Are the vibration modes at the lattice centre odd or even?

[Frank Einstein]

Homework Statement

Good morning. I am currently doing an solid state problem; in this part, I have to tell if these vibration modes are odd or even. I am working at the lattice centre.
The modes are these http://postimg.org/image/8nmv7ickz/.

Homework Equations

None

The Attempt at a Solution

The centre of inversion is the blue cross; I have studied only two dimensional modes, so I don't have very clear how the three dimensional translations have to be done; I think it that this is what happens: http://postimg.org/image/xd01nfxr1/
which would make both modes odd.
Can someone please confirm this?
Thanks for reading.

 

[nilesh_pat]

Yes, both of the modes are odd. The first mode involves a two-dimensional translation, with one atom moving to the left and one atom moving to the right. This is an odd vibration mode because it does not have an inversion center. The second mode involves a three-dimensional translation, with one atom moving up, one atom moving down, and one atom moving to the side. This is also an odd vibration mode because it does not have an inversion center.