The growth of Si3N4 grains in the usual sintering process occurs in an oxynitride liquid formed by reactions between sintering additives, impurity SiO2, and Si3N4. The shape of an Si3N4 grain in the liquid matrix is a hexagonal rod, although the aspect ratio (c/a) varies considerably, depending on the processing conditions and final crystalline forms of α or β. Figure 1 shows two types of microstructures observed in sintered Si3N4-based materials. The microstructure shown in Figure la is normal with unimodal grain-size distribution and that of Figure 1b is abnormal with a microstructure of exceptionally large elongated grains within fine matrix grains. When normal grain growth occurs, the microstructure varies little with sintering time, and the development may be described by a simple law. But, when abnormal grain growth occurs, a duplex grain structure with a bimodal grainsize distribution results; then no simple kinetic law can describe the microstructure development.

The grain growth in the microstructures shown in Figure 1 exemplifies the growth of faceted grains in a liquid matrix. The grain growth in a matrix occurs via growth of larger grains and dissolution of smaller ones by material transport through the liquid phase. The driving force of the material transport for an individual grain is determined by the difference between its size and the critical grain size, which is invariant at the moment of observation. Since the driving force is usually low, the volume change of each grain is relatively slow and analogous to the crystal growth or dissolution in a liquid matrix under low super- or undersaturation. Therefore, knowledge of the growth behavior of faceted crystals under low supersaturation in a liquid may provide fundamental understanding of the grain growth in Si3N4-based materials.

Collimated sputtering is a physical vapor deposition (PVD) method where a collimator is inserted between a conventional “full-face-erosion” sputtering target and a substrate (Figure 1). The collimator is a plate of hexagonal cells that acts as a filter to remove obliquely incident atoms before they arrive at the substrate. Only material with a nearly normal incidence trajectory may pass through the collimator and deposit on the substrate. Collimated sputtering was initially evaluated for conductor-level depositions in order to improve the filling of recessed features. Although the method has been successfully used to fill damascene structures, depositing thick conductor films is inefficient because most of the sputtered material is captured by the collimator, causing the collimator to clog quickly, necessitating frequent replacement.

A more common use of collimated sputtering is associated with the deposition of thin “liner” films. For example, thin, collimated aluminum alloy films have been used as underlayers for aluminum reflow processes. Also, collimated Ti/TiN films are used as contact/adhesion layers for chemically vapor-deposited (CVD) W metallization. Collimation provides better bottom and sidewall coverage for small, high aspect-ratio features than conventionally sputtered films do.

Coliimated sputtered films often exhibit unique properties because the angle of incidence of depositing atoms is controlled. Collimated AlMg alloys have superior electromigration resistance compared to noncollimated AlMg films. Collimated TiN films appear to exhibit denser grain structures when compared to films deposited with higher amounts of obliquely incident flux (Figure 2).

Tonight I will talk about molecular beam epitaxy (MBE) from research to manufacturing. First I will discuss the introduction of MBE in the early 1970s and the exciting achievements made with it. I will conclude with some new directions for MBE.

First let us review this technology. Through MBE, materials like semiconducting materials, metals, and insulating materials are grown, atom layer by atom layer. Figure 1 shows a stainless steel MBE chamber, pumped to a pressure of approximately 10−10 torr, with liquid-nitrogen-cooled shrouds to further condense the water vapor in the vacuum system. To grow gallium arsenide (GaAs), we mount a substrate in the center where it continuously rotates to give us the uniformity we need, and it is heated to about 580° or 600°C. The effusion cells are filled with pure Ga, pure As, and doping elements such as silicon for n-type doping, and then germanium or beryllium for p-type doping. Important in this MBE system are the in situ monitoring techniques. The system contains a reflection high energy electron diffraction (RHEED) apparatus, producing an electron beam with a grazing angle to the substrate of about one degree. The diffracted electrons are projected on a fluorescent screen. Through the diffraction pattern, we can look at the surface as it is cleaned by desorption of the oxide before we deposit and grow semiconducting materials.

