Crystallography

Step 1: Understanding Miller indices.
The Miller indices are derived from the intercepts of a plane with the crystallographic axes. For intercepts of , the Miller indices are calculated by taking the reciprocals of the intercepts and clearing any fractions. The final result is (2 4 3), which corresponds to option (A).
Step 2: Conclusion.
Therefore, the correct answer is option (A) because the Miller indices for this plane are (2 4 3).

Step 1: Understanding Miller indices.
The Miller indices are derived from the intercepts of a plane with the crystallographic axes. For intercepts of , the Miller indices are calculated by taking the reciprocals of the intercepts and clearing any fractions. The final result is (2 4 3), which corresponds to option (A).
Step 2: Conclusion.
Therefore, the correct answer is option (A) because the Miller indices for this plane are (2 4 3).

Step 1: Use Bragg's law.
. For first order, .

Step 2: Find interplanar spacing.
For NaCl (fcc), first diffraction peak is from (111):
.

Step 3: Substitute into Bragg's equation.
.

Step 4: Convert to degrees.
.
But for NaCl's first observable peak (200 reflection), spacing is nm, giving:
.

Step 1: Use the relation for BCC crystal structure.
In a body-centered cubic (BCC) structure, the relation between the atomic radius and the lattice parameter is given by: where is the atomic radius.
Step 2: Calculate the lattice parameter.
Substituting the value of :
Step 3: Conclusion.
Thus, the lattice parameter of Na unit cell is 0.528 nm.

Step 1: Understanding the crystal structure.
The diagram shows the unit cell of CsCl, which consists of Cs and Cl ions arranged in a specific pattern. The body-centered orthorhombic lattice indicates that Cs ions are located at the center of the unit cell, while the Cl ions are at the corners. This is characteristic of the body-centered orthorhombic structure.

Step 2: Analyzing the options.
(A) simple cubic: In a simple cubic structure, atoms or ions are located only at the corners of the unit cell. This does not match the given structure.
(B) body centered orthorhombic: Correct. The Cs ions are at the center and the Cl ions are at the corners, which is characteristic of a body-centered orthorhombic lattice.
(C) face centered cubic: In this structure, atoms or ions are located at the centers of faces, not the corners and the center. Hence, it is not the correct option.
(D) base centered orthorhombic: This type has atoms at the base centers and corners but does not match the description of the CsCl lattice.

Step 3: Conclusion.
The correct answer is (B) body centered orthorhombic. The arrangement of Cs and Cl ions fits this lattice type.

Step 1: Understanding Miller indices.
Miller indices are a notation system in crystallography that describes the orientation of crystal planes in a lattice. The indices are represented as , where , , and are the intercepts of the plane with the axes of the unit cell. The plane intersects the x-axis at 1, the y-axis at infinity, and the z-axis at 1.

Step 2: Identifying the correct plane.
The Miller indices represent a plane that intersects the x and z axes but is parallel to the y-axis. Option (A) correctly shows this plane orientation in a cubic unit cell.

Step 3: Conclusion.
Therefore, the correct answer is (A), as it accurately represents the Miller indices.

Step 1: Apply Bragg's law.
For first order ( ):

Step 2: Relate interplanar spacing to lattice constant.
For cubic crystals:

Step 3: Conclusion.
Hence, unit cell size .

Step 1: Observe the structure.
In the given structure, there are atoms at the corners of the cube and also at the centers of each face of the cube. The arrangement of two types of atoms (black and grey) indicates an interpenetrating lattice, but the overall lattice points correspond to a face-centered arrangement.

Step 2: Identify the Bravais lattice.
A cubic lattice having atoms at the corners and at the centers of each face of the cube corresponds to the face-centered cubic (FCC) structure. Examples include NaCl, which has two different atoms occupying alternate sites within an FCC lattice.

Step 3: Conclusion.
Hence, the Bravais lattice of the given crystal is Face-centered cubic.