Ch. 3 - The Structure of Crystalline Solids Flashcards
Crystalline
A material in which the atoms are situation in a repeating or periodic array over large atomic distances, that is, long-range order exists such that upon solidification, the atoms will position themselves in a repetitive three-dimensional pattern, in which each atom is bonded to its nearest-neighbor atoms.
All metals, many ceramics, and certain polymers have this structure.
Amorphous materials
Materials that do not crystallize and therefore have no long-range atomic order. Also called “noncrystalline” or “supercooled liquid.”
Characterized by atomic or molecular structures that are relatively complex and become ordered only with some difficulty.
Most common in polymers.
Crystal structure
Manner in which atoms, ions, or molecules are spatially arranged.
Lattice
A three-dimensional array of points coinciding with atom positions or sphere centers.
Unit cells
Basic structural unit or building block of the crystal structure and defines the crystal structure by virtue of its geometry and the atom positions within.
Generally a parallelepiped or prism having three sets of parallel faces. Chosen to represent the symmetry of the crystal structure, wherein all the atom positions in the crystal may be generated by translations of the unit cell integral distances along each of its edges.
Coordination number
Number of nearest neighbors, or touching atoms, of each atom. Each atom in a crystalline structure has the same number of nearest neighbors.
Atomic packing factor (APF)
Equal to the volume of units in a unit cell divided by the total unit cell volume.
Assumes the atomic hard sphere model.
Face-Centered cubic (FCC)
Common metallic crystal structure in which the unit cell has a cubic geometry, with atoms located at each of the corners and the centers of all the cube faces.
Each corner atom is shared among 8 unit cells. The face-centered atom only belongs to 2 unit cells. Therefore, a unit cell of this structure contains the equivalent of FOUR atoms.
Coordination number: 12
Atomic packing factor: 0.74
Copper, aluminum, silver, gold.
Body-centered cubic (BCC)
Common metallic crystal structure in which the unit cell has atoms located at all 8 corners and a single atom located at the cube center.
Contains a total of TWO atoms within a single unit cell.
Coordination number: 8
Atomic packing factor: 0.68
Chromium, iron, tungsten.
Hexagonal close-packed (HCP)
Common metallic crystal structure with a hexagonal unit cell. The top and bottom faces consist of 6 atoms that form regular hexagons and surround a single atom in the center. Another plane of 3 atoms sits between the top and bottom planes.
A total of SIX full atoms are contained within a unit cell of this structure; 1/6th from each of the 12 top and bottom face corner atoms, 1/2 of each of the two center face atoms, and 3 from the interior midplane atoms.
Coordination number: 12
Atomic packing factor: 0.74
Magnesium, cadmium, titanium, and zinc.
Polymorphism
Some materials (metals and nonmetals) with more than one crustal structure.
Carbon can be either graphite or diamond.
Iron is BCC at room temperature but turns to FCC at 912°C.
Allotropy
The condition of polymorphism in an elemental solid.
Tin’s allotropic transformation
When held at a low temperature for a prolonged period of time, white tin (with a body-centers tetragonal crystal structure) will transform into gray tin (with a diamond cubic crystal structure). Because of this transformation, a decrease in density occurs (molecules are less tightly packed) so an increase in volume occurs. The volume expansion will cause the white tin to disintegrate into a coarse powder of the gray allotrope.
Crystallographic direction
Defined as a line between two points, or a vector. Notated as [uvw] where u, v, and w correspond to the reduced projections along the x, y, and z axis.
Crystallographic planes
Notated by (hkl). A vector is drawn that follows [hkl]. The plane that corresponds to (hkl) is that which is perpendicular in all directions to the vector [hkl].
