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Incommensurate systems demonstrating glasslike behavior
In spite of a continuing effort, glasses are still an open topic of solid state physics. There is an inherent difficulty in applying concepts developed for crystalline, ordered solids to their noncrystalline counterparts: even though glasses display mechanical properties of solids, the very lack of order makes them more akin to liquids. Together with their French and German colleagues, Katica Biljaković and Damir Starešinić from Institut za fiziku have recently published a paper in Physical Review Letters on features found in specific heat of ThBr4 that link crystalline incommensurate systems and glasslike behavior.
Incommensurate Systems as Model Compounds for Disorder Revealing Low-Temperature Glasslike Behavior
Reményi, S. Sahling, K. Biljaković, D. Starešinić, J.-C. Lasjaunias, J. E. Lorenzo, P. Monceau, A. Cano
Phys. Rev. Lett. 114, 195502 (2015)
ThBr4 is an almost ideal example of a crystal with an incommensurately modulated lattice. Since there are no free electrons to provide screening and no mixing with phonons, the phase and amplitude excitations of the modulated superstructure together with their dispersions can readily be determined (for instance using neutron scattering) at very small wave vectors. The problematic region however is right around k=0, particularly for phasons which are approximately acoustic and their gap cannot be reliably confirmed, let alone determined.
Figure 1. Schematic representation of the low energy vibrational modes in incommensurate compounds. (a) Phonon softening at the incommensurate (IC) wave vector qIC=0.31, on approaching the transition temperature TC. (b) Symmetry breaking of the soft phonon eigenmodes into the amplitudon (optical-like) and phason (acoustic-like) mode. (c) The phason branch in gapped, with gap value Δ and damping constant Γ. (d) 2D picture of the reciprocal space for T>TC with the Bragg peaks in red. (e) Idem for T<TC, with the blue dots as the new Bragg peaks, called satellite peaks, originating from the periodicitiy of the IC superstructure.
The specific heat measurements Cp of crystalline ThBr4 published in this paper circumvent the problem and paint a different picture of this “perfectly ordered” system. The features observed are considered typical to glasses as perfectly disordered systems: a maximum in Cp/T3, also known as the boson peak, and a linear contribution to Cp at very low temperatures which is in glasses commonly assigned to localized excitations of so-called two-level systems.
Based on experience with other incommensurate systems such as charge- and spin-density waves, this paper demonstrates that the boson peak can be explained as a contribution of amplitude excitations using only known parameters of dispersion. Also, theoretical analysis ascribes the linear contribution to to a redistribution of density of states due to the finite lifetime of long-wavelength (k->0) excitations. The estimated (finite) phason dispersion gap (Δ) as well as lifetime (Γ-1) btained from fits are compatible with neutron scattering experiments. More so, the specific heat measurements allow the low-frequency dispersion to be determined with a greater precision than what neutron diffraction can provide.
Figure 2. Temperature dependence of the specific heat cp in of ThBr4 divided by T3 and the contributions of the low energy modes. Experimental data are displayed with full black circles. The dashed black line represents the Debye (acoustic phonon) contribution and the dashed green line the amplitudon contribution. Both are calculated according to the dispersions experimentally determined by inelastic neutron scattering. Full red circles represent the contribution remaining after subtraction of Debye and amplitudon contributions, and assigned to the phason mode. The continuous black line is calculated from the estimated phason dispersion with the finite gap Δ=46 GHz and finite damping Γ=3.8 GHz. The dispersion used in the calculation is presented with the line in the inset and compared to sparse experimentally determined points.
The “glassy” properties of ThBr4 have successfully been explained as due to excitations of the incommensurate superstructure. This points to a possible new understanding glasses as “multiply incommensurate crystals”.