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Electron microscopy for multi-scale porous materials

Part II – Electron tomography in material science

Jeremie Berthonneau*, O. Grauby, A. Baronnet, D. Ferry, D. Chaudanson, F.-J. Ulm, and R.J.-M. Pellenq

* <MSE>², CNRS-MIT Joint Laboratory, Massachusetts Institute of Technology, Civil and Environmental Engineering Department, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

[email protected]

Winter School on Multi-Scale Porous Materials, Marseille Jan. 24, 2017

mailto:[email protected]

[New Yorkers Magazine, 1991]

Why tomography?


?¾ A single projection is insufficient to infer the structure of a 3D object

[Yang, E-Tomo introduction, 2016; images: Encyclopedia Britannica, 2008; Martin et al., 2015]

Basics


Tomography = tomos (part, slices) + graphein (to write)

� Tomography is a method in which a higher dimensional structure is reconstructed from a series of lower dimensional projections (usually by sampling the structure from many different directions)… Projections may be generated from various sources:

Radio-frequency waves

X-rays

Electrons

Ions

Magnetic Resonance Imaging

X-rays Computed Tomography

Electron Tomography

Atomic Probe

Wav

elen

gth

Res

olut

ion

+

+

-

-

[Moldovan et al., ICPMS conf, 2010; * Lucic et al., 2010; **Bals et al., 2013]

History


20001971196819481917

First applications in Biology

¾ Fundamental insights into cellular organization and

ultrastructure*

Extension to Nanomaterials

¾ Fundamental insights into solid state and material

science**

Hounsfield & CormackX-ray computed tomography (CT)

De Rosier & KlugET reconstruction of bacteria

The Radon transform: Allows the reconstruction of the volume of an object from its projections

Tomography = tomos (part, slices) + graphein (to write)

Outlines


1. Electron tomography principle

2. Image processing and denoising

3. Disordered porous silica glass

4. Organic porosity of source rocks

CINaM facility


Tomography holder

CCD camera GATAN Ultrascan® 1000XP

Tilt axis

Parallel Electron Beam

Focal planObject projection in2D

+

Jeol JEM-2010 TEM

+60°-60°

0°

Electron Microscopy FacilitySerge Nitsche (IR) & Damien Chaudanson (IE)

¾ Recent (2015) « tunning » to allow for electron tomography

Sample preparation


[figures from phD thesis, T. Dahmen, 2015]

Single-tilt Double-tilt Conical-tilt

Reconstruction ease and quality- +

1. Drop deposit

� Deposition of any nanomaterials in solution on a “holey carbon” TEM grid

¾ Cheap and easy but limited to individualized nano-particles

Wide variety of TEM tomography holder allowing for various tilt axis geometries:

Available at CINaM so far

Sample preparation


1. Drop deposit

2. Focused Ion Beam (FIB) sectioning

� Extraction of a thin section from any parent sample

¾ Broader range of materials…

[Stardust mission, H. Leroux; Col. with M. Gabié – CP2M, AMU]

3 mm

[*Franck, ed. Springer, 2005; Messaoudi et al., BMC BioInf vol 8, 2007]

2D projections with Δθ = 1°

Source (Electron beam)

y

z

x

ReconstructionAlignmentAcquisition

xy plans

xz plans

yz plans

Analysis

Principle


The principle of electron tomography* resides in the “visualization of slices in the context of a rotational tilt axis”


AcquisitionParallel

Electron Beam

Focal planObject projection in 2D

Reconstruction

Acquisition

AlignmentBright Field Imaging

� Aperture in the back of the focal plane of the objective lens (direct beam)

� Image resulting from the weakening of the direct beam intensity (~ Beer’s law) by its interaction with the sample

� Mass-thickness and diffraction contrast contribute to the image formation

The electron microscope available at CINaM allows electron tomography only on non-crystalline solids (inability to account for the diffraction contrast)

