Structure of Ionic Solids

10 Key excerpts on "Structure of Ionic Solids"

• 

  eBook - PDF

  Crystal Structures

  Lattices and Solids in Stereoview

  • M Ladd(Author)
  • 1999(Publication Date)
  • Woodhead Publishing

    (Publisher)

  For example, if we consider a cube of sodium chloride of side, say, 0.05 mm, then the number of unit cells in that cube is (0.05 * 10 3 ) 3 /(0.564 x 10* 9 ) 3 , or approximately 7 x io 14 There is no unique way in which the multitude of known structures may be subdivided, but a method of classification is desirable and useful. We shall adopt a procedure based on the principal type of interparticle force responsible for cohesion of the crystal structural units in the solid state. Thus, we obtain four classes that may be termed ionic structures, covalent structures, metallic structures and molecular, or van der Waals, structures. Even so, we shall find that certain compounds do not fall clearly into one or other of these classes, so that the final choice is, to some extent, subjective. In this chapter we consider ionic structures. 2.2 IONIC STRUCTURES The structures that we term ionic are formed generally between two species of widely different electronegativity. Electronegativity refers to the tendency of an atom to attract electrons in compound formation; it may be quantified on a relative scale 173 ; Table 2.1 lists the Pauling 18 ' electronegativities for some elements (see also Section 3.3.1). In forming an ionic compound, one species, typically a metal, forms a positive ion by the loss of one electron or more, and the other species, typically a non-metal acquires one electron or more and becomes negatively charged. Then, a Coulombic attractive energy exists between them that is inversely proportional to the distance between the ions and directly proportional to their charges. Specifically, if two ions of numerical charges q+ and q. (including their signs) are distant r apart, the Coulombic, electrostatic energy of Sec. 2.2] Ionic Structures 41 Fig. 2.1. Stereoview of the unit cell and environs of the sodium chloride structure type; the circles in order of decreasing size represent Cl and Na + .

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Structure

  • Gengxiang Hu, Xun Cai, Yonghua Rong(Authors)
  • 2021(Publication Date)
  • De Gruyter

    (Publisher)

  The positive and negative ions must have a certain short-range repulsion to balance with the electrostatic attraction to form a stable crystal. The rejection effect of the short-range repulsion is attributed to the Pauli principle: when two ions are further closer to each other, the electron clouds of the positive and negative ions overlap, and then the electrons tend to make a comovement between the ions. Since these ions have a full shell structure, the codominated electrons tend to occupy the higher energy level so that the energy of the system is increased accompanying with a strong repulsion. The balance of the repulsive interaction and the electrostatic attraction results in the formation of a stable ionic crystal.

  In the study of crystal structures for a long time, some rules of the crystal structure of ionic compounds are found from a large number of experimental data, as well as the crystalline chemistry theory. Before describing structures of the typical ionic crystals, the structural rules of ionic crystal are first introduced.

  2.4.1  Structural rules of ionic crystals

  Based on a plenty of experimental investigations L. Pauling summarized the structural rules of ionic crystals by using the theory of ionic bond as follows.

  1. Rules of anionic coordination polyhedral

  Pauling considered that in the ionic crystals, an anion coordination polyhedron forms around a cation. Also, the balance distance between the positive and negative ions depends on the sum of the ionic radii, while the coordination number of positive ions depends on the ratio of ionic radii. This is Pauling’s first rule, which is consistent with the principle of the minimum internal energy. When this rule is applied, the structures of ionic crystals can be considered that it consists of anion co-ordination polyhedrons connected in a certain way, in which the cations are located at the center of the negative ion polyhedron. Therefore, we can say that the coordination polyhedron is the structural unit of the ionic crystals.

  In order to reduce the total energy of the ionic crystals, the positive and negative ions tend to form close-packed structures with each other as many as possible. A positive ion tends to connect to more negative ions. In other words, one stable structure should have a coordination number as large as possible, while the coordination number depends on the ratio of the negative and positive ion radii, as shown in Table 2.18 . Besides, the structure of the ionic crystal is stable only when the positive and negative ions are in contact with each other. Therefore, for a given coordination number the ratio of the critical ion radius R+ /R−

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Modern Physics

  • Gary N. Felder, Kenny M. Felder(Authors)
  • 2022(Publication Date)
  • Cambridge University Press

    (Publisher)