When an energetic ion penetrates a target, it loses its energy via two nearly independent processes: (1) elastic collisions with the nuclei (nuclear-energy loss (dE/dx)n), which dominate the ion slowing down in the low energy range (i.e., in the stopping region); (2) electronic excitation and ionization (electronic-energy loss (dE/dx)e), which strongly overwhelm (dE/dx)n in the high energy range (typically above 1 MeV/nucleon). Until the 1980s, researchers considered that electronic-energy deposition could participate in damaging creation in many insulators, but the effects observed in bulk metals were solely ascribed to elastic nuclear collisions. This widely held opinion was due to the fact that in metallic systems the numerous very mobile conduction electrons allow a fast spreading of the deposited energy and an efficient screening of the space charge created in the projectile wake so that it seemed unreasonable to hope for damage creation or track formation in metallic targets following high levels of electronic-energy deposition.

A particular case is the observation more than 30 years ago of damage in thin or discontinuous. metallic films after fission fragment irradiation or MeV heavy ion bombardment. The spreading of the deposited energy is then strongly limited by the close vicinity of surfaces and interfaces.

The liquid crystal phase is an anisotropic mesophase, intermediate in order between the liquid and crystal phases. Liquid crystals have less translational order than crystals and more rotational order than isotropic liquids. The liquid crystal phase does not support finite shear stresses and thus behaves like a fluid. Molecules that display a liquid crystal phase are referred to as mesogenic. Mesogenic molecules exhibit shape anisotropy: either large length to diameter ratio (needlelike) or large diameter to thickness ratio (disklike). Because of their shape anisotropy, all liquid crystals display orientational order of their molecular axes.

Until 1956, all known examples of liquid crystals were low molecular weight compounds. Robinson was the first to identify liquid crystallinity in a liquid crystalline polymer (LCP) as the explanation for “a birefringent solution” of a polymeric material, poly-y-benzyl-L-glutamate, in chloroform, previously observed by Elliott and Ambrose. Chemists soon discovered that LCPs may be readily synthesized by covalently stitching small mesogenic units (e.g., rigid monomers) together into a chain using short flexible spacers. Mainchain or sidechain liquid crystal polymers may be formed (Figure 1). An example of a polymer molecule possessing a liquid crystal phase is shown in Figure 2. Liquid crystals may be thermotropic, where liquid crystallinity is exhibited over a range of temperatures, or lyotropic, where nonmesogenic solvent molecules are present in addition to the mesogens, and liquid crystallinity is observed over a range of concentrations as well.

The remarkable properties of diamond, including its hardness, chemical inertness, high thermal conductivity, low coefficient of friction, optical transparency, and semiconducting properties, have led to considerable research in the area of diamond thin-film deposition. Diamond films have been characterized ex situ by a large number of diagnostic techniques including Raman spectroscopy, x-ray diffraction, SEM, and TEM. In situ diagnostics, which can provide information in real time as the film is growing, are less common.

Laser-reflectance interferometry (LRI) has been used to monitor the growth of diamond films in situ. The technique involves measuring the intensity of a laser beam reflected from the substrate surface on which the film is growing. The reflected beam is the sum of beams reflected by the gas-diamond interface and the diamond-silicon interface. Oscillations in the reflectivity are observed as the film grows because of interference between the reflected beams. Each oscillation indicates an increase in film thickness of λ/2n, where λ is the laser wavelength and n is the index of refraction of the film. If the index of refraction of the film is known, the thickness and growth rate can be determined in situ. For LRI measurements with 632.8-nm-wavelength HeNe lasers, the index of refraction of diamond films has been found to be within 10% of the bulk diamond value of 2.4. Each oscillation therefore indicates an increase in film thickness of 0.13 μm.

The reflectivity measured by LRI is also affected by scattering because of surface roughness.

Functionally gradient materials (FGMs) display continuously or discontinuously varying compositions and/or microstructures over definable geometrical distances. The gradients can be continuous on a microscopic level, or they can be laminates comprised of gradients of metals, ceramics, polymers, or variations of porosity/density. Several processing techniques have been explored for the fabrication of FGMs for structural applications, e.g., powder metallurgy, thermal spraying, in situ synthesis, self-propagating high-temperature synthesis, reactive infiltration, etc. Physical and chemical vapor deposition (CVD) techniques are also being explored to process FGM films with nanometer level gradients in composition. This article addresses the issues related to thermal-spray processing of FGMs and will only peripherally compare the advantages and limitations of thermal spray versus other processing techniques as reported in the literature.

