Structure of crystalline solids Materials Science Structure of crystalline solids

The structure of solids We understand how individual atoms may bond What about real materials made of multiple atoms? How do atoms arrange to form solid structures? How do these structures influence a material’s density? How do material properties vary with these different structures?

The structure of solids Crystalline materials have atoms situated in a periodic array over large atomic distances Metals and most ceramics Some properties depend on the crystal structure of the material (e.g. density and ductility) Amorphous materials have no long range order (non-crystalline). Glasses – Silica Plastics Rapidly cooled metals (1x105 °C/s)

The structure of solids Steel, PEO and Silica glass structures (left-right)

Polycrystalline materials ‘Nuclei’ form during solidification, each of which grows into crystals Crystals grow and meet These grains are separated by an amorphous grain boundary

Energy and packing of atoms in solids • Dense, regular packing • Non dense, random packing Dense, regular-packed structures tend to have lower energy

Crystalline solids Lattice: 3D array of regularly spaced points Crystalline material: atoms situated in a repeating 3D periodic array over large atomic distances Hard sphere representation: atoms denoted by hard, touching spheres (a) Reduced sphere representation (b) Unit cell: basic building block unit (such as a flooring tile) that repeats in space to create the crystal structure; it is usually a parallelepiped or prizm

The unit cell Smallest repeating arrangement

Metallic crystal structures Repetitive patterns – unit cells (represents the symmetry of the crystal structure) FCC – Face Centred Cubic BCC – Body Centred Cubic HCP – Hexagonal Close Packed Tend to be densely packed due to non-directional bonding in metals Simple crystal structures, for important engineering materials NOTE: HARD SPHERE MODEL

Simple cubic structure (SC) Cubic unit cell is 3D repeat unit Rare (only Po has this structure) Coordination number (CN) Number of the nearest neighbors or touching atoms Easy for civil engineers SC has CN=6

Simple cubic structure (SC) Simple Cubic has CN=6 Close-packed directions (directions along which atoms touch each other) are cube edges How can we describe packing of these atoms? Coordination # = 6 (# nearest neighbors)

Atomic packing factor Fill a box with hard spheres Packing factor = total volume of spheres in box / volume of box Question: what is the maximum packing factor you can expect? In crystalline materials: Atomic packing factor = total volume of atoms in unit cell / volume of unit cell A value <1 (APF is the fraction of solid sphere volume in a unit cell)

APF for a simple cubic structure = 0.52 Atomic packing factor a R=0.5a close-packed directions contains 8 x 1/8 = 1 atom/unit cell Lattice constant APF for a simple cubic structure = 0.52

Face centred cubic (fcc) Unit cell of cubic geometry with atoms located at each corner and the centre of the cube faces E.g. copper, aluminium, silver, gold, (ductile metals) Coordination number ?... APF ?...

Exercise: Atomic packing for fcc APF for fcc structure ~ 0.74, CN=12

Slip systems Why are fcc metals ductile? Ductility (ease of plastic deformation) is linked to crystal structure and close packed planes Slip occurs on specific atomic planes and in specific crystallographic slip directions, i.e. slip systems Slip planes – most densely packed planes, and in that plane the closely packed direction

Face centred cubic (fcc) For fcc there are 4 close packed planes (face diagonals) and 3 close packed directions, making 12 slip systems Ductile metals as there are many opportunities for planes to slide over each other

Defining crystal directions What do we mean by a [111] plane ? We assign x,y,z a magnitude (0 to 1) for the unit cell This is sufficient to define a plane or a direction

Body centred cubic (bcc) Unit cell of cubic geometry with atoms located at each of the corners and the cube centre E.g. chromium, a-iron, tungsten Experience: Ductile-Brittle transition Feature a fatigue limit CN = 8 APF ?...

Body centred cubic (bcc) The Atomium, André Waterkeyn, 1958 Brussels The bcc unit cell of an iron crystal magnified 165 billion times… shiny! 0.1nm x165 billion

Atomic packing factor – bcc APF for a body-centered cubic structure ~ 0.68

Slip systems in bcc crystals 6 slip planes x 2 slip directions = 12 slip systems {110} planes in the direction of

Hexagonal close packed (hcp) Hexagonal unit cell Top and bottom faces of hexagonal cell consist of 6 atoms (hexagon) with an atom in the centre Middle plane consists of 3 atoms E.g. cadmium, magnesium, titanium and zinc. Least ductile metals (only 1 close packed plane) CN=12, APF~0.74 (like fcc)

Slip systems in hcp crystals 1 slip plane x 3 slip directions = 3 slip systems Most brittle of the metals, but subtle difference between fcc structure {0001} plane

Comparison of crystal structures Crystal structure CN APF CP directions Simple Cubic (SC) 6 0.52 cube edges Body Centered Cubic (BCC) 8 0.68 body diagonal Face Centered Cubic (FCC) 12 0.74 face diagonal Hexagonal Close Pack (HCP) 12 0.74 hex side

Other crystal structures • Structure of Carbon There are many structures for Compounds Polymers (molecular crystals) More complex configurations Polymorphism, etc. Diamond • Structure of NaCl Graphite

Other crystal structures

Single crystal materials When the periodic and repeated arrangement of atoms is perfect and extends throughout the entirety of the specimen Benefits extreme technology Electronic and optical material (Si wafers) High performance turbine blades Abrasive materials (synthetic diamond) Crystal properties reveal features of the atomic arrangement Anisotropic (directional) properties

Polycrystalline materials ‘Nuclei’ form during solidification, each of which grows into crystals Crystals grow and meet These grains are separated by an amorphous grain boundary

Polycrystalline materials Most engineering materials are polycrystalline Collections of very small crystals (grains) Most metals, alloys and ceramics Isotropic properties (same properties in all directions)

Single- vs poly-crystalline • Single Crystals -Properties vary with direction: anisotropic. -Example: the modulus of elasticity (E) in BCC iron: • Polycrystals 200 mm -Properties may/may not vary with direction. -If grains are randomly oriented: isotropic. (Epoly iron = 210 GPa) -If grains are textured, anisotropic.

Amorphous materials Crystalline materials... • atoms pack in periodic, 3D arrays • typical of: -metals -many ceramics -some polymers crystalline SiO2 Noncrystalline materials... • atoms have no periodic packing • occurs for: -complex structures -rapid cooling "Amorphous" = Noncrystalline noncrystalline SiO2

Summary Atoms may assemble into crystalline, polycrystalline or amorphous structures Material properties generally vary with single crystal orientation (i.e., they are anisotropic), but properties are generally non-directional (i.e., they are isotropic) in polycrystals with randomly oriented grains. We will next look at how defects in these structures governs the most important mechanical properties of materials: strength and toughness