R. Cava et al. Progress in Solid State Chemistry 30(2002)1-101 manipulated shortages of such materials(water, oil, chromium, to name some)are important political drivers. The transport, refining, use, and eventual of the ores and their technological products pose equally important social environmental questions. For example, the nuclear fuel cycle must consider the cradle-to-grave(ore body to nuclear reactor to repository) handling of uranium. Solid state chemical issues( the chemical reactions involved)must be considered in the context of geolog cal processes (transport of contaminants by groundwater, long term climate volcanism Many minerals are crystalline silicates and aluminosilicates, and amorphous and glassy silicates (e.g. obsidian glass) are also found in nature. Thus there is strong overlap of the science of Earth materials with fields such as glass, zeolites, and ceramics. Certain binary oxides, notably those of Si, Al, Fe, Mn, and Ti are important in both technology and nature. There are commonalities between sulfide minerals and semiconductors. Equally importantly, many processes-crystallization, melting, dissolution, diffusion, surface reaction, catalysis-are common to Earth and materials science Solid state chemistry and mineralogy share many experimental tools. X-ray dif- fraction using both laboratory and synchrotron sources is used by both communities, sometimes at common beamlines The added information obtained from neutron scat- tering about the positions of light atoms(O and H)and about magnetic order is important to both minerals and materials. Small angle scattering studies reveal mid- range order and heterogeneity in complex ceramic and geologic materials Vibrational, optical, Mossbauer, and nuclear magnetic resonance spectroscopy are used by both communities. Advances in calorimetry and thermal analysis benefit both. The Earth science and solid state chemistry community share interests in com- putational and modeling tools for the prediction of crystallographic, electronic, and vibrational properties [1 Often Earth scientists are the beneficiaries of physical methods developed by the physical sciences. However, the Earth sciences lead technique development and applications in certain areas. The pressure distribution in the Earth is well known. with pressure rising to 3 megabars at the center. The temperature distribution is less well known, and probably locally heterogeneous, but temperatures in the 3000-5000 K range are likely in the core. Thus research at high P and T is critical to the Earth sciences, and the development of shock wave [2, 3], diamond anvil cell [4, 5, 6] and lultianvil [5, 7) apparatus and techniques has been actively pursued by the mineral physics community. An example of overlap with solid state chemistry is the study of phase transitions in hydrogen [8, 9), important to both planetary science(the interior of Jupiter) and to fundamental physics and chemistry. A second example the geological interest in magnesium silicate perovskite in the mantle. This phase with silicon in octahedral coordination, may be the most abundant single phase in the planet [5]. Its crystal chemistry, elasticity, defect structure, and transport proper ties may help define the properties of the lower mantle. Study of these properties made difficult by its high pressure stability field(>26 GPa), can be aided by the study of analogous ceramic perovskites stable under ambient conditions [10]. Under- standing the behavior of these ceramic perovskites can be improved by considering
R.J. Cava et al. / Progress in Solid State Chemistry 30 (2002) 1–101 11 manipulated shortages of such materials (water, oil, chromium, to name some) are important political drivers. The transport, refining, use, and eventual disposal of these ores and their technological products pose equally important social environmental questions. For example, the nuclear fuel cycle must consider the cradle-to-grave (ore body to nuclear reactor to repository) handling of uranium. Solid state chemical issues (the chemical reactions involved) must be considered in the context of geological processes (transport of contaminants by groundwater, long term climate change, volcanism). Many minerals are crystalline silicates and aluminosilicates, and amorphous and glassy silicates (e.g. obsidian glass) are also found in nature. Thus there is strong overlap of the science of Earth materials with fields such as glass, zeolites, and ceramics. Certain binary oxides, notably those of Si, Al, Fe, Mn, and Ti are important in both technology and nature. There are commonalities between sulfide minerals and semiconductors. Equally importantly, many processes—crystallization, melting, dissolution, diffusion, surface reaction, catalysis—are common to Earth and materials science. Solid state chemistry and mineralogy share many experimental tools. X-ray diffraction using both laboratory and synchrotron sources is used by both communities, sometimes at common beamlines. The added information obtained from neutron scattering about the positions of light atoms (O and H) and about magnetic order is important to both minerals and materials. Small angle scattering studies reveal midrange order and heterogeneity in complex ceramic and geologic materials. Vibrational, optical, Mossbauer, and nuclear magnetic resonance spectroscopy are used by both communities. Advances in calorimetry and thermal analysis benefit both. The Earth science and solid state chemistry community share interests in computational and modeling tools for the prediction of crystallographic, electronic, and vibrational properties [1]. Often Earth scientists are the beneficiaries of physical methods developed by the physical sciences. However, the Earth sciences lead technique development and applications in certain areas. The pressure distribution in the Earth is well known, with pressure rising to 3 megabars at the center. The temperature distribution is less well known, and probably locally heterogeneous, but temperatures in the 3000–5000 K range are likely in the core. Thus research at high P and T is critical to the Earth sciences, and the development of shock wave [2,3], diamond anvil cell [4,5,6] and multianvil [5,7] apparatus and techniques has been actively pursued by the mineral physics community. An example of overlap with solid state chemistry is the study of phase transitions in hydrogen [8,9], important to both planetary science (the interior of Jupiter) and to fundamental physics and chemistry. A second example is the geological interest in magnesium silicate perovskite in the mantle. This phase, with silicon in octahedral coordination, may be the most abundant single phase in the planet [5]. Its crystal chemistry, elasticity, defect structure, and transport properties may help define the properties of the lower mantle. Study of these properties, made difficult by its high pressure stability field (26 GPa), can be aided by the study of analogous ceramic perovskites stable under ambient conditions [10]. Understanding the behavior of these ceramic perovskites can be improved by considering
R. Cava et al. /Progress in Solid State Chemistry 30(2002)1-101 the behavior of MgSiO, perovskite, a material very much at the extreme end of the stability field for this structure type. Another example is iron, the major constituent of the Earth's core at pressures up to 3 megabars [11] The chemical analysis of coexisting mineral grains provides a goldmine of infor- mation to the Earth sciences. The distributions of major and trace [12]elements and of isotopes [13] between different phases, as well as their overall abundances, provide nformation on the source regions and pressure temperature history of rocks [14]. To enable these measurements, Earth scientists have developed and utilized specialized instrumentation, including electron microprobe microanalysis(EPMA)[15], the ion microprobe(spatially selective SIMS), and the X-ray microprobe(spatially selective X-ray fluorescence using synchrotron radiation ). The processing of samples for trace element and isotopic analysis requires clean room facilities and procedures on a par with those in the semiconductor industry. Very sensitive high resolution mass spectrometric techniques are then used for isotopic analysis. These methodologies fully to solid state chemistry where they have been underutilize be applied fruit- The fugacities of water, oxygen, carbon dioxide, and other volatile species are mportant variables in Earth processes. Experimental petrologists have developed means to control and measure these variables during synthesis and phase equilibrium experiments at low to moderate pressures. These methodologies, relatively standard in the earth sciences, should find wider application in solid state chemistry 2.2. Nanogeoscience For minerals. as for other solids. most chemical reactions occur at interfaces solid-solid, solid-liquid, solid-gas, solid-supercritical fluid. Furthermore, many min- erals near the Earths surface(in soils, sediments, low grade metamorphic rocks )are very fine grained(micron sized or smaller). There is