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1、材料科学基础Fundamental of Materials,Prof:Tian Min Bo Tel:62795426，62772851 E-mail:Department of Material Science and EngineeringTsinghua University.Beijing 100084,2.1 Space Lattice,.Crystals versus non-crystals 1.Classification of functional materials,Chapter,Fundamentals of Crystallography,Lesson three,
2、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 of one crystal grainsPolycrys
3、talline:grain boundaries,.Space lattice1.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.,2.Two basic features of lattice pointsPerio
4、dicity:Arranged in a periodic pattern.Identity:The surroundings of each point in the lattice are identical.,A lattice may be one,two,or three dimensionaltwo dimensions,Space lattice is a point array which represents the regularity of atom arrangements,Three dimensions,Each lattice point has identica
5、l surrounding environment,.Unit cell and lattice constantsUnit 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 the size and shape of the unit cell.,How to distinguish the
6、size and shape of the deferent 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 angle of 360o/n can bring the crystal into coincidence with itself,the crystal
7、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.,.Seven crystal systems,All possible structure reduce to a small number of basic unit cell geometries.There are only seven,un
8、ique 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,.14 types of Bravais lattices 1.Derivation of Bravais lattices Bravais lattices can be derived by adding points to the cente
9、r of the body and/or external faces and deleting those lattices which are identical.,7428Delete the 14 types which are identical281414,P,I,C,F,2.14 types of Bravais latticeTricl:simple(P)Monocl:simple(P).base-centered(C)Orthor:simple(P).body-centered(I).base-centered(C).face-centered(F)Tetr:simple(P
10、).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,.Primitive CellFor primitive cell,the volume is minimum,Primitive cellOnly includes one lattice point,.Complex LatticeThe example of complex lattic
11、e,Examples and Discussions,1.Why are there only 14 space lattices?,Explain why there is no base centered and face centered tetragonal Bravais lattice.,P C,I F,But 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
12、 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 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,an
13、d 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,