In thermal spraying, feedstock material (in the form of powder, rod, or wire) is introduced into a combustion or plasma flame. The particles melt in transit and impinge on the substrate where they flatten, undergo rapid solidification, and form a deposit through successive impingement. Thermal spraying has been traditionally employed to produce a variety of protective coatings of ceramics, metals, and polymers on a range of substrates. More recently, the process has been used for spray-forming structural components.

Arc spray, combustion, and plasma are the major techniques comprising thermal spray. These classifications are based on the type of heat source and the method by which feedstock is injected. Arc-spray processes use electrically conductive wire as feedstock, while combustion methods use powder or wire.

Recently, organic molecules and their complexes with inorganic or metallic materials have drawn many researchers' interest as candidate materials for nanoscale electronic devices of the next generation, especially since Carter's proposal on molecular electronic devices (MEDs) with the functions of gating, switching, memory, etc. in one molecule. However, in order to build such nanoscopic organic electronic devices to replace conventional silicon-based inorganic devices, one must determine how to produce such nanoscale devices and to recognize the electronic states of a single molecule.

The scanning tunneling microscope (STM) developed by G. Binning and H. Rohrer made it possible to visualize atoms and molecules in real space under various atmospheres. In addition, STMs can be used as nanoscopic tools for manipulation of individual atoms and molecules, thus realizing MEDs and nanotechnology.

In this article, we present our recent achievements concerning the STM as well as in situ x-ray diffraction studies on the molecular structure of ultrathin films prepared by vacuum evaporation. STM observations with atomic resolution reveal the mechanism of nuclei formation and the crystal-growth process in organic molecules. Computer simulations based on STM images of polar organic molecules with electronic dipoles have elucidated the role of electronic interaction for their aggregation structures.

Also, nanometer-sized molecular memory can be created by applying an electronic pulse to the evaporated organic films through the STM tip. Furthermore, we discuss the principle of a newly developed in situ total reflection x-ray diffraction (TRXD) apparatus and its application to the evaluation of crystal structure and molecular orientation in organic thin films during the evaporation process, particularly in regard to the role of the substrate, that is, epitaxial growth on organic molecular crystals.

Powder metallurgical (P/M) processing of FGMs provides a wide range of compositional and microstructural control, along with shape-forming capability. Oxide/metal systems are desirable because this materials combination can be used to easily tailor materials properties. However, there are many problems to be investigated which pertain to each of the processing steps; process innovations will often be required to realize the versatility of this route. In this article, I briefly review the present status of the powder-processing method.

Powder metallurgical fabrication of FGMs involves the following sequential steps with a selected material combination of metals and ceramics: determination of the optimum composition profile for an effective thermal-stress reduction; stepwise or continuous stacking of powder premixes according to the predesigned composition profile; compaction of the stacked powder heap and sintering with or without pressurizing. Besides the conventional powder metallurgical routes, a spray deposition method, using mixed powder suspensions and a slurry stacking method, have been developed to form continuously graded stacking. A powder spray stacking apparatus has been devised, which is fully automatic with computer control. Deposited compacts were cold isostatically pressed (CIP) and consolidated by hot isostatic pressing. Their microstructures show that this process provides fine compositional control with desired profiles.

Differential temperature sintering by laser-beam heating has been studied to add versatility to the P/M process. The surface of the green compacts is scanned with a laser beam using a predesigned scanning pattern to ensure homogeneous heating over the entire surface.

During the past decade, perturbed-angular-correlation (PAC) spectroscopy has emerged as an important technique in several areas of materials science. PAC spectroscopy is used to measure the effects of local fields at well-defined lattice sites in a crystal. These measurements can provide unique information about the structures, kinetics, and energetics associated with point defects, the mechanisms of phase transitions, and the strengths and symmetries of chemical bonds of atoms on surfaces and at interfaces. In what follows, I describe the PAC technique in the context of several examples of these applications and I comment on the historical evolution of this spectroscopy.

