Entropic elasticity and negative thermal expansion in a simple cubic crystal

Abstract

Experiments reveal that negative thermal expansion behavior of a crystalline solid is similar to that of polymers and rubber.

Quantitative understanding of negative thermal expansion in scandium trifluoride from neutron total scattering measurements

“…The prediction from the tension effect is that the distance between mean positions of two bonded atoms should be shorter than the ac-tual mean bond length, and indeed as expected the Sc-F bond and F-F distances show normal positive thermal expansion (Sc-F expansion coefficient α = +15 MK −1 ), whereas a/2 decreases on heating defining the negative thermal expansion. This result for the Sc-F bond is consistent with two recent measurements of the PDF [15,26,56]. Figure 3 also shows the temperature dependence of the mean distance between neighboring Sc atoms.…”

“…A recent paper based on new x-ray total scattering measurements [29] supports the interpretation presented here, based on an earlier preprint of this paper, over the model of uncorrelated F-atom motions proposed in Ref. [26].…”

“…At this point we note that the authors of Ref. [26] have proposed a radically different model. Their central idea is that the ScF 6 octahedra have no internal rigidity in terms of bending of the bonds and that the Sc-F bonds can rotate in an uncorrelated way as independent Einstein oscillators.…”

“…The RUM model with infinite stiffness and the uncorrelated model of Ref. [26] represent two opposite ends of a spectrum. We would argue that the calculated [16,32,33] and measured [33] phonon dispersion curves actually mean that the balance is more towards a RUM model with more polyhedral flexibility than found in corresponding oxides.…”

“…This approach is used to refine configurations of atoms so that both their long-range and their local structure are consistent with experimental data. While there have been a few reports of total scattering measurements of NTE materials [15,[17][18][19][20][21][22][23][24][25][26] [19,21], has the method been used to generate an atomic model of the fluctuations associated with NTE to provide a consistent examination of the tension effect. From our analysis of the atomic configurations across a wide range of temperatures generated in this study we show that the fluctuations associated with the tension effect are a mix of whole-body rotations and bond-bending distortions of ScF 6 octahedra.…”