for ν-values above ~0.32. The BTD transition has also been suggested to be valid for oxide glasses, but, unfortunately, direct prediction of Poisson's ratio from chemical composition remains challenging. With the long-term goal to discover such high-ν oxide glasses, we here revisit whether previously proposed relationships between Poisson's ratio and liquid fragility (m) and atomic packing density (C_g) hold for oxide glasses, since this would enable m and C_g to be used as surrogates for ν. To do so, we have performed an extensive literature review and synthesized new oxide glasses within the zinc borate and aluminoborate families that are found to exhibit high Poisson's ratio values up to ~0.34. We are not able to unequivocally confirm the universality of the Novikov-Sokolov correlation between ν and m and that between ν and C_g for oxide glass-formers, nor for the organic, ionic, chalcogenide, halogenide, or metallic glasses. Despite significant scatter, we do, however, observe an overall increase in ν with increasing m and C_g, but it is clear that additional structural details besides m or C_g are needed to predict and understand the composition dependence of Poisson's ratio. Finally, we also infer from literature data that, in addition to high ν, high Young's modulus is also needed to obtain glasses with high fracture toughness.

Keywords: atomic packing density; liquid fragility; oxide glasses; poisson’s ratio.

Figure 1

Dependence of fracture energy (G_frac) on Poisson’s ratio (ν) for a range of materials, showing a brittle-to-ductile transition in the range of ν from 0.30 to 0.33. The figure is reproduced with the data from Lewandowski et al. [9] and Tian et al. [17]. We also extend it with new G_frac data for silicate glasses [10,18,19,20,21], borate, chalcogenide, and metallic glasses [10,20], and graphene [22,23] obtained by single-edge pre-crack beam (SEPB), chevron notch (CN), single edge notch beam (SENB), indentation fracture (IF), or tensile testing methods. The error of ν and G_frac is estimated to be 0.01 and 15%, respectively. The dashed line is a guide for the eye.

Figure 2

Dependence of Poisson’s ratio (ν) on atomic packing density (C_g) for various glass systems, including those from Table 1. The scale represents the multiplicity of data points. References for literature data are given in the text. C_g is calculated according to Equation (3), building on the structural assumptions described in the Supporting Information. The errors associated with ν and C_g are 0.01 and 0.002, respectively. R² value for a sigmoidal fit to the data is 0.162.

Figure 3

Effect of high-temperature densification, as quantified by the increase in atomic packing factor (C_g), on the Poisson’s ratio (ν) of selected glasses: zinc borates (this study), aluminoborates (this study and Ref. [46]), soda-lime borates (Ref. [80]), sodium borate (Ref. [68]), SiO₂ (Ref. [68]), and aluminotitanophosphates (Ref. [68]). The errors associated with ν and C_g are 0.01 and 0.002, respectively.

Figure 4

Liquid fragility (m) for selected oxide glass-forming systems from this study (Table 1) plotted as a function of Poisson’s ratio (ν). No apparent correlation between m and ν is observed. The errors associated with m and ν are 1 and 0.01, respectively. R² value for a linear fit to the data is 0.034.

Figure 5

Liquid fragility (m) as function of Poisson’s ratio (ν) for (a) oxide glass-formers (including both present compositions from Table 1 and literature data) and (b) various glass-formers from literature. References for literature data are given in the text. The dashed lines are guides for the eye, showing the trends for the majority of the data. The errors associated with m and ν are 1 and 0.01, respectively. R² values for linear fits to the data are 0.078 and 0.178 for (a) and (b), respectively.

Figure 6

Dependence of measured fracture toughness (K_Ic) on the measured Young’s modulus (E) for various glass systems (references are given in the text). Note that the axes are logarithmic. Errors in K_Ic and E are estimated to be smaller than 0.05 MPa m^½ and 2 GPa, respectively.