Localized Symmetry Breaking for Tuning Thermal Expansion

Thermal expansion, the tendency of matter to change in shape and volume in response to a change in temperature, is a significant problem for many materials and engineering applications. Hence, the control of thermal expansion represents a challenge for materials design. In this regard, an international team of researchers from China, Italy, Turkey and United States, has demonstrated that a localized symmetry breaking can be an effective route to achieve controllable thermal expansion. The work, conducted in part at the XAFS beamline of Elettra and at the beamlines 11-ID-C and 20-BM-B of the Advanced Photon Source at Argonne National Laboratory, has been published in the Journal of the American Chemical Society.
ScF₃ nanocrystals with different average sizes (∼13.2, ∼8.1 and ∼6.3 nm) were prepared and the corresponding lattice thermal expansion investigated by high-resolution x-ray diffraction. It is interesting to note that the lattice thermal expansion of ScF₃ is tuned by reducing the crystal size (Figure 1), with an isotropic zero thermal expansion (∼4.0x10^-8 K^-1) achieved over a wide temperature range for nanocrystals with size ∼8.1 nm.
 

Figure 1.  Temperature dependence of the relative lattice constant of ScF3 in bulk and nano forms. By reducing the crystal size, the thermal expansion is tuned from negative to zero to positive.

In order to shed light on the effect of local structure and vibrational dynamics on the tuning of thermal expansion, further studies were carried out by X-ray pair distribution function (PDF) analysis, Extended X-ray Absorption Fine Structure (EXAFS) and first-principles calculations. Firstly, we observed by EXAFS that the fluorine vibrations perpendicular to the Sc-F-Sc linkages, associated with the strong negative thermal expansion (NTE) of bulk ScF₃ through the “guitar-string” effect, are  considerably suppressed in ScF₃ anocrystals (Figure 2a). Secondly, we found out that, in nano ScF₃, the PDF refinements with rhombohedral symmetry are better than those with cubic phase below a certain short-range (Figure 2b). This indicates that a local rhombohedral distortion occurs in ScF₃ nanocrystals. Finally, first-principles calculations showed that the phonon modes with large negative Grüneisen parameters, contributing to NTE in bulk (cubic) ScF₃, disappear in the rhombohedral phase (Figure 2c). Besides, a strong distortion was found in the simulated ScF₃ nanocrystals, highly consistent with  the localized symmetry  breaking  found in the PDF refinements, thus validating the experimental results.
 

Figure 2.  (a) Schematic illustration of the relative thermal ellipsoids of Sc and F atoms in bulk and nano ScF₃. The “guitar-string” effect is considerably suppressed in ScF₃ nanocrystals. (b) Goodness of the PDF refinements, as a function of the local distance, using the cubic and rhombohedral phases for the different ScF₃ nanoscrystals. (c) Grüneisen-weighted phonon density of states (DOS) in cubic and rhombohedral ScF₃, respectively.

In conclusion, we have found out that the thermal expansion of ScF₃ can be well tuned by reducing crystalline sizes and, specifically, a localized symmetry breaking is at the origin of such thermal expansion modification. The present work opens a new way to achieve the control of thermal expansion by breaking local symmetries in materials.

This research was conducted by the following research team:

Lei Hu,^1,3 Feiyu Qin,¹ Andrea Sanson,² Liang-Feng Huang,³ Zhao Pan,¹ Qiang Li,¹ Qiang Sun,⁴ Lu Wang,¹ Fangmin Guo,⁵ Umut Aydemir,^3,6 Yang Ren,⁵ Chengjun Sun,⁵ Jinxia Deng,¹ Giuliana Aquilanti,⁷ James M. Rondinelli,³ Jun Chen,¹ and Xianran Xing,¹

¹ University of Science and Technology Beijing, Beijing, China 
² University of Padova, Padova, Italy 
³ Northwestern University, Evanston, Illinois, United States 
⁴ Zhengzhou University, Zhengzhou, China 
⁵ Argonne National Laboratory, Argonne, Illinois, United States 
⁶ Koc University, Istanbul, Turkey 
⁷ Elettra-Sincrotrone Trieste, Trieste, Italy

Contact persons:

Giuliana Aquilanti, email:
Andrea Sanson, email: