Technology & Engineering
Crystalline Solids
Crystalline solids are materials with a highly ordered atomic structure, where the atoms or molecules are arranged in a repeating pattern. This results in distinct geometric shapes and well-defined melting points. Examples of crystalline solids include salt, diamond, and quartz. Their organized structure gives them unique properties, such as transparency and electrical conductivity, making them important in various technological applications.
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12 Key excerpts on "Crystalline Solids"
eBook - PDFMaterials Science and Engineering
An Introduction
- William D. Callister, Jr., David G. Rethwisch(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
For Crystalline Solids, the notion of crystal structure is presented, specified in terms of a unit cell. The three com- mon crystal structures found in metals are then detailed, along with the scheme by which crystallographic points, directions, and planes are expressed. Single crystals, polycrys- talline materials, and noncrystalline materials are considered. Another section of this chapter briefly describes how crystal structures are determined experimentally using x-ray diffraction techniques. 3.1 INTRODUCTION Solid materials may be classified according to the regularity with which atoms or ions are arranged with respect to one another. A crystalline material is one in which the atoms are situated in a repeating or periodic array over large atomic distances—that is, long-range order exists, such that upon solidification, the atoms will position themselves crystalline 3.2 FUNDAMENTAL CONCEPTS Crystal Structures The properties of some materials are directly related to their crystal structures. For example, pure and undeformed magnesium and beryllium, having one crystal structure, are much more brittle (i.e., fracture at lower degrees of deformation) than are pure and undeformed metals such as gold and silver that have yet another crystal structure (see Section 7.4). Furthermore, significant property differences exist between crystalline and noncrystalline materials having the same composition. For example, noncrystalline ceramics and polymers normally are optically transparent; the same materials in crystalline (or semicrystalline) form tend to be opaque or, at best, translucent. 50 • Chapter 3 / The Structure of Crystalline Solids in a repetitive three-dimensional pattern, in which each atom is bonded to its nearest- neighbor atoms. All metals, many ceramic materials, and certain polymers form crystal- line structures under normal solidification conditions.
- William D. Callister, Jr., David G. Rethwisch(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
For Crystalline Solids, the notion of crystal structure is presented, specified in terms of a unit cell. The three com- mon crystal structures found in metals are then detailed, along with the scheme by which crystallographic points, directions, and planes are expressed. Single crystals, polycrys- talline materials, and noncrystalline materials are considered. Another section of this chapter briefly describes how crystal structures are determined experimentally using x-ray diffraction techniques. 3.1 INTRODUCTION Solid materials may be classified according to the regularity with which atoms or ions are arranged with respect to one another. A crystalline material is one in which the atoms are situated in a repeating or periodic array over large atomic distances—that is, long-range order exists, such that upon solidification, the atoms will position themselves crystalline 3.2 FUNDAMENTAL CONCEPTS Crystal Structures The properties of some materials are directly related to their crystal structures. For example, pure and undeformed magnesium and beryllium, having one crystal structure, are much more brittle (i.e., fracture at lower degrees of deformation) than are pure and undeformed metals such as gold and silver that have yet another crystal structure (see Section 7.4). Furthermore, significant property differences exist between crystalline and noncrystalline materials having the same composition. For example, noncrystalline ceramics and polymers normally are optically transparent; the same materials in crystalline (or semicrystalline) form tend to be opaque or, at best, translucent. 3.3 Unit Cells • 51 in a repetitive three-dimensional pattern, in which each atom is bonded to its nearest- neighbor atoms. All metals, many ceramic materials, and certain polymers form crystal- line structures under normal solidification conditions.