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XRD polykrystalické tenké vrstvy. Conventional Bragg-Brentano symmetric geometry – θ /2 θ scan Asymmetric BB geometry – θ /2 θ scan Parallel beam geometry – 2 θ scan. Phase analysis Lattice parameters Size, strain Texture. Bragg-Brentano conventional powder diffraction geometry. - PowerPoint PPT Presentation
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XRDpolykrystalické tenké vrstvy
• Conventional Bragg-Brentano symmetric geometry – θ/2θ scan
• Asymmetric BB geometry – θ/2θ scan
• Parallel beam geometry – 2θ scan
Phase analysisLattice parametersSize, strainTexture
Bragg-Brentano conventional powder diffraction geometry
1
2
3
h1k1l1
h2k2l2
h3k3l3
Information from the grainsoriented with the
corresponding planesparallel to the surface
Symmetric - 2 scan
Absorpce
sin0
abAIdI
Energie z hloubky t za 1 s
a b
GteA
Lineární absorpční koeficient
sinsin
sinsin G
2
22 sinsin
cossin2
sin
2
cossin
2
2cos
12cos
Asymmetric powder diffraction geometry
1
2
3
h1k1l1
h2k2l2h3k3l3 2 scan
Small constant angle of incidence
Parallel beam = 2 – 10
Picture from Seifert poster
XRD Seifert - FPM
X-ray tube
Detector
Monochromator
Parallel plate collimator
Sample holder
Slits
C. Bragg-Brentano asymmetric powder diffraction geometry
1
2
3
h1k1l1
h2k2l2
h3k3l3
TextureStress
goniometer
goniometer - 2 scan
Philips X’Pert MRD
X-ray tubeParallel plate
collimator
Detector Goebel mirror
Sample stage
Eulerian cradle
Polycapillary
Texture and Stress
5 10 15 20 25 30
0
100
200
300
400
500
I(cp
s)
PbTiO3
scan
Omega sken
Korekce na absorpci a defokusaci
FWHM
- sken
Texture, stress
Pole figures
Pole figure (100) for the samples of different thickness. The asymmetry of the texture (left, middle) as well as the inclination of the texture (right) can be seen in 2.5D plot.
935 nm515 nm 2000 nm
2D reciprocal space scan
scan
scan
2 scan
Ideal single crystal
Ideal polycrystal
Textured polycrystal
0
Zbytková napětí
01211,
2012,
1 32
1, sssssss hklRhklR
Homogenní napětí 1. druhu
Může být určováno přímo známou metodou sin2 kdy musí být vzorek nakláněn na různé úhly ze symetrické polohy tak, aby difraktovaly atomové roviny různě skloněné vůči povrchu. Uvedený výraz platí přesně pouze pro jednoosá napětí 0 pro symetrickoul Braggovu-Brentanovu geometrii).
hklhkl ssd
d1
22 2sin
2
1
Rtg elastické konstanty
Elasticky izotropní materiály
Elastická anizotropie +Reussův model ( konst.
maximální závislost na hkl )
… Poissonovo číslo, E … Youngův modul
cos cot
a
111200
311400
a0
Hodnota bez napětí
tlakové napětí
222 311
Back
44121102222
222222
5.0,)(
sssslkh
lklhkh
Es
Es
1, 21
2 sken
goniometr
goniometr
422 422
Crystallite Group MethodBB - BB -
For thin films and some bulk materials the orientation of grains with respect to the surface may be very important. Differently oriented grains can have very different
defect content and/or be in very different stress state.
Therefore it is desirable to measure various crystallite families (texture components) rather than individual planes. Of course, as it is not the case of single crystals, other
crystallites always contribute to the profile (less for strong texture).
