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![Page 1: Thermodynamic-Stability-of-the-CaMnO …es12.wfu.edu/pdfarchive/poster/ES12_D_Saldana-Greco.pdf• CaO+1.0Ca+2.0O The$structures$computed$are$constructed$with$(√2X√2)R45 $surface$symmetry$and$symmetrical$slabs.$](https://reader034.vdocument.in/reader034/viewer/2022042320/5f09cbf07e708231d42887ce/html5/thumbnails/1.jpg)
• The structures computed are constructed with (√2X√2)R45° surface symmetry and symmetrical slabs.
• The surface termina?ons are designed by varying the stoichiometry of Ca, Mn and O including addi?onal
CaxOy and MnxOy layers.
• Each surface termina?on is iden?fied based on its termina?on (either CaO or MnO2) and whether it contains vacancies (-‐) or adatoms (+).
Thermodynamic Stability of the CaMnO3 (001) Surface
Diomedes Saldana-‐Greco, Chan-‐Woo Lee, Doyle Yuan and Andrew M. Rappe The Makineni Theore?cal Laboratories, Department of Chemistry, University of Pennsylvania,
Philadelphia, PA 19104-‐6323, USA
Mo?va?on
Computa?onal Methods
CaMnO3 (001) Surface Structures
• CaMnO3 has a[racted a[en?on due to its mul?ferroicity, thermoelectric efficiency, collosal magnetoresistance and cataly?c proper?es.
• Recently, an experimental study reported that CaMnO3 acts as an efficient catalyst for water oxida?on, but very li[le is known about the mechanism.
• CaMnO3 surface plays a significant role in the development and understanding of CaMnO3 as a poten?al catalyst.
• Neither experimental nor theore?cal studies have inves?gated the structural composi?on and reconstruc?ons of CaMnO3 surfaces under different environmental condi?ons.
• Density Func?onal Theory (DFT) calcula?ons were performed within GGA using the Perdew-‐Burke-‐Ernzerhof func?onal revised for solids (PBEsol).
• Spin-‐polarized electronic densi?es are used, trea?ng the magne?c moments collinearly.
• Norm-‐conserving, op?mized, designed nonlocal pseudopoten?als for all atoms.
• The Brillouin zone was sampled using 4x4x1 Monkhorst-‐Pack k-‐point mesh for surface structures.
• Density func?onal perturba?on theory (DFPT) was used to calculate phonon frequencies at the Γ point for all secondary phases.
x z
y
x y
z
Symmetrical slabs
Vacuum
Vacuum
CaO-‐stoichiometric
CaO+1.0Ca+2.0O MnO2+1.0Mn+2.0O
CaO+2.0O MnO2+2.0O
CaO-‐0.5Ca MnO2-‐0.5Mn
MnO2-‐stoichiometric
x y
z
The surface free energy, Ωi, of an individual surface slab, i, is defined as the excess amount of free energy needed to create the surface from its bulk form. The following term accounts for the off-‐stoichiometric atoms of component n with respect to m in the slab, Then, Eq. (1) and (2) are merged to rearrange the defini?on of the Gibbs surface free energy,
CaMnO3 surface is considered to be in contact with an atmosphere composed of all its components in equilibrium. This implies that the system acts as a reservoir where removal and/or addi?on of any of its components at the surface leads to a range of thermodynamically stable reconstruc?ons and composi?ons at different condi?ons.
Then, the chemical poten?als are deviated from the total energy of its reference states and the Gibbs free energy is approximated to DFT energies leading to the final equa?on for the surface free energy,
In addi?on, the bulk stability region is defined by a set of boundary condi?ons that determine the stability range of the chemical poten?als with the following condi?ons:
Thermodynamic Stability
-5.0
-5.0
MnO2+2.0O MnO2+0.5Mn+1.0O MnO2 MnO2+1.0Mn+1.0O MnO2+1.0Mn+0.5O MnO2+1.0Mn
CaO+2.0O CaO CaO+1.0Ca+2.0O CaO+1.0Ca+1.0O MnO2+1.0Ca
-8 -6 -4 -2 0 -8 -6 -4 -2 0
-4
-2
0
-3
-1
-5
ΔµO(eV)
ΔµCa(eV) ΔµCa(eV)
C-‐AFM G-‐AFM
500 1500 2000 2500 1000 3000
-4
-2
0
-3
-1
-8 -6 -4 -2 0
②/⑩/⑨/⑧
① ③
④ ⑥
⑤
⑦
⑪
T (K)
ΔµO(eV) 102
10
0.987 0.21
10-10 10-20 10-30 10-50
p(O2) [atm]
10-40
MnO2+2.0O MnO2+0.5Mn+1.0O MnO2 MnO2+1.0Mn+1.0O MnO2+1.0Mn+0.5O MnO2+1.0Mn
CaO+2.0O CaO CaO+1.0Ca+2.0O CaO+1.0Ca+1.0O MnO2+1.0Ca
ΔµCa(eV)
-5
Surface Phase Diagram
Temperature Dependence
0 K 1000 K 1400 K
-5.0 -8 -6 -4 -2 0
-4
-2
0
-3
-1
-5
ΔµO(eV)
ΔµCa(eV)
MnO2+2.0O
MnO2+0.5Mn+1.0O
MnO2
MnO2+1.0Mn+1.0O MnO2+1.0Mn+0.5O
MnO2+1.0Mn
CaO+2.0O
CaO
CaO+1.0Ca+2.0O
CaO+1.0Ca+1.0O
MnO2+1.0Ca
An?ferromagne?c Ordering at the Surface
dx2−y2d
z22
dxy dzydzx
E
Conclusions
Acknowledgement This work is funded by the DOE
• A series of CaO-‐ and MnO2-‐terminated surfaces with different combina?ons of its components’ vacancies, ad-‐atoms and addi?onal layers are reported using ab ini*o thermodynamics to theore?cally predict the surface phase diagram of CaMnO3 (001).
