Outline:

1
New piezoelectric and pyroelectric materials by
first principles design
Serge Nakhmanson North Carolina State University
Outline I. Motivations Why do we need
alternatives to ferroelectric ceramics? II.
Methodology How do we compute
polarization in periodic solids? III. Some
alternatives studied in detail 1.
Boron-Nitride nanotubes 2. Ferroelectric
polymers IV. Conclusions
Acknowledgments NC State University group
Jerry Bernholc Marco Buongiorno Nardelli
Vincent Meunier (now at ORNL)
Wannier functions collaboration Arrigo
Calzolari (U. di Modena) Nicola Marzari (MIT)
Ivo Souza (Rutgers)
Computational facilities DoD Supercomputing
Centers NC Supercomputing Center
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Properties of ferroelectric ceramics
Nature of polarization reduction of symmetry
see G. Saghi-Szabo et. al. PRL 1998, PRB
1999, also D. Vanderbilt and K. Rabe
3
BN nanotubes as possible pyro/piezoelectric
materials
hexagonal BN
excellent mechanical properties light and
flexible, almost as strong as carbon nanotubes
(Zhang and Crespi, PRB 2000) chemically inert
proposed to be used as coatings all insulators
with no regard to chirality and constant band-gap
of around 5 eV intrinsically polar due to the
polar nature of B-N bond most of the BN
nanotubes are non-centrosymmetric (i.e. do not
have center of inversion), which is required for
the existence of non-zero spontaneous
polarization Possible applications in
nano-electro-mechanical devices
actuators, transducers, strain and
temperature sensors
4
BN nanotubes as possible pyro/piezoelectric
materials
hexagonal BN
excellent mechanical properties light and
flexible, almost as strong as carbon nanotubes
(Zhang and Crespi, PRB 2000) chemically inert
proposed to be used as coatings all insulators
with no regard to chirality and constant band-gap
of around 5 eV intrinsically polar due to the
polar nature of B-N bond most of the BN
nanotubes are non-centrosymmetric (i.e. do not
have center of inversion), which is required for
the existence of non-zero spontaneous
polarization Possible applications in
nano-electro-mechanical devices
actuators, transducers, strain and
temperature sensors
5
Ferroelectric polymers
PVDF structural unit
ß-PVDF
See A. J. Lovinger, Science 1983
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Computing polarization
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A simple view on polarization
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Computing polarization in a periodic solid
Modern theory of polarization R. D.
King-Smith D. Vanderbilt, PRB 1993 R.
Resta, RMP 1994
1) Polarization is a multivalued quantity and its
absolute value cannot be computed.
2) Polarization derivatives are well defined and
can be computed.
The scheme to compute polarization with MTP can
be easily formulated in the language of the
density functional theory.
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Berry phases and localized Wannier functions
Computed by finite differences on a fine k-point
grid in the BZ
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Berry phases and localized Wannier functions
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Summary for the theory section

• In an infinite periodic solid polarization can be
  computed from the first principles with the help
  of Berry phases or localized Wannier functions
• This method provides full description of polar
  properties of any insulator or semiconductor

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Boron-Nitride Nanotubes
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Piezoelectric properties of zigzag BN nanotubes
Born effective charges
Piezoelectric constants
(w-GaN and w-ZnO data from F. Bernardini, V.
Fiorentini, D. Vanderbilt, PRB 1997)
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Piezoelectric properties of zigzag BN nanotubes
Born effective charges
Piezoelectric constants
(w-GaN and w-ZnO data from F. Bernardini, V.
Fiorentini, D. Vanderbilt, PRB 1997)
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Piezoelectric properties of zigzag BN nanotubes
Born effective charges
Piezoelectric constants
(w-GaN and w-ZnO data from F. Bernardini, V.
Fiorentini, D. Vanderbilt, PRB 1997)
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Ionic phase in zigzag BN nanotubes
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Ionic phase in zigzag BN nanotubes
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Electronic phase in zigzag BN nanotubes
Berry-phase calculations provide no recipe for
unfolding the electronic phase!
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Problems with electronic Berry phase
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Wannier functions in flat C and BN sheets
Carbon
Boron-Nitride
?
?
No spontaneous polarization in BN sheet due to
the presence of the three-fold symmetry axis
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Wannier functions in C and BN nanotubes
Carbon
Boron-Nitride
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Unfolding the electronic phase
(5,0) -5/3? 2? ?/3
(6,0) -6/3? 1? -?
(7,0) -7/3? 2? -?/3
(8,0) -8/3? 3? ?/3
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Total phase in zigzag nanotubes
Zigzag nanotubes are not pyroelectric! What
about a more general case of chiral nanotubes?
(n,m) R (bohr)
3,1 2.67 -1/3 0.113 -0.222
3,2 3.22 1/3 -1/3 0 mod(p)
4,1 3.39 1 1 0 mod(p)
4,2 3.91 -1/3 1/3 0 mod(p)
5,2 4.62 1 -1 0 mod(p)
8,2 6.78 0 1 0 mod(p)
All wide BN nanotubes are not pyroelectric! But
breaking of the screw symmetry by bundling
or deforming BNNTs makes them weakly pyroelectric.
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Summary for the BN nanotubes

• Quantum mechanical theory of polarization in BN
  nanotubes in terms of Berry phases and Wannier
  function centers individual BN nanotubes have no
  spontaneous polarization!
• BN nanotubes are good piezoelectric materials
  that could be used for a variety of novel
  nanodevice applications
• Piezoelectric sensors
• Field effect devices and emitters
• Nano-Electro-Mechanical Systems (NEMS)
• BN nanotubes can be made pyroelectric by
  deforming or bundling

See Nakhmanson et al. PRB 2003
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Ferroelectric Polymers
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Dipole summation models for polarization in PVDF
Which model is better? Ab Initio calculations can
help! What about copolymers?
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Polarization in ß-PVDF from the first principles
ß-PVDF polar
No sensible comparison to experiment because
ß-PVDF is only 50 crystalline!
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Polarization in PVDF copolymers
Copolymers can be grown 80-90 crystalline!
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Piezoelectricity in PVDF and copolymers
PVDF PVDF/TrFE 75/25 PVDF/TeFE 75/25
-0.268 (-0.130) 1 (-0.26) 2 -0.183 -0.135
-0.270 (-0.145) 1 (-0.09) 2 -0.192 -0.145
-0.332 (-0.276) 1 (-0.25) 2 -0.211 -0.150
1 Tashiro et al. Macromolecules, 1980 2
Carbeck and Rutledge, Polymer, 1996
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Superpolar polymers
100 improvement of polar properties over PVDF
and copolymers better thermal stability Could
be easy and cheap to synthesize
Nakhmanson, Buongiorno Nardelli and Bernholc,
submitted Ask for a preprint!
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Polar materials the big picture
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Conclusions

• Quantum mechanical theory of polarization in
  terms of Berry phases and Wannier function
  centers fully describes polar properties of any
  material
• Polar boron-nitride nanotubes or ferroelectric
  polymers
• are a good alternative/complement to
  ferroelectric ceramics
• Excellent mechanical properties, environmentally
  friendly
• Polar properties still substantial
• Numerous applications sensors, actuators,
  transducers
• Composites?
• Methods for computing polarization can be used
  to study and predict
• new materials with pre-designed polar properties