Classical model of negative thermal expansion in solids with expanding bonds

Abstract

We study negative thermal expansion (NTE) in model lattices with multiple atoms per cell and first-and second-nearest neighbor interactions using the (anharmonic) Morse potential. By exploring the phase space of neighbor distances and thermal expansion rates of the bonds, we determine the conditions under which NTE emerges. By permitting all bond lengths to expand at different rates, we find that NTE is possible without appealing to fully rigid units. Nearly constant, large-amplitude, isotropic NTE is observed up to the melting temperature in a classical molecular dynamics model of a ReO 3 -like structure when the rigidity of octahedral units is almost completely eliminated. Only weak NTE, changing over to positive expansion is observed when the corner-linked octahedra are rigid, with flexible second-neighbor bonds between neighboring octahedra permitting easy rotation. We observe similar changes to thermal expansion behavior for the diamond lattice: NTE when second-neighbor interactions are weak to positive thermal expansion when second-neighbor interactions are strong. From these observations, we suggest that the only essential local conditions for NTE are atoms with low coordination numbers along with very low energies for changing bond angles relative to bond-stretching energies. 65.40.De

Two-dimensional nanoscale correlations in the strong negative thermal expansion material ScF3

“…Recent classical molecular dynamics simulations and general arguments have suggested strict rigidity of molecular units is not possible or necessary for NTE 15,[17][18][19] , fully consistent with the finite correlation length implied by our experiments and divergent kinetic energy density in the thermodynamic limit of the CLM. Here we propose a mechanism of strain relief and kinetic energy lowering consistent with experiments, the quantized nature of the vibrational spectrum, and hierarchy of stiffness present in the bond patterns.…”

“…Building on this idea, some researchers find an adequate description of NTE in terms of rigid molecular units which draw in the lattice when thermally activated, with still finer points of debate on which senses of motion are appropriate for which particular system [13][14][15] , or across which momentum manifolds rigid external modes exist 16 . Others have suggested that molecular rigidity is neither necessary nor favorable as an NTE mechanism 15,[17][18][19] . Separately from any consideration of NTE, studies of the perovskite space group landscape show that the cubic open perovskites in the P m3m structure like ScF 3 and ReO 3 can undergo coordinated tilt patterns 20 of rigid octahedra.…”

Classical, quantum, and thermodynamics of a lattice model exhibiting structural negative thermal expansion

“…Recently strong NTE was discovered in ScF 3 , an open perovskite only four atoms/unit cell that remains cubic at all temperatures T < 1800 K. This model system has the capacity to shed light on the issue of molecular versus bond rigidity due to its simple structure [24,26,41,[43][44][45][46]. We review some features of the 2D CLM presented above in the context of experiments on ScF 3 .…”

“…Figures 4c and 5b show that a corresponding lowering of the CTE and stiffening of the C p /T 3 peak are then expected to occur together in accord with experiments. Long period vibrations Multiple MD simulations aimed at understanding the SNTE modes in the specific case of ScF 3 have been performed and dispersion data extracted [24,26,40,[43][44][45][46]46]. In all but one tour-deforce study [44], these efforts produce mode energies at the M and R points of the simple cubic Brillouin zone in the range 5-10meV, consistently higher than experiments 0.5-4meV [18], suggesting that possibly the slow oscillations realized in the large k limit of our model are not captured in some finite-size simulations (low k in our model).…”

“…New discoveries of robust SNTE have reinvigorated the field and raised the question of whether strict The two-dimensional constrained lattice model (2D CLM) with staggered angle (a) θ and (b) θ = 0. In the rigid limit, the lattice dimensions contract uniformly by a factor cos θ. molecular rigidity is an appropriate starting point [24][25][26], or if instead it is more appropriate to consider only rigidity of the stiffest bonds in a view of the materials as a framework of struts. In an effort to advance the relative importance of molecular or bond stiffness in SNTE systems, the present manuscript regards analytical and numerical descriptions of a simple model supporting a single collective mode capable of producing SNTE.…”