Dedicated Global Optimization Search for Ground State Silica Nanoclusters: (SiO2)N (N = 6−12)

Efficient Global Structure Optimization with a Machine-Learned Surrogate Model

We propose a scheme for global optimization with first-principles energy expressions of atomistic structure. While unfolding its search, the method actively learns a surrogate model of the potential energy landscape on which it performs a number of local relaxations (exploitation) and further structural searches (exploration). Assuming Gaussian processes, deploying two separate kernel widths to better capture rough features of the energy landscape while retaining a good resolution of local minima, an acquisition function is used to decide on which of the resulting structures is the more promising and should be treated at the first-principles level. The method is demonstrated to outperform by 2 orders of magnitude a well established first-principles based evolutionary algorithm in finding surface reconstructions. Finally, global optimization with first-principles energy expressions is utilized to identify initial stages of the edge oxidation and oxygen intercalation of graphene sheets on the Ir(111) surface.

Structure and Properties of Nanosilicates with Olivine (Mg2SiO4) N and Pyroxene (MgSiO3) N Compositions

Magnesium-rich silicates are ubiquitous both terrestrially and astronomically, where they are often present as small particles. Nanosized Mg-rich silicate particles are likely to be particularly important for understanding the formation, processing, and properties of cosmic dust grains. Although astronomical observations and laboratory studies have revealed much about such silicate dust, our knowledge of this hugely important class of nanosolids largely rests on top-down comparisons with the properties of bulk silicates. Herein, we provide a foundational bottom-up study of the structure and properties of Mg-rich nanosilicates based on carefully procured atomistic models. Specifically, we employ state-of-the-art global optimization methods to search for the most stable structures of silicate nanoclusters with olivine (Mg₂SiO₄) _N and pyroxene (MgSiO₃) _N compositions with N = 1-10. To ensure the reliability of our searches, we develop a new interatomic potential that has been especially tuned for nanosilicates. Subsequently, we refine these searches and calculate a range of physicochemical properties of the most stable nanoclusters using accurate density functional theory based electronic structure calculations. We report a detailed analysis of structural and energy properties, charge distributions, and infrared vibrational spectra, where in all cases we compare our finding for nanosilicates with those of the corresponding bulk silicate crystals. For most properties considered, we find large differences with respect to the bulk limit, underlining the limitations of a top-down approach for describing these species. Overall, our work provides a new platform for an accurate and detailed understanding of nanoscale silicates.

Oxygen Vacancies in Oxide Nanoclusters: When Silica Is More Reducible Than Titania

Oxygen vacancies are related to specific optical, conductivity and magnetic properties in macroscopic SiO2 and TiO2 compounds. As such, the ease with which oxygen vacancies form often determines the application potential of these materials in many technological fields. However, little is known about the role of oxygen vacancies in nanosized materials. In this work we compute the energies to create oxygen vacancies in highly stable nanoclusters of (TiO2)N, (SiO2)N, and mixed (TixSi1-xO2)N for sizes between N = 2 and N = 24 units. Contrary to the results for bulk and surfaces, we predict that removing an oxygen atom from global minima silica clusters is energetically more favorable than from the respective titania species. This unexpected chemical behavior is clearly linked to the inherent presence of terminal unsaturated oxygens at these nanoscale systems. In order to fully characterize our findings, we provide an extensive set of descriptors (oxygen vacancy formation energy, electron localization, density of states, relaxation energy, and geometry) that can be used to compare our results with those for other compositions and sizes. Our results will help in the search of novel nanomaterials for technological and scientific applications such as heterogeneous catalysis, electronics, and cluster chemistry.

Properties of hydrated TiO2 and SiO2 nanoclusters: dependence on size, temperature and water vapour pressure

