25/06/2015
X-ray powder diffraction (XRD):Basic principles & practical applications
Ruben SnellingsVITO (BE)
25/06/2015 2© 2014, VITO NV
For starters
» Belgian national» MSc in Geology» 2007-2011: PhD in Geology (KULeuven, BE),
“Pozzolanic properties of natural zeolites”» 2011-2012: Post-doc (UGent, BE),
“Recyclable Concrete”» 2012-2014: Post-doc/Marie Curie Fellow (EPFL, CH),
“SCM reactivity” + XRD responsible» 2014-now: Researcher (VITO, BE),
“Sustainable binders”
25/06/2015 3© 2014, VITO NV
The menu/contents
» Why use X-ray powder diffraction to study cements?
» Basics on Scattering, Diffraction and X-rays
» Practical guidelines for XRD experiments
» Data Analysis: The Rietveld Method
» Examples of applications
» Practical guidelines for XRD data analysis
25/06/2015 4© 2014, VITO NV
XRD and cement – why?
» Delivers information on:» Individual phases contained in (hydrated) cement:
» Content (also during hydration)» Crystal structure, …
» Why would you need this?» To describe hydration kinetics and mechanisms» Parametric studies on effect of e.g. grinding, sulfation, temperature…
» Advantages vs. other techniques (SEM, TGA, calorimetry)? » Takes less time» Extracts wealth of information
25/06/2015 5© 2014, VITO NV
XRD & cement – since when?
1900 20001950
2050
1987:Rietveld methodfor quantitative analysis(Hill & Howard)
1895:Discovery of X-rays(Röntgen)
1912:XRD on crystals(von Laue)
1969:Rietveld methodfor neutron diffraction(Rietveld)
1977:Rietveld methodfor XRD(Cox, Young, Thomas)
1993:1st Rietveld QPA on cement(Taylor & Aldridge)
1928:1st XRD studies on cement(Hansen, Brownmiller)
2000s:Spread of XRD in cement science
25/06/2015 6© 2014, VITO NV
XRD & cement - challenges
» Multitude of phases» Peak overlap» Sensitivity of hydrates to decomposition» Many correlated parameters
» Aim of this workshop:» Explain the basics of XRD» Identify common pitfalls» Demonstrate best practice
25/06/2015 7© 2014, VITO NV
Basic principles of XRD
25/06/2015 8© 2014, VITO NV
Scattering basics
kikf
q
2θIncident radiation:Wavevector: ki
|ki| = 2π/λEnergy: EiPolarisation: pi
Wavevector transfer:q = kf - ki
Energy transfer: ΔE = Ef - Ei
Polarisation change:pi → pf
Scattered radiation:Wavevector: kfEnergy: EfPolarisation: pfScattering angle 2θ
Scattering geometry
25/06/2015 9© 2014, VITO NV
Scattering basics
k0k
Q
2θIncident radiation:Wavevector: k0
|k0| = 2π/λ Wavevector transfer:Q = k - k0
Scattering angle 2θ
Scattered radiation:Wavevector: k
|k| = 2π/λ
Elastic scattering
25/06/2015 10© 2014, VITO NV
Diffraction on crystalsFor an incident beam to be diffracted by a crystal, its
wavelength must be of the same order of magnitude as the interatomic distances (a few angströms)
Photographicplate
Diffractedbeams
crystalIncoming X-rays
Laue experiment (1912)
25/06/2015 11© 2014, VITO NV
Diffraction on crystals» Bragg condition
The diffraction by a 3D lattice of points is equivalent to a reflectionof the incident beam on a family of net planes
plane 1
plane 2
B C
I
G
HF
A D
d
The beams IC and GD scattered by 2 adjacent planes must be in phase to getconstructive interference
FG + GH = nλwith FG = GH = d.sinθ
nλ = 2d sinθ
Bragg’s law
25/06/2015 12© 2014, VITO NV
Diffraction on crystals
» Single crystal vs powder diffraction
singlecrystal
powderI
2θ
Data compressed into one dimension
25/06/2015 13© 2014, VITO NV
Powder diffraction: laboratory configurations
X-ray source detector
sample
2θ
Reflection geometry
X-ray source detector
sample
Transmission geometry
