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Solid State Physics - Coggle Diagram

- - - - example of Solid Material // Crystal Structure
        
        Polycrystalline 多晶态
        
        Group of Crystals = Crystallites 晶粒 or Grains
        
        Arrangement of atoms in polycrystals form patterns as in crystal but the orientation change at the crystallites boundaries
        
        多晶态中的原子排列形成晶体中的形状，但在微晶边界处方向发生变化
        
        Example
        
        Metals, Alloys, Semiconductor
        
        Amorphous
        
        Short Range Order
        
        Equilibrium position of atoms does not form a repeated pattern even within short range
        
        原子的平衡位置即使在 短距离内 也不会形成 重复的形状
        
        Example
        
        Ceramics 陶瓷制品, Glass
        
        Crystalline 晶体
        
        repeated geometric pattern (periodic) throughout material without variation in composition, dimension and orientation
        
        整个材料中重复的几何图案（周期性），成分、尺寸和方向没有变化
        
        Long Range Order
        
        Example
        
        Alloys, Semiconductors
      - Consists of atom or molecules executing thermal motion about an equilibrium position fixed at a point in space
        
        Take the form of Crystalline, Polycrystalline or Amorphous material
        
        Have Strong Bonds between molecules and atoms
        
        Required More Energy to break the bond
      - Crystal Structure
        
        Definition
        
        A lattice with a basis added to each lattice site (lattice point)
    - - Basis
        
        Consists of an atom // a group of atoms // molecules
      - Crystal Period - Lattice
        
        A repeated arrangement of atoms, ions or molecules in metal or other crystalline solid
        
        Lattice Site = Lattice Point
      - Basis Lattice Vector
        
        Lattice point gives a relative position of a basis replica
        
        which also is the Shortest Displacement Vector
    - - No Defects/ Imperfections无缺陷 such as
        -interstice有空隙
        - impurities有杂质,
        -voids/vacancies
        -dislocations有错位
        
        Periodicity in all direction up to infinity 每个方向的周期性都是无限大
        
        Crystal Surface does not exist
      - Why cannot prepare a Prefect Crystal?
        
        The periodicity is interrupted 周期性是中断
        
        The thermal vibration of the atoms around their equilibrium position for T>0K
        
        Impurities in crystal
      - Infinite repetitions of identical structure unit in space
  - - - The atoms form repeating structure //smallest repeating unit
      - Three types
        
        Primitive Unit Cell 原始
        
        Only one lattice point // basis
        
        Smallest area in 2D
        
        Smallest volume in 3D
        
        Could be constructed using primitive lattice vector
        可以使用原始晶格向量构造
        
        All cells have same volume independence of its shape
        晶体有相同的体积但和形状无关
        
        Made by Primitive Translation Vector
        no cell of smaller volume that can be used for building block for crystal structure
        
        Will fill up the space by repetition of suitable crystal translation vector
        
        Conventional 常规 & Non-Primitive Unit Cell 非原始
        
        More than one primitive lattice point or basis
        
        Integral multiples of the area of primitive cell
        
        Method of counting
        -Corner 1/8
        -Edge 1/4
        -Surface 1/2
        -Inside 1
        
        Wigner-Seitz Unit Cell
        
        1) Choose one lattice point located in the center of the cell (every point in the cell closer to the center and also to the other lattice points)
        
        2) Primitive unit cell with full symmetry
        
        3) Draw a line from that points to its nearest neighbour lattice and divide it into 1/2
        
        4) Draw on each line a plane perpendicular to the each line and divide it into 1/2
        
        5) The smallest geometrical shape bounded by these planes and the lattice point in center is Wigner-Seitz Cell
      - Volume
        
        Can be expressed in basis lattice vector
        
        Density of the crystal (p=M/V) is uniform
        Because all unit cell contains same number of atom distribution
    - - Bravais Lattice
        
        All atoms are of the same kind
        
        All lattice points are equivalent
        -located at the unit cell corner
        -some will at faces // center of unit cell
        
        Geometry
        
        2D
        
        has 5 shape
        
        Oblique倾斜
        
        Rectangular(Rhombic),
        
        Centered Rectangular(Orthorhombic)
        
        Hexagonal and
        
        Square
        
        3D
        
        has 14 shape
        
        Triclinic三斜
        
        Monoclinic单斜
        
        Orthorhombic 斜面
        
        Tetragonal 四边形
        
        Rhombohedral 菱面斜
        
        Hexagonal 六边体
        
        Cubic 正方体
      - Non-Bravais Lattice
        
        Atoms can be difference kind
        
        Some lattice points are not equivalent
        
        Combine with two or more Bravais Lattice
    - - Shapes must fill all space 不可以用空隙
      - Example
        
        Square, Rectangular, Oblique, Hexagon
  - - - Definition
        
        Number of Atom per Unit Cell
        
        The product of the number of atoms per lattice point and the number of lattice points per unit cell
        
        Packing Factor
        
        The fraction of space occupied by atoms
        
        Lattice Parameter
        
        Include
        
        Dimensions // length of the sides of the unit cell
        
        Angle between the sides
        
        Translational Symmetry of Lattice
        
        Given by base vector or lattice vector
        
        Choosing condition
        
        Shortest Possible Vector
        
        Correspond to a High Symmetry Unit Cell
        
        Theoretical Density
        
        Metal have close-packed (metallic bonding)
        Large atomic weight
        
        Ceramic have less dense packing
        Light element
        
        Polymers have low packing density (amorphous)
        Lighter elements like C, H, O
        
