This PPT represented the order-disorder transformation in ordered alloys.

1. Ordering Transformation
Designed by Dr. Saeed Hasani
Assistant professor
Yazd University
Iran

2. Long range order (LRO) and short range order (SRO)
If the atoms in a substitutional solid solution, are randomly arranged each
atom position is equivalent and the probability that any given site in the lattice
will contain an A atom will be equal to the fraction of A atoms in the solution XA ,
similarly XB for the B atoms.
2

3. Definition of Superlattices and Ordered Structures
• Often the term superlattice and ordered structure is used interchangeably.
• Although, all ordered structures are superlattices but not all superlattices are ordered
structures (i.e. ordered structures are a subset of superlattice).
• An ordered structure (e.g. CuZn, B2 structure) is a superlattice. An ordered structure is a
product of an ordering transformation of an disordered structure (e.g. CuZn BCC
structure) But, not all superlattices are ordered structures. E.g. NaCl crystal consists of
two subcrystals (one FCC sublattice occupied by Na+ ions and other FCC sublattice by
Cl ions). So, technically NaCl is a superlattice (should have been called a supercrystal!)
but not an ordered structure.
3

4. Definition of Superlattices and Ordered Structures
One interesting class of alloys are those, which show order-disorder transformations.
Typically the high temperature phase is dis-ordered while the low temperature phase is ordered
(e.g. CuZn system next slide).
The order can be positional or orientational.
In case of positionally ordered structures:
 The ordered structure can be considered as a superlattice
 The ‘superlattice’ consists of two or more interpenetrating ‘sub-lattices’
 with each sublattice being occupied by a specific elements
Order and disorder can be with respect to a physical property like magnetization. E.g. in the
Ferromagnetic phase of Fe, the magnetic moments (spins) are aligned within a domain. On heating
Fe above the Curie temperature the magnetic moments become randomly oriented, giving rise to
the paramagnetic phase.
Even vacancies get ordered in a sublattice. A vacancy in a vacancy sublattice is an atom!!
The disordered phase is truly an ‘amorphous structure’!!!
4

5. Definition of Superlattices and Ordered Structures
 A-B bonds are preferred to AA or BB bonds
e.g. Cu-Zn bonds are preferred compared to Cu-Cu or Zn-Zn bonds
 The structure of the ordered alloy is different from that of both the component elements (Cu-FCC,
Zn-HCP)
 The formation of the ordered structure is accompanied by change in properties. E.g. in Permalloy
ordering leads to → reduction in magnetic permeability, increase in hardness etc.
 Ordered solid solutions are (in some sense) in-between solid solutions and chemical compounds
 Degree of order decreases on heating and vanishes on reaching disordering temperature
 Off stoichiometry in the ordered structure is accommodated by:
◘ Vacancies in one of the sublattices (structural vacancies)
◘ Replacement of atom in one sublattice with atoms from other sublattice
5

6. G = H  TS
High T disordered
Low T ordered
470ºC
Sublattice-1 (SL-1)
Sublattice-2 (SL-2)
BCC
SC
SL-1 occupied by Cu and SL-2 occupied by Zn. Origin of SL-2 at (½, ½, ½)
Probabilistic occupation of each BCC lattice site:
50% by Cu, 50% by Zn
the high
temperature
phase is
disordered and
has a BCC
lattice, while the
low temperature
structure is
simple cubic (B2
structure). This
is governed by
the Gibbs free
energy.
B2
structure
Thermodynamic of ordering
6

7. Thermodynamic of ordering
• An atomic disorder to order transformation is a change of phase.
• Solid solutions which have a negative enthalpy of mixing (∆Hmix < 0)
prefer unlike nearest neighbors → show tendency for ordering phases
at low temperature.
• This can be understood from a basic equation of phase equilibria in the
solid state, namely the definition of the Gibbs Free Energy:
• G = H –TS
• where G is the Gibbs free energy ,H is the enthalpy, S is the entropy of
the material
• At high temperatures the TS term dominates the phase equilibria and
the equilibrium phase is more “disordered” (higher entropy) than the
low temperature equilibrium phase.
7

8. Thermodynamic of ordering
8

9. Thermodynamic of ordering
9

10. Types of order ↔ disorder transition
10
• the extent of ordering below Tc does not follow the same pattern in all materials.
In some cases, e.g. FeCo, S decreases slowly as the alloy is heated, and the
disordered state can be retained at room temperature by quenching (part a). In
other cases, e.g. Cu3Au, the disordered state cannot be retained on quenching and
there is an abrupt change to high values of S at temperatures just below Tc (part
b). The two types of behavior are shown in this figure.