25/06/2015 14© 2014, VITO NV
Laboratory Bragg-Brentano (reflection)
25/06/2015 15© 2014, VITO NV
Laboratory Transmission mode
Laboratory source
Synchrotron source (ESRF)Multichannel detector for fast data acquisition
25/06/2015 16© 2014, VITO NV
Data Analysis: the Rietveld method» Rietveld (1969): diffraction pattern analysis by a
curve fitting procedure» First proposed for neutron diffraction» Least-squares minimization between observed and
calculated profiles» Extended to XRD profiles in the 1970’s
25/06/2015 17© 2014, VITO NV
Inside the powder diffraction pattern
2θ - degrees
Coun
ts
1. Peak positions determined by size and
symmetry of the unit cell– the lattice
2. Peak Intensitiesdetermined by the
positions of the atoms in the unit cell – the motif
3. Peak widthsinfluenced by size/strain of
crystallites – the microstructure
25/06/2015 18© 2014, VITO NV
Inside the powder diffraction pattern
2θ - degrees
Coun
ts
1. Peak positions determined by size and
symmetry of the unit cell– the lattice
2. Peak Intensitiesdetermined by the
positions of the atoms in the unit cell – the motif
3. Peak widthsinfluenced by size/strain of
crystallites – the texture
25/06/2015 19© 2014, VITO NV
Inside the powder diffraction pattern
Peak positions» Bragg’s law
» d-spacing formulae» Cubic (a)
» Triclinic (a, b, c, α, β, γ)
λ = 2dhkl sinθ
1𝑑𝑑2
=ℎ2 + 𝑘𝑘2 + 𝑙𝑙2
𝑎𝑎2
1𝑑𝑑2
=1𝑉𝑉2
[ℎ2𝑏𝑏2𝑐𝑐2𝑠𝑠𝑠𝑠𝑠𝑠2𝛼𝛼 + 𝑘𝑘2𝑎𝑎2𝑐𝑐2𝑠𝑠𝑠𝑠𝑠𝑠2𝛽𝛽 + 𝑙𝑙2𝑎𝑎2𝑏𝑏2𝑠𝑠𝑠𝑠𝑠𝑠2𝛾𝛾+ 2ℎ𝑘𝑘𝑎𝑎𝑏𝑏𝑐𝑐2 𝑐𝑐𝑐𝑐𝑠𝑠𝛼𝛼 𝑐𝑐𝑐𝑐𝑠𝑠𝛽𝛽 − 𝑐𝑐𝑐𝑐𝑠𝑠𝛾𝛾 + 2𝑘𝑘𝑙𝑙𝑎𝑎2𝑏𝑏𝑐𝑐 𝑐𝑐𝑐𝑐𝑠𝑠𝛽𝛽 𝑐𝑐𝑐𝑐𝑠𝑠𝛾𝛾 − 𝑐𝑐𝑐𝑐𝑠𝑠𝛼𝛼
25/06/2015 20© 2014, VITO NV
Inside the powder diffraction pattern
2θ - degrees
Coun
ts
1. Peak positions determined by size and
symmetry of the unit cell– the lattice
2. Peak Intensitiesdetermined by the
positions of the atoms in the unit cell – the motif
3. Peak widthsinfluenced by size/strain of
crystallites – the texture
25/06/2015 21© 2014, VITO NV
Inside the powder diffraction pattern
Peak intensities
» For a crystalline phase j in a powder sample:
𝐼𝐼𝑗𝑗,ℎ𝑘𝑘𝑘𝑘 = 𝑆𝑆𝑗𝑗 𝐿𝐿𝐿𝐿 2𝜃𝜃 𝐴𝐴 𝑃𝑃𝑗𝑗,ℎ𝑘𝑘𝑘𝑘𝑭𝑭2𝑗𝑗,ℎ𝑘𝑘𝑘𝑘
Scale factor
Lorentz-polarizationfactor
Absorption factor
Preferred orientationfactor
Structure factor
25/06/2015 22© 2014, VITO NV
Inside the powder diffraction pattern
Peak intensities» Structure factors
» Vector quantity (magnitude F and phase φ)» Summation over all atoms n in unit cell
» X-ray form factor fn (2θ)» Site occupation on
» Interference term: exp(2πi{hx + ky + lz})» Debye-Waller factor Wn
𝐼𝐼ℎ𝑘𝑘𝑘𝑘 ≈ 𝑭𝑭 2ℎ𝑘𝑘𝑘𝑘
𝑭𝑭ℎ𝑘𝑘𝑘𝑘 = �𝑛𝑛
𝑓𝑓𝑛𝑛 𝑐𝑐𝑛𝑛 exp 2𝜋𝜋𝑠𝑠 ℎ𝑥𝑥 + 𝑘𝑘𝑘𝑘 + 𝑙𝑙𝑙𝑙 exp −𝑊𝑊𝑛𝑛
25/06/2015 23© 2014, VITO NV
Inside the powder diffraction pattern
Peak intensities» X-ray form factors fn (2θ): the nature of the atoms
» X-rays interact with atomic electron cloud» The higher Z, the higher fn
» The higher θ, the lower fn
25/06/2015 24© 2014, VITO NV
Inside the powder diffraction pattern
Peak intensities
» Interference term: the position of the atoms
» Reflects atomic structure» Vector dot product between the position of the atom n (rn) in the unit
cell and the scattering vector (Qhkl):
» Not a smooth function of 2θ» Reflections with similar d spacings may have large or small
interference terms
𝒓𝒓𝒏𝒏 = 𝑥𝑥𝑛𝑛𝒂𝒂 + 𝑘𝑘𝑛𝑛𝒃𝒃 + 𝑙𝑙𝑛𝑛𝒄𝒄
𝑸𝑸𝒉𝒉𝒉𝒉𝒉𝒉 = ℎ𝒂𝒂∗ + 𝑘𝑘𝒃𝒃∗ + 𝑙𝑙𝒄𝒄∗
exp(2πi{hx + ky + lz})
25/06/2015 25© 2014, VITO NV
Inside the powder diffraction pattern
Peak intensities: the structure model» Contains lattice parameters
(a, b, c, alpha, beta, gamma)» Symmetry group, space group» Asymmetric unit: atomic coordinates, occupancy, etc.
