From swelling and surface area measurements, it was found that the swelling of a montmorillonite depends linearly on the fraction of its layers that fully expand in water and that this fraction, in turn, depends linearly on the b dimension of the unit cell. Therefore, swelling is a linear function of the b dimension. However, the specific surface area of a montmorillonite is a linear function of its b dimension only if no partially expanded layers exist. It was also found that the distance between fully expanded layers at a given applied pressure is the same for all montmorillonites.

Exchange reactions of Na-montmorillonite with zirconyl chloride solutions give products with basal spacings near 18 Å which are stable to 500°C and have surface areas of the order of 300–400 m2/g. The Na ions are exchanged with tetrameric hydroxy cations [Zr4(OH)14•nH2O]2+. The high surface area is attributed to the porosity formed by stable zirconium oxide “pillars” formed by dehydroxylation of the complex cation. The nitrogen adsorption isotherms are of Langmuir type and are consistent with adsorption in interlayer micropores. Reduced-charge montmorillonites, formed by application of the Hofmann-Klemen procedure, give either similar or slightly smaller surface areas.

The compound Mg2+-Al3+-(Fe(CN)6)4−, with a structure similar to hydrotalcite Mg6Al2(OH)16CO3 ·4H2O, is prepared by a coprecipitation method. Chemical, thermal, and X-ray analysis of the compound lead to the formula: $(M{g}_{0.741}A{l}_{0.259}(OH{)}_2)((F{e}^{II}(CN{)}_6{)}_{0.067}(C{O}_3{)}_{0.002}(H_{2}O{)}_{1.05})$

The compound is dehydrated at 100° to 250°C, and the adsorption of N2, O2, CO2, and H2 on it is measured at −196°C to room temperature by the volumetric method. The water is removed reversibly from 100° to 200°C, and the interstices after dehyration act as sites of adsorption. When dehydration is carried out at 150°C, the adsorptive activity reaches a maximum. Adsorption isotherms of N2 and O2 at −196°C and of CO2 at room temperature are of the Langmuir type, and the saturated amounts of N2, O2, and CO2 adsorbed are 96.3, 65.2, and 91.8 ml (STP)/g, respectively.

Adsorption isotherms of N2 and O2 at room temperature are of the Henry type. The amount of O2 adsorbed is about 67% of that of N2. The isosteric heats of adsorption at room temperature of N2, O2, and CO2 are 5.1, 4.8, and 11.0 kcal/mol, respectively. A dehydrated product of a Mg2+-Al3+-CO32− compound does not permit adsorption of CO2 at room temperature, but permits the adsorption of H2O. Hence, it has a molecular sieve effect. No adsorption of H2 is observed in any of the compounds tested.

The wetting contact angle was measured for water drops settled on the surface of pressed discs of kaolinite, alumina, bentonite, marble, montmorillonite, and quartzite immersed in hexane, octane, dodecane, cis-decalin, and air. Minimum and maximum values of the contact angle were obtained for the given systems of solid-water drop-hydrocarbon, depending on the manner of disc preparation. Using both minimum (θmin) and maximum (θmax) values of the contact angle, values of the dispersion component (γsd) of surface free energy of these solids were calculated from the equation which was derived on the basis of an equilibrium state of the system solid-water drop-hycrocarbon for two different hydrocarbons. The values of γsd for kaolinite, alumina, bentonite, marble, montmorillonite, and quartzite obtained from θmin are 83.5, 98.1, 98.9, 80.2, 95.9, and 89.7 mJ/m2, and from θmax are 73.1, 85.0, 84.4, 75.8, 85.5, and 75.5 mJ/m2. These values for marble and quartzite are similar to those in the literature (marble = 67.7 mJ/m2; quartzite = 71.3 and 76.0 mJ/m2). The values of the dispersion components of surface free energy for marble and quartzite covered with a water film (γsfd) were found to be: 41.8, 36.9; 49.2, 42.5; 49.6, 42.2; 40.2, 38.1; 48.1, 42.8; and 44.9, 38.0 mJ/m2, respectively. Values of γsfd for kaolinite, bentonite, and montmorillonite agreed well with those obtained from hydrocarbon adsorption isotherms determined by differential thermal analysis (35.5, 36.5, and 37.4 mJ/m2).

