thermodynamic-stability-of-the-camno …es12.wfu.edu/pdfarchive/poster/es12_d_saldana-greco.pdf•...

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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 Ca x O y and Mn x O y layers. Each surface termina?on is iden?fied based on its termina?on (either CaO or MnO 2 ) and whether it contains vacancies () or adatoms (+). Thermodynamic Stability of the CaMnO 3 (001) Surface Diomedes SaldanaGreco , ChanWoo Lee, Doyle Yuan and Andrew M. Rappe The Makineni Theore?cal Laboratories, Department of Chemistry, University of Pennsylvania, Philadelphia, PA 191046323, USA Mo?va?on Computa?onal Methods CaMnO 3 (001) Surface Structures CaMnO 3 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 CaMnO 3 acts as an efficient catalyst for water oxida?on, but very li[le is known about the mechanism. CaMnO 3 surface plays a significant role in the development and understanding of CaMnO 3 as a poten?al catalyst. Neither experimental nor theore?cal studies have inves?gated the structural composi?on and reconstruc?ons of CaMnO 3 surfaces under different environmental condi?ons. Density Func?onal Theory (DFT) calcula?ons were performed within GGA using the PerdewBurkeErnzerhof func?onal revised for solids (PBEsol). Spinpolarized electronic densi?es are used, trea?ng the magne?c moments collinearly. Normconserving, op?mized, designed nonlocal pseudopoten?als for all atoms. The Brillouin zone was sampled using 4x4x1 MonkhorstPack kpoint 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 CaOstoichiometric CaO+1.0Ca+2.0O MnO2+1.0Mn+2.0O CaO+2.0O MnO2+2.0O CaO0.5Ca MnO20.5Mn MnO2stoichiometric x y z The surface free energy, Ω i , 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 offstoichiometric 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, CaMnO 3 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) CAFM GAFM 500 1500 2000 2500 1000 3000 -4 -2 0 -3 -1 -8 -6 -4 -2 0 ②/⑩/⑨/⑧ 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 0K 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 dxydzdxy dzy dzx E Conclusions Acknowledgement This work is funded by the DOE A series of CaO and MnO 2 terminated surfaces with different combina?ons of its components’ vacancies, adatoms and addi?onal layers are reported using ab ini*o thermodynamics to theore?cally predict the surface phase diagram of CaMnO 3 (001). The stability region defined by a criteria of boundary condi?ons is dis?nctly dominated by CaMn 2 O 4 , CaMn 7 O 12 and CaO. The stability region shivs as temperature increases leading to the predominance of MnO 2 based surfaces. The Surface phase diagram, specifically the MnO 2 terminated surfaces, is sensi?ve to magne?c ordering. i = 1 2A 2 4G i slab - X j N i j μj 3 5 = 1 2A G i slab - N i Ca μ i Ca - N i Mn μ i Mn - N i O μ i O Γ i m,n = 1 2A N i n - N i m N bulk n N bulk m i = 1 2A G i slab - N i Mn (μCa + μMn +3μO) - Γ i Mn,Ca μCa - Γ i Mn,O μO μCa + μMn +3μO = μCaMnO3 = g bulk CaMnO3 i = 1 2A G i slab - N i Mn g bulk CaMnO3 - Γ i Mn,Ca μCa - Γ i Mn,O μO μCa + μO g bulk CaO μMn + μO g bulk MnO μMn +2μO g bulk MnO2 2μMn +3μO g bulk Mn2O3 3μMn +4μO g bulk Mn3O4 μCa g bulk Ca μMn g bulk Mn 2μCa + μMn +4μO g bulk Ca2MnO4 μCa +2μMn +4μO g bulk CaMn2O4 3μCa +2μMn +7μO g bulk Ca3Mn2O7 4μCa +3μMn + 10μO g bulk Ca4Mn3O10 μCa +7μMn + 12μO g bulk CaMn7O12 (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 E i slab - N i Mn E bulk CaMnO3 - Γ i Mn,Ca ( ΔμCa + E bulk Ca ) + Γ i Mn,O ΔμO + 1 2 E gas O2 (6) Surface Phase diagram of CAFM 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 F vib. , which is equal to E vib. TS vib. , is calculated from the vibra?onal modes of the system. The phonon density of states, σ(ω), enables the F vib. 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, F vib. (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. = Z d!F vib. (T, !)σ(!) F vib. (T, !)= 1 2 ~! - kBT ln ( 1 - e -β~! ) The energe?cs of surface structures with different magne?c ordering are tested finding some discrepancies in the surface phase diagram of Ctype and Gtype an?ferromagne?c (AFM) within the stability of MnO 2 based surfaces. CAFM GAFM E dxydzdxy dzy dzx These discrepancies can be explained by the stability of the CAFM MnO2 stoichiometric surface based on the magne?c alignment in the zaxis. The surface forma?on in MnO2 termina?ons favors the popula?on of dz 2 and dxy surface states due to the symmetry lowering of eg into nondegenerate dz 2 , dx 2 y 2 and t2g into dxy,(dzx, dzy). The surface states of both CAFM and GAFM are predominant by of dz 2 and dxy; however, the surfacesubsurface coupling is stronger in C AFM as higher par?al occupa?on of dz 2 and less reduc?on of dxy are energe?cally favourable by the presence of the ferromagne?c plane orthogonal to the surface.

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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$slabs.$

•  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.