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High Resolution Transmission Electron Microscopy (HRTEM) imaging
In this chapter, we present the TEM system and high resolution images acquired by this system. Two sample sets will be given in the following:
First sample set: soot images, for which we have been interested in GFBF models that are able to make synthetic soot textures generation possible from random number generators.
Second sample set: active phases of hydrotreating catalysts, for which we have proposed an ARFBF approach allowing to discriminate different materials.
All TEM images presented in this work are produced at IFP Energie nouvelles, Phycics and Analysis division, with a JEOL 2100F microscope.
Transmission Electron Microscopy (TEM)
Schematic description of a TEM
A TEM (see Fig. 2.1) is composed by several systems (see Fig. 2.2) which include illuminating system, specimen manipulation system, imaging system as well as vacuum system, with the following properties (see [22]).
The illuminating system is composed by electron gun, condenser aperture and con-denser lenses which include condenser lens 1 and condenser lens 2. We have the following properties:
– condenser aperture determines the aperture of the beam and the size of the diffraction spots,
– condenser lens 1 determines the minimum spot size on the sample,
– condenser lens 2 determines the illuminated area of the sample and the beam parallelism.
The specimen manipulation system is composed by specimen port which has to:
– be thin (10 50 nm, where ‘nm’ denotes nanometers) and representative, as well as
– alter the incident wave function to produce a contrast (diffraction, absorption, phase, electric or magnetic polarization …) and
– degrade as little as possible under the beam.
The imaging system is composed by objective lens, intermediate lens and projector lens. Diffraction lens transfers diffraction pattern or image of the object on the observation screen.
The vacuum system provides an environment in which the electrons travel.
Figure 2.1: Transmission electron microscopy (TecnaI G2 – type of MET used in IFP En-ergies nouvelles). From « https://www.fei.com/products/tem/tecnai/?LangType=1033 ».
In a TEM system, samples are usually observed at magnifications of order 250000. The resolution is limited by the data transferred by the objective lens. It ranges from about 0.1 nm to 0.3 nm. The energy of the incident electron wave ranges from 80 to 300 keV. When the incident electron wave – which can be approximated by a plane wave – pen-etrates the thin sample (approximately 100 nm), the coherent interaction with material inside structure undergoes Bragg scattering. The coherent interaction changes the energy and movement orientation of the incident electron. It is shown that different material structuring lead to different types of interactions.
Specimen preparation
The specimen has to comply with some requirements (see [21]) for being a relevant TEM imaging system:
the specimen must be transparent for the electron beam, thickness of the sample viewing area should be controlled around 100 200nm.
the specimen shall be representative to truly reflect certain characteristics of the analyzed material (sample preparation must not affect these characteristics).
It is problematic to use samples with unknown compositions and thickness (see [16]). An alternative, when dealing with a sample with multiple constituent, is the Electron Energy Loss Spectroscopy (EELS) which allows for obtaining information on the elemen-tary composition of a sample (see [15]) or the chemical environment (see [56]) at the nanometer scale.
In order to produce sufficiently thin sample blocks (thickness in a few tens of nm units) for TEM observation of catalyst support (see Fig. 2.3), transition alumina / amorphous and silica-alumina or more scarcely silica / titania are usually used as supports of catalyst sample preparation. The preparation is as follows:
firstly, the sample is grinded in a mortar, then it is placed into suspension such as ethanol or heptane (sample is soluble in ethanol or heptane), after that, one must take one drop of suspension which is treated in an ultrasonic bath and deposit it on a copper grid coated with a holey amorphous carbon film, the final step consists in placing the dried grid in the microscope.
TEM imaging theory
Details concerning TEM image formation can be found in [20]. Fig. 2.4 illustrates that a part of transmitted electron e are selected in sample outlet of a circular opening (contrast diaphragm). Two points of sample whose diffusion properties are different (type of constituent atoms or the number of atoms with local thickness) can be discriminated. When the thickness of thin blade t is small, the interactions between the electron e and the sample are very limited and the slow-down of speed of e can be negligible. The principle of absorption contrast for specimen observation can be said « amorphous » (dense collection of e without special organization but with a distance between substantially equivalent nearest neighbors). This absorption contrast does not correspond to a real absorption of e in the samples but to a virtual absorption in the image because some e are blocked by the contrast aperture. If an e with high energy passes near an atom (see Fig. 2.5), then: after coulomb interactions between the negative charge of e incident and the charges located in the atom, the attractive or repulsive forces will slow or accelerate e ; it is considered that the isolated atom is at rest (minimum energy state), it will acquire energy from e .
The e arriving near the nucleus undergoes attractive interaction corresponding to a strong deviation. It can be considered as an elastic scattering (no energy change) with relatively large angle of deviation (10 2 radians). The e arriving in the e cloud of the atom can communicate energy (for the same mass particles). Passage of e of the atom in a higher level, or even expulsion generates loss of energy of e incident. It can be con-sidered as inelastic scattering (energy change) with small angle of deviation (10 3, 10 4 radians). Elastic effects open a beam of initially parallel incident e . Inelastic effects have more complex consequences for further analysis (microscopy analysis). The size of the scattering angle is related to the density and thickness of samples, therefore it can affect the pixels of the image (lightening and/or shading different image parts). Images will be displayed on the imaging device after amplification and focus adjustment.