25/06/2015 26© 2014, VITO NV
Inside the powder diffraction patternPeak intensities» Debye-Waller factors (Wn) or atomic displacement (ADP) factors
» Thermal vibrations → atomic position is not frozen→ time and space average of atoms is larger→ destructive interference→ reduction of peak intensities
» Un is mean-square atomic displacement» Bn often preferred since values are around 1» The lighter the atom the larger the ADP
exp −𝑊𝑊𝑛𝑛 = exp −𝐵𝐵𝑛𝑛𝑠𝑠𝑠𝑠𝑠𝑠2𝜃𝜃
λ2= exp −
𝐵𝐵𝑛𝑛4𝑑𝑑2
= exp −2𝜋𝜋2 𝑈𝑈𝑛𝑛𝑑𝑑2
25/06/2015 27© 2014, VITO NV
Inside the powder diffraction pattern
2θ - degrees
Coun
ts
1. Peak positions determined by size and
symmetry of the unit cell– the lattice
2. Peak Intensitiesdetermined by the
positions of the atoms in the unit cell – the motif
3. Peak widthsinfluenced by size/strain of
crystallites – the microstructure
25/06/2015 28© 2014, VITO NV
Inside the powder diffraction patternPeak widths and shapes» Depend on source, instrument and sample
1. Peak description by analytical functions» Gaussian, Lorentzian, or mixed (Pseudo-Voigt)- symmetric
functions» Extended versions (TCHZ,
Pearson VII,…)» fwhm dependence on 2θ
Gauss: 𝑓𝑓𝑓𝑓ℎ𝑓𝑓 = 𝑈𝑈𝑡𝑡𝑎𝑎𝑠𝑠2𝜃𝜃 + 𝑉𝑉𝑡𝑡𝑎𝑎𝑠𝑠𝜃𝜃 + 𝑊𝑊 �1 2
Lorentz: 𝑓𝑓𝑓𝑓ℎ𝑓𝑓 =𝑋𝑋
𝑐𝑐𝑐𝑐𝑠𝑠𝜃𝜃+ 𝑌𝑌𝑡𝑡𝑎𝑎𝑠𝑠𝜃𝜃
Caglioti et al. (1958)
25/06/2015 29© 2014, VITO NV
Inside the powder diffraction patternPeak widths and shapes» Depend on source, instrument and sample
2. Peak description by separating contributions from source and instrument to that of sample (fundamental parametersapproach)
Instrument ⊗ Source ⊗ Sample = Peak shape
[Cheary et al. 2004]
25/06/2015 30© 2014, VITO NV
Inside the powder diffraction patternPeak widths and shapes» Depend on source, instrument and sample
2. Peak description by separating contributions from source and instrument to that of sample (fundamental parameters approach)
» Allows analysis of sample texture (crystallite size, strain)
» Size contribution
» Strain contribution
𝑓𝑓𝑓𝑓ℎ𝑓𝑓 = 𝑘𝑘λ/𝐷𝐷𝑉𝑉𝑉𝑉𝑘𝑘𝑐𝑐𝑐𝑐𝑠𝑠𝜃𝜃 (Scherrer formula)
Volume weighted mean crystallite size
𝑓𝑓𝑓𝑓ℎ𝑓𝑓 = 4𝜀𝜀0𝑡𝑡𝑎𝑎𝑠𝑠𝜃𝜃
ε0 =Δd/d or mean strain
25/06/2015 31© 2014, VITO NV
Practical guidelines for XRD experiments
25/06/2015 32© 2014, VITO NV
Particle size
» For representative measurements:» High number of particles need to
diffract (particle statistics)» Particle sizes < 10-20 µm required» Ideally 1-5 µm
» Extensive dry grinding may lead toamorphization» Wet grinding preferable
» Sample spinning improves statistics
25/06/2015 33© 2014, VITO NV
Sample loading
Slice(cement paste)
Back-loaded
Front-loaded
Preferred orientation to be avoided
25/06/2015 34© 2014, VITO NV
Hydration stoppage
» Harsh drying conditions effect ettringite –AFm phases» To be avoided for QPA
25/06/2015 35© 2014, VITO NV
Ambient exposure
» Hydrated cement samples are prone to carbonation» Ex. 2 h exposure of fresh slice to air» Both fresh and dried samples are sensitive to carbonation
25/06/2015 36© 2014, VITO NV
Placed in the sample holder with Kapton film
Fresh mix
Hydration is observed every 15 minutes. Good
AFt/AFm peaks.
In-situ
Directly placed in sample holder. Polishing on 1200
sandpaper
Slice of paste
Good AFt/AFm peaks.Problem with carbonationif measurements take too
long
Wet slice
Causes strong preferential orientation. Decrease in AFt/AFm intensities with
isopropanol.
Dry slice
Ground, spread on samples holder, back
loading is recommended
Powder
Better random orientation (with back loading).
Artefacts linked to drying.
Dry
Sample preparation
Raw sample
Compacted (slice) Ground
Hydrating sample
Compacted (slice or just
mixed)
Hydrated sample (stopped)
Compacted (slice) Ground
+ teflon coated sample holder+ kapton film
1. 2.
25/06/2015 37© 2014, VITO NV
Sample preparation
» Fresh or dried slices/powders?
