Basic 8Micro-Nano Materials Science
and Analysisand Analysis‐Atomistic simulations in materials scienceAtomistic simulations in materials science
and engineering‐
Assistant Prof. Y. Kinoshita and Prof. N. OhnoAssistant Prof. Y. Kinoshita and Prof. N. OhnoDept. of Comp. Sci. Eng. and Dept. of Mech. Sci. Eng.,
N U i JNagoya Univ., Japan
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Table of Contents
• Outline and procedure of atomistic simulationsp• Examples of atomistic simulations
① Electronic structures of single-walled boron nitride nanotubes① ect o c st uctu es o s g e a ed bo o t de a otubessubjected to tension, torsion, and flattening[Y. Kinoshita and N. Ohno, Phys. Rev. B, 82, 085433 (2010)]
② Flattening-induced electronic changes in multi-walled boron nitride nanotubes[Y. Kinoshita, S. Hase, and N. Ohno, Phys. Rev. B, 80, 125114 (2009)]
• References
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Outline and procedure of atomistic simulations
Start
Initial atomic positions and velocities
Calculation of energy E
C l l ti f t i f F
(1)
(2) Calculation of atomic force F
Updating atomic positions r
(2)
(3) Updating atomic positions r
Physical quantities (T, ij, …)
(3)
Termination condition
Nocondition
End
Yes
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
End
(1) Calculation of energy E
Empirical methodNon-empirical/First-principles
)()(1
)]([)()(ext
rr
rrrr
'
TdvE
)(rE
(2-body)
)](['|'|
)()(21
xc rrrrrrr Edd
)(r : Charge density
),,( rrE(3-body)
Di t b t t)(r
)(ext rv
)]([ rT
: Charge density
: External field
Ki ti
r
: Distance between atom and
: Angle among atom)]([ rT
)]([xc rE: Kinetic energy
: Exchange-correlationenergy
: Angle among atom, , and
Based on quantum mechanics High accuracy
Based on empirical potential Low accuracy
High computational cost Low computational cost
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
(2) Calculation of atomic force F
ii r
EFE
,F
( : Index of atoms i : or di t )( : Index of atoms, i : x-, y-, or z-coordinate)
Ex) Lennard-Jones potential ( : Material constant)
612612
612LJ612LJ 6124,4)(
rrrdr
drr
r
r
rrdrd
rr
rE
rEFrE ii
iii
LJLJ ,)(
21
LJ
dr
d LJ1
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
/r /r
(3) Updating atomic positionsMolecular Dynamics
Energy minimization by an Numerical integration of theMolecular Mechanics
Energy minimization by an optimization algorithm
Final (converged) atomic position i i t t
Numerical integration of theequation of motion
Atomic trajectory is importantis important
Ex) Steepest descent method Ex) Verlet algorithm],,[),( rrrr EE
)()()1( kkk Ea rr)()( kk F
2)()()()(2)(
ttttttt
Frrr
)()( kk aFr )(
m
tt
ttt
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Example of atomistic simulations ~backgrounds~
• Boron nitride nanotube (BNNT)1994 : Theoretical prediction (A R bi l PRB EPL)– 1994 : Theoretical prediction (A. Rubio et al., PRB, EPL)
– 1995 : Experimental synthesis (N. G. Chopra et al., Science)
• Structure– Multi-wall (MW) > Single-wall (SW)– Zigzag > Armchair, Chiral– Interwall spacing : 0.33-0.34 nm
Multi-wall Single-wall
• PropertiesHigh mechanical strength– High mechanical strength
– High thermochemical stability– Electrically insulating unlike carbon nanotubes
Zigzag(n,0)
Armchair(n,n)
Chiral(n,m)
– Electrically insulating, unlike carbon nanotubesindependent of diameters, chiralities and the number of walls
Nanocoatings for conductive nanowires nanotubes etcBasic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Nanocoatings for conductive nanowires, nanotubes etc.
Example of atomistic simulations ~backgrounds~
• Bending (experiment) Bai et al., Nano Lett., 7, 632 (2007)
Insulator
S i d t
– Deformation-induced electronic changes:
Semiconductor
– Deformation-induced electronic changes:Mechanism? Deformation modes? Feasibility?
This work:① Electronic structures of SWBNNTs subjected to tension, torsion,
and flattening② Flattening-induced electronic changes in MWBNNTs
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Example of atomistic simulations ~backgrounds~
Conduction band
Conduction bandminimum (CBM)
Energy of CBM : ECBM
Energy gap : Eg = ECBM – EVBM
Valence bandmaximum (VBM)
Energy of VBM : EVBM
Valence band
Conductor Semiconductor Insulator
Electron
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Conductor Semiconductor Insulator
① Electronic structures of SWBNNTs① Electronic structures of SWBNNTs subjected to tension, torsion, and flattening
Y. Kinoshita and N. Ohno, Phys. Rev. B, 82, 085433 (2010)
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Simulation model• (n,0) zigzag, n = 6, 8, 10
a : Nearest interatomic distance = 0.145 nma : Nearest interatomic distance 0.145 nmLv : Length of vacuum region = 0.5 nm
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Simulation procedure
• Deformation analysesLL
0
0
z
zzzz L
LL
360
Tensile strain
Specific angle0
360
zz LnN
DD
Specific angleof twist (deg/nm)
0
0
DDD
Flattening ratio
• Analytical condition– First-principlesFirst principles– DFT-GGA (PW91)– Ultrasoft pseudopotentialp p– Cut-off energy : 350 eV– k-points: 30 points (-X)
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Energy band structure of (8,0) under flattening
CBMCBM
VBM
VBM and CBM are located at the pointVBM and CBM are located at the point Decrease in CBM energy Decrease in the energy gap
※ Monotonic decrease in ECBM also under tension & torsion
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Change in the energy gap
T i d t i Tension and torsion• The energy gap decreases almost linearly.