11. Types of ordered structures
11
NiAl
SC
Motif: 1Ni + 1Al
Lattice: Simple Cubic
Unit cell formula: NiAl
This is similar to CuZn
Two interpenetrating Simple Cubic
crystals (origin of crystal-1 at (0,0,0) and
origin of crystal-2 at (½,½,½))
B2 (L20)

12. Types of ordered structures
12
disordered state (bcc)
Long range order: out of bcc structure
the B2 (CsCl) structure arises
ordered state (B2)
B2 (L20)

13. Types of ordered structures
13
L10
CuAu (I)
Cu
Au
Cu
Au
Motif: 2Au +2Cu
(consistent with stoichiometry)
Lattice: Simple
Tetragonal
Unit cell
formula:
Cu2Au2
Alternate unit cell (the conventional one)
Unit cell formula: CuAu
We chose this
smaller unit cell

14. Types of ordered structures
14
L10

15. Types of ordered structures
15
Cu3Au
Cu
Au
Motif: 3Cu +1Au
(consistent with stoichiometry)
Lattice: Simple Cubic
Motif: Au at (0,0,0) & Cu at (½, ½, 0), (0, ½, ½), (½, 0, ½)
L12

16. Types of ordered structures
16
L12
ordered state L12 disordered state (fcc)
L12

17. Types of ordered structures
17
DO20
Al3Ni
[001]
[010]
[100]
Formula for Unit cell: Al12Ni4

18. Types of ordered structures
18
Fe3Al
Al
Fe
Fe2 (¼,¼,¼)
Fe1 (½,½,0)
Fe1 (0,0,0)
Dark blue: Fe at corners
Lighter blue: Fe at face centres
V. Light Blue: Fe at (¼,¼,¼)
Fe: Vertex-1, FC-3, (¼,¼,¼)-8 → 12
Al: Edge-3, BC-1 → 4
Unit cell formula: Fe12Al4
DO3

19. Types of ordered structures
19
More views
[100]
Al
Fe
Fe3Al
DO3

20. Types of ordered structures
20
D03 stoichiometry 3:1
Out of the same bcc structure:
DO3

21. Types of ordered structures
21
Different long range ordered structures
in the Cu-Au phase diagram
L12
L12
L10
L12
L10

22. How to identify a ordered structure?
• The existence of ordered domains was initially inferred from
observations of the superlattice peaks in XRD and from resistivity
measurements. Recently, however, the powerful technique of
transmission electron microscopy (TEM) has furnished direct pictorial
evidence of domains.
22

23. How to identify a ordered structure?
23
OrderedDisordered
Cu3Au
(a) XRD patterns

24. How to identify a ordered structure?
24
Superlattice lines
(a) XRD patterns

25. 25
How to identify a ordered structure?
(b) Dilatometry
There is a 0.2% change in lattice parameter between the disordered and ordered phases in FeCo-based alloys.

26. How to identify a ordered structure?
26
(c) Resistivity measurements
These regions are respectively as follows:
Region I: No noticeable changes are observed by increasing the annealing
temperature from 100 C to T1.
Region II: Passing T1, resistivity increases up to T2 due to the short range
ordering.
Region III: By an increase in annealing temperature from T2 to T3,
resistivity decreases with similar rate as the previous stage due to the long
range ordering.
Region IV: Increasing the annealing temperature from T3 to T4, a
noticeable increase in resistivity as well as Region II is obtained due to the
short range ordering.
Region V: No significant change is observed with further increase
in annealing temperature up to 1050 C.

27. How to identify a ordered structure?
27
(c) TEM
High resolution TEM images from ordered
domains in Vicalloys I

28. Antiphase boundaries (APBs)
• When these domains come into
contact, the plane of contact is
known as an antiphase domain
boundary to denote the change in
sublattice occupancy across the
boundary, as shown in the Figure.
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29. Antiphase boundaries (APBs)
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30. Paired dislocation in the ordered phases
• A perfect dislocation in the disordered lattice is merely a partial
dislocation in the ordered structure and its movement in the
superlattice leaves behind a plane that is an APB. In B2 structures for
example, the expected dislocation has a Burgers vector of a/2<111>
and its passage leads to the creation of an APB. In order to avoid the
energy increase associated with the production of such a boundary, the
moving dislocations in an ordered structure are coupled in pairs
(super-dislocations) so that the second dislocation restores the ordered
state. These two dislocations are linked by a small area of antiphase
boundary.
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31. Paired dislocation in the ordered phases
31
Dislocation pairs in the ordered Mg3Cd

32. Slip systems and dislocations in the ordered structures
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The magnitude of the APB energy
dictates the separation distance
between the partials and determines
the ease of cross slip of dislocations in
the ordered alloys. The separation
distance between the partials is low in
alloys with high APB energies and
cross slip occurs easily in these alloys.
Similarly, in alloys with low APB
energies, the partial dislocations are
widely separated and each partial
dislocation can independently cross-
slip. However, the separation distance
between the partials is intermediate
in alloys with moderate APB energy
and requires higher energy to cross
slip. Hence, partial dislocations are
restricted to slip on their slip plane.

33. Recovery in the ordered alloys
During recovery of deformed weakly-ordered alloys at temperatures
below Tc, there are two processes occurring.
• Normal dislocation recovery, which results in softening
• Re-ordering, if the material was disordered before or during
deformation, which results in hardening.
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34. Recrystallization in the ordered alloys
• If deformed in the ordered state, ordered compounds recrystallize more
rapidly than if deformed in the disordered state, and this is attributable to
the larger stored energy.
• Grain boundary mobility is severely reduced by ordering, thus retarding
both recrystallization and grain growth. Deviations from stoichiometry
generally increase diffusivity and increase boundary mobility.
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35. 35
One interesting class of alloys are
those, which show order-disorder
transformations.
With Bests
Saeed Hasani