Simulation of displacement cascades in ?-Fe and Fe-10% Cr

1
Simulation of displacement cascades in ?-Fe and
Fe-10 Cr
Terentiev Dmitry and Malerba Lorenzo
2
Goals

• Methods
• Potentials
• Cr concentration influence
• Temperature dependence and diffusion mechanism of
  SIA
• Small loop diffusion

3
Simulation technique

• Molecular Dynamics
• Microcanonical statistical ensemble
• Periodic boundary conditions
• Simulation cell size 2 000 50 000
• Simulation time up to 20 ns (in case of low T)
• Either pure Fe or 0.2, 3, 5, 7, 9 and 12 Cr
  atoms in Fe matrix
• The interatomic potential
• EAM for ferromagnetic Fe-10Cr Old
• EAM for ferromagnetic Fe-10Cr - New 04.03.24
• Mendeleev potential Phil.Mag. Vol.83, No. 35
  (2003)

4
Definitions and method
Backward jump
Simple 1D jump 0.86 l.u.
Change of direction in lt111gt plane

• ? Mean free path
• v change direction frequency

lt111gt
Free path distance before SIA changes direction
RISIA Distance which SIA passed
for certain time Tsim/K
5
Jump analysis, waiting time distributions
Tch_dir(FeCr)473 fs Tch_dir( Fe)452 fs Tjump
(FeCr) 351 fs Tjump(Fe)389 fs
Tch_d/Tjump slightly increases with incresing of
T and gives 1.6 in average
Tch_dir(FeCr)333 fs Tch_dir( Fe)366
fs Tjump(FeCr)222 fs Tjump(Fe) 241 fs
It looks like crowdion jumps by random
distribution for 1D as well as for jumps with
change of direction. Is it effect of pertrubation
caused by Cr drug and presence of nonisotropic
field caused by impurities ???
Tch_dir(FeCr)192 fs Tch_dir( Fe)244
fs Tjump(FeCr)123 fs Tjump(Fe)124 fs
6
Jump analysis, frequencies of jumps
Though there is no essential influence of Cr on
1D jump frequency, the rotation energy decreases
in presence of Cr atoms. This could affect the
sequences of 1D jumps by defocusing them and
leading to increase of Nch_dir and decrease of
mean free path.
7
Defocusing of crowdion by Cr
Trapping effect gradually disappears with rising
of temperature, but binding energy effect works
on whole considered interval. The crossing of the
curves will give value about 0.5 ??? Is it a
combination of one dimensional nature of jumps
and relative high binding energy ?
Effect of concentrated alloy ??? or activation
energy to make lt111gt jump does not depend on
crowdion type ?
8
Jump analysis, free path

• The behaviour of the Free Path curve and 3D jumps
  ratio vs T confirms assumption about defocusing
  caused by Cr
• Fe-Cr binding energy (for crowdion 0.333 eV
  POT / 0.358 VASP) was not overcome by thermal
  vibrations, and number of Cr interstitials did
  not change essentially
• even at high temperature the Fe-Cr interstitial
  configuration remains the most frequent one
• Although the Cr-Cr interstitial binding energy
  is rather high (0.45- POT / 0.035 VASP) there is
  clear decrease of Cr-Cr crowdion. number
• Effect of low migration barrier or concentrated
  alloy ???

9
Comparison of 2 methods

• Statistical meaning
• IIM 100 intervals, with deltaT200 ps(300K 20
  ns) 100 ps(1200K 10 ns)
• FPM Number ch_dir1000 (300K) 105 (1200K)
• Pure Fe influence of long 1D jumps at low
  temperature, relatively high amount of jumps with
  small free path at high temperature... Problem of
  statistics ?
• FeCr influence of trapping effect at low
  temperature, good agreement for high temperature
  ... what is the influence of trapping effect ?
  How is it localized ?

10
SIA diffusion in Fe-12Cr, comparison with pure Fe
Coefficient of diffusion, obtained by random
method
Correlation factor, fcDMFP/DIIM

• Pure Fe DSIA(Fe) is relatively high, compared
  with Osetsky results, although migration energies
  are quite close to each other. Effect of
  potential, namely, stable crowdion ???
• FeCr Migration energy is slightly higher than in
  pure Fe, no change of the slope is observed at
  low temperature region like in iron. Is it global
  effect of binding with Cr atoms ???

11
Trajectory of SIA during 50ps
300 K
SIA motion in Fe is essentially 1D, whereas in
FeCr no
600 K
Transition from 1D -gt 3D for SIA motion in Fe
900 K
12
Comparison of potentials

• New potential
• Basic properties and comparison with old one
• SIA diffusion description
• Possible mechanismes and temperature influence
• Mendeleev potential, basic properties

