Unified quantifier of mechanical disorder in solids

Area of Science:

• Solid-state physics
• Materials science
• Condensed matter physics

Background:

• Mechanical disorder in solids influences material properties and arises from diverse physical processes.
• Existing dimensionless quantifiers for mechanical disorder are system-specific.
• Quantifying and comparing mechanical disorder across different systems is crucial.

Purpose of the Study:

• To establish a unified, measurable dimensionless quantifier for mechanical disorder in solids.
• To reveal the intrinsic relationship between two previously distinct quantifiers of mechanical disorder.
• To provide a universal metric for comparing mechanical disorder across various physical systems.

Main Methods:

• Utilized two complementary theoretical approaches based on the vibrational spectra of solids.
• Derived a scaling relation connecting spectral broadening of phononic bands and spatial fluctuations of shear modulus.
• Validated the scaling relation using existing simulational data.

Main Results:

• Established a fundamental scaling relation between two coarse-grained dimensionless quantifiers of mechanical disorder.
• Demonstrated that these two quantifiers are intrinsically linked, forming a unified measure.
• The unified quantifier is supported by computational simulation data.

Conclusions:

• The two distinct quantifiers of mechanical disorder are fundamentally related, leading to a unified measure.
• This unified quantifier has implications for understanding the unjamming transition in soft materials.
• Provides a more comprehensive understanding of low-frequency vibrational spectra in disordered and glassy solids.