Post on 14-Jan-2016
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MATERIALS SCIENCEMATERIALS SCIENCE&&
ENGINEERING ENGINEERING
Anandh Subramaniam & Kantesh Balani
Materials Science and Engineering (MSE)
Indian Institute of Technology, Kanpur- 208016
Email: anandh@iitk.ac.in, URL: home.iitk.ac.in/~anandh
AN INTRODUCTORY E-BOOKAN INTRODUCTORY E-BOOK
Part of
http://home.iitk.ac.in/~anandh/E-book.htmhttp://home.iitk.ac.in/~anandh/E-book.htm
A Learner’s GuideA Learner’s GuideA Learner’s GuideA Learner’s Guide
Size Factor compounds: (i) Laves phases (ii) Frank-Kasper PhasesD
These phases have a formula: AB2
Laves phases can be regarded as Tetrahedrally Close Packed (TCP)* structures with an ideal ratio of the radii (rA/rB) = (3/2)1/2 ~1.225 [or usually rA/rB (1.1, 1.6)]
If rA/rB = 1.225 then a high packing density is achieved with the chemical formula AB2 with a average coordination number of 13.3
Crystal structures: Hexagonal → MgZn2 (C15), MgNi2 (C36) FCC → MgCu2 (C14)
There are more than 1400 members belonging to the ‘Laves family’ Many ternary and multinary representatives of the Laves phases have been reported with
excess of A or B elements. Some ternary Laves phases are known in systems with no corresponding binary Laves phases.
The range of existence of the three phases (C15, C36, C14) in ternary Laves phases is influenced by the e/a ratio
D(i) Laves Phases
* Also called Topologically Close Packed structures?
Laves phases containing transition metals as components have interesting Physical and mechanical properties. Engineering materials based on Laves phases are being developed for: High temperature applications
(for use in turbine blade fine precipitates of Laves phases is shown to improve fatigue strength)
Hydrogen storage applications (in nickel-metal hydride batteries)
MgZn2 (Laves)Lattice parameter(s) a = 5.18 Å, c = 8.52 Å
Space Group P 63/mmc (194)
Strukturbericht notation C15
Pearson symbol hP12
Other examples with this structure
NbCr2
Wyckoff position
SiteSymmetry
x y z Occupancy
Mg 4f 3m 0.33 0.67 0.062 1
Zn1 2a -3m 0 0 0 1
Zn2 6h mm2 0.83 0.66 0.25 1
MgZn2 Laves Phase
Mg
Zn2
Zn1
[0001]
HexagonalC14
Zn: Vertex-1, Edge-1, Inside cell-6 → 8Mg: Inside cell-4 → 4
Unit cell formula: Mg4Zn8
MgZn2 Laves PhaseMore views Constructing the hexagonal laves phase
Start with a layer of Zn atoms Put Mg atoms in the depressions formed in the layer (above and below)
Add a hexagonal array of Zn atoms in the depressions formed by the Mg atoms (above and below)
This gives us half the unit cell in ‘c’ direction
Mg (8a) Cu (16d)
MgCu2 (Laves)Lattice parameter(s) a = 7.048 Å
Space Group Fd-3m (227)
Strukturbericht notation C14
Pearson symbol cF24
Other examples with this structure
Au2Pb
MgCu2 Laves Phase Cubic[001]
Wyckoff position
SiteSymmetry
x y z Occupancy
Cu 16d -3m 0.625 0.625 0.625 1
Mg 8a -43m 0 0 0 1
C15
Very frequent structural
type
Unit cell formula: Mg8Cu16
Mg: Vertex-1, FC-3, Inside cell-4 → 8Cu: Inside cell-16 → 16
More views MgCu2 Laves Phase
Successive layers are build on the depressions on the previous layer
More views
Tetrahedra of Cu
Note: the solid lines in the figures are for visualization of atomic positions etc. (they are not meant to show bonds)
MgCu2 Laves Phase
Not to scale
D(ii) Frank-Kasper
Have coordination numbers (CN): CN =12, CN = 14, CN = 15, CN = 16
Al12W (Frank-Kasper)Lattice parameter(s) a = 7.58 Å
Space Group Im-3 (204)
Strukturbericht notation
Pearson symbol cI26
Other examples with this structure
Al12Mn, Al12Mo
Wyckoff position
SiteSymmetry
x y z Occupancy
Al 24g m 0 0.184 0.309 1
W 2a m-3 0 0 0 1
Al12W Frank-Kasper Phase
Al
W
[001]
Cubic CN =12
Unit cell formula: Al24W2
W: Vertex-1, BC-1 → 2Cu: FC-12, Inside cell-12 → 24
Motif: 12Al +W (consistent with stoichiometry)
Lattice: Body Centred Cubic
More views Al12W Frank-Kasper Phase
Icosahedral coordination around W atoms Local icosahedral symmetry is destroyed in the long range packing Note that icosahedral symmetry is not found in crystals This phase is closely related to quasicrystals
More views Al12W Frank-Kasper Phase
[100]
[110]
[111]