Using values of γsfd and contact angles measured in the system solid-water drop-air, the nondispersion component of the surface free energy of solids with adsorbed water film (γsfn) was calculated from the modified Young equation. The values of γsfn for kaolinite and quartzite are as follows: 55.8, 69.0; 85.6, 94.0; 52.1, 75.0; 64.7, 68.9; 54.9,71.3; and 59.2,74.4 mJ/m2. The values of the nondispersion components determined for kaolinite, bentonite, and montmorillonite agreed well with those obtained by differential thermal analysis (67.6, 78.3, and 65.5 mJ/m2, respectively). Further, based on the assumption that the adsorbed water film decreased the surface free energy of these solids by the value of the work of spreading wetting, the nondispersion component (γsn) of the surface free energy of the solids was calculated to be: 86.9,129.6; 169.5, 187.7; 67.1, 144.8; 117.5, 129.3; 83.0, 135.7 and 100.2, 143.4 mJ/m2. These calculated values of the nondispersion component of marble and quartzite surface free energy agree with those obtained from adsorption isotherms determined by chromatographic and differential thermal analysis (marble = 103.8, 106.4; quartzite = 112, 115, 153.6 mJ/m2).

The adsorption of n-octane and water vapor on natural kaolinite was measured. From adsorption isotherms film pressures were determined which were then used to calculate the dispersion and nondispersion components of the kaolinite surface free energy. In addition, thermodesorption of water from the kaolinite surface was determined. These results suggest that physically adsorbed water remained on the kaolinite surface, even at temperatures as great as 125°C. Therefore, experimentally determined dispersion and nondispersion components appear to relate to the surface precovered with a film of water. These values are: γSf(w)d = 34.4 mJ/m2 for dispersion interactions and γSf(w)n = 60.2 mJ/m2 for nondispersion interactions. Assuming a kaolinite surface precovered with a film of water, which decreased the free energy by the work of spreading, the following components of the energy for the bare surface were calculated: γSd = 67.6 mJ/m2 and γSn = 103.4 mJ/m2, for dispersion and nondispersion components, respectively.

Specimen samples of Crook County montmorillonite and Silver Hill illite, purified and prepared in the Na-form, were imaged under 80% relative humidity using an atomic force microscope. The direct images showed clearly the hexagonal array of hexagonal rings of oxygen ions expected for the basal planes of 2:1 phyllosilicates. Fourier transformation of the digital information obtained by the microscope scanning tip led to an estimate of 5.1 ± 0.3 Å for the nearest-neighbor separation, in agreement with the ideal nearest-neighbor spacing of 5.4 Å for hexagonal rings as derived from X-ray powder diffraction data. The atomic force microscope should prove to be a useful tool for the molecular-scale resolution of clay mineral surfaces that contain adsorbed macromolecules.

57Fe Mössbauer spectra have been used to interpret the effects of different cleaning processes on the iron mineralogy of a Weipa, Australia, kaolin. A magnetically separated fraction contained 28% of its iron as hematite likely of secondary origin. An initial centrifugal size separation was shown to give an improved final product, and oxalic acid was found to be more efficient at removing Fe from the kaolinite surface than dithionite bleach. The Mössbauer spectra clearly show that beneficiation steps which give a substantial increase in kaolin brightness result in only minor changes in the clay iron mineralogy. Similar results were also obtained for two commercially available kaolins.

Inverse gas chromatography (IGC) at zero surface coverage was used for determining the surface characteristics of a slate sample. Previously this sample had been characterized by means of X-ray diffraction (XRD), chemical analysis, infrared (IR) spectroscopy and nitrogen adsorption. Quartz, muscovite and chlorite were the minerals foming the slate. A well-defined mesoporous structure with pores of 15 Å of interlayer distance was observed. Chemical analysis and IR spectroscopy corroborated the X-ray results. The surface characteristics of the slate were defined in relation to nonspecific and specific interactions with organic molecules. In accordance with the nonspecific interactions, the London component (γSD) of the surface free energy gave an estimation of the surface energy of the slate sample. The obtained values for γSD were 140.0, 124.8, 108.2 and 96.8 mN m-1 at 100, 110, 120 and 130 °C, respectively. These values were characteristic of an inorganic sample of high surface energy. The values of the thermodynamic variables—differential heat of adsorption, free energy and entropy of adsorption—were in accordance with these results. At the same time, specific interactions were characterized by the ηπ parameter and the acid-base (KA, KB) indices. The positive value of ηπ (0.09 kJ mol-1) indicated the presence of Lewis acidic sites on the slate surface. The value of KA (acid index) of 1.17 was higher than the value of KB (base index) of 0.37; this result confirmed the acidic nature of the studied slate's surface.

