Simulations of Idealized Solid Electrolytes
for Solid State Battery Designs*
N. A. W. Holzwarth**
Department of Physics
Wake Forest University, Winston-Salem, NC, USA, 27109
*Supported by NSF Grant DMR-1105485 and WFU’s Center for Energy,
Environment, and Sustainability.
**With help from: Nicholas Lepley, Ahmad Al-Qawasmeh, Jason Howard,
and Larry Rush (physics graduate students), Yaojun Du (previous physics
postdoc) and colleagues from WFU chemistry department – Dr. Keerthi
Senevirathne (currently at Florida A & M U.), Dr. Cynthia Day, Professor
Michael Gross, Professor Abdessadek Lachgar, and Zachary Hood (currently
at ORNL)
6/03/2015
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Outline
Motivation – Why solid electrolytes?
Computational tools & reality checks
Some examples
Bulk properties
LiPON
Interface properties
Li thiophosphates
Summary and remaining challenges
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Motivation –
Why solid electrolytes?
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Materials components of a Li ion battery
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From Oak Ridge National Laboratory:
Advantages
 Compatible and stable with
high voltage cathodes and
with Li metal anodes
Disadvantages
 Relatively low ionic conductivity
(Compensated with the use of
less electrolyte?)
 Lower total capacity
Demonstrated for LiNi0.5Mn1.5O4/LiPON/Li
 10-6 m LiPON electrolyte layer achieved adequate
conductivity
 10,000 cycles* with 90% capacity retention
*1 cycle per day for 27 years
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From Toyota Motor Company Website:
http://www.toyota-global.com/innovation/environmental_technology/next_generation_secondary_batteries.html
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Motivation: Paper by N. Kayama, et. al in Nature Materials 10, 682-686 (2011)
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Motivation: Paper by N. Kamaya, et. al in Nature Materials 10, 682-686 (2011)
LiPON
RT
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Motivation: Paper by N. Kamaya, et. al in Nature Materials 10, 682-686 (2011)
Li7P3S11
RT
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Motivation: Paper by N. Kamaya, et. al in Nature Materials 10, 682-686 (2011)
Li7P3S11
b-Li3PS4
RT
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Motivation: Paper by N. Kamaya, et. al in Nature Materials 10, 682-686 (2011)
Li10GeP2S12
RT
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Solid Electrolyte Families
Investigated in this Study:
LixPOyNz
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LixPSy
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Computational tools
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Summary of “first-principles” calculation methods
Electronic coordinates

Exact Schrodinger
equation:
Atomic coordinates
H ({ri },{R a }) ({ri },{R a })  E  ({ri },{R a })
where
H ({ri },{R a })  H Nuclei ({R a }) + H Electrons ({ri },{R a })
Born-Oppenheimer approximation
Born & Huang, Dynamical Theory of Crystal Lattices, Oxford (1954)
Approximate factorization:
 ({ri },{R a })  X Nuclei ({R a }) Electrons ({ri },{R a })
Treated with classical mechanics
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Treated with density
functional theory
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
Electronic Schrodinger
equation:
H Electrons ({ri },{R a }) Electrons ({ri },{R a })  U  ({R a }) Electrons ({ri },{R a })
2
a 2
2

Z
e
e
2
H Electrons ({ri }, {R a })  



i 
a
2m i
a ,i | ri  R |
i  j | ri  r j |
For electronic ground state:   0
Density functional theory
Hohenberg and Kohn, Phys. Rev. 136 B864 (1964)
Kohn and Sham, Phys. Rev. 140 A1133 (1965)
Mean field approximation: U 0 ({R a })  U 0 (  (r ) ,{R a })
Kohn-Sham construction:
 (r )   K ( r )    n (r )
2
Electron
density
n
Electrons
HKS
(r ,  (r ),{R a }) n (r )   n n (r )
Independent electron wavefunction
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More computational details:
 2 2
 Z a e2
 (r ')
Electrons
a
2
3
HKS
(r,  (r),{R })  

e d r'
 Vxc   (r) 
a
2m
r r'
a rR
electron-nucleus electron-electron exchangecorrelation
Exchange-correlation functionals:
LDA: J. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992)
GGA: J. Perdew, K. Burke, and M. Ernzerhof, PRL 77, 3865 (1996)
HSE06: J. Heyd, G. E. Scuseria, and M. Ernzerhof, JCP 118, 8207 (2003)
Numerical methods:
“Muffin-tin” construction: Augmented Plane Wave developed
by Slater  “linearized” version by Andersen:
J. C. Slater, Phys. Rev. 51 846 (1937)
O. K. Andersen, Phys. Rev. B 12 3060 (1975) (LAPW)
Pseudopotential methods:
J. C. Phillips and L. Kleinman, Phys. Rev. 116 287 (1959) -- original idea
P. Blöchl, Phys. Rev. B. 50 17953 (1994) – Projector Augmented Wave (PAW)
method
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Outputs of calculations:
Ground state energy:
U 0 (  (r ) ,{R a })

