Variations of Chemical Composition and Band Gap Energies in Hectorite and Montmorillonite Clay Minerals on Sub-Micron Length Scales

Home , Hectorite

2006-2011 Mission Kearney Foundation of Soil Science: Understanding and Managing Soil-Ecosystem Functions Across Spatial and Temporal Scales Final Report: 2009008, 1/1/2011-12/31/2011 Variations of Chemical Composition and Band Gap Energies in Hectorite and Montmorillonite Clay Minerals on Sub-Micron Length Scales

William Horwath*, Yan Ling Liang

The relevance of clay minerals to humanity cannot be underestimated. Clays contribute to a plethora of soil processes and are believed to have played a role in the origin of life on earth (Porter et. al. 2000). In modern times clays are used for environmental remediation, catalytic reactions, industrial processes and chemical filtering. In the natural environment clay minerals can comprise a significant mass of soils, providing physical support and nutrients for plants, fauna and microbial life (Dixon and Weed 1989). A complete knowledge of the chemical, physical and electronic characteristics of clays is indispensible for understanding these natural and industrial processes. Due to the ubiquitous nature of clays minerals, any additional knowledge gained about the subject matter would be beneficial at many scales from soil microaggregates to soil pedons to large scale industrial and environmental systems. Our research focuses on the electronic properties of clay minerals, specifically the band gap energy of clay minerals on a spatially resolved sub-micron scale. Band gap energies are the energies required to promote an electron from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). We are interested in this property because it has been shown to relate with many physical and chemical properties of molecules. For instance, band gap energies have been shown to play a part in determining optical properties of a material, determining the insulating/conducting properties, determining the stability of a product relative to its transition state and reactants, determining the degree of covalent/ionic bond nature between two atoms, determining the enthalpy of a reaction and determining a correlation to magic numbers in metal clusters [Pearson 1997, Pearson 1967]. To gain a more thorough understanding of clay mineral band gaps and the type of variability that can occur in natural environments based on band gap properties; we explored various methods of calculating and measuring band gap information. Three different methods were explored: theoretical modeling, a more commonly used method DR UV-Vis spectroscopy and a more novel method TEM-EELS. Results from the three methods are presented below.

Department of Land, Air and Water Resources, University of California Davis *Principal Investigator For more information contact Dr. William Horwath ([email protected]) Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Project Objectives

 Objective: Correlate the degree of isomorphic substitution (chemical composition) in Hectorite and Montmorillonite clays to the magnitude of the band gap measured on a sub-micron spatially resolved scale. o Hypothesis: We suspect that spatial areas of higher isomorphic substitution will have a smaller band gap, indicating higher reactivity of the area (lower electronic stability).  Objective: Study the variation of chemical composition on the sub-micron spatially resolved scale for Hectorite and Montmorillonite clay minerals. Approach and Procedures

 Clay preparation o Clays were homogenized by ball milling until average particle size was 2 µm. After particle size homogenization, clays were saturated with Ca by multiple washing with 0.1 M Ca(NO3)2. Saturated clays were washed with DI water to remove excess nitrates and Ca precipitation products until no further Ca could be detected using UV-Vis spectroscopy. Particle-size analysis was performed with a Beckman Coulter LS-230 Particle Size Analyzer.  Theoretical Modeling o Theoretical modeling was performed using Materials Studio, CASTEP model. o Hectorite and Montmorillonite crystal structure models were obtained from American Mineralogist Crystal Structure database.  Diffuse Reflectance Ultraviolet-Visible Spectroscopy (DR UV-Vis Spec) o Instrumentation: Thermo Scientific Evolution 220 UV-Vis Spectrometer with Thermo INSIGHT software. . Scan: 190-1100 nm, bandwidth: 1nm, integration time: 0.1 s, data interval: 1 nm, scan speed: 600 nm/min.  Transmission Electron Microscopy-Electron Energy Loss Spectroscopy/Energy Dispersive Spectroscopy (TEM-EELS/EDS) o Instrumentation: JEOL 2500 TEM equipped with Fischione detector . Clays were drop casted on holey carbon grids, decontaminated by exposure to incandescent light and stored under vacuum to minimize carbon contamination. . TEM was aligned using basic alignment procedures, and then subsequently aligned in STEM mode. GIF tuning performed to maximize energy resolution in EELS. Data processed in Digital Micrograph software. . EELS analysis (Digital Micrograph) includes Zero Loss Peak (ZLP) removal, then multiple scattering deconvolution. . EDS quantification (Digital Micrograph) method used is a standardless k-factor method.

2 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath Results

Theoretical Modeling Results and Diffuse Reflectance UV-Vis Spectroscopy Results Figures 1 and 2 show the density of states results modeled using CASTEP, the x axis is the energy of the electron state in eV and y axis is the Density of States (DOS). DOS indicates the probability of a particular electronic state at any energy level. According to the model, Hectorite theoretically has a band gap of approximately 4 eV (Figure 1). The theoretical band gap for Montmorillonite is 0 eV (Figure 2). A 4 eV band gap designates the material as an insulator, while 0 eV band gap indicates the material is a conductor. Figure 3 shows a DR UV-Vis spectrum where the x axis is energy in eV and y axis is arbitrary Abs units. The blue flat line is the Teflon blank (Figure 3). There is little noise in the measurements and the spectrum becomes noisier only at energies less than 2 eV and greater than 6 eV, which can be observed also in the sample spectrums (red and green curves in Figure 3). The red and green curves are Hectorite and Montmorillonite spectrums respectively. Hectorite has a larger range of band gaps from 1.5 eV to 6.5 eV compared to that of Montmorillonite which starts at 2 eV extending to 6.5 eV. Both clays have the majority of its band gaps residing at 4.75 eV.

Figure 1. CASTEP theoretical modeling results for Hectorite clay mineral.

3 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Figure 2. CASTEP theoretical modeling results for Montmorillonite clay mineral.

Figure 3. Diffuse Reflectance UV-Vis data for Hectorite, Montmorillonite and Teflon blank. X axis is energy in eV, y axis is arbitrary Abs units.

4 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

TEM-EELS and TEM-EDS Results

Table 1 summarizes the band gaps and elemental composition of Hectorite clay particle H1 shown in Image 1. The box #s in Table 1 correspond to the appropriately labeled colored boxes in Image 1. O, Si, Mg and Ca atom % does not add up to 100%, the remaining element not included in the tables is C, which accounts for the remaining atoms %. The band gap measured by TEM-EELS ranges from 3.25 to 3.6 eV, giving a range of 0.35 eV. The average band gap value is 3.4 eV. The overall atom % can fluctuate greatly for each individual element (the signals of O, Si, and Mg) depending on the atom % of carbon contributing to the EDS (Table 1). Despite the large variation that can occur with the raw elemental EDS signals, the ratios of these raw elements Si/Mg, Si/O and Mg/O remain relatively stable (Table 1). The Si/Mg ratio ranges from 1.16 to 1.31, giving a range of 0.15. The Si/O ratio ranges from 0.32 to 0.41, range is 0.09. The Mg/O ratio ranges from 0.24 to 0.31, range is 0.07. This seems to indicate that the degree of isomorphic substitution in this particular Hectorite particle is fairly evenly distributed. Calcium atom % was too low to contribute to the EDS signal, which is a sign of a very low level of calcium coverage either on the surface and/or in the interlayers of the clay particle.

In order to determine if a linear correlation of band gap energies with raw elemental atom % or the calculated ratios, the band gap value for each box # was plotted against each element O, Si, Mg and ratios Si/Mg, Si/O and Mg/O for the corresponding box #. The R2 values, slopes and intercepts are summarized in Table 1. Si/Mg and Mg/O ratios gave the best linear correlations with band gap values, while the other elements and ratio gave significantly poorer linear correlation (less than 0.4).

Table 2 summarizes the band gaps and elemental composition of Hectorite clay particle H2 shown in Image 2. The box #s in Table 2 correspond to the appropriately labeled colored boxes in Image 2. O, Si, Mg and Ca atom % do not add up to 100% in Table 2, the remaining element not included in the tables is C, which accounts for the remaining of the atoms %. The band gap measured by TEM- EELS ranges from 3.15 to 3.7 eV, giving a range of 0.55 eV. Box 14 (Table 2) gives a band gap of 5.05 eV, this is considerably larger than the other measured values from the same sample (Boxes 1-13). It is suspected that the EELS signal from the surrounding carbon grid overwhelms the EELS signal from the Hectorite particle, resulting in an inaccurate band gap which also includes a significant amount the carbon grid. Essentially, the band gap measured for box 14 (Table 2) is a mixed signal band gap of the carbon grid and H2 particle. The average band gap (disregarding box 14) is 3.4 eV. The atom % for O, Si and Mg can vary up to 10%, the element ratios appear to be more stable. The Si/Mg ratio ranges from 1.33 to 1.62, range is 0.29. The Si/O ratio ranges from 0.36 to 0.54, range is 0.18. The Mg/O ratio ranges from 0.27 to 0.39, range is 0.12. Calcium atom % was too low to contribute to the EDS signal (Table 2), low levels of calcium surface coverage and/or interlayer coverage is suspected for particle H2. The R2, slope and y-intercept values for the linear plots of band gaps against each element O, Si, Mg and ratios Si/Mg, Si/O and Mg/O are summarized in Table 2. The best correlation was found to be with oxygen, while the rest of the elements and ratios gave very poor correlations.

5 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Atom % Ratios

Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca

1 3.60 43.15 0.88 13.80 0.67 10.56 0.43 0.00 0.00 1.31 N/A N/A 0.32 0.24 N/A

2 3.40 36.33 0.86 13.73 0.65 10.58 0.41 0.00 0.00 1.30 N/A N/A 0.38 0.29 N/A 10.03 3 3.50 38.08 0.96 12.78 0.73 0.48 0.00 0.00 1.27 N/A N/A 0.34 0.26 N/A 16.96 4 3.25 40.93 1.14 0.89 14.11 0.58 0.00 0.00 1.20 N/A N/A 0.41 0.34 N/A

5 3.35 38.12 0.88 14.71 0.66 11.83 0.44 0.00 0.00 1.24 N/A N/A 0.39 0.31 N/A 11.22 6 3.25 38.79 0.96 13.98 0.75 0.49 0.00 0.00 1.25 N/A N/A 0.36 0.29 N/A 23.75 7 3.30 0.90 7.59 0.66 6.55 0.45 0.00 0.00 1.16 N/A N/A 0.32 0.28 N/A

8 3.60 39.41 0.39 14.39 0.30 11.26 0.19 0.00 0.00 1.28 N/A N/A 0.37 0.29 N/A 38.09 11.37 9 3.45 0.46 14.40 0.35 0.23 0.00 0.00 1.27 N/A N/A 0.38 0.30 N/A

10 3.40 34.91 0.33 12.49 0.25 10.04 0.16 0.00 0.00 1.24 N/A N/A 0.36 0.29 N/A

O Si Mg Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca

R^2 = 0.1406 0.003 0.0072 0.5229 0.1656 0.4054

Slope = 15.234 1.0215 -1.2483 0.2502 -0.095 -0.1326

Intercept = -14.793 9.9998 15.012 0.3985 0.6855 0.7412 Table 1. TEM EELS and EDS data for Hectorite particle H1. Box #s correspond to box numbers in Image 1 below with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included. N/A results from the denominator being 0 atom %, rendering the ratios uninformative.

6 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Image 1. Hectorite particle H1 images and box numbers. Corresponds to Table 1.

Spectrum Image

0.50.5 µµm

7 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

H2 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca 1 3.45 37.09 0.86 13.23 0.66 9.87 0.42 0.00 0.00 1.34 N/A N/A 0.36 0.27 N/A 2 3.60 40.02 0.90 17.85 0.74 10.99 0.45 0.00 0.00 1.62 N/A N/A 0.45 0.27 N/A 3 3.70 41.84 0.79 17.21 0.63 12.31 0.39 0.00 0.00 1.40 N/A N/A 0.41 0.29 N/A 4 3.55 41.43 1.00 19.07 0.85 12.66 0.53 0.00 0.00 1.51 N/A N/A 0.46 0.31 N/A 5 3.65 45.12 0.86 22.32 0.73 14.03 0.45 0.00 0.00 1.59 N/A N/A 0.49 0.31 N/A 6 3.15 45.63 0.85 19.56 0.68 13.60 0.43 0.00 0.00 1.44 N/A N/A 0.43 0.30 N/A 7 3.50 45.05 0.96 23.39 0.88 17.27 0.56 0.00 0.00 1.35 N/A N/A 0.52 0.38 N/A 8 3.20 45.90 0.79 20.73 0.67 15.64 0.43 0.00 0.00 1.33 N/A N/A 0.45 0.34 N/A 9 3.35 44.91 1.75 24.44 1.64 17.55 1.07 0.00 0.00 1.39 N/A N/A 0.54 0.39 N/A 10 3.70 42.17 0.42 18.57 0.35 12.57 0.22 0.00 0.00 1.48 N/A N/A 0.44 0.30 N/A 11 3.35 44.31 0.40 19.84 0.34 13.56 0.21 0.00 0.00 1.46 N/A N/A 0.45 0.31 N/A 12 3.55 45.31 0.44 21.13 0.38 14.33 0.23 0.00 0.00 1.47 N/A N/A 0.47 0.32 N/A 13 3.60 45.78 0.47 21.60 0.41 15.40 0.26 0.00 0.00 1.40 N/A N/A 0.47 0.34 N/A 14 5.05 40.28 0.28 17.99 0.23 12.60 0.15 0.00 0.00 1.43 N/A N/A 0.45 0.31 N/A O Si Mg Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca R^2 = 0.1655 0.0494 0.0641 0.0138 0.0035 0.0148 Slope = -2.4683 -1.403 -1.2268 0.0228 -0.006 -0.0097 Intercept = 52.0890 24.832 18.1580 1.3618 0.4776 0.3515 Table 2. TEM EELS and EDS data for Hectorite particle H2. Box #s correspond to box numbers in Image 2 below with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

8 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Spectrum Image

11 µµm

Image 2. Hectorite particle H2 images and box numbers. Corresponds to Table 2. Table 3 below summarizes the band gaps and elemental composition of Hectorite clay particle H3 shown in Image 3. O, Si, Mg and Ca atom % does not add up to 100% in Table 3, the remaining element not included in the tables is C, which accounts for the remaining of the atoms % as previously mentioned. The band gap measured by TEM-EELS ranges from 1.65 to 7.2 eV, giving a range of 5.55 eV. This could suggest that particle H3 has a very large spatial variation in isomorphic substitution from one area to the next. The average band gap is approximately 4.5 eV. Si/Mg ratios range from 1.98 to 3.35, range is 1.37. Si/Ca ratio range from 2.3 to 12.57, range is 10.27. Mg/Ca ratios range from 1.14 to 5.2, range is 4.06. Si/O ratios range from 0.68 to 1.1, range is 0.42. Mg/O ratios range from 0.2 to 0.45, range is 0.25. O/Ca ratios range from 3.37 to 16.21, range is 12.84. The R2, slope and y-intercept values from linear correlation of band gaps to element atom % (O, Si, Mg and Ca) and ratios (Si/Mg, Si/Ca, Mg/Ca, Si/O, Mg/O and O/Ca) for particle H3 are summarized in Table 3. The greatest linear correlation with band gaps was for Si/Mg ratios. The rest of the elements had linear correlations that were much poorer. Calcium concentration on particle H3 is significantly higher, averaging about 3.2 atom %. Possibly the high degree of spatial variation in isomorphic substitution contributed to such high calcium surface and interlayer coverage. Unfortunately, it cannot be distinguished where the calcium is on the surface, but since EDS signals arise from mainly surface elements, there is a good probability a major portion of the calcium signal is from surface sorbed Ca ions. 9 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

H3 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca 13.21 0.53 1 4.25 37.04 1.09 26.86 0.84 3.05 0.30 2.03 8.81 4.33 0.73 0.36 12.14 11.53 0.49 2 7.20 41.04 1.04 28.86 0.81 2.82 0.29 2.50 10.23 4.09 0.70 0.28 14.55 11.67 0.37 3 4.60 41.61 0.80 28.28 0.61 3.33 0.24 2.42 8.49 3.50 0.68 0.28 12.50 12.38 0.32 4 2.30 40.94 0.68 31.00 0.54 3.55 0.19 2.50 8.73 3.49 0.76 0.30 11.53 10.40 0.36 5 2.40 39.22 0.81 31.12 0.66 2.77 0.23 2.99 11.23 3.75 0.79 0.27 14.16 11.32 0.38 6 2.20 31.22 0.76 30.00 0.67 2.50 0.22 2.65 12.00 4.53 0.96 0.36 12.49 12.87 0.29 7 3.50 37.61 0.59 37.69 0.54 2.32 0.16 2.93 16.25 5.55 1.00 0.34 16.21 8 4.10 38.2 0.63 34.71 0.54 15.60 0.34 3.02 0.18 2.23 11.49 5.17 0.91 0.41 12.65 38.33 0.75 9 5.00 34.07 0.63 14.08 0.38 2.71 0.21 2.42 12.57 5.20 0.89 0.37 14.14 14.58 0.47 10 4.30 37.58 0.90 28.88 0.73 3.19 0.27 1.98 9.05 4.57 0.77 0.39 11.78 13.98 0.58 11 4.00 32.72 1.06 31.35 0.93 4.03 0.37 2.24 7.78 3.47 0.96 0.43 8.12 12 5.50 33.03 0.80 36.14 0.76 14.78 0.46 3.83 0.28 2.45 9.44 3.86 1.09 0.45 8.62 13 3.00 31.65 0.61 34.90 0.58 13.53 0.34 3.88 0.22 2.58 8.99 3.49 1.10 0.43 8.16 32.3 0.93 14 1.65 30.44 0.85 9.08 0.45 4.03 0.32 3.35 7.55 2.25 0.94 0.28 8.01 15 3.85 28.24 0.91 28.96 0.86 11.15 0.48 4.53 0.36 2.60 6.39 2.46 1.03 0.39 6.23 16 2.65 15.6 0.56 11.18 0.42 3.62 0.24 3.17 0.24 3.09 3.53 1.14 0.72 0.23 4.92 17 4.50 21.05 1.00 14.37 0.79 4.20 0.45 6.24 0.49 3.42 2.30 0.67 0.68 0.20 3.37 37.47 0.28 14.46 0.14 18 4.60 33.71 0.24 3.21 0.08 2.33 10.50 4.50 0.90 0.39 11.67 19 3.50 35.69 0.20 31.44 0.17 12.56 0.10 3.24 0.06 2.50 9.70 3.88 0.88 0.35 11.02 29.50 0.16 20 6.10 33.81 0.18 11.71 0.09 3.29 0.06 2.52 8.97 3.56 0.87 0.35 10.28 O Si Mg Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca R^2 = 0.058 0.0055 0.0698 4.00E-05 0.166 0.0031 0.046 0.0257 0.025 0.0279 Slope = 1.145 0.3452 0.6022 0.004 -0.1149 0.1209 0.1943 -0.0155 0.0078 0.4058 Intercept = 29.6830 28.3060 9.4508 3.4198 3.0421 8.7223 2.9036 0.9297 0.3114 9.0214 Table 3. TEM EELS and EDS data for Hectorite particle H3. Box #s correspond to box numbers in Image 3 below with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

10 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Spectrum Image

1 µm

Image 3. Hectorite particle H3 images and box numbers. Corresponds to Table 3.