Nanoscale titania (TiO₂) and silica (SiO₂) are massively produced technologically important nanomaterials used in a wide range of technological applications where nano-titania is the active component (e.g. water splitting, pollution remediation, self-cleaning coatings). Generally, these applications entail contact with water and a degree of hydration of these nano-oxides. Although the hydration of nano-silica has been fairly well studied, the corresponding level of microscopic understanding for nano-titania is severely lacking. Here, using accurate electronic structure calculations we perform a detailed and comprehensive study of the hydration of titania nanoclusters. Firstly, using global optimisation, we establish the most energetically stable structures of a set of (TiO₂)_M(H₂O)_N nanoclusters with sizes ranging through M = 4-16 and with N/M ratios of ≤ 1.0. Using this extensive dataset we investigate how the structures, energy gaps, and thermodynamic stabilities of these species depend on size, temperature and water vapour pressure. To provide a broader chemical context for our study we also provide this full set of data for the respective set of (SiO₂)_M(H₂O)_N nanoclusters which we use to compare and contrast their properties with those of nano-titania. Our broad systematic study thus provides a comparative and foundational reference study for a thorough understanding of how hydration affects the structure, energetics and properties of both nano-SiO₂ and nano-TiO₂.

Under what conditions does (SiO)N nucleation occur? A bottom-up kinetic modelling evaluation

Silicon monoxide (SiO) is a structurally complex compound exhibiting differentiated oxide-rich and silicon-rich nano-phases at length scales covering nanoclusters to the bulk. Although nano-sized and nano-segregated SiO has great technological potential (e.g. nano-silicon for optical applications) and is of enormous astronomical interest (e.g. formation of silicate cosmic dust) an accurate general description of SiO nucleation is lacking. Avoiding the deficiencies of a bulk-averaged approach typified by classical nucleation theory (CNT) we employ a bottom-up kinetic model which fully takes into account the atomistic details involved in segregation. Specifically, we derive a new low energy benchmark set of segregated (SiO)_N cluster ground state candidates for N ≤ 20 and use the accurately calculated properties of these isomers to calculate SiO nucleation rates. We thus provide a state-of-the art evaluation of the range of pressure and temperature conditions for which formation of SiO will or will not proceed. Our results, which match with available experiment, reveal significant deficiencies with CNT approaches. We employ our model to shed light on controversial issue of circumstellar silicate dust formation showing that, at variance with the predictions from CNT-based calculations, pure SiO nucleation under such conditions is not viable.

Stability of mixed-oxide titanosilicates: dependency on size and composition from nanocluster to bulk

Nanostructured titanosilicate materials based upon interfacing nano-TiO₂ with nano-SiO₂ have drawn much attention due to their huge potential for applications in a diverse range of important fields including gas sensing, (photo)catalysis, solar cells, photonics/optical components, tailored multi-(bio)functional supports and self-cleaning coatings. In each case it is the specific mixed combination of the two SiO₂ and TiO₂ nanophases that determines the unique properties of the final nanomaterial. In the bulk, stoichiometric mixing of TiO₂ with SiO₂ is limited by formation of segregated TiO₂ nanoparticles or metastable glassy phases and more controlled disperse crystalline mixings only occur at small fractions of TiO₂ (<15 wt%). In order to more fully understand the stability of nano-SiO₂ and nano-TiO₂ combinations with respect to composition and size, we employ accurate all-electron density functional calculations to evaluate the mixing energy in (Ti_xSi_1-xO₂)_n nanoclusters with a range of sizes (n = 2-24) having different titania molar fractions (x = 0-1). We derive all nanoclusters from a dedicated global optimisation procedure to help ensure that they are the most energetically stable structures for their size and composition. We also consider a selection of representative intimately mixed crystalline solid phase (Ti_xSi_1-xO₂)_bulk systems for comparison. In agreement with experiment, we find that homogeneous mixing of SiO₂ and TiO₂ in bulk crystalline phases is energetically unfavourable. Conversely, we find that SiO₂-TiO₂ mixing is energetically favoured in small (Ti_xSi_1-xO₂)_n nanoclusters. Following the evolution of mixing energy with nanocluster size and composition we find that mixing is most favoured in nanoclusters with a diameter of 1 nm with TiO₂ molar fractions between 0.3-0.5. Thereafter, mixed nanoclusters with increasing size have progressively less negative mixing energies up to diameters of approximately 1.5 nm. We propose some chemical-structural principles to help rationale this energetically favourable nanoscale mixing. As a guide for experimentalists to observe and characterize these mixed nano-species we also provide two measurable signatures of mixing based on their unique vibrational and structural characteristics.

