EPMA of Porous Media: A Monte Carlo Approach

Mikrochim. Acta 132, 189±199 (2000)

EPMA of Porous Media: A Monte Carlo Approach LoõÈc Sorbier1;, Elisabeth Rosenberg1 , Claude Merlet2 , and Xavier Llovet3 1 2 3

Institut Franc° ais du Petrole,1 et 4 Avenue de Bois Preau 92852 Rueil Malmaison Cedex, France ISTEEM, CNRS, Universite de Montpellier II, Sciences et Techniques du Languedoc, Place E. Bataillon 34095 Montpellier Cedex 5, France Serveis Cientõ®co-Tecnics, Universitat de Barcelona, LluõÂs Sole i SabarõÂs, 1-3, E-08028 Barcelona, Spain

Abstract. We examine the in¯uence of the sample porosity on the X-ray emission from mesoporous alumina bombarded with kilovolt electrons. Experimental results show that there is a loss of X-rays (Al K and O K) from those samples when compared to a fully dense mono-crystalline alumina (sapphire), which depends on the X-ray line, the measurement time and the embedding medium. Both geometrical and charging effects may be responsible for this signal loss. Monte Carlo simulations of the X-ray intensity emitted from porous alumina, using different models to describe sample porosity, show that the geometrical effect of porosity itself cannot account for the X-ray loss. Charge trapping effect and/or its combination with porosity is therefore expected to be the major cause of the signal loss. Key words: EPMA; catalyst; alumina; porous; Monte Carlo.

Many heterogeneous catalysts in industry consist of metals and promoters supported by porous alumina of very high speci®c surface. The total concentration of those metals often does not exceed 2%wt. It is of great importance for catalyst optimization to know the spatial distribution of active elements inside the matrix. Therefore electron probe micro analysis (EPMA) is widely used to study the local concentration across the diameter of catalyst pellets or extrudates. However, a de®cit of emitted X-rays is observed (as compared with fully dense materials). When traditional EPMA correction procedures are  To whom correspondence should be addressed

employed this leads to unrealistically low total composition [2]. Some authors [1, 2] have suggested that charge trapping effects due to the insulating feature of the material, might be the responsible of the signal loss. The observed X-ray loss might also be due to the effect of the porous geometry of those materials, since measured X-ray intensities appear to depend on the porosity of the catalyst at the impact point of the electron beam. The porosity is thus expected to play a role but not necessarily in a straight way. The aim of this work is to study the effect of the sample porosity on the emitted X-ray intensity in order to verify whether the geometrical arrangement of voids (vacuum) within the sample may be itself partially responsible for the loss of X-ray intensity. Monte Carlo simulations of X-ray emission from porous samples have been performed using the simulation package PENELOPE, together with ionization cross sections computed from an optical-data model. In order to calculate the contribution of the textural effect on the observed signal de®cit, different porous models have been de®ned, from the simplest one to a realistic pore size distribution medium. Also, experimental measurements of X-ray emission from mesoporous alumina are presented. Experimental The studied mesoporous alumina is commonly used as catalyst support in industrial reforming processes. It is a homogeneous, ®ne structured alumina with the following characteristics: 5% loss on ignition, 250 m2 /g speci®c area, 0.6 cm3 /g porous volume (68% porosity). Particle and pore diameters range from 2 to 10 nm. The

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Fig. 1. SEM micrograph of the studied alumina

material is homogeneous at the micron scale, which minimizes the geometrical effects due to the roughness of the surface. A SEM image of a fracture of this sample is presented in Fig. 1; the full size of the micrograph is about 2 mm. Experimental X-ray intensities were acquired using a JEOL electron microprobe JXM8800, equipped with four spectrometers. Al K and O K signals were detected using TAP (thallium acid Ê ) crystals. Measurements were phthalate) and LDE1 (2d ˆ 60 A made using a stationary focused or defocused probe, using 10 nA beam current to avoid irradiation damage, and 10 second counting time on peaks (5 seconds on backgrounds). Chosen integration time and beam current provide a statistical error of about 1%. Al K and O K intensities are compared to a fully dense monocrystalline alumina (sapphire) from Goodfellow. The porous alumina was embedded both in epoxy resin (classical embedding, Struers Citofix) and in a conductive resin (Struers Polyfast). Sapphire standard was embedded in conductive resin only. They were then polished with SiC papers and diamond suspensions up to 2 mm, and coated with an approximately 15-nm-thick Cr layer. Cr coating was made simultaneously on samples and sapphire. Cr was chosen because the Al K and O K rays are nearly equally absorbed and the LDE1 crystal has a sufficient wavelength resolution to separate the O K line from Cr L lines [3] to allow accurate O K peak and background measurements. Cr K was measured on LiF in order to estimate the coating thickness and check its homogeneity. The thickness was determined from average k-ratios measured at different accelerating voltages. C Ê ) to follow the carbon K was measured on LDE2 (2d ˆ 100 A contamination.

