DAFS - Universidad de Zaragoza
DAFS - Universidad de Zaragoza DAFS - Universidad de Zaragoza
Universidad de Zaragoza Curso de Master en Física y Técnologías Físicas Física de Materiales y Grandes Instalaciones Difracción anómala de rayos-X: Diffraction Anomalous Fine Structure (DAFS) Maria Grazia Proietti Cecconi
- Page 2 and 3: GUIÓN Introducción ¿Qué es el D
- Page 4 and 5: k χ( k) = µ − µ 0 µ 0 k del f
- Page 6 and 7: En el caso del DAFS, como en el cas
- Page 8 and 9: Las oscilaciones que se observan po
- Page 10 and 11: Multi-wavelenght Anomalous Diffract
- Page 12 and 13: I − I χ = ⎡cos φ − φ χ +
- Page 14 and 15: DAFS spectroscopy To measure anomal
- Page 16 and 17: Spatial selectivity : GaAs xP 1-x/G
- Page 18 and 19: Incident beam α i ~ α c Introduct
- Page 20 and 21: X-ray absorption at the As K-edge (
- Page 22 and 23: Grazing incidence diffraction [110]
- Page 24 and 25: Grazing incidence anomalous diffrac
- Page 26 and 27: TEM Grazing Incidence MAD : applica
- Page 28 and 29: EDAFS vs EXAFS EXAFS measurements a
- Page 30 and 31: EXAFS (ε // & ε ⊥) Similar resu
- Page 32 and 33: Abs II II EXAFS and EDAFS best fit
- Page 34 and 35: Applications : Nanostructures III-V
- Page 36 and 37: || Structure factor || Applications
- Page 38 and 39: 1.4 1.0 ε zz 0.6 0.2 Applications
- Page 40 and 41: h < max FGa h=2.96 : max FGa h > ma
- Page 42 and 43: CONCLUSIONS Combined MAD & DAFS app
- Page 44 and 45: Manganitas dopadas (RE1-xAxMnO3) Ma
- Page 46 and 47: Medidas de DAFS al umbral K del Fe
- Page 48 and 49: Distorsión trigonal (z’es el eje
- Page 50 and 51: Efectos de polarización en I diff
<strong>Universidad</strong> <strong>de</strong> <strong>Zaragoza</strong><br />
Curso <strong>de</strong> Master en<br />
Física y Técnologías Físicas<br />
Física <strong>de</strong> Materiales y Gran<strong>de</strong>s Instalaciones<br />
Difracción anómala <strong>de</strong> rayos-X:<br />
Diffraction Anomalous Fine Structure<br />
(<strong>DAFS</strong>)<br />
Maria Grazia Proietti Cecconi
GUIÓN<br />
Introducción<br />
¿Qué es el <strong>DAFS</strong>?<br />
Análisis <strong>de</strong> datos <strong>DAFS</strong><br />
Ejemplos <strong>de</strong> aplicación:<br />
Heteroestructuras y Nanoestructuras<br />
auto-organizadas <strong>de</strong> semiconductores<br />
Estado electrónico <strong>de</strong>l Fe en Fe 3 O 4 :<br />
mo<strong>de</strong>los <strong>de</strong> or<strong>de</strong>n orbital y <strong>de</strong> carga
TÉCNICAS<br />
EXPERIMENTALES<br />
µ<br />
I diff<br />
d<br />
I 0<br />
Selectividad química<br />
(µ(E))<br />
11.5 12 12.5 13 13.5<br />
E(KeV)<br />
I<br />
GaAs GaAsP<br />
As K-As K edge<br />
Absorción <strong>de</strong> rayos X<br />
(XAFS)<br />
µ<br />
d<br />
GaAs<br />
K-As<br />
11.5 12 12.5 13 13.5<br />
E(KeV)<br />
Difracción anómala<br />
(<strong>DAFS</strong>)<br />
I<br />
0<br />
Selectividad química<br />
(f(E))<br />
θ<br />
+ Selectividad <strong>de</strong> sitio/espacial<br />
I diff<br />
Difracción <strong>de</strong> rayos X<br />
(XRD)<br />
Q<br />
k k’<br />
Selectividad <strong>de</strong> sitio/ espacia<br />
(I diff (Q))<br />
<strong>de</strong>tector<br />
(Q)
k<br />
χ(<br />
k)<br />
=<br />
µ − µ 0<br />
µ 0<br />
k <strong>de</strong>l fotoelectrón<br />
=<br />
m(E − E )<br />
h<br />
2 0<br />
Dispersión<br />
simple<br />
r j<br />
=<br />
∑<br />
r j<br />
j<br />
kr<br />
2<br />
j<br />
µ<br />
d<br />
3(<br />
ˆ ε ⋅ rˆ<br />
)<br />
EL EXAFS<br />
GaAs<br />
K-As<br />
11.5 12 12.5 13 13.5<br />
E(KeV)<br />
j<br />
j<br />
κ∗χ(κ)<br />
+ 2δ<br />
( k)<br />
+ φ ( k))<br />
e<br />
j<br />
5 10 15<br />
k(Å -1 )<br />
2 2<br />
j −2σ<br />
j k −2r<br />
j<br />
f<br />
( k,<br />
π ) sin( 2kr<br />
f ( k,<br />
π ) = f ( k,<br />
π ) e<br />
iφ<br />
amplitud compleja <strong>de</strong> retrodifusión<br />
<strong>de</strong>sfase <strong>de</strong>l átomo central<br />
1<br />
e<br />
/ λ(<br />
k )<br />
<strong>de</strong>sor<strong>de</strong>n térmico y estático<br />
(Debye-Waller)<br />
pérdidas inelásticas<br />
λ =libre camino<br />
medio <strong>de</strong>l fotoelectrón<br />
Ajustando esta expresión a la χ experimental se<br />
pue<strong>de</strong>n obtener informaciones estructurales<br />
acerca <strong>de</strong>l sistema estudiado, como distancias<br />
interatómicas, números <strong>de</strong> coordinación,<br />
factores <strong>de</strong> Debye-Waller estáticos y<br />
dinámicos, ángulos <strong>de</strong> enlace, composición.....
EL <strong>DAFS</strong><br />
El <strong>DAFS</strong> es la estructura fina que aparece por encima <strong>de</strong> la anomalía que se observa<br />
en la intensidad difractada al cruzar un umbral <strong>de</strong> absorción <strong>de</strong> rayos-X.<br />
Un espectro <strong>DAFS</strong> se mi<strong>de</strong> registrando la intensidad <strong>de</strong> un pico <strong>de</strong> difracción en<br />
función <strong>de</strong> la energía alre<strong>de</strong>dor <strong>de</strong>l umbral <strong>de</strong> absorción <strong>de</strong> Rayos-X <strong>de</strong> una <strong>de</strong> las<br />
especies atómicas <strong>de</strong>l sistema.<br />
I<br />
0<br />
θ<br />
GaAs 1-x P x /GaAs<br />
I<br />
diff<br />
<strong>de</strong>tector<br />
( ) ( ) ( ) 2<br />
r r r<br />
2<br />
Q,<br />
E exp iQ<br />
⋅r<br />
exp − M Q<br />
I diff<br />
2<br />
F = f j<br />
j<br />
j<br />
= ∑<br />
Selectividad espacial<br />
Factor <strong>de</strong> difusión atómica<br />
Selectividad química<br />
Factor <strong>de</strong> fase<br />
Selectividad <strong>de</strong> sitio<br />
(PRB, M.G. Proietti et al, 59, 1999.)