Predicting size-dependent emergence of crystallinity in nanomaterials: titania nanoclusters versus nanocrystals

Bottom-up and top-down derived nanoparticle structures refined by accurate ab initio calculations are used to investigate the size dependent emergence of crystallinity in titania from the monomer upwards. Global optimisation and data mining are used to provide a series of (TiO₂)_N global minima candidates in the range N = 1-38, where our approach provides many new low energy structures for N > 10. A range of nanocrystal cuts from the anatase crystal structure are also considered up to a size of over 250 atoms. All nanocrystals considered are predicted to be metastable with respect to non-crystalline nanoclusters, which has implications with respect to the limitations of the cluster approach to modelling large titania nanosystems. Extrapolating both data sets using a generalised expansion of a top-down derived energy expression for nanoparticles, we obtain an estimate of the non-crystalline to crystalline crossover size for titania. Our results compare well with the available experimental results and imply that anatase-like crystallinity emerges in titania nanoparticles of approximately 2-3 nm diameter.

Formation of Environmentally Persistent Free Radicals on α-Al2O3

Metal oxides exhibit catalytic activity for the formation of environmentally persistent free radicals (EPFRs). Here, we investigate, via first-principles calculations, the activity of alumina α-Al₂O₃(0001) surface toward formation of phenolic EPFRs, under conditions relevant to cooling down zones of combustion systems. We show that, molecular adsorption of phenol on α-Al₂O₃(0001) entails binding energies in the range of -202 kJ/mol to -127 kJ/mol. The dehydroxylated alumina catalyzes the conversion of phenol into its phenolate moiety with a modest activation energy of 48 kJ/mol. Kinetic rate parameters, established over the temperature range of 300 to 1000 K, confirm the formation of the phenolate as the preferred pathways for the adsorption of phenol on alumina surfaces, corroborating the role of particulate matter in the cooling down zone of combustion systems in the generation of EFPRs.

A model for the effects of germanium on silica biomineralization in choanoflagellates

Silica biomineralization is a widespread phenomenon of major biotechnological interest. Modifying biosilica with substances like germanium (Ge) can confer useful new properties, although exposure to high levels of Ge disrupts normal biosilicification. No clear mechanism explains why this disruption occurs. Here, we study the effect of Ge on loricate choanoflagellates, a group of protists that construct a species-specific extracellular lorica from multiple siliceous costal strips. High Ge exposures were toxic, whereas lower Ge exposures produced cells with incomplete or absent loricae. These effects can be ameliorated by restoring the germanium : silicon ratio, as observed in other biosilicifying organisms. We developed simulations of how Ge interacts with polymerizing silica. In our models, Ge is readily incorporated at the ends of silica forming from silicic acid condensation, but this prevents further silica polymerization. Our 'Ge-capping' model is supported by observations from loricate choanoflagellates. Ge exposure terminates costal strip synthesis and lorica formation, resulting in disruption to cytokinesis and fatal build-up of silicic acid. Applying the Ge-capping model to other siliceous organisms explains the general toxicity of Ge and identifies potential protective responses in metalloid uptake and sensing. This can improve the design of new silica biomaterials, and further our understanding of silicon metabolism.

Long range coupling between defect centres in inorganic nanostructures: valence alternation pairs in nanoscale silica

Valence alternation pair (VAP) states are formed by a closed-shell combination of two space- and charge-separated topological defect centres. These pairs of defects, although historically invoked to explain the electronic properties of bulk inorganic glassy materials (e.g., amorphous silicon dioxide) via the concept of negative-U defects, have more recently been found in a number of theoretical studies of silica surfaces and nanoscale silica clusters. Using density functional theory we systematically probe the structure and internal stability of VAPs in a number of silica nanoclusters with respect to the separation of the two constituent defect centres. We find that VAP states in nanosilica are strongly stabilised by the attractive electrostatic interaction between their separated oppositely charged component defects such that VAPs can persist up to an internal separation of a least 1.5 nanometres. Beyond this distance VAPs become unstable with respect to an open-shell combination of topological defects, virtually indistinguishable from two isolated open-shell defect centres. Finally, we theoretically analyse the possibility of experimental observation of VAP states through their infra-red vibrational spectra.

Modelling nano-clusters and nucleation

We review the growing role of computational techniques in modelling the structures and properties of nano-particulate oxides and sulphides. We describe the main methods employed, including those based on both electronic structure and interatomic potential approaches. Particular attention is paid to the techniques used in searching for global minima in the energy landscape defined by the nano-particle cluster. We summarise applications to the widely studied ZnO and ZnS systems, to silica nanochemistry and to group IV oxides including TiO(2). We also consider the special case of silica cluster chemistry in solution and its importance in understanding the hydrothermal synthesis of microporous materials. The work summarised, together with related experimental studies, demonstrates a rich and varied nano-cluster chemistry for these materials.

