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After wide investigations for decades, various models have been proposed to interpret the origin of the boson peak, such as the heterogeneous elasticity theory 17, soft anharmonic potentials 18, 19, phonon-saddle transition in the energy landscape 20, local inversion-symmetry breaking associated with nonaffine shear softening 21, 22, and smeared out van Hove singularity 23, 24. It is widely accepted that the boson peak reflects the intrinsic vibrational properties of structural glasses, and thus plays a key role in fundamentally understanding the nature of structural glasses. This anomaly becomes an anomalous peak upon plotting the reduced VDOS g( ω) /ω 2 over ω ( ω is the frequency), and can also be manifested by a peak in the specific heat ( C p) at 5–20 K in a plot of C p/ T 3 vs. In particular, the boson peak is a universal glassy dynamic feature found in metallic glass (and other structural glasses) 14, 15, 16, which is an anomaly in the vibrational density of states (VDOS), where an excess of vibrational states takes place, departing from the Debye squared-frequency law for crystals at low frequencies of the order of 1 THz. However, despite these efforts, the nature of strain glass is still unclear especially the glassy dynamic features of strain glass are still blurred, as compared with those of metallic glass, the well-known structural glass in metals.ĭue to lacking crystalline periodicity, metallic glass exhibits unique dynamic relaxations distinct from the corresponding crystalline alloys, such as primary α-relaxation, β-relaxation, and boson peak 14, 15, 16.
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The glass behavior of strain glass has been characterized by the slowing-down of dynamics 4, 10, 11, and some phenomenological models have been established to successfully capture the experimental features of strain glass 12, 13. Strain glass is of interest due to its unique functionalities 5, 6, 7, 8, 9 such as slim or even non-hysteretic superelasticity and low-field-triggered large magnetostriction, and thereby is of potential importance to develop novel smart materials. In comparison with spin glass and ferroelectric relaxor, strain glass is a relatively new state of matter in concept, which is a glassy state with local strain order while maintaining average structure unchanged in shape memory alloys 5. The order parameter can be magnetic moment (for ferromagnetic transition), dielectric polarization (for ferroelectric transition) and lattice strain (for ferroelastic/martensitic transition), which corresponds to a different ferroic glassy state, i.e., spin glass, ferroelectric relaxor and strain glass, respectively 1, 2, 3, 4. However, when the frustration caused by point defects or dopants is strong enough in the system, a metastable glassy state with local order of the order parameter may take place 1. Phase transitions in ferroic materials involve long-range ordering of a certain order parameter.
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This work might provide fresh insights in understanding the nature of glassy states and associated vibrational properties. Therefore, this anomaly neither is a relic of van Hove singularity nor can be explained by other theories relying on structural disorder, while it verifies a recent theoretical model without any assumptions of disorder. The simulation studies show that this boson-peak-like anomaly is caused by the phonon softening of the non-transforming matrix surrounding martensitic domains, which occurs in a transverse acoustic branch not associated with the martensitic transformation displacements. An abnormal hump is observed in strain glass around 10 K upon normalizing the specific heat by cubed temperature, similar to the boson peak in metallic glass. Here, we report a glassy feature in strain glass that was thought to be only present in structural glasses. Strain glass is a glassy state with frozen ferroelastic/martensitic nanodomains in shape memory alloys, yet its nature remains unclear.