非均匀形核(heterogeneous nucl) surface energy strain energy,s YG radius total free energy volume 4vG energy △G *吴建生、张寿柏《材料制备新技术》上海交通大学出版社， 1996,p.16 Crystal structure of ice ·s.g.:P63/mmc(194) ·a=4.522A,b=7.367A axis a-axis Covalent bond -basat plane a-axia- step prism facc 12
12 非均匀形核 (heterogeneous nucl) f s c r *吴建生、张寿柏《材料制备新技术》上海交通大学出版社，1996，p.16 Crystal structure of ice • s.g.: P63/mmc (194) • a=4.522 Å, b=7.367 Å
Crystal structure of iodargyrite(碘银 矿，Ag)and ice ·Agl ·lce ·s.g.:P63m(186) ·s.g.:P63/mmc(194) ·a=4.592A,b=7.510A·a=4.522A,b=7.367A 籽晶的选择 ·同一种材料的单晶 ·同一种材料的多晶 ·另一种材料但晶体结构相似 13
13 Crystal structure of iodargyrite (碘银 矿, AgI) and ice • AgI • s.g.: P63/m (186) • a=4.592 Å, b=7.510 Å • Ice • s.g.: P63/mmc (194) • a=4.522 Å, b=7.367 Å 籽晶的选择 • 同一种材料的单晶 • 同一种材料的多晶 • 另一种材料但晶体结构相似
3 060u950 晶体生长的平衡衡形态 磷氯铅矿 石英矿 萤石可矿 方铅矿 14
14 ? 晶体生长的平衡形态 萤石矿 方铅矿 磷氯铅矿 石英矿
Equilibrium crystal shape:the Gibbs-Curie-Wulff theorem ·G.ulf,Z.Kist.,34,449(1901) The equilibrium shape of a crystal is determined by minimizing the surface free energy keeping the volume constant PHYSICAL REVIEW VOLUME 82.NUMBER I APR1L1,1951 Some Theorems on the Free Energies of Crystal Surfaces Bell Teephome Laboratories,Murray Hill,New Jersey (Received December 18.1950) of crystals and of no yinvolve proble kinetic athetere smoothly rounded as well as sharp-cornered forms.The condition considerations,it is suggested that a knowledge of the relative is formulated for thermodynamic stability of a fat crystal face free energies ns may with respect to lo the the h vature;and it is concluded that these limitations are not likely to relations between atomic models of crystal surfac be serious for most real substances,though they are serious for certain idealised theoretical models. At equilibrium,the distance of the crystal faces from a point within the crystal are proportional to the corresponding specific surface energies of these faces. 5 6 const hn h3 Most of the natural crystals appear in equilibrium shapes. 15
15 Equilibrium crystal shape: the Gibbs-Curie-Wulff theorem • G. Wulff, Z. Krist., 34, 449(1901) • The equilibrium shape of a crystal is determined by minimizing the surface free energy keeping the volume constant At equilibrium, the distance of the crystal faces from a point within the crystal are proportional to the corresponding specific surface energies of these faces. Most of the natural crystals appear in equilibrium shapes
晶体的平衡形状在几何上 相似于界面能极图中体积 为最小的内接多边形。 01 V11 Vo1 POLAR PLOT OF SURFACE FREE ENERGY SAMPLES Or PANES NORMAL TO RAOIUS VECTORS OF THIS PLOT 一-EQUILIBRIUM PO￥EDRON FIG.1.Typical polar plot of surface free energy for a crystal and '出eWm寞霆生浆筹招材料制备新技木上海交通大学出版社，1996，p27 Bravais法则 ·当晶体生长到最后阶段而保留下来的一 些主要晶面是具有面网密度较高、而面 网间距dhk较大的晶面。 16
16 晶体的平衡形状在几何上 相似于界面能极图中体积 为最小的内接多边形。 v01 v11 l 11 l 01 *吴建生、张寿柏《材料制备新技术》上海交通大学出版社，1996，p.27 Bravais法则 • 当晶体生长到最后阶段而保留下来的一 些主要晶面是具有面网密度较高、而面 网间距dhkl较大的晶面