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Maxwell's Thermodynamic Relations01:23

Maxwell's Thermodynamic Relations

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Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
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Free energy—abbreviated as G for the scientist Gibbs who discovered it—is a measurement of useful energy that can be extracted from a reaction to do work. It is the energy in a chemical reaction that is available after entropy is accounted for. Reactions that take in energy are considered endergonic and reactions that release energy are exergonic. Plants carry out endergonic reactions by taking in sunlight and carbon dioxide to produce glucose and oxygen. Animals, in turn, break...
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Thermodynamics: Activity Coefficient01:24

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Activity is the measure of the effective concentration of the species in solution. It can be expressed as the product of the molar concentration of the species and its activity coefficient. The activity coefficient is a dimensionless quantity and depends on the total ionic strength of the solution.
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The volume occupied by one mole of a substance is its molar volume. The ideal gas law, PV = nRT,  suggests that the volume of a given quantity of gas and the number of moles in a given volume of gas vary with changes in pressure and temperature. At standard temperature and pressure, or STP (273.15 K and 1 atm), one mole of an ideal gas (regardless of its identity) has a volume of about 22.4 L — this is referred to as the standard molar volume.
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Thermodynamic Potentials01:26

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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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Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1:
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Machine learning for improved density functional theory thermodynamics.

Sergei I Simak1,2, Erna K Delczeg-Czirjak3,4, Olle Eriksson3,4

  • 1Department of Physics, Chemistry and Biology (IFM), Linköping University, 581 83, Linköping, Sweden. sersi78@liu.se.

Scientific Reports
|May 17, 2025
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Summary
This summary is machine-generated.

Machine learning corrects density functional theory (DFT) errors in alloy formation enthalpies. This improves predictions for ternary phase stability, crucial for materials science and high-temperature applications.

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Area of Science:

  • Computational Materials Science
  • Machine Learning in Chemistry
  • Thermodynamics of Alloys

Background:

  • Density functional theory (DFT) is a powerful tool for predicting material properties but suffers from energy resolution errors.
  • These errors significantly impact the accuracy of alloy formation enthalpies, especially in complex ternary systems.
  • Reliable prediction of phase stability is critical for designing new materials for demanding applications.

Purpose of the Study:

  • To develop a machine learning (ML) approach to systematically correct DFT energy errors in alloy formation enthalpies.
  • To enhance the predictive accuracy of first-principles calculations for binary and ternary alloys and compounds.
  • To improve the reliability of phase stability predictions for materials relevant to aerospace and protective coatings.

Main Methods:

  • A neural network model was trained to predict the discrepancy between DFT and experimental enthalpies.
  • The model used a feature set including elemental concentrations, atomic numbers, and interaction terms.
  • Supervised learning, rigorous data curation, and cross-validation (LOOCV, k-fold) were employed to ensure model robustness and prevent overfitting.

Main Results:

  • The ML model successfully learned to predict and correct DFT energy errors for alloy formation enthalpies.
  • Application to Al-Ni-Pd and Al-Ni-Ti systems demonstrated significant improvement in prediction accuracy.
  • The corrected predictions offer more reliable insights into ternary phase stability.

Conclusions:

  • The presented ML approach provides a robust method for correcting DFT energy errors in alloy formation enthalpies.
  • This significantly enhances the reliability of first-principles predictions for alloy phase stability.
  • The corrected predictions are valuable for accelerating the discovery of new materials for high-temperature applications.