Elsevier

Ultramicroscopy

Volume 111, Issue 1, December 2010, Pages 62-65
Ultramicroscopy

On the measurement of thickness in nanoporous materials by EELS

https://doi.org/10.1016/j.ultramic.2010.09.011Get rights and content

Abstract

This work discusses thickness measurements in nanoporous MgO using the log-ratio method in electron energy-loss spectroscopy (EELS). In heterogeneous nanoporous systems, the method can induce large errors if the strength of excitations at interfaces between pores and the matrix is large. In homogeneous nanoporous systems, on the other hand, the log-ratio method is still valid, but the inelastic scattering mean-free-path is no longer equal to that in the same bulk system.

Research Highlights

► Application of EELS in nanoporous materials is different from that in bulk materials. ► The inelastic scattering mean-free-path in nanoporous system is no longer equal to that in the same bulk material. ► Thickness measurement using EELS is only appropriate in homogeneous nanoporous system.

Introduction

Specimen thickness is one of the most crucial parameters for quantitative analysis in transmission electron microscopy (TEM). Several methods have been used to measure relative or absolute specimen thickness. The simplest and the most accurate method involves the use of oxide nanocrystals, which grow naturally as perfect single-crystal cubes, such as MgO, whose orientation can be determined from diffraction data. Other methods include straightforward measurements of planar features intersecting both upper and lower surfaces [1] and contamination spots [2] or lines [3]. More accurate methods, however, are based on convergent beam electron diffraction (CBED), including two-beam CBED [4] and zone-axis-CBED [5] methods. Due to the requirement for strong diffraction, however, these are not applicable to very thin (or porous), fine grained polycrystalline or amorphous specimens. For thin crystals or amorphous materials, the differential characteristic X-ray absorption method has been used, which makes use of the difference in absorption between K and L (or L and M) characteristic lines emitted simultaneously from the same [6] or different [7] elements. This method, unfortunately, is not applicable for specimens containing only light elements.

A method that may, in principle, overcome all the above mentioned limitations is based on electron energy-loss spectroscopy (EELS) [8]. The fundamental assumption of this EELS method is that multiple inelastic scatterings consist of a series of independent events that are thickness dependent, and therefore obey Poisson statistics Pn=(1/n!)(t/λ)nexp(t/λ) for n-fold scattering probability [8]. The thickness t can then be determined from the unscattered (n=0) component (i.e. zero-loss peak):t/λ=ln(Itot/I0)

In this log-ratio formula, λ is the total inelastic scattering mean-free-path (MFP), and I0 and Itot are integrated intensities of the zero-loss peak and the entire energy-loss spectrum, respectively. The absolute thickness can be obtained if the effective total inelastic MFP is known. In practice, λ is sensitively dependent on experimental conditions, such as collection semiangle and beam accelerating voltage [8]. Details of this log-ratio method have been given in many review articles and textbooks [8], [9]. Strictly speaking, the total inelastic scattering Itot also includes a contribution from scattering that is independent of specimen thickness, e.g. surface excitations [10]. As a good approximation, intensities due to surface excitations can be ignored if the specimen is not very thin, generally t/λ>0.1 [9]. One of the advantages of using the log-ratio formula is that the method does not require crystalline perfection. It is therefore widely applied to amorphous materials [11].

In the study of porous materials, the effective thickness of the specimen is crucially important in determining porosity. In specimens that may vary in porosity, thickness is usually measured in terms of mass-thickness (or effective thickness) [12]. Due to high density of nanopores, the effective thickness (or mass thickness) along the path of the electron beam must be shorter than the physical thickness of the specimen. The difference can be used to estimate porosity if the size of the nanopores can be obtained from an image. One may consider the log-ratio EELS technique because the incident electron loses its energy only in the path that contains matter [13], [14]. In nanoporous materials, however, there are many interfaces between material and nanopores. The interfacial excitations alter the effective dielectric response to the electron beam [15]. Although the physical thickness of a porous specimen may not be small, the large portion of surface area may affect the applicability of the EELS method to porous materials. In this note, we re-evaluate the validity of this method in nanoporous materials.

Section snippets

Experimental

The samples used in this study were nanoporous and bulk MgO, and were dehydrated from Mg(OH)2 by thermal annealing at 450 and 1000 °C for 2 h, respectively. The samples dehydrated at 450 °C consist of nanopores, but these are sintered to bulk MgO nanoparticles at 1000 °C. The detailed procedure can be found elsewhere [16]. The TEM specimens were prepared by grinding the samples into powders in dry air, and picking them up using a Cu grid covered with a lacy carbon thin film. The specimens were then

Results and discussion

Fig. 1 compares two spectra acquired in bulk and nanoporous MgO. Both spectra were normalized to their total integrated intensities [0−120 eV]. The relative thicknesses evaluated by the log-ratio methods are about the same, i.e. t/λ=0.80 and 0.78 for bulk and nanoporous MgO, respectively. The ratios of plasmon to zero-loss peak are also about the same; they are 0.055 and 0.052 for bulk and nanoporous MgO, respectively. Following the criterion given by Williams and Carter [9], the errors in

Conclusion

Caution should be exercised when applying the log-ratio method to the measurement of thickness in porous materials. If the nanopores are heterogeneously distributed in the matrix, the strength of excitations at interfaces between pores and the matrix must be examined in order to estimate the error introduced in a thickness measurement. On the other hand, if the nanopores are homogeneously distributed in the matrix, the log-ratio method is in principle still applicable, but MFP in the nanoporous

Acknowledgements

This work is supported by NSF Award DMR0603993. The use of facilities within the Center for Solid State Science at ASU is also acknowledged.

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1

Present address: Center for Functional Nanomaterials, Brookhaven National Laboratory, USA.

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