En el caso <strong>de</strong>l <strong>DAFS</strong>, como en el caso <strong>de</strong>l EXAFS y <strong>de</strong> la difracción <strong>de</strong> fotoelectrones<br />
(fotoemisión), la estructura fina se <strong>de</strong>be a un efecto <strong>de</strong> interferencia cuantomecánica<br />
entre la función <strong>de</strong> onda saliente <strong>de</strong>l fotoelectrón y la misma dispersada por<br />
los átomos vecinos<br />
hν<br />
H = H + H + H<br />
=<br />
=<br />
E<br />
R<br />
I<br />
ˆ e r r r<br />
= − p ⋅ A(<br />
r,<br />
t)<br />
I ∑j<br />
m<br />
H j<br />
2π<br />
f H l l H u<br />
I<br />
I<br />
W ∝ ( )<br />
2 ∑ f H u +<br />
δ ω ω<br />
I ∑<br />
− u f<br />
h f l ω −ω<br />
+<br />
+<br />
+<br />
+...<br />
+ +...<br />
u<br />
l<br />
2<br />
Término perturbativo al Ier<br />
or<strong>de</strong>n:<br />
Fotoelectrón real<br />
Absorción, fotoemisión<br />
(EXAFS, PhD)<br />
Término perturbativo al II or<strong>de</strong>n:<br />
Fotoelectrón virtual<br />
difracción<br />
(<strong>DAFS</strong>)
Resonant atomic scattering factor f<br />
f A(Q,E) = f 0 A(Q) + f’ A(E) + if’’ A(E)<br />
Thomson<br />
II<br />
II<br />
Abs.<br />
II<br />
As<br />
δf<br />
r 0f’’ A(ω, Q=0) = (ω/4πc) σ tot(ω)<br />
f’’ As(E) = f’’ 0As + χ’’ As<br />
f’ As(E) = f’ 0As + χ’ As<br />
In<br />
δf As(E) of As in InAs<br />
f’’ 0As<br />
χ’’ As oscillations<br />
As K-edge : 10867eV<br />
χ’ As oscillations<br />
Energy (eV)<br />
∆f’’ 0As
Las oscilaciones que se observan por encima <strong>de</strong>l umbral <strong>de</strong>pen<strong>de</strong>n <strong>de</strong> la<br />
parte oscilatoria <strong>de</strong>l factor <strong>de</strong> dispersión<br />
Se pue<strong>de</strong> obtener una información <strong>de</strong> tipo electrónico y estructural<br />
análoga a la que se obtiene <strong>de</strong>l XAFS<br />
r "<br />
f µ<br />
( Q = 0,<br />
E)<br />
∝ E ( E)<br />
"<br />
f ⇐ Kramers − Kronig ⇒<br />
f<br />
f<br />
'<br />
"<br />
2<br />
= P<br />
π<br />
2ω<br />
= P<br />
π<br />
∞ ' "<br />
ω f<br />
∫ '2<br />
0 ω −<br />
∞ '<br />
ω<br />
∫<br />
0<br />
'<br />
( ω )<br />
d<br />
'2<br />
ω<br />
'<br />
f '(<br />
ω )<br />
d<br />
'2<br />
'2<br />
ω −ω<br />
'<br />
ω<br />
Teorema óptico<br />
f<br />
'<br />
ω<br />
'<br />
Causalidad<br />
(InP) 3 (GaP) 2 /GaAs K-Ga (006)<br />
I (a.u.)<br />
<strong>DAFS</strong><br />
f"<br />
10.2 10.4 10.6 10.8<br />
E (Kev)<br />
f'
y<br />
0<br />
Structure factor:<br />
Multi-wavelenght Anomalous Diffraction (MAD)<br />
F A<br />
x<br />
N<br />
iQ. rj i<br />
FQE ( , ) f j ( QEe , ) Fe φ<br />
r r r r<br />
= ∑<br />
=<br />
j=<br />
1<br />
r<br />
I ( Q , E ) ∝ FF<br />
|F A | : Thomson scattering of all resonant atoms ; |F N | : scattering of<br />
0 ' ''<br />
all non resonant atoms ; f f +<br />
if ( E : resonant scattering<br />
F T = F A + F N<br />
[ ( ) ] )<br />
F A A A A<br />
*
Multi-wavelenght Anomalous Diffraction (MAD)<br />
2<br />
2<br />
⎡<br />
FA<br />
' ⎤ ⎡<br />
FA<br />
'<br />
⎤<br />
I0( E ) = ⎢ FT<br />
cos(<br />
ϕT<br />
− ϕA<br />
) + f ( ) + ( )<br />
0 A E ⎥ ⎢ FT<br />
sin ϕT<br />
− ϕA<br />
+ f ( E )<br />
0 A ⎥<br />
⎣<br />
fA<br />
⎦ ⎣<br />
fA<br />
⎦<br />
F A do not <strong>de</strong>pend on the energy ; |F T | , φ T - φ A (or |F N | , φ N - φ A )<br />
sligthly <strong>de</strong>pend on E ; f’ A and f’’ A strongly <strong>de</strong>pend on E near an<br />
absorption edge<br />
Then, by measuring I(E) at several energies near an absorption edge<br />
one can <strong>de</strong>termine |F T | , φ T - φ A (or |F N | , φ N - φ A )and|F A |
I<br />
F<br />
diff<br />
0<br />
F<br />
0<br />
Análisis <strong>de</strong> datos <strong>DAFS</strong><br />
Análisis iterativo Kramers-Krönig<br />
Análisis <strong>DAFS</strong> al primer or<strong>de</strong>n (PRB, 59, 5479-5492, 1999, Proietti, M.G. et al.)<br />
( ) ( ) [ ]<br />
( ) ( ) ( ) [ ]<br />
r 2<br />
= F Q,<br />
E<br />
r<br />
F Q,<br />
E<br />
iφ0<br />
= F0<br />
e<br />
"<br />
+ ∆f0<br />
αa<br />
' "<br />
χa<br />
+ χa<br />
r<br />
Q,<br />
E = FT<br />
r r<br />
iφa<br />
Q,<br />
E + αa<br />
Q e<br />
' "<br />
f0a<br />
+ f0a<br />
r 2<br />
( Q,<br />
E)<br />
= FT<br />
2 ⎡ ' 2<br />
2<br />
( ( − ) + ) + ( ( − ) + y"<br />
cos φ<br />
) ⎤<br />
⎢⎣<br />
T φa<br />
βf0a<br />
sen φT<br />
φa<br />
βf0a<br />
⎥⎦<br />
diff<br />
Ajuste <strong>de</strong> la parte lisa <strong>de</strong> I diff<br />
a<br />
β =<br />
F<br />
A<br />
f F<br />
0 A T<br />
0<br />
F A<br />
'<br />
"<br />
2<br />
[ cos(<br />
φ − φ ) χ + sen(<br />
φ − φ ) χ ] términos en<br />
I = F + 2F<br />
α ∆f<br />
+<br />
χ<br />
0<br />
2<br />
0<br />
"<br />
0<br />
0<br />
a<br />
a<br />
0<br />
a<br />
a<br />
x
I − I<br />
χ = ⎡cos φ − φ χ + sen φ − φ χ ⎤ = S<br />
