晶体学课件.ppt
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1、Crystallography Dr.S.Q.Liang Topic I: the 3W for our study 1.Ethics of Graduate Study- Why? . Curiosity to be produced by education Ask for entertainment 2.What the targets of the graduate study? ( ?):knowledge (?):methods (?):thinking ,3.Stratagy And Philosophy forAdvanced Study-the Ways to get the
2、 goals a:be hard, but should be creative b:be active, but not impetuous c: be patient, step by step Simple Complex Specific General Macro Micro Theoretical Applied,Topic II: Four Key Words,Structures Characteristics Relationship Practice,Topic III.About Science (Personal Opinions) Natural Phenomena:
3、 Language Description concepts,definitions,laws Physical Description properties, pictures, models, Mathematic Description symbology,formulas, equations. Should be clear as much as possible,we knew: symmetry of the crystals( point ,translation) 7 crystal systems; 14 Space Lattice (Bravis lattice); sy
4、mbology for lattice points(x,y,z), lattice direction uvw, lattice plane (hkl), their relationships; Reciprocal Space lattice Why 7C.S.? Why 14B.L.? What is the key basis for the classification of C.S., S.L.?,Topic IV.About Crystallography,Things we did not know: What are 32 point groups? What are 23
5、0 space group? What are the relationships between them and the crystal structures, properties of crystals.?,In the study of Crystallography there is a key link-symmetry of the crystals. Remember: the symmetry even is the key to open the door for everything from universe to people , to molecules, to
6、crystals.,Some Ref.Books for Reading 1. 固体科学中的空间群G.本斯著,俞文海译,高等教育出版社,1981年 2 Space Groups for Solid State Scientists G.Burns, A.M.Glazer,Academic Press,1978年 3 晶体学,俞文海,中国科大出版社 4近代晶体学基础,张克从,科学出 版社,1987年 5 梁敬魁,粉末衍射法测定晶体结构,科学出版社,2003年,Crystallography II,Group Theory I-32 point group of the crystal (the
7、first classification) 1.Introduction Crystal = Lattice structure basis 1)Point symmetry 7 C.S. primitive 18011807 lattice 2) Point symmetry Geometric 14B.L. Crystallo- graphy Translational symmetry 1818-1839,Crystal = Lattice structure basis 18011830 3)Point symmetry 32 point group of crystals To de
8、scribe the physical properties of the crystals in quantity and quality,. 1 Monoclinic 1 1 Lattice 2 2 2 basic structure unit The point group can be regarded as the first classification of the crystal,Same crystal system Same Bravis lattice Different basis unit content Different point symmetry collec
9、tions Different crystals This means we can use the point symmetry collection to classify the crystals. By this way, we get 32 point groups Other reasons for the point group study To obtain 32 point system patterns. If adding them to 14B.L., we can obtain some of 230 space groups( the general structu
10、re of the crystals),To symbolize all symmetry operation possessed by crystals. To describe the physical properties of crystal. The essential characteristics of point symmetry collections The production of any two operation is also a member of the collection ( closure). The collection must include an
11、 identity 1 (E) For each operation R, there is an inverse R-1, which is included in the collection to meet R.R-1=1 The multiplication of operations are associative, (AB)C=A(BC) In mathematics, this specific collection is called a group (群).,The order (阶) of group : the number of the elements in the
12、group. Point group (点群) of crystals: 4, 42=2,43, 1 2, 1 1, 4, 42=2,43, 1 2, 1 1,Summary of the crystal systems 1 Triclinic 1 2 Monoclinic Orthorhombic 2 3 Trigonal Cubic 3 4 4 Tetragonal 6 6 Hexagonal,In each crystal, there are different point symmetry collections at different point positions. The h
13、ighest point symmetry collection is called the point group of the crystal. 2. the procedure of 32 point group of the crystal From the pure math combination theory point of view , all possibilities of the combination from 1. 2, 3, 4, 6, 1, 2, 3, 4, 6 are C101+C102+.+C1010,Then check each possibility
14、Meet the crystal system condition? Meet the four basic requirements of the group? If so, we get one point group of the crystal, or vice versa. Some disadvantages of combination method : have enormous possibilities make some confuses need a lot of combination laws of the symmetry operation In order t
15、o overcome these defects, its better for us to discuss the point group for each crystal system individually.,The procedure is that adding more symmetries in a certain crystal system, if these new symmetry elements additions still remain the crystal condition, and also meet the four basic requirement
16、s of the group . We get one point group which below to this crystal system. 3. The crystallographic point group for each crystal system 3.1 Triclinic In this system, we have 1(E) or/ and 1(i) point symmetries. Any other point symmetry elements addition is not allowed since this addition will change
17、the crystal Condition. So we have two point group in Triclinic They are 1, 1,1,Just the same as the symmetry description, we have 4 ways to describe the point group. Symbology Geometry Mathematics Language International Schoenflies 1 C1 general equivalent positions E . 1 S2 symmetry element distribu
18、tion E,i .,1 Triclinic 1 1 Lattice different basic structure unit in the same C.S.,Background knowledge: Stereographic projection 极射赤面投影 N pole A 2-D method to describe the relationship of points, lines, and planes in 3-D. general position in N hemisphere and projection general position in S hemisph
19、ere and projection S pole the enantiomorphical position and its projection 1(C1) 1(S2),The concept of Holosymmetric point group. (全对称点群) the point group in the crystal system with the largest number of symmetry operation. The holosymmetric point group of Triclinic is 1 (S2). 3.2 Monoclinic According
20、 to the definition of this C.S. , we can discuss the possibilities of the point group in monoclinic . 2 2 Five possibilities 1, 1, 2, 2,1 2 combination 1, 2 a point group in Monoclinic,Called 2 (C2) b) 1 2 combination 1,2, called m (C1h),c) 1 2 combination 1002001= -1 0 0 -1 0 0 = 1 0 0 0 -1 0 0 -1
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