• The stability region defined by a criteria of boundary condi?ons is dis?nctly dominated by CaMn2O4, CaMn7O12 and CaO.
• The stability region shivs as temperature increases leading to the predominance of MnO2-‐based surfaces.
• The Surface phase diagram, specifically the MnO2-‐terminated surfaces, is sensi?ve to magne?c ordering.
⌦i =1
2A
2
4Gislab �
X
j
N ijµj
3
5 =1
2A
⇥Gi
slab �N iCaµ
iCa �N i
MnµiMn �N i
OµiO
⇤
�im,n =
1
2A
✓N i
n �N imNbulk
n
Nbulkm
◆
⌦i =1
2A
⇥Gi
slab �N iMn(µCa + µMn + 3µO)
⇤� �i
Mn,CaµCa � �iMn,OµO
µCa + µMn + 3µO = µCaMnO3 = gbulkCaMnO3
⌦i =1
2A
⇥Gi
slab �N iMng
bulkCaMnO3
⇤� �i
Mn,CaµCa � �iMn,OµO
µCa + µO gbulkCaO
µMn + µO gbulkMnO
µMn + 2µO gbulkMnO2
2µMn + 3µO gbulkMn2O3
3µMn + 4µO gbulkMn3O4
µCa gbulkCa
µMn gbulkMn
2µCa + µMn + 4µO gbulkCa2MnO4
µCa + 2µMn + 4µO gbulkCaMn2O4
3µCa + 2µMn + 7µO gbulkCa3Mn2O7
4µCa + 3µMn + 10µO gbulkCa4Mn3O10
µCa + 7µMn + 12µO gbulkCaMn7O12
(1)
(5)
(4)
(3)
(2)
This criteria accounts for the possible precipita?on and arrangement of complex sub-‐phases from the bulk
The bulk is stable when the metal oxides do not precipitate
The Ca and Mn metals are not allowed to leave the bulk and form precipitates
⌦i =1
2A
⇥Ei
slab �N iMnE
bulkCaMnO3
⇤��iMn,Ca
��µCa + Ebulk
Ca
�+ �i
Mn,O
✓�µO +
1
2Egas
O2
◆�(6)
Surface Phase diagram of C-‐AFM CaMnO3 with the stability boundary structures denoted as follows (1)CaMnO3, (2)CaO, (3)MnO, (4)Mn3O4, (5)Mn2O3, (6)MnO2, (7)CaMn2O4, (8)Ca2MnO4, (9)Ca3Mn2O7, (10)Ca4Mn3O10 and (11)CaMn7O12. The right panel shows the T and p(O2) correla?on with ΔµO obtained from thermodynamic tables.
The term Fvib., which is equal to Evib.-‐TSvib., is calculated from the vibra?onal modes of the system. The phonon density of states, σ(ω), enables the Fvib. to be expressed as the integral over all the vibra?onal modes, ω, as shown below The analy?cal expression of the vibra?onal free energy as a func?on of temperature and vibra?onal modes, Fvib.(T, ω) can be wri[en as As Gibbs free energy of each compound is explicitly calculated, the stability region of bulk CaMnO3 as a func?on of T can be evaluated.
F vib. =
Zd!F vib.(T,!)�(!)
F vib.(T,!) =1
2~! � kBT ln
�1� e��~!�
The energe?cs of surface structures with different magne?c ordering are tested finding some discrepancies in the surface phase diagram of C-‐type and G-‐type an?ferromagne?c (AFM) within the stability of MnO2 based surfaces.
C-‐AFM G-‐AFM
E
dx2−y2
dz22
dxy
dzydzx
These discrepancies can be explained by the stability of the C-‐AFM MnO2 stoichiometric surface based on the magne?c alignment in the z-‐axis. The surface forma?on in MnO2 termina?ons favors the popula?on of dz2 and dxy surface states due to the symmetry lowering of eg into non-‐degenerate dz2, dx2-‐y2 and t2g into dxy, (dzx, dzy). The surface states of both C-‐AFM and G-‐AFM are predominant by of dz2 and dxy; however, the surface-‐subsurface coupling is stronger in C-‐AFM as higher par?al occupa?on of dz2 and less reduc?on of dxy are energe?cally favourable by the presence of the ferromagne?c plane orthogonal to the surface.