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Over time, several different materials have been used for the pendulum rod such as steel, wood, and invar. The best material is quartz because of its proven stability and low thermal expansion. Steel is used for the pendulum rod in simple ordinary clocks because it is cheap and has relatively low thermal expansion. Wood is sometimes recommended because of its low linear thermal expansion coefficient along the grain, but it is an inherently unstable material. It warps, splits, and exhibits a high mechanical creep under load. Worst of all, wood expands and contracts considerably with relative humidity. Invar is a mixture of 36% nickel and 63% iron. It is magnetic and rusts in a humid environment. A new material of interest for the pendulum rod is carbon fibre, but it may not work too well as a pendulum rod as the epoxy absorbs moisture, changing the rod's length and weight.

The big attraction of quartz as a pendulum material is its good dimensional stability over time. Stability over time is the biggest and most needed characteristic in an accurate pendulum. In contrast to invar, which was known to be unstable almost from its beginning, quartz has a long history of being a stable material. Dimensional stability is not the same as low thermal expansion. If a pendulum is temperature compensated, as all accurate pendulums are, then it does not matter much what the thermal expansion coefficient is, so long as the compensation has been done accurately. The accuracy of temperature compensation is limited by factors other than the thermal expansion coefficient. Because of their low density, quartz pendulum rods do have one drawback: they have a much higher sensitivity to barometric pressure changes than invar.

This chapter describes some transient temperature measurements made on a pendulum with a quartz pendulum rod. Time offset error occurs because different parts of the pendulum change temperature at different rates. Before and after a temperature change, the pendulum is the right length (hopefully) and runs at the right rate. But during the temperature change, the pendulum is the wrong length, due to its different parts changing temperature at different rates, and it runs at the wrong rate during the temperature change interval. Experiments were carried out to measure the pendulum temperatures using small thermistors. The pyrex sleeve provides about one-third of the temperature compensation, while two thin-walled pyrex tubes located on opposite sides of the quartz pendulum rod provide the other two-third. The temperature data provide an interesting look into the thermodynamics of a pendulum. The suspension spring assembly changes temperature relatively slowly, whereas the bob, with its large thermal mass, changes temperature the slowest of any part of the pendulum.

This chapter focuses on current knowledge about how shear strength (the force needed to slide one surface over another) originates at the atomic level. For adhesive friction, friction originates from the forces needed to move the atoms on one surface over the atomic structure of the opposing surface. The Frenkel-Kontrova model, the Tomlinson model, and molecular dynamic simulations are typically used to show how the atomic structure of the surfaces leads to static friction. One exciting aspect of these friction models is the prediction of superlubricity or negligible friction for incommensurate sliding surfaces, which is now being realized in experiments. As atoms and molecules slide over surfaces, kinetic friction originates from phonon and electronic excitations; the last part of this chapter discusses how these energy dissipation mechanisms are studied with the quartz crystal microbalance (QCM) and the blow-off techniques.

This chapter discusses the physical principle, design, and characterization of piezoelectric scanners, which is the heart of STM and AFM. The concept of piezoelectricity is introduced at the elementary level. Two major piezoelectric materials used in STM and AFM, quartz and lead zirconate titanate ceramics (PZT), are described. After a brief discussion of the tripod scanner and the bimorph, much emphasis is on the most important scanner in STM and AFM: the tube scanner. A step-by-step derivation of the deflection formula is presented. The in-situ testing and calibration method based on pure electrical measurements is described. The formulas of the resonance frequencies are also presented. To compensate the non-linear behavior of the tube scanner, an improved design, the S-scanner, is described. Finally, a step-by-step procedure to repole a depoled piezo is presented.