Hloubka průniku
Hloubka průniku
Efektivní hloubka průniku
Informační hloubka
Přispívající tloušťka
Ekvivalentní tloušťka
Nekonečná tloušťka
t
t
tdtdII0
11
ln rt
Poměr energií difraktovaných tenkou vrstvou
na povrchu a tenkou vrstvou v hloubce t
rzdIzdIrGr )0(/)(;1
ln1
ere
Gt
Gtt t
i e
te
GAdzdzz
1
1/
0 0
GtRR
RGR
tzI
zI
Re)1(
1ln
1
)(
)(
G
e
G
Gt
eq
1
Hloubka průniku
- 2
2SB, PB)
Titanium Oxide - At 520 KTitanium Oxidea: 3.77100
Titanium Dioxideb: 5.44900
RutileP42/mnm
4.59774.5977 2.9564
AnataseI41/amd
3.77103.77109.430
BrookitePbca
9.1745.449 5.138
400
350
300
250
200
150
100
50
0
Powder Simulation
20.0 25.0 30.0 35.0 40.0 45.0 50.0
350
300
250
200
150
100
50
0
Powder Simulation
20.0 25.0 30.0 35.0 40.0 45.0 50.0
180
160
140
120
100
80
60
40
20
0
Powder Simulation
20.0 25.0 30.0 35.0 40.0 45.0 50.0
Rutile
Anatase
Brookite
10 30 50 70
2
0
200
400
600
I(cp
s)
3 deg, 100 C3 deg, 300 CBB, 300 C
Thickness - 0.6 mParallel beam geometryBragg-Brentano symmetric geometry
Anatase
Amorphous
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0 0.1 0.2 0.3 0.4 0.5 0. 6 0.7 0.8 0.9 1
measurements from both XRD7 and X’Pert diffractometers-2 scans2 and
Williamson-Hall plot
sin
Inte
gral
bre
adth
(1
/d) h = 800 nm
ann. 300 Co
Williamson-Hall plot
Crystallite size> 100 nm
Microstrain~ 0.15 %
~ 1/crystallite size
~ microstrain
sin41
)/1( hkl
hkl
hkl e
Dd
Apparent crystallite sizeLattice strain e=d/d
Texture indices
2.0/250 2.0/300 1.7/300 1.5/300 1.2/300
101 1.2 1 1.2 1.6 1.7
004 3 2.1 1.3 1.1 1.1
112 0.5 0.5 0.8 1 0.9
200 1.2 0.9 0.7 1 1.1
105 1.6 1.2 1.1. 0.9 1
211 0.6 0.5 0.6 0.9 0.9
Thicker Thinner
Fiber texture
Residual stress
• isotropic elastic constants (E = 190 GPa, ν = 0,31)
• tensile stress• at 500 C drop of stress• stresses ~ 200 - 300 MPa • typical stress anisotropy
1.2632
1.2634
1.2636
1.2638
1.2640
1.2642
1.2644
1.2646
1.2648
1.2650
1.2652
1.2654
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
d-sp
acin
g (A
)
sin ² (Psi)
Stress: 383,5 ± 19,9 MPaPhi = 0,0°
1,54 m at 300 C for (215)
Typical linear dependence
Isotropic stress, absence of tri-axial stresses
Stress
Thickness [nm]
[MPa]
300 C
350 C 500 C
200 341 151
630 187 187 42
800 219 209 -
1000 184 154 -
1500 240 163 -
1700 280 232 -
2000 293 252 -
0 . 0 0 . 2 0 . 4 0 . 6 0 . 8
1 . 6 9 8
1 . 6 9 9
1 . 7 0 0
1 . 7 0 1
d(
10
5)
[A]
s in2
1 . 5 m , 3 0 0 ° C
1 . 5 m , 3 5 0 ° C
Stress anisotropy
(103
)
(004
)
(112
)
(200
)
(105
)
(211
)
(116
)
(220
)
(215
)
0.000
0.001
0.002
0.003
0.004
0.005
0.006
sl
ope
of s
in2
plo
t
diffraction peak
0.2 m, 300°C 0.8 m, 300°C 0.8 m, 350°C 1.5 m, 300°C 1.5 m, 350°C
105 211
300 ºCTensile stress~ 200 MPa
500 ºCno stress
Diffraction peaksFor different inclinations
X-ray reflectivity
1n
510~,),(1 in
Refraction index
eer 2
2
4
re = 2.818 10-15 m - wavelength
electron densityabsorption length
2c
Critical angle
)(2
1 21
20 iffN
rn at
Total reflection
Surface roughness, film thickness
1 2 3100
101
102
103
104
105
106
107
Ref
lect
ivity
angle (deg)
t=0,054m
1 2 310-5
10-4
10-3
10-2
10-1
100
