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transcript
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Good Diffraction Practice
Webinar Series
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X-ray Reflectometry – Jul 21, 2010
Two-Dimensional XRD – Aug 11, 2010
Powder XRD – Sep 30, 2010
www.bruker-webinars.com
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Welcome
Dr. Martin ZimmermannApplications Scientist, XRDBruker AXS GmbHKarlsruhe, Germanymartin.zimmermann@bruker-axs.de+49.721.595.4655
Peter LaPumaVice President of Sales & MarketingBruker AXS Inc.Madison, Wisconsin, USApeter.lapuma@bruker-axs.com+1.608.276.3000
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Overview
Introduction
Appropriate samples for XRR
Adapting the experimental setup
Performing an XRR experiment
Data interpretation
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What is X-ray Reflectometry (XRR)?
A surface-sensitive x-ray scattering technique
• Non-destructive method• Wavelength probes on nanometer scale• Works for crystalline and amorphous materials
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What is X-ray Reflectometry (XRR)?
A surface-sensitive X-ray scattering technique
• Non-destructive method• Wavelength probes on nanometer scale• Works for crystalline and amorphous materials
What does XRR provide?
• Layer thickness 0.1 nm – 1000 nm• Material density < 1-2%• Roughness of surfaces and interfaces < 3-5 nm
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The general scattering geometry
ikr fk
r
if kkqrrr
−=θ2
22 )exp()()( rdrqirqS
V
rrrrr∫∝ ρ θ
λsin2
=d
Probed quantity Probed lengthscale
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Wavevector transfer has a non-zero component perpendicular to the sample surface
For Cu-Kα (λ=1.54Å)
XRR probes the laterally averaged electron density
yxzyxz
,),,()( ρρ =
The specular XRR scattering geometry
q=(0,0,q )z
ki kf
θ θ
zx
θsin2kqz =
22 )exp()()( ∫∝ dzziqzqS zz ρ
][140/2 1−= nmqz θ
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The reflectivity from a substrate –in one minute
0 z
ρ( )z
exp(iqz)
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The reflectivity from a substrate –in one minute
0 z
ρ( )z
exp(iqz)
R exp(-iqz)
T exp(iQz)
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The reflectivity from a substrate –in one minute
0 z
ρ( )z
exp(iqz)
R exp(-iqz)
T exp(iQz)
ρπ erqQ 162 −=2
2)()(QqQqqRqr FF +
−==
Fresnel reflectivity
with
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Density dependency of the reflectivity
The higher the electron density ρ(z) of a material the higher the critical angle
The higher the electron density, the more intensity is scattered at higher angles
This limits the accessible angular range for light materials like soft-matter films
ρθ ∝c
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2⎟⎠⎞
⎜⎝⎛≈
θθcr
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Influence of roughness (1)
Wavinesssmall inclinations of the surface normalon a large scale of some 100 nm
wavinessbroadening of the specularreflected beam
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Influence of roughness (1)
Wavinesssmall inclinations of the surface normalon a large scale of some 100 nm
waviness
microscopicroughness
broadening of the specularreflected beam
Microscopic Roughnesslarge inclinations of the surface normal on an atomic scale of a few nanometers
leads to diffuse reflection of the incident beam the intensity of the specular reflected beam decreases
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Influence of roughness (2)
Modeling microscopic roughness
Interface is represented by an ensemble of sharp interfaces
⎟⎟⎠
⎞⎜⎜⎝
⎛−= 2
2
2 2exp
21)(
σπσzzw
rms-roughness σ: = standard deviation of the Gaussian distribution
)(zw
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Influence of roughness (2)
Modelling microscopic roughness
Interface is represented by an ensemble of sharp interfaces
⎟⎟⎠
⎞⎜⎜⎝
⎛−= 2
2
2 2exp
21)(
σπσzzw
rms-roughness σ: = standard deviation of the Gaussian distribution
modified reflection coefficients for rough interfaces:
( )2/exp 22zqσ−
)(zw
)()( zFz qRqR = Exponential decay
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Influence of roughness (3)
Roughness decreases the reflected intensity dramatically
XRR is highly sensitive to roughness
Roughness causes diffuse scattering
The interface roughness should not be larger than
2-3 nm.
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The interference of the waves reflected from the interfaces causes oscillations of period
The minimal observable thicknessis limited by the maximal measurable range
The maximal observable thicknessis limited by the instrumental resolution
The sample should have thicknesses observable with the
instrumental setup.