( ) ( )<br />
' " ac ac0<br />
<strong>DAFS</strong> ⎣ 0 a a 0 a a⎦ D<br />
I ac0<br />
f F<br />
S i<br />
D =<br />
2<br />
0<br />
A<br />
FA 0<br />
''<br />
∆f0A<br />
'<br />
; % χ = χa +<br />
"<br />
χa<br />
∑ ∑<br />
χ = χ = A ( k) sen(2 kr + ψ ) χ = A ( k)cos(2 kr + ψ )<br />
" '<br />
EXAFS a j j j a j j j<br />
j j<br />
GaAsP/InP<br />
(006)<br />
χ<br />
<strong>DAFS</strong><br />
=<br />
I<br />
ac<br />
− I<br />
I<br />
ac0<br />
ac0<br />
S<br />
D<br />
=<br />
∑<br />
j<br />
A<br />
j<br />
( k)<br />
sen(<br />
2kr<br />
π<br />
+ ψ j + ∆ϕ<br />
− )<br />
2<br />
( β, ( φ − φ ) ) ∆φ(<br />
β,<br />
( φ −φ<br />
) )<br />
SD T a<br />
T a<br />
Las oscilaciones <strong>DAFS</strong> se pue<strong>de</strong>n analizar<br />
como un espectro EXAFS, tras corregir<br />
por un factor <strong>de</strong> fase y uno <strong>de</strong> amplitud<br />
que <strong>de</strong>pen<strong>de</strong>n <strong>de</strong> la cristalografía <strong>de</strong>l<br />
sistema. Se pue<strong>de</strong>n calcular si esta es<br />
conocida u obtener <strong>de</strong>l ajuste <strong>de</strong> la parte<br />
lisa <strong>de</strong>l espectro.<br />
j
Using the path formalism for <strong>de</strong>scribing the wave function of<br />
the virtual photoelectron :<br />
[ − i ( 2kR<br />
+ ϕ ( k ) ]<br />
∑ Γj<br />
iχ ′<br />
j = − Aγj<br />
( k ) exp<br />
γ = 1<br />
γj<br />
γj<br />
χ ′ +<br />
)<br />
j<br />
If all crystallographic sites are equivalent :<br />
II<br />
II<br />
γ<br />
Abs.<br />
II<br />
As<br />
In<br />
Formally equivalent to EXAFS<br />
Use EXAFS multishell fit co<strong>de</strong>s (Ifeffit)<br />
M.G. Proietti, H. Renevier et al., Phys. Rev. B 59, (1999), 5479
<strong>DAFS</strong> spectroscopy<br />
To measure anomalous diffraction (diffuse scattering) intensity<br />
- as a function of the x-ray beam energy (energy step of about 1eV)<br />
- at fixed scattering vector<br />
- over a 1000eV range with a high S/N ratio (at least 10 3 )<br />
monochromator<br />
Monochromatic SR<br />
experiment mirror<br />
mirror<br />
slits<br />
<strong>DAFS</strong> @ BM2-ESRF<br />
H. Renevier et al., J. Synch. Rad. 10, (2003), 435<br />
slits<br />
• 7-circle diffractometer<br />
• Diffraction : vertical/<br />
horizontal planes<br />
• Polarisation analysis
Spatial selectivity : GaAs xP 1-x/GaAs epilayer (x≈0.20)<br />
<strong>DAFS</strong> : to investigate the strain<br />
accomodation in the strained epilayer<br />
θ 1 ≠ θ 2<br />
θ 1<br />
RX<br />
I(E)<br />
GaAsP<br />
θ2 Tensile in plane strain<br />
GaAs<br />
[100]<br />
• Chemical selectivity<br />
ε = (aGaAsP-aGaAs)/aGaAs • Spatial selectivity,<br />
•The x-rays probe the entire thickness of the epilayer<br />
• The data analysis is easy (one site) as well as the experiment<br />
M.G. Proietti, H. Renevier et al., Phys. Rev. B 59, (1999), 5479.<br />
15/50
Spatial selectivity : GaAs xP 1-x/GaAs epilayer<br />
GaAsP/GaAs thin film, (006) weak reflection, FWHM=0.02°<br />
Quick <strong>DAFS</strong>, assisted with feedback : 2000eV, 7 minutes !!<br />
Diffracted Intensity<br />
Intensité normalisée<br />
Χ(k)<br />
0.2<br />
0.1<br />
0<br />
0.05<br />
χ(k)<br />
0<br />
-0.05<br />
<strong>DAFS</strong><br />
Ga Kedge<br />
10500 11000 11500 12000<br />
Energie (eV)<br />
200ms/pt<br />
Energy<br />
4 6 8 10 12 14 16<br />
k (Å -1 k(Å ) -1 )<br />
As Kedge<br />
10 ms/pt<br />
E<strong>DAFS</strong> oscillations<br />
Ga Kedge<br />
0.2<br />
-0.2<br />
0<br />
0.2<br />
-0.2<br />
0.2<br />
-0.2<br />
-0.2<br />
(006) reflection, Ga K-edge<br />
0.2<br />
0<br />
0<br />
0<br />
2 4 6 8 10 12<br />
k (Å -1 )<br />
k(Å-1 )<br />
FT<br />
ε = 0.4%<br />
[110]<br />
ε = 0.6%<br />
[110]<br />
ε = 0.7%<br />
[110]<br />
t=4000Å<br />
ε = 0.7%<br />
-<br />
[110]<br />
t=600Å<br />
0 1 2 3 4 5 6<br />
R (Å -1 )<br />
R(Å)<br />
16/50
TEM<br />
InAs/InP QWrs<br />
AFM<br />
200nm<br />
GaN/AlN QDs<br />
Introduction<br />
Physical properties of nanostructures <strong>de</strong>pend on :<br />
-The internal atomic structure<br />
(strain, composition, <strong>de</strong>fects, ...)<br />
-The morphology (shape, size, size distribution, …)<br />
• Knowledge of the local structure at atomic scale and<br />
morphology of nano-islands during growth is a key to<br />
control and un<strong>de</strong>rstand the growth mechanism<br />
(thermodynamic, growth kinetic)<br />
17/50
Inci<strong>de</strong>nt<br />
beam<br />
α i ~ α c<br />
Introduction : Grazing Inci<strong>de</strong>nce X-ray Scattering<br />
GID : Grazing<br />
Inci<strong>de</strong>nce Diffraction<br />
D<br />
h<br />
ω<br />
d<br />
2θ<br />
slits<br />
GID<br />
strain<br />
composition<br />
Detector<br />
0D or 1D<br />
2θ<br />
q y<br />
α f<br />
GISAXS : Grazing<br />