  Because the ions in an ionic bond have full outer shells, they pack together like spheres. (Figure 11.2 distorts sizes to show the crystal structure clearly; for a more accurate picture, imagine the blue and red dots as electron clouds packed together so closely that they overlap.) Not all ionic crystals follow the interlaced fcc lattice of NaCl. Different crystals have different structures because of the relative sizes of the ions, which determine what packing structure is most efficient. Ionic crystals are generally soluble in water because the polar water molecules (posi- tive on one side and negative on the other) can pull apart ionic bonds. 504 11 Solids • Covalent solids As you might guess, covalent crystals are held together by covalent bonds. For example, diamond is a covalent crystal in which each carbon atom is bonded with four others. The structure of the lattice is determined by the geometry of those bonds; in the case of diamond, the carbon bonds form at equal angles and make a tetrahedral structure. Each pair of adjacent carbon atoms shares two electrons between them. • Metals In metallic crystals like copper and gold, some of the outer electrons from each atom are effectively shared by the entire lattice, somewhat like one enormous covalent molecule. Those collective electrons are referred to as an “electron gas.” The solid is held together by the attraction between the positively charged lattice and the negatively charged electron gas. Because the bonds in a metal aren’t directly between atoms, it’s usually possible to insert different kinds of atoms into the lattice. So it’s easier to make alloys – different materials mixed together with various proportions – from metals than from other types of solids. For example, the bronze age in human history was marked by the discovery that melting copper with a small admixture of tin led to a stronger metal than either one by itself.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Quantum Nanochemistry, Volume Four

  Quantum Solids and Orderability

  • Mihai V. Putz(Author)
  • 2016(Publication Date)
  • Apple Academic Press

    (Publisher)

  The crystalline lattices that present a single type of bonding between the particles are called homodesmics , and those that present multiple types of bonding are called heterodesmics . 4.4.1.1 The Ionic Compounds. The Formal Ions’ Paradigm The ions formation in a particle ensemble is predictable, when, in the first place, stable electronic configurations of the particles are made (elec-tronic configurations with null or maximum spin). In case of the solid substances, the ions formation is much more encountered; on the diversity 426 Quantum Nanochemistry—Volume IV: Quantum Solids and Orderability of the obtaining experimental condition is corresponding a relatively wide variety of ions. To make an example, we specify that the ions Cr 2+ , V 2+ , O 2– , are encountered almost exclusively in solid state. The interaction of the ions in the lattice is of an electrostatic nature. It consists of the attraction between cations and anions and the rejection between ions of the same sign. The force field which is created by a mono-atomic ion is uniformly distributed in the surrounding space. The lack of ionic interaction localization brings to the tendency of the anions and cations to surround them reciprocally as many as possible. The mono-atomic ions (K + , O 2– , etc.) can be considered with a good approximation as being of spherical form. In many crystals there can be encountered polyatomic ions, which bring to a more complicated geom-etry of the structure of the electrostatic field. By polyatomic ions we understand only those groups that can be passed unmodified in another combination. Thus, the group that has a tetrahedral shape (SO 4 ) 2– represents a poly-atomic ion, different than the groups, that are tetrahedral as well, e.g. MgO 4 , from the structure of the spin Al 2 MgO 4 and that are not alike in the chemical interactions.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Manual of Mineral Science

  • Cornelis Klein, Barbara Dutrow(Authors)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  (Data from Evans, R. C. 1952. Crystal chemistry. Cambridge University Press, London.) salt solution. These properties are in stark contrast to properties of the individual, uncombined elements; the shining metal (Na) or the greenish, acrid gas (Cl 2 ). In other words, the properties conveyed to the crystal by its constituent elements are the properties of the ions, not the elements. Ionically bonded crystals are generally of moder- ate hardness and specific gravity, and have fairly high melting points. These crystals are strong when forced together but weak when cleaved or sheared. Once the bonds are broken, recombining them is difficult. They can be recombined by dissolving the ionic solid or by heating it sufficiently to excite the valence electrons. Ionic solids are poor conductors of electricity and heat. The lack of electrical conductivity is due to the stability of the ions, which neither gain nor lose electrons easily. Because the electrostatic charge constituting the ionic bond is evenly spread over the ion, a cation will tend to surround itself with as many anions as can fit around it. This means that the ionic bond is nondirectional, and the symmetry of the resultant crystals is generally high (see Fig. 3.12 and Table 3.10; Chapter 6 for a discus- sion of symmetry). Table 3.10 summarizes selected properties related to the different bond types. Metallic Bond In metallic bonds, the valence electrons owe no affin- ity to any particular nucleus and are free to drift through the structure or even out of it entirely, without disrupting the bonding mechanism. This bond is schematically illustrated in Figs. 3.15a and b, which shows positively charged spherical ions in a dense cloud of mobile, delocalized valence electrons.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Principles of Inorganic Chemistry