The crystal chemical features of the bulk and the uppermost (001) surface layers of freshly cleaved surfaces of two trioctahedral Fe-rich mica-1M (space group C2/m) polytypes, i.e. a tetraferriphlogopite from an alkaline-carbonatitic complex near Tapira, Belo Horizonte, Minas Gerais, Brazil, and an Fe2+-bearing phlogopite containing less tetrahedral Fe3+ from the Kovdor carbonatite-bearing, alkaline-ultrabasic complex, Kola Peninsula, Russia, are explored here. Mineral-surface effects were investigated by X-ray Photoelectron Spectroscopy (XPS) and compared to the bulk structure derived from single-crystal X-ray diffraction data. Based on microprobe analysis and the X-ray study, the chemical formulae are [XII](K0.99)[VI](Fe0.082+Fe0.153+Mg2.76Ti0.01)[IV](Fe0.823+Si3.18)O10.37F0.24(OH)1.39 and [XII](K0.94Na0.06)[VI](Fe0.172+Fe0.053+Mg2.75Mn0.01Ti0.05)[IV](Fe0.163+Al0.84Si3.00)O10.21F0.35(OH)1.44 for tetraferriphlogopite and Fe-bearing phlogopite, respectively. The tetrahedrally coordinated sites of the two minerals differ, where Fe-for-Si substitution is at 20.5% in tetra-ferriphlogopite and at 4% in Fe-bearing phlogopite.

The bulk study showed that Fe3+ substitution increases the tetrahedral sheet thickness and the mean tetrahedral edge lengths in tetra-ferriphlogopite compared to Fe-bearing phlogopite. The tetrahedral rotation angle (α) changes remarkably from tetra-ferriphlogopite (α = 10.5°) to the Fe-bearing phlogopite (α = 8.5°), thus indicating a significantly greater initial lateral sheet misfit (leading to a greater tetrahedral ring distortion) between the tetrahedral and the octahedral sheets in the tetra-ferriphlogopite compared to Fe-bearing phlogopite. The Fe3+ substitution for Si and the differences in lateral dimensions of the tetrahedral and octahedral sheets affect the tetrahedral flattening angle (τ), with τ = 109.9° for tetraferriphlogopite and τ = 110.7° for Fe-bearing phlogopite.

The binding energy (BE) of photoelectron peaks in XPS is dependent on the chemical state of atoms and on their local environment at the near surface. The Mg in both phlogopites is bonded to F, with the BE of Mg1s increasing as coordinated oxygen atoms are substituted by fluorine. For Fe-rich phlogopite (BE = 1306.8 eV), the binding energy is greater than for tetra-ferriphlogopite (BE = 1305.9 eV), and this is consistent with the bulk composition having greater F-for-OH substitution in Fe-rich phlogopite (F0.35vs. tetra-ferriphlogopite, F0.24 atoms per formula unit).

We give a new proof of rationality of stable commutator length (scl) of certain elements in surface groups: those represented by curves that do not fill the surface. Such elements always admit extremal surfaces for scl. These results also hold more generally for non-filling $1$–chains.

Given a fixed graph H that embeds in a surface $\Sigma$ , what is the maximum number of copies of H in an n-vertex graph G that embeds in $\Sigma$ ? We show that the answer is $\Theta(n^{f(H)})$ , where f(H) is a graph invariant called the ‘flap-number’ of H, which is independent of $\Sigma$ . This simultaneously answers two open problems posed by Eppstein ((1993) J. Graph Theory17(3) 409–416.). The same proof also answers the question for minor-closed classes. That is, if H is a $K_{3,t}$ minor-free graph, then the maximum number of copies of H in an n-vertex $K_{3,t}$ minor-free graph G is $\Theta(n^{f'(H)})$ , where f′(H) is a graph invariant closely related to the flap-number of H. Finally, when H is a complete graph we give more precise answers.

Glacier mass-balance observations at seasonal resolution have been performed since 1914 at two sites on Claridenfirn, Switzerland. The measurements are the longest uninterrupted records of glacier mass balance worldwide. Here, we provide a complete re-analysis of the 106-year series (1914–2020), focusing on both point and glacier-wide mass balance. The approaches to evaluate and homogenize the direct observations are described in detail. Based on conservative assumptions, average uncertainties of $\pm$0.25 m w.e. are estimated for glacier-wide mass balances at the annual scale. It is demonstrated that long-term variations in mass balance are clearly driven by melting, whereas decadal changes in accumulation are uncorrelated with mass balance and can only be relevant in short periods. Mass change of Claridenfirn is impacted by dry calving at a frontal ice cliff. Considerations of ice volume flux at a cross-profile reveal long-term variations in frontal ice loss accounting for $\sim$9% of total annual ablation on average. The effect of changes in frontal ablation mostly explains $\lt$10% of the mass-balance difference relative to the period 1960–1990, but accounts for $\sim$20% in 2010–2020. Glacier mass changes are discussed in the context of observations throughout the European Alps indicating that Claridenfirn is regionally representative.

We show that every coarse moduli space, parametrizing complex special linear rank-2 local systems with fixed boundary traces on a surface with nonempty boundary, is log Calabi–Yau in that it has a normal projective compactification with trivial log canonical divisor. We connect this to a novel symmetry of generating series for counts of essential multicurves on the surface.