4. BACKSCATTERED ELECTRON MICROSCOPY AND ENERGY DISPERSIVE X-
4.2. Materials and experimental methods
4.2.3. Sources of experimental uncertainty
In addition to the usual uncertainties associated with experimental measurements, such as accuracy of calibration and variation of experimental conditions, a few sources of uncertainty specific to BSE-EDX analysis warrant further discussion here. The extent to which useful
compositional information may be gleaned from a BSE micrograph is limited by the topographic variation of the specimen surface, which may give rise to darker and lighter regions that obscure the underlying compositionally-dependent backscattering efficiency of the material. Such variations are observable in the BSE micrographs of the mechanically polished SVC because of the variation in hardness among the sand, hydrates, and anhydrous particles. Small (2002) demonstrated the magnitudes of topographic errors across a range of accelerating voltages using spherical analytical glass standards; measurements on resin-mounted and polished glass shards reveal a relative error in mass fraction measurement on the order of 10% with an excitation voltage of 10 keV to values between 25 and 60% with an excitation voltage of 25 keV.
Therefore, given the 10 keV excitation voltage used in this study, the errors associated with topographic variation are expected to be small.
An essential component of the quantitative analysis of heterogeneous materials is delineating the region from which the signal originates. Although electron microscopes are capable of producing an electron beam on the order of nanometers in width, the volume in which electron collisions occur, that is, the interaction volume, is considerably larger in most materials. For high-vacuum SEM, Kanaya and Okayama [140] derived a semi-empirical expression for the depth of
interaction volume in pure materials, 𝑑𝐾𝑂 [μm], that is directly proportional to the excitation voltage of the electron beam 𝐸0 [keV] and inversely proportional to atomic number, 𝑍, and to the mole density, 𝜌 𝐴⁄ :
𝑑𝐾𝑂 = 0.0276𝐴𝐸05 3⁄
𝑍8/9𝜌 , (4.1)
where 𝐴 is atomic mass [g/mol] and 𝜌 is the density of the medium [g/cm3]. The exponential dependence of 𝑑𝐾𝑂 on accelerating voltage suggests that 𝐸0 should be minimized; however, the optimal value of 𝐸0 is constrained by the requirement for sufficient BSE compositional contrast and sufficient X-ray generation rates. For the carbon-coated samples used in this study, an excitation voltage of 10 keV was found to yield good peak separation in the BSE grayscale
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histogram and near the recommended X-ray collection rate (approximately 3000 counts per second for the Oxford X-Max 50 detector). Whereas Eq. (4.1) provides an indication of size of interaction volume for pure elements, a more rigorous characterization can be achieved by simulating the flight paths of incident electrons, wherein the probabilities of elastic and inelastic scattering are governed by effective atomic cross-sectional areas [141]. Using Monte Carlo simulations of electron trajectories in cementitious targets, Wong and Buenfeld [142] estimated the interaction volume in ettringite to be on the order of 1-100 μm3 for 𝐸0 ranging from 10-20 keV. Considering that the densities of the anhydrous particles in this study are greater than that of ettringite, a 1 μm diameter of the interaction volume may be treated as a conservatively large estimate for all anhydrous particles of interest herein.
The importance of estimating the interaction volume is due to the effect of partial volume averaging (PVA). PVA occurs when the observable interaction volume, herein referred to as the
“probe” volume, is greater than the volume of the feature of interest, and in the case of particles embedded in a resin medium, the sum of elemental mass fractions probed by the electron beam, neglecting the contribution from the resin, is necessarily less than unity. In such situations, renormalization of the mass fractions may be appropriate, but in scenarios in which a particle is interspersed within a medium of comparable composition, for instance anhydrous particles within C-S-H, PVA may lead to a locally measured composition that is characteristic of neither the particle nor the medium. Moreover, the extent of the interaction volume will be greater in the direction of the phase with lower mean Z due to the lower occurrence of electron scattering events. Consequently, the fraction of pixels near a feature boundary will determine whether a feature’s composition can be accurately measured; features smaller than the interaction volume cannot be probed in isolation; whereas, the mean composition of very large features is relatively insensitive to PVA of the boundary pixels. Therefore, the likelihood of misclassifying particles smaller than the interaction volume may be high, and it is necessary to estimate the proportion of these particles relative to the entire population.
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Figure 4.1: a, b, and c) Probability density function representation of particle size (diameter) distributions for BFS, FAF, and OPC particles, respectively, as measured by laser diffraction of particles suspended in propan-2-ol [138]. Darker regions of each histogram to the left of the diameter on the x-axis indicate the fraction of particles smaller than the nominal probe diameter at the corresponding value. Note that the abscissa is presented on the logarithmic scale. d) Summary of the probability that a particle is smaller than the nominal probe diameter.
With an estimate of the approximate diameter of the interaction volume, the fractions of anhydrous particles smaller than the probe volume (and necessarily partial-volume averaged) may be calculated from particle size distributions of the isolated, unreacted binder particles measured via laser diffraction [138]. For the BFS, FAF, and OPC particles used this study, Figs.
4.1a - 4.1c illustrate the measured distribution of particle diameters, with shaded areas representing the fraction of particles with diameters less than or equal to the nominal probe diameters of 1, 2, 4, and 10 μm (marked on the abscissas). As noted in Table 4.2, the mean values of particle diameter are substantially lower than the medians for all three particles, and for all three particle types, the maximum of the probability density function lies below the 1 μm
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threshold. Ostensibly, the large proportion of small BFS, FAF, and OPC particles would suggest that SEM-EDX analysis is ill-suited to characterizing these particles; however, as shown in Fig.
2.1d, particles less than 1 μm in diameter only comprise about 5 % of each unreacted material’s population, and would be expected to comprise a much smaller fraction of the material’s
population after reaction. Thus, PVA is not deemed to be a significant source of error in estimating the area fractions of remaining unreacted particles within the SVC mortar.