Book contents
- Frontmatter
- Dedication
- Contents
- Boxes
- Preface
- Part 1 Getting Started
- Part II Static Properties
- Part III Dynamical Properties
- 9 Lattice Dynamics
- 10 Density’Functional Perturbation Theory
- 11 Dielectric Properties
- 12 Phonons
- 13 Vibrational Spectroscopy
- 14 A Few Examples of Phonon Analysis
- 15 Advanced Topics in Density Functional Perturbation Theory
- 16 Molecular Dynamics
- 17 Analysis of theMolecular Dynamics Simulations
- 18 Computational Perspectives
- References
- Index
12 - Phonons
from Part III - Dynamical Properties
Published online by Cambridge University Press: aN Invalid Date NaN
Book contents
- Frontmatter
- Dedication
- Contents
- Boxes
- Preface
- Part 1 Getting Started
- Part II Static Properties
- Part III Dynamical Properties
- 9 Lattice Dynamics
- 10 Density’Functional Perturbation Theory
- 11 Dielectric Properties
- 12 Phonons
- 13 Vibrational Spectroscopy
- 14 A Few Examples of Phonon Analysis
- 15 Advanced Topics in Density Functional Perturbation Theory
- 16 Molecular Dynamics
- 17 Analysis of theMolecular Dynamics Simulations
- 18 Computational Perspectives
- References
- Index
Summary
We analyse the energy derivatives in terms of atomic displacements. We derive the interatomic force constants tensor, and from there we obtain the dynamical matrix. We introduce the phonons as quanta of atomic motion in crystals. They are obtained by diagonalization of the dynamical matrix. To comprehensively grasp phonons, we employ the quasiharmonic approximation, limiting energy development to second-order terms. Phonons are defined by their wavevectors and frequencies, governing their orientation and energy, respectively. Unlike particles, they are quasi-particles and follow Bose–Einstein statistics as bosons.
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- Information
- Computational Mineral PhysicsA Practical Guide for Earth Scientists, pp. 183 - 207Publisher: Cambridge University PressPrint publication year: 2026
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