currently great interest in that part of the planet dubbed the"critical zone-the atmosphere, ocean, land surface and shallow interior directly affecting and affected by human activities. In the critical zone, nanosized materials abound dust particles, soil particles, clays, zeolites, oxides and oxyhydroxides. These particles interact strongly with both organic and inorganic constituents and transport both nutrients and pollutants. Minerals interact with life ranging from bacterial to human The dusty surfaces of Mars, asteroids, our Moon, and other moons also may harbor nanoparticles and host nanoscale phenomena. Interstellar dust grains may be nano- particles. Even in the Earth's deep interior, grain size reduction during phase trans formation may lead to transformational plasticity, a nanoscale process. The unity and breadth gained by thinking of these diverse topics as involving similar underlying fundamental issues represents far more than an opportunistic desire to hitch a ride on the nanotechnology bandwagon. Rather, the whole field of geology has much to gain from the growing realization that phenomena at the nanoscale often dominate geologic processes, that these phenomena can be studied using the concepts and techniques of physics and chemistry, and that this molecular level understanding can and must be incorporated into models of geologic processes at the outcrop, regional
12 R.J. Cava et al. / Progress in Solid State Chemistry 30 (2002) 1–101 the behavior of MgSiO3 perovskite, a material very much at the extreme end of the stability field for this structure type. Another example is iron, the major constituent of the Earth’s core at pressures up to 3 megabars [11]. The chemical analysis of coexisting mineral grains provides a goldmine of information to the Earth sciences. The distributions of major and trace [12] elements and of isotopes [13] between different phases, as well as their overall abundances, provide information on the source regions and pressure temperature history of rocks [14]. To enable these measurements, Earth scientists have developed and utilized specialized instrumentation, including electron microprobe microanalysis (EPMA) [15], the ion microprobe (spatially selective SIMS), and the X-ray microprobe (spatially selective X-ray fluorescence using synchrotron radiation). The processing of samples for trace element and isotopic analysis requires clean room facilities and procedures on a par with those in the semiconductor industry. Very sensitive high resolution mass spectrometric techniques are then used for isotopic analysis. These methodologies are well known to the Earth science community. They can probably be applied fruitfully to solid state chemistry where they have been underutilized. The fugacities of water, oxygen, carbon dioxide, and other volatile species are important variables in Earth processes. Experimental petrologists have developed means to control and measure these variables during synthesis and phase equilibrium experiments at low to moderate pressures. These methodologies, relatively standard in the Earth sciences, should find wider application in solid state chemistry. 2.2. Nanogeoscience For minerals, as for other solids, most chemical reactions occur at interfaces: solid–solid, solid–liquid, solid–gas, solid–supercritical fluid. Furthermore, many minerals near the Earth’s surface (in soils, sediments, low grade metamorphic rocks) are very fine grained (micron sized or smaller). There is currently great interest in that part of the planet dubbed the “critical zone”—the atmosphere, ocean, land surface, and shallow interior directly affecting and affected by human activities. In the critical zone, nanosized materials abound: dust particles, soil particles, clays, zeolites, oxides and oxyhydroxides. These particles interact strongly with both organic and inorganic constituents and transport both nutrients and pollutants. Minerals interact with life, ranging from bacterial to human. The dusty surfaces of Mars, asteroids, our Moon, and other moons also may harbor nanoparticles and host nanoscale phenomena. Interstellar dust grains may be nanoparticles. Even in the Earth’s deep interior, grain size reduction during phase transformation may lead to transformational plasticity, a nanoscale process. The unity and breadth gained by thinking of these diverse topics as involving similar underlying fundamental issues represents far more than an opportunistic desire to hitch a ride on the nanotechnology bandwagon. Rather, the whole field of geology has much to gain from the growing realization that phenomena at the nanoscale often dominate geologic processes, that these phenomena can be studied using the concepts and techniques of physics and chemistry, and that this molecular level understanding can and must be incorporated into models of geologic processes at the outcrop, regional