min {R a } U 0 (  (r ) ,{R a })
 Determine formation energies

 Determine structural parameters

 (r )    n (r )
2
Stable and meta-stable structures
 Self-consistent electron density
n
 n 
 One-electron energies; densities of states
Nuclear Hamiltonian (usually treated classically)
H
Nuclei

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a
{R }

Pa2

a
a 2M
 U 0 (  (r ) ,{R a })
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 Normal modes
of vibration
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Codes used for calculations
Function
Generate atomic
datasets
DFT; optimize
structure
Structural visualization
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Code
Website
ATOMPAW http://pwpaw.wfu.edu
PWscf
abinit
XCrySDen
VESTA
http://www.quantum-espresso.org
http://www.abinit.org
http://ww.xcrysden.org
http://jp-minerals.org/vesta/en/
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ATOMPAW Code for generating atomic datasets for PAW calculations
Holzwarth, Tackett, and Matthews, CPC 135 329 (2001) http://pwpaw.wfu.edu
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Atomic PAW datasets
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Validation
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Li3PO4 crystals
(Pmn21)
(Pnma)
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Validation of calculations
A: B. N. Mavrin et al, J. Exp. Theor. Phys. 96,53 (2003); B: F. Harbach and F. Fischer, Phys. Status Solidi
B 66, 237 (1974) – room temp. C: Ref. B at liquid nitrogen temp.; D: L. Popović et al, J. Raman
Spectrosc. 34,77 (2003).
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Heats of formation – Experiment & Calculation
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Estimate of ionic conductivity assuming
activated hopping
:
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Arrhenius activation energies –
Experiment and Calculation
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What is meant by “first principles”?
A series of well-controlled approximations
 Born-Oppenheimer Approximation
 Density Functional Approximation
 Local density Approximation (LDA)
 Numerical method: Projector Augmented Wave
Validation
 Lattice vibration modes
 Heats of formation
 Activation energies for lattice migration
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How can computer simulations contribute
to the development of materials?
 Computationally examine known materials and predict
new materials and their properties
 Structural forms
 Relative stabilities
 Direct comparisons of simulations and experiment
 Investigate properties that are difficult to realize
experimentally including
Of particular interest in battery materials - Model ion migration mechanisms
 Vacancy migration
 Interstitial migration
 Vacancy-interstitial formation energies
 Model ideal electrolyte interfaces with anodes
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Systematic study of LiPON materials – LixPOyNz –
(Yaojun A. Du and N. A. W. Holzwarth, Phys. Rev. B 81, 184106 (2010) )
Typical composition of
amorphous LiPON films
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Experimentally
known structure
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Computationally
predicted structure
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Computationally
predicted structure
Experimentally
realized structure
SD-Li2PO2N
Pbcm
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Cmc21
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Synthesis of Li2PO2N by Keerthi Senevirathne,
Cynthia Day, Michael Gross, and Abdessadek Lachgar
Method: High temperature solid state synthesis based on
reaction
Li 2 O  15 P2 O 5  15 P3 N 5  Li 2 PO 2 N
Structure from X-ray refinement: Cmc21
Li
P
O
N
Li ion
PO2N2 ion
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Comparison of synthesized and predicted
structures of Li2PO2N:
Synthesized
Predicted
Li
P
O
SD-Li2PO2N (Cmc21)
N
s2-Li2PO2N (Aem2)
Calculations have now verified that the SD structure is more stable than the
s2 structure by 0.1 eV/FU.
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Comparison of synthesized Li2PO2N with Li2SiO3
SD-Li2PO2N (Cmc21)
Li2SiO3 (Cmc21)
a=9.07 Å, b=5.40 Å, c=4.60 Å
a=9.39 Å, b=5.40 Å, c=4.66 Å
K.-F. Hesse, Acta Cryst. B33, 901 (1977)
Li
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P
O
N
Si
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Electronic band structure of SD-Li2PO2N
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More details of SD-Li2PO2N structure
Ball and stick model
Li
P
O
N
b
c
Isosurfaces (maroon) of
charge density of states
at top of valence band,
primarily p states on N.
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Vibrational spectrum of SD-Li2PO2N
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Stability of SD-Li2PO2N in air
5
2Li 2 PO 2 N(s)  O 2 (g)  Li 4 P2O 7 (s)  2NO(g)
2
Thermogravimetric analysis