Resolution

λ𝑒 =ℎ

2𝑚0𝑒𝑉 1 + Τ𝑒𝑉 2𝑚0𝑐2

𝑑 =λ𝑒

2𝑛 sin 𝛼

…depending on the acceleration voltage, 0.05 < d < 0.23 nm

Acquisition


Tilt axis


Focal planObject projection in 2D

θ = -30°θ = -20°

θ = -10° θ = 10°θ = 20°

θ = 30°

Reconstruction

Acquisition

AlignmentBright Field Electron Tomography

� High tilt tomography holder

� Goniometer

� Good microscope alignment (eucentricity)…Limited angular tilt whendealing with FIB thinsections… (~ +/- 40°)

[GATAN Digital Micrograph]

Image alignment


Reconstruction

Acquisition

Alignment

1. Lateral alignment combining translation correction (cross correlation) and filtering (bandpass/hanning window)

Cro

ss c

orre

latio

n

608.9 nm

639.

6 nmθ = -30° θ = -20° θ = -10°

θ = 10° θ = 20° θ = 30°

[GATAN Digital Micrograph]

Noticeable stage shifts occur during tilting (imperfections of mechanical tilt system) …

¾ Lateral shift (x’y’): need to bring the projections into a common coordinate system

Image alignment


Translation/Rotation with local minima

639.

6 nm

y y

1. Lateral alignment combining translation correction (cross correlation) and filtering (bandpass/hanning window)

2. Optimized alignment (translation/rotation) using 3D landmarks (local minima) inTomoJ*

608.9 nm 316.9 nm

Reconstruction

Acquisition

Alignment

[*Messaoudi et al., 2007]

Noticeable stage shifts occur during tilting…

¾ Lateral shift (x’y’)

¾ Axial shift: need to optimize the spatial positions of the focus planes

Reconstruction


Reconstruction

Acquisition

Alignment

[*Messaoudi et al., 2007]

Final step for tomogram computation, can be achieved with different algorithms (WBP, ART, SIRT, etc.)

WBP ART SIRT

¾ Coefficient of determination =

Back projection Vs. Iterative techniques on

noisy projections of phantom data*

1.5 % 25.4 % 25.6 %

Reconstruction

The reconstruction of the volume in 3D is based on the sum of the projected 2D images (tilt series), therefore the number of images

acquired is determinant … beware of the missing wedge !


Acquisition

Alignment

Treatment

Reconstruction

Grey level projections according to a single

direction*

80 projections (-/+ 80° with Δθ = 2°)

60 projections (-/+60° with Δθ = 2°)

[*McIntosh et al., 2005]Original image

Outlines






� The reconstructed tomograms usually have three majors defects:a) Variable grey level lines in the xy plansb) Smears at θmin and θmax due to the “missing wedge”c) The features are elongated according to the z-direction

¾ Denoising, filtering, and elongation correction using dedicated software

x

z

ab

110

nm

c

Main artifacts



Tomogram denoising1. Suppression of the background noise within the tomogram

[D. Lottin, PhD thesis – CINaM/CNRS, 2013; *IDDN.FR.001.380022.000.RP.2011.000.31235]

Background suppression

608.9 nm

639.

6 nm

� Denoising of the background: homogenization of the average gray level and suppression of “hot spots”

� Superposition of experimental and calculated projections over the angular range

y

Alignment Reconstruction (SIRT)

y

200 nm


Tomogram filtering1. Suppression of the background noise within the tomogram

2. Control of the reconstruction fidelity with respect to the object

¾ Optimal gray level thresholding by superposition

[D. Lottin, PhD thesis – CINaM/CNRS, 2013; *IDDN.FR.001.380022.000.RP.2011.000.31235]

1. Suppression of the background noise within the tomogram


3. Suppression of missing wedge artefacts: elongation correction*

¾ Limited specimen tilting range gives rise to a region in the Fourier space of the reconstructed object where experimental data are unavailable = missing wedge

[*Kovacik et al., J Structural Bio, vol. 186, 2014]


Elongation correction

Geometric area of available data

Impulse response of Ω2showing the main artefacts due to the missing data

Fourier transformation


Elongation correction

¾ Fourier Angular Filter*Damping of the sharp transition of the non-zero

data region to the zero-filled missing wedge region in the Fourier space

[*Kovacik et al., J Structural Bio, vol. 186, 2014]

1. Suppression of the background noise within the tomogram


3. Suppression of missing wedge artefacts: elongation correction*

Intensity map of the difference between the impulse response before (Ω2) and after filteringa. Suppression of the side rays (1 and 2)b. Suppression of the side minima in x (3

and 4)c. Reduction of the magnitude of central

peak

¾ Comparison before versus after denoising, filtering, and elongation correction

y

z

110

nm50

nm

[n.b. color of the pore phase was changed for clarity]

Treatment’s result

Outlines






Why does it matter?


