Elastic properties of amorphous and crystalline B_1-xC_x and boron at low temperatures

We present measurements of the internal friction (Q^-1) and speed of sound variation (δv/v_o) of amorphous boron (a-B) and amorphous B₉C (a-B₉C). The elastic properties of these materials, which can only be produced as thin films, are consistent with those of other amorphous solids measured to date and exhibit good agreement with the tunneling model (TM) of amorphous solids. The TM parameter P̄γ_t²/ρv_t² extracted from the elastic data has the same order of magnitude as that observed for all amorphous solids studied to date; a review will be presented. Using the results from the elastic measurements, we calculate the T² thermal conductivity A expected in the TM regime (7 ≤ 1 K) for a-B. The predicted thermal conductivity falls within the expected range for amorphous solids and agrees with the thermal conductivity of the crystalline icosahedral boride MB_68-δ (M=Y, Gd), which has been previously shown to exhibit glass-like excitations. We have also measured the internal friction and speed of sound variation of bulk polycrystalline c-B_1-xC_x at low temperatures (0.07 K < T < 10 K). The elastic properties evolve towards the behavior characteristics of amorphous solids for increasingly carbon-deficient (x < 0.20) specimens. The magnitude of the internal friction for the most carbon-deficient crystalline c-B_1-xC_x sample (x = 0.1, c-B₉C) is comparable to that for a-B and a-B₉C, thereby confirming the inherent glass-like vibrational properties of carbon-deficient C-B_1-xC_x. Such behavior supports the glass-like character of carbon-deficient c-B_1-xC_x high temperature (T > 50 K) thermal transport reported previously and provides the first experimental evidence for the presence of two-level systems (TLS) in these crystalline solids. However, discrepancies with the tunneling model are present; the data for c-B_1-xC_x bear some similarity to those for amorphous metals in which electronic relaxation channels are active, although details are still unclear. Previous studies have shown that the TM quantity C = Pγ_t²/ρv_t² ("tunneling strength") is essentially independent of the material's shear modulus G = ρv_t² over a factor of ∼ 17. The elastic data presented in this work now extend the observed independence of the tunneling strength, C, over a factor of ∼ 70 in shear modulus.