curve in air
Note: no structural changes were observed while heating in
vacuum up to 1050o C.
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Ionic conductivity of SD-Li2PO2N
NEB analysis of Em
(vacancy mechanism)
Em  0.4 eV; E f  2 eV
 E A  Em  12 E f  1.4 eV
6
o
  10 S/cm at 80 C
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Sample has appreciable
population of vacancies
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Summary of the Li2PO2N story
 Predicted on the basis of first principles theory
 Subsequently, experimentally realized by Keerthi
Seneviranthe and colleagues; generally good
agreement between experiment and theory
 Ion conductivity properties not (yet) competitive
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Systematic study of LixPSy materials – (N. D. Lepley and N. A. W.
Holzwarth, J. Electrochem. Soc. 159, A538 (2012), Phys. Rev. B 88,
104103 (2013) )
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Comparison of some lithium
phosphates and thiophosphates
Crystallizes (experimentally and
computationally) into P 1 structure
Experimentally amorphous;
computationally metastable
in P 1 structure
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Some lithium thiophosphate
crystal structures
Experimentally amorphous;
computationally metastable
Experimentally and computationally
metastable in P 1 structure
in P 1 structure
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Vacancy migration analysis from NEB results
for Li7P3S11:
Li
P
Em  0.15 eV; E f  0 eV
S
 E A  Em  12 E f  0.15 eV
Experiment -- A Hayashi et al., J. Solid State Electrochem. 14, 1761 (2010):
  2  3  103 S/cm
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E A  0.12  0.18 eV
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Systematic study of LixPSy materials – (N. D. Lepley and N. A. W.
Holzwarth, J. Electrochem. Soc. 159, A538 (2012), Phys. Rev. B 88,
104103 (2013) )
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Pnm 21 structured materials
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Pnma structured materials
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Pnma structured materials
More detailed look at b-Li3PS4 structure
Li sites:
d sites (100% occ.)
b sites ( 70% occ.)
c sites ( 30% occ.)
P
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S
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Possible vacancy migration paths
in b-Li3PS4
P
Li sites:
d sites (100% occ.)
b sites ( 70% occ.)
c sites ( 30% occ.)
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S
NEB diagram:
Em  0.3 eV; E f  0 eV
 E A  Em  12 E f  0.3 eV
Experimental values:
E A  0.4  0.5 eV
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From ORNL: Experiment on electrolyte Li3PS4
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Systematic study of LixPSy materials – (N. D. Lepley and N. A. W.
Holzwarth, J. Electrochem. Soc. 159, A538 (2012), Phys. Rev. B 88,
104103 (2013) )
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Investigation of Li4P2S6
Collaboration with Zachary D. Hood at ORNL
Synthesis:
2Li 2S + P2S5 
 Li 4 P2S6 + S
900o C
Sulfur removed by treatment with solvent; sample prepared
for electrochemical applications using ball milling.
Scanning Electron Micrograph of prepared sample:
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Crystal structure: Space Group P63/mcm (#193)
Projection on to hexagonal plane:
Li
P
S
a
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a
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Crystal structure: Space Group P63/mcm (#193)
Li4P2S6 units:
Li
P
S
c
2.3 Å
2.1 Å
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Crystal structure: Space Group P63/mcm (#193)
Disorder in P-P placements:
+(1/2-z)
c
Li
+z
-z
P
-(1/2-z)
S
Site label z
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Site label z
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Examples:
Structure “b”
DE = 0.03 eV
100% z
DE = 0
Structure “c”
50% z
50% z
Li
DE = 0
Structure “d”
50% z
50% z
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P
S
56
Structural variation can be mapped on to a
two-dimensional hexagonal lattice with each P configuration
taking z or z settings; Li and S configurations fixed
Li
P
S
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in
Temperature dependence of X-ray powder diffraction
^
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Comparison of 13 K
X-ray data with simulations
Extra peaks
Note: simulations
scaled by 102%
to compensate
for systematic
LDA error.
Simulations consistent
with incoherent average
over all P z and z
configurations
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In terms of diffracting plane spacing:
d   / (2sin)
X-ray spectrum
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Neutron spectrum
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Structural parameters
Exp. 293K (X-ray)*
Exp. 300K (X-ray)