R. Cava et al. /Progress in Solid State Chemistry 30(2002)1-101 and planetary scale. A recent book summarizes many of the issues(Reviews in Mineralogy and Geochemistry: Nanoparticles and the Environment, 2000[17D) The examples below illustrate specific topics in which solid state chemistry play in important part in understanding Earth materials 2.3. TiO2 Phases: poly morphism and surface energetics Titania is an important accessory oxide mineral and is used widely in technology Rutile is the stable high temperature phase, but anatase and brookite are common in fine grained (nanoscale) natural and synthetic samples. Upon heating concomitant with coarsening, the following transformations are all seen, each under somewhat different conditions of particle size, starting material, temperature, and other para- meters: anatase to brookite to rutile. brookite to anatase to rutile. anatase to rutile and brookite to rutile. These variable transformation sequences imply very closely balanced energetics as a function of particle size. It has been proposed that the sur- face enthalpies of the three polymorphs are sufficiently different that crossover in thermodynamic stability can occur under conditions that preclude coarsening, with anatase and/or brookite stable at small particle size [16, 17]. Previously, using high temperature oxide melt calorimetry for nanocrystalline Al2O3, it was shown that ne defect spinel phase observed for nanosized particles, is more stable in enthalpy than nanophase a, corundum, the macrocrystalline thermodynamically stable phase [18]. The goal of the recent work summarized here [19] is to gather calorimetric evidence concerning the analogous proposed phase stability reversal for nanocrystal line TiO2. Such information is essential for understanding fundamental solid state chemistry, for predicting phase equilibria, for controlling nucleation, grain growth and phase transformation, and thus is fundamental to technological applications Energetics of anatase, brookite, and rutile have been measured by high temperature oxide melt drop solution calorimetry at 975 K with 3Na2004MoO3 solvent using a Calvet twin microcalorimeter Figure 1 shows the transformation enthalpies of nanocrystalline samples(kJ/mol) versus surface areas(m/mol ). A linear fit for each structure yields both the surface enthalpy(slope)and the bulk phase transformation enthalpy(intercept). Figure 1 represents the enthalpy of nanorutile. Bulk rutile is taken as the reference point of zero enthalpy for all samples. a linear fit using these three nanorutile data is therefore forced through the origin to derive the surface enthalpy of nanocrystalline rutile 2.2+0.2 J/m. Figure 1(b) shows the anatase data. A linear fit yields the surface enthalpy of anatase as 0. 4+0. 1 J/m and the enthalpy of phase transformation of bulk rutile to bulk anatase as 2.61+0. 41 kJ/mol. Figure 1(c)represents the enthalpy of the one nanocrystalline brookite(NB) and the bulk brookite-rutile phase transformation enthalpy (0.710.38 kJ/mol)of Mitsuhashi and Kleppa. Attempts to obtain pure brookite of other surface areas, either by direct synthesis or by coarsening the initial brookite sample were not successful. Therefore the linear fit is constrained by only two points. It gives the surface enthalpy of brookite as 1.0+0.2 J/m2. Figure I(d)summarizes the enthalpy of nanocrystalline titania. The intersections of the linear fits of brookite and rutile and of brookite and anatase place a limit on
R.J. Cava et al. / Progress in Solid State Chemistry 30 (2002) 1–101 13 and planetary scale. A recent book summarizes many of the issues (Reviews in Mineralogy and Geochemistry: Nanoparticles and the Environment, 2000 [17]). The examples below illustrate specific topics in which solid state chemistry plays an important part in understanding Earth materials. 