As mentioned above, because of different structures / different parts inside the sample, when the electron beam penetrates the sample, the energy and orientation of transmission beam change, thus the intensity of transmission is different. This irregular distribution of the intensity is called contrast. The number of e collected at a point of the detector I(x; y) (I is considered as one image) is different from that collected at a neighboring point I(x + dx; y + dy). The contrast is defined as C = I(x + dx; y + dx) I(x; y) ; (2.1) where I(x; y) denotes a pixel of image I.
TEM has high spatial resolution and can provide rich analytic structure information. It is widely used to characterize nanostructure of materials, particularly heterogeneous catalysts (see [65]). It is possible to consider supported nanoparticles as ideal systems, because supported nanoparticles are often ideal phase objects as well as can easily be pre-pared and observed (see [54]). TEM exists on several forms as HRTEM, STEM (Scanning Transmission Electron Microscope), AEM (Analytical Electron Microscope)… We will explore HRTEM for visualizing soot and catalyst nanostructure in this work.
HRTEM
HRTEM acquires an image by using a wide aperture to let the central spot and the diffracted spots closest to the diffraction pattern, in addition with observing an inter-ference between these beams. The enlarged image shows all the crystal symmetry and periodicity properties corresponding to the cliche area of selected diffraction. The juxta-position of aligned black and white dots with distances between rows equal the spacing in the real crystal. The enlarged image is a projection of the atomic structures.
HRTEM imaging has some limitations as follows:
the imaged material sample must satisfy specific positioning conditions in order to avoid overlaps between adjacent columns of the atomic projections;
the microscope must be able to resolve involved inter-atomic distances (various lens aberration issues);
visualization on the sensors of an amplitude can suffer from loss of phase informa-tion.
The atomic columns can appear as white or black.
In practice, it’s possible to resolve up to 0:2 nm between the planes. HRMET images of atomic structure only represent a certain projection of these structures (see [20]).
Observations of soot nanostructure by HRTEM
In the range of pollution related to transport, Diesel Particle Matter (DPM) emissions have a significant impact on global climate change by strong absorption of solar radiation in the atmosphere, and on health by penetrating through the human respiratory system. Soot are produced by the incomplete combustion of the fuels. For diesel engines, DPM emissions are limited by means of Diesel Particulate Filters (DPF). The exhaust gas is forced through porous ceramic channels walls, wherein the particles are trapped. These filters are very efficient (> 99% of efficiency) but some issues need to be solved on the regeneration procedure by the vehicles. When a soot load of several grams per liter is de-posited, a regeneration of the filter has to be done by increasing temperature and causes fuel penalty. In the recent years, efforts to link soot nanostructure and re-activity have been done to improve DPF regeneration and HRTEM is often used to visualize the soot nanostructure (see [112]).
A stochastic modeling based on empirical bi-variate distributions has been proposed in [75] for soot particle structure description. This model have been applied to quali-tatively replicate observed particle shapes and provide quantitative improvements over older single-variable models. One model of soot particle nucleation which can predict the classical picture of soot particle inception and the classical description of soot parti-cle structure and growth in laminar premixed hydrocarbon flames are proposed in [33]. The density of active sites which can describe surface growth depends on the chemical environment (see [33]). In flame environments, coronene (C24H12) and pyrene (C16H10) molecule represent the types of soot precursor molecule. A stochastic modeling « basin-hopping global optimization » was used to locate minima on the potential energy surface of the molecular clusters such that its size is similar to small soot particles. Varying soot density on this model and observing how the shape of the particle size distribution changes can inform us on the density of nascent soot. Fig. 2.7 shows an HRTEM image of soot. TEM-style projections of the resulting geometries of the molecule clusters are similar to those observed experimentally in TEM images of soot particles (see [100]).
Observations of active phase of hydrotreating cat-alysts
Catalyst is an additional substance participating in a chemical reaction and can make the reaction occur faster and/or require less activation energy. Usually, only tiny amounts are required. Because of non-consumption in the catalyzed reaction, catalysts can con-tinue to catalyze the reaction of further quantities of reactant. Catalyst has active phase and support components. Hayden and all have demonstrated the importance of initial oxide state and particularly the active-support interactions on the final sulphided state in a way of oxidising atmosphere or 5% H2S=H2 (at a pressure of 68 Pa) and at variable temperature (775-875 K) (see [45]). The morphology with inter-distance between two neighboring white/black fringes (active phase) is in relation to the quantity of oxygen in catalyst (see [59]). Some fringes are curved with radii of curvature as high as 2 to 5 nm (see [24]), and Iwata and all proposed that this curved property may provide default active sites (see [50]). HRTEM (High Resolution Transmission Electron Microscopy) is used as a valuable tool for imaging the crystal structure of crystalline nanomaterials such as catalyst at the atomic scale.