Exp. 300K (neutron)
Exp. 15K (X-ray)
Exp. 15K (neutron)
Calc. structure “b”
Calc. structure “c”
Calc. structure “d”
a (Å)
c (Å)
zP
zS
6.070
6.075
6.075
6.051
6.055
6.07
6.06
6.06
6.557
6.597
6.595
6.548
6.553
6.50
6.54
6.54
0.1715
0.172
0.173
0.172
0.172
0.18
0.17
0.17
0.3237
0.324
0.326
0.324
0.326
0.33
0.33
0.33
Hood
et al.
with
102%
LDA
corr.
*Mercier et al., J. Solid State Chem. 43, 151 (1982)
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Stability: Li4P2S6 is much less reactive than other
lithium thio-phosphates, but it decomposes in air,
especially at higher temperature
Decomposition
products:
P2O5
Li4P2O7
Li2SO4
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Ionic conductivity and Activation Energy
2.38 x 10-7 S/cm at 25˚C and 2.33 x 10-6 S/cm at 100˚C
Li4P2S6 pressed pellets with blocking (Al) electrodes
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Li/ Li4P2S6 /Li cells could not be cycled
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Simulations of ion mobility using Nudged Elastic Band Model
Vacancy
mechanism:
DE>0.6 eV
Li
P
S
Interstitial
mechanism:
DE>0.1 eV
Possible
interstitial sites
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Models of Idealized Interfaces
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Crystal structure of bulk Li3PS4 – g-form
Pmn21 (#31)
Note: Li3PS4 is also found in
the b-form with Pnma (#62)
structure
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g-Li3PS4 [0 1 0] surface
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Simulations of ideal g-Li3PS4 [0 1 0] surface
in the presence of Li
Initial configuration:
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Computed optimized
structure:
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More simulations of ideal
g-Li3PS4 [0 1 0] surface
in the presence of Li –
supercells containing
12 Li atoms and
2 or 4 electrolyte layers
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g-Li3PS4 [0 1 0] surface in the presence of Li –
supercells containing 12 Li atoms and 2 or 4 electrolyte layers
(greater detail)
2 electrolyte layers
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4 electrolyte layers
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Computational counter example –
stable interface:
Li/b-Li3PO4
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Computational counter example –
stable interface:
Li/SD-Li2PO2N
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Mystery:
 Models of ideal Li3PS4 surfaces are computational
found to be structurally (and chemically) altered by
the presence of Li metal. (Also found for b-Li3PS4
and for various initial configurations of Li metal.)
 Experimentally, the ORNL group has found that solid
Li3PS4 electrolyte samples can be prepared in
Li/ Li3PS4/Li cells and cycled many times
Possible solution:
 Thin protective buffer layer at Li3PS4 surface can
stabilize electrolyte – for example Li2S/Li3PS4/Li2S
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Idealized Li2S/Li3PS4/Li2S system
Details:
Thin film of cubic Li2S
oriented in its non-polar
[1 1 0] direction, optimized
on [0 1 0] surface of
g-Li3PS4. While the Li2S film
was slightly strained, the
binding energy of the
composite was found to be
stable with a binding energy
of -0.9 eV.
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Plausible explanation -Idealized Li2S/Li3PS4/Li2S
system optimized
in presence of Li
In practice, a single Li2S
buffer layer may not be
sufficient. These are not
explicitly prepared in
constructing b-Li3PS4
electrolytes, but may be
formed during the first few
cycles.
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Li/Li4P2S6/Li interfaces
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Models of Li4P2S6/Li interfaces -- Surface parallel to P-P bonds:
Surface with vacuum
Surface with lithium
Li
P
S
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Models of Li4P2S6/Li interfaces -- Surface perpendicular to P-P bonds:
Surface with vacuum
Surface with lithium
Li
P
S
Experimentally, Li4P2S6/Li has not been stably cycled (yet).
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Things we have learned so far in studying the lithium
phosphate and thiophosphate families of materials
LixPSy
LixPOyNz
Lower conductivity &
greater stability
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Higher conductivity &
lesser stability
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Additional thoughts
 Limitations of first principles modeling
 Small simulation cells
 Zero temperature
 Possible extensions
 Develop approximation schemes for treatment
of larger supercells
 Use molecular dynamics and/or Monte Carlo
techniques
 Ideal research effort in materials includes close
collaboration of both simulations and experimental
measurements.
 For battery technology, there remain many
opportunities for new materials development.
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