2.3. TiO2 Phases: polymorphism and surface energetics Titania is an important accessory oxide mineral and is used widely in technology. Rutile is the stable high temperature phase, but anatase and brookite are common in fine grained (nanoscale) natural and synthetic samples. Upon heating concomitant with coarsening, the following transformations are all seen, each under somewhat different conditions of particle size, starting material, temperature, and other parameters: anatase to brookite to rutile, brookite to anatase to rutile, anatase to rutile, and brookite to rutile. These variable transformation sequences imply very closely balanced energetics as a function of particle size. It has been proposed that the surface enthalpies of the three polymorphs are sufficiently different that crossover in thermodynamic stability can occur under conditions that preclude coarsening, with anatase and/or brookite stable at small particle size [16,17]. Previously, using high temperature oxide melt calorimetry for nanocrystalline Al2O3, it was shown that g, the defect spinel phase observed for nanosized particles, is more stable in enthalpy than nanophase a, corundum, the macrocrystalline thermodynamically stable phase [18]. The goal of the recent work summarized here [19] is to gather calorimetric evidence concerning the analogous proposed phase stability reversal for nanocrystalline TiO2. Such information is essential for understanding fundamental solid state chemistry, for predicting phase equilibria, for controlling nucleation, grain growth, and phase transformation, and thus is fundamental to technological applications. Energetics of anatase, brookite, and rutile have been measured by high temperature oxide melt drop solution calorimetry at 975 K with 3Na2O4MoO3 solvent using a Calvet twin microcalorimeter. Figure 1 shows the transformation enthalpies of nanocrystalline samples (kJ/mol) versus surface areas (m2 /mol). A linear fit for each structure yields both the surface enthalpy (slope) and the bulk phase transformation enthalpy (intercept). Figure 1 represents the enthalpy of nanorutile. Bulk rutile is taken as the reference point of zero enthalpy for all samples. A linear fit using these three nanorutile data is therefore forced through the origin to derive the surface enthalpy of nanocrystalline rutile as 2.2±0.2 J/m2 . Figure 1(b) shows the anatase data. A linear fit yields the surface enthalpy of anatase as 0.4±0.1 J/m2 and the enthalpy of phase transformation of bulk rutile to bulk anatase as 2.61±0.41 kJ/mol. Figure 1(c) represents the enthalpy of the one nanocrystalline brookite (NB) and the bulk brookite–rutile phase transformation enthalpy (0.71±0.38 kJ/mol) of Mitsuhashi and Kleppa. Attempts to obtain pure brookite of other surface areas, either by direct synthesis or by coarsening the initial brookite sample were not successful. Therefore the linear fit is constrained by only two points. It gives the surface enthalpy of brookite as 1.0±0.2 J/m2 . Figure 1(d) summarizes the enthalpy of nanocrystalline titania. The intersections of the linear fits of brookite and rutile and of brookite and anatase place a limit on
R.. Cava et al. Progress in Solid State C/ suface area(mmol) 12000 surface area(m/mol) Fig. 1. Enthalpy of nanocrystalline samples with respect to bulk rutile(kJ/mol) versus surface area (m/mol)(a) for nanorutile(b)for nanoanatase, dashed curves represent 95% confidence limits for the mean,(c)for nanobrookite(6), and(d) phase stability crossover of titania. The lines are taken from Fig. I(a, b, and c)and the darker line segments indicate the energetically stable phases, from Ranade et al. 2002[ 19]( Reprinted by permission from National Academy of Sciences, USA) the stability field of various polymorphs. Rutile is energetically stable for surface area<592 m2/mol(7 m2/g), brookite is energetically stable from 592 to 3 174 m2/mol (7 to 40 m/g), and anatase is energetically stable for greater surface areas. The anatase and rutile energetics cross at 1452 m/mol(18 m/g). The dark solid lines epresent the phases of lowest enthalpy as a function of surface area. The energetic stability crossovers are confirmed Of course phase stability in a thermodynamic sense is governed by the Gibbs free energy(AG=AH- TAS)rather than the enthalpy. Low temperature heat capacity and entropy data are available for anatase and rutile (6), but not for brookite. The data for anatase probably refer to a fine grained(perhaps nanophase) sample, but no characterization is given. Thus the anatase entropy may contain contributions from both bulk and surface terms. the data suggest that rutile and anatase have the same entropy within experimental error(S(298 K, rutile)=50.6+0. 6 J/mol K and S(298 K, anatase)=49.9+0.3 J/mol K). Thus the TAS will not significantly perturb the quence of stability seen from the enthalpies This work can be generalized to other nanophase materials. Zirconia and zinc oxide are important from the materials science point of view. Iron and manganese oxides are important as both minerals and materials. An understanding of the patterns of surface energetics for different polymorphs will give predictive power. Measure ments of heat capacities on carefully controlled nanophase samples will shed light
