1、材料科學基礎Fundamental of Materials2.1 Space Lattice.Crystals versus non-crystals 1. Classification of functional materialsChapter Fundamentals of CrystallographyLesson three2. Classification of materials based on structure Regularity in atom arrangement periodic or not (amorphous)Crystalline: The materi

2、als 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 of one crystal grainsPolycrystalline: grain boundaries.Space lattice1. Definition: Space lattice consists of an array of regularly arranged geometrical poin

3、ts, called lattice points. The (periodic) arrangement of these points describes the regularity of the arrangement of atoms in crystals.2. Two basic features of lattice pointsPeriodicity: Arranged in a periodic pattern.Identity: The surroundings of each point in the lattice are identical. A lattice m

4、ay be one , two, or three dimensionaltwo dimensionsSpace lattice is a point array which represents the regularity of atom arrangements (1) (2) (3) a bThree dimensions Each lattice point has identical surrounding environment.Unit cell and lattice constantsUnit cell is the smallest unit of the lattice

5、. The whole lattice can be obtained by infinitive repetition of the unit cell along its three edges.The space lattice is characterized by the size and shape of the unit cell.How to distinguish the size and shape of the deferent unit cell ? The six variables , which are described by lattice constants

6、 a , b , c ; , , Lattice Constantsa c b a c b 2.2 Crystal System & Lattice Types If a rotation around an axis passing through the crystal by an angle 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 ro

7、tation axis. We identify 14 types of unit cells, or Bravais lattices, grouped in seven crystal systems.Seven crystal systems All possible structure 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-dimensio

8、nal.We must consider how atoms can be stacked together within a given unit cell.Seven Crystal SystemsTriclinicabc ，90Monoclinicabc ， 90 90Orthorhombicabc ，90Tetragonalabc ，90Cubicabc ，90Hexagonalabc ，90120Rhombohedralabc ，90.14 types of Bravais lattices 1. Derivation of Bravais lattices Bravais latt

9、ices can be derived by adding points to the center of the body and/or external faces and deleting those lattices which are identical. 7428Delete the 14 types which are identical281414+PICF2. 14 types of Bravais latticeTricl: simple (P)Monocl: simple (P). base-centered (C)Orthor: simple (P). body-cen

10、tered (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).Crystal systems(7)Lattice types (14)PCFI A B C1Triclinic2Monoclinic or (90or 90 )3Orthorhombicor or4Tetragonal5Cubic6Hexag

11、onal7RhombohedralSeven crystal systems and fourteen lattice types.Primitive CellFor primitive cell, the volume is minimumPrimitive cellOnly includes one lattice point. Complex LatticeThe example of complex lattice120o120o120oExamples and Discussions1. Why are there only 14 space lattices? Explain wh

12、y there is no base centered and face centered tetragonal Bravais lattice.P CI FBut the volume is not minimum.2. Criterion for choice of unit cell Symmetry As many right angle as possibleThe size of unit cell should be as small as possibleExercise1. Determine the number of lattice points per cell in

13、the cubic crystal systems. If there is only one atom located at each 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 h