Fresh• Limited disturbance of
hydrates • Slice surface will be prone to
dessication: drastic change in H2O content, difficult to quantify
• Freshly cut sample are proneto carbonation
Dried• AFt/AFm reflections reduced
by vacuum drying• Also isopropanol treatment
has an effect on AFt/AFmphases
• Possible carbonation• Bound H2O has to be
measured by TGA
25/06/2015 38© 2014, VITO NV
Reporting XRD dataData collection properties and settings ExamplesEquipment Manufacturer Panalytical, Bruker, Rigaku,…
Model X’Pert3 Powder, D8 Advance,…Diffractometer geometry Measurement setup Bragg-Brentano, transmission; θ-θ, θ-2θ
Goniometer radius 240 mmX-ray source X-ray radiation CuKα1,2 (λ = 1.5408 Å),…
Generator operation 45 kV, 40 mADiffractometer optics* Incident divergence slit 0.5 ° (fixed, programmable)*devices depend on equipment Incident anti-scatter slit 0.5 °
Incident Soller slits 0.04 radSpecific beam conditioning devices Johansson monochromator, Göbbel
Mirror,…Receiving anti-scatter slit 0.5 ° (fixed, programmable)Receiving Soller slits 0.04 rad
Detector Type Point scintillation counter, linear position sensitive (1D), 2D position sensitive
Model X’Celerator, Lynxeye,...Scanning mode Step, continuous,…Detector length 2.122 °2θ (1D detector),…
Sample Dimensions 26 mm diameter, 25 x 15 mm,…Spinning speed 8 rpmSample type Powder, sliceSample pre-treatment Grinding, hydration stoppage, etc.Sample loading Back loading, side-loading,…
Scan parameters Angular range 5-70 °2θStep size 0.02 °2θTime per step 30 sTotal measurement time 30 min
25/06/2015 39© 2014, VITO NV
Data analysis – the Rietveld method
25/06/2015 40© 2014, VITO NV
Data Analysis: the Rietveld method» Rietveld (1969): diffraction pattern analysis by a
curve fitting procedure» First proposed for neutron diffraction» Least-squares minimization between observed and
calculated profiles» Extended to XRD profiles in the 1970’s
25/06/2015 41© 2014, VITO NV
Applications of the Rietveld method in powder diffraction
» Phase identification (crystalline and amorphous)» Crystal structure refinement» Crystal structure determination (not trivial)» Quantitative phase analysis» Microstructural analyses (crystallite size – microstrain)» Texture analysis (orientation)
Kinetic studies
Polymorphism
Phase transitions
In-situ chemistry
Thermal expansion
25/06/2015 42© 2014, VITO NV
The Rietveld method: basics
𝑘𝑘𝑖𝑖 𝑐𝑐𝑎𝑎𝑙𝑙𝑐𝑐 = �𝑗𝑗=1
𝑁𝑁𝑁𝑁ℎ𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁
𝑆𝑆𝑗𝑗 �𝑘𝑘=1
𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑘𝑘𝑁𝑁
𝐿𝐿𝐿𝐿𝑘𝑘 𝐹𝐹𝑘𝑘,𝑗𝑗2𝐺𝐺𝑗𝑗 2𝜃𝜃𝑖𝑖 − 2𝜃𝜃𝑘𝑘,𝑗𝑗 𝐴𝐴𝑗𝑗 𝑃𝑃𝑘𝑘,𝑗𝑗 + 𝑏𝑏𝑘𝑘𝑏𝑏𝑖𝑖
Observedpattern
Calculatedpattern
Crystal structure(s)
Phase scale factors
Diffraction optics
Instrumental factors
Other samplecharacteristics
Iterative LS minimization
𝑆𝑆𝑦𝑦 = �𝑖𝑖𝑓𝑓𝑖𝑖 𝑘𝑘𝑖𝑖 𝑐𝑐𝑏𝑏𝑠𝑠 − 𝑘𝑘𝑖𝑖 𝑐𝑐𝑎𝑎𝑙𝑙𝑐𝑐
2
25/06/2015 43© 2014, VITO NV
The Rietveld method: the intensity equation
» The intensity yi(calc) at 2θ angle i is determined by:
» background contribution
» overlapping diffraction peaks depending on:
» diffraction intensities of the individual peaks
» peak shape and peak position with respect to i
𝑘𝑘𝑖𝑖 𝑐𝑐𝑎𝑎𝑙𝑙𝑐𝑐 = �𝑗𝑗=1
𝑁𝑁𝑁𝑁ℎ𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁
𝑆𝑆𝑗𝑗 �𝑘𝑘=1
𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑘𝑘𝑁𝑁
𝐿𝐿𝐿𝐿𝑘𝑘 𝐹𝐹𝑘𝑘,𝑗𝑗2𝐺𝐺𝑗𝑗 2𝜃𝜃𝑖𝑖 − 2𝜃𝜃𝑘𝑘,𝑗𝑗 𝐴𝐴𝑗𝑗 𝑃𝑃𝑘𝑘,𝑗𝑗 + 𝑏𝑏𝑘𝑘𝑏𝑏𝑖𝑖
25/06/2015 44© 2014, VITO NV
Agreement tests
» How good is good enough?» Need to monitor progress of fit» Need to compare different model fits» Need to measure data quality
» Solutions:» Visual inspection of fit» Numeric factors
» R-factors» ‘Goodness of fit’ » Durbin-Watson statistic
» Monitoring of chemical parameters» bond lenghts and angles for structure refinements
25/06/2015 45© 2014, VITO NV
Overview of numeric agreement factors
𝑅𝑅𝑁𝑁 = ∑ 𝑦𝑦𝑖𝑖 𝑉𝑉𝑜𝑜𝑁𝑁 −𝑦𝑦𝑖𝑖 𝑐𝑐𝑁𝑁𝑘𝑘𝑐𝑐∑ 𝑦𝑦𝑖𝑖 𝑐𝑐𝑁𝑁𝑘𝑘𝑐𝑐
(‘R-pattern’)
𝑅𝑅𝑤𝑤𝑁𝑁 = ∑𝑤𝑤𝑖𝑖 𝑦𝑦𝑖𝑖 𝑉𝑉𝑜𝑜𝑁𝑁 −𝑦𝑦𝑖𝑖 𝑐𝑐𝑁𝑁𝑘𝑘𝑐𝑐2
∑ 𝑤𝑤𝑖𝑖 𝑦𝑦𝑖𝑖 𝑉𝑉𝑜𝑜𝑁𝑁2
⁄1 2
(‘R-weighted pattern’)
𝑆𝑆 = 𝑆𝑆𝑦𝑦𝑁𝑁−𝑃𝑃
⁄1 2= 𝑅𝑅𝑤𝑤𝑤𝑤
𝑅𝑅𝑒𝑒(‘Goodness-of-fit’ indicator)
where 𝑅𝑅𝑁𝑁 = 𝑁𝑁−𝑃𝑃∑𝑤𝑤𝑖𝑖 𝑦𝑦𝑖𝑖 𝑉𝑉𝑜𝑜𝑁𝑁
2
⁄1 2
