Evidence for broken ergodicity in strain glass

A recent study has indicated that there exists a different class of glass, the strain glass, in the nontransforming composition regime of Ti-Ni alloys. However, the critical proof for a glass, the evidence for the nonergodicity in the glassy state, has been missing in this system. By a zero-field-cooling/field-cooling measurement of static strain, we show experimentally that the ergodicity of the frozen strain glass is indeed broken. The creep measurement clearly shows the slowing down of kinetics upon strain glass transition. These features are physically parallel to other well-known glasses such as cluster-spin glasses and ferroelectric relaxors; thus, we introduce the notion of a ferroic glass and suggest a common underlying physics.

Figure 1

(Color online) Procedure of the zero-field-cooling (ZFC)/field-cooling (FC) measurement for strain glass, which can reveal the nonergodicity of a glass system. The strain glass sample was first cooled to a temperature $\left(T_{\text{low}}\right)$ well below the glass transition temperature $T_g$ under zero stress (ZFC, process 1). Then, an external tensile stress was applied and the sample was heated to a temperature $\left(T_{\text{high}}\right)$ far above $T_g$ under this stress (field heating or FH, process 2). Thereafter, the sample was cooled to $T_{\text{low}}$ again with the stress (FC, process 3) and then heated to $T_{\text{high}}$ again at the same stress (FH, process 4). The static strain curves that measured in process 2 and process 4 are called the ZFC curve and the FC curve, respectively, and their deviation is a signature for nonergodicity.

Figure 2

(Color online) The ZFC/FC curves of strain glass in comparison to that of a ferroelectric relaxor and cluster-spin glass, which demonstrate the broken ergodicity of these glasses. (a) ZFC/FC curves of ${\mathrm{Ti}}_{48.5}{\mathrm{Ni}}_{51.5}$ strain glass show a large deviation below $T_g$ $\left(168\mathrm{K}\right)$, which is very similar to (b) the ZFC/FC curves of a ferroelectric relaxor [PLZT $8∕65∕35$ (reproduced from Ref. 12)] and (c) the ZFC/FC curves of a cluster-spin glass [${\mathrm{La}}_{0.7}{\mathrm{Ca}}_{0.3}{\mathrm{Mn}}_{0.7}{\mathrm{Co}}_{0.3}{\mathrm{O}}_3$ (reproduced from Ref. 8)]. The inset depicts the unfrozen strain state above $T_g$, whereas the two panels on the left exhibit two different frozen strain states below $T_g$.

Figure 3

(Color online) The slowing down of kinetics of ${\mathrm{Ti}}_{48.5}{\mathrm{Ni}}_{51.5}$ strain glass. (a) The kinetics of strain relaxation in strain glass measured at different test temperatures, where $\epsilon \left(t\right)∕\epsilon \left(0\right)$ is a normalized strain. (b) Average relaxation time $\tau$ and the exponent $\beta$ (inset) as a function of temperature, which were obtained by fitting curves in (a) with the Kohlrausch-Williams-Watts relation, $\epsilon \left(t\right)∕\epsilon \left(0\right)=a+b\exp [-{(t∕\tau )}^{\beta }]$. The lines are guides for the eye. The experiment was performed with a dynamic mechanical analyzer in a three-point bending mode. The ${\mathrm{Ti}}_{48.5}{\mathrm{Ni}}_{51.5}$ strain glass sample with a size of $60\times 7\times 0.75{\mathrm{mm}}^3$ was cooled to different test temperatures spanning $T_g$ at zero field (stress) first; then, it was suddenly loaded with a constant stress $\left(20\mathrm{MPa}\right)$, and subsequently a time dependent relaxation of strain, i.e., the creep curve of strain, was recorded.