What is the lattice constant of a zincblende structure with two types of atoms?

[orangeincup]

Homework Statement

A material contains two types of atoms (A and B) in a zincblende structure. Atom A is group V with a hard sphere radius of 2.5 Å. Atom B is group III with a hard sphere radius of 1.6 Å.
(a) What is the lattice constant of this material assuming that nearest neighbour atoms touch? (working on this one right now)
(b) What is the volume density of valence electrons in this material?
(c) What is the surface density of B atoms on the (110) plane in this material?

Homework Equations

The Attempt at a Solution

a) [/B]Since it's a face centered structure it should have 8X 1/8 + 6* 1/2 atoms, so 4
Is it correct to say ( r1+r2 ) *4 = my lattice constant for A?

 

[ehild]

Homework Statement

A material contains two types of atoms (A and B) in a zincblende structure. Atom A is group V with a hard sphere radius of 2.5 Å. Atom B is group III with a hard sphere radius of 1.6 Å.
(a) What is the lattice constant of this material assuming that nearest neighbour atoms touch? (working on this one right now)
(b) What is the volume density of valence electrons in this material?
(c) What is the surface density of B atoms on the (110) plane in this material?

Homework Equations

The Attempt at a Solution

a) [/B]Since it's a face centered structure it should have 8X 1/8 + 6* 1/2 atoms, so 4
Is it correct to say ( r1+r2 ) *4 = my lattice constant for A?

No it is not right. If there are 4 units in a cube, how can the side of the cube 4 times the interatomic distance?
this helps http://www.ehow.com/how_8721263_determine-lattice-parameter-zincblende.html

 

[orangeincup]

a) (4/3)^1/2*(1.6+2.5) = 4.73 A

b) Volume density of valence electrons is 8/((4.73*10^-8)^3) = 7.56*10^22 cm^3

c) 4/(sqrt2(4.73*10^-8)^2) = 1.26*10^15 atoms/cm^3

 

[ehild]

a) (4/3)^1/2*(1.6+2.5) = 4.73 A

b) Volume density of valence electrons is 8/((4.73*10^-8)^3) = 7.56*10^22 cm^3

How many valence electrons are there in one AB unit? How many units are there in the unit cell?

c) 4/(sqrt2(4.73*10^-8)^2) = 1.26*10^15 atoms/cm^3

The surface density is asked, it has atoms/cm^2 unit.
How did you get that formula?

 

[orangeincup]

How many valence electrons are there in one AB unit? How many units are there in the unit cell?

The surface density is asked, it has atoms/cm^2 unit.
How did you get that formula?

4 *(1/4) + 2*(1/2) + 2*1=4?

How many valence electrons are there in one AB unit? How many units are there in the unit cell?

The surface density is asked, it has atoms/cm^2 unit.
How did you get that formula?

I confused it with a volume density formula.

4/(4.73*10^-8)^3) = 3.78*10^22 cm^3 = volume density

sqrt2/((4.73*10^-8)^2)=6.32*10^14 surface density