Class 6 Class 6 Class 6 Class 6 Structures of Crystalline Materials Structures of Crystalline Materials Structures of Crystalline Materials Structures of Crystalline Materials READING • Chapters 17 in DeGraef and McHenry , pp. 463-466, 476-489 • REFERENCE: Ch. 2 in Rohrer; relevant material on ceramic and metallic structures from any Introduction to Materials book. Prof. M.L. Weaver
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Class 6Class 6Class 6Class 6Structures of Crystalline MaterialsStructures of Crystalline MaterialsStructures of Crystalline MaterialsStructures of Crystalline Materials
READING• Chapters 17 in DeGraef and McHenry, pp. 463-466, 476-489
• REFERENCE: Ch. 2 in Rohrer; relevant material on ceramic and metallicstructures from any Introduction to Materials book.
“the sim lest”“the sim lest”•Recall, that (a) coulombic attraction between delocalized valence electrons and positively charged cores is isotropic (non-directional); (b) typically, only one elementis resent so all atomic radii are the same c nearest nei hbor distances tend to be
small; and (d) electron cloud shields cores from each other.
•For these reasons, metallic bonding leads to close packed, dense crystal structures thatmaximize space filling and coordination number (number of nearest neighbors).
•The CCP (FCC) structure in (a) has 4 octahedral interstitial sites per cell; one site is at thece cen er s own n a an e res are a e m po n s o a e ce e ges · .
• There are also 8 tetrahedral, 4-coordinate sites per unit cell at the (±1/4, ±1/4, ±1/4) positions entirely within the cell.
Alternative view of CCP(FCC) structure in (a):
Prof. M.L. Weaver
• Although similar sites occur in the BCC lattice in (b), they do not possess ideal tetrahedral
or octahedral symmetry. Primitive Hexagonal lattice…?
•It is important to understand how the sites are configured with respect to the closest packed layers: •The 4 coplanar atoms in the octahedralsymmetry are usually called the in-
plane or equatorial ligands, while thetop and bottom atoms are the axial or
.•This representation is convenient sinceit emphasizes the arrangement of px, py
and pz orbitals that form chemical bonds (see pp. 15&16, Class 1 notes).
•Of the six nearest neighbors to the octahedral site in the CCP structure, three are in oneclose packed layer and the remaining three are in the adjacent layer.
•The most symmetric octahedral position is, thus, midway between the 2 close-packed p anes.
•For the tetrahedral positions, three of the atoms that make up the tetrahedron lie in the.
•We expect the interstitial atom to occupy a position equidistant between the 4 ligands.•Because this position is not halfway between the 2 close-packed planes, as the octahedralsite is, the sites above (T+) and below ( T-) a central reference plane are distinct.
Prof. M.L. Weaver
• It is useful to remember that for each close packed site in the FCC and HCP structures,
there is one 6-coordinate octahedral site and two 4-coordinate tetrahedral sites (1 T+ siteand 1 T- site).