Explore BrainMass

Explore BrainMass

    Simple Cubic "Non-Bravais" Lattice

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    A simple cubic structure is constructed in which two planes of A atoms followed by two planes of B atoms alternate in the [100] direction (see attached).
    a) What is the crystal structure (viewed as a non-Bravais lattice with four atoms per unit cell)?
    b) What are the primitive translation vectors of the reciprocal lattice?
    c) What is the structure amplitude (geometric structure factor) for this non-Bravais lattice?

    © BrainMass Inc. brainmass.com December 24, 2021, 10:40 pm ad1c9bdddf
    https://brainmass.com/physics/scalar-and-vector-operations/simple-cubic-non-bravais-lattice-498944

    Attachments

    SOLUTION This solution is FREE courtesy of BrainMass!

    a) The crystal structure is tetragonal with lattice vectors of length 4a in the [100] direction and legths a in the [010] and [001] directions.

    b) The primitive translation vectors of the reciprocal lattice are pi/(2a) * (1,0,0), 2 pi/a * (0,1,0) and 2 pi/a * (0,0,1).

    c) The structure amplitude in the [100] direction is given by F_100 = f_1 (|1 + i|^2)/4 + f_2 (|-1-i|^2) / 2 = (f_1 + f_2)/2 and in the [010] and [001] directions by F_010 = F_001 = f_1 + f_2.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 10:40 pm ad1c9bdddf>
    https://brainmass.com/physics/scalar-and-vector-operations/simple-cubic-non-bravais-lattice-498944

    ADVERTISEMENT