Crystal structure prediction from first principles

The prediction of structure at the atomic level is one of the most fundamental challenges in condensed matter science. Here we survey the current status of the field and consider recent developments in methodology, paying particular attention to approaches for surveying energy landscapes. We illustrate the current state of the art in this field with topical applications to inorganic, especially microporous solids, and to molecular crystals; we also look at applications to nanoparticulate structures. Finally, we consider future directions and challenges in the field.

Molecular dynamics simulation of amorphous SiO2 nanoparticles

Molecular dynamics simulation of amorphous SiO2 spherical nanoparticles has been carried out in a model with different sizes, 2, 4, and 6 nm, under non-periodic boundary conditions. We use the pair interatomic potentials which have weak Coulomb interaction and Morse type short-range interaction. Models have been obtained by cooling from the melt via molecular dynamics (MD) simulation. Structural properties of amorphous nanoparticles obtained at 350 K have been studied via partial radial distribution functions (PRDFs), mean interatomic distances, coordination numbers, and bond-angle distributions, which are compared with those observed in the bulk. Calculations of the radial density profile in nanoparticles show the tendency of oxygen to concentrate at the surface as observed previously in other amorphous clusters or thin films. Size effects on structure of nanosized models are significant. The calculations show that if the size is larger than 4 nm, amorphous SiO2 nanoparticles have a distorted tetrahedral network structure with the mean coordination number ZSi-O approximately 4.0 and ZO-Si approximately 2.0 like those observed in the bulk. Surface structure, surface energy, and glass transition temperature of SiO2 nanoparticles have been obtained and presented.

Structural and Dynamic Properties of (SiO2)6 Silica Nanostructures: A Quantum Molecular Dynamics Study

Structural and dynamic properties of the building block of silica nanowires, (SiO2)6, are investigated by Born-Oppenheimer quantum molecular dynamics simulations. Thirteen conformers have been identified, seven of which have not been reported before. The energy component analysis shows that the lower electrostatic interaction differentiates the global minimum from the other structures. We also observe that the maximum hardness principle can be employed to justify the molecular stability for this system. Time profiles of a few density functional reactivity indices exhibit correlations of dynamic fluctuations between HOMO and LUMO and between chemical potential and hardness. Electrophilicity, nucleaofugality, and electrofugality indices are found to change concurrently and significantly, indicating that the nanostructures sampled during the dynamic process are exceedingly reactive and rich in chemistry.

Energetics and structures of the initial stages of nucleation of (SiO2)Nspecies: possible routes to highly symmetrical tetrahedral clusters

A detailed survey of the low energy isomer spectrum of (SiO(2))(N), N= 6-10, 13, 16 has been performed using interatomic potential based global optimisations refined via high-level density functional calculations. Within these spectra, including many isomers reported for the first time, structurally and energetically viable pathways for the initial stages of silica cluster growth through SiO(2) nucleation are identified. The role of the exceptionally stable (SiO(2))(8) ground state "magic" cluster is highlighted in the possible formation of highly symmetric fully tetrahedral clusters of size (SiO(2))(10) and (SiO(2))(16). These clusters are found to form a part of a natural (SiO(2))(N)N= 7, 10, 13, 16 sequence together with the C(3v) ground states for (SiO(2))(7) and (SiO(2))(13). The fully tetrahedral clusters are argued to be likely relatively long-lived metastable species in the process of gas phase SiO(2) nucleation due to the manner of their termination. It is speculated that larger tetrahedral (SiO(2))(40) clusters may exhibit porous structures.

Density functional theory study of geometrical structures and electronic properties of silica nanowires

Silica nanowires are expected to possess structural diversity like bulk silica. We modeled three silica nanowires based on the side-shared two-membered rings, spiro-united two-membered rings, and three-membered rings, respectively. By performing density functional theory calculations, we studied their geometrical structures and electronic properties with and without the presence of external electric field. It is found that the stability of silica nanowires increases with length and diameter. As indicated by calculated large HOMO-LUMO gaps, silica nanowires are expected to be good insulating materials. The energy gaps, however, gradually decrease with applied electronic field and finally close, resulting in the breakdown of the insulating nanowires. Moreover, it is shown that the breakdown threshold remarkably increases with the nanowire diameter. These significant findings from the present calculations for the simplest silica nanowires will provide relevant insight into the structures and properties of much more complicated real silica nanowires.