(‘R-expected’)
𝐷𝐷𝑊𝑊 = ∑𝑖𝑖=2𝑁𝑁 ∆𝑦𝑦𝑖𝑖−∆𝑦𝑦𝑖𝑖−1 2
∑𝑖𝑖=1𝑁𝑁 ∆𝑦𝑦𝑖𝑖 2
(‘Durbin-Watson statistic)
where ∆𝑘𝑘𝑖𝑖 = 𝑘𝑘𝑖𝑖 𝑐𝑐𝑏𝑏𝑠𝑠 − 𝑘𝑘𝑖𝑖 𝑐𝑐𝑎𝑎𝑙𝑙𝑐𝑐
25/06/2015 46© 2014, VITO NV
Examples
25/06/2015 47© 2014, VITO NV
XRD – latest developments and applications
» Latest developments:1. Spread of Rietveld quantitative phase analysis (software
developments – spread of expertise)2. New, performant detector systems enable in situ studies, acquisition
of large, systematic sets of data
» Applications/examples:1. Quantitative phase analysis
a. Anhydrous cementsb. Hydrated cementsc. Blended cements/novel cements
2. Durability studies – tracking of deterioration processes
25/06/2015 48© 2014, VITO NV
Examples and applications
1. Rietveld refinement: steps towards convergence
2. Quantitative phase analysis
3. Durability studies
25/06/2015 49© 2014, VITO NV
Example 1: refinement strategy
» Mix of TiO2 (rutile) and Ca3SiO5 (alite, major phase in cement) at RT
25/06/2015 50© 2014, VITO NV
Example 1: refinement strategy
Background (2 coefficients refined)
Rwp = 53.8%
25/06/2015 51© 2014, VITO NV
Example 1: refinement strategy
Rutile introduced
Rwp = 43.9%
25/06/2015 52© 2014, VITO NV
Example 1: refinement strategy
Rwp = 37.0%
Alite introduced
25/06/2015 53© 2014, VITO NV
Example 1: refinement strategy
Rwp = 10.4%
Alite and rutile lattice parametersrefined
25/06/2015 54© 2014, VITO NV
Example 1: refinement strategy
Rwp = 8.74%
Alite and rutile peak width refined
25/06/2015 55© 2014, VITO NV
Example 1: refinement strategy
Rwp = 8.37%
Alite and rutile atomic displacement factors introduced
25/06/2015 56© 2014, VITO NV
Example 1: refinement strategy
Rwp = 7.64%
Alite preferred orientation correction introduced
25/06/2015 57© 2014, VITO NV
Example a-c – Quantitative phase analysis
Quantifying the phase composition of cements
25/06/2015 58© 2014, VITO NV
Example 2: quantitative phase analysis of Portland cement
» Phase scale factors Sj yield mass fractions mj
M = mass per formula unitZ = number of formula units per unit cellV = unit cell volume
» If amorphous or unidentified phases are present, absolute QPA can be obtained using internal or external standard addition.
𝑘𝑘𝑖𝑖 𝑐𝑐𝑎𝑎𝑙𝑙𝑐𝑐 = �𝑗𝑗=1
𝑁𝑁𝑁𝑁ℎ𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁
𝑆𝑆𝑗𝑗 �𝑘𝑘=1
𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑘𝑘𝑁𝑁
𝐿𝐿𝐿𝐿𝑘𝑘 𝐹𝐹𝑘𝑘,𝑗𝑗2𝐺𝐺𝑗𝑗 2𝜃𝜃𝑖𝑖 − 2𝜃𝜃𝑘𝑘,𝑗𝑗 𝐴𝐴𝑗𝑗 𝑃𝑃𝑘𝑘,𝑗𝑗 + 𝑏𝑏𝑘𝑘𝑏𝑏𝑖𝑖
𝑓𝑓𝑗𝑗 =𝑆𝑆𝑗𝑗 𝑍𝑍𝑍𝑍𝑉𝑉 𝑗𝑗∑𝑖𝑖 𝑆𝑆𝑖𝑖 𝑍𝑍𝑍𝑍𝑉𝑉 𝑖𝑖
25/06/2015 59© 2014, VITO NV
QPA: accounting for amorphous/unknown phases
» Approaches to determine the amorphous content:
1. Internal standard approach:Addition of a known amount of standard to the sample
2. External standard approach:The absolute phase contents are calculated by comparison to a separatelymeasured standard monitor sample (the standard must be measured usingidentical measurement conditions as the sample)
3. PONKCS methodCalibration needed of individual amorphous phases. Different amorphous phases can be quantified separately.
25/06/2015 60© 2014, VITO NV
QPA: accounting for amorphous/unknown phases
» Internal standard method: sample preparation and choice of standard» Avoid amorphisation during mixing/grinding (use McCrone micronising mill)» Avoid reactions between the sample and the lubricant or the internal
standard during grinding» Choose the correct internal standard:
» Should be complete crystalline (or of known crystallinity)» Should have the right Lin. Absorption Coefficient (LAC)» Should have the right hardness» Should preferably be highly symmetrical with adequate peak positions» The standard should not be present in the sample
» Choose the correct amount of internal standard
» To remember: 1. No knowledge of sample chemistry required2. Additional sample preparation needed (mixing and grinding)
25/06/2015 61© 2014, VITO NV
QPA: accounting for amorphous/unknown phases
» Internal standard method: calculationThe weight fraction of phase k is calculated as follows:
where ws = known crystallinity of the internal standard;fs = weight fraction of the standard in the sample.