H4 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca 1 4.00 35.05 0.89 26.13 0.71 13.92 0.47 0.33 0.14 1.88 79.18 42.18 0.75 0.40 106.21 2 4.00 32.93 0.81 24.55 0.63 13.43 0.42 0.34 0.14 1.83 72.21 39.50 0.75 0.41 96.85 3 4.25 35.46 1.17 25.17 0.90 14.71 0.61 0.45 0.16 1.71 55.93 32.69 0.71 0.41 78.80 4 4.10 36.72 1.49 29.19 1.22 13.15 0.78 0.00 0.00 2.22 N/A N/A 0.79 0.36 N/A 5 4.55 31.67 1.27 31.27 1.11 11.87 0.66 0.67 0.26 2.63 46.67 17.72 0.99 0.37 47.27 O Si Mg Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca R^2 = 0.2693 0.5029 0.3276 0.5036 0.52 0.0444 0.1308 0.6586 0.0715 0.1158 Slope = -4.5723 8.7991 -2.5981 0.7455 1.1736 -28.479 -27.509 0.3898 -0.0274 -63.598 Intercept = 53.4780 -9.5181 24.2760 -2.7584 -2.8517 169.84 141.41 -0.8329 0.5050 331.67 Table 4. TEM EELS and EDS data for Hectorite particle H4. Box #s correspond to box numbers in Image 4 below with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

11 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Table 4 summarizes the band gaps and elemental composition of Hectorite clay particle H4 shown in Image 4. O, Si, Mg and Ca atom % does not add up to 100% in Table 4, the remaining element not included in the table is C, which accounts for the remaining atoms %. The band gap measured by TEM-EELS ranges from 4.0 to 4.55 eV, giving a range of 0.55 eV. The small number of boxes taken resulted from the particle being too small and the EDS signal being too low, larger areas had to be summed for an acceptable signal for quantification. The average band gap is 4.25 eV. Si/Mg ratios range from 1.71 to 2.63, range is 0.92. Si/Ca ratios range from 46.67 to 79.18, range is 32.51. Mg/Ca ratios range from 17.72 to 42.18, range is 24.46. Si/O ratio ranges from 0.71 to 0.99, range is 0.28. Mg/O ratios range from 0.36 to 0.41, range is 0.05. O/Ca ratios range from 47.27 to 106.21, range is 58.94. Ratios where calcium is the dominator tend on the larger side due to the small Ca atom %. The R2, slope and y-intercept values from linear correlation of band gaps to element atom % and ratios for particle H4 are summarized in Table 4. The best linear correlation was given by Si/O ratio, while Ca and Si atom % also gave nearly as good quality linear fits as Si/O ratio. Calcium sorption on particle H4 accounts for an average of 0.4 atom %, though there is a large standard deviation associated, giving a possibly calcium coverage range of 0.15 to 0.9 atom %.

Image 4. Hectorite particles H4 and H5 images and box numbers. Corresponds to Tables 4 & 5.

12 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Table 5 below summarizes the band gaps and elemental composition of Hectorite clay particle H5 shown in Image 4. O, Si, Mg and Ca atom % does not add up to 100% in Table 5, the remaining element not included in the tables is C, which accounts for the remaining of the atoms %. The band gap measured by TEM-EELS ranges from 3.65 to 4.6 eV, giving a range of 0.95 eV. The average band gap is 4.2 eV. Si/Mg ratios range from 1.76 to 2.6, range is 0.84. Si/Ca ratios range from 25.88 to 95.17, range is 69.29. Mg/Ca ratios range from 12.91 to 54.03, range is 41.12. Si/O ratios range from 0.72 to 0.97, range is 0.26. Mg/O ratios range from 0.34 to 0.47, range is 0.13. O/Ca ratios range from 29.49 to 126.45, range is 96.96. Ratios where calcium is the dominator is one or more magnitude greater than other ratios due to the small Ca atom %. The best linear correlation with band gap values (Table 5) was given by Si/O ratio, with Si and Ca atom % giving also a good linear fit. Calcium surface/interlayer coverage accounted for an average of 0.6 atom %. Table 6 summarizes the band gaps and elemental composition of Hectorite clay particle H6 shown in Image 5. O, Si, Mg and Ca atom % does not add up to 100% in Table 6, the remaining element not included in the tables is C, which accounts for the remaining of the atoms %. The band gap measured by TEM-EELS ranges from 4.05 to 4.4 eV, giving a range of 0.35 eV. The average band gap is 4.2 eV. O, Si, Mg and Ca atom % does not add up to 100% in Table 6, the remaining element not included in the tables is C which accounts for the remaining of the atoms %. Box 1 (Table 6) gave an extremely high level of calcium (5.64 atom %), the EDS signal used for this quantification was sufficiently high and there does not appear to be any reason to disregard this value. Si/Mg ratios range from 1.69 to 2.01, range is 0.32. Si/Ca ratios range from 4.11 to 45.45, range is 41.34. Mg/Ca ratios range from 2.29 to 24.24, range is 21.95. Si/O ratios range from 0.72 to 0.85, range is 0.13. Mg/O ratios range from 0.4 to 0.48, range is 0.08. O/Ca ratios range from 5.59 to 57.82, range is 52.23. The best linear correlation (Table 6) was given by Ca atom %, with Si/O ratio being nearly equally well fitted with the band gaps. The average calcium % coverage is 2.5 atom %, this is skewed by the large calcium coverage found in box 1. The most common coverage is 0.75 atom.

13 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

H5 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca 1 4.30 35.20 1.04 28.23 0.81 14.84 0.54 0.58 0.15 1.90 48.67 25.59 0.80 0.42 60.69 2 4.50 36.67 0.99 27.60 0.79 15.67 0.52 0.29 0.12 1.76 95.17 54.03 0.75 0.43 126.45 3 4.60 33.25 1.36 23.80 1.09 12.67 0.73 0.48 0.21 1.88 49.58 26.40 0.72 0.38 69.27 4 4.35 36.32 0.99 32.49 0.82 12.51 0.48 0.73 0.14 2.60 44.51 17.14 0.89 0.34 49.75 5 4.20 38.59 0.83 31.52 0.69 15.44 0.45 0.44 0.12 2.04 71.64 35.09 0.82 0.40 87.70 6 4.20 38.67 0.69 30.08 0.56 15.60 0.36 0.54 0.10 1.93 55.70 28.89 0.78 0.40 71.61 7 4.10 36.77 1.00 31.76 0.83 14.65 0.52 0.56 0.15 2.17 56.71 26.16 0.86 0.40 65.66 8 4.25 37.59 0.75 33.75 0.65 16.07 0.41 0.56 0.12 2.10 60.27 28.70 0.90 0.43 67.13 9 3.75 38.13 0.73 34.58 0.62 14.81 0.39 0.48 0.11 2.33 72.04 30.85 0.91 0.39 79.44 10 4.20 36.88 0.79 31.65 0.65 15.92 0.42 0.57 0.12 1.99 55.53 27.93 0.86 0.43 64.70 11 4.30 36.06 1.01 34.82 0.88 17.10 0.57 0.70 0.17 2.04 49.74 24.43 0.97 0.47 51.51 12 3.65 38.04 0.91 33.39 0.78 16.65 0.50 1.29 0.17 2.01 25.88 12.91 0.88 0.44 29.49 13 3.80 32.93 1.00 29.36 0.86 12.30 0.52 0.42 0.16 2.39 69.90 29.29 0.89 0.37 78.40 14 4.50 35.30 0.63 26.97 0.50 14.71 0.33 0.53 0.09 1.83 50.89 27.75 0.76 0.42 66.60 15 4.00 38.04 0.47 30.99 0.38 14.84 0.24 0.58 0.07 2.09 53.43 25.59 0.81 0.39 65.59 16 4.00 37.50 0.41 33.32 0.34 15.63 0.22 0.55 0.06 2.13 60.58 28.42 0.89 0.42 68.18 17 3.50 35.80 0.56 32.52 0.48 15.45 0.31 0.89 0.10 2.10 36.54 17.36 0.91 0.43 40.22 18 4.00 37.80 0.28 32.16 0.23 15.59 0.15 0.62 0.04 2.06 51.87 25.15 0.85 0.41 60.97 19 4.45 36.54 0.24 30.99 0.20 15.03 0.13 0.64 0.04 2.06 48.42 23.48 0.85 0.41 57.09 O Si Mg Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca R^2 = 0.0531 0.3153 0.0259 0.2445 0.1604 0.0627 0.1544 0.3197 0.0029 0.1437 Slope = -1.2309 -5.2256 -0.6864 -0.3404 -0.2623 12.164 10.739 -0.1186 -0.005 24.794 Intercept = 41.7310 52.6830 17.867 2.0115 3.1599 5.2854 -17.34 1.3379 0.4304 -36.296 Table 5. TEM EELS and EDS data for Hectorite particle H5. Box #s correspond to box numbers in Image 4 above with respective EELS band gap information and EDS chemical composition information.

14 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

H6 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca 1 4.40 31.52 0.82 23.18 0.59 12.94 0.42 5.64 0.32 1.79 4.11 2.29 0.74 0.41 5.59 2 4.35 35.22 0.77 25.29 0.60 14.62 0.40 0.80 0.13 1.73 31.61 18.28 0.72 0.42 44.03 3 4.20 29.27 0.92 23.75 0.72 11.81 0.48 0.61 0.17 2.01 38.93 19.36 0.81 0.40 47.98 4 4.30 34.67 0.78 29.43 0.65 16.77 0.45 0.78 0.14 1.75 37.73 21.50 0.85 0.48 44.45 5 4.40 36.33 0.56 28.88 0.45 15.43 0.31 0.71 0.10 1.87 40.68 21.73 0.79 0.42 51.17 6 4.25 35.85 1.03 28.18 0.84 15.03 0.57 0.62 0.19 1.87 45.45 24.24 0.79 0.42 57.82 7 4.25 30.52 0.82 24.74 0.67 14.66 0.46 0.69 0.15 1.69 35.86 21.25 0.81 0.48 44.23 8 4.40 31.01 0.61 22.34 0.45 12.68 0.31 2.98 0.19 1.76 7.50 4.26 0.72 0.41 10.41 9 4.20 35.54 0.57 28.44 0.46 15.50 0.31 1.23 0.11 1.83 23.12 12.60 0.80 0.44 28.89 10 4.05 36.24 0.57 29.01 0.46 15.87 0.31 0.70 0.10 1.83 41.44 22.67 0.80 0.44 51.77 11 4.30 32.71 0.64 26.10 0.52 14.79 0.36 0.71 0.12 1.76 36.76 20.83 0.80 0.45 46.07 12 4.20 34.49 0.31 27.06 0.25 15.18 0.17 1.29 0.07 1.78 20.98 11.77 0.78 0.44 26.74 13 4.15 35.08 0.33 27.35 0.26 15.37 0.18 0.84 0.06 1.78 32.56 18.30 0.78 0.44 41.76 14 4.30 35.66 0.37 28.23 0.30 15.80 0.20 0.81 0.07 1.79 34.85 19.51 0.79 0.44 44.02 15 4.20 31.83 0.27 24.76 0.21 13.73 0.15 1.31 0.06 1.80 18.90 10.48 0.78 0.43 24.30 O Si Mg Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca R^2 = 0.0281 0.1244 0.0614 0.2204 0.0501 0.1238 0.1147 0.1992 0.0421 0.1139 Slope = -3.9019 -8.0822 -3.3037 6.2218 -0.1682 -43.397 22.72 -0.156 -0.0483 -51.37 Intercept = 50.364 60.906 28.764 -25.211 2.5212 215.05 113.47 1.4489 0.6408 256.95 Table 6. TEM EELS and EDS data for Hectorite particle H6. Box #s correspond to box numbers in Image 5 below with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

15 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Spectrum Image

0.50.5 µµm

Image 5. Hectorite particle H6 images and box numbers. Corresponds to Table 6.

Table 7 summarizes the band gaps and elemental composition of Hectorite clay particle H7 shown in Image 6. O, Si, Mg and Ca atom % does not add up to 100% in Table 7, the remaining element not included in the tables is C, which accounts for the remaining of the atoms %. The band gap measured by TEM-EELS ranges from 3.5 to 3.65 eV, giving a range of 0.15 eV. The average band gap is 3.55 eV. Si/Mg ratios range from 1.75 to 1.98, range is 0.23. Si/Ca ratios range from 47.33 to 84.0, range is 36.67. Mg/Ca ratios range from 24.48 to 43.03, range is 18.55. Si/O ratios range from 0.94 to 1.02, range is 0.08. Mg/O ratios range from 0.47 to 0.56, range is 0.09. O/Ca ratios range from 48.44 to 82.18, range is 33.74. The best linear correlation (Table 7) was given by O atom %, with Si/Ca and Mg/Ca ratios being nearly equally well fitted with the band gaps. The average calcium coverage is 0.55 atom %.

16 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

H7 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca 1 3.50 32.05 1.00 32.76 0.91 16.78 0.60 0.39 0.15 1.95 84.00 43.03 1.02 0.52 82.18 2 3.65 35.36 0.75 34.55 0.66 17.87 0.43 0.73 0.13 1.93 47.33 24.48 0.98 0.51 48.44 3 3.60 34.68 0.91 35.48 0.83 17.54 0.52 0.67 0.16 2.02 52.96 26.18 1.02 0.51 51.76 4 3.55 34.07 0.88 33.31 0.79 19.07 0.54 0.49 0.15 1.75 67.98 38.92 0.98 0.56 69.53 5 3.65 34.44 1.22 32.37 1.05 16.35 0.71 0.57 0.18 1.98 56.79 28.68 0.94 0.47 60.42 6 3.55 34.15 0.60 33.85 0.53 17.52 0.35 0.64 0.10 1.93 52.89 27.38 0.99 0.51 53.36 O Si Mg Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca R^2 = 0.7173 0.0573 0.0241 0.532 0.1039 0.6157 0.6185 0.3918 0.4453 0.5287 Slope = 15.627 4.5818 -2.4182 1.5091 0.5059 -174.83 -98.983 -0.3251 -0.3064 -154.07 Intercept = -21.873 17.3020 26.1870 -4.8259 0.1151 686.8 386.13 2.1533 1.6118 613.04 Table 7. TEM EELS and EDS data for Hectorite particle H7. Box #s correspond to box numbers in Image 6 below with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

17 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

H8 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca 1 3.85 35.30 0.81 36.34 0.75 10.25 0.38 0.53 0.12 3.55 68.57 19.34 1.03 0.29 66.60 12.78 2 4.00 35.33 0.70 36.80 0.65 0.36 0.45 0.11 2.88 81.78 28.40 1.04 0.36 78.51 3 4.35 34.13 0.91 35.17 0.86 10.34 0.43 0.66 0.14 3.40 53.29 15.67 1.03 0.30 51.71 4 4.30 36.41 0.71 37.65 0.65 12.08 0.34 0.38 0.10 3.12 99.08 31.79 1.03 0.33 95.82 5 4.00 35.59 0.56 36.63 0.52 11.41 0.27 0.51 0.08 3.21 71.82 22.37 1.03 0.32 69.78 O Si Mg Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca R^2 = 0.0213 0.0187 0.0004 0.0195 0.0096 0.0019 0.0041 2.00E-05 0.0029 0.0019 Slope = -0.5541 -0.5703 0.1054 0.0676 -0.117 3.4385 1.9589 -0.0001 0.0069 3.3011 Intercept = 37.624 38.856 10.94 0.229 3.7103 60.809 15.482 1.0334 0.2933 58.951 Table 8. TEM EELS and EDS data for Hectorite particle H8. Box #s correspond to box numbers in Image 6 below with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

18 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

H9 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca 1 3.85 27.82 0.80 41.39 0.85 18.16 0.54 0.78 0.16 2.28 53.06 23.28 1.49 0.65 35.67 2 4.65 31.16 1.00 40.26 1.01 19.36 0.66 0.52 0.17 2.08 77.42 37.23 1.29 0.62 59.92 3 4.80 27.01 1.08 41.25 1.14 17.82 0.73 0.82 0.19 2.31 50.30 21.73 1.53 0.66 32.94 4 3.85 30.73 0.82 40.80 0.86 19.08 0.54 0.62 0.15 2.14 65.81 30.77 1.33 0.62 49.56 5 4.50 29.65 0.68 41.01 0.71 18.69 0.45 0.64 0.13 2.19 64.08 29.20 1.38 0.63 46.33 O Si Mg Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca R^2 = 0.0149 0.0683 0.0123 0.0027 0.0012 0.0132 0.0104 0.0067 0.0207 0.0068 Slope = -0.489 -0.2568 -0.1566 -0.014 0.0074 2.7726 1.4087 0.0184 0.0058 1.9945 Intercept = 31.392 42.054 19.3 0.7367 2.1692 50.13 22.345 1.324 0.6119 36.248 Table 9. TEM EELS and EDS data for Hectorite particle H9. Box #s correspond to box numbers in Image 6 below with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

H10 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca 1 4.6 30.03 1.86 35.77 1.71 11.42 0.98 0.00 0.00 3.13 N/A N/A 1.19 0.38 N/A Table 10. TEM EELS and EDS data for Hectorite particle H10. Box #s correspond to box numbers in Image 6 below with respective EELS band gap information and EDS chemical composition information.

19 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

H11 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca 1 4.20 30.75 1.07 33.35 0.98 19.08 0.69 0.69 0.17 1.75 48.33 27.65 1.08 0.62 44.57 Table 11. TEM EELS and EDS data for Hectorite particle H11. Box #s correspond to box numbers in Image 6 below with respective EELS band gap information and EDS chemical composition information.

