Bonding in solids

Alternatively, when a powdered crystalline solid diffracts monochromatic X-radiation, the diffraction pattern will be a series of concentric rings, rather than spots, because of the random orientation of the crystals in the sample (Fig. 4.2). The structural information in this pattern is limited however, because even solid compounds that have the same structure but different composition will almost inevitably have different d values, each individual solid chemical compound will have its own characteristic powder diffraction pattern. 

X-Ray powder diffraction patterns are catalogued in the JCPDS data file, and can be used to identify crystalline solids, either as pure phases or as mixtures. Again, both the positions and the relative intensities of the features are important in interpretation of powder diffraction patterns, although it should be borne in mind that diffraction peaJc heights in the readout from the photon counter are somewhat dependent on particle size. 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 mechanism of formation may be deduced—for instance, is it a corrosion product (if so, what is it, and where does it come from) or a contaminant introduced with the feedwater  

Bonding in metals involves delocalization of electrons over the whole metal crystal, rather like the tt electrons in graphite (Section 3.2) except that the delocalization, and hence also the high electrical conductivity, is three dimensional rather than two dimensional. Metallic bonding is best described in terms of band theory, which is in essence an extension of molecular orbital (MO) theory (widely used to represent bonding in small molecules) to arrays of atoms of quasi-infinite extent. 

Because the band is partially filled and extends throughout the crystal, electrons can move freely through it, with the number flowing in any one 

For hydrogen, only the Is orbital is energetically accessible for band formation. For elements of lithium through fluorine, the 2s and, at somewhat higher energy, the three 2p orbitals are available, and, depending on the ways in which the atomic orbitals align with the crystal structure, these may form either a continuous s,p band or a pair of bands with the same 

In oixr discussion on the formation of solids from atoms we encountered hve general types of bonding in solids  

For some of these cases, it is possible to estimate the strength of bonding without involving a detailed description of the electronic behavior. Specifically, for van der Waals bonding and for purely ionic bonding it is sufficient to assume simple classical models. For van der Waals bonding, one assumes that there is an attractive potential 

For the calculation of has using the Lennard-Jones parameters see the following discussion and Table 1.2. 

Use of this potential can then provide a quantitative measure of cohesion in these solids. One measure of the strength of these potentials is the vibrational frequency that would correspond to a harmonic oscillator potential with the same curvature at the minimum this is indicative of the stiffness of the bond between atoms. In Table 1.1 we present the frequencies corresponding to the Lennard-Jones potentials of the common noble gas elements (see following discussion and Table 1.2 for the relation between this frequency and the Lennard-Jones potential parameters). For comparison, the vibrational frequency of the H2 molecule, the simplest type of covalent bond between two atoms, is about 500 meV, more than two orders of magnitude larger the Lennard-Jones potentials for the noble gases correspond to very soft bonds indeed  

A potential of similar nature, also used to describe effective interactions between atoms, is the Morse potential  

In this section, we discuss two models of bonding in solids. The first is a simple, qualitative model for metals the second is more quantitative and therefore more useful. It explains not only the properties of metals but also differences in electrical conductivity of metals, metalloids, and nonmetals. 

Metals are good electrical conductors because the mobile electrons carry the current, and they conduct heat well because the mobile electrons disperse heat more quickly than do the localized electron pairs or fixed ions in other materials. 

The band model proposes that the lower energy MOs are occupied by the valence electrons and make up the valence band. The empty MOs that are higher in energy make up the conduction band. In Li metal, the valence band is derived from the 2s AOs, and the conduction band is derived mostly from an intermingling of the 2s and 2p AOs. In Li2, two valence electrons fill the lowest energy MO and leave the antibonding MO empty. Similarly, in Li metal, 1 mol of valence electrons fills the valence band and leaves the conduction band empty. 

The key to understanding metallic properties is that in metals, the valence and conduction bands are contiguous, which means that electrons can Jump from the filled valence band to the unfilled conduction band if they receive even an infinitesimally small quantity of energy. In other words, the electrons are completely delocalized they are free to move throughout the piece of metal. Thus, metals conduct electricity so well because an applied electric field easily excites the highest energy electrons into empty orbitals, and they move through the sample. 

CHAPTER 12 Intermolecular Forces Liquids, Solids, and Phase Changes 

We have seen that crystalline solids can be divided into three classes, depending on the fundamental particle or unit of the solid, ionic solids consist of oppositely charged ions packed together, molecular solids contain molecules, and atomic solids have atoms as their fundamental particles. Examples of the various types of solids are given in Table 14.4. 

Give an example of an ionic solid, a molecular solid, and an atomic solid. Ionic Solids 

Ionic solids are stable substances with high melting points that are held together by the strong forces that exist between oppositely charged ions. 

The structures of ionic solids can be visualized best by thinking of the ions as spheres packed together as efficiently as possible. For example, in NaCl the larger Cl ions are packed together much like one would pack balls in a box. The smaller Na ions occupy the small spaces ( holes ) left among the spherical Cl ions. 