Hyperfine Interactions

The field of hyperfine interactions encompasses spectroscopic techniques that use the electric and magnetic nuclear moments to measure the specific extranuclear environment of the nuclear moments. Examples of these techniques are nuclear-magnetic-resonance (NMR), nuclear-quadrupole-resonance (NQR), electron-paramagnetic-resonance (EPA), muon-spin-rotation (MSR), Mössbauer-effect (ME), and perturbed-angular-correlation (PAC) spectroscopies. Each of these techniques is well-suited to certain types of measurements but useless for others. For example, NMR spectroscopy can be particularly useful for measuring chemical shifts associated with nuclei of atoms that are major constituents of crystalline solids. However, nuclear electricquadrupole interactions associated with some NMR-active nuclei are not only difficult to measure but they often obscure much of the chemical-shift information by producing spectral-line broadening. PAC spectroscopy can be used to accurately measure the nuclear electric-quadrupole interactions at the sites of nuclei of atoms that are trace dopants in crystals. But the PAC technique is insensitive to the effects of local charge distributions that produce the NMR chemical shifts. ME spectroscopy can be used to measure both of these effects as well as nuclear magnetic-dipole interactions. However, ME measurements are often only practical on crystals that have one of several elements as a major constituent, that is, either Fe or Sn. In addition, the ME sensitivity depends on temperature, and the NMR and EPR sensitivities also depend on temperature. However, the PAC measurement is independent of temperature, which can be a great advantage for studying phenomena such as phase transitions.

In the late 1980s, a number of exciting yet puzzling observations resulted from experiments investigating the coupling between two ferromagnetic layers separated by a nonferromagnetic spacer layer. A pioneering experiment by Grünberg et al. showed that Fe layers separated by a thin Cr spacer aligned with antiparallel magnetization, but with Au as the spacer layer, a parallel alignment occurred. The long-range magnetic dipole from each layer would tend to explain antiparallel alignment; small pinholes in the spacer layer would produce parallel alignment. Alternatively, the layers might be coupled through the spacer-layer conduction electrons by the Ruder man-Kittel-Kasuya-Yosida (RKKY) effect. This was expected to produce an oscillation in coupling as the spacer thickness increased, that is, an oscillation between parallel and antiparallel alignment. Oscillatory coupling was first observed by Parkin et al. Researchers had also found that, at spacer thicknesses where antiparallel alignment occurred, the Fe/Cr/Fe system can exhibit a giant magnetoresistance (GMR) effect, that is, an anomalously large change in resistance when a magnetic field is applied. The potential technological importance of the GMR effect to magnetic sensing and magnetic information storage added further impetus to the already rapidly growing area of research in magnetic multilayers.

Conventionally, the term “defects” in liquid-crystalline systems refers to microscopic faults in the orientational order, which are usually visible optically. These are discussed in other articles in this issue. Our use of the term defect is entirely different. The defects we shall be considering, “hairpins,” occur on the scale of several angstroms and are abrupt reversals in the trajectory of a single liquid-crystalline-polymer (LCP) chain (Figure 1). In comparison to conventional defects, the direct observation of hairpin defects is much more difficult, yet their presence has important effects. Among the affected properties are the dimensions and the elasticity of the chains, the elastic behavior of the bulk nematic, and its dielectric response. Their presence should also give rise to a family of interfacial phase transitions in solutions of LCPs in nematic solvents. In turn, these are of interest in the design of liquid-crystalline displays. Hairpins in LCPs are superficially reminiscent of similar configurations in proteins and in homopolymers that undergo fold crystallization. These similarities are misleading because hairpins in proteins are permanent structures due to the chemical bonds. The folds in crystalline polymers are also fixed structures. In marked contrast, hairpin defects are mobile topological excitations that are created and annihilated continuously. Our emphasis in this article is on main-chain, semiflexible, nematic LCPs, consisting of mesogenic monomers joined by flexible spacer chains (Figure la). These polymers combine the orientational order of monomeric nematics with the flexibility and randomness inherent in polymers. The appearance of an oriented, nematic phase can be controlled either by temperature or by concentration.

This article will begin with an introduction to acoustic cavitation, the physical phenomenon responsible for the chemical effects of ultrasound. Some recent applications of sonochemistry to the synthesis of nanophase and amorphous metals, as well as to heterogenous catalysis, will then be highlighted. Finally, we will examine the effects of ultrasound on metal powders in liquid-solid slurries.

The chemical effects of ultrasound do not come from a direct interaction of sound with molecular species. Ultrasound has frequencies from around 15 kilohertz to tens of megahertz. In liquids, this means wavelengths from centimeters down to microns, which are not molecular dimensions. Instead, when sound passes through a liquid, the formation, growth, and implosive collapse of bubbles can occur, as depicted in Figure 1. This process is called acoustic cavitation.