Image 6. Hectorite particles H7, H8, H9, H10 and H11 images and box numbers. Corresponds to Tables 7, 8, 9, 10 and 11.

20 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Table 8 summarizes the band gaps and elemental composition of Hectorite clay particle H8 shown in Image 6. O, Si, Mg and Ca atom % does not add up to 100% in Table 8, the remaining element not included in the tables is C, which accounts for the remaining of the atoms %. The band gap measured by TEM-EELS ranges from 3.85 to 4.35 eV, giving a range of 0.5 eV. The average band gap is 4.1 eV. Si/Mg ratios range from 2.88 to 3.55, range is 0.67. Si/Ca ratios range from 10.5 to 79.18, range is 68.68. Mg/Ca ratios range from 4.5 to 42.18, range is 37.68. Si/O ratios range from 0.37 to 1.38, range is 1.01. Mg/O ratios range from 0.29 to 0.62, range is 0.33. O/Ca ratios range from 11.67 to 106.21, range is 94.54. The best linear correlation (Table 8) was given by O atom %, with Si and Ca atom % being nearly equally well fitted with the band gaps. The average calcium coverage is 0.65 atom %. Table 9 summarizes the band gaps and elemental composition of Hectorite clay particle H9 shown in Image 6. The band gap measured by TEM-EELS ranges from 3.85 to 4.8 eV, giving a range of 0.95 eV. The average band gap is 4.3 eV. Si/Mg ratios range from 2.08 to 2.31, range is 0.23. Si/Ca ratios range from 53.06 to 77.42, range is 24.36. Mg/Ca ratios range from 21.73 to 37.23, range is 15.5. Si/O ratios range from 1.29 to 1.53, range is 0.24. Mg/O ratios range from 0.62 to 0.66, range is 0.04. O/Ca ratios range from 32.94 to 59.92, range is 26.98. The best linear correlation with the band gap (Table 9) was given by Si atom %. No other element atom % or ratio seems to give a reasonably close linear fit with the band gap as Si. The average calcium coverage is 0.7 atom %. Tables 10 and 11 summarize the band gaps and elemental composition of Hectorite clay particles H10 and H11 respectively. The corresponding image to Tables 10 and 11 is Image 6. Due to their low EDS signals, these two particles were only able to be measured as a whole particle, they were not divided into various boxes. No linear correlation with the band gap was made for H10 and H11. Particle H10 did not have any measurable Ca EDS signal, while H11 has an average Ca coverage of .69 atom %. Table 12 below is a summary of the average band gap values, elemental atomic % and ratios from each observe Hectorite particle (H1 through H11). O, Si, Mg and Ca atom % does not add up to 100% in Table 12, the remaining element not included in the tables is C, which accounts for the remaining of the atoms %. All elemental atom % when comparing one Hectorite particle to the next have roughly the same variation range as did the variation ranges within the same Hectorite particle. Si/Mg ratios range from 1.28 to 3.13, range is 1.85. This interparticle range (Table 12) is larger than any range observed within the same Hectorite particle, which has a maximum range of 1.37 (Table 13a). Inter-particle Si/Ca ratios range from 10.5 to 79.18, range is 68.68, which places this value in the larger variation range compared to values found in Table 13a, but is not the largest. Inter-particle Mg/Ca ratios range from 4.5 to 42.18, giving range of 37.68, also on the larger end of range values shown in Table 13a. Inter-particle Si/O ratios range from 0.37 to 1.38, giving a range of 1.01, not larger than the values shown in Table 13a but comparable. Inter-particle Mg/O ratios range from 0.29 to 0.63, giving range of 0.34, this is only slightly higher than the values in Table 13a. Inter-particle O/Ca ratios range from 11.67 to 106.21, giving range of 94.54, not the largest variation when comparing to Table 13a (intra-particle variations) but is comparable to the larger values. The best linear correlation with the band gap (Table 12) was given by the Si/O ratio, with Si atom percent being almost as good a linear fit.

21 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Ratios H# Band gap (eV) O ±O Si ±Si Mg ±Mg Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca 1 3.60 39.41 0.39 14.39 0.30 11.26 0.19 0.00 0.00 1.28 N/A N/A 0.37 0.29 N/A 2 3.55 45.31 0.44 21.13 0.38 14.33 0.23 0.00 0.00 1.47 N/A N/A 0.47 0.32 N/A 3 4.60 37.47 0.28 33.71 0.24 14.46 0.14 3.21 0.08 2.33 10.50 4.50 0.90 0.39 11.67 4 4.00 35.05 0.89 26.13 0.71 13.92 0.47 0.33 0.14 1.88 79.18 42.18 0.75 0.40 106.21 5 4.00 37.80 0.28 32.16 0.23 15.59 0.15 0.62 0.04 2.06 51.87 25.15 0.85 0.41 60.97 6 4.30 35.66 0.37 28.23 0.30 15.80 0.20 0.81 0.07 1.79 34.85 19.51 0.79 0.44 44.02 7 3.55 34.15 0.60 33.85 0.53 17.52 0.35 0.64 0.10 1.93 52.89 27.38 0.99 0.51 53.36 8 4.00 35.59 0.56 36.63 0.52 11.41 0.27 0.51 0.08 3.21 71.82 22.37 1.03 0.32 69.78 9 4.50 29.65 0.68 41.01 0.71 18.69 0.45 0.64 0.13 2.19 64.08 29.20 1.38 0.63 46.33 10 4.60 30.03 1.86 35.77 1.71 11.42 0.98 0.00 0.00 3.13 N/A N/A 1.19 0.38 N/A 11 4.20 30.75 1.07 33.35 0.98 19.08 0.69 0.69 0.17 1.75 48.33 27.65 1.08 0.62 44.57 O Si Mg Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca R^2 = 0.385 0.4044 0.0118 0.236 0.2993 5.00E-05 9.00E-06 0.4490 0.1184 0.0030 Slope = -7.119 12.137 0.7647 1.0868 0.8374 0.5197 0.1086 0.5007 0.1002 -4.6947 Intercept = 64.59 -18.964 11.741 -3.7587 -1.3247 35.473 17.551 -1.153 0.0187 58.883 Table 12. TEM EELS and EDS data for Hectorite particles H1-H11, average values. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

Table 13 is a summary of the R2 values that correspond to Table 12. The orange highlighted cells are the elemental atom % or ratio which gave the greatest linear correlation with band gap values, while the purple highlighted cells are those that gave comparable linear correlations to the orange cells. O atom %, Si atom %, Si/Mg and Si/O ratios (Table 13) seemed to correlate well with the band gap values more often when compared to other atom % or ratios. No one single element or ratio gave the best linear correlations consistently. About 50% of the highlighted R2 values were under 0.5, which indicates a poor linear relationship despite it being the best correlation when compared to other elements and ratios with the same H#.

22 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

H# O Si Mg Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca 1 R^2 = 0.1406 0.0030 0.0072 N/A 0.5229 N/A N/A 0.1656 0.4054 N/A 2 R^2 = 0.1655 0.0494 0.0641 N/A 0.0138 N/A N/A 0.0035 0.0148 N/A 3 R^2 = 0.0580 0.0055 0.0698 0.0000 0.1660 0.0031 0.0460 0.0257 0.0250 0.0279 4 R^2 = 0.2693 0.5029 0.3276 0.5036 0.5200 0.0444 0.1308 0.6586 0.0715 0.1158 5 R^2 = 0.0531 0.3153 0.0259 0.2445 0.1604 0.0627 0.1544 0.3197 0.0029 0.1437 6 R^2 = 0.0281 0.1244 0.0614 0.2204 0.0501 0.1238 0.1147 0.1992 0.0421 0.1139 7 R^2 = 0.7173 0.0573 0.0241 0.5320 0.1039 0.6157 0.6185 0.3918 0.4453 0.5287 8 R^2 = 0.0213 0.0187 0.0004 0.0195 0.0096 0.0019 0.0041 0.0000 0.0029 0.0019 9 R^2 = 0.0149 0.0683 0.0123 0.0027 0.0012 0.0132 0.0104 0.0067 0.0207 0.0068 Table 13. Summary of R2 values for particles H1-H9 averages, R2 values corresponds to Table 12 values.

Ranges Particle Min. Band Gap (eV) Max. Band Gap (eV) Band Gap Range (eV) Ca atom % Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca H1 3.25 3.60 0.35 0.00 0.15 N/A N/A 0.09 0.07 N/A H2 3.15 3.70 0.55 0.00 0.29 N/A N/A 0.18 0.12 N/A H3 1.65 7.20 5.55 3.20 1.37 10.27 4.06 0.42 0.25 12.84 H4 4.00 4.55 0.55 0.40 0.92 32.51 24.46 0.28 0.05 58.94 H5 3.65 4.60 0.95 0.60 0.84 69.29 41.12 0.26 0.13 96.96 H6 4.05 4.40 0.35 0.75 0.32 41.34 21.95 0.13 0.08 52.23 H7 3.50 3.65 0.15 0.55 0.23 36.67 18.55 0.08 0.09 33.74 H8 3.85 4.35 0.50 0.65 0.67 68.68 37.68 1.01 0.33 94.64 H9 3.85 4.80 0.95 0.70 0.23 24.36 15.5 0.24 0.04 26.98 H10 N/A N/A #VALUE! N/A N/A N/A N/A N/A N/A N/A H11 N/A N/A #VALUE! N/A N/A N/A N/A N/A N/A N/A Ca atom % Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca R^2 = 0.9118 0.5807 0.3403 0.3875 0.032 0.2038 0.2661 Slope = 0.5407 0.1882 -6.7111 -4.1826 0.0304 0.0262 -8.8236 Intercept = 0.1663 0.3508 49.074 28.709 0.2655 0.1001 65.106 Table 13a. Summary of the minimum band gap values, maximum band gap values, band gap ranges, average Ca atom %, and Si/Mg, Si/Ca, Mg/Ca, Si/O, Mg/O and O/Ca ranges for particles from Tables 1-11. 23 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Table 13a is a summary of the minimum band gap values, maximum band gap values, band gap ranges, average Ca atom %, and Si/Mg, Si/Ca, Mg/Ca, Si/O, Mg/O and O/Ca ranges for particles from Tables 1-11. In order to calculate the R2, slope and y-intercept values band gap ranges were plotted against Ca atom %, Si/Mg, Si/Ca, Mg/Ca, Si/O, Mg/O and O/Ca ranges. The highest correlation found was between band gap ranges and Ca atom % (table 13a). Variation range of Si/Mg ratio also gave a decent linear correlation with band gap ranges.

Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Al ±Al Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al 1 3.95 31.09 1.16 32.71 1.09 0.00 0.00 1.04 0.29 0.00 0.00 N/A N/A N/A 1.05 0.00 N/A 31.45 N/A 29.89 2 5.70 35.27 1.31 35.48 1.23 0.00 0.00 2.35 0.33 0.00 0.00 N/A N/A N/A 1.01 0.00 N/A 15.10 N/A 15.01 3 4.10 38.01 1.30 35.99 1.20 0.00 0.00 0.00 0.00 0.00 0.00 N/A N/A N/A 0.95 0.00 N/A N/A N/A N/A 4 4.10 38.48 1.02 41.13 0.95 0.00 0.00 2.25 0.26 0.00 0.00 N/A N/A N/A 1.07 0.00 N/A 18.28 N/A 17.10 5 3.90 41.29 1.03 39.32 0.96 0.43 0.16 2.21 0.26 0.00 0.00 91.44 N/A N/A 0.95 0.01 N/A 17.79 5.14 18.68 6 3.65 29.92 1.34 25.54 1.19 0.00 0.00 2.44 0.42 0.00 0.00 N/A N/A N/A 0.85 0.00 N/A 10.47 N/A 12.26 7 3.95 23.40 2.15 25.19 2.04 1.39 0.45 1.65 0.63 0.00 0.00 18.12 N/A N/A 1.08 0.06 N/A 15.27 1.19 14.18 8 3.60 34.39 1.50 35.22 1.35 0.00 0.00 3.70 0.47 0.00 0.00 N/A N/A N/A 1.02 0.00 N/A 9.52 N/A 9.29 9 4.20 23.79 2.02 34.70 1.99 0.96 0.46 2.41 0.67 0.00 0.00 36.15 N/A N/A 1.46 0.04 N/A 14.40 2.51 9.87 10 4.10 19.92 2.71 24.96 2.79 0.00 0.00 0.00 0.00 0.00 0.00 N/A N/A N/A 1.25 0.00 N/A N/A N/A N/A 11 5.50 38.29 0.71 39.04 0.66 0.00 0.00 2.18 0.18 0.00 0.00 N/A N/A N/A 1.02 0.00 N/A 17.91 N/A 17.56 12 3.95 39.27 0.58 38.49 0.54 0.26 0.10 2.22 0.15 0.19 0.06 148.04 202.58 1.37 0.98 0.01 206.68 17.34 8.54 17.69 O Si Mg Al Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al R^2 = 0.0387 0.0872 0.0333 0.0002 0.0168 0.0014 0.013 0.0484 0.0107 Slope = 2.1002 2.5492 -0.126 0.0245 -0.0107 0.0089 1.4465 -0.8991 1.2708 Intercept = 23.887 23.211 0.7855 1.7672 0.0609 1.0202 7.8483 5.2465 8.0937 Table 14. TEM EELS and EDS data for Montmorillonite particle M1. Box #s correspond to box numbers in Image 7 below with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

24 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Table 14 above summarizes the band gaps and elemental composition of Montmorillonite clay particle M1 shown in Image 7. The band gap measured by TEM-EELS ranges from 3.6 to 5.7 eV, giving a range of 2.1 eV. The average band gap is 4.6 eV. O, Si, Mg, Al and Ca atom % does not add up to 100% in Table 14, the remaining element not included in the table is C which accounts for the remaining of the atoms %. Si/Mg ratios range from 18.12 to 148.04, range is 129.92. Si/O ratios range from 0.85 to 1.46, range is 0.61. Mg/O ratios range from 0.01 to 0.06, range is 0.05. Si/Al ratios range from 9.52 to 31.45, range is 21.93. Al/Mg ratios range from 1.19 to 8.54, range is 7.35. O/Al ratios range from 9.29 to 29.89, range is 20.6. The best linear correlation with band gaps (Table 14) was given by Si atom %. The majority of the boxes (Table 14, Image 7) resulted in a calcium signal that was too low to be quantified, however summing over a larger area (box # 12, Table 14) gave an average calcium coverage is 0.19 atom %. The degree of isomorphic substitution (based on Mg atom %) is random and low and was only measurable in boxes 5, 7 and 9 (Image 7, Table 14).

Spectrum Image

0.20.2 µµm

Image 7. Montmorillonite particle M1 images and box numbers. Corresponds to Table 14. Table 15 summarizes the band gaps and elemental composition of Montmorillonite clay particle M2 shown in Image 8. The band gap measured by TEM-EELS ranges from 3.8 to 4.55 eV, giving a range of 0.75 eV. The average band gap is 4.3 eV. Same as with other tables O, Si, Mg, Al and Ca atom % does not add up to 100% in Table 15, the remaining element not included in the table is C, which accounts for the remaining of the atoms %. Si/Mg ratios range from 14.87 to 112.69, range is 97.82. Si/Ca ratios range from 59.87 to 171.45, range is 111.58. Mg/Ca ratios range from 0 to 5.0, range is 5. Si/O ratios range from 0.92 to 1.55, range is 0.63. Mg/O ratios range from 0 to 0.07, range is 0.07. O/Ca ratios range from 52.46 to 143.0, range is 90.54. Si/Al ratios range from 3.11 to 18.22, range is 15.11. Al/Mg ratios range from 3.64 to 10.5, range is 6.86. O/Al ratios range from 2.8 to 13.35, range is 10.55. The best linear correlation with band gaps (Table 15) was given by Si/Al ratios, with O/Al ratios being nearly as well fitted to the band gaps. The average calcium coverage is 0.35 atom %. Isomorphic substitution of Mg for Al is more evenly distributed and prominent in M2 compared with M1. Mg atom % can range from 0 % to 2.65 %, 2.65 % being an area with higher isomorphic substitution.

