Understanding of crystal wave vector

In summary, the conversation discusses the concepts of wave functions, wave vectors, and crystal wave vectors in relation to electrons and crystals. The group velocity and phase velocity are also mentioned. The main question is whether the crystal wave vector is a sum of individual wave vectors and why the electron wave vector is used in calculating density of states. The group velocity is defined as 'delta_omega/delta_k' and its intuitive meaning is unclear.
  • #1
Urmi Roy
753
1
Hi All,

From the Schrodinger wave equation, I kind of understand what a wave function and hence a wave vector is, so I understand what a wave vector of an electron wave is.
However while talking about crystals, there is also a 'crystal wave vector'. Is this a vector sum of wave vectors of individual electrons?
While finding density of states of electrons, why is the electron wave vector used instead of the crystal wave vector?
 
  • #3
So I've read that crystal wave vector corresponds to the group velocity while the electron's individual wave vector corresponds to it's phase velocity. However I'm still not sure if that means that the crystal wave vector means that it's effectively a 'net' or a sum of the individual ones.

The basic problem is that the group velocity is defined as 'delta_omega/delta_k', so what does this mean intuitively?
 

1. What is a crystal wave vector?

A crystal wave vector, also known as a reciprocal lattice vector, is a mathematical representation of the periodicity of a crystal lattice. It describes the direction and magnitude of the wave associated with the lattice vibrations in a crystal.

2. How is the crystal wave vector related to the crystal structure?

The crystal wave vector is directly related to the crystal structure. Each point in the reciprocal lattice corresponds to a specific set of lattice planes in the crystal structure. The direction of the crystal wave vector is perpendicular to these lattice planes.

3. What is the significance of the crystal wave vector in material science?

The crystal wave vector is crucial in understanding the properties and behavior of materials. It helps determine the diffraction pattern of a crystal, which provides information about its atomic arrangement and symmetry. It also plays a role in studying the electronic and vibrational properties of materials.

4. How is the crystal wave vector calculated?

The crystal wave vector can be calculated using the formula k = 2π/a, where k is the crystal wave vector, and a is the lattice constant. It can also be calculated using the Bragg equation, = 2dsinθ, where n is the order of diffraction, λ is the wavelength of the incident radiation, d is the lattice spacing, and θ is the angle of diffraction.

5. How does the crystal wave vector affect material properties?

The crystal wave vector has a significant impact on material properties. It influences the electronic band structure, which determines the electrical conductivity and optical properties of a material. It also affects the phonon dispersion, which governs the thermal and mechanical properties of materials. Understanding the crystal wave vector can provide insight into the behavior and performance of various materials in different applications.

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