Crystal Structure of CeramicsCrystal Structure of Ceramics

CHAPTER Crystal Structure ： Crystal Structure of Ceramics I Introduction to Ceramics  Chemical Composition mostly are compounds composed of metallic and nonmetallic elements, i.e., composed of at least two different elements, usually considering metallic element as cation, and nonmetallic element as anion example ： Al2O3, SiO2, TiO2, AlN, BN, …… exceptions ： diamond, graphite,……  Bonding • mostly mixed ionic and covalent bonding T 12.1 • % ionic character = ( 1-e –(0.25)(XA-XB)2 ) 100 • exception ： diamond, silicon, graphite, ……  Coordination number (CN) ： 4, 6, and • considering the ceramics to be made up of cations and anions • CN relative size of cation and anion  Crystal Structure • considering the ceramics to be made up of cations and anions II General Features of Ceramic Crystal Structures  The crystal sturctures may be thought of as being composed of cations, and anions F 12.2 F 3.7-4  Two characteristics influencing the crystal structure: ˙magnitude of the electrical charge (electrically neutral) ˙relative sizes of the cations and anions ( CN)  The chemical formula of a compound indicates the ratio of cations to anions, for example: CaF2., Ca+2 : F-1=1:2 (the crystal must be electrically neutral)  Basis (group) or lattice point # 18 F 3.3-1 ˙metals ： one basis usually represents one atom  all the atoms are located at the positions of lattice points, i.e., there are atoms only at the positions of lattice points (lattice sites) ˙ceramics ： one basis usually represents at least one cation and one anion F 24.3 e.g., NaCl ： one Na+ and one ClF 3.3-1 ZnO ： one Zn+2 and one O-2 CaF2 ： one Ca+2 and two F-1 F 3.7-3 F 3.7-4 F 3.7-3 one lattice point represents at least one cation and one anion F 3.7-2 F 3.7-4 If the lattice point is assigned to the center of the anion, the cations will not be at the positions of lattice points Where are the cations accommodated ：  Interstices ： the space among lattice points sublattice III Interstices in Crystal Structure Interstices ≡ Interstitial site ≡Interstitial position ≡ sublattice A Interstices in SC Structure 1 , , cube at 2  location ： center of the number ： one per unit cell shape ： cubic CN ： rcation / ranion = 0.732~1.0  example ： CsCl     Interstices T 12.2  Shape of interstices ： the geometric shape by connecting straight lines through all the nearest surrounding atoms (or ions) F 11.5 B Interstices in the FCC F 11.7 Structure  the largest hole in an FCC structure is at the center of the unit cell and at the center of each edge F 12.8  It has eight sides, celled an octahedral site There are four octahedral sites per FCC  i.e.,12 1 / 4 11 unit cell T 12.2  CN =  rcation / ranion = 0.414~0.732  the size of the octahedral hole is defined as the F 3.6-1 4r / k /can r 0be 414 a 2r of2kthealargest   FCC   radius sphere that placed An atom within it roughly 40% of the size of the host atoms can “fit” into an octahedral interstitial position in the FCC structure F 11.9  the FCC sturcture also contains tetrahedral sites, in the l/4, m/4, n/4 positions, where l, m, and n are or Each cell contains eight of these ¼, ¼,, ¼-type tetrahedral sites The k/r ratio for tetrahedral sites is 0.225 F 11.10 F 11.11 Atoms up to ~20% of the size of the host atoms can “fit” in the tetrahedral positions in FCC structures F 12.7 F 3.7-4 F 3.7-3 F 3.6-1 C Interstices in the BCC Structure  The BCC structure also contains both octahedral and tetrahedral sites  the octahedral sites are located in the center of each face and the center of each edge, giving a total of six sites per a unit 2r cell 2k  a  BCC  4r /    k / r 0.155 The tetrahedral sites in BCC structures are located in the ¼, ½, 0-type positions, which are on the {100} faces, a total of 12 tetrahedral sites per unit cell, k/r =0.29 F 3.3-1 D interstices in the HCP Structure F 3.6-1  Also contains both octahedral and tetrahedral interstices  octahedral sites per “big” cell or sites per unit cell  k/r = 0.414  12 tetrahedral sites per big cell or per unit cell Each small unit cell contains 2, each edge contains 2×(1/3) and are located at the center line  k/r = 0.225  Since both FCC and HCP are close-packed crystal structures, the relative sizes of the interstitial sites are the same in these two types of crystals F 11.15 T 3.6-1 10