Inci<strong>de</strong>nce Small<br />
Angle Scattering<br />
ex situ study<br />
in situ study during<br />
the growth<br />
(photon in–photon out)<br />
q z<br />
q x<br />
GISAXS<br />
Shape<br />
(facets),<br />
size,<br />
correlation<br />
2D <strong>de</strong>tector<br />
Courtesy G. Renaud<br />
18/50
Local structure study of InAs/InP QWrs<br />
Quantum size effect : materials for opto-electronic<br />
(lasers 1.5µm)<br />
Stranski-Krastanow growth (strain release via a 2D-3D<br />
growth transition)<br />
Self-organized 2D growth driven by anisotropic strain at<br />
interface<br />
Physical properties<br />
•strain<br />
•composition<br />
•interface<br />
Growth mechanism control<br />
InAs/InP QWrs<br />
ε≅-3,3%<br />
2,2 ML éq.<br />
λ≅24nm<br />
1MLInAs = 3Å<br />
Fils : [1-10]<br />
[110]<br />
-<br />
[110]<br />
AFM<br />
19/50
X-ray absorption at the As K-edge (EXAFS)<br />
P : next nearest neighbors<br />
In As/P In : first nearest neighbors<br />
contribution<br />
II<br />
I<br />
II<br />
Abs.<br />
I<br />
I<br />
Abs.<br />
II<br />
I<br />
χ(k)<br />
0.05<br />
0<br />
-0.05<br />
-0.1<br />
3 5 7 9 11 13 15<br />
k (Å -1 )<br />
k(Å-1 )<br />
résiduel<br />
20/50
As-O<br />
As K-edge EXAFS (BM8-ESRF)<br />
Intensité Normalisée<br />
| FT(k 2 χ(k)) |<br />
0.02<br />
0.01<br />
0<br />
2<br />
1.5<br />
1<br />
0.5<br />
0.026<br />
0.02<br />
0.014<br />
11860 11880 11900 11920 11940<br />
11800 12000 12200 12400 12600 12800<br />
Energie (eV)<br />
energy<br />
Radial distribution<br />
0<br />
0 1 2 3 4 5<br />
R(Å)<br />
R(Å)<br />
χ(k)<br />
0.08<br />
0.04<br />
0<br />
-0.04<br />
-0.08<br />
EXAFS<br />
-0.12<br />
2 4 6 8 10 12 14<br />
k(Å -1 ) k(Å-1 )<br />
absence of 2 cd shell !<br />
Various As sites,<br />
needs of spatial<br />
selectivity<br />
résiduel<br />
21/50
Grazing inci<strong>de</strong>nce diffraction<br />
[110]<br />
1 1<br />
o<br />
Λ = = ≈190<br />
A<br />
δQ Q tanδω<br />
-<br />
Intensity<br />
E = 11.867 keV, ID1, ESRF<br />
(4-40) InP substrat<br />
scan Q ⊥ (Å -1 )<br />
• Diffraction with the polarization ⊥ to the surface<br />
•scan Q ⊥ : short range correlations, shape<br />
• radial scan Qr ([1-10]) : perfect pseudomorphy<br />
22/50
Grazing inci<strong>de</strong>nce diffraction<br />
BM2-D2AM-ESRF<br />
In-plane scattering Spatial selectivity<br />
[110]<br />
Intensité (unité arb.)<br />
Intensity<br />
10 5<br />
10 4<br />
Correlation<br />
statellite -1<br />
QWrs<br />
substrat InP<br />
(440) InP (440)<br />
substrat<br />
InAs bulk<br />
1/d=0.93<br />
0.94 0.95 0.96 0.97 0.98<br />
q=2sin(θ)/λ (Å -1 )<br />
radial scan : Qr=1/d (Å -1 )<br />
•a InAs=0.60584nm (1/d 440=0.934 Å -1) ; a InP=0.58686nm (1/d 440=0.964 Å -1)<br />
• Diffraction in the vertical plane : polarization ⊥ to the surface<br />
• Radial scan : strain, correlation, shape and composition sensitive<br />
23/50
Grazing inci<strong>de</strong>nce anomalous diffraction : As K-edge (11867 eV)<br />
GI<strong>DAFS</strong> spectra of the correlation satellites (-1) (BM2-D2AM-ESRF)<br />
Intensity (a.u.)<br />
(440)<br />
Energy<br />
(420)<br />
In-plane reflections<br />
The GI<strong>DAFS</strong> oscillations :<br />
a) As local atomic environment<br />
b) QWrs strain accomodation<br />
c) QWrs composition<br />
- ∆φ=φ T-φ A, |F As |/(f 0As x|F T |) : give S D (E<strong>DAFS</strong> normalisation factor)<br />
and ∆ψ=φ 0-φ A (crystallographic phase shift)<br />
- One assume one equivalent crystallographic site (Zinc-Blen<strong>de</strong>)<br />
24/50
GI-<strong>DAFS</strong> (Grazing Inci<strong>de</strong>nce <strong>DAFS</strong>)<br />
k(Å -1 )<br />
R(Å)<br />
Nearest Neighbors As-In 2.60Å<br />
Next NN<br />
(out of plane)<br />
As-As 4.29Å<br />
60 +/-15%<br />
Nanostructures<br />
II<br />
II<br />
Abs.<br />
II<br />
As-P 4.17 +/- 0.02Å<br />
40 +/- 15%<br />
Interface InAs/InP<br />
(bulk InP : P-P 4.15Å)<br />
S. Grenier, M.G. Proietti, H. Renevier, et al., Europhysics Letters, 57, (2002), 499<br />
25/50
TEM<br />
Grazing Inci<strong>de</strong>nce MAD : application to buried InAs/InP QWrs<br />
α i<br />
l-scan √I<br />
-exp.<br />
-- cal.<br />
E=10367eV<br />
RX<br />
InAs QWrs<br />
|F A |= |F As | QWrs<br />
ooo : exp<br />
--- : cal..<br />
a>a InPaa InP<br />
InAs QWrs<br />
InP<br />
(442)<br />
• strain : 6% ([001])<br />
• height : 2.4 nm<br />
a
Diffraction Intensity (a.u.)<br />
GI<strong>DAFS</strong> oscillations analysis<br />
80<br />
70<br />
60<br />
50<br />
40<br />
30<br />
As K-edge CP1276<br />
l=1.9<br />
h=k=3.98<br />
11,7 11,8 11,9 12<br />
Energy E(keV) (keV)<br />
E<strong>DAFS</strong> fit (Ifeffit co<strong>de</strong>)<br />
∆φ/β fit (DPU co<strong>de</strong>)<br />
Phase and amplitu<strong>de</strong> factors<br />
S D , (φ 0-φ A)<br />
I3701<br />
