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1、材料科学基础Fundamental of Materials Science,Prof: Tian Min Bo Tel: 62795426 ，62772851 E-mail: Department of Material Science and Engineering Tsinghua University. Beijing 100084,Lesson three,2.1 Space Lattice,2.1.1 Crystals versus non-crystals 1. Classification of functional materials,Chapter 2,Fundamenta
2、ls of Crystallography,2. Classification of materials based on structure Regularity in atom arrangement periodic or not (amorphous),Crystalline: The materials atoms are arranged in a periodic fashion. Amorphous: The materials atoms do not have a long-range order (0.11nm).,Single crystal: in the form
3、of one crystal grains Polycrystalline: grain boundaries,2.1.2 Space lattice 1. Definition: Space lattice consists of an array of regularly arranged geometrical points, called lattice points. The (periodic) arrangement of these points describes the regularity of the arrangement of atoms in crystals.,
4、2. Two basic features of lattice points Periodicity: Arranged in a periodic pattern. Identity: The surroundings of each point in the lattice are identical.,A lattice may be one , two, or three dimensional two dimensions,Space lattice is a point array which represents the regularity of atom arrangeme
5、nts,Three dimensions,Each lattice point has identical surrounding environment,2.1.3 Unit cell and lattice constants Unit cell is the smallest unit of the lattice. The whole lattice can be obtained by infinitive repetition of the unit cell along its three edges. The space lattice is characterized by
6、the size and shape of the unit cell.,How to distinguish the size and shape of the different unit cell ? The six variables , which are described by lattice constants a , b , c ; , , ,Lattice Constants,2.2 Crystal System & Lattice Types,If a rotation around an axis passing through the crystal by an an
7、gle of 360o/n can bring the crystal into coincidence with itself, the crystal is said to have a n-fold rotation symmetry. And axis is said to be n-fold rotation axis. We identify 14 types of unit cells, or Bravais lattices, grouped in seven crystal systems.,2.2.1 Seven crystal systems,All possible s
8、tructure reduce to a small number of basic unit cell geometries. There are only seven, unique unit cell shapes that can be stacked together to fill three-dimensional. We must consider how atoms can be stacked together within a given unit cell.,Seven Crystal Systems,2.2.2 14 types of Bravais lattices
9、 1. Derivation of Bravais lattices Bravais lattices can be derived by adding points to the center of the body and/or external faces and deleting those lattices which are identical.,7428 Delete the 14 types which are identical 281414,P,I,C,F,2. 14 types of Bravais lattice Tricl: simple (P) Monocl: si
10、mple (P). base-centered (C) Orthor: simple (P). body-centered (I). base-centered (C). face-centered (F) Tetr: simple (P). body-centered (I) Cubic: simple (P). body-centered (I). face-centered (F) Rhomb: simple (P). Hexagonal: simple (P).,Seven crystal systems and fourteen lattice types,2.2.3 Primiti
11、ve cell For primitive cell, the volume is minimum,Primitive cell Only includes one lattice point,2.2.4 Complex lattice The example of complex lattice,Examples and Discussions,1. Why are there only 14 space lattices?,Explain why there is no base centered and face centered tetragonal Bravais lattice.,
12、P C,I F,But the volume is not minimum.,2. Criterion for choice of unit cell Symmetry As many right angle as possible The size of unit cell should be as small as possible,Exercise,1. Determine the number of lattice points per cell in the cubic crystal systems. If there is only one atom located at eac
13、h lattice point, calculate the number of atoms per unit cell. 2. Determine the relationship between the atomic radius and the lattice parameter in SC, BCC, and FCC structures when one atom is located at each lattice point. 3. Determine the density of BCC iron, which has a lattice parameter of 0.2866nm.,4. Prove that the A-face-centered hexagonal lattice is not a new type of lattice in addition to the 14 space lattices. 5. Draw a primitive cell for BCC lattice.,Thank you !,3,