  • Brian W. Pfennig(Author)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  As the charge on the cation increases, the 438 8 STRUCTURE AND BONDING IN SOLIDS electrons are held tighter by the positively charged nucleus, and the crystal radius decreases. For example, for four-coordinate Mn n+ , the crystal radii for the 4+, 5+, 6+, and 7+ oxidation states are 39, 33, 25.5, and 25 pm, respectively. Likewise, the greater the coordination number of the cation, the more anionic neighbors it has in the crystalline solid, the greater the degree of anion-anion repulsion, and the larger the crystal radius. Consider, for example, the crystal radii of La 3+ in 6-, 7-, 8-, 9-, 10-, and 12-coordinate environments, which are 103.2, 110, 116.0, 121.6, 127, and 136 pm, respectively. For transition metal cations, the configuration of the d- electrons also plays a role. As we will learn in a later chapter, the five d-orbitals in a six-coordinate, octahedral environment split into two different energy levels: a higher-lying e g (antibonding) set and a lower-lying t 2g set, as shown in Figure 8.78. For the d 4 –d 7 electron configurations, there are two possible ways of arranging the electrons: the high-spin (HS) case, where the electrons fill in the two different sets of orbitals unpaired first, and the low-spin (LS) case, where the electrons pair up in the lower-energy level before populating the higher-lying set of d-orbitals. The ionic radius naturally depends on whether the transition metal ion is HS or LS because the higher-lying e g orbitals are more antibonding. As early as 1929, Linus Pauling, who is arguably the most influential chemist of the twentieth century, developed a set of five principles that can be used to rationalize the structures of many ionic solids. Pauling’s rules, which follow, are based on a completely ionic, hard-spheres, electrostatic model.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Callister's Materials Science and Engineering

  • William D. Callister, Jr., David G. Rethwisch(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  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. For those that do not crystallize, this long-range atomic order is absent; these noncrystalline or amorphous materials are discussed briefly at the end of this chapter. Some of the properties of crystalline solids depend on the crystal structure of the material, the manner in which atoms, ions, or molecules are spatially arranged. There is an extremely large number of different crystal structures all having long-range atomic order; these vary from relatively simple structures for metals to exceedingly complex ones, as displayed by some of the ceramic and polymeric materials. The present dis- cussion deals with several common metallic crystal structures. Chapters 12 and 14 are devoted to crystal structures for ceramics and polymers, respectively. When crystalline structures are described, atoms (or ions) are thought of as being solid spheres having well-defined diameters. This is termed the atomic hard-sphere model in which spheres representing nearest-neighbor atoms touch one another. An example of the hard-sphere model for the atomic arrangement found in some of the common elemental metals is displayed in Figure 3.1c. In this particular case all the atoms are identical. Sometimes the term lattice is used in the context of crystal structures; in this sense lattice means a three-dimensional array of points coinciding with atom posi- tions (or sphere centers). crystal structure lattice (a) (b) (c) Figure 3.1 For the face-centered cubic crystal structure, (a) a hard-sphere unit cell representation, (b) a reduced- sphere unit cell, and (c) an aggregate of many atoms.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Inorganic 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.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Materials Principles and Practice

  Electronic Materials Manufacturing with Materials Structural Materials

  • Charles Newey, Graham Weaver(Authors)
  • 2013(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  Because defects in the structure of a material play an important role in fracture, the tensile strength predicted by the atomic separation model is an order of magnitude higher than the measured tensile strength. There is a very strong (quantum mechanical) repulsion between atoms which get close enough for their cores to interact. The energy trade-off between repulsion of the atomic cores and the attraction due to the outer electrons determines the amount of 'sticking'. 112 3.4 Ionic bonds and ionic crystals Ionically bonded crystals are within a wider group of engineering materials classed as ceramics, being generally hard, brittle and insulating. Sodium chloride (common salt) is often the first ionic compound to which people are introduced, although it is not well known for its engineering properties and after a brief scientific comparison we will deal with it no further. We will however examine various oxides which form structures with significant engineering implications arising from their refractory or electrical nature. Many compounds are not purely ionic. For example silicates contain both ionic and covalent bonds. But here we will discuss materials which have a predominant ionic component. Let's begin by looking at the nature of the bond. 3.4.1 The ionic bond mechanism In ionic solids the atoms are bound together as charged ions. The electrostatic forces involved are not directional so a feature of all ionic crystals is that the nearest neighbours of any ion are several ions of opposite sign. The resulting electrostatic attraction balances the repulsive forces. What are the repulsive effects? There are two: (a) The inevitable core repulsion. This dictates how close the nearest neighbours can get. (b) Ions of like sign repel. Electrostatic forces vary as 1/r 2 — the attraction of (oppositely charged) nearest neighbours is tempered by a repulsion of (similarly charged) next nearest neighbours.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Physical Chemistry

  • 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.

  Sign up to read

  Learn more about book