3-CRYSTAL STRUCTURE-CHPT 3-MIAE 221-2023

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1 CRYSTAL STRUCTURE Chapter 3 MIAE 221 – Materials Science

Topic #3A - MIAE 221 (adapted from Callister) 2 CRYSTAL STRUCTURE - Chapter 3 (arrangement of atoms into solid structure) Why study this? • Ductile - brittle transition in metals. • Crystalline versus amorphous - transparency In gases, atoms have no order. If atoms are bonded to each other but there is no repeating pattern (only short range order ) . e.g. water, glasses – they are non-crystalline ( AMORPHOUS ) If atoms are bonded together in a regular, repeating 3-D pattern they form a CRYSTAL . These have long range order (like a brick wall).

Chapter 3 - 3 • Non-dense , random packing • Dense, ordered packing Dense, ordered packed structures tend to have lower energies. Energy and Packing Energy r typical neighbor bond length typical neighbor bond energy Energy r typical neighbor bond length typical neighbor bond energy Topic #3A - MIAE 221 (adapted from Callister)

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Topic #3A - MIAE 221 (adapted from Callister) 4 • atoms pack in periodic, 3D arrays • typical of: Crystalline materials... -metals -many ceramics -some polymers • atoms have no periodic packing • occurs for: Noncrystalline materials... -complex structures -rapid cooling crystalline SiO 2 noncrystalline SiO 2 " Amorphous " = Noncrystalline MATERIALS AND PACKING

Topic #3A - MIAE 221 (adapted from Callister) 5 Many of the properties of materials (especially mechanical) are determined by the arrangement of the constituent atoms. This arrangement is called the material’s crystal structure . ( Atomic structure relates to the number of protons, neutrons and electrons of an atom – crystal structure pertains to the arrangement of atoms in the crystalline solid material). Most METALS (>99%) are CRYSTALLINE . CERAMICS are CRYSTALLINE except for GLASSES which are AMORPHOUS . POLYMERS (plastics) tend to be either: • AMORPHOUS or a mixture of • CRYSTALLINE + AMORPHOUS (aka Semi-crystalline )

Topic #3A - MIAE 221 (adapted from Callister) 6 CRYSTALS There are different ways of arranging atoms in crystals. Assume atoms are hard spheres and pack like pool/snooker balls (touching). Each type of atom has a preferred arrangement depending on Temperature and Pressure (most stable configuration). These patterns are known as SPACE LATTICES and can be defined by their UNIT CELLS .

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Topic #3A - MIAE 221 (adapted from Callister) 7 Unit Cell Unit cell: smallest repetitive volume which contains the complete lattice pattern of a crystal. The unit cell is the smallest entity that exhibits the chemical and physical properties of the material. The size of these UNIT CELLS are given by Lattice parameters which are typically on the order of a few tenths of a nanometer (10 -9 m) (or a few Angstroms - 10 -10 m) Unit cells are the most elementary arrangement of atoms which can generate the entire crystal upon application of suitable translation, rotation, mirror, or inversion operations.

Topic #3A - MIAE 221 (adapted from Callister) 8 Unit cell for the Simple cubic crystal structure Unit cell Crystal Lattice a a a

Topic #3A - MIAE 221 (adapted from Callister) 9 Metallic Crystal Structures • How can we stack metal atoms to minimize empty space? 2-dimensions vs. Now stack these 2-D layers to make 3-D structures

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Topic #3A - MIAE 221 (adapted from Callister) 10 • Metals tend to be densely packed because. - Typically, only one element is present, so all atomic radii are the same. - Metallic bonding is not directional. - Nearest neighbor distances tend to be small in order to lower bond energy. - Electron cloud shields cores from each other • Metals have the simplest crystal structures. Metallic Crystal Structures

Topic #3A - MIAE 221 (adapted from Callister) 11 Most metals crystallize into one of three densely packed structures: BODY CENTERED CUBIC - BCC FACE CENTERED CUBIC - FCC HEXAGONAL (CLOSE PACKED) - HCP Actual size of UNIT CELLS is VERY, VERY SMALL!! Iron unit cell length is 0.287 x 10 -9 m (0.287 nm ) A one mm length of iron crystal has ≈ 3.5 million unit cells