More specifically, sound passing through a liquid consists of expansion waves and compression waves. As sound passes through a liquid, if the expansion wave is intense enough (that is, if the sound is loud enough), it can pull the liquid apart and form a bubble (a cavity). The compression wave comes along and compresses this cavity, then another expansion wave re-expands it. So we have an oscillating bubble going back and forth, say, 20,000 times a second.

The improvement of mechanical properties by microstructural control has been one of the main topics of interest in the development of silicon nitride ceramics. Toughening, by developing an in situ composite or self-reinforced microstructure, has attracted particular attention.

Microstructural design is a key factor in the optimization of processing parameters. The microstructures of sintered materials are composed of silicon nitride grains and grain boundaries, which can be either crystalline, amorphous, or partially crystalline, depending on the composition, amount of sintering additives, and processing parameters. Silicon nitride ceramics have been fabricated with an addition of metal oxides and rare-earth oxides that form a liquid phase during sintering and accelerate grain boundary diffusion. The effect of composition of the glassy phase on the mechanical properties of ceramics is presented by Becher et al. and Hoffmann elsewhere in this issue. This article focuses specifically on the design and control of grain size.

As it is well recognized, many processing parameters affect grain growth behavior and the resulting microstructure. During sintering, the α- to β-phase transformation leads to a self-reinforcing microstructure on account of the anisotropic grain growth of the stable hexagonal β- Si3N4 phase. Therefore, α-rich powders are widely used for starting materials. Phase transformation accelerates anisotropic grain growth, resulting in an increase in the fracture toughness of Si3N4 ceramics. Kang and Han discuss the effect of phase transformation on nucleation and grain growth in an article in this issue. The effect of the grain-size distribution on microstructural development is described in this article, based on studies conducted mostly with β-Si3N4 powders.

More than 25 years have passed since Intermetallic Compounds, edited by Westbrook, was published. Since that time, enormous advances have been made in the understanding and usage of intermetallic compounds. It is known that intermetallic compounds are generally brittle. Thus, alloys that contain intermetallics may also be brittle. However, many intermetallic compounds are known to have extraordinary functions and characteristics that are not observed in ordinary metals and alloys. Thus, they function as magnetic materials, superconductors, semiconductors, hydrogen absorbing alloys, shape memory alloys, and so on.

Many high-strength structural alloys like maraging steels and duralumins are strengthened by fine precipitates of intermetallic phases. Nickel-based superalloys, which are used for airplane-engine parts, contain 60-70% of Ni3Al-based intermetallics by volume fraction and exhibit high strength at high temperatures. Hard metals, which are used for cutting tools, are composed of a large amount of hard but brittle intermetallics like WC and a small amount of ductile cobalt. Intermetallic compounds like TiAl are also investigated for their applications as structural materials where high strength at high temperatures is required.

In a strict sense, intermetallic compounds are composed of two or more metallic elements. In a wider sense, they are composed of metallic and/or semimetallic elements. Each is characterized by an ordered arrangement of two or more kinds of atoms, that is, the formation of a superlattice, and have various kinds of interatomic bonding, ranging from metallic to covalent or ionic bonding. The ordering of atoms and the strong interatomic bonding result in many attractive properties for intermetallic compounds.

Langmuir-Blodgett (LB) films have been applied to molecular electronics, nonlinear optics, and biosensors. Their useful properties can be accessed by using a defect-free monolayer—the precursor of LB films. In order to prepare a defect-free or defect-diminished monolayer, it is necessary to estimate the molecular arrangements and structural defects in the monolayer. The actual structure of monolayers on the surface of water have been proposed on the basis of recent morphological and structural studies. Molecular-aggregation processes or monolayer-formation processes do not always match the general concept concluded from surface pressure-area (π-A) isotherms. Therefore, a universal understanding has not been reached. Here we present a novel and systematic classification for the aggregation structure of monolayers on the water surface and also demonstrate how to prepare defect-diminished monolayers.