25 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

M2 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Al ±Al Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al 1 3.80 36.78 1.58 37.20 1.44 0.00 0.00 3.10 0.49 0.00 0.00 N/A N/A N/A 1.01 0.00 N/A 12.00 N/A 11.86 2 3.95 38.61 1.06 42.22 0.99 0.00 0.00 4.92 0.36 0.27 0.12 N/A 156.37 0.00 1.09 0.00 143.00 8.58 N/A 7.85 3 3.80 41.42 0.90 38.96 0.84 1.55 0.22 8.40 0.38 0.31 0.12 25.14 125.68 5.00 0.94 0.04 133.61 4.64 5.42 4.93 4 3.95 36.35 0.90 37.89 0.87 1.66 0.23 8.92 0.41 0.57 0.13 22.83 66.47 2.91 1.04 0.05 63.77 4.25 5.37 4.08 5 4.15 44.16 1.05 40.57 0.97 0.00 0.00 3.43 0.30 0.00 0.00 N/A N/A N/A 0.92 0.00 N/A 11.83 N/A 12.87 6 4.30 41.77 0.92 43.09 0.89 0.55 0.17 5.04 0.29 0.00 0.00 78.35 N/A N/A 1.03 0.01 N/A 8.55 9.16 8.29 7 4.55 41.53 0.92 44.48 0.93 1.32 0.19 4.81 0.33 0.52 0.12 33.70 85.54 2.54 1.07 0.03 79.87 9.25 3.64 8.63 8 3.95 39.77 1.04 45.64 1.06 1.17 0.24 7.46 0.43 0.38 0.14 39.01 120.11 3.08 1.15 0.03 104.66 6.12 6.38 5.33 9 3.95 35.92 1.20 42.90 1.20 1.62 0.32 9.32 0.52 0.00 0.00 26.48 N/A N/A 1.19 0.05 N/A 4.60 5.75 3.85 10 4.20 37.48 0.95 47.33 0.95 0.42 0.17 4.41 0.31 0.39 0.11 112.69 121.36 1.08 1.26 0.01 96.10 10.73 10.50 8.50 11 4.35 37.79 1.00 49.72 1.07 0.00 0.00 3.41 0.31 0.29 0.12 N/A 171.45 0.00 1.32 0.00 130.31 14.58 N/A 11.08 12 4.55 37.96 1.02 50.87 1.11 0.86 0.22 4.88 0.36 0.48 0.13 59.15 105.98 1.79 1.34 0.02 79.08 10.42 5.67 7.78 13 4.05 39.87 1.17 45.50 1.23 1.84 0.31 8.53 0.53 0.76 0.18 24.73 59.87 2.42 1.14 0.05 52.46 5.33 4.64 4.67 14 3.75 35.10 2.14 38.96 2.29 2.62 0.80 12.54 1.21 0.00 0.00 14.87 N/A N/A 1.11 0.07 N/A 3.11 4.79 2.80 15 4.30 37.12 1.07 50.64 1.17 0.00 0.00 2.78 0.32 0.00 0.00 N/A N/A N/A 1.36 0.00 N/A 18.22 N/A 13.35 16 3.90 35.99 1.14 55.70 1.30 0.00 0.00 4.42 0.38 0.00 0.00 N/A N/A N/A 1.55 0.00 N/A 12.60 N/A 8.14 17 4.05 36.08 1.19 51.58 1.33 1.59 0.31 8.11 0.52 0.00 0.00 32.44 N/A N/A 1.43 0.04 N/A 6.36 5.10 4.45 18 3.90 33.80 2.27 44.36 2.42 2.09 0.69 11.91 1.20 0.00 0.00 21.22 N/A N/A 1.31 0.06 N/A 3.72 5.70 2.84 19 3.90 35.79 1.52 52.39 1.71 0.00 0.00 4.64 0.55 0.00 0.00 N/A N/A N/A 1.46 0.00 N/A 11.29 N/A 7.71 20 4.30 39.04 0.28 44.45 0.28 0.94 0.06 5.61 0.10 0.37 0.04 47.29 120.14 2.54 1.14 0.02 105.51 7.92 5.97 6.96 21 3.95 38.28 0.34 46.78 0.35 1.29 0.08 6.29 0.13 0.43 0.05 36.26 108.79 3.00 1.22 0.03 89.02 7.44 4.88 6.09 22 4.30 39.30 0.30 45.50 0.31 0.89 0.07 5.34 0.11 0.38 0.04 51.12 119.74 2.34 1.16 0.02 103.42 8.52 6.00 7.36 O Si Mg Al Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al R^2 = 0.1638 0.1103 0.0693 0.258 0.1139 0.165 0.1026 0.0032 0.0051 0.0847 0.0657 0.2011 0.0233 0.1952 Slope = 4.3161 7.045 -0.8973 -5.8988 0.3429 49.658 84.414 0.3633 0.0512 -0.0275 58.533 7.28 2.0397 5.7177 Intercept = 20.541 16.518 4.5946 30.39 -1.1672 -174.5 -283.06 -0.2707 0.9842 0.137 -185.51 -21.109 -4.2909 -16.118 Table 15. TEM EELS and EDS data for Montmorillonite particle M2. Box #s correspond to box numbers in Image 8 below with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

26 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Table 16 summarizes the band gaps and elemental composition of Montmorillonite clay particle M3 shown in Image 9. The band gap measured by TEM-EELS ranges from 3.5 to 4.0 eV, giving a range of 0.5 eV. The average band gap is 3.75 eV. Si/Mg ratios range from 148.88 to 238.81, range is 89.93. Si/O ratios range from 0.92 to 1.39, range is 0.47. Si/Al ratios range from 9.68 to 29.85, range is 20.17. Al/Mg ratios range from 5.42 to 10.88, range is 5.46. O/Al ratios range from 6.94 to 28.65, range is 21.71. The best linear correlation with band gaps (Table 16) was given by Si/Al ratios, with Si/O ratios being nearly as well fitted to the band gaps. There is no detectable calcium coverage on particle M3. Based on Mg atom %, particle M3 has an isomorphic substitution of 0.16 atom % where Mg is substituting for Al.

Spectrum Image

0.50.5 µµm

Image 8. Montmorillonite particle M2 images and box numbers. Corresponds to Table 15.

27 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Spectrum Image

0.20.2 µµm

Image 9. Montmorillonite particle M3 images and box numbers. Corresponds to Table 16.

28 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

M3 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Al ±Al Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al 1 3.95 30.19 1.61 30.72 1.54 0.00 0.00 1.36 0.44 0.00 0.00 N/A N/A N/A 1.02 0.00 N/A 22.59 N/A 22.20 2 3.50 32.90 1.43 35.31 1.36 0.00 0.00 2.02 0.37 0.00 0.00 N/A N/A N/A 1.07 0.00 N/A 17.48 N/A 16.29 3 3.50 32.00 1.62 30.11 1.50 0.00 0.00 1.68 0.46 0.00 0.00 N/A N/A N/A 0.94 0.00 N/A 17.92 N/A 19.05 4 3.95 17.75 1.03 18.60 0.96 0.00 0.00 1.44 0.34 0.00 0.00 N/A N/A N/A 1.05 0.00 N/A 12.92 N/A 12.33 5 4.05 37.84 1.23 40.40 1.17 0.00 0.00 1.53 0.32 0.00 0.00 N/A N/A N/A 1.07 0.00 N/A 26.41 N/A 24.73 6 3.95 36.46 1.16 42.38 1.11 0.00 0.00 1.42 0.27 0.00 0.00 N/A N/A N/A 1.16 0.00 N/A 29.85 N/A 25.68 7 3.90 38.68 1.38 35.77 1.27 0.00 0.00 1.35 0.34 0.00 0.00 N/A N/A N/A 0.92 0.00 N/A 26.50 N/A 28.65 8 4.00 38.33 1.30 37.83 1.20 0.00 0.00 2.48 0.37 0.00 0.00 N/A N/A N/A 0.99 0.00 N/A 15.25 N/A 15.46 38.27 9 4.00 1.12 41.04 1.10 0.00 0.00 1.56 0.26 0.00 0.00 N/A N/A N/A 1.07 0.00 N/A 26.31 N/A 24.53 10 3.95 34.30 1.22 41.60 1.20 0.00 0.00 1.76 0.31 0.00 0.00 N/A N/A N/A 1.21 0.00 N/A 23.64 N/A 19.49 11 3.95 30.11 1.71 33.31 1.67 0.00 0.00 1.50 0.47 0.00 0.00 N/A N/A N/A 1.11 0.00 N/A 22.21 N/A 20.07 12 3.90 32.53 1.33 37.47 1.31 0.00 0.00 1.55 0.33 0.00 0.00 N/A N/A N/A 1.15 0.00 N/A 24.17 N/A 20.99 13 3.90 20.07 1.97 27.97 2.01 0.00 0.00 2.89 0.66 0.00 0.00 N/A N/A N/A 1.39 0.00 N/A 9.68 N/A 6.94 14 3.95 36.36 0.77 38.71 0.73 0.26 0.13 1.41 0.19 0.00 0.00 148.88 N/A N/A 1.06 0.01 N/A 27.45 5.42 25.79 15 3.95 35.84 0.61 37.94 0.57 0.00 0.00 1.95 0.16 0.00 0.00 N/A N/A N/A 1.06 0.00 N/A 19.46 N/A 18.38 16 4.00 34.30 0.82 39.17 0.79 0.00 0.00 1.68 0.21 0.00 0.00 N/A N/A N/A 1.14 0.00 N/A 23.32 N/A 20.42 17 4.00 24.30 1.35 29.90 1.35 0.00 0.00 1.96 0.38 0.00 0.00 N/A N/A N/A 1.23 0.00 N/A 15.26 N/A 12.40 18 3.95 35.31 0.40 38.21 0.39 0.16 0.07 1.74 0.10 0.00 0.00 238.81 N/A N/A 1.08 0.00 N/A 21.96 10.88 20.29 O Si Mg Al Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al R^2 = 0.0053 0.0483 0.0115 0.06 0.0634 0.0218 Slope = 2.9221 8.6127 -0.2845 0.1764 9.0462 5.2834 Intercept = 21.109 1.6966 2.8498 0.4069 -14.114 -1.0008 Table 16. TEM EELS and EDS data for Montmorillonite particle M3. Box #s correspond to box numbers in Image 9 above with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

29 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

M4 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Al ±Al Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al 1 3.80 22.74 1.27 22.83 1.14 0.00 0.00 2.24 0.46 0.00 0.00 N/A N/A N/A 1.00 0.00 N/A 10.19 N/A 10.15 2 3.55 22.95 1.17 23.76 1.03 0.00 0.00 2.26 0.39 0.00 0.00 N/A N/A N/A 1.04 0.00 N/A 10.51 N/A 10.15 3 3.60 27.40 1.18 25.06 1.05 0.86 0.27 2.36 0.37 0.00 0.00 29.14 N/A N/A 0.91 0.03 N/A 10.62 2.74 11.61 4 3.80 18.99 1.11 19.99 1.00 0.00 0.00 1.05 0.38 0.00 0.00 N/A N/A N/A 1.05 0.00 N/A 19.04 N/A 18.09 5 3.65 28.04 1.01 29.70 0.92 0.57 0.23 4.19 0.36 0.00 0.00 52.11 N/A N/A 1.06 0.02 N/A 7.09 7.35 6.69 6 4.50 23.90 0.95 23.73 0.85 0.73 0.23 2.65 0.33 0.00 0.00 32.51 N/A N/A 0.99 0.03 N/A 8.95 3.63 9.02 7 4.15 23.26 1.13 23.83 1.00 0.00 0.00 3.17 0.40 0.00 0.00 N/A N/A N/A 1.02 0.00 N/A 7.52 N/A 7.34 8 3.90 28.63 1.01 25.39 0.90 0.00 0.00 2.86 0.35 0.00 0.00 N/A N/A N/A 0.89 0.00 N/A 8.88 N/A 10.01 9 4.10 25.29 0.91 24.91 0.81 0.62 0.22 2.26 0.30 0.00 0.00 40.18 N/A N/A 0.98 0.02 N/A 11.02 3.65 11.19 10 4.10 25.38 0.83 26.53 0.75 0.00 0.00 2.62 0.28 0.00 0.00 N/A N/A N/A 1.05 0.00 N/A 10.13 N/A 9.69 25.50 11 4.15 0.73 25.83 0.67 0.66 0.18 3.41 0.27 0.00 0.00 39.14 N/A N/A 1.01 0.03 N/A 7.57 5.17 7.48 12 4.10 27.58 0.83 26.16 0.75 0.41 0.20 3.10 0.29 0.25 0.12 63.80 104.64 1.64 0.95 0.01 110.32 8.44 7.56 8.90 13 4.10 22.43 0.90 24.83 0.82 0.00 0.00 1.91 0.31 0.00 0.00 N/A N/A N/A 1.11 0.00 N/A 13.00 N/A 11.74 14 3.85 26.29 0.79 26.53 0.72 0.46 0.18 3.56 0.28 0.00 0.00 57.67 N/A N/A 1.01 0.02 N/A 7.45 7.74 7.38 15 3.90 27.15 0.75 27.32 0.67 0.76 0.18 3.35 0.26 0.00 0.00 35.95 N/A N/A 1.01 0.03 N/A 8.16 4.41 8.10 16 3.80 25.64 0.85 23.78 0.76 0.50 0.20 2.35 0.28 0.00 0.00 47.56 N/A N/A 0.93 0.02 N/A 10.12 4.70 10.91 17 3.80 15.97 1.37 13.76 1.17 0.00 0.00 1.88 0.45 0.00 0.00 N/A N/A N/A 0.86 0.00 N/A 7.32 N/A 8.49 18 3.60 25.31 0.44 25.29 0.40 0.49 0.11 2.95 0.15 0.00 0.00 51.61 N/A N/A 1.00 0.02 N/A 8.57 6.02 8.58 19 3.60 25.65 0.41 25.65 0.37 0.54 0.10 2.97 0.14 0.00 0.00 47.50 N/A N/A 1.00 0.02 N/A 8.64 5.50 8.64 O Si Mg Al Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al R^2 = 0.0004 0.001 0.0009 0.0009 0.0049 0.0162 0.0048 0.0031 0.0067 0.0093 Slope = -0.2636 0.4017 0.0384 0.0832 -6.7829 0.0312 0.0034 -0.6077 -0.971 -0.9675 Intercept = 25.6640 22.9020 0.1977 2.3672 52.602 0.8718 3.0E-05 12.011 6.8614 13.464 Table 17. TEM EELS and EDS data for Montmorillonite particle M4. Box #s correspond to box numbers in Image 10 below with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included. 30 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Spectrum Image

0.50.5 µµm

Image 10. Montmorillonite particle M4 images and box numbers. Corresponds to Table 17.

31 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

M5 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Al ±Al Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al 1 2.85 3.57 0.16 1.66 0.11 0.00 0.00 0.26 0.07 0.00 0.00 N/A N/A N/A 0.46 0.00 N/A 6.38 N/A 13.73 2 2.55 3.45 0.36 1.99 0.25 0.00 0.00 0.00 0.00 0.00 0.00 N/A N/A N/A 0.58 0.00 N/A N/A N/A N/A 0.29 3 2.45 3.36 0.27 1.88 0.18 0.00 0.00 0.11 0.00 0.00 N/A N/A N/A 0.56 0.00 N/A 6.48 N/A 11.59 O Si Mg Al Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al R^2 = 0.961 0.7033 0.0345 0.8578 0.07 0.1713 Slope = 0.4962 -0.6769 0.1423 -0.2678 4.7225 14.686 Intercept = 2.1617 3.6146 -0.1890 1.2346 -8.0681 -29.99 Table 18. TEM EELS and EDS data for Montmorillonite particle M5. Box #s correspond to box numbers in Image 11 below with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included. Table 17 summarizes the band gaps and elemental composition of Montmorillonite clay particle M4 shown in Image 10. The band gap measured by TEM-EELS ranges from 3.55 to 4.5 eV, giving a range of 0.95 eV. The average band gap is 4.0 eV. Si/Mg ratios range from 29.14 to 63.8, range is 34.66. Si/O ratios range from 0.86 to 1.11, range is 0.25. Mg/O ratios range from 0 to 0.03, range is 0.03. Si/Al ratios range from 7.09 to 19.04, range is 11.95. Al/Mg ratios range from 2.74 to 7.74, range is 5. O/Al ratios range from 6.69 to 18.09, range is 11.4. The best linear correlation with band gaps (Table 17) was given by Si/O ratios. There is no detectable calcium coverage on particle M4. The isomorphic substitution of Mg for Al in particle M4 is fairly evenly distributed. Isomorphic ranges from 0 to 0.86 atom % (Table 17). Table 18 above summarizes the band gaps and elemental composition of Montmorillonite clay particle M5 shown in Image 11. The band gap measured by TEM-EELS ranges from 2.45 to 2.85 eV, giving a range of 0.4 eV. The average band gap is 2.65 eV. Si/O ratios range from 0.46 to 0.58, range is 0.12. Si/Al ratios range from 6.38 to 6.48, range is 0.1. O/Al ratios range from 11.59 to 13.73, range is 2.14. The best linear correlation with band gaps (Table 18) was given by O atom %, with Si/O ratios being nearly equally well fitted. There is no detectable calcium coverage on particle M5. Isomorphic substitution on particle M5 was not detectable (Table 18).

32 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Spectrum Image

0.50.5 µµm

Image 11. Montmorillonite particle M5 images and box numbers. Corresponds to Table 18. Table 19 below summarizes the band gaps and elemental composition of Montmorillonite clay particle M6 shown in Image 12. The band gap measured by TEM-EELS ranges from 6.6 to 8.9 eV, giving a range of 2.3 eV. The average band gap is 7.75 eV. Si/O ratios range from 0.34 to 0.56, range is 0.22. Si/Al ratios range from 7.53 to 7.76, range is 0.23. The best linear correlation with band gaps (Table 19) was given by O atom %, with Si/O ratios and Si atom % being nearly equally well fitted. There is no detectable calcium coverage on particle M6. Isomorphic substitution on particle M6 was not detectable (Table 19).

33 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

M6 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Al ±Al Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al 1 6.60 3.00 0.18 1.28 0.11 0.00 0.00 0.17 0.07 0.00 0.00 N/A N/A N/A 0.43 0.00 N/A 7.53 N/A 17.65 2 8.90 3.00 0.14 1.32 0.09 0.00 0.00 0.17 0.06 0.00 0.00 N/A N/A N/A 0.44 0.00 N/A 7.76 N/A 17.65 3 8.55 3.31 0.25 1.13 0.15 0.00 0.00 0.00 0.00 0.00 0.00 N/A N/A N/A 0.34 0.00 N/A N/A N/A N/A 4 6.60 2.61 0.23 1.47 0.15 0.00 0.00 0.00 0.00 0.00 0.00 N/A N/A N/A 0.56 0.00 N/A N/A N/A N/A O Si Mg Al Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al R^2 = 0.4212 0.3039 0.0067 0.3639 0.0097 Slope = 0.1506 -0.0624 0.0065 -0.0446 0.3515 Intercept = 1.8257 1.778 0.0352 0.7848 1.1301 Table 19. TEM EELS and EDS data for Montmorillonite particle M6. Box #s correspond to box numbers in Image 12 below with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

Spectrum Image

0.50.5 µµm

Image 12. Montmorillonite particle M6 images and box numbers. Corresponds to Table 19.

34 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Table 20 below summarizes the band gaps and elemental composition of Montmorillonite clay particle M7 shown in Image 13. The band gap measured by TEM-EELS ranges from 3.1 to 5.7 eV, giving a range of 2.6 eV. The average band gap is 4.4 eV. Si/Mg ratios range from 22.35 to 57.83, range is 35.48. Si/Ca ratios range from 84.1 to 322.21, range is 238.11. Mg/Ca ratios range from 1.82 to 6.1, range is 4.28. Si/O ratios range from 0.9 to 1.22, range is 0.32. Mg/O ratios range from 0 to 0.04, range is 0.04. O/Ca ratios range from 78.14 to 296.64, range is 218.5. Si/Al ratios range from 9.66 to 12.26, range is 6.88. Al/Mg ratios range from 3.93 to 8.19, range is 4.26. O/Al ratios range from 5.33 to 16.05, range is 10.72. The best linear correlation with band gaps (Table 20) was given by Ca atom %. Ca coverage ranged from 0 to 0.49 atom %, the distribution of Ca atoms appears to be evenly distributed on a 0.25 µm scale. Isomorphic substitution on particle M7 does seem to be consistently distributed. Mg atom % values and Al/Mg ratios do not indicate an unusually high level of isomorphic substitution than other Montmorillonite particles observed.

