Ahypothetical ax type of ceramic material is known to have a density of 2.10 g/cm3 and a unit cell of cubic symmetry with a cell edge length of 0.57 nm. the atomic weights of the a and x elements are 28.5 and 30.0 g/mol, respectively. on the basis of this information, which of the following crystal structures is (are) possible for this material: sodium chloride, cesium chloride, or zinc blende?

Zinc blende  

Step-by-step explanation:

Step 1. Calculate the volume of the unit cell

V = l³

V = (0.57)³

V = 0.1852 nm³                Convert to m³

V = 0.1852 × (10⁻⁹)³

V = 1.852 × 10⁻²⁸ m³        Convert to cm³

V = 1.852 × 10⁻²⁸ × 100³

V = 1.852 × 10⁻²⁸× 10⁶

V = 1.852 × 10⁻²² cm³

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Step 2. Calculate the mass of a unit cell

ρ = m/V                                             Multiply each side by V

m = Vρ

m = 1.852 × 10⁻²² × 2.10

m = 3.889 × 10⁻²² g                          Convert to u

m = 3.889 × 10⁻²² × 1/(1.661 × 10⁻²⁴)

m = 234 u

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Step 3. Calculate the number of formula units per unit cell

AX = 28.5 + 30.0

AX = 58.5u

Formula units = 234/58.5= 4.00 ≈ 4

There are 4 formula units per unit cell

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Step 4. Determine the type of unit cell

NaCl = simple cubic cell       = 1 formula unit

CsCl = one-formula-unit cell  = 1 formula unit

The zinc blende structure is shown below. The A atoms are FCC, while the X atoms are at half the tetrahedral sites.

A atoms = 8×⅛  + 6×½ = 1 + 3 = 4

X atoms = 4×1                          = 4

The zinc blende structure has four formula units.

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explanation:

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