Dispersion relation ~ modern phyics (solid state physics)

[adamaero]

Homework Statement

Which cannot be the structure of two acoustic branches, nor three acoustic branches?
Simple cubic, FCC, BCC, diamond cubic, NaCl lattice

Homework Equations

N/A
http://solid.fizica.unibuc.ro/cursuri/solid_en/curs_solid_EN.pdf#page=61
http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/bravais.html
http://image.slidesharecdn.com/crys...-in-material-science-24-638.jpg?cb=1412805736

The Attempt at a Solution

The dispersion relation only identifies acoustic branches which means there is only one atom in the basis of this crystal. But I don't know why.
Why is this true?
(And sorry I misspelt in the title.)

 

[ehild]

Homework Statement

Which cannot be the structure of two acoustic branches, nor three acoustic branches?
Simple cubic, FCC, BCC, diamond cubic, NaCl lattice

Homework Equations

N/A
http://solid.fizica.unibuc.ro/cursuri/solid_en/curs_solid_EN.pdf#page=61
http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/bravais.html
http://image.slidesharecdn.com/crys...-in-material-science-24-638.jpg?cb=1412805736

The Attempt at a Solution

The dispersion relation only identifies acoustic branches which means there is only one atom in the basis of this crystal. But I don't know why.
Why is this true?
(And sorry I misspelt in the title.)

I do not understand your question. The dispersion relations are relations between wavenumber vector and frequency of a wave. When the base of the crystal consists of a single atom, it can only vibrate with respect to the atoms in the other cells. At k=0, the frequency of the vibration is also 0. Such wave is called an acoustic wave. In a 3D crystal, there are three branches of acoustic waves, one branch for longitudinal and two branches for transverse waves. In highly symmetric crystals the two transverse branches coincide.
In case a base of more than one atom, the atoms of the base can vibrate with respect to each other giving rise to optical branches.
In the examples of your first reference, one-dimensional crystals (chains of atoms) are discussed. In one dimensional word, the atoms can only vibrate along the chain.