14 R.J. Cava et al. / Progress in Solid State Chemistry 30 (2002) 1–101 Fig. 1. Enthalpy of nanocrystalline samples with respect to bulk rutile (kJ/mol) versus surface area (m2 /mol) (a) for nanorutile (b) for nanoanatase, dashed curves represent 95% confidence limits for the mean, (c) for nanobrookite (6), and (d) phase stability crossover of titania. The lines are taken from Fig. 1(a, b, and c) and the darker line segments indicate the energetically stable phases, from Ranade et al. 2002 [19] (Reprinted by permission from National Academy of Sciences, USA). the stability field of various polymorphs. Rutile is energetically stable for surface area 592 m2 /mol (7 m2 /g), brookite is energetically stable from 592 to 3174 m2 /mol (7 to 40 m2 /g), and anatase is energetically stable for greater surface areas. The anatase and rutile energetics cross at 1452 m2 /mol (18 m2 /g). The dark solid lines represent the phases of lowest enthalpy as a function of surface area. The energetic stability crossovers are confirmed. Of course phase stability in a thermodynamic sense is governed by the Gibbs free energy (G=HTS) rather than the enthalpy. Low temperature heat capacity and entropy data are available for anatase and rutile (6), but not for brookite. The data for anatase probably refer to a fine grained (perhaps nanophase) sample, but no characterization is given. Thus the anatase entropy may contain contributions from both bulk and surface terms. The data suggest that rutile and anatase have the same entropy within experimental error (S0 (298 K, rutile)=50.6±0.6 J/mol K and S0 (298 K, anatase)=49.9±0.3 J/mol K). Thus the TS will not significantly perturb the sequence of stability seen from the enthalpies. This work can be generalized to other nanophase materials. Zirconia and zinc oxide are important from the materials science point of view. Iron and manganese oxides are important as both minerals and materials. An understanding of the patterns of surface energetics for different polymorphs will give predictive power. Measurements of heat capacities on carefully controlled nanophase samples will shed light
R. Cava et al. /Progress in Solid State Chemistry 30(2002)1-101 on surface entropies. A comprehensive picture involving surface enthalpies, entropies and free energies with the effects of hydration is essential to understanding nano- phase stability and reactivity in both natural and synthetic systems, and is thus useful to both Earth science and solid state chemistry 2.4. Uranyl minerals Complicated assemblages of fine-grained low-temperature minerals challenge our understanding of mineralogy, both chemically and geologically. The crystal struc- tures of minerals in complex geochemical environments should be related to the occurrences and distribution of the minerals. Recently, with the introduction of synchrotron radiation and CCD-based detectors of X-rays, it has become possible to solve the structures of crystals with an effective volume of less than (20 um) 3, 20, 21, 22]. Details of the structural relationships of fine-grained low-temperature minerals are now attainable, and should revolutionize understanding and applications of low-temperature mineralogy Synergisms between mineralogy and solid state chemistry exist in many areas One topical example is uranyl(U)minerals. Uranyl minerals are extraordinarily complex, and our understanding of this important mineral group lags behind that of almost all other important groups. More than 180 uranyl minerals have been described; these are key to understanding the genesis of uranium ore deposits [23] and are also important in the environment. They form due to the weathering of uranium mine and mill tailings, where soils are contaminated with actinides [24 and will be the main products of alteration of spent nuclear fuel in a geological repository that is oxidizing and moist, such as the proposed repository at Yucca Mountain [25, 26]. It is likely that many of the radionuclides contained in nuclear waste forms will be incorporated into the uranyl alteration phases that form in the repository [27, 28 The structural hierarchy of uranyl minerals and inorganic compounds has been established on the basis of the polymerization of those polyhedra of higher