Atomic Scale Structure： Atomic Packing and Coordination Numbers Chapter 3 Atomic Scale Structure： Atomic Packing and Coordination Numbers

I. Introduction Atomic packing： arrangement of the atoms surrounding a centered atom or ion ： coordination number  type of bonding, relative size of atoms or ions Atomic packing (Atomic Scale Structure) : a few A  short range order.(SRO) Crystalline structure : > a few nm)  long range order.(LRO) F22

Several important macroscopic properties of materials can be estimated on the basis of only a knowledge of the atoms present, the type of bonding between atoms, and the shape of the bond-energy curve. Other properties such as density, largely depend on the arrangement of the atoms in the solid. The arrangement of atoms within a solid can be principally characterized by the number of nearest neighbors, or coordination number, CN, which is influenced primarily by the type of bonding present and by the relative sizes of the atoms or ions .

II. Radius of Atoms and Ions Atomic radius Ionic radii e.g., Consider the ionic compound CsC1. r(Cl -) + r(Cs +) = X0 (CsCI) Using this procedure, a self-consistent set of ionic radii can be calculated. F 3.1 F 3.2 T 3.1 F 12.3 F 3.2 T 12.3

III. Determination of Coordination Number Coordination Number (CN) ● type of bonding i.e., metallic, covalent, ionic ● relative size of atoms or ions Type of bonding ● Metals：pure metallic element, i.e., composed of one single element e.g., Fe, Cu, Al,…...  metallic bonding

● ceramics：mostly are compounds composed of metallic and nonmetallic elements, i.e., composed of at least two different elements, usually metallic elements form cations, and nonmetallic elements form anions e.g., Al2O3, SiO2, TiO2, AlN, BN, diamond, graphite, …… Usually considered to have ionic bonding,i.e.,being made up of cations and anions. (mostly mixed ionic and covalent bonding, exception： a few with pure covalent bonding, e.g., diamond)

A. Metallic Bonding CN is primarily determined by geometric arrangement (consideration) ＊all atoms：spherical , same size. ＊CN：8-12. ＊usually described by crystalline structure. F3.1 F3.2 T3.1

B. Ionic Bonding F 12.1 F 2.6-1 F 12.2 T 12.2 T 12.3 CN can be determined using the following constraints: (1) cations “touch” anions, (2) the number of anions surrounding a given cation will be as high as geometrically possible, (3) the ions cannot overlap. r/R must always be less than or equal to one, for most ironically bonded compounds, r(cation) < r(anion). r(aion)/r(cation) is used to estimate the CN of cation. If, however, r(anion) < r(cation) then the r(aion)/R(cation) ratio should be used to estimate the CN of the anion. Once the CN of the smaller ion is known, the CN of the larger ion can be determined based on the cation : anion ratio, or the stoichiometry of the compound.

C. Covalent Bonding In contrast to the ionic materials for which CN is determined by geometry, the number of nearest neighbors in a covalently bonded material is determined by the number of electrons in the valence shell of each atom. NB= (8 –NV ) CN=NB (A double bond is counted as two bonds but as one coordination.) 　where NB is the number of covalent bonds formed and NV is the number of valence electrons in the neutral atom. F 12.10 F 12.12 F 12.15 F 12.17

IV. Effects of Coordination Number on Material Properties : density 。atomic mass 。 CN CN density ● Since the CN of most ceramic materials are smaller that that of metallic materials, ceramics are usually lighter (smaller density ) than metals. CN metallic bonding：8-12 covalent bonding：mostly 4 ionic bonding：4-8

linear tetrahedral octahedral cubic planar

f22_03_pg71 Amorphous and Crystalline Atomic scale structure (SRO) Same Crystalline structure (LRO) Different f22_03_pg71.jpg