The rate of decrease hardly depends on the diameter• The rate of decrease hardly depends on the diameter Flattening
• The energy gap decreases quadratically or exponentially• The energy gap decreases quadratically or exponentially• The amount of decrease significantly depends on the diameter• A few times larger decrease in E than tension and torsion
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
• A few times larger decrease in Egap than tension and torsion
CBM charge density
• Bond formation between neighboring boron atoms
Decrease in CBM energy
• Bond strength:Flattening>Tension TorsionFlattening>Tension, Torsion
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Deformation force
• Required force: Flattening << Tension, Torsion• Forces rapidly increase later under flattening
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Energy gap vs. Deformation force
Flattening with a force smaller than that applied for g pptension or torsion leads to the larger decrease in Egap
Flattening offers a larger obtainable range of Egap than
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
tension and torsion
Feasibility of flattening BNNTs Flattening of CNTs by AFM tip Barboza et al., PRL, 102, 025501 (2009)
1tan2
)1()2(12
2/32/1
2/30
RFD
ratioFlattening:]J[102.1const.:
diameterTube:radiustipAFM:Force:18
0
)()(
DRF
– When = 0.4, R = 30 nm ,• (6,0) CNT: F = 15.4 N/m (Barboza et al.)• (6,0) BNNT: F = 16.8 N/m (This work)( )
Flattening BNNTs is technically feasibleFlattening BNNTs is technically feasible.
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Summary ①
Electronic structures of (n,0) SWBNNTs under tension, torsion, and flattening have been investigated by first-principles
• Tension, torsion, and flattening decrease the energy
and flattening have been investigated by first-principles.
, , g gygaps of SWBNNTs.
Fl tt i ith f ll th th t li d f• Flattening with a force smaller than that applied for tension or torsion causes a larger decrease in the energy gapenergy gap.
• The force required for flattening SWBNNTs is not q gunrealistic.
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
②②Flattening‐induced electronic changes in MWBNNTs
Y. Kinoshita, S. Hase, and N. Ohno, Phys. Rev. B, 80, 125114 (2009)
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Simulation model• (n,0) zigzag, ni+1 – ni = 8, i : i-th tube from the innermost
most stable (S. Okada et al., PRB, 65, 165410 (2002))
– Single‐wall (SW) : (5,0), (13,0), (21,0)– Double‐wall (DW) : (5,0)@(13,0), (13,0)@(21,0)( ) ( , )@( , ), ( , )@( , )– Triple‐wall (TW) : (5,0)@(13,0)@(21,0)
※Three dimensional periodic boundary conditionBasic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
※Three-dimensional periodic boundary condition
Simulation procedure
• Flattening deformationEquilibrium condition– Equilibrium condition
Atomic force < 0.01 eV/ÅStress < 0 01 GPaStress zz < 0.01 GPa
– Under flatteningAtomic force < 0 01 eV/ÅAtomic force < 0.01 eV/ÅStrain zz = 0
• Analytical condition– First-principles
0
DDD
Flattening ratio :
– DFT-GGA (PW91)– Ultrasoft pseudopotential 0D
0D
: Diameter of the outermost tubeat equilibrium
– Cut-off energy : 350 eV– k-points: 1 x 1 x 4
at equilibrium
D : Distance between imaginary walls
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
imaginary walls
Energy band of (13,0) SW
hardly changesy g
E is the main factor in determining E ECBM is the main factor in determining Eg
※Tendency of change in band structure : (5 0) SW (21 0) SW ≈ (13 0) SW
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
(5,0) SW, (21,0) SW ≈ (13,0) SW
Energy band of (13,0)@(21,0) DW
hardly changesy g
(13,0)@(21,0) DW ≈ SWs
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Energy band of (5,0)@(13,0) DW
hardly changesy g
ECBM is the main factor in determining Eg
※Tendency of change in band structure : (5 0)@(13 0)@(21 0) TW ≈ (5 0)@(13 0) DW
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
(5,0)@(13,0)@(21,0) TW ≈ (5,0)@(13,0) DW
Energy gap vs. Flattening ratio
Eg in the SWs :g
* Monotonic decrease* (5,0) > (13,0) > (21,0)( , ) ( , ) ( , )
Eg in (13,0)@(21,0) DW* M t i d* Monotonic decrease* > (13,0) SW, (21,0) SW
Eg in (5,0)@(13,0) DW and TW* Increase and then decrease* ↑ to ↓, earlier in TW
E – curves : MWs ≠ SWs Eg – curves : MWs ≠ SWsEffects of interwall interaction