IUPAC

d

[Foam structure from Subramanian et al., 2013]

Pore size, d

microporous mesoporous macroporous2 nm 50 nm

Quantitative knowledge of the 3D arrangement (morphology + topology) of pore networks is crucial to understand and predict the transport and mechanical properties

Morphology� Pore size distribution (PSD)

� Pore volume, Vp� Specific surface area, As

Topology� Tortuosity

� Connectivity� Percolation threshold

+

¾ Evaluation of the potential of Electron Tomography to realistically describe the 3D arrangement (morphology) of a disordered mesoporous solid

𝜑 =𝑉𝑝𝑉𝑡


Vycor ® porous glass[*Off lattice reconstruction of Vycor from Pellenq et al., 2001; Data set Vycor ® type 7930 from Corning Inc.]

Solid density Bulk density Porosity Specific surface area Average pore sizeρ s (g/cm3) ρ (g/cm3) φ (%) A s (m2/g) r H (nm)

Vycor 7930 2.18 1.50 28.0 250.0 4.0

Sample

Porous Vycor Glass (PVG)

� Prepared by phase separation of an alkali borosilicate glass and acid leaching

� Strongly interconnected and almost pure SiO2 skeleton (biphasic media)

¾ Model structure of disordered mesoporous media*


Morphological characterization[*Gille et al., J. Porous Materials, 2002]

Standard methods allowing morphological characterization of porous networks are:

• Mercury intrusion porosimetry (MIP) for the macropores (> 50 nm)

• Small angle scattering (SAS) for the mesopores (1.5 – 50 nm)

• Gas adsorption isotherms for the micro to macropores (0.4 − 100 nm)

¾ Definition of the pore size distribution densities from these three methods*

Vp = 0.227 cm3/g dp = 7.0 nm lp = 10.6 nm~ cylindrical pores


Electron tomography

Tilt axis


0°

θ = -40°θ = -25°

θ = -10° θ = 10°θ = 25°

θ = 40°

-40° 40°

Tilt series Reconstruction

Treatment

SiO2 skeleton Porous network

Pore size distribution


[*Vicente et al., J. Porous Media vol 16, 2013; computation performed using iMorph: http://imorph.fr]

Aperture computation*: the pore size at any given point (P) within the pore phase corresponds to the largest sphere (with aperture radius r from 0.35 to 5.0 nm) that contains P

Ape

rtur

e ra

dius

cla

ss (n

m)

0.0

10.0

5.0

2.5

7.5

210 nm

Vp = 0.115 cm3/g

dp = 3.6 nm

210 nm

Allows a granulometricanalysis of the pore network (PSD)

s p

[*Pellenq & Levitz, Mol Phy, vol. 100, 2002]

� Chord length distribution* = stochastic geometrical tool describing the structural disorder of the pore network, fp(r), and the solid matrix, fs(r)

Chord length distribution


𝜑 = 16.8 %

� solid

� pores

210 nm

� The in-pore chord length distribution allows one to estimate the geometric specific surface area (Ssp) from the mean chord length* (<ℓ>)

[*Ioannidou et al., PNAS, vol 113, 2016; **Pellenq & Levitz, Mol Phy, vol. 100, 2002]

𝑆𝑠𝑝 =4𝜑

𝜌𝑠 1 − 𝜑 ℓ

With ρs = 2.18 g/cm3

(solid density of amorphous silica)

