Answer to Question #178804 in General Chemistry for Sarasania

Question

The unit cell of an oxide crystal with a cubic lattice parameter of 4.00 Å

contains the following atoms (the ordered sets are the coefficients of location that

define rj

):

B at (0,0,0)

A at (1/2,1/2,1/2)

O at (1/2,0,0)

O at (0,1/2,0)

O at (0,0,1/2).

(i) Sketch the unit cell, including all atoms that are within or partially within

the cell.

(ii) What is the formula unit of this compound?

(iii) Specify the lattice and the basis of this crystal.

(iv) What are the coordination numbers of A and B?

(v) Determine the A–O and B–O bond lengths.

(vi) If A and B are not the same size, which is smaller?

(vii) Specify the sequence of atoms found along the 111 and 110 direc-

tions.

(viii) Specify the contents of the (200) plane and the contents of the (110)

plane.

Answer 1

i)

ii) formula is AB₄

iii) Simple unit cubic cell

iv) coordination of A = 8

coordination of B = 12

v) bond length d_A-O = a/$\sqrt2$ = 4/$\sqrt2$ = 2$\sqrt2$

d_B-O = a/2 = 4/2 = 2

Where a = lattice paramete = 4.0

vi) B is smaller by bond length

vii)

viii)