Earth Materials. John O'Brien

      2.2.4 Atomic and ionic radii

Atomic radii are defined as half the distance between the nuclei of identical, bonded neighboring atoms. Because the electrons in higher quantum levels are farther from the nucleus, the effective radius of electrically neutral atoms generally increases from the top to bottom (row 1–row 7) in the periodic table (see Table 2.3). However, atomic radii generally decrease within rows from left to right (Figure 2.6). This occurs because the addition of electrons to a given quantum level does not significantly increase atomic radius, while the increase in the number of positively charged protons in the nucleus causes the electron cloud to contract as electrons are pulled closer to the nucleus. Atoms with large atomic numbers and large electron clouds include cesium (Cs), rubidium (Rb), potassium (K), barium (Ba), and uranium (U). Atoms with small atomic numbers and small electron clouds include hydrogen (H), beryllium (Be), and carbon (C).

Figure 2.7 Radii (in angstroms) of some common cations in relationship to the atomic radius of the neutral atoms.

      Electrons in the outer, higher energy electron levels are least tightly bound to the positively charged nucleus. This weak attraction results because these electrons are farthest from the nucleus and because they are shielded from the nucleus by the intervening electrons that occupy lower quantum level positions closer to the nucleus. These outer electrons or valence electrons are the electrons that are involved in a wide variety of chemical reactions, including those that produce minerals, rocks, and a wide variety of synthetic materials. The loss or gain of these valence electrons produces anions and cations, respectively.

When atoms are ionized by the loss or gain of electrons, their ionic radii, invariably change. This results from the electrical forces that act between the positively charged protons in the nucleus and the negatively charged electrons in the electron clouds. The ionic radii of cations tend to be smaller than the atomic radii of the same element (Figure 2.7). As electrons are lost from the electron cloud during cation formation, the positively charged protons in the nucleus tend to exert a greater force on each of the remaining electrons. This force draws electrons closer to the nucleus, reducing the effective radius of the electron cloud as it contracts. The larger the charge on the cation, the more its radius is reduced by the excess positive charge in the nucleus. This is well illustrated by the radii of the common cations of iron (Figure 2.8). Ferric iron (Fe⁺³) has a smaller radius (0.64 Å) than does ferrous iron (Fe⁺² = 0.74 Å). Both iron cations possess much smaller radii than neutral iron (Fe⁰ = 1.23 Å) in which there is no excess positive charge in the nucleus.

Figure 2.8 Radii (in angstroms) of some common anions in relationship to the atomic radius of the neutral atoms.

The ionic radii of anions are significantly larger than the atomic radii of the same neutral (uncharged) element (Figure 2.8). When electrons are added to the electron cloud during anion formation, the positively charged protons in the nucleus exert a smaller force on each of the electrons. This allows the electrons to move farther away from the nucleus, which causes the electron cloud to expand, increasing the effective radius of the anion. The larger the charge on the anion, the more its effective radius is increased.

Figure 2.9 Radii (in angstrom units) of some common anions and cations of sulfur in relationship to the neutral atom radius.

The expansion of anions and the contraction of cations are well illustrated by the common ions of sulfur (Figure 2.9). The divalent sulfur (S⁻²) anion possesses a relatively large average radius of 1.84 Å. In this case, the two electrons gained during the formation of a divalent sulfur anion produce a large deficit between positive charges in the nucleus and negative charges in the electron cloud. This leads to a significant increase in the effective ionic radius compared to that of electrically neutral sulfur (S⁰ = 1.03 Å). Neutral sulfur in turn is much larger than the divalent sulfur cation (S⁺² = 0.37 Å) and the very small, highly charged hexavalent sulfur cation (S⁺⁶ = 0.12 Å). Keep in mind that the effective radius of a particular anion does vary somewhat. As we will see in the following sections, it depends on the environment in which bonding occurs, the number of nearest neighbors and the type of bond that forms.

2.3 CHEMICAL BONDS

      2.3.1 The basics

      Atoms in minerals, rocks, and other Earth materials are held together by forces or mechanisms called chemical bonds. The nature of these bonds strongly influences the properties and behavior of these materials. The nature of the bonds is, in turn, strongly influenced by the electron configuration of the elements that combine to produce the mineral, rock or other material.

      Five principle bond types and many hybrids occur in minerals. The three most common bond types are (1) ionic, (2) covalent, and (3) metallic. They can be modeled based on the behavior of valence electrons in the outer quantum levels of atoms. During bonding, valence electrons display varying tendencies to change position based on their periodic properties. In discussing chemical bonds, it is useful to divide elements into those that are metallic and those that are nonmetallic.

      Ionic bonds involve the linking together of metallic and nonmetallic elements, covalent bonds involve the linking of two nonmetallic elements, and metallic bonds involve the linking of two metallic elements. Hybrids between these bond types are common. Minerals with such hybrid or transitional bonds commonly possess combinations of features characteristic of each bond type. Other bond types include van der Waals and hydrogen bonds. Chemical bonding is a very complicated process; the models used below are simplifications designed to make this complex process easier to understand to a reasonable degree.

Another useful concept for understanding chemical bonds, developed originally by Linus Pauling (1929), is the concept of electronegativity (see Table 2.3). Electronegativity (En) is an empirical measure that expresses the tendency of an element to attract electrons when atoms bond. Highly electronegative elements (En > 3.0) have a strong tendency to attract electrons and become anions during bonding. Many column 16 (group VIA) and column 17 (group VIIA) elements are highly electronegative, requiring capture of two or one electrons, respectively, to achieve a stable electron configuration. Elements with low electronegativity (En < 1.5) are electropositive, metallic elements with a tendency to give up electrons to more electronegative elements during bonding to become positively charged cations. Highly electropositive elements include column 1 (group IA) and column 2 (group IIA) elements that tend to release one or two electrons, respectively, to achieve a stable electron configuration. Electronegativity is a very helpful concept in discussions of how atoms