Τ𝑆𝑔𝑒𝑜 0.65𝑟𝑐 + 1

¾ Sgeo = 253.3 m2/g which is in good agreement with the specific surface area provided by Corning (As = 250 m2/g)

Geometric surface area


We compute Ssp at different rc(cutoff length for the CLD neglecting pores, anfractuosity, and roughness sizes)*

Extrapolation of rc to zero gives Sgeo

[*Pellenq et al., 2001; **Pellenq & Levitz, Mol Phy, vol. 100, 2002; ***Coasne et al., Langmuir, 2010]

Discussion


Polarizability (a03)

0 5 10 15 20 25 30

SB

ET

(m2 /

g)

60

80

100

120

140

160

180

200

220

Ne N2

Exp. data

GCMC data (this work)

H2

Xe

Kr

Ar

Intrinsic Ssp

1 2 3Dads /�DO

¾ This discrepancy was also documented on similar materials were the underestimation was

evaluated at ~ 20%, in agreement with our observation***

� The surface area may be considered in term of geometry (Sgeo) or specifically to a probing gas (As or Ssp)

Studied through GCMC on off lattice 3D reconstruction*,**

Discussion


¾ The main limitation of Electron Tomography resides in the restricted field of view (here only the mesopore network is reconstructed)

� Evaluation of the potential of Electron Tomography to realistically describe the 3D arrangement (morphology) of a disordered mesoporous solid

200 nm

Gas sorption E Tomo

Vp (cm3/g) 0.227* 0.115

rH (nm) 3.5* 1.8

As/Sgeo (m2/g) 195.0** 253.3

[*Gille et al., 2002; **Pellenq & Levitz, 2002]

Outlines







Why does it matter?[Hanchen, 2014; Louks et al., J Sed Res vol 79, 2009; Obliger et al., J Phys Chem Let, 2016]

How can we make the link between the hydrocarbon recovery from source rocks… and the diffusion mechanisms of alkanes (CnH2n+2) in complex porous structures?

¾ Calls for a multiscale strategy where an accurate characterization of the pore networks is paramount

5 nm

Free volume theory

Surface diffusion

¾ The organic pore network plays a central role but cannot be fully covered by conventional techniques

[Louks et al., J Sed Res vol 79, 2009; Louks et al., AAPG bul vol 96, 2012; Curtis et al., AAPG bul vol 96, 2012]

FIB tomography

X-Ray tomography

Molecular simulation

Fracture pores

Organic matter pores

Interparticle pores

Intraparticle pores


A multi-scale porosity…

[scheme modified after Bjørlykke, 1989; *molecular models from Bousige et al., Nature Materials, 2016]

LEF

MAR

Molecular models* showed a large amount of micro-pores and that, for a given ρ, mature kerogens (MAR-K) exhibits slightly larger pores than immature ones (LEF-K)


0.1 nmResolution

…Evolving with thermal maturity


[scheme modified after Bjørlykke, 1989; *Hubler et al., 2016]

…Evolving with thermal maturity

¾ What is the impact of thermal maturity on the organic meso-pore network ?

CT scans* showed that the Euclidian distance between macro-pores (dexp = 50 nm) and organic phase become consistently shorter with thermal maturity

ANT

HAY

50 nmResolution

MOLECULAR MODELING*

- Thermal maturity affects the micro-porosity of

kerogens- Box sizes of 5 nm

ELECTRON TOMOGRAPHY

- Direct observation of pores (1 < d < 50 nm)- Topology from 3D

reconstructions

X-RAY TOMOGRAPHY- Euclidian distance

between macro-pores and organic phases decreases

with maturity- Spatial resolution: 50 nm

Multiscale

[*Bousige et al., Nature Materials, 2016]


Experimental approach

Organic-rich source rock samples

(LEF, HAY, MAR)

Kerogens isolated by acid demineralization

method*Gas (N2 and CO2)

adsorption isotherms

Organic matter extracted using dual

beam FIB

3D geometrical characterization

(Electron tomography)

Gas (N2) adsorption isotherms

Objectives:1. Reconstruct the organic porous network at the nano-scale from TEM imaging2. Characterize the 3D volumes and compare with BET results3. Study the evolution of the pore network with respect to thermal maturity4. Provide insights in the features that govern fluid transport