Ref
lect
ivity
2 (degrees)
Perfectly smooth surface
0.3 nm roughness
)/sin16exp( 2220 igRR
Reflectivity is sensitive onlyto the projection of the surface profileto its normal direction
It cannot distinguish betweenmechanically and chemically rough surface
~ 1/t
Kiessig maxima mt cim
22 sinsin2
Visible up to ~ 300 nm
250 ºC
350 ºC
450 ºC
TiO2 200 nm
Increasing roughness with annealing temperature
TiO2 200 nm250 ºC
Ω scans
TiO2 1 700 nm
Ω scan
350 ºC
Reflectivity curves
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.510-2
10-1
100
101
102
103
104
105
106
107
t= 1.0 m t= 1.7 m t= 0.054 m t= 1.24 m
Re
flekt
ivita
úhel (stupně) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
10-2
10-1
100
101
102
103
104
105
106 as deposited
350 oC
450 oC
Ref
lect
ivity
2
Increase of roughness with film thicknessReduction of very thin surface layer with
annealing temperature
2
Reflectivity curves fitting
Incident angle (°)1.110.90.80.70.60.50.40.30.20.10
Inte
nsity
(co
unts
/s)
0
1
10
100
1,000
10,000
100,000
Incident angle (°)0.50.40.30.20.10
Inte
nsity
(co
unts
/s)
0
1
10
100
1,000
10,000
100,000 0,054 m 350 C
0,8 m 300 CTwo layer model necessarySurface porous layer
Fitted
Experimental
Surface roughnessThickness
[nm]Fitted
thickness[nm]
Electron density[g.cm-3]
Roughness [nm]
54 57 3.42 1.2
100 93 3.58 1.7
200 200 3.48 1.8
630 569 3.53 4.12nd layer 57 3.64 7
1000 968 3.89 22nd layer 49 3.68 5
1700 1791 3.89 22nd layer 55 3.74 5
Depth profiling
Rutile growths on the interface while anatase is on the top
Different angles of incidence ()
0.5 0.75 1.01.52.0
Anatase 101
Rutile 110
thickness – 1 m
0.5 0.75 1.01.52.0
Angles of incidence in degreesAnatase
Rutile
Rutile growths on the interface while anatase is on the top
thickness 935 nm
Effective penetration depth
100 nm
4
150 nm200 nm300 nm00 nm
Reflection on multilayers
Bragg maxima of multilayer
Period d
Kiessig maxima
Total thickness T
indk 22 cos2
BA ddd
)sin(sin2 12
k
d
d = T
Number of ML periods
10x(GaAs 7nm/AlAs 15 nm),CuK1
Kinematical approx:No total reflection region,wrong positions of the satellites (refraction not considered)
1 2 3 410-6
1x10-5
1x10-4
10-3
10-2
10-1
100
101
102
103
104
Ref
lect
ivity
2 (degrees)
Annealing of amorphous9x(5 nm Si/ 1 nm W)
Experimental set-up
X-ray tubeCuK
Göbel mirror
Sample
Secondary graphite monochromator
Detector
Slit 0.1mm
Slit 0.05 mm
Diffuse scatteringnon-specular conditions Thermal fluctuations
Correlated layer distortions
Height-height correlationfunction
)0,0(),(),( zYXzYXC
hRRC 22 )/exp()(
Effective cut-off length of theself-affine surface
)0,0(),(),( kjjk zYXzYXC
For multilayers
)/||exp( kjkjjk ZZCCC
Vertical interface roughnesscorrelation
Fe/Au (70Å/21Å)x13
-6000 -4000 -2000 0 2000 4000 60002000
4000
6000
1.11
2.22
3.33
Sample inclination
Dete
ctor
angle
-0.56 -0.560-1.11 1.11 1.67-1.67
Low correlation of the interface roughness
Dynamická difrakce
Dynamical diffraction Shift from the kinematical Bragg position (due to refraction)
Finite width of the diffraction curve (even for T→0)