A Family of Stable Silica Fullerenes with Fully Coordinated Structures

Theoretical electronic structure techniques have become an indispensable and powerful tool for predicting molecular properties and designing new materials. The discovery of C(60) opened a challenging field in nanoscale materials science, and since then people have been looking for its inorganic analogues. On the basis of the B3LYP/6-31G(d) calculations, here we provide theoretical evidence for a family of stable silica fullerenes with fully coordinated structures, which exhibit highly structural and energetic stabilities, very large energy gaps, and extremely good resistibilities to breakdown of the insulating capability in an applied electric field. Our calculations indicate that the discrete silica fullerenes are a possible polymorph of silica and can be synthesized under some conditions. They are expected to find novel applications in silica-based molecular devices. The present results may provide an aid in the experimental design for controllably producing desired silica clusters.

Silica Nanoarchitectures with Tailored Pores Based on the Hybrid Three- and Four-Membered Rings

Inspired by the recent developments in the controlled synthesis of porous materials, we present herein the structural prediction of silica nanoarchitectures by using the three- (3MRs) and four-membered rings (4MRs), which are more frequently found in the nanometer-sized particles than in the bulk form, as building blocks. The proposed models include the active molecular rings, thin nanowires, hollow nanotubes, discrete fullerene-like cages, and porous zeolite-like three-dimensional networks. Their geometrical and electronic structures and properties were studied by performing density functional calculations. These silica nanostructures were proved, using molecular dynamics simulations, to possess intrinsic structural stabilities with highly symmetrical geometries and regular nanochannels. These atomically well-defined clusters, (SiO)(n), are chemically more reactive than those proposed earlier and are energetically more favorable for n > 20 in high-level density functional calculations over the corresponding two-membered ring (2MR) chains and rings as well as the pure 3MR networks. The nanoparticles and nanodevices based on them are expected to have potential technological applications that mainly make use of their characteristic geometrical structures (nanosized pores) and novel electronic properties.

A Synthetic Route toward Well-Defined Stoichiometric Silica Fullerene and Nanotubes Based on Metastable Four-Membered Rings

On the basis of computational considerations, using metastable four-membered rings as building blocks, we propose novel synthetic routes toward well-defined stoichiometric silica nanofullerenes and nanotubes. The viability of the routes has been demonstrated by performing high-level density functional calculations, and the so-formed nanoarchitectures were proved to be energetically and structurally stable. Such nanostructures, if synthesized, are expected to have potential application in nanotechnology.

Structural Preferences of Single-Walled Silica Nanostructures: Nanospheres and Chemically Stable Nanotubes

Structural preferences of single-walled and coordinatively saturated spherical and tubular nanostructures of silica have been determined by ab initio calculations. Two families of spherical (SiO2)n clusters derived from Platonic solids and Archimedean polyhedra are depicted, with n ranging from 4-120. The analogue of a truncated icosidodecahedron, Ih-symmetric Si120O240, is favored in energy, closely followed by the Ih-symmetric Si60O120-truncated icosahedron. The silica nanotubes derived from spherical clusters are capped by Si2O2 rings, whereas the tubular section consists of single oxygen bridges. Periodic studies performed with open-ended silica nanotubes and the alpha-quartz polymorph of silica, along with a comparisons to fullerenes and carbon nanotubes, suggest that tubes with diameters of approximately 1 nm should be chemically stable.

Structural Model of Silica Nanowire Assembled from a Highly Stable (SiO2)8 Unit

The ground-state structures of silica clusters (SiO2)n for n = 1-8 were studied by performing calculations at the B3LYP/6-311+G(d) level of density functional theory. The results indicate that the growth mode of a silica nanowire based on small silica clusters may change at different wire lengths. A linear chain might be assembled from the smallest clusters of rhombic two-membered ring (2MR) with n < or = 5, while the growth motif changes at n = 6 into a more compact form composed of three-membered-rings (3MRs). The 3MR-containing structures become energetically favorable configurations for even longer silica clusters. In particular, the closed molecular ring consisting of 3MRs at n = 8 (i.e., (SiO2)8) with a high symmetry shows extreme energetic stability and relatively high chemical reactivity and thus is considered to be an important building block to assemble into silica nanowires. The relative stability of so-assembled silica nanowires were evaluated and compared with the models of silica nanowires in the literature.

