Large isotropic negative thermal expansion above a structural quantum phase transition

Abstract

Perovskite structured materials contain myriad tunable ordered phases of electronic and magnetic origin with proven technological importance and strong promise for a variety of energy solutions. An always-contributing influence beneath these cooperative and competing interactions is the lattice, whose physics may be obscured in complex perovskites by the many coupled degrees of freedom, which makes these systems interesting. Here, we report signatures of an approach to a quantum phase transition very near the ground state of the nonmagnetic, ionic insulating, simple cubic perovskite material ScF 3 , and show that its physical properties are strongly effected as much as 100 K above the putative transition. Spatial and temporal correlations in the high-symmetry cubic phase determined using energy-and momentum-resolved inelastic x-ray scattering as well as x-ray diffraction reveal that soft mode, central peak, and thermal expansion phenomena are all strongly influenced by the transition. The class of materials with the perovskite structure and chemical formula ABX 3 contains examples of perhaps every possible type of physical behavior [1,2], much of which is difficult to understand because of the shear complexity of matter. A rich terrain of structural transitions associated with BX 6 octahedral tilting in perovskites strongly effects electronic conduction and magnetic exchange pathways, defining the framework of interactions governing a range of physical properties. The A-site tolerance appears to be an important parameter in determining the structural phase stability [1-3], but stable A-site-free perovskite structures are also thermodynamically stable. These are rare cases among oxides (X = O) because the B ions must take on rare hexavalent (+6) electronic configurations, and the only known instance is ReO 3 . In perovskites based on fluorine (X = F), however, the B ions assume the common trivalent (+3) configuration in an expanded suite of A-site-free perovskite lattices.Figure 1(a) shows a structural phase diagram of BF 3 perovskites, where B is a trivalent metal ion [4]. The 3d metal trifluorides display a reversible [5] structural cubic-torhombohedral (c-r) phase boundary. This sequence of 3d transition metal trifluoride compounds is rhombohedral at room temperature, with the exception of B = Sc, which appears at the zero-temperature terminated c-r phase boundary. Indeed, no rhombohedral phase transition has been observed for ScF 3 down to 0.4 K [6], suggesting that near this composition, the structural phase can be driven by a parameter other than temperature, implying that the ground state of this ionic insulator is very near a quantum phase transition (QPT). Cubic ScF 3 further stands out among substances in that it has the most stable structural phase of any known solid trifluoride, * Corresponding author: jason.hancock@uconn.edu retaining high cubic symmetry and a four-atom unit cell up to its high melting point, >1800 K [6,7]. Separate from the QPT reported here, further interest in this system is due t...

Negative Thermal Expansion Near the Precipice of Structural Stability in Open Perovskites

“…Inset focuses on available data for ReO 3 on 4 different samples, one (ReO 3 -I) over an extended temperature range (Chatterji et al, 2009b) and the other 3 (ReO 3 -II a-c) over a smaller temperature range, investigating the effects of compositional disorder (Rodriguez et al, 2009) (see section 5). Data taken from: ZrW 2 O 8 (Mary et al, 1996), CaZrF 6 (Hancock et al, 2015), ScF 3 -I (Handunkanda et al, 2015), ScF 3 -II (Greve et al, 2010), ReO 3 -I (Chatterji et al, 2009b), and ReO 3 -II (Rodriguez et al, 2009). …”

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

“…The associated soft modes reside on onedimensional manifolds along the simple cubic Brillouin zone (BZ) edges. Recent inelastic X-ray scattering (IXS) work analyzing the temporal correlations of single-crystal ScF 3 has indeed shown the presence of a soft mode manifold circumscribing the BZ edges 12 . Here we extend this study using high energy resolution diffuse X-ray scattering and find that these soft modes imply 2D spatial correlations associated with NTE.…”

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

“…2D nanoscale correlations Recent inelastic X-ray scattering work [18,47] has shown that ScF 3 features an incipient soft mode instability via its excitation spectrum. Specifically, the 'central peak' phenomenon and a dispersionless branch of modes circumscribing the edges of the simple cubic Brillouin zone softens to zero temperature according to classical scaling and a putative transition temperature T =-39 K. The dispersionless nature of modes in one dimension of reciprocal space and observed diffuse X-ray scattering rods suggest a dimensional lowering in this system, permitting application of the 2D CLM [47].…”

“…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). The origin of the lengthened oscillation period in the 2D CLM is the large translational motion of molecules throughout the crystal and may be important to address in quantitative comparisons of computational results with experiments.…”

“…For example, metallic ReO 3 and insulating ScF 3 with open perovskite structure display SNTE over a wide range of temperatures [15,16], but why do other open perovskites most commonly exhibit positive thermal expansion (PTE)? Why is SNTE so rare and inevitably yields to PTE in response to disorder [16][17][18] and application of pressure? In pursuit of conceptual control of the phenomenon, innovative approaches have been offered which link thermally-activated transverse vibration of structural units to a tendency to draw in lattice dimensions.…”