order- disorder structure kinetics

1. Order- Disorder Transformation
Presented By:
Zaahir Salam
M.Tech NS&T

2. What Does Order and Disorder Mean?
 Order and Disorder designate the presence or absence of
some symmetry or correlation in a many-particle system.
 In physics systems typically are ordered at low
temperatures; upon heating, they undergo one or several
phase transitions into less ordered states.
 Examples for such an order-disorder transition are:
 The melting of ice: solid-liquid transition, loss of crystalline order
 The demagnetization of iron by heating above the Curie
temperature: ferromagnetic-paramagnetic transition, loss of
magnetic order.

3.  The degree of freedom that is ordered or disordered can be translational (crystalline
ordering), rotational (ferroelectric ordering), or a spin state (magnetic ordering).
 Depending on how the correlations decay with distance, one speaks of long-range
order or short-range order.
Long-range order (LRO): Short-range order (SRO):
Differentiation „” of probalilities of Tendency for A-(B-) atoms to be
preferencially surrounded by B- or A-atoms
particular sublattice sites being occupied (correlation functions).
by particular atoms.
 If a disordered state is not in thermodynamic equilibrium, it is quenched disorder.
For instance, a glass is obtained by quenching (supercooling) a liquid.
 Some other quenched states are called spin glass, orientational glass and the opposite
of quenched disorder is annealed disorder.

4. Ordered Phases
 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.
 In such solutions PAB, the number of A-B bonds,
PAB = Na z XAXB (bonds mol-1)
where Na Avogadro's number, and z is the number of bonds per atom.
Positionally ordered A B
Probability of
occupation:
A  50%
B  50%
Probabilistically ordered
PROBABILISTIC
OCCUPATION

5. is the difference between A-B bond energy and the average of A-A and B-B .
 = 0 , ∆H =0 - Ideal Solution.
 < 0 the atoms in the solution will prefer to be surrounded by atoms of
mix
the opposite type and this will increase P .
Whereas  > 0, P Will tend to be less than in a random solution.
AB
AB
∆Hmix= Ω Xa Xb
Ω= Na z 
Ω <0 the no of A-B bonds is greater than this, the solution is said to contain
short range order (SRO)
s = PAB – PAB(random)
PAB(max) –PAB(random)
PAB(max)- max no. of bonds possible
PAB(random)- no. of bonds in random solution.

6. Cu-Au alloys
Cu and Au – FCC structured and totally miscible.
At Higher Temp: Cu or Au can occupy any site and the lattice can be
considered as fcc with a “random” atom at each lattice( Fig 1.20 a).
At Lower Temp: XCu=XAu =0.5 i.e 50/50 Cu/ Au mixture. (ordered
structure) (Fig 1.20 b)
CuAu Superlattice.
Cu3 Au Superlatice.

7. The necessary condition for the formation of a superlattice, i.e. an ordered solid solution, is
that dissimilar atoms must attract each other more than similar atoms. In addition, the alloy
must exist at or near a composition which can be expressed by a simple formula such as AB,
A3B or AB3. The following are common structures:
Cu3Au
CuAu

8. Disorder to Order Transformation
An atomic disorder to order transformation is a change of phase.
It entails a change in the crystallographic symmetry of the high temperature,
disordered phase, usually to a less symmetric low temperature atomically ordered phase.
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
Order Parameter
Disorder Order
Thermodynamic parameter, called the order parameter, ƞ which can be used as a measure
of the extent of the transformation.
This order parameter ƞ, is one which has an equilibrium value, so that we can always
write:
 G 

  
 0
 T , P
since G, the Gibbs free energy is a minimum at equilibrium

9. G = H - TS
At constant T and P the system in equilibrium will be the one with the lowest
Gibbs Free Energy
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.
↑ T  Disordered
G  H  T S
↓ T  Ordered
Examples: Liquid to Solid
Disorder to Order
In both cases the high temperature equilibrium phase is more
“disordered” than the low temperature “ordered” phase.

10. A Phase Diagram Which Includes a Typical Disorder to Order Transformation

11. High Temperature, Low Temperature, ordered
disordered phase (FCC, cF4) phase (L10, tP4)

12. Ordering Transformations:
 What Happens when Ordered Single Crystal( CuZn or Cu3Au) is
Heated from low temperatures to above the disordering temperature.
 Here We quantify the degree of order in crystal by defining Long
Range Order parameter L,
rA  X A
L
1 X A
 rA → probability that A sublattice is occupied with the right atom
 XA → mole fraction of A in the alloy
 L → Long Range Order
 L=1 : Fully Ordered Alloy (all Atoms occupy their correct sites).
 L=0 : Completely Random Distribution

13. At 0K : Min Free Energy by choosing Highly order Arrangement (L=1) :
Lowest internal energy. Configurational Entropy =0;
At higher temp: Min free energy state will contain some disorder. (diffusion)
Entropy effects become increasingly important with rising temperature so L
continuously decreases until above some critical ( Tc) L=0.
Results for CuZn and Cu3Au Superlattices
Second Order
1 Long Range
Order
~ First Order
Short Range
Order
CuZn Type
0
T TC
No Sudden change in order at Tc : U and H Substantial change in order at Tc :
will be continous (U ,H )disorder state> (U,H) Ordered State
Above Tc it is impossible to distinguish separate sublattices extending over long distances and L=0;
Solid solutions which have a negative enthalpy of mixing (Hmix < 0) prefer unlike nearest
neighbours → show tendency for ordering phases at low temperature.

14.  Two Mechanism to create
disordered superlattice ordered superlattice
Continuous increase in SRO
Mechanism
Nucleation and Growth
1. Continuous increase in SRO
Local rearrangements occurring homogenously throughout the crystal
which finally leads to LRO.
2. Nucleation and Growth
Due to an energy barrier to the formation of ordered domain,
transformation takes place with the help of nucleation and growth.

15.  The two are equivalent to spinodal decomposition and precipitation
as mechanisms for formation of coherent zones in alloys with
∆Hmix >0 .
 1st mechanism: Second order transformations or at very high
supercooling below Tc.
 2nd mechanism: more common.
Atoms can order on either the A or B sublattice , the independently nucleated domains will be “out of phase”
Domains Subsiquintly grow together a boundary will form (antiphase domain boundary (APB)) across which
atoms will have wrong neighbours.

17. Examples of common ordered structures (superlattices)
L10: CuAu (I) L12: Cu3Au DO3: Fe3Al
Structure Examples
L20 CuZn, FeCo, NiAl, FeAl, AgMg
L12 Cu3Au, Au3Cu, Ni3Mn, Ni3Fe, Ni3Al, Pt3Fe
L10 CuAu, CoPt, FePt
DO3 Fe3Al, Fe3Si, Fe3Be, Cu3Al
DO19 Mg3Cd, Cd3Mg, Ti3Al, Ni3Sn

18. CuAu
Cu
Au
Cu
Au
CuAu
a = 3.96Å, c =
Lattice parameter(s) Wyck
3.67Å
off
Space Group P4/mmm (123) x y z
positio
Strukturbericht notation L10 n
Pearson symbol tP4 Au1 1a 0 0 0
Other examples with this Au2 1c 0.5 0.5 0
TiAl
structure Cu 2e 0 0.5 0.5

19. Cu3Au
Cu
Au
Cu
Au
Cu3Au
Lattice parameter(s) a = 3.75 Å
Space Group Pm-3m (221)
Strukturbericht notation L12
Pearson symbol cP4
Other examples with this structure Ni3Al, TiPt3

20. Thank You