Monte Carlo Simulation The PENELOPE Simulation Package The simulation package PENELOPE (PENetration and ENergy LOss of Positrons and Electrons) is a FORTRAN subroutine package that simulates the combined transport of electrons and photons in matter [6]. PENELOPE allows the user to write his own

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simulation program, with arbitrary geometry and scoring, without any previous knowledge of scattering and transport theories. Thus, it is well suited for simulating in complex geometry such as porous media. Thus, the main program, to be provided by the user, only has to control the evolution of the tracks simulated by PENELOPE and keep score of relevant quantities. The differential cross sections (DCS) adopted in PENELOPE are simple analytical functions of the scattering angle and energy loss that allow random sampling of the scattering angle and energy loss in a completely analytical way. Although these DCSs are approximations to the actual ones, they lead to essentially the same simulation results, provided the scattering is multiple (i.e. the average number of events along an electron trajectory must be of the order of 20 or larger [7]). The DCSs implemented in the code as well as the simulation algorithm have been described in detail elsewhere (see [6] and references therein). Brie¯y, elastic scattering of electrons is simulated by a combination of Wentzel (screened Rutherford) differential cross section (DCS) and a ®xed-angle scattering process, which is referred to as the W2D model [7]. Inelastic collisions are described in terms of a simple generalized oscillator strength model proposed by Liljequist [8]. The simulation of the electron trajectories may be performed on the basis of a ``mixed'' procedure (combining detailed simulation with multiple scattering theories); however, in the simulations of the present work, we have only used the detailed method (interaction by interaction). PENELOPE has been shown to be well suited for its application in the energy range of interest in EPMA [10]. Simulation of X-Ray Intensity from Massive Samples Following Castaing's de®nition, the depth distribution of ionization or function (z) is de®ned in such a way that (z)
z gives the intensity generated in a depth element z ‡
z in the sample divided by the intensity emerging from a self-supporting layer of the same mass thickness
z. For each electron trajectory, the function (z) evaluated at a mass depth zi is given by: …zi † ˆ

X 1 e; j …Eseg † Sseg …i†
z e; j …E0 † seg

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EPMA of Porous Media

where e, j (E) is the ionization cross section for the jshell of the element of interest, Sseg(i) is the path segment contained between [z, z ‡
z], Eseg is the electron energy in this path segment (assumed to be constant) and E0 is the electron incident energy. Using this de®nition, factors such as the density of emitting atoms and the ¯uorescence yield cancel out. In the simulations of this work, we have used total ionization cross sections derived from an optical-data model proposed by Mayol and Salvat [9], which has been shown to give reliable results as regards K-shell ionization [10]. The estimator h(zi)i of (zi) is then obtained by simulating a large number of electron trajectories N. At the end of the simulation, the estimator of the emerging intensity hIi is computed by numerical integration of h(zi)i as follows, hIi ˆ

…1 0

ÿ1 z

h…z†ie sin…† d…z†

 Ns  X ÿl …iÿ1†
z sin…† h…zi †ie ˆ 
z iˆ1

where 1 is the photon mass absorption coef®cient of line 1, Ns is the number of slices used to evaluate (z) and  is the take-off angle (in the program, the absorption of emitted photons in the emitting slice was also taken into account).

Simulation of X-ray Intensity from Porous Media In porous media, electron trajectories are simulated in matter volumes using PENELOPE while in void volumes the electron is let to ¯y with no interaction, until next interface is reached. Here, it should be noted that the dimensions of matter volumes must be large enough to ensure that multiple scattering is reached. In practice, we must ensure that the ``size'' of matter volumes is at least about 20 times the elastic mean free path of electrons in the material. Although in our material this condition is not ful®lled (in bulk alumina the elastic mean free path is larger than 1 nm, except for electron energies below the Al K-shell ionization threshold, and in mesoporous alumina particle sizes are about 10 nm), we can consider to a good approximation that the adopted simulation scheme is accurate enough for the purposes of this work. The principle of the simulation algorithm is the following (see Fig. 2). The hypothesis is made that the electron lies in matter: 1. A free path DS is sampled (by JUMP subroutine). 2. A path in matter DSINMAT (the length to the next matter/void interface) and a path in void DSINVOID (the length between the next matter/void and void/matter interfaces) are calculated. 3. If DS>DSINMAT, the electron travels a length DSINMAT in matter, then a path DSINVOID in

Fig. 2. Flow diagram of the MAIN program for simulating electron penetration in porous materials with PENELOPE

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void, contribution for (z) is recorded and points 2 and 3 are repeated until total length traveled in matter is equal to DS. Then algorithm goes to 5. 4. If DS