35 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

M7 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Al ±Al Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al 1 3.10 37.79 0.77 38.66 0.69 1.32 0.16 5.23 0.27 0.22 0.09 29.29 175.73 6.00 1.02 0.03 171.77 7.39 3.96 7.23 2 3.45 39.30 0.80 35.54 0.70 0.69 0.16 4.86 0.25 0.38 0.08 51.51 93.53 1.82 0.90 0.02 103.42 7.31 7.04 8.09 3 3.90 38.94 0.80 40.23 0.74 1.28 0.16 5.67 0.27 0.21 0.09 31.43 191.57 6.10 1.03 0.03 185.43 7.10 4.43 6.87 4 3.25 41.59 0.62 44.56 0.60 0.78 0.13 5.66 0.21 0.45 0.08 57.13 99.02 1.73 1.07 0.02 92.42 7.87 7.26 7.35 5 3.30 41.10 0.51 43.60 0.48 1.04 0.11 5.15 0.17 0.18 0.06 41.92 242.22 5.78 1.06 0.03 228.33 8.47 4.95 7.98 6 3.85 39.32 0.84 38.81 0.77 1.41 0.18 5.73 0.29 0.21 0.09 27.52 184.81 6.71 0.99 0.04 187.24 6.77 4.06 6.86 7 3.55 41.95 0.67 46.26 0.65 0.68 0.14 5.57 0.23 0.37 0.08 68.03 125.03 1.84 1.10 0.02 113.38 8.31 8.19 7.53 8 3.45 41.67 0.72 48.00 0.72 0.73 0.14 4.74 0.24 0.41 0.09 65.75 117.07 1.78 1.15 0.02 101.63 10.13 6.49 8.79 9 3.40 39.40 0.86 47.20 0.86 0.73 0.17 3.85 0.28 0.00 0.00 64.66 N/A N/A 1.20 0.02 N/A 12.26 5.27 10.23 10 3.45 38.29 1.15 41.21 1.08 0.93 0.28 6.15 0.43 0.49 0.15 44.31 84.10 1.90 1.08 0.02 78.14 6.70 6.61 6.23 11 3.60 41.09 0.72 43.81 0.67 1.96 0.16 7.71 0.27 0.39 0.09 22.35 112.33 5.03 1.07 0.05 105.36 5.68 3.93 5.33 12 3.95 44.42 0.89 42.20 0.81 1.00 0.18 6.53 0.32 0.29 0.11 42.20 145.52 3.45 0.95 0.02 153.17 6.46 6.53 6.80 13 5.10 33.11 1.42 37.76 1.31 0.00 0.00 4.00 0.48 0.00 0.00 N/A N/A N/A 1.14 0.00 N/A 9.44 N/A 8.28 14 3.20 30.32 1.14 27.60 0.95 0.55 0.24 4.31 0.38 0.00 0.00 50.18 N/A N/A 0.91 0.02 N/A 6.40 7.84 7.03 15 3.50 40.11 0.60 39.44 0.54 1.11 0.12 5.08 0.20 0.30 0.07 35.53 131.47 3.70 0.98 0.03 133.70 7.76 4.58 7.90 16 3.95 41.57 0.51 42.18 0.46 0.97 0.10 5.16 0.17 0.37 0.06 43.48 114.00 2.62 1.01 0.02 112.35 8.17 5.32 8.06 17 3.90 39.70 0.49 43.62 0.47 1.10 0.10 5.70 0.17 0.22 0.06 39.65 198.27 5.00 1.10 0.03 180.45 7.65 5.18 6.96 18 4.20 39.95 0.52 45.40 0.51 0.90 0.11 4.72 0.18 0.27 0.06 50.44 168.15 3.33 1.14 0.02 147.96 9.62 5.24 8.46 19 4.10 41.87 0.57 45.55 0.55 0.90 0.12 5.47 0.20 0.35 0.07 50.61 130.14 2.57 1.09 0.02 119.63 8.33 6.08 7.65 20 3.90 41.47 0.63 44.29 0.59 1.27 0.13 6.47 0.23 0.32 0.08 34.87 138.41 3.97 1.07 0.03 129.59 6.85 5.09 6.41 21 3.60 41.30 0.80 41.02 0.73 1.73 0.18 7.62 0.31 0.44 0.10 23.71 93.23 3.93 0.99 0.04 93.86 5.38 4.40 5.42 22 3.20 36.12 1.69 40.30 1.57 0.00 0.00 5.40 0.61 0.00 0.00 N/A N/A N/A 1.12 0.00 N/A 7.46 N/A 6.69 Table 20. TEM EELS and EDS data for Montmorillonite particle M7. Box #s correspond to box numbers in Image 13 below with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

36 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

M7 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Al ±Al Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al 23 3.50 28.09 2.07 34.30 1.90 0.00 0.00 1.75 0.68 0.00 0.00 N/A N/A N/A 1.22 0.00 N/A 19.60 N/A 16.05 24 4.25 34.30 1.04 32.62 0.91 1.20 0.24 5.73 0.39 0.00 0.00 27.18 N/A N/A 0.95 0.03 N/A 5.69 4.78 5.99 25 4.70 39.00 0.68 39.21 0.62 1.16 0.15 5.71 0.24 0.26 0.08 33.80 150.81 4.46 1.01 0.03 150.00 6.87 4.92 6.83 26 5.40 40.00 0.53 43.53 0.50 1.25 0.12 5.87 0.19 0.33 0.07 34.82 131.91 3.79 1.09 0.03 121.21 7.42 4.70 6.81 27 5.70 41.17 0.50 43.32 0.47 1.30 0.10 6.35 0.18 0.41 0.06 33.32 105.66 3.17 1.05 0.03 100.41 6.82 4.88 6.48 28 5.40 41.32 0.50 43.76 0.47 0.85 0.10 5.65 0.17 0.39 0.06 51.48 112.21 2.18 1.06 0.02 105.95 7.75 6.65 7.31 29 5.30 41.02 0.51 43.85 0.49 1.01 0.11 5.12 0.17 0.36 0.06 43.42 121.81 2.81 1.07 0.02 113.94 8.56 5.07 8.01 30 4.50 41.53 0.58 45.11 0.55 0.78 0.11 4.67 0.19 0.14 0.07 57.83 322.21 5.57 1.09 0.02 296.64 9.66 5.99 8.89 31 3.60 37.89 0.81 40.32 0.75 0.92 0.16 4.24 0.26 0.00 0.00 43.83 N/A N/A 1.06 0.02 N/A 9.51 4.61 8.94 32 9.35 38.82 0.20 41.04 0.19 1.06 0.04 5.31 0.07 0.32 0.03 38.72 128.25 3.31 1.06 0.03 121.31 7.73 5.01 7.31 33 5.35 41.63 0.28 44.69 0.27 1.15 0.06 5.87 0.10 0.40 0.04 38.86 111.73 2.88 1.07 0.03 104.08 7.61 5.10 7.09 O Si Mg Al Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al R^2 = 0.01 0.0126 0.0107 0.0066 0.0325 0.0024 0.0106 0.0056 0.0022 0.0091 0.0087 0.0078 0.0013 0.0121 Slope = 0.2877 0.4093 0.0369 0.0739 0.0238 -0.7034 6.4895 0.1268 0.0028 0.0008 5.5491 -0.1851 -0.0584 -0.1686 Intercept = 38.044 39.774 0.8083 5.0561 0.1576 41.663 85.877 2.3614 1.0458 0.0206 84.421 8.9173 5.2194 8.3371 Table 20 cont. TEM EELS and EDS data for Montmorillonite particle M7. Box #s correspond to box numbers in Image 13 below with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

37 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Spectrum Image

11 µµm

Image 13. Montmorillonite particle M7 images and box numbers. Corresponds to Table 20.

Table 21 below summarizes the band gaps and elemental composition of Montmorillonite clay particle M9 shown in Image 14. The band gap measured by TEM-EELS ranges from 4.45 to 6.5 eV, giving a range of 2.05 eV. The average band gap is 5.5 eV. Si/Mg ratios range from 59.77 to 111.6, range is 51.83. Si/Ca ratios range from 102.11 to 202.33, range is 100.22. Si/O ratios range from 1.03 to 1.2, range is 0.17. Mg/O ratios range from 0 to 0.02, range is 0.02. O/Ca ratios range from 90.72 to 179.04, range is 88.32. Si/Al ratios range from 10.69 to 16.91, range is 6.22. Al/Mg ratios range from 5.59 to 7.81, range is 2.22. O/Al ratios range from 8.92 to 15.22, range is 6.3. The best linear correlation with band gaps (Table 21) was given by Si/Al ratios, O/Al ratios also give nearly as good linear fits. Ca coverage ranged from 0 to 0.49 atom % and the distribution of Ca atoms appears to be random. On average, there appear to be little detectable Ca ion coverage. Isomorphic substitution on particle M9 does not seem to be consistently distributed; there are areas where no calcium is detected and other areas (box 4 & 6, Table 21) where there is detected calcium coverage. The calcium coverage did not correlate with areas where Mg isomorphic substitution occurred. Mg atom % values and Al/Mg ratios are comparable to other Montmorillonite particles observed.

38 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

M9 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Al ±Al Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al 0.00 1 6.50 41.67 0.46 46.53 0.44 0.00 0.00 3.59 0.14 0.00 N/A N/A N/A 1.12 0.00 N/A 12.96 N/A 11.61 2 5.10 42.64 1.03 47.99 0.98 0.00 0.00 3.13 0.28 0.47 0.13 N/A 102.11 0.00 1.13 0.00 90.72 15.33 N/A 13.62 3 4.65 45.21 1.13 46.96 1.07 0.00 0.00 2.97 0.31 0.00 0.00 N/A N/A N/A 1.04 0.00 N/A 15.81 N/A 15.22 43.82 4 4.85 0.99 45.33 0.91 0.49 0.17 2.92 0.26 0.00 0.00 92.51 N/A N/A 1.03 0.01 N/A 15.52 5.96 15.01 5 4.45 42.97 0.90 48.56 0.86 0.00 0.00 3.00 0.24 0.24 0.11 N/A 202.33 0.00 1.13 0.00 179.04 16.19 N/A 14.32 48.41 6 6.20 40.39 1.54 1.55 0.81 0.39 4.53 0.54 0.00 0.00 59.77 N/A N/A 1.20 0.02 N/A 10.69 5.59 8.92 46.87 7 5.60 42.96 0.63 0.60 0.42 0.12 3.28 0.18 0.00 0.00 111.60 N/A N/A 1.09 0.01 N/A 14.29 7.81 13.10 O Si Mg Al Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al R^2 = 0.6055 0.0007 0.1359 0.6136 0.1362 0.0241 0.2915 0.2835 0.1475 0.2914 0.7855 0.0581 0.7256 Slope = -1.5106 -0.0375 0.1541 0.568 -0.087 9.7387 -54.665 0.0386 0.0039 -48.396 2.2132 1.0765 -2.4049 Intercept = 50.869 47.436 -0.5766 0.3151 0.5654 -14.267 335.17 0.8993 -0.0149 296.77 26.208 -2.9781 25.946 Table 21. TEM EELS and EDS data for Montmorillonite particle M9. Box #s correspond to box numbers in Image 14 below with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included. Table 22 summarizes the band gaps and elemental composition of Montmorillonite clay particle M10 shown in Image 14. The band gap measured by TEM-EELS ranges from 3.45 to 5.6 eV, giving a range of 2.15 eV. The average band gap is 4.5 eV. Si/Mg ratios range from 59.54 to 160.97, range is 101.43. Si/Ca ratios range from 126.64 to 253.1, range is 126.46. Mg/Ca ratios range from 0 to 3.09, range is 3.09. Si/O ratios range from 0.93 to 1.23, range is 0.3. Mg/O ratios range from 0 to 0.02, range is 0.02. O/Ca ratios range from 120.47 to 208.0, range is 87.53. Si/Al ratios range from 9.03 to 20.21, range is 11.18. Al/Mg ratios range from 4.4 to 8.63, range is 4.23. O/Al ratios range from 8.39 to 18.27, range is 9.88. The best linear correlation with band gaps (Table 22) was given by Si/Mg ratios, O atom % and Al/Mg ratios also give nearly as good linear fits. Ca coverage ranged from 0 to 0.27 atom % and the distribution of Ca atoms appears to be random. On average Ca ion coverage accounts for 0.25 atom %. Isomorphic substitution by Mg on particle M10 seem to be fairly equally distributed. Mg atom % values are comparable to other Montmorillonite particles observed. Al/Mg ratios are on the higher end indicating a lower degree of isomorphic substitution but still within the range of other particles observed.

39 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Image 14. Montmorillonite particle M9-M13 images and box numbers. Corresponds to Tables 21-25. Table 23 summarizes the band gap and elemental composition of Montmorillonite clay particle M11 shown in Image 14. Due to the small size and low EDS signal from this particle, the entire particle had to be summed to produce sufficient signal for quantification. Average Ca coverage is 0.51 atom %. Isomorphic substitution based on Al/Mg ratio 4.39 is within the range of observed degree of substitution, this ratio indicates an average degree of substitution compared to other observed Montmorillonite particles.

40 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

M10 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Al ±Al Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al 0.00 1 5.05 40.80 1.10 41.15 0.99 0.00 2.71 0.30 0.00 0.00 N/A N/A N/A 1.01 0.00 N/A 15.18 N/A 15.06 0.00 2 4.55 43.11 0.65 47.69 0.62 0.00 2.36 0.17 0.25 0.08 N/A 190.76 0.00 1.11 0.00 172.44 20.21 N/A 18.27 3 5.30 41.60 0.67 50.62 0.68 0.61 0.12 3.19 0.19 0.20 0.09 82.98 253.10 3.05 1.22 0.01 208.00 15.87 5.23 13.04 4 4.50 39.28 0.81 42.27 0.77 0.71 0.17 4.68 0.27 0.25 0.11 59.54 169.08 2.84 1.08 0.02 157.12 9.03 6.59 8.39 5 4.80 35.91 2.14 33.24 1.90 0.00 0.00 3.33 0.69 0.00 0.00 N/A N/A N/A 0.93 0.00 N/A 9.98 N/A 10.78 0.00 6 3.45 42.48 1.29 44.14 1.17 0.00 2.47 0.33 0.00 0.00 N/A N/A N/A 1.04 0.00 N/A 17.87 N/A 17.20 7 3.90 40.99 0.93 46.68 0.88 0.00 0.00 2.52 0.24 0.00 0.00 N/A N/A N/A 1.14 0.00 N/A 18.52 N/A 16.27 8 4.40 43.37 0.73 45.59 0.69 0.00 0.00 3.18 0.21 0.36 0.09 N/A 126.64 0.00 1.05 0.00 120.47 14.34 N/A 13.64 9 4.40 40.83 0.66 48.29 0.65 0.68 0.12 3.69 0.20 0.22 0.08 71.01 219.50 3.09 1.18 0.02 185.59 13.09 5.43 11.07 50.24 10 4.05 40.97 0.97 1.00 0.84 0.19 3.70 0.31 0.00 0.00 59.81 N/A N/A 1.23 0.02 N/A 13.58 4.40 11.07 11 5.45 35.08 1.80 34.18 1.58 0.00 0.00 3.15 0.65 0.00 0.00 N/A N/A N/A 0.97 0.00 N/A 10.85 N/A 11.14 12 5.60 40.45 0.86 43.82 0.83 0.68 0.17 4.77 0.28 0.00 0.00 64.44 N/A N/A 1.08 0.02 N/A 9.19 7.01 8.48 13 5.50 41.55 0.58 48.29 0.57 0.30 0.10 2.59 0.16 0.27 0.07 160.97 178.85 1.11 1.16 0.01 153.89 18.64 8.63 16.04 14 4.25 42.99 0.65 47.61 0.62 0.36 0.12 3.01 0.18 0.23 0.08 132.25 207.00 1.57 1.11 0.01 186.91 15.82 8.36 14.28 15 4.60 39.28 0.81 42.27 0.77 0.71 0.17 4.68 0.27 0.25 0.11 59.54 169.08 2.84 1.08 0.02 157.12 9.03 6.59 8.39 16 4.80 41.99 0.43 47.58 0.42 0.36 0.08 2.78 0.12 0.27 0.06 132.17 176.22 1.33 1.13 0.01 155.52 17.12 7.72 15.10 17 5.25 40.39 0.37 45.45 0.35 0.42 0.07 3.10 0.11 0.25 0.05 108.21 181.80 1.68 1.13 0.01 161.56 14.66 7.38 13.03 18 5.05 41.87 0.41 47.75 0.40 0.44 0.08 3.23 0.12 0.24 0.05 108.52 198.96 1.83 1.14 0.01 174.46 14.78 7.34 12.96 O Si Mg Al Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al R^2 = 0.1174 0.0398 0.0171 0.0319 0.0125 0.1205 0.0301 0.0167 0.0041 0.0162 0.024 0.0671 0.1168 0.0777 Slope = -1.2868 -1.625 0.0685 0.2276 0.0246 31.987 28.486 0.268 -0.0085 0.0017 22.261 -1.5394 2.042 -1.4137 Intercept = 46.788 52.49 0.0162 2.2122 0.0389 -93.124 -19.304 -0.1893 1.1388 0.0005 -3.1585 21.581 -5.4817 19.68 Table 22. TEM EELS and EDS data for Montmorillonite particle M10. Box #s correspond to box numbers in Image 14 above with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

41 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

M11 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Al ±Al Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al 1 3.80 41.92 0.95 47.08 0.93 0.98 0.21 4.30 0.32 0.51 0.13 48.04 92.31 1.92 1.12 0.02 82.20 10.95 4.39 9.75 Table 23. TEM EELS and EDS data for Montmorillonite particle M11. Box #s correspond to box numbers in Image 14 above with respective EELS band gap information and EDS chemical composition information.