Studied materials

Specific preparation

Methods

[*Suleimenova et al., Fuel vol 135, 2014]


Experimental approach

LEF is thermally immature (oil-prone) whereas MAR and HAY are thermally overmature (dry gas reservoir)

� Source rocks from three different formations (Lower Eagle Ford, Marcellus, and Haynesville) containing variable amounts of organic material (TOC, wt.%) with different thermal maturities


Materials[*from Leco TOC and RockEval analysis performed by SDR and Geomark Research LTD]

� N2 adsorption isotherms performed on the source rocks show type IV (MAR/HAY) and type V (LEF) adsorption branches

[*IUPAC classification of isotherms]


Adsorption isotherms

IV: typical of meso-porous materials

V: porous materials with weak interaction between the adsorbate and adsorbent

Thermal maturity



Sample As (m2/g) Vp (10-2 cm3/g) rH (nm)

LEF/K 2.28/20.80 1.36/10.71 23.9/20.6

HAY 7.22 1.06 5.9

MAR/K 26.33/160.89 2.30/13.47 3.5/3.4

¾ Overall, the average pore size* (rH) decreases with thermal maturity as As increases more than Vp

𝑟𝐻 =4𝑉𝑝𝐴𝑠

rH

…very similar to the grounded source rocks…

[*Clarkson et al., Fuel vol 103, 2013; **Wang et al., Energy & Fuels vol 28, 2014]

� As and rH as a function of VR0 in North American* and Chinese** source rocks

¾ Hypothesis: the transition from oil-prone to gas-prone is accompanied with the closure of meso and macro-pores and the formation of meso to micro-pores (r < 3 nm)

Oil-prone

Gas-prone



[*collaboration with Jae Jin Kim and Ruarri Day-Stirrat, Shell Technology Center in Houston]

Organics in primarylocation (kerogen)

Migrated hydrocarbons(~bitumen)

LEF: fresh outcrops from the Lower Eagle Ford formation (TX, USA)


FIB sampling

Ker

ogen

~Bitu

men

[*collaboration with Jae Jin Kim and Ruarri Day-Stirrat, Shell Technology Center in Houston]

LEF MARHAY

¾ Approach allowing to compare the organic hosted porosity at different thermal maturities (LEF / HAY-MAR) as well as different nature of organic material (kerogen/bitumen)

HCs generation: oil-prone HCs generation: gas-prone

Organic material


TEM samples

Organicmeso-pores(2 – 50nm)

Organicmacro-pores

Interparticle porosity

Inclusion

Inclusions

Clay particle

5 nm

[*Bousige et al., Nature Materials, 2016]

Kerogen microstructure*

Organicmicro-pores

(< 2 nm)


Bright field imaging

Organicmeso-pores(2 – 50nm)

Organicmacro-pores

Interparticle porosity

Inclusion

Inclusions

Clay particle


Bright field electron tomography

Kerogen mesostructure

Electron tomographyacquisition on the porous

organic matter...

… therefore excluding the inter and intra particle porosity (due to the diffraction contrast)

MAR HAY

HAY

LEF

210 nm

Filtered tomogramsLEF

252 nm


210 nm

y

zx

The tomograms evidencesignificantly differentkerogen mesostructures…

Quantitative approach

[*Vicente et al., J. Porous Media vol 16, 2013; computation performed using iMorph: http://imorph.fr]

Aperture computation*: the pore size at any given point (P) within the pore phase corresponds to the largest sphere (with aperture radius r from 0.7 to 15.0 nm) that contains P

Ape

rtur

e ra

dius

cla

ss (n

m)

0.0

10.0

5.0

2.5

7.5



210 nm

HAY

210 nm

210 nm

y

x

Allows a granulometricanalysis of the pore network (PSD)

Easily visualized on the aperture map*


[computation performed using iMorph: http://imorph.fr]


¾ Support the hypothesis of closure of meso and macro-pores and formation of meso to micro-pores (cf. BET) with respect to thermal maturity

