Expanding atomic displacements in terms of all lattice wave modes?

In summary, the expression "In general, one can expand the atomic displacements in terms of all the lattice wave modes (resembles a Fourier series expansion)" refers to the expansion of atomic displacements in a 3D lattice in terms of all possible lattice wave modes. This concept is similar to normal mode decomposition of a system of coupled oscillators, but with the added constraint of periodic boundary conditions in an infinite system. This expression is not commonly found in literature, but can be explained in books on solid state theory.
  • #1
zhanhai
69
0
I find the expression:

"In general, one can expand the atomic displacements in terms of all the lattice wave
modes (resembles a Fourier series expansion)"

at:
https://courses.cit.cornell.edu/ece407/Lectures/handout17.pdf

But I have not found the expression in any other literature. (In fact, some literature, like P.Y. Yu and M. Cardona: Fundamentals of Semiconductors, a long wavelength limitation seems to have been imposed.) Is the above-cited expression correct (in 3D lattice)?

Thank for your assistance.
 
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  • #2
Yes, that's true. Should be explained in any book on solid state theory.
 
  • #3
Have you ever done normal mode decomposition of a system of coupled oscillators? This is the same, except that the system is infinite, but periodic boundary conditions are imposed.
 

Related to Expanding atomic displacements in terms of all lattice wave modes?

1. What are atomic displacements in the context of lattice wave modes?

Atomic displacements refer to the movement or vibration of atoms within a crystal lattice. In terms of lattice wave modes, this refers to the displacement of atoms from their equilibrium positions due to the propagation of lattice waves through the crystal.

2. How are atomic displacements related to lattice wave modes?

Lattice wave modes are essentially collective vibrations of atoms within a crystal lattice. As these waves propagate through the crystal, they cause the atoms to move from their equilibrium positions, resulting in atomic displacements.

3. How can atomic displacements be expanded in terms of all lattice wave modes?

In order to expand atomic displacements in terms of all lattice wave modes, one must use a mathematical technique called Fourier analysis. This allows us to break down the complex motion of atoms into a series of simpler, sine and cosine waves.

4. Can atomic displacements be measured experimentally?

Yes, atomic displacements can be measured experimentally using techniques such as x-ray diffraction or neutron scattering. These methods allow us to observe the changes in atomic positions within a crystal lattice as lattice waves propagate through it.

5. What is the significance of expanding atomic displacements in terms of all lattice wave modes?

Expanding atomic displacements in terms of all lattice wave modes allows us to better understand the behavior of crystals and their response to external stimuli. It also helps us to study the properties of different lattice wave modes and their effects on the overall structure and dynamics of crystals.

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