M12 Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Al ±Al Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al 1 4.10 41.48 0.33 47.81 0.33 0.77 0.07 4.99 0.11 0.26 0.05 62.09 183.88 2.96 1.15 0.02 159.54 9.58 6.48 8.31 2 3.55 41.49 0.86 45.50 0.83 0.96 0.20 6.81 0.32 0.38 0.13 47.40 119.74 2.53 1.10 0.02 109.18 6.68 7.09 6.09 3 4.80 39.27 0.63 52.82 0.68 0.37 0.13 4.92 0.22 0.32 0.09 142.76 165.06 1.16 1.35 0.01 122.72 10.74 13.30 7.98 4 4.05 42.26 0.89 44.37 0.84 0.88 0.20 5.87 0.31 0.24 0.12 50.42 184.88 3.67 1.05 0.02 176.08 7.56 6.67 7.20 5 3.30 41.53 0.95 49.54 0.95 0.77 0.20 4.59 0.31 0.00 0.00 64.34 N/A N/A 1.19 0.02 N/A 10.79 5.96 9.05 46.28 6 3.90 43.84 0.69 0.65 0.65 0.13 3.86 0.21 0.00 0.00 71.20 N/A N/A 1.06 0.01 N/A 11.99 5.94 11.36 7 4.85 41.80 0.62 44.77 0.59 0.97 0.14 6.34 0.22 0.32 0.09 46.15 139.91 3.03 1.07 0.02 130.63 7.06 6.54 6.59 8 4.25 39.92 0.53 51.60 0.55 0.52 0.11 4.82 0.18 0.27 0.07 99.23 191.11 1.93 1.29 0.01 147.85 10.71 9.27 8.28 9 3.60 43.53 0.63 46.21 0.59 0.76 0.12 3.76 0.19 0.00 0.00 60.80 N/A N/A 1.06 0.02 N/A 12.29 4.95 11.58 10 3.90 41.24 0.43 48.65 0.43 0.69 0.09 4.91 0.14 0.28 0.06 70.51 173.75 2.46 1.18 0.02 147.29 9.91 7.12 8.40 11 3.50 41.82 0.65 46.55 0.63 0.89 0.14 5.28 0.22 0.23 0.09 52.30 202.39 3.87 1.11 0.02 181.83 8.82 5.93 7.92 O Si Mg Al Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al R^2 = 0.2067 0.0574 0.1272 0.0483 0.2583 0.2359 0.1823 0.0431 0.1199 0.1099 0.1434 0.0254 0.3988 0.0963 Slope = -1.1946 1.3042 -0.1302 0.4087 0.1413 27.35 69.892 0.6013 0.0678 -0.0028 53.795 -0.6035 2.8625 -1.0578 Intercept = 46.41 42.452 1.2667 3.477 -0.3537 -39.156 -154.59 -0.4306 0.8763 0.0291 -107.37 12.051 -4.194 12.645 Table 24. TEM EELS and EDS data for Montmorillonite particle M12. Box #s correspond to box numbers in Image 14 above with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

42 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Table 24 summarizes the band gaps and elemental composition of Montmorillonite clay particle M12 shown in Image 14. The band gap measured by TEM-EELS ranges from 3.3 to 4.85 eV, giving a range of 1.55 eV. The average band gap is 4.05 eV. Si/Mg ratios range from 46.15 to 142.76, range is 96.61. Si/Ca ratios range from 119.74 to 202.39, range is 82.65. Mg/Ca ratios range from 1.16 to 3.87, range is 2.71. Si/O ratios range from 1.05 to 1.35, range is 0.3. Mg/O ratios range from 0 to 0.02, range is 0.02. O/Ca ratios range from 109.18 to 181.83, range is 72.65. Si/Al ratios range from 6.68 to 12.29, range is 5.61. Al/Mg ratios range from 4.95 to 13.3, range is 8.35. O/Al ratios range from 6.09 to 11.58, range is 5.49. The best linear correlation with band gap values (Table 24) was given by atom Al/Mg ratios. The average calcium coverage is 0.28 atom %. Calcium appears to be evenly distributed throughout particle M12. Isomorphic substitution is very well distributed throughout the particle and the degree of isomorphic substitution based on Al/Mg ratios indicate it to be on the low to medium range. Table 25 below summarizes the band gaps and elemental composition of Montmorillonite clay particle M13 shown in Image 14. The band gap measured by TEM-EELS ranges from 3.45 to 4.1 eV, giving a range of 0.65 eV. The average band gap is 3.8 eV. Si/Mg ratios range from 47.49 to 119.95, range is 72.46. Si/Ca ratios range from 121.21 to 231.23, range is 110.02. Mg/Ca ratios range from 1.41 to 3.91, range is 2.5. Si/O ratios range from 1.08 to 1.3, range is 0.22. Mg/O ratios range from 0 to 0.03, range is 0.03. O/Ca ratios range from 103.72 to 190.32, range is 86.6. Si/Al ratios range from 6.72 to 15.48, range is 8.76. Al/Mg ratios range from 3.71 to 12.78, range is 9.07. O/Al ratios range from 5.75 to 12.55, range is 6.8. The best linear correlation with band gap values (Table 25) was given by atom Si/Al ratios with O/Al ratios giving a similarly good fit. The average calcium coverage is 0.3 atom %. Calcium appears to be evenly distributed throughout particle M13. Isomorphic substitution is very well distributed throughout the particle and the degree of isomorphic substitution based on Al/Mg ratios indicate it to be on the low to medium range. Table 26 below is a summary of the average band gap values, elemental atomic % and ratios from each observed Montmorillonite particle (M1 through M13). O, Si, Mg, Al and Ca atom % does not add up to 100% in Table 26, the remaining element not included in the tables is C which accounts for the remaining of the atoms %. Si/Mg ratios range from 51.12 to 238.81, range is 187.69. This interparticle range (Table 26) is larger than any range observed within the same Montmorillonite particle, which has a maximum range of 129.92 (Table 28). Interparticle Si/Ca ratios range from 92.31 to 231.23, range is 138.92, which places this value in the mid range variation compared to values found in Table 28. Interparticle Mg/Ca ratios range from 1.37 to 2.96, giving range of 1.59, on the lower end of range values shown in Table 28. Interparticle Si/O ratios range from 0.43 to 1.21, giving a range of 0.78, the range is larger than the values shown in Table 28 indicating higher interparticle variations than intraparticle. Interparticle Mg/O ratios range from 0 to 0.03, giving range of 0.03, this is in the mid range of values shown in Table 28. Interparticle O/Ca ratios range from 82.2 to 206.68, giving range of 124.48, in the midrange of values when comparing to Table 28. Interparticle Si/Al ratios range from 6.48 to 21.96, giving range of 15.48, this also falls into the midrange of values found in Table 28. Interparticle Al/Mg ratios range from 4.17 to 10.88, range is 6.71 which place it in the midrange of values shown in Table 28. An interparticle O/Al ratio range from 7.09 to 20.29, giving range of 13.2 and places it in the midrange with values in Table 28. The best linear correlation with the band gap (Table 26) was given by the O/Al ratio.

43 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

M13

Atom % Ratios Box # Band gap (eV) O ±O Si ±Si Mg ±Mg Al ±Al Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al 1 4.05 41.87 0.68 50.87 0.69 0.86 0.14 3.59 0.21 0.22 0.09 59.15 231.23 3.91 1.21 0.02 190.32 14.17 4.17 11.66 2 3.90 40.14 0.91 50.77 0.93 0.80 0.19 4.39 0.30 0.26 0.13 63.46 195.27 3.08 1.26 0.02 154.38 11.56 5.49 9.14 3 3.70 40.45 1.01 47.27 1.01 0.55 0.24 7.03 0.38 0.39 0.15 85.95 121.21 1.41 1.17 0.01 103.72 6.72 12.78 5.75 0.89 4 4.10 41.40 0.72 51.10 0.73 0.15 3.30 0.22 0.30 0.09 57.42 170.33 2.97 1.23 0.02 138.00 15.48 3.71 12.55 5 3.85 41.01 0.85 50.54 0.86 0.73 0.19 4.77 0.28 0.00 0.00 69.23 N/A N/A 1.23 0.02 N/A 10.60 6.53 8.60 6 3.45 41.89 1.44 50.02 1.45 0.65 0.32 4.95 0.48 0.00 0.00 76.95 N/A N/A 1.19 0.02 N/A 10.11 7.62 8.46 51.29 7 3.80 40.73 0.97 1.01 1.08 0.21 4.83 0.32 0.00 0.00 47.49 N/A N/A 1.26 0.03 N/A 10.62 4.47 8.43 0.42 8 3.95 42.19 0.91 50.38 0.91 0.19 4.14 0.28 0.00 0.00 119.95 N/A N/A 1.19 0.01 N/A 12.17 9.86 10.19 4.78 9 3.85 39.42 0.92 51.41 0.96 0.64 0.19 0.32 0.37 0.13 80.33 138.95 1.73 1.30 0.02 106.54 10.76 7.47 8.25 10 3.85 42.49 1.29 45.91 1.26 0.87 0.29 4.59 0.42 0.00 0.00 52.77 N/A N/A 1.08 0.02 N/A 10.00 5.28 9.26 O Si Mg Al Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al R^2 = 0.0031 0.0805 0.0649 0.4431 0.0698 0.0183 0.2656 0.3348 0.0328 0.0622 0.2625 0.548 0.2164 0.5308 Slope = 0.3 2.875 0.2667 -3.665 0.245 -15.65 268.04 4.886 0.0611 0.0063 215.75 9.7292 -7.217 7.5848 Intercept = 40.004 38.887 -0.2777 18.747 -0.7892 131.53 -946.25 -17.502 0.9794 -0.0062 -761.34 -26.239 34.523 -19.972 Table 25. TEM EELS and EDS data for Montmorillonite particle M13. Box #s correspond to box numbers in Image 14 above with respective EELS band gap information and EDS chemical composition information. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included.

44 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Ratios M# Band gap (eV) O ±O Si ±Si Mg ±Mg Al ±Al Ca ±Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al 1 3.95 39.27 0.58 38.49 0.54 0.26 0.10 2.22 0.15 0.19 0.06 148.04 202.58 1.37 0.98 0.01 206.68 17.34 8.54 17.69 2 4.30 39.30 0.30 45.50 0.31 0.89 0.07 5.34 0.11 0.38 0.04 51.12 119.74 2.34 1.16 0.02 103.42 8.52 6.00 7.36 3 3.95 35.31 0.40 38.21 0.39 0.16 0.07 1.74 0.10 0.00 0.00 238.81 N/A N/A 1.08 0.00 N/A 21.96 10.88 20.29 4 3.60 25.65 0.41 25.65 0.37 0.54 0.10 2.97 0.14 0.00 0.00 47.50 N/A N/A 1.00 0.02 N/A 8.64 5.50 8.64 5 2.45 3.36 0.27 1.88 0.18 0.00 0.00 0.29 0.11 0.00 0.00 N/A N/A N/A 0.56 0.00 N/A 6.48 N/A 11.59 6 6.60 3.00 0.18 1.28 0.11 0.00 0.00 0.17 0.07 0.00 0.00 N/A N/A N/A 0.43 0.00 N/A 7.53 N/A 17.65 7 5.35 41.63 0.28 44.69 0.27 1.15 0.06 5.87 0.10 0.40 0.04 38.86 111.73 2.88 1.07 0.03 104.08 7.61 5.10 7.09 9 5.60 42.96 0.63 46.87 0.60 0.42 0.12 3.28 0.18 0.00 0.00 111.60 N/A N/A 1.09 0.01 N/A 14.29 7.81 13.10 10 5.05 41.87 0.41 47.75 0.40 0.44 0.08 3.23 0.12 0.24 0.05 108.52 198.96 1.83 1.14 0.01 174.46 14.78 7.34 12.96 11 3.80 41.92 0.95 47.08 0.93 0.98 0.21 4.30 0.32 0.51 0.13 48.04 92.31 1.92 1.12 0.02 82.20 10.95 4.39 9.75 12 4.10 41.48 0.33 47.81 0.33 0.77 0.07 4.99 0.11 0.26 0.05 62.09 183.88 2.96 1.15 0.02 159.54 9.58 6.48 8.31 13 4.05 41.87 0.68 50.87 0.69 0.86 0.14 3.59 0.21 0.22 0.09 59.15 231.23 3.91 1.21 0.02 190.32 14.17 4.17 11.66 O Si Mg Al Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al R^2 = 0.0021 0.0018 0.0001 0.004 0.0005 0.003 0.0028 0.0004 0.0157 0.0028 0.003 0.0012 0.0004 0.036 Slope = 0.6216 0.6833 0.004 0.107 -0.0037 -3.3738 -4.5382 -0.0258 -0.0284 -0.0005 -4.2095 0.1485 -0.06 0.7632 Intercept = 30.4 33.334 0.5214 2.6949 0.1997 90.99 115 1.5479 1.1253 0.0158 103.58 12.474 5.7815 8.8159 Table 26. TEM EELS and EDS data for Montmorillonite particles M1-M13, average values. R2, slope and intercept values from linear fit of atom % and ratios against band gap values included. Table 27 is a summary of the R2 values that correspond to Table 26. The orange highlighted cells are the elemental atom % or ratio, which gave the greatest linear correlation with band gap values, while the purple highlighted cells are those that gave comparable linear correlations to the orange cells. O atom %, Si/Al and O/Al ratios (Table 27) seemed to correlate well with the band gap values more often when compared to other atom % or ratios. No one single element or ratio gave the best linear correlations consistently. More 50% of the highlighted R2 values were under 0.5, which indicates a poor linear relationship despite it being the best correlation when compared to elements and ratios with the same M#.

45 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Table 28 is a summary of the minimum band gap values, maximum band gap values, band gap ranges, average Ca atom %, and Si/Mg, Si/Ca, Mg/Ca, Si/O, Mg/O, O/Ca, Si/Al, Al/Mg and O/Al ranges for particles from Tables 12-25. In order to calculate the R2, slope and y- intercept values band gap ranges were plotted against Ca atom %, Si/Mg, Si/Ca, Mg/Ca, Si/O, Mg/O, O/Ca, Si/Al, Al/Mg and O/Al ranges. The highest correlation found was between band gap ranges and Si/Ca and O/Ca ratios (Table 27). Variation range of Al/Mg ratio also gave a decent linear correlation with band gap ranges.

M# O Si Mg Al Ca Si/Mg Si/Ca Mg/Ca Si/O Mg/O O/Ca Si/Al Al/Mg O/Al 1 R^2 = 0.0387 0.0872 0.0333 0.0002 0.0168 0.0000 0.0000 0.0000 0.0014 0.0000 0.0000 0.0130 0.0484 0.0107 2 R^2 = 0.1638 0.1103 0.0693 0.2580 0.1139 0.1650 0.1026 0.0032 0.0051 0.0847 0.0657 0.2011 0.0233 0.1952 3 R^2 = 0.0053 0.0483 0.0000 0.0115 0.0000 0.0000 0.0000 0.0000 0.0600 0.0000 0.0000 0.0634 0.0000 0.0218 4 R^2 = 0.0004 0.0010 0.0009 0.0009 0.0000 0.0049 0.0000 0.0000 0.0162 0.0048 0.0000 0.0031 0.0067 0.0093 5 R^2 = 0.9610 0.7033 0.0000 0.0345 0.0000 0.0000 0.0000 0.0000 0.8578 0.0000 0.0000 0.0700 0.0000 0.1713 6 R^2 = 0.4212 0.3039 0.0000 0.0067 0.0000 0.0000 0.0000 0.0000 0.3639 0.0000 0.0000 0.0097 0.0000 0.0000 7 R^2 = 0.0100 0.0126 0.0107 0.0066 0.0325 0.0024 0.0106 0.0056 0.0022 0.0091 0.0087 0.0078 0.0013 0.0121 9 R^2 = 0.6055 0.0007 0.1359 0.6136 0.1362 0.0241 0.2915 0.0000 0.2835 0.1475 0.2914 0.7855 0.0581 0.7256 10 R^2 = 0.1174 0.0398 0.0171 0.0319 0.0125 0.1205 0.0301 0.0167 0.0041 0.0162 0.0240 0.0671 0.1168 0.0777 12 R^2 = 0.2067 0.0574 0.1272 0.0483 0.2583 0.2359 0.1823 0.0431 0.1199 0.1099 0.1434 0.0254 0.3988 0.0963 13 R^2 = 0.0031 0.0805 0.0649 0.4431 0.0698 0.0183 0.2656 0.3348 0.0328 0.0622 0.2625 0.5480 0.2164 0.5308 Table 27. Summary of R2 values for particles M1-M13 averages, R2 values corresponds to Table 27 values.

46 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Range s Particl Min. Band Gap Max. Band Gap Band Gap Range Ca atom Mg/C e (eV) (eV) (eV) % Si/Mg Si/Ca a Si/O Mg/O O/Ca Si/Al Al/Mg O/Al M1 3.60 5.70 2.10 0.19 129.92 N/A N/A 0.61 0.05 N/A 21.93 7.35 20.60 111.5 M2 3.80 4.55 0.75 0.35 97.82 8 5.00 0.63 0.07 90.54 15.11 6.86 10.55 M3 3.50 4.00 0.50 0.00 89.93 N/A N/A 0.47 N/A N/A 20.17 5.46 21.71 M4 3.55 4.50 0.95 0.00 34.66 N/A N/A 0.25 0.03 N/A 11.95 5.00 11.40 M5 2.45 2.85 0.40 0.00 N/A N/A N/A 0.12 N/A N/A 0.10 N/A 2.14 M6 6.60 8.90 2.30 0.00 N/A N/A N/A 0.22 N/A N/A 0.23 N/A N/A 238.1 218.5 M7 3.10 5.70 2.60 0.40 35.48 1 4.28 0.32 0.04 0 6.88 4.26 10.72 100.2 M9 4.45 6.50 2.05 0.00 51.83 2 N/A 0.17 0.02 88.32 6.22 2.22 6.30 126.4 M10 3.45 5.60 2.15 0.25 101.43 6 3.09 0.30 0.02 87.53 11.18 4.23 9.88 M12 3.30 4.85 1.55 0.28 96.61 82.65 2.71 0.30 0.02 72.65 5.61 8.35 5.49 110.0 M13 3.45 4.10 0.65 0.30 72.46 2 2.50 0.22 0.03 86.60 8.76 9.07 6.80 Ca atom Mg/C % Si/Mg Si/Ca a Si/O Mg/O O/Ca Si/Al Al/Mg O/Al 0.347 0.345 0.007 R^2 = 0.0485 0.0034 6 0.0055 0.0007 0.066 3 0.0226 0.2152 7 - 41.56 - - 40.72 - - 0.677 Slope = 0.0437 2.4427 3 0.094 0.0056 0.0062 6 1.3166 1.3128 3 60.63 41.17 9.631 Intercept = 0.0973 82.514 3 3.3712 0.3363 0.0449 7 11.746 7.8067 1 Table 28. Summary of the minimum band gap values, maximum band gap values, band gap ranges, average Ca atom %, and Si/Mg, Si/Ca, Mg/Ca, Si/O, Mg/O, O/Ca, Si/Al, Al/Mg and O/Al ranges for particles from Tables 12-25.