The volumetric distribution of the aperture diameter is used to obtain the incremental and cumulative distribution… Noticeable

difference between LEF and MAR/HAYrH

¾ Chord length distributions within the porous and solid phases

[computation performed using iMorph: http://imorph.fr]

LEF MARHAY

210 nm252 nm 210 nm

Chord length distribution


¾ Confirm the increase of accessible surface area as a function of thermal maturity and the predominance of micro-pores in MAR and HAY with respect to LEF

� The in-pore chord length distribution allows one to estimate the geometric specific surface area (Ssp) from the mean chord length* (<ℓ>)

[*Ioannidou et al., PNAS, vol 113, 2016]

𝑆𝑠𝑝 =4𝜑

𝜌𝑠 1 − 𝜑 ℓ

With 0.8 < ρs < 1.4 g/cm3

Geometric surface area


Thermal maturity

HAY

[*Pardo-Alonso et al., Procedia Materials Science vol 4, 2014]

� Definition of the minimal geometrical path in a porous media, performed using Fast Marching method* from face to face

𝜏 =λ𝐿

X Y Z

LEF - - 1.45 + 0.27

HAY 1.21 + 0.05 1.38 + 0.10 1.20 + 0.15

MAR 1.71 + 0.16 1.73 + 0.12 1.30 + 0.27

LEF

Tortuosity


Shortest distance maps from one face of the image to any point in the pores (here z direction)

zz


ConnectivityLEF

HAY5.6 vol.% of the organic pores are isolated

94.4 vol.% of the organic pore volume is connected to all faces

One macro-pore accounts for 79.1 vol.% of the organic pore volume and connect the faces in z-direction

� Connectivity is one of the main topological properties

Linked to the notion of path-connected space through a percolation threshold of one voxel (0.35 < χ < 0.42 nm)… regardless of the microporosity

¾ τ and χ will define the regime of hydrocarbon transport*

[*See for instance Obliger et al., J Phys Chem Let, 2016; Falk et al., Nature Com., 2015]

5 nm 40 nm¾ Implement a multiscale transport model that accounts for both the micro and meso

structure of kerogen and allows coupling between diffusion and potential hydrodynamic flow (geometrical contribution of the structure)

Summary


MICRO-SCALE• Alkane transport is governed by

diffusion, and diffusion coef. of alkane mixtures follow a free volume theory*

• Transition between flexible and rigid kerogen matrix triggered by thermal maturity**

MESO-SCALE• Progressive closure of meso and macro-

pores and formation of meso to micro-pores (nm size)

• Switch from a disconnected macro-porosity to a connected micro to meso-porosity

[*Obliger et al., J Phys Chem Let, 2016; **Valdenaire, GameChanger Project, 2016]


Toward carbon neutral energy[*Friedlingstein et al., Nature Geoscience, 2014; **Tao & Clarens, Env. Sci. Technol. vol . 47,2013]

Slow the growth of CO2 emissions (political agreements)

Capture and store CO2 Geological sequestration

Two main solutions

Deep saline aquifers Source rocks**

1990 1995 2000 2005 2010 2015 2020 2025 2030


Carbon Capture and Storage[*Tao & Clarens, Env. Sci. Technol. vol . 47,2013]

Marcellus shale formation

¾ Based on this model, the authors* estimate that the Marcellus shale could store between 10.4 and 18.4 billion tones of CO2 between now and 2030 (~ half of the expected total U.S. CO2

emissions from power plants over that time)

Existing fracking wells…(average production life ~ 10 years)

� Computational model* based on historical and projected CH4 production and CH4/CO2sorption equilibria and kinetics


CO2/CH4 adsorption[*Brochard et al., Langmuir, 2012]

¾ Theoretical study* of the competitive adsorption of CO2 and CH4 in disordered microporous carbon structure (akin of an overmature kerogen) showed…

i) Preferential adsorption of CO2 and desorption of CH4

ii) Differential swelling

5 nm

« Le microscope est un prolongement de l’esprit plutôt que de l’œil » Gaston Bachelard (1884-1962)

Thank you

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