A COMPARISON OF THE ELECTRON AND
ION IRRADIATION EFFECTS ON THE
STABILITY RANGE OF ORDERED
STRUCTURES IN Ni4 Mo
M. SUNDARARAMAN* and S. BANERJEE
Presented by G. K. DEY
Materials Science Division
Bhabha Atomic Research Division
Mumbai 400085
* email:msraman@apsara.barc.ernet.in
Outline
•Ordering – chemical, magnetic, & electric
• Evolution of Ordering
• Competing superlattices in Ni4Mo alloy
• Influence of radiation on order  disorder
• Order evolution
-- under electron irradiation
-- under heavy ion irradiation
Comparison of electron and ion irradiation results
Conclusions
Ordering – Chemical, ferromagnetic, ferroelectric
Empty
lattice
Atoms A & B
Electric/
magnetic
moments
Chemical Ordering
Ferromagnetic
Ferroelectric Ordering
Outline
•Ordering – chemical, magnetic, & electric
• Evolution of Ordering
• Competing superlattices in Ni4Mo alloy
• Influence of radiation on order  disorder
• Order evolution
-- under electron irradiation
-- under heavy ion irradiation
Comparison of electron and ion irradiation results
Conclusions
Evolution of order
Nucleation and Growth
Continuous Ordering
Order evolution could be either first or second order
Evolution of Ordering: Discrete Mode
(Nucleation & Growth)
Disordered
Matrix
Nucleation
Evolution of Ordering – Static Concentration Waves
Single Variant <100>
K vector – B2 Ordering
3 variants <100> K vector
– L12 ordering
Continuous Ordering
Amplification of concentration wave with time
First & second order transitions: Thermodynamic viewpoint
nth order transformation:  nF / Tn
First Order
 0; 
n1
F / T
Second order
F
E
Cp
Temperature 
n1
0
First & second order transitions: Landau Plots
First Order
(Discrete)
Second order
(Continuous)
Energy barrier
Nucleation & growth
Outline
•Ordering – chemical, magnetic, & electric
• Evolution of Ordering
• Competing superlattices in Ni4Mo alloy
• Influence of radiation on order  disorder
• Order evolution
-- under electron irradiation
-- under heavy ion irradiation
Comparison of electron and ion irradiation results
Conclusions
Ordered States in Ni4 Mo
* Above 1140 K alloy is in SRO state
* Below 1140 K alloy is in LRO state
* By conventional solutionising and quenching treatment
alloy can not be produced in the completely disordered state
(CDO)
* LRO and SRO are two different states
Description of LRO and SRO structures
LRO state
Cp  c [ 1  2 l Cos2  p / 5  Cos4  p / 5]
p = 0,1,2,3 for <1 ½ 0> modulation
SRO state
Cp  c [ 1  2 s sin {(p 1/ 2) / 2}]
p = 0,1,2,3, 4 for 1/5<1 ½ 0> modulation
[001] Projection
Structural description of <1 ½ 0> Ordering
Different from SRO
intensifying to
become LRO
SRO <1 ½ 0>
LRO 1/5 <420>
Isostructural
microdomains
Disordered matrix
Multiple microdomains
Concentration wave packets
Microdomains
Outline
•Ordering – chemical, magnetic, & electric
• Evolution of Ordering
• Competing superlattices in Ni4Mo alloy
• Influence of radiation on order  disorder
• Order evolution
-- under electron irradiation
-- under heavy ion irradiation
Comparison of electron and ion irradiation results
Conclusions
Outline
•Ordering – chemical, magnetic, & electric
• Evolution of Ordering
• Competing superlattices in Ni4Mo alloy
• Influence of radiation on order  disorder
• Order evolution
-- under electron irradiation
-- under heavy ion irradiation
Comparison of electron and ion irradiation results
Conclusions
Electron Irradiation Results
1 MeV electrons
Dose rate = 10-3 dpa/s
Evolution of Order in Ni4Mo under electron
Irradiation
170 K
Disordering of LRO state
473 K
Persistence of 1½ 0 order (SRO)
in initial SRO state
Evolution of Order in Ni4Mo under electron Irradiation
<1 ½ 0> & 1/5 <420> diffraction spots
remain linked during evolutionary stages
Damage rate: 10—3 dpa/s
S Banerjee, K Urban, M. Wilkens
Acta Met., 32 (1984) 299
Ordering Mechanisms Maps for Ni4Mo under e- irradiation
A: Destruction of LRO
B: No significant change of order for S=0, S=1
C: Continuous ordering by decay of <1 ½ 0>
waves & simultaneous amplification of LRO
D: Initially as in region C, after <1 ½ 0> disappear,
D1a domains nucleate & grow
E: Nucleation & growth of D1a
F: Destruction of <1 ½ 0>
G: <1 ½ 0> order decays at T > 550 K
H: <1 ½ 0> grows
I: Destruction of <1 ½ 0> & transition to LRO
No LRO state below 450 K
No SRO State below 200 K
S Banerjee, K Urban, M. Wilkens Acta Met., 32 (1984) 299
Ordering & Disordering Jumps
 