CP1276<br />
sim <strong>DAFS</strong> from XAFS<br />
27/50
E<strong>DAFS</strong> vs EXAFS EXAFS measurements at the<br />
ε ⊥<br />
As K-edge (ESRF- BM30)<br />
ε // & ε ⊥<br />
Multifit by Ifeffit co<strong>de</strong><br />
Differences between the<br />
two samples show up in E<strong>DAFS</strong><br />
but not in EXAFS<br />
I3701<br />
CP1276<br />
Probing different As environments<br />
E<strong>DAFS</strong> measurements at the<br />
As K-edge (ESRF- BM2)<br />
CP1276<br />
I3701<br />
ε ⊥<br />
28/50
Abs II<br />
EXAFS and E<strong>DAFS</strong> best fit results<br />
II<br />
Sample→<br />
paths (Å)↓<br />
(As abs-As II) //<br />
(As abs-As II) ⊥<br />
(As abs-P II) //<br />
(As abs-P II) ⊥<br />
(As abs-In III) //<br />
(As abs-In III) ⊥<br />
%P //<br />
%P ⊥<br />
Abs.<br />
II<br />
As,P<br />
In<br />
InAs<br />
Bulk<br />
4.284<br />
4.284<br />
-<br />
-<br />
5.023<br />
5.023<br />
-<br />
-<br />
InAs/InP<br />
(pseud.)<br />
4.15<br />
4.29<br />
-<br />
-<br />
4.87<br />
5.13<br />
-<br />
-<br />
Pure strained InAs<br />
II shell<br />
Strain<br />
or<br />
distances<br />
InAsP alloy ?<br />
P content<br />
CP1276<br />
(EXAFS ε ⊥ & ε //)<br />
4.16±0.06<br />
4.23±0.04<br />
4.19±0.07<br />
4.17±0.03<br />
4.88±0.03<br />
4.93±0.06<br />
0.3±0.1<br />
0.5±0.1<br />
CP1276<br />
(<strong>DAFS</strong> ε ⊥ )<br />
-<br />
4.30±0.04<br />
-<br />
4.20±0.06<br />
-<br />
-<br />
-<br />
0.4±0.2<br />
I3701<br />
(EXAFS ε ⊥ & ε //)<br />
4.15±0.06<br />
4.25±0.04<br />
4.15±0.07<br />
4.18±0.03<br />
4.87±0.03<br />
4.94±0.06<br />
0.4±0.1<br />
0.6±0.1<br />
I3701<br />
(<strong>DAFS</strong> ε ⊥ )<br />
-<br />
4.22±0.04<br />
-<br />
4.19±0.06<br />
-<br />
-<br />
-<br />
0.4±0.3<br />
29/50
EXAFS (ε // & ε ⊥)<br />
Similar results for the 2 samples<br />
Mixing of two different As<br />
environments<br />
Strained InAs & InAsP alloy<br />
?<br />
Intermixing As/P<br />
at the QWrs/capping<br />
interface<br />
P diffused QWrs<br />
Nice example of <strong>DAFS</strong> spatial<br />
selectivity and of strong<br />
EXAFS/<strong>DAFS</strong> complementarity<br />
GI<strong>DAFS</strong> probes the QWrs As atoms (the<br />
contribution of each atom <strong>de</strong>pends on Q)<br />
EXAFS probes all As atoms<br />
E<strong>DAFS</strong> (ε ⊥)<br />
Different results for the 2 samples<br />
Different As-As and As-P II shell dist.<br />
CP1276: InAs QWrs + As/P<br />
intermixing at interface<br />
& capping<br />
I3701: InAsP QWrs + As/P<br />
intermixing at interface<br />
& capping<br />
30/50
GI<strong>DAFS</strong> oscillations analysis<br />
CP1276<br />
k (Å -1 )<br />
I3701<br />
Different<br />
growth methods<br />
(IMM Madrid/ Ec.<br />
Centrale Lyon)<br />
GI<strong>DAFS</strong> lineshape<br />
give<br />
S D, φ 0 - φ A<br />
E<strong>DAFS</strong> fit<br />
(Ifeffit co<strong>de</strong>)<br />
31/50
Abs II<br />
II<br />
EXAFS and E<strong>DAFS</strong> best fit results<br />
Abs.<br />
Sample→<br />
paths (Å)↓<br />
(As abs -As II ) //<br />
(As abs -As II ) ⊥<br />
(As abs -P II ) //<br />
(As abs -P II ) ⊥<br />
(As abs -In III ) //<br />
(As abs -In III ) ⊥<br />
%P //<br />
% P ⊥<br />
II<br />
InAs<br />
Bulk<br />
4.284<br />
4.284<br />
-<br />
-<br />
5.023<br />
5.023<br />
-<br />
-<br />
As,P<br />
In<br />
InAs/InP<br />
(pseud.)<br />
4.15<br />
4.29<br />
-<br />
-<br />
4.87<br />
5.13<br />
-<br />
-<br />
II shell<br />
distances<br />
CP1276<br />
(EXAFS e ⊥ & e<br />
// )<br />
4.16±0.06<br />
4.23±0.04<br />
4.19±0.07<br />
4.17±0.03<br />
4.88±0.03<br />
4.93±0.06<br />
0.3±0.1<br />
0.5±0.1<br />
Strain<br />
P content<br />
CP1276<br />
(<strong>DAFS</strong> e ⊥<br />
)<br />
-<br />
4.30±0.04<br />
-<br />
4.20±0.06<br />
-<br />
-<br />
-<br />
0.4±0.2<br />
Pure strained InAs<br />
or<br />
InAsP alloy ?<br />
I3701<br />
(EXAFS e ⊥ & e // )<br />
4.15±0.06<br />
4.25±0.04<br />
4.15±0.07<br />
4.18±0.03<br />
4.87±0.03<br />
4.94±0.06<br />
0.4±0.1<br />
0.6±0.1<br />
I3701<br />
(<strong>DAFS</strong> e ⊥<br />
)<br />
-<br />
4.22±0.04<br />
-<br />
4.19±0.06<br />
-<br />
-<br />
-<br />
0.4±0.3<br />
32/50
EXAFS (ε // & ε ⊥)<br />
Similar results for the 2 samples<br />
Mixing of two different As<br />
environments<br />
Strained InAs & InAsP alloy<br />
?<br />
Intermixing As/P<br />
at the QWrs/capping<br />
interface<br />
P diffused QWrs<br />
Nice example of <strong>DAFS</strong> spatial<br />
selectivity and of strong<br />
EXAFS/<strong>DAFS</strong> complementarity<br />
GI<strong>DAFS</strong> probes the QWrs As atoms (the<br />
contribution of each atom <strong>de</strong>pends on Q)<br />
EXAFS probes all As atoms<br />
E<strong>DAFS</strong> (ε ⊥)<br />
Different results for the 2 samples<br />
Different As-As and As-P II shell dist.<br />
CP1276: InAs QWrs + As/P<br />
