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Related Concept Videos

Calculating Standard Free Energy Changes02:49

Calculating Standard Free Energy Changes

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The free energy change for a reaction that occurs under the standard conditions of 1 bar pressure and at 298 K is called the standard free energy change. Since free energy is a state function, its value depends only on the conditions of the initial and final states of the system. A convenient and common approach to the calculation of free energy changes for physical and chemical reactions is by use of widely available compilations of standard state thermodynamic data. One method involves the...
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One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...
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The free energy change associated with dissolving a solute in a liter of solvent is called the free energy of a solution, ΔGsolution. The overall ΔGsolution is expressed as the balance of ΔGinteraction against the always-favorable free-energy of mixing, ΔGmixing. Solution formation is favorable if  ΔGsolution is less than zero, whereas it is unfavorable if ΔGsolution is greater than zero. In short, for a solution to form and complete dissolution to take place,...
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The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature-dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered:
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Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
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Equilibrium calculations for systems involving multiple equilibria are often complex. For example, to calculate the solubility of a sparingly soluble salt in an aqueous solution in the presence of a common ion, one must consider all the equilibria in this solution. Calculations for these systems can be complicated and tedious, so a systematic approach with a series of steps is often helpful. The process is detailed below.
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A Generalized Solid Solution Framework for the Gibbs Free Energy Calculation.

Yang Huang1,2,3, Jingrun Chen2,3,4

  • 1School of Artificial Intelligence and Data Science, University of Science and Technology of China, Hefei 230026, China.

Journal of Chemical Theory and Computation
|September 17, 2025
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Summary
This summary is machine-generated.

This study introduces a generalized solid solution model using graph neural networks to calculate Gibbs free energy for alloys. The model accurately predicts phase transitions and diagrams for complex systems like Mo-Nb-Ta-W.

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Area of Science:

  • Materials Science
  • Computational Materials Science
  • Thermodynamics

Background:

  • Calculating configurational Gibbs free energy is crucial for predicting alloy behavior.
  • Existing methods like cluster expansion have limitations in applicability and accuracy.

Purpose of the Study:

  • To develop a generalized solid solution model for accurate Gibbs free energy calculations.
  • To unify existing approaches and enable broad applicability across crystal structures.

Main Methods:

  • Utilizing a crystal graph-based on-site energy approach with linear graph neural networks.
  • Incorporating mean-field theory for fractional occupation and ideal mixing for entropy.
  • Implementing softmax transformation, gradient projection, and renormalization for composition control.

Main Results:

  • Achieved a mean absolute error (MAE) of 1.24 meV for the Mo-Nb-Ta-W system.
  • Accurately predicted phase transition temperatures and types (separation, order-disorder) for binary alloys.
  • Successfully predicted ternary phase diagrams and identified stable configurations below the convex hull.

Conclusions:

  • The generalized solid solution model offers a unified and broadly applicable approach for thermodynamic calculations.
  • The model demonstrates high predictive accuracy for complex alloy systems.
  • This method advances the prediction of phase diagrams and material behavior at finite temperatures.