U
   0 e xp  Em   / kT
2
 






A V A V

B V B V


Asymmetric energy barrier for
vacancy-atom Interchange in ordered alloy
Order-parameter vs. temperature plots
- equilibrium condition
- steady state condition under irradiation
 dS 
 
 
   k CACB  k CACB
 dt  t
k 
  Z CV Z  CV
Z CV  Z  CV
equilibrium
Under irradiation
S. Banerjee, K. Urban, Phys. Stat. Sol., 81, (1984) 145
Comparison between theory
& experiment
Outline
•Ordering – chemical, magnetic, & electric
• Evolution of Ordering
• Competing superlattices in Ni4Mo alloy
• Influence of radiation on order  disorder
• Order evolution
-- under electron irradiation
-- under heavy ion irradiation
Comparison of electron and ion irradiation results
Conclusions
Ion Irradiation Results
300 keV Ni+ ions
Dose rate = 10-3 dpa/s
Displacement cascades produced by 60 keV Au++ ions
in ordered Ni4 Mo (D1a)
Black-white contrast
From Dislocation
loops (g = 200)
M. Sundararaman,
S. Banerjee,
H. Wollenberger,
Acta Met., 43,
(1995) 107
Disordered zones
images with
Superlattice reflection
(g = 1/5 <420>
Evolution of Order in Ni4Mo under ion
Irradiation
Gradual decay of SRO and LRO states to CDO state
Evolution of Order in Ni4Mo under ion
Irradiation
Decay of LRO and
gradual development
of SRO intensity
300 keV Ni+ ;
Irradiation
temperature - 600 K
Dose rate - 10-3 dpa/s
Evolution of Order in Ni4Mo under ion
Irradiation
i-SRO
i-LRO
Development of SRO in the initially SRO and LRO specimens
Evolution of order in Ni4Mo under ion
Irradiation
i-SRO
i-LRO
Final steady states at different irradiation temperatures
Loop size greater than 10 nm
Dislocation loops in irradiated Ni4Mo;T = 900 C
Frank loops
Steady state structures in Ni4Mo under ion irradiation
Initial state
<1 ½ 0>
Domains
A
B
C
D
1/5 <420>
E
F
Transitions
<1 ½ 0> disappears
<1 ½ 0> decays
<1 ½ 0> grows
experimentally inaccessible
1/5 <420> decays & <1 ½ 0> grows
1/5 <420> persists
Cascade dynamics
Displacement cascade – 10-13 s
Thermal spike – 10-11 s
Final order decided by disordering and reordering within
thermal spike
Quenching of thermal spike
- Amorphous
- Complete disorder
- Partial Order
Substrate / sample
temperature / thermal
conductivity
Net vacancy concentration inside the cascade
By diffusion to periphery form loops around cascade
Comparison of electron and ion
irradiation results
Comparison between electron & ion
irradiation
Experiment
Steady state structures developed
during e- and ion irradiation
Theory
Stochastic potential for maximum
order versus T
Lower bound for LRO stability matches with experiment for e- irradiation
Conclusions
Distinct stability regimes for the CDO, the SRO and the LRO
states could be obtained for electron and ion irradiation
Cascade effect decreases the temperature range of stability of
LRO state while increases the temperature range of stability of
SRO state
For electron irradiation, mixed state (SRO and LRO) can coexist between 450 K and 800 K. No mixed state exist for ion
irradiation
Low temperature for stability of LRO calculated by Kinetic and
stochastic models match with experimental observation for
electron irradiation
Acknowledgments
Dr. U.D. Kulkarni, BARC
Prof. K. Urban, KFA, Jülich
Prof. H. Wollenberger, HMI, Berlin
Thank
you
Reaction kinetics model
Kinetics: Rate of Change of point-defect
concentrations (Vacancy, V, & Interstitial, I)
dCV
 P(1  ZSCV )  K r CICV  K  ( CV  Ct )  K  ( CV  Ct )  K S ( CV  Ct )CS
dt
Production Recombination  transfer  transfer Annihilation at sinks
dCV
 P(1  ZSCV )  K r CICV  K  ( CV  Ct )  K  ( CV  Ct )  K S ( CV  Ct )CS
dt
dCI
ˆ C )  K C C
 P(1  ZSCV )  CI ( K r CV  K
r V
IS I S
dt
, : sublattice sites
S. Banerjee, K. Urban, Phys. Stat. Sol., 81, (1984) 145
Radiation Effects in Solids
Radiation Enhanced / Induced Segregation
Radiation Enhanced / Induced Diffusion
Radiation Enhanced / Induced Phase Transformation
-Generation of new phases-vacancy ordered
Radiation Enhanced / Induced Redistribution
Irradiation induced processes
Disordering – temperature independent
Reordering - temperature dependent
Net effect decides the final structure
Radiation Induced Disordering e-
e-
Replacement Collison
v
v
Random
Recombination
v
I
I
I
Ion
M. Sundararaman, S. Banerjee, &
H. Wollenberger, Acta Met., 43, (1995) 107
Displacement
Cascade
Stochastic treatment
Probability of exchange of atoms from one 420 plane to the another
is used in stochastic treatment to derive potential similar to
thermodynamic model
In the absence of irradiation the potential are free energy functional.
Under irradiation they are no longer free energy functional
The steady state probability distribution under irradiation given by
P*irr(N) = P*irr(cW) exp[Wq Dy’q(q)
Dy’q(q) = Stochastic potential
W number of atomic sites in 420 plane
C = concentration of Mo in the plane
q  LRO or SRO
 = order parameter
Stochastic treatment of ordering in Ni4Mo
under electron irradiation
CDO to SRO / LRO
Lower critical temperature
CDO to SRO / LRO
Upper critical temperature
Bellon and Martin, Phy. Rev. B39, (1988)