bond- valence [29, 30(Fig. 2). The majority of inorganic uranyl compounds contain sheets of polyhedra of higher bond-valence, although structures containing finite clusters, chains and frameworks of polyhedra of higher bond-valence also occur. Structural units tend to be complex in uranyl minerals, even when they are of low dimensional ity. For example, the chain that is the basis of the structure of the uranyl sulfate uranopilite contains clusters of six uranyl pentagonal bipyramids that share equatorial edges and vertices, with the clusters cross-linked to form chains by sharing vertices with sulfate tetrahedra 31]. In uranopilite, the chains are linked directly by hydrogen bonds, as well as to interstitial H2O groups The majority of uranyl minerals have structures based upon sheets of polymerized polyhedra of higher bond-valence. Tremendous structural complexity exists within the more than 100 sheets observed in inorganic uranyl compounds, and it is difficult to probe the relationships between these sheets. A topological approach has been developed to facilitate understanding complex sheets based on the arrangement of the anions in the sheet [30 The utility of this approach is that sheets that appear
R.J. Cava et al. / Progress in Solid State Chemistry 30 (2002) 1–101 15 on surface entropies. A comprehensive picture involving surface enthalpies, entropies and free energies with the effects of hydration is essential to understanding nanophase stability and reactivity in both natural and synthetic systems, and is thus useful to both Earth science and solid state chemistry. 2.4. Uranyl minerals Complicated assemblages of fine-grained low-temperature minerals challenge our understanding of mineralogy, both chemically and geologically. The crystal structures of minerals in complex geochemical environments should be related to the occurrences and distribution of the minerals. Recently, with the introduction of synchrotron radiation and CCD-based detectors of X-rays, it has become possible to solve the structures of crystals with an effective volume of less than (20 µm) [3,20,21,22]. Details of the structural relationships of fine-grained low-temperature minerals are now attainable, and should revolutionize understanding and applications of low-temperature mineralogy. Synergisms between mineralogy and solid state chemistry exist in many areas. One topical example is uranyl (U6+ ) minerals. Uranyl minerals are extraordinarily complex, and our understanding of this important mineral group lags behind that of almost all other important groups. More than 180 uranyl minerals have been described; these are key to understanding the genesis of uranium ore deposits [23], and are also important in the environment. They form due to the weathering of uranium mine and mill tailings, where soils are contaminated with actinides [24], and will be the main products of alteration of spent nuclear fuel in a geological repository that is oxidizing and moist, such as the proposed repository at Yucca Mountain [25,26]. It is likely that many of the radionuclides contained in nuclear waste forms will be incorporated into the uranyl alteration phases that form in the repository [27,28]. The structural hierarchy of uranyl minerals and inorganic compounds has been established on the basis of the polymerization of those polyhedra of higher bondvalence [29,30](Fig. 2). The majority of inorganic uranyl compounds contain sheets of polyhedra of higher bond-valence, although structures containing finite clusters, chains and frameworks of polyhedra of higher bond-valence also occur. Structural units tend to be complex in uranyl minerals, even when they are of low dimensionality. For example, the chain that is the basis of the structure of the uranyl sulfate uranopilite contains clusters of six uranyl pentagonal bipyramids that share equatorial edges and vertices, with the clusters cross-linked to form chains by sharing vertices with sulfate tetrahedra [31]. In uranopilite, the chains are linked directly by hydrogen bonds, as well as to interstitial H2O groups. The majority of uranyl minerals have structures based upon sheets of polymerized polyhedra of higher bond-valence. Tremendous structural complexity exists within the more than 100 sheets observed in inorganic uranyl compounds, and it is difficult to probe the relationships between these sheets. A topological approach has been developed to facilitate understanding complex sheets based on the arrangement of the anions in the sheet [30]. The utility of this approach is that sheets that appear