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Research World(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 3 Solid Single crystalline form of solid Insulin. Solid is one of the major states of matter. It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a gas does. The atoms in a solid are tightly bound to each other, either in a regular geometric lattice (Crystalline Solids, which include metals and ordinary water ice) or irregularly (an amorphous solid such as common window glass). The branch of physics that deals with solids is called solid-state physics, and is the main branch of condensed matter physics (which also includes liquids). Materials science is primarily concerned with the physical and chemical properties of solids. Solid-state chemistry is especially concerned with the synthesis of novel materials, as well as the science of identification and chemical composition. ________________________ WORLD TECHNOLOGIES ________________________ Metamorphic banded gneiss Microscopic description Model of closely packed atoms within a crystalline solid. ________________________ WORLD TECHNOLOGIES ________________________ The atoms, molecules or ions which make up a solid may be arranged in an orderly repeating pattern, or irregularly. Materials whose constituents are arranged in a regular pattern are known as crystals. In some cases, the regular ordering can continue unbroken over a large scale, for example diamonds, where each diamond is a single crystal. Solid objects that are large enough to see and handle are rarely composed of a single crystal, but instead are made of a large number of single crystals, known as crystallites, whose size can vary from a few nanometers to several meters. Such materials are called polycrystalline. Almost all common metals, and many ceramics, are polycrystalline.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 3 Solid Single crystalline form of solid Insulin Solid is one of the major states of matter. It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a gas does. The atoms in a solid are tightly bound to each other, either in a regular geometric lattice (Crystalline Solids, which include metals and ordinary water ice) or irregularly (an amorphous solid such as common window glass). The branch of physics that deals with solids is called solid-state physics, and is the main branch of condensed matter physics (which also includes liquids). Materials science is primarily concerned with the physical and chemical properties of solids. Solid-state chemistry is especially concerned with the synthesis of novel materials, as well as the science of identification and chemical composition. ________________________ WORLD TECHNOLOGIES ________________________ Metamorphic banded gneiss Microscopic description Model of closely packed atoms within a crystalline solid ________________________ WORLD TECHNOLOGIES ________________________ The atoms, molecules or ions which make up a solid may be arranged in an orderly repeating pattern, or irregularly. Materials whose constituents are arranged in a regular pattern are known as crystals. In some cases, the regular ordering can continue unbroken over a large scale, for example diamonds, where each diamond is a single crystal. Solid objects that are large enough to see and handle are rarely composed of a single crystal, but instead are made of a large number of single crystals, known as crystallites, whose size can vary from a few nanometers to several meters. Such materials are called polycrystalline. Almost all common metals, and many ceramics, are polycrystalline.
eBook - PDF- Wenceslao González-Viñas, Héctor L. Mancini(Authors)
- 2015(Publication Date)
- Princeton University Press(Publisher)
In solids, atoms or molecules are not like isolated entities. On the contrary, their 1 Also, there is the Bose-Einstein condensate state. Crystalline Solids 7 properties are modified by their proximity to other atoms or molecules, which modify the energy levels of their outer electrons. Solids whose structures have spatial regularity or periodicity are known as crystalline; solids that have no order are called amorphous (the experimental determination of these structures is briefly treated in section 2.6). There are also intermediate types of materials, as shown in section 1.1. A complete theory of these materials must correlate macroscopic properties like elasticity and hardness, electrical and thermal conductivity, and optical reflectivity with their spatial structures. Some general properties are due to the kind of bond between the solid constituents. This is the initial criterion for the classification that we use. 1. Ionic materials (ionic crystals). A regular distribution of positive and negative ions results when some valence electrons are transferred from one component to another (fig- ure 2.1), which is the case for NaCl, KCl, and CsCl, among other materials. The atoms are distributed in a stable way because of the very strong electric interactions. For example, the distance between Na + and Cl − in NaCl is 2.81 × 10 −10 m. Ionic materials are poor conductors of heat and electricity, hard, brittle, and have a high melting point. The atoms can absorb energy in the far infrared (< 1 eV), creating, for example, a vibrating mode in the crystal lattice. Figure 2.1 Scheme of an ionic solid. 2. Covalent materials. As we see later (figure 2.8), there is a continuous gradation between ionic and covalent bonds. Nevertheless, a pure covalent bond joins atoms direc- tionally, as with covalent molecules (figure 2.2).