Or departing from the Rietveld calculation output:
𝑊𝑊𝐴𝐴𝐴𝐴𝑉𝑉𝐴𝐴𝑁𝑁ℎ𝑉𝑉𝐴𝐴𝑁𝑁 = 1 −�𝑛𝑛
𝑊𝑊𝑛𝑛
(%)100..
..××=
e% of Sampldded% of Std.A
StdPhasContCalckPhaseContCalcwk
25/06/2015 62© 2014, VITO NV
QPA: accounting for amorphous/unknown phases
» External standard method: calculation» The weight fraction of phase k is calculated using:
Where ws is the crystallinity of the standardµm and µms are the mass attenuation coefficients of the bulk sample and the standard, resp.µms is calculated from the XRF oxide composition and TG bound water
» Again, the amorphous weight fraction is:
𝑊𝑊𝐴𝐴𝐴𝐴𝑉𝑉𝐴𝐴𝑁𝑁ℎ𝑉𝑉𝐴𝐴𝑁𝑁 = 1 −�𝑛𝑛
𝑊𝑊𝑛𝑛
25/06/2015 63© 2014, VITO NV
4. Amorphous content determinationWhite cement Slag White Cement
anhydrous anhydrous w/c 0.4
OxideMAC
[cm2/g] mass fractionmass
fraction mass fraction
CaO 124.04 0.7221 0.3388 0.5158
SiO2 36.03 0.2136 0.3067 0.1526
Al2O3 31.69 0.0143 0.1881 0.0102
Fe2O3 214.9 0.0035 0.0040 0.0025
MgO 28.6 0.0086 0.1148 0.0061
Na2O 24.97 0 0.0044 0.0000
K2O 122.3 0.0011 0.0038 0.0008
SO3 44.46 0.019 0.0192 0.0136
TiO2 124.6 0.009 0.0157 0.0064
P2O5 39.66 0.004 0.0001 0.0029
H2O 10.07 0.2857
SUM 0.9952 0.9956 0.9966
MAC 101.46 66.86 75.26
Chemical composition needs to be known:
Calculation:
𝑍𝑍𝐴𝐴𝑀𝑀𝑆𝑆𝐴𝐴𝑆𝑆𝑃𝑃𝑆𝑆𝑆𝑆 = �𝑖𝑖
𝑊𝑊𝑖𝑖𝑍𝑍𝐴𝐴𝑀𝑀𝑖𝑖
To note: H2O has a low MAC, cement pastes will have much lower MACs thananhydrous cement.
MAC calculation
25/06/2015 64© 2014, VITO NV
Example 2a: quantitative phase analysis of Portland cementPortland cement is a complex mix of phases, whole patten fittingmethods (e.g. Rietveld) can deal with peak overlap in the XRD scans
Differences in strength development and durability can becorrelated with the phase composition
25/06/2015 65© 2014, VITO NV
Example 2a: quantitative phase analysis of Portland cement
» Rietveld QPA in production process and quality control in cementplants:
Rapson and Storer (2006)
25/06/2015 66© 2014, VITO NV
Example 2b: Hydration kinetics of blended cement
» In-situ XRD of a hydrating zeolite blended cement
Snellings et al. (2010)
25/06/2015 67© 2014, VITO NV
Example 2b: Hydration kinetics of cement
» In-situ synchrotron XRD of a hydrating cement paste
Snellings et al. (2010)
25/06/2015 68© 2014, VITO NV
Example 2c: PONKCS – quantification of amorphous phases
» Partial Or No Known Crystal Structure (PONKCS) method» Calibration of a phase of unknown structure:
» Mix of the amorphous phase α and a standard (weight fractions known)
» In unknown mixes the refined amorphous phase scale factor canthen be recalculated into a weight fraction
𝑊𝑊𝛼𝛼 = 𝑊𝑊𝑁𝑁𝑆𝑆𝛼𝛼𝜌𝜌𝛼𝛼𝑉𝑉𝛼𝛼2
𝑆𝑆𝑁𝑁𝜌𝜌𝑁𝑁𝑉𝑉𝑁𝑁2
𝜌𝜌𝛼𝛼𝑉𝑉𝛼𝛼2 =𝑊𝑊𝛼𝛼𝑊𝑊𝑁𝑁
𝑆𝑆𝑁𝑁𝜌𝜌𝑁𝑁𝑉𝑉𝑁𝑁2
𝑆𝑆𝛼𝛼
Peak phasecalibration factor
25/06/2015 69© 2014, VITO NV
» Partial Or No Known Crystal Structure (PONKCS) method (Scarlett & Madsen, 2006)
» Application to cements (Snellings et al., 2014)
» E.g. Anhydrous blended cement
Example 2c: PONKCS – quantification of amorphous phases
% Measured Slag 39.8
σ Slag 0.3
% Weighed Slag 39.5
Absolutedeviation Slag 0.3
25/06/2015 70© 2014, VITO NV
» Partial Or No Known Crystal Structure (PONCKS) method (Scarlett & Madsen, 2006)
» Application to cements – model mixes (Snellings et al., 2014)
» E.g. hydrated blended cement – distinction MK/C-S-H
Example 2c: PONCKS – quantification of amorphous phases
Binary mix Average σ Weighed
Absolutedeviation
Sample Wt% MK
Wt% MK
Wt% MK Wt% MK
White Cement 70
– MK 30 27.5 0.5 27.8 0.3
25/06/2015 71© 2014, VITO NV
» Partial Or No Known Crystal Structure (PONKCS) method (Scarlett & Madsen, 2006)
» Application to cements – model mixes (Snellings et al., 2014)
Example 2c: PONKCS – quantification of amorphous phases
25/06/2015 72© 2014, VITO NV
Example 3 – Durability testing
Quick ponding tests as a proxy for chloride and sulfate resistance
Delivers:Calibration of transport/thermodynamic models for concrete service life
predictions
