The three specifications requested from the participants with respect to the analysis step were: duration of the measurement, model used to fit scattering results (Mie or Fraunhofer), and, if Mie, complex refractive index used (real and imaginary) for both cement and medium.
The reported measurement duration varied from 4i−120 s. This is a wide range that seems to depend primarily on the commercial device used. Nevertheless, the majority of measurements were of 60 s duration or less, and this is clearly one reason that LAS has become so prevalent within the cement industry. However, no clear correlation was observed between measurement time and PSD results, and presumably this is because each instrument determines the length of measurement necessary to reach some internally set signal-to-noise ratio.
As stated in the introduction, of the two optical models for interpreting angle-dependent scattering by particles, Fraunhofer and Mie, only the second one requires the refractive indices to be specified. According to ISO 13320-1, the Fraunhofer model works well for particle sizes >50 µm. For particle sizes <50 µm, the Mie model is preferred if a reasonable estimate of the refractive indices are available. In the intermediate range from about 1 µm to 50 µm, the appropriateness of the choice of optical model will depend on whether the relative refractive indices (ratio of particle to medium) are high or low, and thus the decision is more complicated. In the submicrometer range, the Fraunhofer model is not applicable. The availability of different optical models on a particular commercial instrument may also be a limiting factor for some users. It was found that 80% of the participants used either Fraunhofer,Mie, or both. It is surprising that as many as 16% of the participants seem unaware of which optical model they are using to analyze their data.
The choice of complex refractive index is critical if the Mie optical model is used to interpret the data and produce the PSD of the cement. For the cement phase, the value of the real component of the index reported by round robin participants varies from 1.23 to 1.88. But if we exclude the single value at 1.23, the minimum value is then 1.6 and the range is significantly narrowed. The median value is 1.73, if 1.23 is excluded. Most participants (64%) used 0.1 for the imaginary (absorption) component of the refractive index of cement, a value that is widely reported by instrument manufacturers and in the literature. Other values reported were 0.01 (by 27% of the participants) and 1.5 by a single participant. A consensus value for the real and complex indices would yield 1.73 and 0.1, respectively. It should be noted that the data set produced using the refractive index value of 1.5, far from the mean, nevertheless was not determined to be an outlier in the subsequent statistical analysis. Sources for the refractive index values reported by the participants were not requested and were not shown. Because these values can vary with powder composition, it is an interesting observation that each participant apparently selects a single set of values and applies them to all cements regardless of composition. If some consideration was given to the compositional variations during the selection process, it was not possible to determine this from the round robin study.
The influence of variations in the real and imaginary components on the cement PSD calculated using the Mie optical model was examined at NIST. The imaginary refractive component primarily impacted the fine fraction of the PSD, as indicated in Fig. 6 for CCRL 135 cement in IPA. When the real component was fixed at 1.7 (i.e., close to the consensus value derived from the round robin results) and the imaginary component was allowed to vary, only sizes below 10 µm were significantly impacted. These results demonstrate that ignoring absorption or using a value for the imaginary component that is too small, leads to an underestimation of the fine fraction, particularly sizes below 2 µm. The impact of the imaginary component also depends on the value of the real component. For highly refractive materials, having a real component above 1.7, the effect of absorption on the PSD quickly becomes negligible. The effect of varying the real component, with the imaginary component fixed at 0.1 (i.e., the consensus round robin value) is shown in Fig. 7. For values of 1.7 and higher, only the fine fraction is significantly impacted by changes in the real component, and the effect is relatively small. However, for values below 1.7, the entire PSD changes drastically with relatively small changes in the real component. The behavior is similar for smaller fixed values of the imaginary component, where we find that the critical value for the real component (i.e., the value at which further increases have minimal impact on the calculated PSD) decreases with decreasing imaginary component. In other words, the more refractive materials (high real component) are less subject to absorptive effects, and the less transparent materials (high imaginary component) can exhibit strong refractive index effects if the real component is below a critical value.
FIG. 6−Calculated cumulative PSD for cement powder (CCRL 135) dispersed in IPA as a function of the imaginary component (Im) of the complex refractive index, with the real component fixed at 1.7.
FIG. 7−Calculated cumulative PSD for cement powder (CCRL 135) dispersed in IPA as a function of the real component (Re) of the complex refractive index, with the imaginary component fixed at 0.1.
A standardized test method would have to account for the possibility that either the Fraunhofer or the Mie model might not be available to every user. An ASTM standard should also recommend refractive indices to be used for certain types of cement, or, alternatively, a method for estimating these values based on the known composition of the powder. Further studies to establish the influence of the model choice and model parameters were conducted at NIST (Hackley et al., 2004).