XRR from Multilayers: Thickness fringes (1)
dqz /2π=Δ
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Thickness fringes (2): Amplitude
Amplitude of the thick-ness fringes increases with increasing density contrast
XRR is quite sensitive to variations of the electron density
The sample should have a good contrast in the
electron density.
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X-ray ReflectometryDemands on Sample Properties
Golden Rule:
You should be able to see your reflection on the surface of the
sample!
Flat and lateral homogeneous - not structured
Sample roughness < 5nm
Good contrast in electron density for layered samples
Length of at least 2-5 mm in beam direction
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Audience poll
Please use your mouse to answer the question to the right of your screen:
What percentage of your samples match the criteria for XRR samples?
o < 10 %o 10 % - 30 % o 30 % - 50 % o 50 % - 80 % o 80 % - 100 %o 100 %
Criteria for XRR samples
Flat and lateral homogeneous -not structured
Sample roughness < 5nm
Good contrast in electron density for layered samples
Length of at least 2-5 mm in beam direction
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Instrumental resolution in XRR
qki
kf
θ θ
The ideal instrument
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Instrumental resolution in XRR
The scattering function S is convoluted with the resolution function R of the instrument:
Δθi Δθf
qki
kf
ΔqzΔqz
Δqx
θ θ
∫ −= dQQqRQSqI )()()( 2
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Rough estimation of the resolution: FWHM of the direct beam ΔΨ
Instrumental resolution in XRR
θθ Δ=Δ )cos(2kqz
The scattering function S is convoluted with the resolution function R of the instrument:
Δθi Δθf
qki
kf
ΔqzΔqz
Δqx
θ θ
θΔ=Δ zx qq
∫ −= dQQqRQSqI )()()( 2
2/ψθ Δ=Δ
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Rough estimation of the resolution: FWHM of the direct beam ΔΨ
Observation of thickness fringes requires resolution better than
Instrumental resolution in XRR
θθ Δ=Δ )cos(2kqz
The scattering function S is convoluted with the resolution function R of the instrument:
Δθi Δθf
qki
kf
ΔqzΔqz
Δqx
θ θ
θΔ=Δ zx qq
d2/λθ <<Δ∫ −= dQQqRQSqI )()()( 2
2/ψθ Δ=Δ
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The experimental setup for XRR
Parallel beam geometry
Setups with different resolutions
The footprint
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Simplest setup for XRR
Reasonable resolution requires slit of 50-100 µm Intensity is on the order of 107 cpsFull energy spectrum creates high background
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Principle of the Göbel Mirror
Mirror converts ≈0.35° into a parallel beam of 1.2 mm (60-mm mirror)Integrated intensity >109 cpsMainly Kα-radiation is reflected
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Handling the high flux: AutomatedAbsorber
Scintillation counters linear up to 2 x 105 cps
10,000 times more intensity from the tube side
4-position wheel with places for 4 different absorber foils
standard absorption factors:
1 - ~10 - ~100 - ~10000Rotary absorber
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The standard XRR setup for thin films
Slits can be easily exchanged to tune resolutionA reasonable resolution requires a slit size of 0.1 – 0.2 mm Integrated intensity ≈ 2x108 cps
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Reflectometry with different slits
with 0.1 mm slit
~ 6.5 h
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Reflectometry with different slits
with 0.6 mm slitwith 0.1 mm slit
~ 5 min~ 6.5 h
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XRR setup for very thin layers
Full beam on primary sideSoller with resolution down to 0.1°Integrated intensity ≈ 8x108 cps
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Limits of X-Ray Reflectometry Thin layers Example: LaZrO on Si
2θ [°]1412108642
Inte
nsity
[au]
-81*10
-71*10
-61*10
-51*10
-41*10
-31*10
-21*10
-11*10
01*10
Si (111)
6.7 nm LaZrO
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XRR with an analyzer crystal
Analyzer crystal separates Kα1, suppresses diffuse scattering and fluorescenceCrystal can accept the full incident beamIntegrated intensity ≈ 3x107 cps (for a 3-bounce analyzer)
Analyzer crystal improves the resolution:
1-bounce Ge(220)3-bounce Ge(220)
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XRR setup for thick layers
Analyzer crystal: 1-bounce Ge(220s)3-bounce Ge(220s)
Monochromator crystal: 4-bounce Ge
Monochromator cystals provide highly parallel and monochromatic beamCrystals can accept the full incident beam Integrated intensity ≈ 105 - 106 cps
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Limits of X-ray Reflectometry Thick layers example: SiO2 on Si
Int. [a
u]
5
10
100
1000
1e4
2θ [°]
0.11 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Si
1014 nm SiO2:H
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For Cu-Kα radiation: λ ≈ 1.54 ÅValues for Δθ were obtained by scanning the direct beamObtained from the rough estimation
Resolution of differents setups
θλ Δ≈ 2/d
Tube side Detector side Δθ [deg] dmax [nm]
GM + 1.2mm 0.2° soller 0.06° 73
GM + 0.2mm 0.2mm slits 0.029° 150
2xGe(220a) 0.2mm slits 0.026° 170
GM 3xGe(220s) 0.013° 340
2xGe(220a) 3xGe(220s) 0.01° 440
4xGe(220s) 3xGe(220s) 0.006° 735
4xGe(440s) 3xGe(220s) < 0.006° > 735
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Please use your mouse to answer the question to the right of your screen:
What is the typical film thickness of your XRR samples?
