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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
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Finite-temperature mechanical instability in disordered lattices.
1Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.
Physical Review. E
|March 18, 2016
Summary
Thermal fluctuations surprisingly stabilize disordered mechanical systems. This study reveals distinct scaling behaviors for shear modulus in triangular and square lattices, offering insights into finite-temperature stability.
Area of Science:
- Condensed Matter Physics
- Materials Science
- Statistical Mechanics
Background:
- Mechanical instability is crucial in ordered and disordered systems.
- The impact of thermal fluctuations on mechanical instabilities is not well understood.
- Disordered systems exhibit diverse mechanical behaviors.
Purpose of the Study:
- To develop a theory for finite-temperature mechanical stability in disordered systems.
- To investigate the influence of thermal fluctuations on mechanical instabilities.
- To analyze the critical behavior of disordered lattices near mechanical instability.
Main Methods:
- Developed an analytic theory using renormalization of rigidity and coherent potential approximation.
- Studied two specific disordered lattices: a randomly diluted triangular lattice and a randomly braced square lattice.
- Analyzed the scaling of shear modulus with temperature (T).
Main Results:
- Thermal fluctuations were found to stabilize both studied disordered lattices.
- The triangular lattice exhibited shear modulus scaling as G∼T(1/2).
- The square lattice displayed shear modulus scaling as G∼T(2/3).
Conclusions:
- Finite-temperature effects significantly alter mechanical stability in disordered systems.
- Distinct universality classes of mechanical instability show different thermal scaling behaviors.
- The findings provide a framework for understanding and predicting the behavior of experimental systems under thermal stress.
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