47 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Chemical Variation on Submicron scale

Table 29 below summarizes the chemical composition of each box # for Hectorite particles H1 to H4. Table 30 and 31 summarizes the chemical composition of each box # for Hectorite particles H5 to H11. Bulk Hectorite chemical composition is + M 0.3(Mg,Li)3Si4O10(OH)2. Table 29, 30 and 31 are incomplete since Li and H content cannot be measured with EDS, because of this the degree of isomorphic substitution has to be inferred from Si:Mg ratios based on the bulk chemical composition. Si:Mg ratios of 1.33:1 will give a chemical composition of Mg3Si4 which is ideal and suggest no isomorphic substitution by Li. Si:Mg ratios higher than 1.33:1 gives a chemical composition of Mg(3-x)Si4 which indicates that Mg is x moles less than 3 and there is some isomorphic substitution by Li. Si:Mg ratios less than 1.33:1 indicate that the chemical formula is Mg(3+y)Si4 meaning there are 3+y moles of Mg per 4 moles of Si. O:Mg ratios were not used as an indication of isomorphic substitution because most contamination that occurs in TEM samples can contain oxygen, Si is less likely to be present as an contaminant. Hectorite particles H1, H2 and H10 did not have any measureable calcium content. Particles H1 and H2 also had Si:Mg ratios close to or less than 1.33:1. H10 had an high Si:Mg ratio of 3.13, but it is suspected because of the low EDS signal, the calcium signal essentially became undetectable even if there was sufficient Ca coverage on this particle. Generally, if the Si:Mg ratio was sufficiently higher than 1.5:1 there was detectable Ca coverage on the clay particle (Tables 29-31). The chemical composition of the Hectorite particles (Tables 29, 30, 31) did not vary greatly within any particular particle. Between clay particles however, the Si content seem to vary more. Si stayed within ±0.5 of the average value for the same clay particle, Ca distribution seemed very evenly divided when standardized to Mg, O fluctuated more than both Si and Ca but possibly due to contamination which occurs mainly in the form of carbon and oxygen. Contamination was not observed in our experiments but it is possible that such low levels existed where one could not observe it.

48 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

H1 H2 H3 H4 Box # Band gap (eV) O Si Mg Ca Band gap (eV) O Si Mg Ca Band gap (eV) O Si Mg Ca Band gap (eV) O Si Mg Ca 1 3.60 4.09 1.31 1.00 0.00 3.45 3.76 1.34 1.00 0.00 4.25 2.80 2.03 1.00 0.23 4.00 2.52 1.88 1.00 0.02 2 3.40 3.43 1.30 1.00 0.00 3.60 3.64 1.62 1.00 0.00 7.20 3.56 2.50 1.00 0.24 4.00 2.45 1.83 1.00 0.03 3 3.50 3.80 1.27 1.00 0.00 3.70 3.40 1.40 1.00 0.00 4.60 3.57 2.42 1.00 0.29 4.25 2.41 1.71 1.00 0.03 4 3.25 2.90 1.20 1.00 0.00 3.55 3.27 1.51 1.00 0.00 2.30 3.31 2.50 1.00 0.29 4.10 2.79 2.22 1.00 0.00 5 3.35 3.22 1.24 1.00 0.00 3.65 3.22 1.59 1.00 0.00 2.40 3.77 2.99 1.00 0.27 4.55 2.67 2.63 1.00 0.06 6 3.25 3.46 1.25 1.00 0.00 3.15 3.36 1.44 1.00 0.00 2.20 2.76 2.65 1.00 0.22 7 3.30 3.63 1.16 1.00 0.00 3.50 2.61 1.35 1.00 0.00 3.50 2.92 2.93 1.00 0.18 8 3.60 3.50 1.28 1.00 0.00 3.20 2.93 1.33 1.00 0.00 4.10 2.45 2.23 1.00 0.19 9 3.45 3.35 1.27 1.00 0.00 3.35 2.56 1.39 1.00 0.00 5.00 2.72 2.42 1.00 0.19 10 3.40 3.48 1.24 1.00 0.00 3.70 3.35 1.48 1.00 0.00 4.30 2.58 1.98 1.00 0.22 11 3.35 3.27 1.46 1.00 0.00 4.00 2.34 2.24 1.00 0.29 12 3.55 3.16 1.47 1.00 0.00 5.50 2.23 2.45 1.00 0.26 13 3.60 2.97 1.40 1.00 0.00 3.00 2.34 2.58 1.00 0.29 14 5.05 3.20 1.43 1.00 0.00 1.65 3.56 3.35 1.00 0.44 15 3.85 2.53 2.60 1.00 0.41 16 2.65 4.31 3.09 1.00 0.88 17 4.50 5.01 3.42 1.00 1.49 18 4.60 2.59 2.33 1.00 0.22 19 3.50 2.84 2.50 1.00 0.26 20 6.10 2.89 2.52 1.00 0.28 Table 29. Chemical composition of Hectorite particles H1-H4 calculated from TEM-EDS data. Values are standardized to Mg content giving moles of O, Si, and Ca per mol Mg.

49 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

H5 H6 H7 H8 Box # Band gap (eV) O Si Mg Ca Band gap (eV) O Si Mg Ca Band gap (eV) O Si Mg Ca Band gap (eV) O Si Mg Ca 1 4.30 2.37 1.90 1.00 0.04 4.40 2.44 1.79 1.00 0.44 3.50 1.91 1.95 1.00 0.02 3.85 3.44 3.55 1.00 0.05 2 4.50 2.34 1.76 1.00 0.02 4.35 2.41 1.73 1.00 0.05 3.65 1.98 1.93 1.00 0.04 4.00 2.76 2.88 1.00 0.04 3 4.60 2.62 1.88 1.00 0.04 4.20 2.48 2.01 1.00 0.05 3.60 1.98 2.02 1.00 0.04 4.35 3.30 3.40 1.00 0.06 4 4.35 2.90 2.60 1.00 0.06 4.30 2.07 1.75 1.00 0.05 3.55 1.79 1.75 1.00 0.03 4.30 3.01 3.12 1.00 0.03 5 4.20 2.50 2.04 1.00 0.03 4.40 2.35 1.87 1.00 0.05 3.65 2.11 1.98 1.00 0.03 4.00 3.12 3.21 1.00 0.04 6 4.20 2.48 1.93 1.00 0.03 4.25 2.39 1.87 1.00 0.04 3.55 1.95 1.93 1.00 0.04 7 4.10 2.51 2.17 1.00 0.04 4.25 2.08 1.69 1.00 0.05 8 4.25 2.34 2.10 1.00 0.03 4.40 2.45 1.76 1.00 0.24 9 3.75 2.57 2.33 1.00 0.03 4.20 2.29 1.83 1.00 0.08 10 4.20 2.32 1.99 1.00 0.04 4.05 2.28 1.83 1.00 0.04 11 4.30 2.11 2.04 1.00 0.04 4.30 2.21 1.76 1.00 0.05 12 3.65 2.28 2.01 1.00 0.08 4.20 2.27 1.78 1.00 0.08 13 3.80 2.68 2.39 1.00 0.03 4.15 2.28 1.78 1.00 0.05 14 4.50 2.40 1.83 1.00 0.04 4.30 2.26 1.79 1.00 0.05 15 4.00 2.56 2.09 1.00 0.04 4.20 2.32 1.80 1.00 0.10 16 4.00 2.40 2.13 1.00 0.04 17 3.50 2.32 2.10 1.00 0.06 18 4.00 2.42 2.06 1.00 0.04 19 4.45 2.43 2.06 1.00 0.04 Table 30. Chemical composition of Hectorite particles H5-H8 calculated from TEM-EDS data. Values are standardized to Mg content giving moles of O, Si, and Ca per mol Mg.

50 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

H9 H10 H11 Box # Band gap (eV) O Si Mg Ca Band gap (eV) O Si Mg Ca Band gap (eV) O Si Mg Ca 1 3.85 1.53 2.28 1.00 0.04 4.60 2.63 3.13 1.00 0.00 4.20 1.61 1.75 1.00 0.04 2 4.65 1.61 2.08 1.00 0.03 3 4.80 1.52 2.31 1.00 0.05 4 3.85 1.61 2.14 1.00 0.03 5 4.50 1.59 2.19 1.00 0.03 Table 31. Chemical composition of Hectorite particles H9-H11 calculated from TEM-EDS data. Values are standardized to Mg content giving moles of O, Si, and Ca per mol Mg.

51 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

M1 M2 M3 Box # Band gap (eV) O Si Mg Al Ca Band gap (eV) O Si Mg Al Ca Band gap (eV) O Si Mg Al Ca 1 3.95 29.89 31.45 0.00 1.00 0.00 3.80 11.86 12.00 0.00 1.00 0.00 3.95 22.20 22.59 0.00 1.00 0.00 2 5.70 15.01 15.10 0.00 1.00 0.00 3.95 7.85 8.58 0.00 1.00 0.05 3.50 16.29 17.48 0.00 1.00 0.00 3 4.10 N/A N/A N/A N/A N/A 3.80 4.93 4.64 0.18 1.00 0.04 3.50 19.05 17.92 0.00 1.00 0.00 4 4.10 17.10 18.28 0.00 1.00 0.00 3.95 4.08 4.25 0.19 1.00 0.06 3.95 12.33 12.92 0.00 1.00 0.00 5 3.90 18.68 17.79 0.19 1.00 0.00 4.15 12.87 11.83 0.00 1.00 0.00 4.05 24.73 26.41 0.00 1.00 0.00 6 3.65 12.26 10.47 0.00 1.00 0.00 4.30 8.29 8.55 0.11 1.00 0.00 3.95 25.68 29.85 0.00 1.00 0.00 7 3.95 14.18 15.27 0.84 1.00 0.00 4.55 8.63 9.25 0.27 1.00 0.11 3.90 28.65 26.50 0.00 1.00 0.00 8 3.60 9.29 9.52 0.00 1.00 0.00 3.95 5.33 6.12 0.16 1.00 0.05 4.00 15.46 15.25 0.00 1.00 0.00 9 4.20 9.87 14.40 0.40 1.00 0.00 3.95 3.85 4.60 0.17 1.00 0.00 4.00 24.53 26.31 0.00 1.00 0.00 10 4.10 N/A N/A N/A N/A N/A 4.20 8.50 10.73 0.10 1.00 0.09 3.95 19.49 23.64 0.00 1.00 0.00 11 5.50 17.56 17.91 0.00 1.00 0.00 4.35 11.08 14.58 0.00 1.00 0.09 3.95 20.07 22.21 0.00 1.00 0.00 12 3.95 17.69 17.34 0.12 1.00 0.09 4.55 7.78 10.42 0.18 1.00 0.10 3.90 20.99 24.17 0.00 1.00 0.00 13 4.05 4.67 5.33 0.22 1.00 0.09 3.90 6.94 9.68 0.00 1.00 0.00 14 3.75 2.80 3.11 0.21 1.00 0.00 3.95 25.79 27.45 0.18 1.00 0.00 15 4.30 13.35 18.22 0.00 1.00 0.00 3.95 18.38 19.46 0.00 1.00 0.00 16 3.90 8.14 12.60 0.00 1.00 0.00 4.00 20.42 23.32 0.00 1.00 0.00 17 4.05 4.45 6.36 0.20 1.00 0.00 4.00 12.40 15.26 0.00 1.00 0.00 18 3.90 2.84 3.72 0.18 1.00 0.00 3.95 20.29 21.96 0.09 1.00 0.00 19 3.90 7.71 11.29 0.00 1.00 0.00 20 4.30 6.96 7.92 0.17 1.00 0.07 21 3.95 6.09 7.44 0.21 1.00 0.07 22 4.30 7.36 8.52 0.17 1.00 0.07 Table 32. Chemical composition of Montmorillonite particles M1-M3 calculated from TEM-EDS data. Values are standardized to Al content giving moles of O, Si, Mg and Ca per mol Al.

52 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

+ The bulk chemical composition of Montmorillonite is M 0.33(Al,Mg)2(Si4O10)(OH)2. Since both Al and Mg can be measured, one can directly estimate the degree of isomorphic substitution based on the Mg values from Tables 32, 33, 34 and 35. Particles M1, M3, M5, M6, M8 and M9 have very little isomorphic substitution based on measured Mg values (Tables 32-34), these particles also had very little to no Ca coverage. However, there are particles that have some degree of isomorphic substitution but still showed no Ca coverage, for instance, particle M4. More often when there is a consistent and significant amount of isomorphic substitution of Mg for Al, there seems to be Ca sorption onto the surface/interlayer of Montmorillonite particles. Ca surface coverage in Montmorillonite clay particles measured appear to be more randomly distributed compared to Hectorite clay particles measured. Si seems to vary much more in Montmorillonite particles than in Hectorite particles. Within a Montmorillonite clay particle, one can find that Si can vary ±8.0 from its average value. There is an equally large variation of Si content between particles. Isomorphic substitution by Mg can be random (M2, M4) or can be evenly distributed throughout the clay particle (M7, M10, M12, M13). There is no significant difference in Ca coverage between Montmorillonite particles with even Mg distribution and those with random Mg distribution.

53 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

M4 M5 M6 Box # Band gap (eV) O Si Mg Al Ca Band gap (eV) O Si Mg Al Ca Band gap (eV) O Si Mg Al Ca 1 3.80 10.15 10.19 0.00 1.00 0.00 2.85 13.73 6.38 0.00 1.00 0.00 6.60 17.65 7.53 0.00 1.00 0.00 2 3.55 10.15 10.51 0.00 1.00 0.00 2.55 N/A N/A N/A N/A N/A 8.90 17.65 7.76 0.00 1.00 0.00 3 3.60 11.61 10.62 0.36 1.00 0.00 2.45 11.59 6.48 0.00 1.00 0.00 8.55 N/A N/A N/A N/A N/A 4 3.80 18.09 19.04 0.00 1.00 0.00 6.60 N/A N/A N/A N/A N/A 5 3.65 6.69 7.09 0.14 1.00 0.00 6 4.50 9.02 8.95 0.28 1.00 0.00 7 4.15 7.34 7.52 0.00 1.00 0.00 8 3.90 10.01 8.88 0.00 1.00 0.00 9 4.10 11.19 11.02 0.27 1.00 0.00 10 4.10 9.69 10.13 0.00 1.00 0.00 11 4.15 7.48 7.57 0.19 1.00 0.00 12 4.10 8.90 8.44 0.13 1.00 0.08 13 4.10 11.74 13.00 0.00 1.00 0.00 14 3.85 7.38 7.45 0.13 1.00 0.00 15 3.90 8.10 8.16 0.23 1.00 0.00 16 3.80 10.91 10.12 0.21 1.00 0.00 17 3.80 8.49 7.32 0.00 1.00 0.00 18 3.60 8.58 8.57 0.17 1.00 0.00 19 3.60 8.64 8.64 0.18 1.00 0.00 Table 33. Chemical composition of Montmorillonite particles M4-M6 calculated from TEM-EDS data. Values are standardized to Al content giving moles of O, Si, Mg and Ca per mol Al.

54 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

M7 M8 M9 Box # Band gap (eV) O Si Mg Al Ca Band gap (eV) O Si Mg Al Ca Band gap (eV) O Si Mg Al Ca 1 3.10 7.23 7.39 0.25 1.00 0.04 3.40 17.50 7.38 0.00 1.00 0.00 6.50 11.61 12.96 0.00 1.00 0.00 2 3.45 8.09 7.31 0.14 1.00 0.08 2.90 N/A N/A N/A N/A N/A 5.10 13.62 15.33 0.00 1.00 0.15 3 3.90 6.87 7.10 0.23 1.00 0.04 3.00 N/A N/A N/A N/A N/A 4.65 15.22 15.81 0.00 1.00 0.00 4 3.25 7.35 7.87 0.14 1.00 0.08 2.80 N/A N/A N/A N/A N/A 4.85 15.01 15.52 0.17 1.00 0.00 5 3.30 7.98 8.47 0.20 1.00 0.03 4.45 14.32 16.19 0.00 1.00 0.08 6 3.85 6.86 6.77 0.25 1.00 0.04 6.20 8.92 10.69 0.18 1.00 0.00 7 3.55 7.53 8.31 0.12 1.00 0.07 5.60 13.10 14.29 0.13 1.00 0.00 8 3.45 8.79 10.13 0.15 1.00 0.09 9 3.40 10.23 12.26 0.19 1.00 0.00 10 3.45 6.23 6.70 0.15 1.00 0.08 11 3.60 5.33 5.68 0.25 1.00 0.05 12 3.95 6.80 6.46 0.15 1.00 0.04 13 5.10 8.28 9.44 0.00 1.00 0.00 14 3.20 7.03 6.40 0.13 1.00 0.00 15 3.50 7.90 7.76 0.22 1.00 0.06 16 3.95 8.06 8.17 0.19 1.00 0.07 17 3.90 6.96 7.65 0.19 1.00 0.04 18 4.20 8.46 9.62 0.19 1.00 0.06 19 4.10 7.65 8.33 0.16 1.00 0.06 20 3.90 6.41 6.85 0.20 1.00 0.05 21 3.60 5.42 5.38 0.23 1.00 0.06 22 3.20 6.69 7.46 0.00 1.00 0.00 23 3.50 16.05 19.60 0.00 1.00 0.00 24 4.25 5.99 5.69 0.21 1.00 0.00 25 4.70 6.83 6.87 0.20 1.00 0.05 26 5.40 6.81 7.42 0.21 1.00 0.06 27 5.70 6.48 6.82 0.20 1.00 0.06 28 5.40 7.31 7.75 0.15 1.00 0.07 29 5.30 8.01 8.56 0.20 1.00 0.07 30 4.50 8.89 9.66 0.17 1.00 0.03 31 3.60 8.94 9.51 0.22 1.00 0.00 32 9.35 7.31 7.73 0.20 1.00 0.06 33 5.35 7.09 7.61 0.20 1.00 0.07 Table 34. Chemical composition of Montmorillonite particles M7-M9 calculated from TEM-EDS data. Values are standardized to Al content giving moles of O, Si, Mg and Ca per mol Al.