o Very Thin layers < 10 nm
o Thin layers 10 nm – 100 nm
o Medium 100 nm – 200 nm
o Thick layers 200 nm – 350 nm
o Very Thick layers > 350 nm
Audience Poll
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Influence of X-ray wavelength on the reflectivity
Higher wavelength + better resolution of fringes and higher critical angle- high air-absorption reduces intensity + air scattering
290 nm boron on silicon
(2.29Å)
(1.54Å) Poll Results
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Adapting the optics to the sample
brings the best results
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Easy change of the resolution on the tube side…
Rotary absorber
X-ray tube
Goebel mirrorslit-holder
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…and more resolution…
Rotary absorber
Goebel mirrorslit-holder
X-ray tube
2-bounce Ge(220a)
monochromator
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…and even more resolution
Rotary absorber
Goebel mirrorslit-holder
X-ray tube
4-bounce Ge(220s)
monochromator
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Automated change of the resolution on the detector side
Motorized switch between• one high-resolution beam path• and two high-flux beam paths
PATHFINDERoptics
Motorized slit Use of multiple beampath optics allows changing the resolution within seconds
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Automated change of the resolution on the detector side
Soller + slit Motorized slit
Double slit system for intermediate resolution
Analyzer
Analyzer crystal with high resolution
Soller for high flux / low resolution
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Documentation of the experimental setup
A detailed documentation of the experimental setup is mandatory for proper data-analysis
• Resolution function• Footprint correction
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Geometrical corrections –The footprint (1)
d : beam widthL : sample length || beamD : illuminated area
L
d
θ
D
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Geometrical corrections –The footprint (1)
)/arcsin( LdB =θ)sin(/)sin( BB θθ=
θsin/dD =
d : beam widthL : sample length || beamD : illuminated area
L
d
θ
D
Footprint of the beam on surface
Beam matches the sample size at
Below θB the intensity is reduced by
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Geometrical corrections –The footprint (2)
Beamsize : 200 µm
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Controlling the footprint – The Knife Edge Collimator (1)
The KEC allows the removal of the footprint effect by making the probed area smaller than the sample sizeFor higher angles, the KEC needs to be lifted from the surface to gain fluxThe measurement with KEC will be upscaled to the curve without KEC
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0,0 0,5 1,0 1,5 2,0104
105
106
107
108
with KECwithout KEC
Inte
nsity
2θ [deg]
Controlling the footprint – The Knife Edge Collimator (2)
Measurement with KEC must be performed up to at least 2θB
The high-angle measure-ment without KEC must have an overlap with the KEC – measurement to rescale the data properly
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Performing an XRR measurement
Sample alignment procedure
Measurement strategy• Statistics• Diffuse scattering
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Sample alignment in 5 steps…
Ideal sample alignment
Situation after sample mounting
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Sample alignment (1): Defining the 2θ scale
2θ
2 =0°θ
Detector scan without sample
2θ aligned to primary beam
0I
θΔ2Instrumental resolution
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z
I(z )=I /21/2 0
Sample alignment (2): First height alignment
2/0I
2/1z
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ω
Sample alignment (3): Coarse alignment of the surface normal
maxω maxω
2/maxI
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z
I(z )=I /21/2 0
Sample alignment (4): Fine height alignment
2/0I
2/1z
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Sample alignment (5): Alignment of the reflection condition
ω
ω–offset of surface relative to drive:
max2/2 ωθω −=Δ
°= 4.02θ
maxω
Waviness /domains on the sample surface
θΔ
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Sample alignment: Remarks
Bθω
Determination of the footprint angle θB
If the rocking-curve in reflection condition is slighty distorted, e.g. peak shoulders, align the sample at higher angles (reduction of the illuminated area)
If the triangle is not symmetric, the sample is not centered along the beam.