In a molecular solid the fundamental particle is a molecule. Examples of molecular solids include ice (contains H2O molecules), dry ice (contains CO2 molecules), sulfur (contains Sg molecules), and white phosphorus (contains tetrahedral molecules). 

The Chemical Bond Chemical Bonding Across the Periodic Table, First Edition. 

We classify crystalline solids into categories according to the types of particles in the crystal and the bonding or interactions among them. The four categories are (1) metallic solids, (2) ionic solids, (3) molecular solids, and (4) covalent solids. Table 13-10 summarizes these categories of solids and their typical properties. 

Scanning tnnneling microscope image of nickel atoms on the snrface of nickel metal. 

Metal ions in electron cloud Anions, cations Molecules (or atoms) Atoms 

MetalUc bonds (due to attraction between cations and e s) Electrostatic Dispersion, dipole-dipole, and/or hydrogen bonds Covalent bonds 

O Spheres in the same plane, packed as closely as possible. Each sphere touches six others. 

The MCAT does not directly test your knowledge of the structure of solids beyond Ionic add molecular solids however, it is good to at least be aware dial atoms can form substances in many ways- Molecular solids are actually less common than other types of solids. There has been an MCAT passage on this topic. 

An amorphous solid has no characteristic shape and melts over a temperature range. Glass (Si02) is an amorphous solid usually with some impurities added to lower the melting point. Some substances are capable of forming both crystalline and amorphous solids. 

Polymers are solids with repeated structural units. They can be crystalline or amorphous. Generally, rapid cooling of liquid polymers results in amorphous solids and slow cooling results in crystalline solids. There are many polymers found in living systems. Examples of biopolymers are DNA, glycogen, and protein. 

What is the empirical formula of a neutral compound containing 58.6% oxygen, 39% sulfur, 2.4% hydrogen by mass  

Approximately how many grams of sulfur trioxide are produced by the complete oxidation of 1 mole of sulfur dioxide  

Examples of three types of crystalline solids. Oniy part of the structure is shown in each case. The structures continue in three dimensions with the same patterns, (a) An atomic soiid. Each sphere represents a carbon atom in diamond, (b) An ionic soiid. The spheres represent aiternating Na+ and Cl ions in soiid sodium chioride. (c) A moiecuiar soiid. Each unit of three spheres represents an H2O moiecuie in ice. The dashed lines show the hydrogen bonding among the poiar water moiecuies. 

AIMS To understand the interparticle forces in crystalline soiids. To iearn about how the bonding in metals determines metaiiic properties. 

Ionic solids were also discussed in Section 1 1.5. 

When spheres are packed together, there are many small empty spaces (holes) left among the spheres. 

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If the field gradient has no axial symmetry, then a more complicated expression is found, involving an asymmetry parameter which is often moderate. In particular, the study of this parameter has been useful for the determination of resonance structures and for the understanding of the bonding in solid iodine. The contribution of each of the molecular electrons to q is given by a relation of the form... 

W.C. Hamilton and J.A. Ibers, Hydrogen Bonding in Solids, Benjamin, New York, 1968. 

Application of ligand field spectroscopy to problems of chemical bonding in solids. D. Reinen, Angew. Chem., Int. Ed. Engl., 1971,10, 901-909 (30). 

Bonding in solids may be described in terms of bands of molecular orbitals. In metals, the conduction bands are incompletely filled orbitals that allow electrons to flow. In insulators, the valence bands are full and the large band gap prevents the promotion of electrons to empty orbitals. 

Novack A (1974) Hydrogen Bonding in Solids. Correlation of Spectroscopic and Crystallographic Data. 18 177-216... 

Burdett, J.K. Chemical Bonding in Solids Oxford University Press, New York,... 

Hydrogen bonding in solid ice creates a three-dimensional network that puts each oxygen atom at the center of a distorted tetrahedron. Figure 11-16 shows that two arms of the tetrahedron are regular covalent O—H bonds, whereas the other two arms of the tetrahedron are hydrogen bonds to two different water molecules. 

As described in Section 10-, the bonding in solid metals comes from electrons in highly delocalized valence orbitals. There are so many such orbitals that they form energy bands, giving the valence electrons high mobility. Consequently, each metal atom can be viewed as a cation embedded in a sea of mobile valence electrons. The properties of metals can be explained on the basis of this picture. Section 10- describes the most obvious of these properties, electrical conductivity. 

Probing Hydrogen Bonding in Solids Using Solid State NMR Spectroscopy A. E. Aliev K. D. M. Harris... 

Aliev AE, Harris KDM (2004) Probing Hydrogen Bonding in Solids Using State NMR Spectroscopy 108 1-54... 

Molecular Orbital Theory and Chemical Bonding in Solids... 

MOLECULAR ORBITAL THEORY AND CHEMICAL BONDING IN SOLIDS... 

The bonding in solids is similar to that in molecules except that the gap in the bonding energy spectrum is the minimum energy band gap. By analogy with molecules, the chemical hardness for covalent solids equals half the band gap. For metals there is no gap, but in the special case of the alkali metals, the electron affinity is very small, so the hardness is half the ionization energy. 

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