Negative thermal expansion (NTE)-the phenomenon where some materials shrink rather than expand when heated-is both intriguing and useful but remains poorly understood. Current understanding hinges on the role of specific vibrational modes, but in fact thermal expansion is a weighted sum of contributions from every possible mode. Here we overcome this difficulty by deriving a real-space model of atomic motion in the prototypical NTE material scandium trifluoride, ScF 3 , from total neutron scattering data. We show that NTE in this material depends not only on rigid unit modes-the vibrations in which the scandium coordination octahedra remain undistorted-but also on modes that distort these octahedra. Furthermore, in contrast with previous predictions, we show that the quasiharmonic approximation coupled with renormalization through anharmonic interactions describes this behavior well. Our results point the way towards a new understanding of how NTE is manifested in real materials.

Using calculations of the phonon distribution in ScF3 across the whole of reciprocal space, we show that the important phonons for the negative thermal expansion in this material are those associated with the rigid unit modes (RUMs) and associated quasi-RUMs. We discuss the role of the bond-bending flexibility within the ScF6 octahedra, and how this enables other phonons to make an additional but ultimately much weaker contribution to negative thermal expansion. These results inform recent discussions on the role of correlated atomic motions in giving rise to negative thermal expansion in ScF3.

The counterintuitive phenomenon of pressure-induced softening in materials is likely to be caused by the same dynamical behavior that produces negative thermal expansion. Through a combination of molecular dynamics simulation on an idealized model and neutron diffraction at variable temperature and pressure, we show the existence of extraordinary and unprecedented pressure-induced softening in the negative thermal expansion material scandium fluoride ScF 3. The pressure derivative of the bulk modulus B, B 0 ¼ ð∂B=∂PÞ P¼0 , reaches values as low as −220 AE 30 at 50 K, and is constant at −50 between 150 and 250 K.

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Objective: The aim of this retrospective study was to investigate clinical effects of the treatment of intra-articular distal humeral fractures via the combined posterior olecranon osteotomy and anterior approach and the combined lateral Kaplan approach associated with the medial approach. Methods: Between July 2010 and September 2019, 28 cases of intercondylar fractures of the distal humerus (AO/OTA type C) were treated by open reduction and internal fixation (ORIF) via the posterior and anterior approach and combined lateral-medial approach, which were divided into the P-A (n = 13) and L-M (n = 15) groups, respectively. The outcomes in terms of function were assessed using the range of motion (ROM) of the elbow and forearm, humerotrochlear (HT) angle, Visual Analogue Scale (VAS) scores, Mayo Elbow Performance Score (MEPS), and efficacy grade evaluated using the scoring system of Orthopaedic Trauma Association (OTA) at the one-year follow-up. Results: The flexion-extension of elbows and pronation-supination of forearms were respectively 114.1° ± 12.4° and 157.3° ± 9.6° in the P-A group and 117.1° ± 14.5° and 161.3° ± 10.7° in the L-M group. No significant difference was observed between the two groups for the elbow and forearm ROM (p > 0.05). Furthermore, surgery duration, blood loss volume, HT angle, MEPS, VAS scores, OTA rating, and the morbidity of postoperative complications during the one-year follow-up did not differ between groups. Conclusion: The posterior olecranon osteotomy and anterior approach can be used efficiently for exposure of complex distal humeral injuries with similar clinical efficacy and complications in the treatment of intra-articular distal humeral fractures as compared to the lateral-medial approach.