intermixing at interface<br />
& capping<br />
I3701: InAsP QWrs + As/P<br />
intermixing at interface<br />
& capping<br />
33/50
Applications : Nanostructures III-V : BQ GaN/AlN<br />
~ 30o TEM<br />
[0001]<br />
AlN<br />
GaN QDs<br />
BV BV<br />
h= 4 nm<br />
D b = 30 nm<br />
BC BC<br />
{ 11<br />
03}<br />
5 nm<br />
A.D. Andreev et E.P. O’Reilly, APL 79, (2001), 521<br />
P<br />
Nitri<strong>de</strong> : InN (1,9eV), GaN (3,5eV), AlN<br />
(6,2eV) + alloys : visible spectra + UV A<br />
and B : LEDs (B, V) , LDs at 0,4µm<br />
- QDs : dislocations free<br />
- 3D electronic onfinement :<br />
- higher PL intensity<br />
- PL intensity : T in<strong>de</strong>pendant<br />
- Wurtzite (hexagonal cell) : [0001] :<br />
polar axis) : spontaneous + piezo-electric<br />
polarizations : electric field<br />
- PL red shift<br />
- carriers separation<br />
Important parameters :<br />
<strong>de</strong>formation, size, composition<br />
34/50
Applications : Nanostructures III-V : BQ GaN/AlN<br />
GaN QDs (4ML)<br />
wetting layer (2ML)<br />
AlN buffer (40 ML)<br />
Saphir or SiC substrates<br />
AlN capping of a GaN/AlN QDs layer : strain,<br />
composition, mechanism ?<br />
AFM<br />
- Modified Stranski –<br />
Krastanow growth (MBE)<br />
- AlN, GaN mismatch :<br />
2,4 %<br />
Ga + N<br />
GaN thickness ><br />
critical thickness<br />
GaN QDs<br />
AlN<br />
RHEED<br />
35/50
|| Structure factor ||<br />
Applications : Nanostructures III-V : BQ GaN/AlN : GIMAD<br />
F Ga<br />
F T<br />
0ML<br />
2ML<br />
10ML<br />
2.9<br />
h<br />
3 2.9 h 3<br />
[10-10] dir. : radial scan<br />
√I<br />
GaN<br />
√I √I<br />
AlN (30-30)<br />
α i =0.15°
Applications : Nanostructures III-V : BQ GaN/AlN : GI<strong>DAFS</strong><br />
2 ML AlN<br />
Energy (eV)<br />
E<strong>DAFS</strong><br />
k(Å -1 ) = 0,512x√(E-E seuil )<br />
Out of plane strain, composition :<br />
[0001]<br />
E<br />
• I(E), fixed Q : max. of F Ga<br />
• K-edge (10367eV), BM2, ESRF<br />
• E : [0001], ⊥ to the growth plane<br />
k<br />
Wurtzite structure<br />
B d Ga-Ga(N) (a diff.,c)<br />
(hexagonal symmetry )<br />
N<br />
Ga<br />
37/50
1.4<br />
1.0<br />
ε zz<br />
0.6<br />
0.2<br />
Applications : Nanostructures III-V : BQ GaN/AlN<br />
Results : strain (in-plane and out-of-plane), absolute<br />
composition in diffraction selected iso-strain volumes<br />
GaN (biaxial strain)<br />
10 ML<br />
Biaxial <strong>de</strong>formation<br />
2 ML<br />
0M L<br />
5 ML<br />
GaN/AlN/Saphire QDs<br />
-2.5 -2.0 -1.5 -1.0<br />
ε xx = (a-a GaN,bulk)/a GaN,bulk<br />
J. Coraux et al. Phys. Rev. B 73, 2006<br />
ε zz<br />
1.5<br />
1.0<br />
11ML<br />
0.5<br />
0.0<br />
18ML<br />
8ML GaN/AlN/SiC QDs<br />
4ML<br />
2ML<br />
• d Ga-N NN : strain in<strong>de</strong>pendant<br />
• Al content ≅ 0, no Al/Ga<br />
intermixing insi<strong>de</strong> the QDs<br />
0ML<br />
-1.4 -1.2 -1.0 -0.8 -0.6<br />
εxx 38/50
BQ GaN/AlN 10ML : EXAFS vs <strong>DAFS</strong><br />
k χ ϕ ϕ<br />
χ ϕ ϕ<br />
χ = ′<br />
− ) ′′<br />
( ) cos( −<br />
Q 0 A)<br />
EXAFS + sin( 0<br />
r E<strong>DAFS</strong> from EXAFS<br />
kχ(k)<br />
sample<br />
a (Å)<br />
C (Å)<br />
x_Al<br />
c/a<br />
Bulk<br />
3,188<br />
5,186<br />
-<br />
1,626<br />
GaN<br />
biaxial<br />
3,11<br />
5,26<br />
-<br />
1,69<br />
k (nm -1 )<br />
exp. E<strong>DAFS</strong><br />
<strong>DAFS</strong><br />
3,14 (diff.)<br />
5,23±0,03<br />
0,0±0,1<br />
1,67<br />
EXAFS<br />
3,15<br />
5,19±0,03<br />
0,22±0,07<br />
1,64<br />
A<br />
EXAFS<br />
X ray absorption (EXAFS)<br />
-GaK-edge<br />
- E ⊥ and // to growth plane<br />
-BM30, ESRF<br />
EXAFS : probe all Ga atoms (WL,<br />
interfaces, ... )<br />
E<strong>DAFS</strong> : max of F Ga : probe<br />
mainly the QD’s core (iso-strain<br />
volume)<br />
39/50
h < max FGa<br />
h=2.96 : max FGa<br />
h > max FGa<br />
BQ GaN/AlN : E<strong>DAFS</strong> simulations<br />
Finite Element Simulation (coll. C. Priester)<br />
GaN/AlN/Saphire (D 15nm X H 3nm) QDs + 5 ML AlN capping<br />
ε xx<br />
A j = Ga j ; k = 0, l = 0<br />
ε zz<br />
40/50
BQ GaN/AlN : E<strong>DAFS</strong> simulations<br />
h=2.96 : max FGa ; k = 0, l = 0<br />
Ga-N<br />
Ga-Ga<br />
in progress ...<br />
41/50
CONCLUSIONS<br />
Combined MAD & <strong>DAFS</strong> approach to<br />
free-standing and capped nanostructures<br />
MAD<br />
• Mo<strong>de</strong>l-free chemical imaging<br />
in the reciprocal space<br />
• Average strain and size<br />
• Powerful tool for the<br />
simulation (FEM) of the<br />
true heterostructure<br />
•In situ structural evolution<br />
during growth (J.<br />
Coraux et al. APL 2006)<br />
<strong>DAFS</strong><br />
• local environment of chemical<br />
specie located in a diffraction<br />
selected iso-strain volume<br />