We are interested in the characterization of hydrotreating catalysts with sulphide phases supported on alumina (see [101]) and more specially the active phases of these catalysts. Samples are observed with Transmission Electron Microscope in bright field mode at magnification of the order of 250000. We focus on the analysis of CoMoS sites which produce alternations of black and white fringes as observed in Fig. 2.8 and Fig. 2.10. CoMoS refers to a class of active phases involving Cobalt, Molybdenum and Sulphur atomic structures. The catalytic activity and selectivity depend on the morphology of these sites (see [73] and [101]).
TEM in general has played a very important role in investigating micro-structure of catalysts. Sanders and Pollack showed that TEM was the first method to demonstrate the structure of the active phase of M oS2 in nanometric stacked lamellar sheets (see [79, 91]). Eltzner showed that STEM also demonstrated the proximity of promoters (Ni, Co) to molybdenum and tungsten (see [26]). We present here the HRTEM images and the analyzed samples of two types (X and Y) of catalysts.
Table of contents :
1 General introduction
1.1 Context and motivation
1.2 Contributions
1.3 Thesis outline
2 High Resolution Transmission Electron Microscopy (HRTEM) imaging
2.1 Transmission Electron Microscopy (TEM)
2.1.1 Schematic description of a TEM
2.1.2 Specimen preparation
2.1.3 TEM imaging theory
2.1.4 HRTEM
2.2 Observations of soot nanostructure by HRTEM
2.3 Observations of active phase of hydrotreating catalysts
2.3.1 HRTEM images and sub-images of catalyst X (CatX)
2.3.2 HRTEM images and sub-images of catalyst Y (CatY )
2.4 Structure of fringes (active phases) of catalyst in spatial domain and in frequency domain
3 Generalities on stochastic modeling
3.1 Introduction
3.2 Short versus long memory process
3.2.1 Stationary processes
3.2.2 Short memory process
3.2.3 Long memory process
3.3 Self-similar process
3.3.1 Continuous time self-similar process
3.3.1.1 Self-similar process in continuous time
3.3.1.2 Self-similar process with stationary increments in continuous time
3.3.2 Discrete time self-similar process
3.3.2.1 Self-similar process in discrete time
3.3.2.2 Second order self-similar process in discrete time
3.3.3 Relationships between (asymptotical) self-similarity and short/long memory behaviors
3.4 Examples of self-similar and/or long range dependence processes in continuous time
3.4.1 Gaussian H-SSSI models – fractional Brownian motion
3.4.1.1 Brownian motion
3.4.1.2 Fractional Brownian Motion (FBM)
3.4.2 Non-Gaussian H-SSSI models
3.5 Examples of self-similar and short/long range dependence processes in discrete time
3.5.1 FGN process
3.5.2 k-factor GARMA process
3.5.2.1 Properties
3.5.2.2 ARFIMA process
3.5.2.3 FI process
3.6 2-D stochastic modeling
3.6.1 2-D isotropic FBF modeling
3.6.2 2-D ARMA, AR, MA modeling
3.6.2.1 AR model
3.6.2.2 MA model
3.6.2.3 Causality
4 2-D G-AR-FBF modeling and parameter estimation
4.1 2-D Auto-Regressive Fractional Brownian Field
4.1.1 ARFBF Definition and Spectral Characterization
4.1.2 ARFBF modeling procedure
4.2 2-D K-factor Generalized Fractional Brownian Fields
4.2.1 2-D K-GFBF modeling
4.2.1.1 Modulated Fractional Brownian Field BHq
4.2.1.2 Generalized Fractional Brownian Fields BGHK with K spectral poles
4.2.1.3 A particular sub-class of GFBF: the CMFBF
4.3 Hurst parameter estimation of 2-D FBF
4.3.1 Log-RDWP estimation method
4.3.2 Log-RPWP estimation method
4.3.3 Results of Hurst parameter estimation
4.3.4 Performance of Log-RPWP Hurst parameter estimator
5 Application to HRTEM image characterization
5.1 K-factor GFBF samples and Soot HRTEM textures
5.2 Convolution mixture of FBF and modulated FBF modeling for HRTEM catalyst texture synthesis
5.2.1 Motivation
5.2.2 CMFBF modeling for catalyst HRTEM image
5.2.2.1 Step 1: FBF modeling and suppression
5.2.2.2 Step 2: Modulated FBF parameter estimation
5.2.3 Synthesis of catalyst HRTEM images from CMFBF
5.3 Morphology analysis of catalyst active phase using ARFBF modeling
5.3.1 Problem formulation
5.3.1.1 Pre-processing – WHFR
5.3.2 ARFBF modeling of HRTEM image
5.3.2.1 FBF modeling and suppression
5.3.2.2 AR modeling
5.3.3 Morphological analysis of HRTEM ARFBF features
5.3.3.1 Morphological analysis
5.3.3.2 Lobe detection
5.3.3.3 Characterization on average spatial distance between atomic layers G, distance variation 4G and tangential length L
5.3.4 Statistical analysis for catalyst discrimination
5.3.4.1 Statistical distributions of G, 4G and L
5.3.4.2 Kolmogorov-Smirnov test for catalyst discrimination
6 General conclusion
7 Appendix: résumé substantiel
Bibliography