Columnar-to-disk structural transition in nanoscale (SiO2)N clusters

Extensive large-scale global optimizations refined by ab initio calculations are used to propose (SiO2)N N = 14-27 ground states. For N < 23 clusters are columnar and show N-odd-N-even stability, energetically and electronically. At N = 23 a columnar-to-disk structural transition occurs reminiscent of that observed for SiN. These transitions differ in nature but have the same basis, linking the nanostructural behavior of an element (Si) and its oxide (SiO2). Considering the impact of devices based on the nanoscale manipulation of the result is of potential technological importance.

Structure and Stability of Small TiO2 Nanoparticles

The effect of the nanostructure on the photochemistry of TiO2 is an active field of research owing to its applications in photocatalysis and photovoltaics. Despite this interest, little is known of the structure of small particles of this oxide with sizes at the nanometer length scale. Here we present a computational study that locates the global minima in the potential energy surface of Ti(n)O2n clusters with n = 1-15. The search procedure does not refer to any of the known TiO2 polymorphs, and is based on a novel combination of simulated annealing and Monte Carlo basin hopping simulations, together with genetic algorithm techniques, with the energy calculated by means of an interatomic potential. The application of several different methods increases our confidence of having located the global minimum. The stable structures are then refined by means of density functional theory calculations. The results from the two techniques are similar, although the methods based on interatomic potentials are unable to describe some subtle effects. The agreement is especially good for the larger particles, with n = 9-15. For these sizes the structures are compact, with a preference for a central octahedron and a surrounding layer of 4- and 5-fold coordinated Ti atoms, although there seems to be some energy penalty for particles containing the 5-fold coordinated metal atoms with square base pyramid geometry and dangling Ti=O bonds. The novel structures reported provide the basis for further computational studies of the effect of nanostructure on adsorption, photochemistry, and nucleation of this material.

Novel structures and energy spectra of hydroxylated (SiO2)8-based clusters: Searching for the magic (SiO2)8O2H3− cluster

The prominent (SiO(2))(8)O(2)H(3) (-) mass peak resulting from the laser ablation of hydroxylated silica, attributed to magic cluster formation, is investigated employing global optimization with a dedicated interatomic potential and density functional calculations. The low-energy spectra of cluster isomers are calculated for the closed shell clusters: (SiO(2))(8)OH(-) and (SiO(2))(8)O(2)H(3) (-) giving the likely global minima in each case. Based upon our calculated cluster structures and energetics, and further on the known experimental details, it is proposed that the abundant formation of (SiO(2))(8)O(2)H(3) (-) clusters is largely dependent on the high stability of the (SiO(2))(8)OH(-) ground state cluster. Both the (SiO(2))(8)O(2)H(3) (-) and (SiO(2))(8)OH(-) ground state clusters are found to exhibit cagelike structures with the latter containing a particularly unusual tetrahedrally four-coordinated oxygen center not observed before in either bulk silica or silica clusters. The bare ground state (SiO(2))(8)O(2-) cluster ion core is also found to have four tetrahedrally symmetric Si==O terminations making it a possible candidate, when combined with suitable cations, for extended cluster-based structures/materials.

Interaction of SiO2 with Single-Walled Carbon Nanotubes

The effects of coating of a single-walled carbon nanotube (SWNT) with a nonbonded layer of silica are investigated via model system employing fully coordinated silica clusters. The geometric and electronic structures of the SWNT@SiO(2) composite system are calculated using periodic density functional (DF) calculations for a range of confining silica coatings. We show that silica can provide a protective bound coating to a single walled nanotube, which, importantly, only weakly perturbs the underlying properties of both components. Detailed analysis of the charge redistribution and changes in electronic structure upon coating the SWNT are performed to support this conclusion. Furthermore, as allowed by our versatile model system, the energetics of rotating a silica "bearing" around a nanotube "spindle" is also calculated to indicate the possibilities for SWNT@SiO(2)-based nanomechanical devices.