        Composites have intermediate values
      - Cubic
        
        SC
        
        Properties
        
        Low APF = 0.52
        
        Closed Packed Direction = Cube Edge
        
        Coordinate number = 6
        
        Number of atoms per unit cell = 1
        
        FCC
        
        Properties
        
        High APF = 0.74
        
        Closed Packed Direction = Face Diagonals
        
        Coordinate Number = 12
        
        No of atoms per unit cell = 4
        
        BCC
        
        Properties
        
        APF = 0.68
        
        Closed Packed Direction = Body Diagonals
        
        Coordinate Number = 8
        
        No. of atoms per unit cell = 2
    - - Chapter 5: Symmetry Operation
        
        Crystal Symmetry
        
        Have Inherent Symmetry 固有的对称性
        
        Definite Ordered Arrangement of Face and Edges of Crystal
        known as Crystal Symmetry
        
        Could Study Internal Structure of Crystal
        
        Crystal posses具有 difference symmetries or symmetry element
        
        Q&A
        
        What is Symmetry?
        
        If a lattice is not changed after an operation associated with an operator
        The lattice is symmetric with w.r.t that operation
        
        Then, What is Symmetry Operation?
        
        1 more item...
        
        What are the important factor to determine Crystal Structure?
        
        Lattice Arrangement
        
        Crystal axes, a, b and c
        
        Type of Basis
        
        Set of Symmetry Operation
        
        Law in this Chapter
        
        Law of Rational Indices 有理指数定律
        
        state that
        The ratio of intercept of different faces of a crystal with the three axes are constant and
        can be expressed in rational number
        任意晶面在适当选择的3D坐标轴上的intercept 都是有理数的
        
        Law of Constancy of Symmetry
        
        state that
        All crystals of a substance have the same element of symmetry
        
        Plane Symmetry
        
        Axis Symmetry
        
        Center Symmetry
        
        Total number of elements of symmetry in cubic crystal = 9 (Plane) + 13 (Axes) + 1 (Center) = 23
      - Week 4
      - Chapter 6:
        Determination of Crystal Structure
        
        Method to Determine the Crystal Structure of a Material
        
        Using X-ray Diffraction
        
        Definition：
        The atomic planes of a crystal causes an incident beam of X-rays to interfere 干扰 with one another as they leave the crystal
        
        Diffraction Grating must have spacing comparable to the wavelength, λ of diffracted radiation (X-rays)
        
        In Crystals:
        Diffraction grating are planes of atoms
        Spacing is the distance between parallel planes of atom
        
        To resolve解决 a spacing that is bigger than wavelength, λ
        
        λ < a : Transmission Dominated 投射为主
        
        λ ~ a : Diffraction Dominated 衍射为主
        
        λ > a : Reflected Dominated 反射为主
        
        λ << a : Diffraction effect cannot show the crystal structure in detail
        
        λ >> a : Diffraction angle is too small
        Max. peaks are very close - diffraction pattern difficult to see
        
        Source of Diffraction
        
        X-ray Diffraction
        -Used for Investigate of Crystal Structure 晶体结构研究
        
        Electron Diffraction
        -Used for Surface Study of Material 材料表面研究
        -Has short penetrating power
        
        Neutron Diffraction
        -Used for High Precision Study 高精度研究
        -Could study magnetic structure of material based on its magnetic moment
        
        How?
        
        Measure the inter-planar spacing, d (the distance between equivalent planes of atoms)
        -Function of Lattice Parameter (a, b, c, α, β, γ)
        -Function of Crystal Symmetry
        
        How to measure the spacing?
        
        X-Ray
        
        Founded by Wihelm Conrad Rontgen on 1895
        
        E(keV) = hv = hc/λ
        
        History? Lazy...
        
        X-ray Generation
        
        High energy electrons bombarding metal anode
        
        Process 1
        
        Deceleration of electron in the metal target
        
        Process 2
        
        1 more item...
        
        Electron decelerated by nucleus field
        Loss KE in form of EM radiation
        
        Continuous Spectrum // White Spectrum // Bremsstrahlung is form
        
        Why XRD?
        
        Measure the average spacing between layers of atoms
        
        Determine the orientation of a single crystal
        
        Find the crystal structure of an unknown material
        
        Measure the size, shape and internal stress of small crystalline regions
        
        Bragg's Law
      - Recap
        
        Crystal // Basic of Crystallography
        A solid in which atoms are arranged in some regular repetition pattern in all direction
        
        Structures
        The framework 骨架 of its body
        
        Unit Cell
        The smallest volume element
        -Dimension: a, b, c (Three axes)
        -Angle: α, β, γ
    - - Miller Indices
        
        Direction
        
        Direction and their Multiple are identical相同
        
        [ 2 2 0] = 2 x [ 1 1 0]
        
        For one: [ u v w ]
        For Family: < u v w >
        
        Transform to lattice vector
        
        R = ua + vb + wc
        
        Plane
        
        Connecting at least 3 difference lattice points
        because of the periodicity of lattice
        
        For one: ( h k l )
        For Family: { h k l }
        
        Procedure
        
        If plane does not intercept an axis = 0 or ∞
        
        If the reciprocal of the intercept is fraction
        multiply by the lowest common denominator
        
        If passing through origin, method
        1) consider an equivalent plane in an adjacent unit cell
        2) Select a different origin for the same plane