This chapter describes five different ways of fastening things to a quartz pendulum rod. To connect to a metal rod, a hole is drilled in it or a thread is cut on it. But how do you fasten something to quartz? Quartz is like glass it is brittle and breaks easily. Five types of fasteners are described here, with some pros and cons on each. The five fasteners are cemented sleeve, clamp ring, solder joint, dowel pin, and split sleeve. Any of the fasteners can be used at either the top or bottom of a quartz rod, for connecting to a suspension spring, bob, or rating nut. In most cases, the fastener material should be invar because of its low thermal expansion coefficient.

The prefix “piezo” (pronounced pie-ease-o) comes from the Greek word for pressure or mechanical force. Piezoelectricity refers to the linear coupling between mechanical stress and electric polarization (the direct piezoelectric effect) or between mechanical strain and applied electric field (the converse piezoelectric effect). The equivalence between the direct and converse effects was established earlier using thermodynamic arguments (Section 6.2). The principal piezoelectric coefficient, d, relates polarization, P, to stress, X, in the direct effect (P = dX) and strain, x, to electric field E (x = dE). Thus the units of d are [C/N] or [m/V] which are equivalent to one another. Typical sizes for useful piezoelectric materials range from about 1 pC/N for quartz crystals to about 1000 pC/N for PZT (lead zirconate titanate) ceramics. To understand how the piezoelectric effect varies with direction and how it is affected by symmetry, it is necessary to determine how piezoelectric coefficients transform between coordinate systems. Since polarization is a vector and stress a second rank tensor, the physical property relating these two variables must involve three directions: . . . Pj = djklXkl . . . . In the new coordinate system . . . P'i = aijPj = aijdjklXkl . . . . Transforming the stress to the new coordinate system gives . . . P'i= aijdjklamkanlX'mn = d'imnX 'mn. . . . Thus piezoelectricity transforms as a polar third rank tensor. . . . d'imn = aijamkanldjkl . . . . In general there are 33 = 27 tensor components, but because the stress tensor is symmetric (Xij = Xji), only 18 of the components are independent. Therefore the piezoelectric effect can be described by a 6 × 3 matrix.

The rat-a-tat of automatic gunfire burst through the morning air in Anantnag. For the locals of this troubled district in the south of Kashmir, it came as a shock but no longer a surprise. Separatist militants had once again clashed with army forces. Several civilians were caught in the crossfire. One died; three others were wounded. It was Saturday, July 1, 2017. Hours earlier, at midnight, India had adopted a new national sales tax, designed to stitch the country’s twentynine states together into one economic union. The new system—known as the Goods and Services Tax, or GST—was heralded as an economic reform that would spur growth, enlarge the tax base, and make it easier to do business. Kashmir was the only state still debating whether to join. It was a symbolic outlier. Some distance from the gunfire, sixteen-year-old Zeyan Shafiq was just waking up. He hadn’t heard the shooting; his home was well insulated. When he opened his eyes, he told me, the first thing he did was to reach for his iPhone. He looked at the screen and sighed. The wireless internet at home was down. So was mobile data. Shafiq got out of bed, put on his slippers, and shuffled toward the front door, where he knew he would have a stronger mobile signal. No luck. He couldn’t catch the internet. Shafiq looked up at the skies, opened his lungs, and let out a bellow of frustration. For Shafiq, it was easy to guess what had happened. There must have been what locals called an encounter—a skirmish between Kashmiri separatists and the state. These days, encounters were inevitably followed by the government shutting down the internet. The digital blackouts weren’t aimed at stopping separatists or terrorists from communicating. They were usually already dead. The shutdowns were to prevent people from sharing videos and photos of the violence on social media. In effect, 13 million Kashmiris were collateral damage, unable to do something as simple as check email. There was a time when curfews were merely physical, imposed with barbed wire, barriers, and troops on the streets.

