Unit Cells and Metallic Crystal Structures Quiz

Atomic Structure

• Protons are positively charged, neutrons are neutral, and electrons are negatively charged.
• The nucleus of a hydrogen atom contains one proton and one electron in the 1st shell.
• Charge magnitude is 1.60 x 10^-19 Columb.
• Atomic number (Z) is the number of protons in the nucleus, which is the same for all atoms of the same element.
• Mass of a proton or neutron is 1.67 x 10^-27 kg, and mass of an electron is 9.11 x 10^-31 kg.
• Atomic mass (A) is the sum of the mass of protons and neutrons within a nucleus.

Crystalline Solids

• Crystalline materials have atoms arranged in a repeating or periodic array over large atomic distances.
• Examples of crystalline materials include metals, ceramics, and some polymers.
• Amorphous materials have short-range order of atoms, but are not periodic.

Crystal Structure

• Crystal structure refers to the 3D arrangement of atoms, ions, or molecules.
• Lattice is a 3D array of points coinciding with atom positions (or sphere centers).
• Unit cells are small repeat entities within the whole structure, typically parallelepipeds or prisms.
• Face-centered cubic (FCC) crystal structure has a coordination number of 12, and an atomic packing factor (APF) of volume of atoms in a unit cell / total unit cell volume.

FCC Crystal Structure

• FCC has a unit cell of cubic geometry, with atoms located at each of the corners and the centers of all the cube faces.
• Examples of metals with FCC structure include copper, aluminum, silver, lead, nickel, platinum, and gold.
• The aggregate of atoms in the unit cell represents a section of crystal consisting of many FCC unit cells.

Body-Centered Cubic (BCC) Crystal Structure

• BCC crystal structure has a unit cell edge length (a) and atomic radius (R) related by 𝑎 = 4𝑅 / √3.
• The atomic packing factor for BCC is 0.68.

Hexagonal Close-Packed (HCP) Crystal Structure

• HCP crystal structure has an ideal c/a ratio of 1.633.
• The atomic packing factor for HCP is 0.74.

Density Computations

• Iron has a BCC crystal structure, an atomic radius of 0.124 nm, and an atomic weight of 55.85 g/mol.
• Theoretical density of iron can be computed and compared to the experimental value of 7.87 g/cm³.
• Radius of an iridium atom can be calculated given its FCC crystal structure, density of 22.4 g/cm³, and atomic weight of 192.2 g/mol.
• Radius of a vanadium atom can be calculated given its BCC crystal structure, density of 5.96 g/cm³, and atomic weight of 50.9 g/mol.