Most of the material from H. Kamyab, P. Henocq, M. Antoni (EPFL)
25/06/2015 73© 2014, VITO NV
Method : Quick Ponding tests on paste
wax
Paste sample
15, 20, 38 h1,2 weeksNaCl 0.5 M
Na2SO4 0.05 M
15 min measurement time to avoid surface carbonationRemoval of 200 μm layers
by polishing
exposed surface
25/06/2015 74© 2014, VITO NV
Method: Quick ponding – Cl/sulfate» Identify Friedel’s salt/gypsum at different depths
» Time-depth profiles of chloride/sulfate binding in the matrix» Needed for modelling: mass balance of deterioration reactions
dept
h
CC-blended cement0.5 M NaCl - 15 h
CC-blended cement0.5 M NaCl – 400 µm depth
time
25/06/2015 75© 2014, VITO NV
Method: Quick ponding – Cl/sulfate» Identify Friedel’s salt/gypsum at different depths
» Time-depth profiles of chloride/sulfate binding in the matrix» Needed for modelling: mass balance of deterioration reactions
Position [°2Theta] (Copper (Cu))10 15 20 25 30 35
Counts
2000
4000
6000 1-3_29d_poli_1
AFt
CaCO3
AFt AFt
Limestone blended cement28 d immersion in 0.05 M Na2SO4
Slice 1 (200 µm depth)
25/06/2015 76© 2014, VITO NV
Method: Quick ponding – Cl/sulfate» Identify Friedel’s salt/gypsum at different depths
» Time-depth profiles of chloride/sulfate binding in the matrix» Needed for modelling: mass balance of deterioration reactions
Position [°2Theta] (Copper (Cu))10 15 20 25 30 35
Counts
0
1000
2000 1-3_29d_poli_2
AFt
CaCO3
AFt AFt
GypGyp
Limestone blended cement28 d immersion in 0.05 M Na2SO4
Slice 2 (300 µm depth)
25/06/2015 77© 2014, VITO NV
Method: Quick ponding – Cl/sulfate» Identify Friedel’s salt/gypsum at different depths
» Time-depth profiles of chloride/sulfate binding in the matrix» Needed for modelling: mass balance of deterioration reactions
Position [°2Theta] (Copper (Cu))10 15 20 25 30 35
Counts
0
1000
2000 1-3_29d_poli_3
CH
AFt
CH
CH
CaCO3
AFt AFt
Gyp G
G
Limestone blended cement28 d immersion in 0.05 M Na2SO4
Slice 3 (460 µm depth)
25/06/2015 78© 2014, VITO NV
Method: Quick ponding – Cl/sulfate» Identify Friedel’s salt/gypsum at different depths
» Time-depth profiles of chloride/sulfate binding in the matrix» Needed for modelling: mass balance of deterioration reactions
Position [°2Theta] (Copper (Cu))10 15 20 25 30 35
Counts
0
1000
2000
3000
1-3_29d_poli_4
CH
AFt
CH
CH
CaCO3
AFt AFt
Limestone blended cement28 d immersion in 0.05 M Na2SO4
Slice 4 (600 µm depth)
25/06/2015 79© 2014, VITO NV
Method: Quick ponding – Cl/sulfate» Example of sulfate ingress modelling (Stadium®) – by P. Henocq
» DOH=17 10-11 m2/s ( close to DOH determined by migration test)» XRD can be used to verify/calibrate modelled
dissolution/precipitation mechanisms» Presence of Ca(OH)2 induces the peak of gypsum
Gypsum Portlandite
25/06/2015 80© 2014, VITO NV
Practical guidelines for data analysis
25/06/2015 81© 2014, VITO NV
Qualitative phase analysis» Identification of crystalline phase based on characteristic peak
«fingerprint» patterns
» Database of «trustworthy» PDF patterns includes» Major clinker phases and polymorphs (Ca silicates, aluminates,
ferrites)» Minor clinker phases (alkali sulfates, oxides)» Sulfate addition phases» Common SCM phases (except natural pozzolans)» Hydrate/carbonate phases
» Search/match table for rapid manual identification» Often many phases are suggested by the software, difficult to find
plausible matches for minor phases
25/06/2015 82© 2014, VITO NV
Qualitative phase analysis» Identification of all phases in a cement is not trivial: additional
information is very useful:» Microscopic observations» Bulk sample chemistry» Knowledge of the origin of the materials» Phase enrichment using selective dissolution is particularly
useful to identify minor phases» Iterative procedure between pattern fitting and
identification helps to spot minor phases
ID QPA Final QPAAll peakscovered?