• local lattice accomodation to<br />
strain, local composition<br />
42/50
Or<strong>de</strong>n <strong>de</strong> carga y reflexiones<br />
prohibidas en la magnetita<br />
Los óxidos <strong>de</strong> valencia mixta <strong>de</strong> metales <strong>de</strong> transición tienen una<br />
fenomenología muy variada e interesante<br />
Superconductividad<br />
Magnetoresistencia,<br />
Transiciones <strong>de</strong> fase metal-aislante ....<br />
Ocupación parcial <strong>de</strong> los orbitales 3d<br />
Estados <strong>de</strong> oxidación diferente<br />
Or<strong>de</strong>n orbital Or<strong>de</strong>n <strong>de</strong> carga<br />
Los electrones d no eligen el orbital a<br />
ocupar al azar in<strong>de</strong>pendientemente <strong>de</strong><br />
los <strong>de</strong>más, sino respectando un or<strong>de</strong>n<br />
y dando lugar a un or<strong>de</strong>n periódico <strong>de</strong><br />
los orbitales d ocupados<br />
La carga electrónica que pue<strong>de</strong><br />
fluctuar entre sitios<br />
cristalográficamente equivalentes,<br />
por <strong>de</strong>bajo <strong>de</strong> T c se localiza, los iones<br />
con valencia diferente se or<strong>de</strong>nan<br />
periódicamente y la s disminuye<br />
or<strong>de</strong>nes <strong>de</strong> magnitud
Manganitas dopadas<br />
(RE1-xAxMnO3)<br />
Magnetita<br />
(Fe 3O 4)<br />
(Fe 3+ )T d(Fe 3+ )O h(Fe 2+ )O hO 4<br />
Espinela invertida<br />
8(Fe3+)Td (½ ½ ½)<br />
16(Fe3+)/ (Fe 2+) Oh (1/8 1/8 1/8)<br />
32 O2- (u u u ) u ≅ 0.255<br />
T>Tc → cúbico (F d-3m )<br />
a = 8.396Å<br />
TTc<br />
Fluctuación <strong>de</strong> la<br />
carga<br />
(conductor)<br />
T
Estado electrónico <strong>de</strong> los sitios octaédricos <strong>de</strong>l Fe<br />
<strong>DAFS</strong><br />
E ⇒ K- edge Fe<br />
Shift químico<br />
r<br />
f ( Q,<br />
E)<br />
= f0<br />
f " ∝ µ<br />
Reflexión observada<br />
por difracción <strong>de</strong><br />
neutrones a T
Medidas <strong>de</strong> <strong>DAFS</strong> al umbral K <strong>de</strong>l Fe<br />
Linea CRG-D2AM <strong>de</strong>l ESRF<br />
Goniómetro 7 círculos +monocromador<br />
Reflexiones prohibidas (002) y (006)<br />
Medidas en función <strong>de</strong> T(20 K y 300K)<br />
Medidas en función <strong>de</strong> φ (analizador <strong>de</strong> MgO(111))<br />
---- T=20K<br />
_____ T=300K<br />
Resonancia antes <strong>de</strong>l umbral (prepico)<br />
Resonancia en el umbral<br />
Región extendida<br />
El espectro no cambia para T>T c
Anisotropía <strong>de</strong>l factor <strong>de</strong> dispersión reflexiones ATS<br />
f<br />
La susceptibilidad eléctrica <strong>de</strong> un cristal para los Rayos X es<br />
generalmente pequeña, pero en proximidad <strong>de</strong> un umbral <strong>de</strong> absorción<br />
la anisotropía <strong>de</strong>l enlace químico o <strong>de</strong>l entorno local pue<strong>de</strong> generar<br />
una anisotropía consi<strong>de</strong>rable en la parte anómala <strong>de</strong>l factor <strong>de</strong><br />
dispersión<br />
f es un tensor<br />
=<br />
⎛<br />
⎜<br />
⎜<br />
⎜<br />
⎝<br />
f<br />
f<br />
f<br />
xx<br />
yx<br />
zx<br />
⎞<br />
⎟<br />
⎟<br />
⎟<br />
⎠<br />
Magnetita: reflexiones (0 0 4n+2)<br />
Transiciones dipolares eléctricas<br />
1s→4p<br />
f<br />
f<br />
f<br />
xy<br />
yy<br />
zy<br />
f<br />
f<br />
f<br />
xz<br />
yz<br />
zz<br />
Nuevas reglas <strong>de</strong> extinción para las<br />
reflexiones prohibidas en cristales<br />
con planos o ejes <strong>de</strong> <strong>de</strong>slizamiento<br />
(Dmitrienko, Acta Cryst. 1984)<br />
Fe tetraédrico (A)<br />
Simetría <strong>de</strong> grupo puntual<br />
Td (cúbica)<br />
Fe octaédrico (B)<br />
Simetría <strong>de</strong> grupo puntual<br />
D3d (trigonal)<br />
isótropo<br />
anisótropo
Distorsión trigonal<br />
(z’es el eje trigonal)<br />
tensor f diagonal<br />
fxx=fyy=f⊥<br />
fzz=f//<br />
16<br />
3<br />
( ) 2<br />
f −<br />
2<br />
I002 ∝ 16 fb<br />
= // f⊥<br />
f<br />
f<br />
1<br />
a<br />
F<br />
⎛ f<br />
⎜<br />
= ⎜ 0<br />
⎜<br />
⎝ 0<br />
2<br />
= f<br />
3<br />
=<br />
xx<br />
⊥<br />
4i<br />
f<br />
0<br />
yy<br />
1<br />
+ f<br />
3<br />
4 Fe octaédricos:<br />
(1) (1/8 1/8 1/8) z’(111)<br />
(2) (3/8 3/8 1/8) z’(-1-11)<br />
(3) (3/8 1/8 3/8) z’(1-11)<br />
(4) (1/8 1/8 1/8) z’(-111)<br />
//<br />
0 ⎞ ⎛ f⊥<br />
0<br />
⎟ ⎜<br />
0 ⎟=<br />
⎜ 0 f<br />
f ⎟ ⎜<br />
zz⎠<br />
⎝ 0<br />
1<br />
fb<br />
=<br />
3<br />
⊥<br />
[ + − − ]<br />
1 2 3 4<br />
f f f f<br />
0 ⎞ ⎛ f<br />
⎟ ⎜<br />
0 ⎟=<br />
⎜ f<br />
f ⎟ ⎜<br />
// ⎠ ⎝ f<br />
( f − f )<br />
002 b<br />
//<br />
⊥<br />
⎛ 0<br />
⎜<br />
= 16i⎜<br />
f<br />
⎜<br />
⎝ 0<br />
a<br />
b<br />
b<br />
f<br />