55 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

M10 M11 M12 Box # Band gap (eV) O Si Mg Al Ca Band gap (eV) O Si Mg Al Ca Band gap (eV) O Si Mg Al Ca 1 5.05 15.06 15.18 0.00 1.00 0.00 3.80 9.75 10.95 0.23 1.00 0.12 4.10 8.31 9.58 0.15 1.00 0.05 2 4.55 18.27 20.21 0.00 1.00 0.11 3.55 6.09 6.68 0.14 1.00 0.06 3 5.30 13.04 15.87 0.19 1.00 0.06 4.80 7.98 10.74 0.08 1.00 0.07 4 4.50 8.39 9.03 0.15 1.00 0.05 4.05 7.20 7.56 0.15 1.00 0.04 5 4.80 10.78 9.98 0.00 1.00 0.00 3.30 9.05 10.79 0.17 1.00 0.00 6 3.45 17.20 17.87 0.00 1.00 0.00 3.90 11.36 11.99 0.17 1.00 0.00 7 3.90 16.27 18.52 0.00 1.00 0.00 4.85 6.59 7.06 0.15 1.00 0.05 8 4.40 13.64 14.34 0.00 1.00 0.11 4.25 8.28 10.71 0.11 1.00 0.06 9 4.40 11.07 13.09 0.18 1.00 0.06 3.60 11.58 12.29 0.20 1.00 0.00 10 4.05 11.07 13.58 0.23 1.00 0.00 3.90 8.40 9.91 0.14 1.00 0.06 11 5.45 11.14 10.85 0.00 1.00 0.00 3.50 7.92 8.82 0.17 1.00 0.04 12 5.60 8.48 9.19 0.14 1.00 0.00 M13 13 5.50 16.04 18.64 0.12 1.00 0.10 Box # Band gap (eV) O Si Mg Al Ca 14 4.25 14.28 15.82 0.12 1.00 0.08 1 4.05 11.66 14.17 0.24 1.00 0.06 15 4.60 8.39 9.03 0.15 1.00 0.05 2 3.90 9.14 11.56 0.18 1.00 0.06 16 4.80 15.10 17.12 0.13 1.00 0.10 3 3.70 5.75 6.72 0.08 1.00 0.06 17 5.25 13.03 14.66 0.14 1.00 0.08 4 4.10 12.55 15.48 0.27 1.00 0.09 18 5.05 12.96 14.78 0.14 1.00 0.07 5 3.85 8.60 10.60 0.15 1.00 0.00 6 3.45 8.46 10.11 0.13 1.00 0.00 7 3.80 8.43 10.62 0.22 1.00 0.00 8 3.95 10.19 12.17 0.10 1.00 0.00 9 3.85 8.25 10.76 0.13 1.00 0.08 10 3.85 9.26 10.00 0.19 1.00 0.00 Table 35. Chemical composition of Montmorillonite particles M10-M13 calculated from TEM-EDS data. Values are standardized to Al content giving moles of O, Si, Mg and Ca per mol Al.

56 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

Discussion

Prior to discussing results presented above, we briefly explain our divergence from the original Kearney project proposed two years ago. The original Kearney proposal was to study and calculate bulk scale thermodynamic properties with atomic scale properties (band gap), which can be calculated using Pearson’s Hard-Soft Acid-Base Principle. This proved to be more challenging than expected mainly because the bulk scale thermodynamics were not linear as presented by other researchers. Non-linear van’t Hoff curves basically indicated a temperature dependence of the system, which raises the question how one would measure a temperature dependent band gap, and if such a thing can be measured. As a result of these hindrances and the later discovery of the difficulties with band gap measurements using TEM-EELS, it was decided to scale down the study to a more manageable size. It was decided the most important contribution from our study to the Kearney mission is the investigation of clay mineral (soil component) at a scale which is scarcely looked into, not until more recently [Smith et. al. 2004, Smith et. al. 2004a]. Currently to the authors knowledge there have been no other published studies attempting to look at band gap energies of natural clay minerals at sub-micron spatial scales using TEM-EELS, neither have there been spatially resolved chemical composition information presented for natural clay minerals. In this study we evaluate three methods of calculating and measuring band gap information (Theoretical modeling, DR UV- Vis spectroscopy and TEM-EELS). In particular we focus on the more novel method (TEM-EELS) and the type of information which we can gather from it. Comparing the three methods, one finds that for the Hectorite clay mineral all three methods coincide well and give similar band gap energies, while for Montmorillonite there are some discrepancies between measured and modeled data. Theoretical modeling results for Hectorite indicated a band gap of approximately 4 eV (Figure 1). This modeled band gap was similar to experimentally measured band gap 4.75 eV (DR UV-Vis data, Figure 3) and those measured by TEM-EELS which can range from 2.0-7.2 eV, with the majority of band gaps at approximately 4 eV. Unlike Hectorite, modeling results for Montmorillonite did not correlate with experimentally measured band gap values. Modeled band gap for Montmorillonite is 0 eV (Figure 2), while the measured band gaps were 4.75 (DR UV-Vis spec., Figure 3) and ranged from 2.5-9,4 eV with the majority being approximately 4.5 eV (TEM-EELS). The reason for this discrepancy in modeled and measured Montmorillonite band gaps is still uncertain. The modeled band gaps represent the energy levels for only one particular crystal structure and chemical composition. For this reason, modeling will result in one distinct band gap energy while in measured results there is a range of band gaps since crystal structure and chemical composition may vary between samples. Though modeling is an easy and sometimes accurate way to determine band gap energies, it should not be taken as absolute fact unless there is measured data to prove it whenever possible. Theoretical modeling is a resourceful tool to determine possible band gap energies for materials which lack of literature data. Conventionally, band gap energies are most often measured with DR UV-Vis spectroscopy. DR UV-Vis spectroscopy offers great energy resolution and simple data processing; however it lacks spatial resolution and can be used only to make bulk band gap measurements of clays. From Figure 3 one observes that both Hectorite and Montmorillonite have essentially the same average band

57 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

of 4.75 eV, average being where the majority of the band gaps reside, which is evident from the high Abs counts. It is also apparent from Figure 3 that Hectorite has a larger range of band gaps (1.5-6.5 eV) compared to that of Montmorillonite (2-6.5 eV). Hectorite having a larger range of band gaps could possibly suggest that it has a larger variation of isomorphic substitution than Montmorillonite. It is also possible that the same chemical and structural variation in both clays lead to a larger range of band gaps in Hectorite. A band gap range occurs for two possible reasons; the first reason is that it is inherent of the electronic state of the material and the second being that it is the summation of all band gaps from the measured area. TEM-EELS measurements show the opposite where Montmorillonite particles had a band gap range of 2.5-9.4 eV while Hectorite ranged from 2-7.2 eV. It is possible that this is a sampling artifact where it was simply coincidental that the band gaps for the Hectorite particles measured did not reside in the larger end of band gap energies. A larger sampling set is needed to determine which clay has a wider range of band gap energies. It must also be considered that the upper end of eV measureable using DR UV-Vis spectroscopy is 6.5 eV, so it is possible the Montmorillonite does have a wider range of band gap energies than Hectorite as indicated by TEM-EELS but was not measureable by DR UV-Vis spectroscopy. Wider ranges of band gap energy indicate more energetically heterogeneous reaction sites on clays [Pearson 1997]. In spite of this inconsistency, both DR UV-Vis and TEM-EEL spectroscopies point toward Hectorite having lower band gap energies than Montmorillonite which means that there are sites on Hectorite that are more chemically active than Montmorillonite. The third method explored, TEM-EELS, is the most experimental and novel of the three methods. In addition to being able to obtain band gap information, this method can provide chemical composition information from the same spatially resolved area using EDS. It is possible to obtain elemental and bonding information from EELS, however these methods are not very well established. TEM-EELS offers many advantages, but also has the disadvantage of having a significantly poorer energy resolution than DR UV-Vis spectroscopy. EELS can have energy resolution of 0.1 eV at best but most instruments give a resolution of 1 eV, while DR UV-Vis spectroscopy commonly has energy resolution of 0.01 eV. Promising as TEM-EELS may be, there are still many challenges because of it novel status and often unestablished methods. This section aims at exploring the type of chemical and electronic (band gap) information that can be obtained from TEM-EELS/EDS on natural clay minerals. To examine objectives 1 and 2 presented above, TEM-EELS and TEM-EDS data were collected from 11 Hectorite clay particles and 12 Montmorillonite clay particles along with TEM images of these particles. Objective 1 aimed at correlating the degree of isomorphic substitution to band gap energies, the reasoning being that smaller band gaps will occur in areas where isomorphic substitution occurs because it destabilizes that particular area by creating electronic charge. Ideally one would find direct correlations between band gap energies and density of calcium ions sorbed onto surface and into interlayers of any particular clay particle, with the greater density of Ca ions indicating a higher degree of isomorphic substitution and smaller band gap energy. To test this, spatially resolved band gap energies for each particle were plotted against Ca atom % of the same area, and the linear correlation was investigated. No apparent correlation was found between Ca ion density and band gap energies for Hectorite or Montmorillonite. However, Ca atom % can vary depending on the other elemental % (C, O, Si, Mg) and since C and O can vary greatly depending on contamination level on the clay particle (though there was no observable contamination

58 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

in our samples), a more stable measure of isomorphic substitution would be Si/Mg ratios for Hectorite and Al/Mg ratios for Montmorillonite. High Si/Mg ratios would indicate higher degree of isomorphic substitution in Hectorite since Mg is being substituted by Li. Small Al/Mg ratios would indicate higher degree of isomorphic substitution in Montmorillonite since Al is being replaced by Mg. For Hectorite there was better linear correlation of Si/Mg ratio with band gap energies, in magnitude of R2 value, for only three of the eleven particles inspected (Table 13). The Si/Mg ratio was not anymore strongly correlated with band gap energies than other parameters considered (O atom %, Si atom %, Mg atom %, Ca atom %, Si/Ca ratio, Mg/Ca ratio, Si/O ratio, Mg/O ratio, O/Ca ratio). In fact, there was not a single parameter, which can be said to have a strong relationship with band gap and thus contribute significantly to determining band gap energies (Table 13). Very similar results were found for Montmorillonite, Ca atom % did not correlate to band gap energies well, and neither did Al/Mg ratios (Table 27). Depending on the Montmorillonite particle inspected, nearly all parameters considered (O atom %, Si atom %, Al atom %, Ca atom %, Si/Mg ratio, Si/O ratio, Si/Al ratio, Al/Mg ratio, O/Al ratio) at one point or another was best fitted with band gaps. However, most of these correlations were quite poor, R2 less 0.5 (Table 27). There was no distinct correlation of band gap energies to chemical composition for either clay mineral. Several reasons may have contributed to the lack of any significant relationships, the most evident being the poor energy resolution of the TEM instrument (0.8-1.0 eV). Low EDS signals can make elemental quantification difficult, which can also contribute to poor correlations, but this is not a suspect culprit since EDS signals for all particles were quantifiable with the selected spatial scale. It is also possible that there simply is no clear relation between band gap energies and isomorphic substitution because there are other chemical, structural or electronic factors contributing to band gap determination in any spatially resolved area. The last possibility is that the spatial scale which was investigated was too large for any differences to be noticeably distinguished, spatial scales observed were between 0.1-0.5 µm. The spatial scale in this case was limited by EDS signal intensity capable of giving quantifiable data. There were however some interesting observations concerning isomorphic substitution and calcium sorption. For instance Hectorite particle H3 showed a surprisingly large degree of calcium coverage compared to all other Hectorite particles observed. It was stated in the results that particle H3 has a very large band gap range and could indicate large spatial variation in isomorphic substitution from one area to the next. To elucidate this matter, Table 13a summarizes the ratio ranges and band gap ranges in all Hectorite particles observed. Inspecting Table 13a one does not find that a larger range of ratios necessarily correlate with larger band gap ranges, indicating that larger band gap ranges may not be solely determined by distribution of isomorphic substitution. It is also possible that the areas selected for elemental quantification were large enough so that the chemical compositions were averaged from one area to the next and if concentrated pockets of isomorphic substitution did occur, it was not observed due to the spatial scale. However, we did observe that larger band gap ranges correlated very well (R2 is >0.9) with amount if calcium sorption on Hectorite particles (Table 13a), this correlation did not apply for Montmorillonite particles (Table 28). In Hectorite particle H6, one finds an area (Box 1, Table 6) of or very high calcium coverage, but this area does not indicate a high level of isomorphic substitution. It is possible that the actually spatial area that calcium covers is in a localized section in box 1 and the

59 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

remainder of that box has normal levels of isomorphic substitution causing the overall Si/Mg ratio to appear average in comparison to other inspected areas. This example shows that it is indeed possible to have areas within clay particles containing localized high levels of calcium coverage and have also been observed by other authors (Nagy et. al 2003, Scheidegger et. al. 1996 and Jozja et. al. 2006). It is suspected that these localizations occur because of high degrees of isomorphic substitution and the need to balance anionic charges [Sparks 1995, Sparks 2003]. Logically this makes sense, however we were not able to confirm this with the data currently collected. Generally, if the Si:Mg ratio was sufficiently higher than 1.5:1 there was detectable Ca coverage on the Hectorite clay particle (Tables 29-31). In Montmorillonite, particles with very little isomorphic substitution by Mg tend to have little to no detectable calcium coverage (Tables 32-35). Montmorillonite particle M7 (Table 20) showed the most isomorphic substitution based on Mg atom %, the calcium sorption on M7 was not particularly higher than other particles observed. Montmorillonite particle M9 (Table 21) was interesting in the sense that areas where there was detectable Mg isomorphic substitution there did not appear to be measurable calcium coverage on a 0.2 µm spatial scale. It was also observed that particle M4 with a higher degree of isomorphic substitution did not always have calcium sorption (Table 26). It can however be said that generally Montmorillonite particles with detectable isomorphic substitution (Table 26) based on Mg atom % also had some level of calcium sorption. Objective 2 aimed to investigate the sub-micron level of chemical composition variation that can be measured with TEM-EDS (Tables 29-35). The chemical composition for Hectorite particles changed only very slightly within the same clay particle. There were larger variations in oxygen and calcium distribution compared to silicon. The spatial resolution ranged from (0.1 µm)2 to (0. 5 µm)2. There was greater variability in chemical composition when comparing one Hectorite particle to the next, however in the same clay particle the chemical composition remained fairly consistent on the 0.1-0.5 µm scale. Montmorillonite generally had larger chemical variations in all elements measured (O, Si, Mg, Ca) with spatial changes. Si values nearly doubled in areas of Montmorillonite whereas in Hectorite Si values did not fluctuate more than 50% from the average. The spatial resolution of Montmorillonite ranged from (0.067 µm)2 to (0.4 µm)2. Investigating on a smaller spatial scale may allow us to see even more distinct variations than observed here. EDS signal intensities will always dictate the quantifiable spatial resolution and as a result the area which one can gather a meaningful band gap. Nanometer resolution is possible, but not practical since it takes a long time (>4 hrs) to obtain a large enough EDS signal for quantification in nm spatial scales for each particle. We found that chemical composition can vary within one clay particle as much as between different clay particles. Inter-particle and intra-particle ratios (Si/Mg, Si/Ca, Mg/Ca, Si/O, Mg/O and O/Ca) showed very little differences (Tables 12 and 13a). This indicates that chemical composition within a Hectorite particle can vary as much as between two Hectorite clay particles. Very similarly, Montmorillonite inter-particle ranges had the propensity to vary as much as intra-particle ranges (Tables 26 and 28). TEM-EELS/EDS prove to be a useful method for obtaining band gap and chemical composition information of natural clays, but not without difficulties. The energy resolution of EELS is often very poor in comparison to UV-Vis spectroscopy methods, this limits the electronic information one can gather, this disadvantage could outweigh the nm spatial resolution achievable and render the data collected extremely difficult to analyze. In addition, EELS data is difficult to process since it is possible to introduce artefacts during

60 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath data analysis (ZLP removal, multiple scattering deconvolution) causing a false band gap measurement if one is not careful. TEM-EDS is very valuable for chemical analysis, the spatial scale at which one can obtain such information will depend on the material and length of EDS signal collection. Despite these challenges, we were able to observe that chemical composition information could not be directly correlated with band gap information and there was no clear relationship between degree of isomorphic substitution and band gap energies at the spatial scales investigated. There was not always direct spatial correlation of isomorphic substitution with calcium sorption on all particles but we observed that generally clay particles with a measureable degree of isomorphic substitution there exist some level of calcium sorption on the particle. On a 0.1-0.5 µm spatial scale, chemical composition tends to be fairly evenly distributed and the variation of chemical composition is minimal. Compared to more conventional methods such as DR UV-Vis, TEM-EELS proved to be appropriate for measuring band energies for natural clay minerals and data from the two methods are comparable. References

Jozja, N., Baillif, P., Touray, J.C., et. al. (2006). Incidence of lead uptake on the microstructure of a (Mg,Ca)-bearing bentonite (Prrenjas, Albania). European Journal of Mineralogy, 18, 361-368. Nagy, N.M., Konya, J., Beszeda, M., et. al. (2003). Physical and chemical formations of lead contaminants on clay and sediment. Journal of Colloid and Interface Sciences, 263, 13-22. Pearson, R.G. (1967). Application of the principle of Hard and Soft acids and bases to organic chemistry. Journal of the American Chemical Society. 89(8), 1827-1836. Pearson, R.G. Chemical Hardness. Weinheim: Wiley-VCH, 1997. Porter, T.L., Eastman, M.P., Whitehorse, R., et. al. (2000). The interaction of biological molecules with clay minerals: A scanning force microscopy study. Scanning, 22, 1-5. Scheidegger, A.M., Fendorf, M., Sparks, D.L. (1996). Mechanism of nickel sorption on pyrophyllite: Macroscopic and microscopic approaches. Soil Science Society of America Journal, 60, 1763-1772. Smith, A.D., Schofield, P.F., Scholl, A., et. al. (2004). XPEEM valance state imaging of mineral-microgrowths with a spatial resolution of 100 nm. Journal de Physique IV France, 104, 373-376. Smith, A.D., Schofield, P.F., Cressey, G., et. al. (2004b). The development of x-ray photoemission electron microscopy (XPEEM) for valance imaging of mineral intergrowths. Mineralogical Magazine, 68(6), 859–869. Sparks, D.L. Environmental Soil Chemistry. San Diego: Academic Press, 1995. Sparks, D.L. Environmental Soil Chemistry: Second Ed. San Diego: Elsevier, 2003. Dixon, J.B., Weed, S.B. Minerals in Soil Environments (Second Ed.). Madison: Soil Science Society of America, 1989.

61 Chemical Hardness Quantification of Clay Minerals Using Hard-Soft Acid-Base Principle—Horwath

This research was funded by the Kearney Foundation of Soil Science: Understanding and Managing Soil-Ecosystem Functions Across Spatial and Temporal Scales, 2006-2011 Mission (http://kearney.ucdavis.edu). The Kearney Foundation is an endowed research program created to encourage and support research in the fields of soil, plant nutrition, and water science within the Division of Agriculture and Natural Resources of the University of California.