In Zinc blend structure (r[zn2+]+r[s2-]) is equal to? (if edge lenght is a)
To determine the value of the zinc blend structure, we need to calculate the distance between the zinc cations (Zn2+) and the sulfur anions (S2-).
In a zinc blend structure, each zinc cation is surrounded by four nearest-neighbor sulfur anions and vice versa. The arrangement can be visualized as a face-centered cubic (FCC) lattice, with zinc ions occupying the tetrahedral holes and sulfur ions occupying the octahedral holes.
To find the distance between the zinc cations and sulfur anions, we need to consider the edge length (a) of the unit cell.
In a face-centered cubic lattice, the distance between the corners of the cube (c) and the center of each face (r) are related by the equation:
c = 2√2r
Since the zinc ions occupy the tetrahedral holes, the distance between the zinc cations and the center of the face can be calculated using the edge length (a) as:
c = a / 2
Therefore, the distance between the zinc cations (r[zn2+]) and the sulfur anions (r[s2-]) can be calculated as:
r[zn2+] + r[s2-] = (c/2) + (c/4)
Substituting c = 2√2r, we get:
r[zn2+] + r[s2-] = (√2r/2) + (√2r/4)
= (√2r + (√2r/2))/2
= (√2r + r√2/2)/2
= (√2 + √2/2)r/2
= (3√2/2)r/2
= (3√2r)/4
Therefore, the zinc blend structure (r[zn2+] + r[s2-]) is equal to (3√2r)/4, where r represents the edge length (a) of the unit cell.