On my way to Vilnius, capital of Lithuania, one late November I realized that I had not packed any winter clothes. It turns out that I was not the first to make this blunder. None of the half a million or so Germans, French, Swiss, Poles, Italians, and other nationalities who passed through the town or in its vicinity in June 1812 had packed any winter clothes, something many of them were to later regret. They were on their way, although they did not know it at the time, to Moscow. What they also did not know was that they were going to make what was arguably the world’s worst aller-retour journey ever: Vilna to Moscow and back (at that time the town was known under its Polish name and had recently been acquired by the Russians in the process of the annihilation of the Polish state). It was June, and they were in a good mood, as the Russian Tsar had recently fled Vilna followed by his quarrelling generals, and they were under the command of possibly the most competent military leader since Alexander the Great: Napoleon Bonaparte. The lack of warm clothing was not going to bother me, however. By the morning the snow had melted, and luckily I was not on my way to Moscow on foot. I was in Vilnius to search for some buttons, preferably made of tin. The story of Napoleon’s buttons and their allegedly fateful role in the disastrous 1812 campaign is widespread among scientists and science teachers. This is partly due to the popular book with the same name by the chemists Penny LeCouteur and Jay Burreson, and I wanted to find out whether there could be any truth in it, or whether it was just another of the legends and rumours that has formed around this war. Briefly, the story goes like this: metallic tin is a dense material (lots of atoms per cubic centimetre) and was supposedly the material used for many of the buttons of what was known as la Grande Armée. Unfortunately, metallic tin has a nasty Mr Hyde variation, known as grey tin.

Chapter 5 examines one of Sha Po’s most fascinating and important periods of cultural development, the Bronze Age, a period during which the local community was making wider and more specialised use of the coastal landscape. On the plateau there was some form of stilt-house settlement associated with the specialised manufacture of fine quartz rings, while on the backbeach we have the region’s best evidence for non-ferrous metallurgy in the form of in situ bronze casting. The evidence for craft specialisation tells us that society was undergoing change and could perhaps support the work of artisans through some form of surplus production of food. Moreover, access to more advanced technology and exotic materials are both indications of a widening of external contacts, trade, and exchange, while a heightened interest in personal ornamentation and display points towards greater competition and the emergence of social hierarchies.

It has been a quiet 20 million years for the pebble: an interlude, at somewhere around 3–4 kilometres under the sea floor. The rock has still been crystallizing, but only very slowly. The water has by now mostly been squeezed out, so little fluid has flowed through that rock. At this depth it is hot, well above 1008°C. The pebble-form is sterile, lifeless. The time is now a little under 400 million years ago. We are in the Devonian Period. Above, at the Earth’s surface, changes have been taking place, but as far as they affected the pebble they could be on another planet. In the sea, the graptolites have been going through an evolutionary rollercoaster, with explosions of diversity separated by bad times, when they only just survive. Soon, one of those bad times will be terminal, and they will disappear from the open seas, never to return. By contrast, the fish are beginning to thrive both in the sea and in rivers and lakes. The land is greening, almost explosively, as plants evolve furiously. None of this affects the future pebble. But something soon will. The sea above has been gradually shallowing, filled in with sediment from the encroaching land. Eventually, it changed, some few million years ago, into a vast coastal plain, traversed by rivers. We are about at the time, now, when that lowland is about to rear up to form a range of mountains that—although much reduced from their early glory—can still be climbed today. What took them so long? For the Iapetus Ocean to the north, which, 50 million years ago, was more than 1000 kilometres across, had effectively disappeared 20 million years ago, the ocean plate sliding beneath the northern continent of Scotland and north America. But on Avalonia, the effect was as if these continents had just slid neatly into place, with only minor distortion of the Avalonian crust (and, in truth, these landmasses did approach each other partly from the side, rather than headon). Did the mountain-building force still come from the north, perhaps as some mysteriously delayed intensification of the vice-like grip that held these landmasses together?

