61晶体结构613金属结构 HCP的APF 六棱锥体积=(3a3sin60°)c=(3a2sin60°)1.633a 由等边三角形的性质,a=2R 理想HCP晶胞品格参数比c/a=1 g,Co,Ti的比值略低于理想值 明处于略微压缩的状态。 其它金属的c/a值略大于理想值 MetasTructure =上 Structure Radius 614碳结构 0.1363 金刚石晶胞 每亚晶胞2原子 Gold FCC 0.1442|Iron(a 每晶胞8原子 0.1750 BCC 0.1430 Nickel 0.1445 0.1387Cadmiu 0.1490 Silver FCC 0.1445 Zinc HHHH 0.1332 Chromium Cobalt cP0.1253 61晶体结构64碳结构 原子堆砌密度 Atomic packing factor, APF 晶胞参数 原子体积= Fullerenes
6 a 3 a m = c/2 a a/2 3 a m = c a a a c , 1.633 2 3 2 2 = − = 理想HCP晶胞晶格参数比 c/a = 1.633 Mg，Co，Ti的比值略低于理想值，说 明处于略微压缩的状态。 其它金属的c/a值略大于理想值 HCP的APF 6.1 晶体结构 6.1.3 金属结构 底面积= o o sin 60 3 sin 60 2 6 2 2 a a = 六棱锥体积 = （3a2sin60°）c = (3a2sin60°)1.633a 由等边三角形的性质， a = 2R 0.74 [3(2 ) sin 60 ](1.633 2 ) 6 4 / 3 AFP 2 3 = × × = = R R R o π 晶胞体积 原子体积 a c Metal Structure Radius (nm) Metal Structure Radius (nm) Aluminum FCC 0.1431 Molybde num BCC 0.1363 Copper FCC 0.1278 Tungsten BCC 0.1371 Gold FCC 0.1442 Iron (α) BCC 0.1241 Lead FCC 0.1750 Tantalu m BCC 0.1430 Nickel FCC 0.1246 Titanium (α) HCP 0.1445 Platinum FCC 0.1387 Cadmiu m HCP 0.1490 Silver FCC 0.1445 Zinc HCP 0.1332 Chromium BCC 0.1249 Cobalt HCP 0.1253 金刚石晶胞 每亚晶胞2原子 每晶胞8原子 6.1.4 碳结构 6.1 晶体结构 6.1.4 碳结构 原子堆砌密度 Atomic packing factor, APF 3 8R a = 8 3 4 3 πR × 0.34 (8 / 3) 8(4/3 ) APF 3 3 = = R πR 晶胞参数 原子体积＝ 0 8r = 3a a0 Graphite Fullerenes
615陶瓷结构 61晶体结构61.5陶瓷结构 Ionic character of some ceramic materials 立方晶格中的间隙位置 Material Percent lonic character octahedral tetrahedral CMNA 83 18 12 BCC 陶瓷晶体结构的控制因素 Tetrahedral octahedral g The crystal must be electrically neutral; that is, all the cation positive charges must be balanced by an equal number of ar Each ca efers to have as many nearest-neighbor anions as possible. The anions also desire a ma FCO lonic Radii (for a Coordination Number of 6) lonic Radius lonic Radius Anion 0.133 0.140 88883 Stable Unstable
7 6.1.5 陶瓷结构 Material Percent Ionic Character CaF2 89 MgO 73 NaCl 67 Al2O3 63 SiO2 51 Si3N4 30 ZnS 18 SiC 12 Ionic Character of Some Ceramic Materials 立方晶格中的间隙位置 6.1 晶体结构 6.1.5 陶瓷结构 BCC SC 2 1 , 2 1 , 2 1 2 1 ,1, 2 1 octahedral octahedral BCC 4 3 , 2 1 1, tetrahedral FCC 4 3 , 4 1 , 4 1 Tetrahedral FCC 2 1 , 2 1 , 2 1 ,1 2 1 0, octahedral octahedral The crystal must be electrically neutral; that is, all the cation positive charges must be balanced by an equal number of anion negative charges. Each cation prefers to have as many nearest-neighbor anions as possible. The anions also desire a maximum number of cation nearest neighbors. 陶瓷晶体结构的控制因素 Ionic Radius Ionic Radius Cation (nm ) Anion (nm ) Al3+ 0.053 Br- 0.196 Ba2+ 0.136 Cl- 0.181 Ca2+ 0.100 F- 0.133 Cs+ 0.170 I- 0.220 Fe2+ 0.077 O2- 0.140 Fe3+ 0.069 S2- 0.184 K+ 0.138 Mg2+ 0.072 Mn2+ 0.067 Na+ 0.102 Ni2+ 0.069 Si4+ 0.040 Ti4+ 0.061 Ionic Radii (for a Coordination Number of 6) Stable Stable Unstable