Solved:
Answered by AI, Verified by Human Experts
Show that the atomic packing factor for BCC is 0.68.
Show that the atomic packing factor for BCC is 0.68.
Theatomic packing factor(APF) is defined as the ratio of the totalatomic volumeto theunit cell volume. The atomic packing factor for the bcc crystal structure is0.68.In abody-centered cubic(bcc) crystal structure, there are 2 atoms at the corners of the cube, and 1 atom at the center of the cube. The APF for a bcc crystal structure can be determined by calculating the volume of all the atoms in a unit cell and dividing it by the volume of the unit cell.The atomic packing factor for the bcc crystal structure is 0.68.The atomic packing factor (APF) is the ratio of the total atomic volume to the unit cell volume. The APF provides information about how much space in acrystalis occupied by atoms. For example, if the APF is high, it means that the crystal structure is densely packed with atoms.In a body-centered cubic (bcc) crystal structure, there are 2 atoms at thecorners of the cube, and 1 atom at the center of the cube.To calculate the APF for the bcc crystal structure, we need to determine the volume of all the atoms in a unit cell and divide it by the volume of the unit cell. Since there are 3 atoms in a bcc unit cell, we need to determine thevolumeof each atom and multiply it by 3.The volume of a sphere can be calculated using the formula V = (4/3)πr³, where V is the volume and r is the radius of the sphere.For the bcc crystal structure, the APF is calculated as follows:APF = (Volume of atoms in a unit cell) / (Volume of the unit cell)APF = (3 × (4/3)πr³) / (a³)Where a is the length of the cube edge.Since theradiusof the bcc atom is (a/2)√3, we can substitute this value into the above equation to get:APF = (3 × (4/3)π(a/2)³√3) / (a³)APF = (3 × (π√3/8) × a³) / (a³)APF = 3 × π√3 / 8APF= 0.68To know more aboutatomic packing factorherebrainly.com/question/32823686#SPJ3...