MTE 583_Class_6

7/27/2019 MTE 583_Class_6

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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.

Prof. M.L. Weaver

7/27/2019 MTE 583_Class_6


Crystalline StructuresCrystalline Structures –– The BasicsThe BasicsCrystalline StructuresCrystalline Structures –– The BasicsThe Basics

•Crystal structure of a material is way in which atoms, ions, molecules are spatiallyarranged in 3-D space.

.

•A lattice is a 3-D array of points in space. Every lattice point must have identical surroundings.

•Unit cell: smallest repetitive volume whichcontains the complete lattice pattern of acrystal. A unit cell is chosen to represent

•Each crystal structure is built by stackingunit cells and placing identical objects(motifs, basis) on each lattice point.

the highestlevel of geometricsymmetry of the

crystal structure. It’sthe basic structuralunit or building block o crys a s ruc ure.

7 crystal systems in 3-D14 crystal lattices in 3-D

a, b, and c are the lattice constantsare the interaxial angles

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Metallic Crystal StructuresMetallic Crystal Structures

“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).

•Most elemental metals

Room temperature

crystal structurecrystallize in the FCC

(face-centered cubic),BCC (body-centered cubic,

Crystal structure just before it melts

or exagona c ose packed) structures.

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Stacking of Metallic Crystal StructuresStacking of Metallic Crystal Structures

• How can we stack metal atoms to minimize emptys ace?

• Which plane is more close-packed?-

vs.

Prof. M.L. Weaver

ow stac t ese - ayers to ma e - structures

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Atomic structures are close-packed in three dimensions

Close-packed hexagonal: ABABAB stacking sequence

Face-centered cubic: ABCABC stackin se uence

Packing fraction for CPH and FCC structures is 0.74 – meaning

spheres occupy 74% of all available space

Prof. M.L. Weaver Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

Figure 4.8

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Non Close-Packed StructuresNon Close-Packed Structures

Bod -centered cubic:

ABABAB packing sequencePacking fraction = 0.68

Fi ure 4.9

Packing fraction ≤ 0.64


Figure 4.10

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Metal Unit CellsMetal Unit Cells

Red lines define the cell while spheres represent

individual atoms

Shaded regions represent close or closest packed plane


Figure 4.11

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FCCFCC –– Stacking Sequence (continued)Stacking Sequence (continued)

2D Projections:

A sites BBB

B BCAB B

BBB B

CA CA

B BC sites

B sites B BB sites

Prof. M.L. Weaver

7/27/2019 MTE 583_Class_6


Comparing HCP and FCCComparing HCP and FCC

• structures is noteworthy, both have

12 CN, APF=0.74 and identical

densities.

FCC: HCP:

• The only significant difference

between the structures is in the

stacking sequence (ABCAB), i.e.

in FCC is positioned.

•Example, cobalt undergoesmartensitic transformation fromFCC to HCP at ~695 K.

• The lattice constant of FCC Co is3.5446 Å, with a nearest-neighbor

distance of 2.5064 .•While for HCP Co, the latticeconstants a and c are 2.5071 and Equivalent

to above but

Prof. M.L. Weaver • Note that AB in FCC would be equivalent to AB in HCP, without the third close packed layer.

. , , -neighbor distance is 2.4971 Å, and

the ratio c/a equals 1.623.

rotated

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Interstitial SitesInterstitial Sites

• ,well defined interstitial positions:

•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…?

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Interstitial Sites (continued)Interstitial Sites (continued)

•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).

MTE 583_Class_6

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