Solid State Physics Devices Electronics

Step 1: Recall the formula for interplanar spacing in a cubic lattice. The interplanar spacing for a cubic lattice with lattice constant is given by: where are the Miller indices of the plane.
Step 2: Identify the given values. We are given: - Interplanar spacing, - Miller indices for the plane,
Step 3: Substitute the values into the formula and solve for . Thus, the lattice constant is .

Step 1: Define the First Brillouin Zone. The First Brillouin Zone is a fundamental concept in solid-state physics used to describe electron wave propagation in a crystal lattice.
Step 2: Evaluate each statement. - A. Wigner-Seitz cell of reciprocal lattice: This is the standard definition of the First Brillouin Zone. The Wigner-Seitz cell is the region of space that is closer to one particular lattice point than to any other. When applied to the reciprocal lattice, this defines the Brillouin zone. This statement is correct. - B. Primitive unit cell: The First Brillouin Zone is, by its construction as a Wigner-Seitz cell, a primitive unit cell of the reciprocal lattice. It has the volume of one primitive cell. This statement is correct. - C. The locus of all k-values...which are Bragg reflected: The boundaries of the Brillouin Zone are defined by planes that are the perpendicular bisectors of the vectors connecting the origin of the reciprocal lattice to the nearest lattice points. These planes represent the wave vectors ( -values) that satisfy the Bragg condition for diffraction, . Therefore, the zone represents the set of k-vectors that are not Bragg reflected, and its boundaries are where Bragg reflection begins. The statement is conceptually correct in linking the zone to Bragg reflection. - D. Wigner-Seitz cell of direct lattice: This is incorrect. The Wigner-Seitz cell of the *direct* lattice is a primitive cell in real space, not reciprocal space. The Brillouin zone is exclusively a concept of the reciprocal lattice.
Step 3: Conclude the correct statements. Statements A, B, and C are correct descriptions of the Brillouin zone. Statement D is incorrect. Therefore, the correct option includes A, B, and C only.

Step 1: Determine the coordination number for each crystal structure. The coordination number is the number of nearest neighbors of an atom in the crystal lattice. - A. Diamond: In the diamond cubic structure, each carbon atom is tetrahedrally bonded to four other carbon atoms. The coordination number is 4. - B. Sodium Chloride (NaCl): In the rock salt structure, each ion (e.g., Na ) is surrounded by six ions of the opposite charge (e.g., Cl ) in an octahedral arrangement. The coordination number is 6. - C. Cesium Chloride (CsCl): In the CsCl structure, each ion is at the center of a cube of eight ions of the opposite charge. The coordination number is 8. - D. Zinc (HCP): Zinc has a Hexagonal Close-Packed (HCP) structure. In any close-packed structure (HCP or FCC), each atom is in contact with 12 other atoms (6 in its own plane, 3 above, and 3 below). The coordination number is 12.
Step 2: Arrange the structures in ascending order of their coordination number. The coordination numbers are: - Diamond (A): 4 - Sodium Chloride (B): 6 - Cesium Chloride (C): 8 - Zinc (HCP) (D): 12 Arranging these in ascending order gives the sequence: A (4)