The pebble is on the beach, once more, unmarked by its brief contact with human sentience. Almost unmarked. The fingerprints that it lightly bears will, however, be washed away by the next tide. It has a long future, still, but probably not as a pebble—though quite how long it remains as a pebble may well depend on human action. Not on immediate, direct human action—whether it is scooped up by a digger and converted into concrete for a sea-front esplanade, for instance, or even collected as a souvenir by some passing tourist. Either of these fates should cause only a brief deflection from its long-term future (the esplanade is, after all, only a cliff to be attacked by the elements, while beach souvenirs are soon discarded). A larger perturbation of its trajectory more probably hinges on wider human effects—but more of that anon. We might assume, first, that nature runs its course. A pebble on a beach, its natural environment, is changing all the time. Not long ago, it was part of a slab of slate in a cliff, then it briefly became an angular chunk of rock, before the waves and water smoothed it down. They are still smoothing it, wearing away at it, making it smaller. Even the contact with human hands probably removed a grain or two. A pebble has the appearance of permanence, but it is not permanent. How long does it take to wear down a pebble? This can happen astonishingly quickly. Even over a single tide, being washed backwards and forwards by every incoming wave, a pebble can become detectably lighter—by less than one tenth of one per cent, admittedly, but that weight difference can easily be measured using modern electronic scales. Over a season, on an exposed part of the coast, a pebble can lose between a third and a half of its mass. The rates will vary—on a stormy day the banging of pebbles against each other can produce distinct percussion marks on their surfaces, while on a calm day the attrition rate will drop markedly. Night and day, though, the pebble is disintegrating.

In this chapter we treat plane waves specified by a wave normal and a particle motion vector . Two types of waves, longitudinal waves and shear waves, are observed in solids. For low symmetry directions, there are generally three different waves with the same wave normal, a longitudinal wave and two shear waves. The particle motions in the three waves are perpendicular to one another. Only longitudinal waves are present in liquids because of their inability to support shear stresses. The transverse waves are strongly absorbed. Acoustic wave velocities (v) are controlled by elastic constants (c) and density (ρ). For a stiff ceramic (c ∼ 5 × 1011 N/m2) and density (ρ ∼ 5 g/cm3 = 5000 kg/m3), the wave velocity is about 104 m/s. For low frequency vibrations near 1 kHz the wavelength λ is about 10 m. The shortest wavelengths are around 1 nm and correspond to infrared vibrations of 1013 Hz. Acoustic wave velocities for polycrystalline alkali metals are plotted in Fig. 23.2. Longitudinal waves travel at about twice the speed of transverse shear waves since c11 > c44. Sound is transmitted faster in light metals like Li which have shorter, stronger bonds and lower density than heavy alkali atoms like Cs. The tensor relation between velocity and elastic constants is derived using Newton’s Laws and the differential volume element shown in Fig. 23.3(a). The volume is equal to (δZ1) (δZ2) (δZ3). Acoustic waves are characterized by regions of compression and rarefaction because of the periodic particle displacements associated with the wave. These displacements are caused by the inhomogeneous stresses emanating from the source of the sound. In tensor form the components of the stress gradient are ∂Xij/∂Zk and will include both tensile stress gradients and shear stress gradients, as pictured in Fig. 23.3(b). The force F acting on the volume element is calculated by multiplying the stress components by the area of the faces on which the force acts.

Geomorphology is the study of form and structure of sand dunes. Dunes are found in three types of landscapes: sea coasts and lakeshores, river valleys, and arid regions. Coastal dunes are formed along coasts in areas above the high water mark of sandy beaches. They occur in both the northern and southern hemi sphere from the Arctic and Antarctic to the equator, and in arid and semi-arid regions. They are very common in temperate climates but are less frequent in tropical and subtropical coasts. Dunes are also common around river mouths where the sand carried in water is deposited (Carter et al. 1990b). During floods rivers overflow their banks and deposit sand in river valleys that is subsequently dried by wind and shaped into dunes. In dry regions with less than 200 mm of precipitation per year, the weathering of sandstone and other rocks produce sand that is subject to mass movement by wind because of sparsity of vegetation. There are many similarities in processes and patterns of dune form and structure among these three systems, however each location has its own unique features. In this chapter the emphasis will be on the geomorphology of dune systems along the coasts of oceans and lakes. Coastal geomorphologists have been attempting to classify the coastal land forms but they defy a simple classification because of tremendous variability in plant taxa, sand texture, wind velocity, climate, sand supply, coastal wave energy and biotic influences including human impact. According to Carter et al. (1990b) the great variety of coastal land forms around the world is primarily related to sediment availability, climate, wave energy, wind regime and types of vegetation. Classification based on these criteria would be more useful in distinguishing between shoreline dune forms than the use of subjective terms—for example white, grey or yellow dunes—sometimes employed by plant ecologists (Tansley 1953). Cowles (1899) said ´a dune complex is a restless maze´ because the great topographic diversity depends on changes in the dune terrain from day to day, month to month, season to season and year to year.

