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1、资料科学根底Fundamental of MaterialsProf: Tian Min Bo Prof: Tian Min Bo : 62795426 : 62795426 ，6277285162772851 : tmbmail.tsinghua.edu : tmbmail.tsinghua.eduDepartment of Material Science and EngineeringDepartment of Material Science and EngineeringTsinghua University. 100084Tsinghua University. 1000842.1
2、 Space Latticeuu.Crystals versus non-crystalsuu 1. Classification of functional materialsChapter Fundamentals of CrystallographyLesson threeLesson three2. Classification of materials based on structure Regularity in atom arrangement periodic or not (amorphous)Crystalline: The materials atoms are Cry
3、stalline: The materials atoms are arranged arranged in a periodic fashion. in a periodic fashion.Amorphous: The materials atoms do not Amorphous: The materials atoms do not have have a long-range order (0.1 a long-range order (0.11nm).1nm).Single crystal: in the form of one crystalSingle crystal: in
4、 the form of one crystal grains grainsPolycrystalline: Polycrystalline: grain boundaries grain boundariesuu.Space latticeuu1. Definition:uu Space lattice consists of an array of regularly arranged geometrical points, called lattice points. The (periodic) arrangement of these points describes the reg
5、ularity of the arrangement of atoms in crystals.2. Two basic features of lattice points2. Two basic features of lattice pointsPeriodicity: Arranged in a periodic pattern.Periodicity: Arranged in a periodic pattern.Identity: The surroundings of each point in Identity: The surroundings of each point i
6、n the lattice are identical. the lattice are identical. A lattice may be one , two, or three A lattice may be one , two, or three dimensionaldimensionaltwo dimensionstwo dimensionsSpace lattice is a point array which represents the regularity of atom arrangements (1) (2) (3) a bThree dimensions Each
7、 lattice point has identical surrounding environmentuu.Unit cell and lattice constantsuuUnit 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.uuThe space lattice is characterized by the size and shape of the u
8、nit cell.How to distinguish the size and shape of the deferent unit cell ? The six variables , which are described by lattice constants a , b , c ; , , Lattice Constantsa c b a c b2.2 Crystal System & Lattice Types If a rotation around an axis passing through the crystal by an angle of 360o/n can br
9、ing 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 the crystal into coincidence with itself, the crystal is said to have a n-fold rotation symmetry. And axis is said to b
10、e n-fold rotation axis.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. We identify 14 types of unit cells, or Bravais lattices, grouped in seven crystal systems.uu.Seven crystal systems All possible str
11、ucture reduce to a small All possible structure reduce to a small number of basic unit cell geometries.number of basic unit cell geometries.There are only seven, unique unit cell shapes There are only seven, unique unit cell shapes that can be stacked together to fill three-that can be stacked toget
12、her to fill three-dimensional.dimensional.We must consider how atoms can be stacked We must consider how atoms can be stacked together within a given unit cell.together within a given unit cell.Seven Crystal SystemsSeven Crystal SystemsTriclinicTriclinicabc abc ，9090MonoclinicMonoclinicabc abc ， 90
13、90 9090OrthorhombicOrthorhombicabc abc ， 9090TetragonalTetragonala abc bc ， 9090CubicCubica ab bc c ， 9090HexagonalHexagonala abc bc ， 9090120120RhombohedralRhombohedral a ab bc c ， 9090uu.14 types of Bravais latticesuu 1. Derivation of Bravais latticesuu Bravais lattices can be derived by adding po
14、ints to the center of the body and/or external faces and deleting those lattices which are identical. 74742828Delete the 14 types which are identicalDelete the 14 types which are identical282814141414+PICF2. 14 types of Bravais lattice2. 14 types of Bravais latticeTricl: simple (P)Tricl: simple (P)M
15、onocl: simple (P). base-centered (C)Monocl: simple (P). base-centered (C)Orthor: simple (P). body-centered (I). Orthor: simple (P). body-centered (I). base-centered (C). face-centered base-centered (C). face-centered (F)(F)Tetr: simple (P). body-centered (I)Tetr: simple (P). body-centered (I)Cubic:
16、simple (P). body-centered (I). Cubic: simple (P). body-centered (I). face-centered (F) face-centered (F)Rhomb: simple (P). Rhomb: simple (P). Hexagonal: simple (P).Hexagonal: simple (P).Crystal systemsCrystal systems(7)(7)Lattice types (14)Lattice types (14)P PC CF FI I A B C A B C1 1TriclinicTricli
17、nic2 2MonoclinicMonoclinic or or (90or (90or 90 ) 90 )3 3OrthorhombicOrthorhombicor oror or4 4TetragonalTetragonal5 5CubicCubic6 6HexagonalHexagonal7 7RhombohedralRhombohedralSeven crystal systems and fourteen lattice typesuu.Primitive CelluuFor primitive cell, the volume is minimumPrimitive cellOnl
18、y includes one lattice pointuu. Complex LatticeuuThe example of complex lattice120o120o120oExamples and Discussions1. Why are there only 14 space lattices?1. Why are there only 14 space lattices?l Explain why there is no base centered and face centered tetragonal Bravais lattice.P CI FBut the volume
19、 is not minimum.2. Criterion for choice of unit cell2. Criterion for choice of unit cell Symmetry Symmetry As many right angle as possible As many right angle as possibleThe size of unit cell should be as small as The size of unit cell should be as small as possiblepossibleExercise1. Determine the n
20、umber of lattice points 1. Determine the number of lattice points per cell in the cubic crystal systems. If per cell in the cubic crystal systems. If there is only one atom located at each there is only one atom located at each lattice point, calculate the number of lattice point, calculate the numb
21、er of atoms per unit cell.atoms per unit cell.2. Determine the relationship between the 2. Determine the relationship between the atomic radius and the lattice parameter in atomic radius and the lattice parameter in SC, BCC, and FCC structures when one SC, BCC, and FCC structures when one atom is lo
22、cated at each lattice point.atom is located at each lattice point.3. Determine the density of BCC iron, which 3. Determine the density of BCC iron, which has a lattice parameter of 0.2866nm.has a lattice parameter of 0.2866nm.4. Prove that the A-face-centered hexagonal 4. Prove that the A-face-centered hexagonal lattice is not a new type of lattice in lattice is not a new type of lattice in addition to the 14 space lattices.addition to the 14 space lattices.5. Draw a primitive cell for BCC lattice.5. Draw a primitive cell for BCC lattice.Thank you !3
