Adobe PDF - Tahan.com
Adobe PDF - Tahan.com
Adobe PDF - Tahan.com
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
The End<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 32
¡£¢<br />
Future Work<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 31
¤¦¥¦§ ¨©¥¦§<br />
<br />
<br />
Results/Analysis<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 30
Results/Analysis<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 29
!$ " <br />
%&<br />
<br />
<br />
$!#"<br />
!$ " <br />
%&<br />
<br />
<br />
)($ "<br />
('$$" <br />
%&<br />
<br />
<br />
$!#"<br />
!$" <br />
<br />
<br />
$ "<br />
%& *<br />
Results/Analysis<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 28
Results/Analysis<br />
<br />
<br />
$!#"<br />
<br />
<br />
)($ "<br />
<br />
<br />
(+$ "<br />
<br />
<br />
($"<br />
<br />
<br />
$ "<br />
*<br />
,<br />
-<br />
.<br />
/<br />
0<br />
1<br />
2<br />
3<br />
3<br />
4<br />
3<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
2<br />
3<br />
3<br />
4<br />
3<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
2<br />
3<br />
3<br />
4<br />
3<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
;<br />
<<br />
=<br />
4<br />
><br />
?<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
;<br />
3<br />
3<br />
4<br />
2<br />
@<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
,<br />
-<br />
.<br />
/<br />
0<br />
A<br />
B<br />
?<br />
4<br />
3<br />
><br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
@<br />
?<br />
4<br />
=<br />
@<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
;<br />
3<br />
<<br />
4<br />
<<br />
=<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
2<br />
3<br />
3<br />
4<br />
3<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
;<br />
?<br />
@<br />
4<br />
;<br />
><br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
''$DC<br />
$C<br />
$+<br />
<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 27
E<br />
<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 26<br />
KLK<br />
Results/Analysis<br />
R, growth rate (# adatoms/MC time)<br />
0.2<br />
0.1<br />
0<br />
kT=0.025<br />
kT=0.1<br />
kT=0.2<br />
kT=0.6<br />
kT=1.0<br />
kT=1.4<br />
kT=1.8<br />
kT=2.0<br />
Zoom in: Long−Range Model, Rock Salt: F<br />
Growth Rate vs. Change in Chemical Potential G<br />
20x20x60<br />
Hsubstrate=20, salt<br />
JI5 runs/data point<br />
−0.1<br />
−0.75 −0.65 −0.55 −0.45 −0.35 −0.25<br />
∆µ
NM O M O <br />
E<br />
0Q<br />
Results/Analysis<br />
R, growth rate (# adatoms/MC time)<br />
0.5<br />
0<br />
−0.5<br />
kT=0.025<br />
kT=0.05<br />
kT=0.1<br />
kT=0.2<br />
kT=0.6<br />
kT=1.0<br />
kT=1.4<br />
kT=1.8<br />
kT=2.0<br />
Long−Range Model, Rock Salt: S<br />
Growth Rate vs. Change in Chemical Potential G<br />
20x20x60 lattice<br />
Hsubstrate=20, salt<br />
JI5 runs/data point<br />
−1<br />
−2.5<br />
−2 P<br />
−1.5 −1 −0.5<br />
∆µ<br />
R Q<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 25
Results/Analysis<br />
<br />
<br />
!#"<br />
)<br />
<br />
<br />
T!#"<br />
<br />
<br />
!!"<br />
<br />
<br />
U$"<br />
<br />
<br />
($"<br />
,<br />
-<br />
.<br />
/<br />
0<br />
/<br />
V<br />
W<br />
2<br />
3<br />
3<br />
4<br />