No
Yes
25/06/2015 83© 2014, VITO NV
Qualitative phase analysis: phase enrichment
» Selective dissolution: OPC» OPC is a complex mixture of phases, several phases show strongly
overlapping reflection patterns» Selective dissolutions concentrate minor phases: important aid in
identification
CEMI 52.5R
Ca-silicates
Aluminate, ferrite, sulphates
25/06/2015 84© 2014, VITO NV
Quantitative phase analysis - refinement tips
» Always good to: » start with good literature structure models» minimize the number of refined variables» final refinement should include all varied parameters
» In QPA:» Refine only scale factors and lattice parameters» Constrain parameter variation within a sensible interval» Check fit and contribution of individual phases visually» Check for parameters hitting limits of preimposed interval
25/06/2015 85© 2014, VITO NV
Parameters to be refined for QPA
Reflection peak properties Crystal structure parameters Refined in Rietveld QPAPosition Lattice symmetry Not applicable, fixed
Unit cell parameters YesIntensity Atom type No
Atomic fractional coordinates NoSite occupancies NoAtomic displacement parameters No
Profile shape, width Crystallite size Yes, usually part of analytical peak shape function
Lattice strain No
25/06/2015 86© 2014, VITO NV
Parameters to be refined for QPAData analysis properties and settings ExamplesAnalysis software Qualitative analysis Diffrac.Suite Eva, HighScore,…
Quantitative analysis Topas (Academic), HighScore (Plus), GSAS, FullProf,…
Phase information Pattern references PDF number, COD number,… Crystal structure references ICSD number, publication reference
Refinement strategy Refined global parameters, and sequence of refinement
Specimen displacement, background type and number of coefficientsa
Refined phase specific parameters, and sequence of refinement
Scale factors, lattice parameters, peak shape type and parameters, site occupanciesa, preferred orientation correctiona,…
Parameter constraints Limits on lattice parameter shift, peak shape parameters,…
Fixed parameters Atomic positions, atomic displacement parameters,…
Figures Measured diffraction patterns, calculated patterns, difference plot
At least one figure enabling a visual assessment of the data collection and analysis quality
Numerical criteria of fitting Agreement indices Rwpb, Rp
c,…Result presentation Back-calculation approach g/100 g anhydrous, g/100 g paste,…
25/06/2015 87© 2014, VITO NV
Data analysis: recalculation formulae
» Rietveld QPA results need to be rescaled to take intoaccount the incorporation of bound water
» Calculation of the Degree of Hydration (DOH):» Correction must be made for the dilution effect
𝐷𝐷𝐷𝐷𝐷𝐷 𝑡𝑡 = 1 −𝑊𝑊𝑁𝑁𝑛𝑛ℎ𝑦𝑦𝑎𝑎𝐴𝐴𝑉𝑉𝐴𝐴𝑁𝑁,𝑎𝑎𝑖𝑖𝑘𝑘𝐴𝐴𝑑𝑑𝑖𝑖𝑉𝑉𝑛𝑛 𝑐𝑐𝑉𝑉𝐴𝐴𝐴𝐴𝑁𝑁𝑐𝑐𝑑𝑑𝑁𝑁𝑎𝑎 𝑡𝑡
𝑊𝑊𝑁𝑁𝑛𝑛ℎ𝑦𝑦𝑎𝑎𝐴𝐴𝑉𝑉𝐴𝐴𝑁𝑁 𝑡𝑡 = 0
time
Anhydrouscement
FreeWater
Hydrates
Bound H2O
Measured by XRDon dried sample
𝑊𝑊𝑘𝑘,𝑎𝑎𝑖𝑖𝑘𝑘𝐴𝐴𝑑𝑑𝑖𝑖𝑉𝑉𝑛𝑛 𝑐𝑐𝑉𝑉𝐴𝐴𝐴𝐴𝑁𝑁𝑐𝑐𝑑𝑑𝑁𝑁𝑎𝑎 = 𝑊𝑊𝑘𝑘,𝑋𝑋𝑅𝑅𝑋𝑋/ 1 − 𝑉𝑉𝑐𝑐𝑙𝑙𝑎𝑎𝑡𝑡𝑠𝑠𝑙𝑙𝑉𝑉𝑠𝑠𝑜𝑜𝑉𝑉𝐴𝐴𝑛𝑛𝑎𝑎,𝑇𝑇𝑇𝑇
25/06/2015 88© 2014, VITO NV
Data analysis: recalculation
88
·(1+w/c)
not in [%]
/(1+H2Obound)
/(1+w/c)
25/06/2015 89© 2014, VITO NV
Data analysis: recalculation formulae
» fresh specimen (disc):» per 100g paste m=mXRD» per 100g anhydrous m=mXRD·(1+w/c)
» dried specimen (powder):» per 100g paste m=mXRD*(1+H2Obound)/(1+w/c)» per 100g anhydrous m=mXRD*(1+H2Obound)
Wt.%
C3S
Age (days)
*Data from Arnaud Muller, hydrationof white cement +
10% SF
H2Obound on ignited basis
25/06/2015 90© 2014, VITO NV
Conclusions & Perspectives
25/06/2015 91© 2014, VITO NV
XRD has become a quantitative characterisation tool in cementitious materials+ Assets
+ Phase assemblage characterisation: quantification of individual phases+ Straightforward sample preparation+ Short measurement times+ Accessible in most material science labs+ Automated analysis possible (e.g. cement production)
─ Limitations─ Accuracy: 2-3 wt.% for major phases, 1-2 wt.% for minor phases (can be
better)─ Expert knowledge needed for non-routine analyses
XRD – a tool for routine analysis
25/06/2015 92© 2014, VITO NV
But there’s more…
» XRD should be used together with other techniques to verify andcomplete the characterisation of the microstructure
» See poster for examples of electron microscopy» Book on microstructural charactisation of cementitious materials:
• Edited by K. Scrivener, R. Snellings, B. Lothenbach• Chapters on Sample preparation, Calorimetry, Chemical
shrinkage, XRD, TGA, Solid NMR, H NMR, Electronmicroscopy, MIP, Gas sorption,…