As the feature size of ULSI (ultralarge-scale integration) circuit devices shrinks, interconnects need to be scaled to maximize the wiring density and wire ability. This increased density leads to smaller contacts or via holes connecting the wires. The reduction in size increases the aspect ratio of these features for the same dielectric thickness. Conventional physical vapor deposition (PVD) techniques such as sputtering are unable to fill high aspect-ratio contacts/vias with aluminum conformally, as shown in Figure 1. This poor conformity is attributed to the shadowing effect by already-deposited nondirectional sputtering atoms and leads to void formation and open failures. Chemical vapor deposition (CVD) is a solution for achieving conformal filling.

This is a prime reason why CVD has been investigated since the 1980s and why a large number of metals have been proposed. Above all, because tungsten as a refractory metal has high resistance to electromigration (EM) failures and tungsten hexafluoride (WF6) as a source gas has some advantages in manufacturing, for example, high vapor pressure (boiling point = 17.4°C) and purity, W-CVD with WF6 based on H2 or SiH4 reduction has been widely studied. Blanket W-CVD has been used for actual via-hole filling for 0.5-μm devices. Figure 2 shows a cross-sectional view of five-level interconnects using W plugs in 0.35-μm devices. Another advantage of W-CVD is that W deposits selectively into via holes if a low flow-rate ratio of reductants to WF6 is used.

We have successfully developed an acoustic guitar (Figure 1) composed of graphite. Trademarked the RainSong® graphite guitar, this instrument uses no endangered tropical tonewoods. The instrument's sound quality is equal to that of a fine wooden guitar. At high frequencies, the clarity, sustain, and play-ability surpasses that of wooden guitars. Because of its construction, the instrument is sturdy and is impervious to humidity, heat, and water.

The development of this guitar required analysis of the theory of anisotropic sound propagation in the guitar soundboard and body, and resulted in two patents. We designed prototype guitars in collaboration with Pimentel & Sons, Guitar Makers, and used combinations of unidirectional and woven graphite and aramid fibers in an epoxy-resin matrix.

The goal of our project was to accurately duplicate—panel by panel—the acoustic properties of a fine wooden guitar. We had the resulting acoustic modes and frequencies verified in the laboratory. We then developed and constructed open-mold and resin-transfer molding tooling for a family of classical, steel-string acoustic and hollow-body electric guitars, which are now in commercial production.

Possibly the first all-composite acoustic guitar, the RainSong® represents a fundamental change in stringed-instrument construction, perhaps the first since the 17th Century Italian masters.

The RainSong® technology allows musicians to skirt the effects of climate and transport damage on their instruments. The instrument contains essentially no wood, and hence negates environmental concerns about rapid depletion of the virgin-forest woods, from which stringed instruments have traditionally been made.

The majority of sophisticated ultra-high-vacuum (UHV) systems for deposition of thin films, such as molecular beam epitaxy (MBE) machines, contain some kind of electron diffraction apparatus which is used to scrutinize the surface structure of the film while it is grown. Reflection high energy electron diffraction (RHEED) is probably the most frequently employed configuration. An excellent introduction to RHEED, including a treatment of electron diffraction, reciprocal-space description, reflection from imperfect surfaces, etc., was recently published in the MRS Bulletin by Lagally and Savage. Hence, we will not review these basics here. Rather, we will assume the reader to be familiar with that article, and will refer to it as LS.

The materials discussed in LS include Si, Ge on Si, and GaAs. The applications of MBE for synthesis of semiconductor thin films and heterostructures are widely recognized. MRS has recently bestowed its greatest honor, the Von Hippel Award, to Alfred Y. Cho for his pioneering work on MBE synthesis of GaAs and its application to new devices.

In contrast, here we focus on complex oxides—cuprates, titanates, manganates, etc. This is a relatively new area of application for both MBE and RHEED. Actually, it was only after the discovery of high-temperature superconductivity (HTS) that many MBE systems were designed and built specifically for metallic oxide deposition. More recently, some of these machines have also been employed to synthesize other interesting oxides, for example, ferroelectrics and ferromagnets. In all these studies, RHEED has been the principal diagnostic tool and source of information about the growing film surface.

Natural nuclear tracks in solids have existed since close to the beginning of the solar system, billions of years ago. Only during the last few decades have we learned how to employ tracks practically. Uses now range from radiation dosimetry to microchemical analysis, virus counting, oil and uranium exploration, and aiding earthquake prediction. The key to these applications is track etching, which in insulators allows tracks to be revealed simply and then enlarged. Etching also makes it possible to produce minute holes with clean, geometric shapes.