3<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
2<br />
3<br />
3<br />
4<br />
3<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
2<br />
3<br />
3<br />
4<br />
3<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
?<br />
><br />
4<br />
@<br />
3<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
?<br />
?<br />
4<br />
><br />
<<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
,<br />
-<br />
.<br />
1<br />
0<br />
X<br />
2<br />
3<br />
3<br />
4<br />
3<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
2<br />
3<br />
3<br />
4<br />
3<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
2<br />
3<br />
3<br />
4<br />
3<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
2<br />
3<br />
3<br />
4<br />
3<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
;<br />
<<br />
=<br />
4<br />
B<br />
=<br />
5<br />
6<br />
7<br />
8<br />
9<br />
:<br />
7<br />
''$C<br />
$C<br />
$+<br />
<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 24
NM O M O <br />
E<br />
\ ]<br />
¡£¢ Y[Z<br />
0Q<br />
Results/Analysis<br />
Nearest−Neighbor Model, Rock Salt:<br />
Growth Rate vs. Change in Chemical Potential G<br />
R, growth rate (# adatoms/MC time)<br />
0.3<br />
0.2<br />
0.1<br />
0<br />
kT=0.025<br />
kT=0.05<br />
kT=0.1<br />
kT=0.2<br />
kT=0.6<br />
kT=1.0<br />
kT=1.4<br />
kT=1.8<br />
kT=2.0<br />
20x20x60 latice<br />
Hsubstrate=20, salt<br />
I10 runs/data point<br />
−0.1<br />
−2.5<br />
−2 P<br />
−1.5 −1 −0.5<br />
∆µ<br />
Q<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 23
e cd Y_^a` baM<br />
g<br />
g<br />
g<br />
Y[Z<br />
b Y_^a`<br />
cd Y_^a` b cd<br />
f<br />
Results/Analysis<br />
¡£¢<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 22<br />
Y[Z
i i h<br />
q r s t jlknmpo<br />
Development & Implementation<br />
k<br />
Species 1: 1-<br />
Species 2: 1+<br />
}substrate<br />
j<br />
i<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 21
i kt `<br />
ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ<br />
ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ<br />
i wvxzyz{}|~y h u `<br />
‚ € wvxƒ„{}……zƒ ‚ v†ƒwƒz…ˆ‡ Œ‹<br />
‚ zv†ƒ~‰ƒ…Š‡ ‚ M vxzƒz ` kt h<br />
k“’•”—–˜”¦ t ¢–šœ› \ž£Ÿ—› i uz¡Š¢ ¢£¥¤¦£Ÿ¥–<br />
‘<br />
k ” ”|„t ¨§~© ¡‰uz¢ wv†|„y}||„y wvx„{}…~‰y<br />
<br />
k ” ”M t ›«ª¬‰š wv‡#‰…„{Š…w wvM ‡¨yy}|w<br />
M<br />
k®M~” ”|„t ¨§~© ¡‰uz¢ wv†|„y}||„y wvx„{}…~‰y<br />
|<br />
k®M~” ”M t ›«ª¬‰š wvx|z„{}… wv†{}…|„{}|<br />
‡<br />
k ”¦M~”|„t ¨§~© ¡‰uz¢ wv†|„y}||„y wvx„{}…~‰y<br />
y<br />
k ”¦M~”M t ›«ª¬‰š wvx|z…¯{ wv†{}…|ƒz|<br />
<br />
k®M~”¦M~”|„t ¨§~© ¡‰uz¢ wv†|„y}||„y wvx„{}…~‰y<br />
{<br />
°±ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ²<br />
ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ<br />
Development & Implementation<br />
k<br />
Species 1: 1-<br />
Species 2: 1+<br />
}substrate<br />
j<br />
i<br />
k®M~”¦M~”M t ›«ª¬‰š wv†|„y M ‰ƒ wvx„{}…ƒ¯{ ³<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 20<br />
ƒ
i k„t `<br />
d»x»f»¼d½ ` ¾ ¸ ¿¸ i•¸º¹ ¸ ¾<br />
¸ ` ‘ ` ›‰ÀÂÁ Ão ” ‘<br />
›ÅÄ~ÆfÇÃo ” ‘ ¾<br />
‘ k“’È”–˜”¦ t ¢É–šÊ› \ž£Ÿ› ižuz¡Š¢ ¢¦£Ë¤Ì£ŸÍ– ¢ ¡ ŸË ¤<br />
ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ<br />
k ” ”|¯t ¨§~© ¡‰uz¢ ~v†‰|zy}|z|zy ~v†‰zy}|w ~v†‰zy<br />