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Energy gap vs. Flattening ratio
Eg in the SWs :g
* Monotonic decrease* (5,0) > (13,0) > (21,0)( , ) ( , ) ( , )
Eg in (13,0)@(21,0) DW* M t i d* Monotonic decrease* > (13,0) SW, (21,0) SW
Eg in (5,0)@(13,0) DW and TW* Increase and then decrease* ↑ to ↓, earlier in TW
E – curves : MWs ≠ SWs Eg – curves : MWs ≠ SWsEffects of interwall interaction
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Energy gap vs. Flattening ratio
Eg in the SWs :g
* Monotonic decrease* (5,0) > (13,0) > (21,0)( , ) ( , ) ( , )
Eg in (13,0)@(21,0) DW* M t i d* Monotonic decrease* > (13,0) SW, (21,0) SW
Eg in (5,0)@(13,0) DW and TW* Increase and then decrease* ↑ to ↓, earlier in TW
E – curves : MWs ≠ SWs Eg – curves : MWs ≠ SWsEffects of interwall interaction
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Energy gap vs. Flattening ratio
Eg in the SWs :g
* Monotonic decrease* (5,0) > (13,0) > (21,0)( , ) ( , ) ( , )
Eg in (13,0)@(21,0) DW* M t i d* Monotonic decrease* > (13,0) SW, (21,0) SW
Eg in (5,0)@(13,0) DW and TW* Increase and then decrease* ↑ to ↓, earlier in TW
E – curves : MWs ≠ SWs Eg – curves : MWs ≠ SWsEffects of interwall interaction
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Energy gap vs. Flattening ratio
Eg in the SWs :g
* Monotonic decrease* (5,0) > (13,0) > (21,0)( , ) ( , ) ( , )
Eg in (13,0)@(21,0) DW* M t i d* Monotonic decrease* > (13,0) SW, (21,0) SW
Eg in (5,0)@(13,0) DW and TW* Increase and then decrease* ↑ to ↓, earlier in TW
E – curves : MWs ≠ SWs Eg – curves : MWs ≠ SWsEffects of interwall interaction
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
CBM charge density of SWs and (13,0)@(21,0) DW
Bond formationBond formation
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
0.003
CBM charge density of SWs and (13,0)@(21,0) DW
(
Electronic bonds : (5,0) > (13,0) > (21,0)
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
CBM charge density of SWs and (13,0)@(21,0) DW
Electronic bonds : (13,0) < (13,0)@(21,0)
< in
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
CBM charge density of (5,0)@(13,0) DW
Charge transfer from inner to outerBond formationBond formation
0.003
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
CBM charge density of (5,0)@(13,0)@(21,0) TW
Charge transfer Bond formationg Bond formation
0.003
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
CBM charge density of (5,0)@(13,0) DW and TW
(5,0)@(13,0) DWBNNT (5,0)@(13,0)@(21,0) TWBNNT
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
Summary ②Electronic structures of SW- and MWBNNTs under flattening compression have been investigated using first-principles.
• Single-walled BNNTs (SWBNNTs) :– The energy gap monotonically decreases with increasing flatteningThe energy gap monotonically decreases with increasing flattening
deformation.– The amount of the decrease becomes smaller in proportion to the
tube diameter.
• Multi-walled BNNTs (MWBNNTs) :• Multi-walled BNNTs (MWBNNTs) : – nin > nc : The energy gap monotonically decreases.– ni < n : The energy gap first increases and then decreasesnin < nc : The energy gap first increases and then decreases.
Innermost tube : (nin , 0) zigzagn : Critical value an interger between 5 and 13nc : Critical value, an interger between 5 and 13.
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University
References• Atomistic simulations
– Richard M. Martin, Electronic structure, Cambridge, (2004)– J. M. Thijssen, Computational Physics, Cambridge, (2007)
• Research examples– A. Rubio et al., Phys. Rev. B, 49, 5081 (1994)
X Bl t l E h L tt 28 335 (1994)– X. Blase et al., Europhys. Lett., 28, 335 (1994)– N. G. Chopra et al., Science, 269, 966 (1995)– S Okada et al Phys Rev B 65 165410 (2002)S. Okada et al., Phys. Rev. B, 65, 165410 (2002)– X. Bai et al., Nano. Lett., 7, 632 (2007)– A. P. M. Barboza et al., Phys. Rev. Lett., 102, 025501 (2009)– Y. Kinoshita, S. Hase, and N. Ohno, Phys. Rev. B, 80, 125114 (2009)– Y. Kinoshita and N. Ohno, Phys. Rev. B, 82, 085433 (2010)
Basic 8 Micro-Nano Materials Science and Analysis Assistant Prof. Y. Kinoshita and Prof. N. Ohno-Atomistic simulations in materials science and engineering-COE for Education and Research of Micro-Nano Mechatronics, Nagoya University