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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.