Stochasticity in materials structure, properties, and processing-A review

Area of Science:

• Materials Science
• Statistical Mechanics

Background:

• Stochasticity, defined as unpredictable fluctuations in material structure, chemistry, or kinetics, is a fundamental aspect of materials science.
• Existing research often focuses on specific types of stochasticity, necessitating a broader framework.

Purpose of the Study:

• To review and categorize the concept of stochasticity in materials.
• To develop a mathematical framework for describing materials stochasticity.
• To explore the implications of stochasticity for materials properties and design.

Main Methods:

• Review of existing literature on materials stochasticity.
• Development of a generalized mathematical framework for stochasticity.
• Analysis of specific classes of stochasticity including equilibrium, structural/compositional, kinetic, and frustration/degeneracy.

Main Results:

• Six classes of stochasticity are identified, with a focus on four inherent to materials.
• A mathematical framework is presented and applied to describe these inherent stochastic phenomena.
• Stochasticity at small scales influences macroscopic properties, and processing can amplify these effects.

Conclusions:

• Stochasticity is a critical factor influencing material properties and behavior across various scales.
• Predicting and controlling materials stochasticity offers a new avenue for innovative materials design.
• Integrating stochastic descriptions into materials design can lead to enhanced performance and novel functionalities.