If the rocking-curve in reflection condition is strongly distorted, e.g. multiple peaks, rotate the sample 90° or translate the sample along the beam
No improvement: Reduce the beam size/width and/or if available use KEC
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Proper analyses require that the statistics is better than the amplitude of the oscillations
The decay of the reflected intensity requires longer counting time at larger angles to keep the statistics good
Keeping the statistics high – Variable counting time
)()( θθ II ±
1000 count level
CPS
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What do we measure?
Data provided by S. Tiemeyer, TU Dortmund
GaAswafer
Can we analyze this measurement
properly?
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Measuring the diffuse background
XRR
ki kf
Δqx
θ θ
Δθ
longitudinaldiffuse scan
diffuse scattering
Imperfections - like roughness - cause diffuse scattering
Diffuse scattering contributes to the reflectivity
Theory of XRR does not account for diffuse scattering
Perform a longitudinal diffuse scan to estimate the diffuse scattering in the specular direction
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True specular reflectivity
Diffuse scattering limits the accessible 2θ range
Measurement of the diffuse scattering is time-consuming
Choose large step-size and interpolate
Extracting the true specular reflectivity
Data provided by S. Tiemeyer, TU Dortmund
)2()2()2( θθθ diffXRRTS III −=
GaAswafer
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Analysis of XRR curves
Fitting of XRR curves
Examples
Limitations
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Account for the instrumental setup
Analytical calculation of the resolution functionCalculation of the footprint-correction
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Evaluation of SampleFitting Procedure
Sample Model parameterized by {p1,…pN}
Tolerance
XRR Simulation
Comparison with Experiment, χ2 cost function
Minimization of χ2 using Genetic Algorithm, Levenberg-Marquardt, Simplex,Simulated Annealing, etc. in view of {p1..pN}
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Amorphous HfO2 film – Ultra thin films
θ [degees]
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XRR on MEMS – Ru/SiN film
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GMR Heterostructure – 8 Layers
Sample courtesy of Dr. Schug, IBM Mainz
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Limits of XRR: Uniqueness of the solution (1)
Data provided by S. Tiemeyer, TU Dortmund
Everything depends
on the sample model...
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Limits of XRR: Uniqueness of the solution (2)
0 1 2 3 4 5 6
100
101
102
103
104
105
106
107
meas sin-function (2-layers)
Inte
nsity
[a
.u.]
2θ [degrees]
007.02 =χ
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0 1 2 3 4 5 6
100
101
102
103
104
105
106
107
meas error-function (3-layers)
Inte
nsity
[a
.u.]
2θ [degrees]
007.02 =χ
Limits of XRR: Uniqueness of the solution (3)
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Limits of XRR: What can we really have access to?
0 1 2 3 4 5 6
100
101
102
103
104
105
106
107
meas simulation
Inte
nsity
[a
.u.]
2θ [degrees]
006.02 =χ
What does the sample-modellook like???
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Limits of XRR: What can we really have access to?
0 1 2 3 4 5 6
100
101
102
103
104
105
106
107
meas simulation
Inte
nsity
[a
.u.]
2θ [degrees]
006.02 =χ
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Choose the right optics
Align the sample properly
Remember to account for diffuse scattering
Do not over-interpret your data
Never forget about the limited spatial resolution
Summary
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Summary
Choose the right optics
Align the sample properly
Remember to account for diffuse scattering
Do not over-interpret your data
Never forget about the limited spatial resolution
Thank you for your attention…
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Any Questions?
Please type any questions you may have in the Q&A panel and then
click Send.
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To Learn More About XRD and XRR
Bruker Training Central (BTC) – Online Training CoursesWeb-based training courses delivered through your browserInclude slides, audio, video and participant Q&AUpcoming live:• Aug 11 – Good Diffraction Practice II: Two-Dimensional XRD (1 hr)• Sep 30 – Good Diffraction Practice III: Powder XRD (1 hr)• Oct 5-6 – X-ray Reflectometry (2 hrs)
On-demand:• Fundamentals of Powder XRD• Powder XRD Data Acquisition & Analysis• Basics of Two-Dimensional XRD• Getting Started with LEPTOS• Getting Started with TOPAS www.brukersupport.com
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