eBook - PDF- George C. King(Author)
- 2023(Publication Date)
- Wiley(Publisher)
8 Solids In Chapter 2, we discussed why a substance occurs in gaseous, liquid, or solid form. We saw that it was due to a competition between the binding energy of the constituent molecules and their thermal, kinetic energy. In gases, the kinetic energy dominates and the molecules are essentially free to move around their container, unaffected by their neighbours except for elastic collisions. Solids lie at the other extreme. In solids, the binding energy dominates and the molecules or atoms are tightly bound and closely packed together rigid. This results in the most characteristic property of solids. They have appreciable stiffness and maintain their shape. Solids appear in a wide variety of forms. Of these, Crystalline Solids provide an ideal form to understand the structure and properties of solids. This is because of their high degree of regularity; a reoccurring pattern of atomic positions that extends over many atoms. Consequently, we will focus most of our attention on the crystalline state of matter. Nearly everything we know about crystal structures has been learnt from dif- fraction experiments. In this chapter, we introduce the principles of X-ray crystallography and how it is used to determine crystal structure. We also relate the properties of solids to the forces acting between their constituent atoms. This follows on from our discussion of interatomic forces in Chapter 2. 8.1 Types of solids Solids may be classified as crystalline, amorphous, or polymeric. We may distinguish between crystalline and amorphous solids as follows. At sufficiently low temperatures, most substances will condense to form a solid. If the substance is cooled sufficiently slowly, the atoms have time to arrange themselves into a reg- ular array with long-range order. By this, we mean that there is a well-defined spatial relationship between atoms that are far from each other, i.e. much further than the mean distance between the atoms.
eBook - PDFPhases of Matter and their Transitions
Concepts and Principles for Chemists, Physicists, Engineers, and Materials Scientists
- Gijsbertus de With(Author)
- 2023(Publication Date)
- Wiley-VCH(Publisher)
260 10 Solids In this chapter, we discuss the third type of “bricks”: aspects of structure, bonding, and dynamics of solids. Contrary to our treatment of gases and liquids, the dielectric behavior of solids, which is strongly related to ferroelectricity, is not discussed in this chapter but in Chapter 17. We start with lattice concepts and deal subsequently with perfect structures. Thereafter, we continue with some dynamical aspects and an overview of defects in crys- tallographic structures. Finally, we discuss a macroscopic approach to solids. An overview of the various types of solids precedes this all. 10.1 Inorganics and Metals Crystalline Solids can be divided into single crystals and polycrystals and for both a regularly ordered structure exists at an atomic scale. This structure is largely maintained throughout the whole material in single crystals, while in polycrystals regions with different crystallo- graphic orientation exist. These regions are referred to as grains and the boundaries between them as grain boundaries. X-ray diffraction indicates the presence of long-range order for Crystalline Solids (Figure 10.1a), while for amorphous solids and glasses, long-range order is absent (Figure 10.1b), although the local coordination may be similar to that in the corre- sponding crystalline solid. Crystalline Solids generally show a distinct melting point. Below the melting point the crystalline structure is present, while above the melting point an amorphous, liquid struc- ture arises. Despite the long-range order, various defects may be present in single crystals (Section 10.10). They can be divided into point defects (interstitials, vacancies, substitutional atoms), line defects (dislocations), planar defects (stacking faults), and volume defects (inclu- sions, pores) (Figure 10.1c).
eBook - PDF- David Ball(Author)
- 2014(Publication Date)
- Cengage Learning EMEA(Publisher)
21.1 Synopsis First, we will consider the general types of solids. Many solids do not exist as a ran-dom arrangement of atoms and molecules. Some do, but we will focus on those solids that exist as some regular arrangement of atoms or molecules. We will find that there are only a few possible ways for regular arrangements, called crystals, to exist. First, we will describe those ways. It turns out that the regularity of crystals can be described by a very small arrangement of atoms and molecules; this very small arrangement, repeated many times in three dimensions, can tell us a lot about the properties of the solid. How do we determine these regular arrangements? As with spectroscopy, we can use electromagnetic radiation as a probe. But rather than absorbing or emitting radiation, Crystalline Solids can diffract radiation under certain conditions. These conditions are dictated by the structure of the crystal, and there is a simple rule for relating the diffraction effect to the crystal’s structure. We will also find that the type of crystal a certain compound makes is not necessarily arbitrary, that there is a recognizable energy of interaction between the components of certain crystals, that crystals are not perfect, and that society actually takes advantage of such imperfections in a big way. The Solid State: Crystals 21 21.1 Synopsis 21.2 Types of Solids 21.3 Crystals and Unit Cells 21.4 Densities 21.5 Determination of Crystal Structures 21.6 Miller Indices 21.7 Rationalizing Unit Cells 21.8 Lattice Energies of Ionic Crystals 21.9 Crystal Defects and Semiconductors 21.10 Summary Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience.
