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25/06/2015

X-ray powder diffraction (XRD):Basic principles & practical applications

Ruben SnellingsVITO (BE)

[email protected]

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

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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

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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

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Basic principles of XRD

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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

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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)

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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

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Diffraction on crystals

» Single crystal vs powder diffraction

singlecrystal

powderI

2θ

Data compressed into one dimension

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Powder diffraction: laboratory configurations

X-ray source detector

sample

2θ

Reflection geometry

X-ray source detector

sample

Transmission geometry

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Laboratory Bragg-Brentano (reflection)

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Laboratory Transmission mode

Laboratory source

Synchrotron source (ESRF)Multichannel detector for fast data acquisition

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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

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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

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2θ - degrees

Coun

ts






crystallites – the texture

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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

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2θ - degrees

Coun

ts






crystallites – the texture

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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

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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

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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

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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})

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Peak intensities: the structure model» Contains lattice parameters

(a, b, c, alpha, beta, gamma)» Symmetry group, space group» Asymmetric unit: atomic coordinates, occupancy, etc.

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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

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2θ - degrees

Coun

ts






crystallites – the microstructure

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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)

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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]

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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

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Practical guidelines for XRD experiments

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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

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Sample loading

Slice(cement paste)

Back-loaded

Front-loaded

Preferred orientation to be avoided

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Hydration stoppage

» Harsh drying conditions effect ettringite –AFm phases» To be avoided for QPA

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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

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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.

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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

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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

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Data analysis – the Rietveld method

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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

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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

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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

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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






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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

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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

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Examples

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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

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Examples and applications

1. Rietveld refinement: steps towards convergence

2. Quantitative phase analysis

3. Durability studies

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Example 1: refinement strategy

» Mix of TiO2 (rutile) and Ca3SiO5 (alite, major phase in cement) at RT

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Background (2 coefficients refined)

Rwp = 53.8%

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Rutile introduced

Rwp = 43.9%

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Rwp = 37.0%

Alite introduced

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Rwp = 10.4%

Alite and rutile lattice parametersrefined

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Rwp = 8.74%

Alite and rutile peak width refined

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Rwp = 8.37%

Alite and rutile atomic displacement factors introduced

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Rwp = 7.64%

Alite preferred orientation correction introduced

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Example a-c – Quantitative phase analysis

Quantifying the phase composition of cements

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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.






𝑓𝑓𝑗𝑗 =𝑆𝑆𝑗𝑗 𝑍𝑍𝑍𝑍𝑉𝑉 𝑗𝑗∑𝑖𝑖 𝑆𝑆𝑖𝑖 𝑍𝑍𝑍𝑍𝑉𝑉 𝑖𝑖

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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.

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» 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)

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» 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

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» 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

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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

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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

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Example 2a: quantitative phase analysis of Portland cement

» Rietveld QPA in production process and quality control in cementplants:

Rapson and Storer (2006)

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Example 2b: Hydration kinetics of blended cement

» In-situ XRD of a hydrating zeolite blended cement

Snellings et al. (2010)

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Example 2b: Hydration kinetics of cement

» In-situ synchrotron XRD of a hydrating cement paste

Snellings et al. (2010)

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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

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» Partial Or No Known Crystal Structure (PONKCS) method (Scarlett & Madsen, 2006)

» Application to cements (Snellings et al., 2014)

» E.g. Anhydrous blended cement


% Measured Slag 39.8

σ Slag 0.3

% Weighed Slag 39.5

Absolutedeviation Slag 0.3

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» 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

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» Partial Or No Known Crystal Structure (PONKCS) method (Scarlett & Madsen, 2006)

» Application to cements – model mixes (Snellings et al., 2014)


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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)

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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

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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

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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)

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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

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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

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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

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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

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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

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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

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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,…

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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

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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

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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

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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,…

x-ray powder diffraction (xrd): basic principles ...documents.epfl.ch/users/s/st/ston/www/2...

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