The origin of uniaxial negative thermal expansion in layered perovskites

Abstract

Why is it that ABO 3 perovskites generally do not exhibit negative thermal expansion (NTE) over a wide temperature range, whereas layered perovskites of the same chemical family often do? It is generally accepted that there are two key ingredients that determine the extent of NTE: the presence of soft phonon modes that drive contraction (have negative Grüneisen parameters); and anisotropic elastic compliance that predisposes the material to the deformations required for NTE along a specific axis. This difference in thermal expansion properties is surprising since both ABO 3 and layered perovskites often possess these ingredients in equal measure in their high-symmetry phases. Using first principles calculations and symmetry analysis, we show that in layered perovskites there is a significant enhancement of elastic anisotropy due to symmetry breaking that results from the combined effect of layering and condensed rotations of oxygen octahedra. This feature, unique to layered perovskites of certain symmetry, is what allows uniaxial NTE to persist over a large temperature range. This fundamental insight means that symmetry and the elastic tensor can be used as descriptors in high-throughput screening and to direct materials design.

A systematic study of the negative thermal expansion in zinc-blende and diamond-like semiconductors

“…Mechanism (i) has been proposed to explain the NTE of ZrW O 2 8 , where the rotation of the two-linked tetrahedral WO 4 causes significant distortions within the octahedral ZrO 6 rigid units, which consumes the open spaces in the crystal [21][22][23]. Mechanism (ii) considers high-spin state usually being relatively larger in radius than the low-spin state for an atom with given valence and coordination number [24][25][26]. Mechanism (iii) is the volume change involved with the variation of magnetic moment such as in Fe-36Ni [27].…”

Negative thermal expansion in high pressure layered perovskite Ca2GeO4

“…It is noteworthy that there is no direct transition between I4 1 /acd and Pbca without unravelling the antiphase P 4 rotations to transform them to in-phase X 2 + rotations. It is this so-called symmetry trapping that we have previously argued prevents the transition to the energetic ground state 7 thus allowing octahedral tilts that have been shown to drive NTE 8,10 to remain low in frequency without condensing. Lattice parameters were extracted from the temperature dependent powder X-ray diffraction data by performing sequential Pawley refinement and are shown in Fig.…”

“…1 inset), these modes drive substantial NTE along c over a wide temperature range. 10 By studying the nature of the compliance matrix in the Ruddlesden-Popper series Ca n+1 -Ge n O 3n+1 as a function of n we recently predicted that the magnitude of NTE should be maximised for n = 1 11 in which an analogous phase competition to that observed in the n = 2 structure occurs (see Fig. 1).…”

“…We have previously shown that the character of the low energy vibrations giving rise to NTE along c are the same as those giving rise to PTE along a. 10 Therefore a and c were fitted in tandem using least squares optimisation where the optimisation function was the sum of the errors normalised by lattice parameter for both a and c. This meant that a single characteristic frequency could be applied to both models. The characteristic phonon frequency, k 2 , is found to be 155 K (13.4 meV, 108 cm À1 ).…”

“…The average thermal expansion coefficient along the c direction, a c , in Ca 2 GeO 4 (100-400 K) is À6.3 ppm K À1 , which is substantially larger than for Ca 2 MnO 4 measured over the same temperature range (a c = À4.4 ppm K À1 ). 10 It is worth noting that in our previous computational studies of NTE in these systems, 10 we used Ca 2 GeO 4 as a substitute for Ca 2 MnO 4 by applying a 4.3 GPa biaxial pressure to account for the in-plane exchange striction associated with Mn sites. The effect of this was to harden the soft phonon modes in our calculations with respect to the unstrained Ca 2 GeO 4 phase.…”