<br />
k ”M¬”M t ›Îª¬‰š ~v†‰ƒzy}…Š‡# ~v†«‡‡¯zƒ… ~vM y}<br />
M<br />
ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ<br />
k®M¬” ”|¯t ¨§~© ¡‰uz¢ ~v†‰|zy}|z|zy ~v†‰zy}|w ~vx|„yy<br />
|<br />
k®M¬” ”M t ›Îª¬‰š ~v†‰ƒzy}…Š‡# ~v†«‡‡¯zƒ… ~vÏy<br />
‡<br />
k ”M¬”|¯t ¨§~© ¡‰uz¢ ~v†‰|zy}|z|zy ~v†‰zy}|w ~vxzzy<br />
y<br />
k ”M¬”M t ›Îª¬‰š ~v†‰ƒzy}…Š‡# ~v†«‡‡¯zƒ… ~vÐ{y}<br />
<br />
k®M¬”M¬”|¯t ¨§~© ¡‰uz¢ ~v†‰|zy}|z|zy ~v†‰zy}|w ~vxƒ„yy<br />
{<br />
k®M¬”M¬”M t ›Îª¬‰š ~v†‰ƒzy}…Š‡# ~v†«‡‡¯zƒ… vxz<br />
ƒ<br />
` wvxƒƒzy…zŷ ‡<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 19<br />
u‰Ñ<br />
µ·<br />
´<br />
°ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ²<br />
ŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽŽ<br />
³<br />
Development & Implementation
` ×ÙØ<br />
Ò Ó Ò<br />
YÖÕ<br />
] hßÞ ` àÞâá ¹äãÐå†æ Y_^‰ç«Y_^éèå“êßëÞ„ì èåë hÛÚÝÜ<br />
h k„t `<br />
‚ zvxƒ M | M { ‚ vxƒ M | M { €<br />
zvxƒ M | M { ‚ vxƒ M | M { ‚<br />
Œ‹<br />
Ô<br />
Development & Implementation<br />
k<br />
Species 1: 1-<br />
Species 2: 1+<br />
}substrate<br />
j<br />
i<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 18
¢YÖÕ£¢¸¥¤§¦<br />
r <br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 17<br />
Development & Implementation<br />
(i) list,í Generate a , of all possible events per time step; There<br />
possible events: an evaporation or an adsorption could happen on<br />
each<br />
are¨©î<br />
of sites;<br />
ï<br />
theî<br />
surface<br />
(ii) Calculate the<br />
ðÊñ<br />
rates ) of adsorption and evaporation for each site on<br />
the surface rates); (¨©î (ò<br />
(iii) Normalize these¨óî<br />
rates, giving probabilities,ô£õ, for<br />
evaporation/adsorption on site 1, on site 2, . . . on site N, which all add<br />
to unity;<br />
(iv) Generate a random numberöø÷_ùûúü¤¦ý<br />
choose the first eventí õ<br />
such that þ ¿<br />
An event will always be chosen;<br />
and<br />
ö.<br />
(v) Generate new<br />
ô£õ˜ÿ<br />
based on chosen<br />
õ<br />
configuration¡<br />
eventí<br />
õ.
g<br />
g<br />
Y[Z<br />
such that þ ¿<br />
õ ô õ ÿ ö;<br />
¢YÖÕ£¢<br />
s<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 16<br />
r<br />
¢YÖÕ£¢¸@¤§¦<br />
possible<br />
¢YÖÕ?¢¸@¤§¦<br />
Methodology<br />
(i) Randomly select theð<br />
from surface sites;<br />
(ii) Generate a<br />
an¨©nüý<br />
, of possible events at¨©nüý.<br />
ñ<br />
list,í<br />
pair<br />
In our case,í<br />
ï<br />
#";<br />
(iii) Define the probability each event will occur by normalizing the event<br />
ü! ö© ü ö©<br />
(iv) Generate a random and numberöø÷_ùûúü¤¦ý<br />
choose the first eventí õ<br />
rates$&%'()*,+-%.),/0),12%435(6*,38723 92/-:;:;*='%4$&()%:.<br />
(v) Generate new configuration¡<br />
based on chosen eventí<br />
õ;
BDC E GFH A<br />
YÖÕ ` Ißç`<br />
ŽŽŽ<br />
ŽŽŽ<br />
ò<br />
C EDA B<br />
¿ K èåá ¹ ç§L Y_^ çY_^ èå” J<br />
¿ àèåá ¹ çæ Y_^‰çY_^èå ª„èNMzkPO ‚ QRt ” ”<br />
J<br />
O Y_^ ç ¡ ` k£”#]z”¡ t<br />
BDC E SUT ¤è,VUWçYX&Z[\XÚ¤è A<br />
YÖÕ<br />
Methodology<br />
‚ QRt<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 15<br />
ª„èNMzkPO
YÖÕ<br />
¾ ¤V_^çMa` Y[Z<br />
b cUdfe>gihkj l mon prqksut<br />
YÖÕ<br />
ì ›«’„š xìzy à,{ æ Ão | w<br />