eBook - PDFMaterials in Mechanical Extremes
Fundamentals and Applications
- Neil Bourne(Author)
- 2013(Publication Date)
- Cambridge University Press(Publisher)
A.1 Structures A.1.1 Crystalline and amorphous There are two classes of material commonly encountered: Crystalline Solids where atoms are at ordered positions; and amorphous substances where their location follows a distribution of interatomic spacings and where the structure is disordered. Crystalline materials are formed by cooling from a liquid where material is dissolved in the fluid. If forming from melt, small crystals nucleate from inhomogeneities, growing until they fuse to form a polycrystalline microstructure. A non-crystalline material with no long-range order is termed amorphous or glassy. Ionically bonded substances crystallise readily and are commonly encountered in nature as are covalent crystals such as diamond and 492 Appendix A: Topics from materials science silica. Polymers are found in amorphous and partially crystalline states where not only interatomic, but also Van der Waals’ bonding is important. The theory of cohesion underlying that of strength is defined by the electrostatic attractions between atoms: the valence electrons which form bonds below the finis extremis in condensed matter. There are different bonding types including covalent with Sigma and Pi bonding, ionic, and metallic and weaker bonds including hydrogen and Van der Waals’ forces. Van der Waals’ attractions exist because of correlations in the fluctuating polarisations of nearby electron distributions which result from quantum dynamics. The result of such interactions is a necessarily anisotropic force field acting over longer distances. Covalent bonding results from the sharing of electrons in an orbital so that they are delocalised. However, there is a strong directionality associated with the bond that means that covalent solids are strong in compression since slip is difficult but weak in tension which results in them being brittle.
eBook - PDFMaterials Science and Engineering, P-eBK
An Introduction
- William D. Callister, Jr., David G. Rethwisch, Aaron Blicblau, Kiara Bruggeman, Michael Cortie, John Long, Judy Hart, Ross Marceau, Ryan Mitchell, Reza Parvizi, David Rubin De Celis Leal, Steven Babaniaris, Subrat Das, Thomas Dorin, Ajay Mahato, Julius Orwa(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
All unit cells interlock in the same way and have the same orientation. Single crystals exist in nature, but they can also be produced artificially. They are ordinarily diffi- cult to grow because the environment must be carefully controlled. If the extremities of a single crystal are per- mitted to grow without any external constraint, the crystal assumes a regular geometric shape having flat faces, as with some of the gemstones; the shape is indicative of the crystal struc- ture. An iron pyrite single crystal is shown in figure 3.18. Within the past few years, single crystals have become extremely important in many modern technologies, in particular elec- tronic microcircuits, which employ single crys- tals of silicon and other semiconductors. 3.14 Polycrystalline materials Most Crystalline Solids are composed of a collection of many small crystals or grains; such materials are termed polycrystalline. Various stages in the solidification of a polycrystalline specimen are represented schematically in figure 3.19. Initially, small crystals or nuclei form at various positions. These have random crystallographic orientations, as indicated by the square grids. The small grains grow by the successive addition from the surrounding liquid of atoms to the structure of each. The extremities of adjacent grains impinge on one another as the solidification process approaches completion. As indicated in figure 3.19, the crystallographic orientation varies from grain to grain. Also, there exists some atomic mismatch within the region where two grains meet; this area, called a grain boundary, is discussed in more detail in section 4.6. 3.15 Anisotropy TABLE 3.4 Modulus of elasticity values for several met- als at various crystallographic orientations Modulus of elasticity (GPa) Metal [100] [110] [111] Aluminium 63.7 72.6 76.1 Copper 66.7 130.3 191.1 Iron 125.0 210.5 272.7 Tungsten 384.6 384.6 384.6 Source: R.
