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The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...
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Phases of Ca from first principles.

S L Qiu1, P M Marcus

  • 1Department of Physics, Florida Atlantic University, Boca Raton, FL 33431-0991, USA.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|August 12, 2011
PubMed
Summary
This summary is machine-generated.

This study calculates calcium (Ca) crystal structures under high pressure, revealing fewer distinct phases than previously thought. It identifies stable structures and predicts phase transition pressures for Ca over a wide pressure range.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Computational Materials Science

Background:

  • Understanding the behavior of materials under extreme pressure is crucial for materials science.
  • Calcium (Ca) exhibits complex phase transitions under pressure, necessitating detailed theoretical investigation.

Purpose of the Study:

  • To systematically calculate and identify stable crystal structures of calcium (Ca) under high pressure.
  • To determine the thermodynamic properties and phase transition pressures of Ca over a multi-megabar range.

Main Methods:

  • First-principles calculations employing energy minimization under constant volume constraints.
  • Systematic exploration of 11 of 14 Bravais symmetries for one-atom-per-cell structures.
  • Calculation of Gibbs free energy (G(p)) for non-vibrating lattices to determine phase stability.

Main Results:

  • Identified a reduced number of distinct Ca phases, with orthorhombic phases being equivalent to higher-symmetry ones.
  • Confirmed the stability of the simple cubic phase as a ground state under specific conditions.
  • Calculated Gibbs free energy functions to map the ground state and relative stabilities across various pressures.

Conclusions:

  • The high-pressure phase diagram of Ca is simpler than previously assumed, with specific high-symmetry phases dominating.
  • Thermodynamic calculations accurately predict phase transition pressures, providing a comprehensive understanding of Ca's behavior under extreme conditions.