Some widely used techniques for the direct physical investigation of the structure of adsorbed surfactant films are introduced. Neutron reflection has yielded very detailed information about adsorbed surfactant films, although it is not readily accessible to many researchers. There are however commercial instruments available for a number of other techniques which are to be found in numerous laboratories. Scanning probe microscopies (STM and AFM) are capable of producing quite remarkable images of surfactant layers on solids and clearly show how surfactants form aggregates at surfaces. Ellipsometry is capable of yielding adsorbed layer thickness and refractive index from which composition with respect to solvent and surfactant can be deduced. The quartz crystal microbalance (QCM) and its variant, QCM-D, can give adsorbed amounts (including hydration in aqueous systems). Brewster angle microscopy (BAM) is a useful tool for the visualization of phase behaviour in surfactant films.

This chapter recounts the early attempts at guessing the inner structure of crystals. The Ancients thought quartz was the result of the congelation of water. The first to think that the symmetry of quartz was due to a hexagonal packing of elementary particles, in the manner of the honeycomb, was Cardano (1550), but the first serious considerations of the different ways to pack globules were by Kepler in his study of six-cornered snowflakes. These ideas were taken up by Hooke and Bartholin. Huygens explained the double refraction of calcite by a stacking of prolate ellipsoids, Guglielmini related the external shapes of crystals to their shapes at the start of growth, and Bergman showed that the calcite scalenohedron can be interpreted as a stacking of cleavage rhombohedra. Our understanding of crystals was further improved by the observation of the constancy of interfacial angles by Steno in quartz, and observation generalized to all crystals by Carangeot and Romé de l’Isle.

This chapter covers the current state of knowledge about how the shear strength (the force needed to slide one surface over another) originates at the atomic level. For adhesive friction, friction originates from the forces needed to move the atoms on one surface over the atomic structure of the opposing surface; the simplest model for adhesive friction is the cobblestone model. The Frenkel–Kontorova model, the Prandtl–Tomlinson model, and molecular dynamic simulations are typically used to show how the atomic structure of the surfaces leads to static friction. One exciting aspect of these friction models is the prediction of superlubricity or negligible friction for incommensurate sliding surfaces, which is now being realized in experiments. Also discussed is why superlubricity is not observed in real-life situations. As atoms and molecules slide over surfaces, kinetic friction originates from phonon and electronic excitations, which are typically studied using the quartz crystal microbalance (QCM).

This chapter examines the manner in which time is conceptualised within the contexts of prehistory and deeper history. By privileging historical records, it shows how the federal recognition process also subordinates oral tradition or archaeological evidence, creating circumstances where dynamic, contingent histories are replaced by strategic essentialism with embedded notions of static and timeless cultures. The chapter looks at quartz crystals placed in the corners of the Magunkaquog building foundation in Ashland, Massachusetts to call attention to parallel processes, a variety of liminality between the ancient past and present (late eighteenth and early nineteenth centuries) — neither past nor present — when ancient beliefs with cultural plasticity were woven into Christian structures. This archaeological example illustrates the presencing of the past and suggests that we cannot understand processes of hybridisation unless we stop dignifying the prehistory-history divide.