13
Basic properties
Parameters (all energies are given in eV units)z Old New Experimental (E) or ab initio/VASP (V)
Cohesive energy, Ecoh, in pure Fe -4.28 4.28 -4.28 (E)
Cohesive energy, Ecoh, in pure Cr -4.10 4.10 -4.10 (E)
Vacancy formation energy,EVf, in pure Fe 1.543 2.05 1.53-2.2 (E)
Substitutional energy of a Cr atom in Fe, EfCr 0.227 0.28 0.14 (V)
Vacancy binding energy at 1nn distance, EbV-V(1nn) 0.19 0.2 0.19 (V)
Vacancy binding energy at 2nn distance, EbV-V(2nn) 0.21 0.283 0.28 (V)
Cr-Vacancy binding energy, EbCr-V(1nn) 0.035 0.043 0.029 (V), lt0.1(E)
Fe-Fe crowdion formation energy, Eflt111gt(Fe-Fe) 4.02 7.44 4.11 (V)
Fe-Fe dumbbell formation energy, Eflt110gt(Fe-Fe) 4.15 7.18 3.41 (V)
Fe-Cr crowdion formation energy, Eflt111gt(Fe-Cr) 3.92 7.46 2.70 (V)
Fe-Cr dumbbell formation energy, Eflt110gt(Fe-Cr) 3.98 7.24 3.06 (V)
Cr-Cr crowdion formation energy, Eflt111gt(Cr-Cr) 4.02 7.38 2.67 (V)
Cr-Cr dumbbell formation energy, Eflt110gt(Cr-Cr) 4.02 7.08 2.67 (V)
Binding energy for Fe-Cr crowdion, Eblt111gt(Fe-Cr) 0.333 0 0.358 (V)
Binding energy for Fe-Cr dumbbell, Eblt110gt(Fe-Cr) 0.26 0.22 -0.005 (V)
Binding energy for Cr-Cr crowdion, Eblt111gt(Cr-Cr) 0.45 0.36 0.035 (V)
Binding energy for Cr-Cr dumbbell, Eblt110gt(Cr-Cr) 0.476 0.66 -.548
Migration energy for Cr to vacancy, EmigCr-V(in Fe) 0.728 0.8 0.58 (V)
Migration energy for Fe to vacancy, EmigFe-V(in Fe) 0.7 0.87 0.684 (V)
Activation energy for Cr diffusion Eact(Cr) Evf EmigCr-V EbCr-V 2.27 2.85 2.27 (V)
Activation energy for Fe diffusion Eact(Fe) Evf EmigFe-V 2.268 2.95 2.39 (V)
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Static Barriers
Fe
Fe
Saddle point energies for crowdion jump Old
potential 1. Fe Fe Fe 4.13 4.02 0.11
eV 2. Fe Cr Fe 4.01 3.92 0.09 eV 3. Cr
Cr Fe 4.12 4.00 0.12 eV New potential 1.
Fe Fe Fe 8.02 7.45 0.57 eV 2. Fe Cr
Fe 8.02 7.46 0.56 eV 3. Cr Cr Fe 7.96
7.38 0.58 eV
New potential provides a different mechanism of
SIA diffusion at least at low temerature
Cr
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Adjacment of time interval comparison of D

• 0.067 eV
• 0.076 eV
• 0.29 eV
• 0.055 eV
• 0.25 eV

• New Old very close to Osetsky (FS pot)
• MP predicts higher migration energy
• MP has no low energy tail, as well as
  SonedaPotential

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Diffusion mechanismes
Old potential all temperature interval
Mendeleev potential at 600K up to 1200K
New potential after 600K, lt110gt dumbbell does
not exist anymore
New potential in some cases, at low
temperature
New potential at low temperature interval and
up to 600K
New potential at low T less than 300K
17
Chromium concentration
At low temperature pure trapping effect With
rising of temp. the SIA are most efficiently
slowed down when the Cr concentration is around 7
Trapping effect is increasing with Cr
concentration No essential influence of
temperature
18
Small loopsformation and binding
- New predicts in 1.5 time higher formation
energy then Old - Reasonable agreement between
Soneda results and Old potential
- New predicts in 2.5 time higher binding
energy then Old - New and Old gives a
maxium at for Ebind for perfect 7 SIA loop, in
contrast to Soneda results
19
SIA loops diffusivity

• Both of potentials predict the same migration
  energy
• Migration almost does not depend on cluster size
• Accordingly to used model crowdions are
  independent

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Experimetal monitoring of microstructure
The motion of loops was very hardly observed at
the all temperatures examined. Loops begun to
shrink and dissappear abive around 750K. From the
comparison between Fe and FeCr, it can be state
that the both the shrinkage and the motion of
loops are significantly suppressed by Cr addition
under the thermal aging
Arakawa et al. JNM (2003) accepted
Evidence of rotation
OP 3SAI loop
NP 4SAI loop
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Effect of Cr and temperature in defect
accumulation behaviour, experiment
Fe-10Cr
Dislocation loops of interstitial lt111gt or lt100gt
type nucleate and grow much faster in presence of
Cr, but their density decreases and their size
increases with temperature
Yoshida et al. JNM 155-157 (1988)
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Conclusions

• Characteristics of the SIA diffusion have been
  considered using MD simulation
• Diffusivity of SIA has been calculated by
  different potentials and different approaches
• Barries for common accepted mechanism of
  interstitial jump were estimated (with Cr atoms)
• Different mechanismes of SIA jump have been
  discussed
• Chromium concentration influence on diffusivity
  of SIA was chekced in interval 0-12 Cr using 2
  potentials
• Diffusivity of small SIA clusters has been
  considered and first results agrees with a model
  of independent crowdion