b<br />
0<br />
0<br />
f<br />
f<br />
f<br />
b<br />
a<br />
b<br />
f<br />
f<br />
f<br />
b<br />
b<br />
a<br />
0⎞<br />
⎟<br />
0⎟<br />
0⎟<br />
⎠<br />
⎞<br />
⎟<br />
⎟<br />
⎟<br />
⎠
Zona <strong>de</strong>l umbral (DANES) Mo<strong>de</strong>lo reflexión ATS<br />
2 16<br />
∝ 16 = // f⊥<br />
3<br />
I002 fb<br />
( ) 2<br />
f −<br />
Simulación “ab initio”:<br />
Calculos XANES <strong>de</strong> la sección<br />
eficaz <strong>de</strong> absorción s para un<br />
cluster FeO 6 con Fe(D)3d<br />
1s → 4p<br />
" ωmc<br />
µ = N σ f = 2<br />
4πNe "<br />
f ⇐ Kramers − Kronig ⇒<br />
'<br />
' 2 ω<br />
f P<br />
'2<br />
π ∫<br />
0 ω<br />
∞<br />
=<br />
f<br />
" (<br />
ω<br />
−ω<br />
'<br />
)<br />
'2<br />
d<br />
'<br />
ω<br />
µ<br />
f<br />
'<br />
7115 7120 7125 7130 7135<br />
E (KeV)<br />
f "<br />
µ ⊥≠µ //<br />
∆E≈2eV
Efectos <strong>de</strong> polarización en I diff<br />
I ∝<br />
diff<br />
' ˆ F εˆ<br />
σπ<br />
εσπ hkl<br />
( 1 0 0)<br />
εˆ<br />
( 0 senθ cosθ)<br />
εˆ<br />
=<br />
σ = π<br />
Rotación en φ <strong>de</strong>l cristal<br />
⎛cosφ − sinφ<br />
⎜<br />
−1<br />
= R(<br />
φ ) F00<br />
R(<br />
φ ) R(<br />
φ ) = ⎜ sinφ<br />
cosφ<br />
⎜<br />
⎝ 0 0<br />
'<br />
F00l l<br />
Polarización <strong>de</strong>l<br />
haz inci<strong>de</strong>nte σ<br />
φ = 0 ⇒ I<br />
σ −σ<br />
φ = 45º<br />
⇒ I<br />
I(<br />
002 ) ⇒ I<br />
I(<br />
006 ) ⇒ I<br />
σ −σ<br />
σ −π<br />
σ −π<br />
I<br />
I<br />
= 0<br />
σ−σ<br />
σ−π<br />
I<br />
= 16 f<br />
∝ 16 f<br />
∝ 16 f<br />
σ −π<br />
2<br />
b<br />
= 16 f<br />
I<br />
(max) = 4%<br />
Iσ<br />
(max) = 40%<br />
I<br />
b<br />
b<br />
b<br />
σ −π<br />
−σ<br />
2<br />
2<br />
2<br />
σ −σ<br />
2<br />
( sin 2φ)<br />
sin<br />
sin<br />
= 0<br />
2<br />
2<br />
θ<br />
(max)<br />
(max)<br />
θ<br />
2<br />
( ) 2<br />
cos 2φ<br />
0⎞<br />
⎟<br />
0⎟<br />
1⎟<br />
⎠
Prepico<br />
Cálculos “ab initio” <strong>de</strong> f para transiciones <strong>de</strong><br />
dipolo + cuadrupolo<br />
Fe D 3d + FeT d<br />
(FDMNES, Y. Joly, CNRS Grenoble)<br />
Término mixto dipolo – cuadrupolo<br />
asociado a los átomos tetraédricos<br />
Misma periodicidad <strong>de</strong>l<br />
término dipolar octaédrico<br />
La simulación “ab initio”<strong>de</strong>l cluster<br />
octaédrico en aproximación dipolar<br />
no reproduce la estructura antes<br />
<strong>de</strong>l umbral <strong>de</strong>l Fe y que<br />
correspon<strong>de</strong> al prepico <strong>de</strong>l espectro<br />
<strong>de</strong> absorción(XANES).<br />
¿Transiciones <strong>de</strong> cuadrupolo<br />
1s → 3d ?<br />
¿hibridización <strong>de</strong> orbitales<br />
3d Fe T d con los 2p <strong>de</strong>l O?<br />
I pp (006)/I p (006) ≠ I pp (002)/I p (002)<br />
Los términos <strong>de</strong> tipo<br />
cuadrupolar en la amplitud<br />
<strong>de</strong> difusión <strong>de</strong>pen<strong>de</strong>n <strong>de</strong> k<br />
(<strong>de</strong>)<br />
Or<strong>de</strong>namiento <strong>de</strong> los orbitales<br />
p-d vacíos<br />
<strong>de</strong> los átomos <strong>de</strong> Fe<br />
tetraédricos
Conclusiones<br />
Medidas a RT<br />
Fe2+ Fe3+ e<br />
τhopping >> τRayos-X ≈ 10-15 El <strong>DAFS</strong> nos proporciona por primera vez evi<strong>de</strong>ncia DIRECTA<br />
sobre el estado electrónico <strong>de</strong>l Fe.<br />
El <strong>DAFS</strong> <strong>de</strong> las reflexiones prohibidas se interpreta<br />
perfectamente en el esquema <strong>de</strong> la anisotropía <strong>de</strong>l f (ATS)<br />
Los sitios <strong>de</strong>l Fe octaédrico, consi<strong>de</strong>rados<br />
tradicionalmente fluctuantes entre dos estados <strong>de</strong><br />
valencia Fe2+ y Fe3+, son electronicamente<br />
IDENTICOS<br />
s<br />
No hay fluctuación <strong>de</strong> carga para T>Tc<br />
Medidas a baja T Misma <strong>de</strong>pen<strong>de</strong>ncia en E y en f para T
Grazing Inci<strong>de</strong>nce Diffraction Anomalous Fine Structure (GI<strong>DAFS</strong>)<br />
1) 2D FEM similations to fit<br />
the anomalous diffraction<br />
data, including <strong>DAFS</strong> line<br />
shape (β, ∆φ), can give the<br />
true structure : shape,<br />
size strain and composition<br />
ε xx<br />
ε zz<br />
Simulation of As 1-x P x composition<br />
in the wires lead to x ~ 0<br />
Chemical composition ?<br />
Diffraction Intensity Intensity (a.u.)<br />
Tedious task, not always successful !<br />
80<br />
70<br />
60<br />
50<br />
40<br />
30<br />
2) Energy scan, fixed Q : max.<br />
of F A (h=k=3.98, l=1.9)<br />
Diffraction selected local structure :<br />
• lattice strain accomodation<br />
• composition<br />
11,7 11,8 11,9 12<br />
Energy (keV)<br />
E(keV)<br />
As K-edge BM2, ESRF