Crystal Properties of SolidExamples of CrystalsFace-Centered Cubic (FCC) Crystal Structure (I)Face-Centered Cubic Crystal Structure (II)Body-Centered Cubic (BCC) Crystal Structure (I)Body-Centered Cubic Crystal Structure (II)Volume densityHexagonal Close-Packed Crystal Structure (I)Hexagonal Close-Packed Crystal Structure (II)Atomic Packing Factor-Atomic Packing Factor-Crystal StructureSemiconductor MaterialsCrystal Properties of SemiconductorsCrystal Properties of Solid Crystalline materials: The constituent atoms arranged in a pattern that repeats itself periodicallyin 3-dimensions. Three types of solids, classified according to atomic arrangementCrystal grains of a ceramic material(a) Crystalline (b) Amorphous (c) Polycrystalline(c)Grain boundary(b)CrystalliteNucleiLiquid(a)Solidification of a polycrystalline solid from the melt. (a)Nucleation. (b) Growth. (c) The solidified polycrystalline solid. Forsimplicity, cubes represent atoms.Crystal Properties of Solid PolycrystallineGrainCrystal Properties of SolidStrained bondBroken bond (danglingbond)Grain boundaryVoid, vacancySelf-interstitial type atomForeign impurity PolycrystallineThstrained bondsboundary isenergies thanedisogthorainandrdesbointeeithinundarieandsatogrhavtyains.eembroatoinkmthees.n boTgrnds,structurevoids, vacancietsainhig,"rwrstitial" p heainofshehavgerd thehes boundarie here tExamples of CrystalsQuartzSnowCopper oxideSalt (NaCl) crystal Gold (Au) crystals at 1000 CExamples of CrystalsSalt (NaCl) crystalExamples of CrystalsCarbonNanotubeCarbonNanofiberFullereneTEM image ofCarbon NanotubeExamples of CrystalsSingle crystal Diamonds.Single crystal Silicon.Atomic Resolution Images of Solid Surfaces STM (Scanning Tunneling Microscope) images of solid surfaceSilicon (Si) surface Iron silicide surfaceAtomic Resolution Images of Solid Surfaces 3D-STM (Scanning Tunneling Microscope) images of solid surfaceSilicon (Si) surface Hydrogen bonds on a Silicon surface.Atomic Resolution Images of Solid Surfaces Scanning Tunneling MicroscopeAtomic Resolution Images of Solid Surfaces Scanning Tunneling MicroscopeDigital Instrument (Nano Scope Multimode)· Contact mode Atomic Force Microscopy (AFM)· Non Contact AFM· Tapping mode AFM· Magnetic Force Microscopy (MFM)· Electric Force Microscopy (EFM)· Surface Potential Microscopy (SPM)· Lateral Force Microscopy (LFM)· Scanning Tunneling Microscopy (STM)· Chemical Force Microscopy (CFM)Atomic Resolution Images of Solid Surfaces TEM (Tunneling Electron Microscope) images of solid surfaceHigh resolution image of a quasiperiodicalgrain boundary in gold.Atomic Resolution Images of Solid Surfaces TEM (Tunneling Electron Microscope) images of solid surfaceJEOL (Japan), Model:JEM-2011ㆍAcc. voltage: 100∼200KVㆍResolution lattice: 0.14nm, point to point: 0.23nmㆍLaB6 single crystal filament (thermal type)ㆍMagnification: X2000∼X1,500,000ㆍPump: Diffusion Pump, Rotary Pump, Ion PumpㆍSelected area diffraction: 200∼2000mmㆍHigh dispersive diffraction: 5∼80mㆍScanning microscope accessorySEM (Scanning Electron Microscope) HITACHI (S-4300)1) Secondary electron image resolution- 1.5 nm at 15 kV- 5.0 nm at 1 kV2) Magnification : 20 to 500,000 x3) Accelerating voltage : 0.5 - 30 kV4) Gun source : Cold Field Emission gun5) Specimen stage- X Movement : 0 to 25 mm- Y Movement : 0 to 25 mm- Z Movement : 5 to 30 mm - Tilt angle : -5° to +45°- Rotation : 360°- Max. specimen size : 100mmφ6) Image Analysis Software JEOL (JSM-5410, JAPAN)ㆍAcc. voltage: 5∼30KVㆍTungsten Filament (thermal type)ㆍMagnification: X35∼X200,000ㆍPump: Diffusion Pump X 1ea, Rotary Pump X 1eaCrystal Structures The periodic arrangement of the atoms is called the Lattice. Unit Cell: Representative of the entire lattice and is regularly repeatedthroughout the crystal. Primitive Cell: Smallest unit cell which can be repeated to form the lattices.Primitive Cella/2Unit CellaEach crystal built up of a repetitive stacking of unit cells each identical in size, shape, and orientation with every other one.Crystal Structures Coordinates of position in the unit cell x, y, z expressed in terms of the unit cell edges. Examplereached by moving along the axis a distance of 3x the length of the vector , the parallel to , a distance 2× ,and finally parallel to , a distance equal to the length of .czbyaxrxyzvvvv++=rv321avbvbvcvcvCrystal Lattice GroupcxycbbaaOαβγUnit Cell Geometryz Bravais latticesLength and AngleTriclinic a≠b≠c α≠β≠γ≠90° K2CrO7Monoclinic a≠b≠c α=γ=90°≠β β-S, CaSO4⋅2H2OOrthorhombica≠b≠c α=β=γ=90° α-S, Ga, Fe3CTetragonala=b≠c α=β=γ=90° β-Sn, TiO2Cubic a=b=c α=β=γ=90° Cu, Ag, Zn, NaClHexagonal a1=a2=a3≠c α=β=90°, γ=120° Zn, CdRhombohedrala=b=c α=β=γ≠90° As, Sb, BiCrystal (Bravais) Lattice Group (I)Orthorhombic a≠b≠c, α=β=γ=90°Orthorhombic a≠b≠c, α=β=γ=90°Orthorhombica≠b≠c, α=β=γ=90°Monoclinic a≠b≠c, α=γ=90° β≠90°Monoclinic a≠b≠c, α=γ=90° β≠90°Triclinic a≠b≠c, α≠β≠γ≠90°Crystal (Bravais) Lattice Group (II)Rhombohedral a=b=c, α=β=γ≠90°Hexagonal a1=a2=a3≠c, α=β=90° γ=120°Orthorhombic a≠b≠c, α=β=γ=90°Crystal (Bravais) Lattice Group (III)Cubic a=b=c, α=β=γ=90°Cubic a=b=c, α=β=γ=90°Cubica=b=c, α=β=γ=90°Tetragonal a=b≠c, α=β=γ=90°Tetragonal a=b≠c, α=β=γ=90°Miller Convention SummaryConvention Interpretation(hkl) Crystal Plane{hkl} Equivalent Planes[hkl] Crystal Direction<hkl> Equivalent Directions Examples• plane {111}: (111) (-111) (1-11) (11-1)• direction <111>: [111] [-111] [1-11] [11-1]Crystal Plans Identification of a plan in a crystalz11/211zt∞acyxintercept ata/2yintercept atbUnit cellintercept abMiller Indices (hkl)1∞(210)xCrystal Plans Identification of a plan and direction in a crystalcxycbbaaOαβγUnit Cell GeometryzabczyoxoPzo[121]yCrystal Plans Miller IndexMiller Index ExamplesMiller Index ExamplesCrystal Planes in the Cubic Lattice Various plans in cubic lattice(111)-zyxzx(110)z-yyz(010)(010)(010)(010)x(100)(001)(110)(010)xzy(111)yCrystal Plans Interplanar spacingThe value of d, the distance between adjacent planes in the set (hkl), may be found from the following equations Cubic :  Tetragonal :  Hexagonal : lkhad2222++=clakhd2222221++=222222341clakhkhd++=+3Crystal