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Related Concept Videos

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration01:16

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A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
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Isolated atoms have discrete energy levels that are well described by the Bohr model. And, it quantifies the energy of an electron in a hydrogen atom as En. Higher quantum numbers 'n' yield less negative, closer electron energy levels.
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Particles in a solid are tightly packed together (fixed shape) and often arranged in a regular pattern; in a liquid, they are close together with no regular arrangement (no fixed shape); in a gas, they are far apart with no regular arrangement (no fixed shape). Particles in a solid vibrate about fixed positions (cannot flow) and do not generally move in relation to one another; in a liquid, they move past each other (can flow) but remain in essentially constant contact; in a gas, they move...
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The formation of a solution is an example of a spontaneous process, a process that occurs under specified conditions without energy from some external source.
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When an object is acted upon by a variable force, the amount of work done and the change in energy of the object can be more complex to calculate compared to when a constant force is applied. Work is the product of force and displacement, while energy is the capacity of a system to do work. When a constant force is applied to an object, the work done can be calculated as the product of the force and the distance moved in the direction of the force. However, when a variable force is applied, the...
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Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
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Low-Cost Vibrational Free Energies in Solid Solutions with Machine Learning Force Fields.

Kasper Tolborg1,2,3, Aron Walsh2,4

  • 1Department of Chemistry and Bioscience, Aalborg University, Fredrik Bajers Vej 7H, 9220 Aalborg Ø, Denmark.

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Summary

This study introduces a low-cost method to include vibrational entropy in cluster expansion calculations for alloys. This improves the accuracy of predicted phase diagrams, aiding materials design.

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Area of Science:

  • Computational materials science
  • Thermodynamics
  • Solid-state physics

Background:

  • Accurate phase diagram prediction is crucial for alloy design.
  • Cluster expansion is a key method for disordered crystals.
  • Vibrational entropy effects are often omitted due to high computational cost.

Purpose of the Study:

  • To develop a computationally inexpensive method for incorporating vibrational free energy into cluster expansions.
  • To enhance the accuracy of computational predictions for alloy phase diagrams.

Main Methods:

  • Fitting a machine learning force field (MLFF) to relaxation trajectories from cluster expansion construction.
  • Calculating phonon dispersions and vibrational free energies using the MLFF.
  • Applying the method to (pseudo)binary systems like Na1-xKxCl and Ag1-xPdx.

Main Results:

  • The MLFF approach accurately captures vibrational properties.
  • Inclusion of vibrational effects significantly improves agreement with experimental miscibility gaps.
  • Demonstrated success in two distinct alloy systems.

Conclusions:

  • The developed methodology enables routine inclusion of vibrational effects in phase diagram calculations.
  • This leads to more accurate predictions of material properties and stability.
  • Facilitates rational design of alloys and solid solutions.