Asymmetry of the maximum – due to the Borrmann effect
Strongly interacts with the atoms – Anomalously high absorption
Weakly interacts with the atoms – Anomalously low absorption
The Borrmann effectThe Borrmann effect
Wavefields in crystal
Tloušťka
strain
Epitaxní vrstvy
ImplantaceSi – B+
bez implantace
D = 6,2.1015
D = 3,1.1014
D = 6,2.1015
a žíhání 1000 ºC
X-ray grazing incidence diffraction
W ~ 1.8 nm na Al2O3
a|| = 0.3184 nma0 = 0.3165 nm|| = 0.6 %<D||> 5 nm
sken
Mozaiková rozorientace ~ 1.1º
MBEMo 22 nm (111)na(001) GaAs
Tři doményMo[110] || GaAs [110] GaAs [1-10] GaAs [100]Mismatch B || -10.2 % ┴ +3.7 % C ┴ +27 %<D> ~ 13 nm
Jedna doménaNb[110] || GaAs [100]Nb(001) || GaAs (001)
Mismatch 21.1 %
Standing waves
Standing waves
)cos(
||
||2
||
||1||)(
02
0
22
0 rhE
E
E
EErI hh
Reciprocal lattice vectorAmplitude of incoming wave
Phase of (Eh/E0)Amplitude of diffracted wave
Reflection curve – 1Phase – 2Intensity at atomic planes – 3
Maximum interactionfor = 0, at high angle side of reflection curve
Monolayer of adsorbed atoms
Yield of the fluorescent radiation
High sensitivity to displacement of layer~ 1 % !!!
Adsorbed layersThree adatomsat 0, 1/3, 2/3
Parallel planes
Inclined planes
ExperimentMeasurements of secondary radiationunder the condition of diffraction
Determination of coherent position – mean plane of the adsorbed atomsand coherent fraction – static and dynamic displacement of atoms from the coherent position
FluorescencePhotoelectronsAuger electronsCompton radiation
Chemical selectivitySpatial resolution on atomic scaleDepth-resolved studies
Organic materialsLong-period standing waves are necessary
Total reflection SW is formed as an interference between incidentand specularly reflected waves
Bragg diffraction from layered synthetic microstructures with large period
10-200 layer pairs (low and high electron density)
Fixed period XSW
Height dependence of electric field intensitygenerated during specular reflection of an X-ray plane wave from the mirror surfaceat three angles of incidence
Marker atom A – two E-field maximamarker atom B – five E-field maxima
= 0.1 c
= c
XSW applicationMonitoring of membrane-related dynamic processes
membrane-lipid phase transitionsion movement in membrane
Protein foldingMembrane-protein insertionLipid and/or protein distributionsSurface binding
Distribution of marker atom above the substrate surface
Theoretical model Experimental fluorescence, Reflectivity data
Layered model of refractive indexbased on the known structure
Adjusting of interfacial roughness
Features of XSW
Resolution ~ 1 % of LSM d (for 50 Å - 0.3 Å, 925 Å - 3 Å)
Element specificity (not suitable for light elements, O, P, S)
Structure-determination measurement on isolated lipid membranes(protein monolayers ~ 10 pmol (100 ng) of cytochrome c)
Calculation of the angle-dependent electric-field profileand fluorescence-yield profile normal to the surfaceAdjusting two parameters
Membrane-topology measurements on minimally perturbed systems(Fe XSW on Fe-cytochrome c)