Molecular Dynamics Study of Atomic Displacements in Binary Solid Solutions'

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Molecular Dynamics Study of Atomic Displacements
in Binary Solid Solutions.

• Student Y. Puzyrev
• Advisor Dr. J. S. Faulkner, FAU
• ORNL collaborators
• Drs. C. J. Sparks, G. E. Ice

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My thanks to...

• Dr. J. S. Faulkner
• Dr. Fernando Medina
• Dr. Warner Miller
• The members of my committee
• Dr. C. J. Sparks, ORNL
• Dr. G. E. Ice, ORNL
• Dr. Thomas Hutchinson, SURA
• All graduate students

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Outline

• Molecular Dynamics.
• Diffuse Scattering.
• Atomic displacements.
• Comparing theoretical calculations with
  experimental data.
• Conclusion.

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Semi-empirical Molecular Dynamics

• Solves classical equations of motion using
  potentials from quantum theory.
• INTERACTION many-body interaction is given by
  embedded atom method (EAM) potential.
• INTEGRATOR 6th order Gear predictor-corrector
  is used as the method of integration of equations
  of motion for NPT ensemble with periodic BC.
• PROPERTIES calculated using atomic
  configuration.

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Embedded Atom Method

• The embedded atom potential is constructed using
• electronic density
• embedding energy function
• pair interaction

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Thermal Expansion.

• The parameters a and ß in the pair potential term
  are adjusted so that the lattice constants are
  fitted to the experimental values for Cu and Au.
• Z0 is taken to be 11 and ? is taken to be 2.
• The embedding function and electronic density
  were not changed to preserve local interactions.

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Phase transition
The upper bound of the melting temperature was
determined for CuAu alloy.
Melting
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Debye-Waller Factor of Pure Cu
We calculate the intensity of the Bragg peaks as
a function of the reciprocal space vector.

• DWF is calculated for T 295 K and T 723 K
  from the ratio of Bragg peak intensities as a
  slope of linear function.
• The scattering pattern is produced by the MD
  simulation.

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Diffuse Scattering.
For binary alloys
For pure materials
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TDS of Pure Cu

• TDS is calculated using the ensemble of atomic
  configurations obtained from the MD calculation.
• Each configuration includes 32000 atoms.
• The experiment is easy because we are sweeping
  along one direction in k-space

C.J. Sparks, G.E. Ice (ORNL) private
communication
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TDS of Pure Cu

• The comparison is made with Cu crystal TDS
  measured at temperatures T295 K and T723 K.
• The plots are given along 0k0 and h30 directions
  in a reciprocal space.

C.J. Sparks, G.E. Ice (ORNL) private
communication
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TDS inversion temperature

• The TDS temperature inversion of the intensity at
  0.2 away from Bragg peak for copper takes place
  at T 500 K as predicted by Warren.
• The MD calculation of the intensity at 0.2 away
  from the Bragg peak shows the inversion effect
  also around that temperature.
• - B. E. Warren X-ray diffraction, p. 201

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TDS Inversion Temperature

• As described by Warren and observed by Cartz at
  high temperatures the decrease of TDS can be
  observed in limited regions of reciprocal space.
• MD simulation reproduces this inversion for Cu
  at T723K beyond h 5 along h60 direction.
• These theoretical results have inspired interest
  in new experiments.

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Size effect in binary alloys

• Temperature displacements of atoms at room
  temperature are appreciably larger than static
  displacements and its influence on average
  positions of atoms can be significant.
• In binary alloys with size mismatch the
  procedure of eliminating the temperature diffuse
  scattering (TDS) in diffuse x-ray diffraction
  experiment is complicated.
• It is imperative to remove TDS contribution
  theoretically and correct data for evaluating
  short range order (SRO) and static displacements
  experimentally.

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Vegard's Law
Cu-Pd and Cu-Au obey Vegard's Law. Both exhibit
convex up behavior. The lines are the theoretical
results and the crosses are the experimental
values.
Experimental data ref. Pearson, A handbook of
lattice spacings and structure of metal and
alloys, Pergamon press, 1964.
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Size Effect in Cu-Au Alloy

• Nearest neighbor distances calculated using MD
  and compared with extended x-ray absorption fine
  structure XAFS experiment.
• The crossover is approximately at 86 of the Au
  concentration as observed in XAFS.
• The same position of the crossover is predicted
  by MD
• Frenkel et. al., J. Phys. IV 7(C2), 1005 (1997)

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Size effect in Cu-Au alloy
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The crossover temperature dependence
The position of the crossover does not depend on
the temperature.
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Size effect in Cu-Pd alloy

• The position of the crossover
• has moved towards the lower
• concentration of the bigger atom (Palladium).
• The experimental data ref. Alloy phase diagrams,
  x-ray database, ASM Handbook, Volume 3, 1992.

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Size effect in Cu-Al alloy

• The position of the crossover has moved even
  more towards the lower concentration of the
  bigger atom (Aluminum).
• The experimental data ref. Alloy phase diagrams,
  x-ray database, ASM Handbook, Volume 3, 1992.

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Conclusion and work to be done

• MD works well for pure metals and gives results
  of great interest to experimentalists.
• MD gives good predictions for atomic
  displacements in alloys.
• There is a reason to believe that MD will give
  the TDS for alloys, but further experiments are
  needed.

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Other work on atomic displacements in Cu-Au

• SQS14 is LAPW first principles calculation by
  Zunger et. al., ref. Phys. Rev. 60 1687 (1998).
• MLOC is Monte-Carlo simulation by Malis et. al.,
  ref. Philosophical magazine B, 79 p. 869 (1999).

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Scattering factors of Cu and Au
The sum is over the neighbor shell indices lmn

• Dependence of the atomic scattering factors on
  is weak in comparison with the
  energy dependence.
• If one can make fAfB then only measures
  intensity is due to TDS.

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Conversion of the Copper-Gold Data to Electron
Units

• Compton and Resonant Raman inelastic scattering
  is separated and removed from integrated
  intensities.
• Scattering factors are corrected for x-ray
  absorption fine structure (XAFS) and Lorentzian
  hole width of an inner shell.
• Ni standard integrated intensities are obtained
  to compute conversion factor.

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Scattering intensity maps for Cu47.2Au52.8 and
Cu85.2Al14.8