The document discusses Laves phases, which have the chemical formula AB2 and typically a radius ratio of rA/rB between 1.1-1.6. There are three common crystal structures for Laves phases - hexagonal (MgZn2), face-centered cubic (MgCu2), and double hexagonal (MgNi2). Laves phases can have interesting physical and mechanical properties and are being developed for high temperature applications like turbine blades and hydrogen storage in battery materials.

1. Laves Phase

2. B32
structure;
AlLi, NaTl
Zintl
Phase
CaF2; Anti CaF2
structure; i.e
sites between
cation and
anions are
changed in case
of Mg2Sn
Correlation with Cubic Laves Phase: Double Diamond cubic
structure
AB2; MgCu2
8Mg: 4 out 4 inside
tetrahedral
interstices;
16 Cu: 4 Tetrahedral
cluster of Cu in
alternate Tetrahdearl
interstice

3. Laves Phase: AB2 type
➢ Typical Laves phases reported in MgCu2, MgZn2, MgNi2
➢ MgCu2: It is a cubic phase, diamond cubic with 8 Mg atoms. Alternate
tetrahedral (vacant) positions are occupied by tetrahedra of Cu, i.e 4x4=16 Cu
atoms. Designated as C15 structure. Total number of atoms are 24, Pearson
symbol is cF24. Large atom Mg has 16 ligancy: 12Cu and 4 Mg. Radius ratio Cu
to Mg:0.8; Cu has 12 ligancy: 6Cu and 6 Mg. (6.5Å)
➢ MgZn2 (a=5.22, c=8.567) and MgNi2 (a=4.815; c=15.8) is hexagonal but MgNi2
is having double hexagonal layer in c axis. They are designated as C14, C36
structure.
➢ The tetrahedral packing or clustering is highly dominant. It is known as size
factor compound. The ratio of bigger (Mg) to smaller atoms, Cu are 1.224
comes from sqrt of 3/2. 4 Cu atoms touch each other along face diagonal
length. I.e. 4d=sqrt(2)a.
➢ The distance between Mg in corner and the tetrahedral position, i.e D=
¼(sqrt3)a.
➢ Thus D/d=sqrt(3/2)= 1.225. It is ideal ratio. The structure can exist from 1.05
to 1.6 with distortion.

4. Mg (8a) Cu (16d)
MgCu2 (Laves)
Lattice parameter(s) a = 7.048 Å
Space Group Fd-3m (227)
Strukturbericht notation C15
Pearson symbol cF24
Other examples with this
structure
Au2Pb
MgCu2 Laves Phase Cubic
[001]
Wyckoff
position
Site
Symmetry
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 → 8
Cu: Inside cell-16 → 16

6. Mg (8a) Cu (16d)
MgCu2 (Laves)
Lattice parameter(s) a = 7.048 Å
Space Group Fd-3m (227)
Strukturbericht notation C15
Pearson symbol cF24
Other examples with this
structure
Au2Pb
MgCu2 Laves Phase Cubic
[001]
Wyckoff
position
Site
Symmetry
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 → 8
Cu: Inside cell-16 → 16

7. MgCu2 Type MgZn2 Type MgNi2 Type
AgBe2 NbCo2 BaMg2 TaCr2 HfCr2
BiAu2 NbCr2 CaAg2 TaFe2 HfMn2
CaAl2 PbAu2 CaCd2 TaMn2 HfMo2
CeCo2 PrNi2 CaLi2 TiCr2 ReBe2
CeFe2 TaCo2 CaMg2 TiFe2 FeB2
CeMg2 TaCr2 CrBe2 TiMn2 MoBe2
CeNi2 TiBe2 FeBe2 UNi2 NbCo2
GdFe2 TiCo2 HfFe2 VBe2 TaCo2 with
excess of
B metal
GdMn2 TiCr2 KNa2 WBe2 TiCo2
HfCo2 UAl2 MnBe2 WFe2 WBe2
HfFe2 UCo2 MoBe2 ZrCr2 ZrFe2
HfMo2 UFe2 MoFe2 ZrIr2
HfV2 UMn2 NbFe2 ZrMn2
HfW2 ZrCo2 NbMn2 ZrRe2
KBi2 ZrCr2 ReBe2 ZrRu2
LaAl2 ZrFe2 SrMg2 ZrOs2
LaMg2 ZrMo2 TaCo2 ZrV2
LaNi2 ZrV2
NaAu2 ZrW2
LAVES Phase: AB2 type

8. Size Factor compounds: (i) Laves phases (ii) Frank-Kasper Phases
D
❑ 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?

9. ❑ 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)

10. MgZn2 (Laves)
Lattice parameter(s) a = 5.18 Å, c = 8.52 Å
Space Group P 63/mmc (194)
Strukturbericht notation C14
Pearson symbol hP12
Other examples with this
structure
NbCr2
Wyckoff
position
Site
Symmetry
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]
Hexagonal
C14
Zn: Vertex-1, Edge-1, Inside cell-6 → 8
Mg: Inside cell-4 → 4
Unit cell formula: Mg4Zn8

11. MgZn2
Hexagonal

12. MgNi2
Double
Hexagonal phase

14. ❑ Superconducting :
❑ C14 or C15: (HfZr) V2: alloying Nb very ductile Superconducting materials based on
Laves Phase
❑ Hf-V is very brittle
❑ Nb-Hf-V
❑ Fusion Reactor Magnets
❑ Hydrogen Storage Materials
❑ AB2; A= Hydride Forming elements, B= non or not so strong hydride forming
❑ C14 or C15;
❑ ZrV2= H/M=1,8; ZrMn2, TiCr2
❑ RNi2: LaNi2
❑ Multicomponent: ZrMnCoV; Zr-Mn-Ni-V-Cr
❑ Magnetic Materials
❑ TFe2 (T= Ti, Zr, Hf, Nb, Mo)
❑ RFe2: TbFe2, Sm2Fe2; (Tb(1-x) DyxFe2, High Power Transducer
❑ (hydrogenation and dehydrogenation gives to fine gaint magnetostrictive
materials
❑ NbCo2
Application of Laves Phases