eBook - PDF- A.K. Macpherson(Author)
- 2012(Publication Date)
- North Holland(Publisher)
Although this theory is, at present, incomplete, it a p p e a r s that the development of this kind of theory will be essential to future research. T w o chapters discussing the most impor-tant numerical m e t h o d s for modelling then follow. T h e concluding chapter gives a brief outline of some of the special experimental techniques used in material studies at the a t o m i c level. 4 Structure of Solids [Ch. 1 In this introductory chapter, the general principles of crystalline structure will be presented. As in all fields of science, a characteristic terminology has developed a n d it is necessary to provide a brief introduction to lattice terminology. A discussion of the type of macroscopic properties which m a y be predictable will follow. A survey of the binding energies in materials is necessary to place the macroscopic, as c o m p a r e d to microscopic, properties in perspective. T h e chapter will conclude with a brief description of the X-ray crystallography which will be useful in C h a p t e r 9. 1.2 Crystal Structures Progress in the study of solids has utilized the fact that m o s t materials are formed in a regular crystal lattice. T h e lattices contain translational sym-metry. This m e a n s that the a r r a n g e m e n t of a t o m s a b o u t each lattice site will be the same. Mathematically, the lattice sites with translational symmetry m a y be expressed in terms of three n o n -c o p l a n a r basic vectors χ γ , x 2 , x$ a n d the integers Z l 5 Z 2 , Z 3 as L = l l X l + l 2 x 2 + hx 3 . (1.1) T h e lattice vector s h o w n in Fig. 1.1 represents the lattice site (2, 1,1). T h e crystal can be represented by a collection of identical three-dimensional shapes which are repeated to fill the whole crystal. This shape is k n o w n as a unit cell. A typical cell would be the volume defined by ΧχΧ 2 χ 3 m Fig. 11· T h e cell can have m a n y different shapes a n d contain m o r e t h a n one a t o m . If the unit cell contains only o n e a t o m a n d t h a t is in the centre of the cell, it is k n o w n as a Bravais lattice. A useful unit cell is the W i g n e r -S e i t z cell. *5 Fig. 1.1. Lattice vector L in a lattice:
eBook - PDFInorganic Chemistry
An Industrial and Environmental Perspective
- Thomas W. Swaddle(Author)
- 1997(Publication Date)
- Academic Press(Publisher)
For example, a solid deposit accumulating in a heat exchanger can be quickly identified from its X-ray powder diffraction pattern, and its source or mech- anism of formation may be deducedmfor instance, is it a corrosion product (if so, what is it, and where does it come from) or a contaminant introduced with the feedwater? 4.2 Bonding in Solids Bonding in solids takes several forms. Some elements such as carbon or com- pounds such as silica (SiO2 in its various formsusee Section 7.5) can form quasi-infinite networks of covalent bonds, as discussed in Section 3.2; such Crystalline Solids are typically very high melting (quartz has mp 1610 ~ On the other hand, small, discrete molecules like dihydrogen (H2) or sulfur ($8, Section 3.4) interact only weakly with one another through van der Waals forces (owing to electric dipoles induced by the electrons and nuclei of one molecule in the electron cloud of a neighbor and vice versa) and form low melting crystals (H2 has mp -259 ~ a-S melts at 113 ~ When a metal M of low electronegativity (X) combines with a nonmetal X of high X, the product is likely to be a high-melting solid consisting of ions M m+ and X x-, held together in a regular pattern (the crystal lattice) by electrostatic forces rather than electron-sharing bonding (covalency). The energy of these electrostatic interactionswcalled the lattice energy, U-- makes formation of the ionic solid possible by compensating for the energy 72 Chapter 4 Crystalline Solids inputs, such as ionization potential needed to form the ions, and is clearly dependent to some degree on the structure of the crystal at the atomic or molecular level (Section 4.7). Bonding in metals involves delocalization of electrons over the whole metal crystal, rather like the 7r electrons in graphite (Section 3.2) except that the delocalization, and hence also the high electrical conductivity, is three dimensional rather than two dimensional.
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