}~ c € l mƒ‚ n „ qksut b<br />
¾ Zv¤W<br />
Methodology<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 14
k£”#] t<br />
¸ çV_Zcè<br />
` ‡0ˆC EDA B<br />
A BDC E † g Y[Z àÚÝÜæ ÚÝÜ v k… t<br />
E BDC A X“çX¤è‰Zcè,ZŠ‹XM¦ç^X¤XÚŠfZ[ŒZMY§Ž<br />
ÚÝÜ<br />
Õ k… t<br />
…<br />
¤èè¤V_^çMWDXÚç[‰^<br />
Methodology<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 13
Background<br />
Only discrete placement<br />
on our perfect 3-d lattice.<br />
Solid-on-Solid (SOS)<br />
restriction for<br />
adatom placement<br />
on the crystal surface.<br />
Periodic Boundary Conditions (PBC)<br />
real adatom in crystal matrix<br />
"images"<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 12
‘<br />
‘<br />
` Zf^ ‚ Z è Y[Z<br />
M’ “’<br />
|”’<br />
Background<br />
k<br />
MELT<br />
adsorbed adatom at site (i,j,k)<br />
H<br />
L<br />
}<br />
substrate<br />
j<br />
i<br />
L<br />
2<br />
N = L = # of surface sites (w/ SOS)<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 11
–˜— •<br />
›š— œ – — ž •<br />
•<br />
Background<br />
1:1 1:2<br />
• –˜Ÿ¡ œ ¢¤£ ¥ ›šŸ¡ œ ¦£<br />
[111]<br />
[001]<br />
1<br />
2<br />
1<br />
2<br />
( -n ) + ( +n) -2n ( +n)<br />
3 ( ) + 3<br />
Species: quantity([color]charge)<br />
1<br />
2<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 10<br />
•
•<br />
•<br />
•<br />
¥ ¥ •<br />
•<br />
— œ œ ¨ ©«ª ¬ ©®<br />
§<br />
² ›š°¯<br />
›š°¯&›š°¯<br />
²´± ±³²<br />
Background<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 9
•<br />
Background<br />
Perovskite Unit Cell<br />
Crystal Lattice<br />
B Sublattice<br />
B Sublattice with pretty cubes<br />
B atom<br />
=<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 8
•<br />
•<br />
 ÃÅÄ ÆÃÅÄ<br />
· ¸¹Dº» µ<br />
¿¾ ¼½i¾<br />
Ä<br />
ÁÀa½<br />
ÂÃÆ Â ÃÆ<br />
Ä<br />
Background<br />
Unit Cell, Perovskite Alloy - ABO 3<br />
A atom: fixed Group II metal<br />
B atom: fractional, metals from<br />
O atom: Oxygen<br />
Groups II-VII<br />
can be different elements, ie fractional<br />
fixed: always the same element<br />
no matter the location<br />
within the crystal matrix<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 7<br />
¹Dº » Ç‹È#É ÊÈ#É ¸<br />
¹Dº » Ç«È;Ê Ç‹È#Ê ¸
Background<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 6
•<br />
•<br />
•<br />
•<br />
Introduction & Motivation<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 5
•<br />
•<br />
Ë<br />
Introduction & Motivation<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 4
ÖkÔ°â¥üöä‰ÛÜÍÏÕ.àöáãâ¥ä‰Ñ,Ò°ÛPáãÔ°å‰Ù<br />
æ.áãå‰ÍÏÛPáãçkèéÔ°å‰ÛÜÍ0ÖêÒÕÅÑ,Ô<br />
è˜ÖìëUÑ,íÔ°ÕÅáãÛÜ߉â¥Ù æ<br />
ÕÅÔ°ÎÞÛPߥîk͓ߌÒï°áãÔ°Õ Ý<br />
ÖkÕ#×ÚÙÛÜÒ°Ñþý\×ÚüÚÍÏÙ ÌfÍÏÎ<br />
T-PLOTT: <strong>Tahan</strong> Pain-Level-of-Talk Topography<br />
why?<br />
ðñáãÍÏòaÔ°Í“Ñ,Í“ç_ÛÜÕÅáãç ÖkÕØ×ÚÙÛÜÒ°ÑÙ Ð.ÍÏÑÒ°Ó°ÔÕ4ÖkÕØ×ÚÙÛÜÒ°ÑÙ ÌfÍÏÎ<br />
how?<br />
ðñÍ“ÕÅÔ°ï°Ù÷öáãÛÜÍ4ëUÑÑÔG×ÚÙ<br />
ÖkÕØ×ÚÙÛÜÒ°ÑÝ ÕÅÔ°ÎÞÛPß<br />
ÕÅÔ°ÎÞÛPߥàÚáãâ¥äŒÑÒ°ÛÜáãÔ°å‰Ù Ý<br />
new!<br />
ÌfÍÏÎóëUÑí°Ô°ÕÅáãÛÜ߉âõôHàöáãâ¥ä‰Ñ,Ò°ÛPáãÔ°å<br />
àöáãâ¥ä‰Ñ,Ò°ÛPÍÏøûÖêÕ#×ÚÙÛÜÒ°ÑÙ<br />
Ò°å‰ø8â¥Ô°ÕÍÏùúùúù Ð.Ôç_÷8àÚÒ°Ñ,Û<br />
joy<br />
pain<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 3
¥<br />
Preliminary Overview<br />
Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 2