posiciones picos drx
TRANSCRIPT
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Structures of SolidsStructures of Solids& X& X--ray Diffractionray Diffraction
Chemistry 123Chemistry 123Dr. Patrick WoodwardDr. Patrick WoodwardSupplemental Lecture 4Supplemental Lecture 4
Crystalline SolidsCrystalline Solids
Crystal LatticeCrystal Lattice A 3D array of points where each pointA 3D array of points where each pointhas an identical environment.has an identical environment.
Unit CellUnit Cell The repeating unit (a unit cell is to a crystal,The repeating unit (a unit cell is to a crystal,like alike a brickbrick is in a house). In a given crystal all unitis in a house). In a given crystal all unitcells are identical.cells are identical.
CaFCaF22 Unit CellUnit Cell
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CrystalCrystal
SystemsSystemsCubicCubicTetragonalTetragonalHexagonalHexagonal
RhombohedralRhombohedralOrthorhombicOrthorhombic
MonoclinicMonoclinicTriclinicTriclinic
The crystal systems eachhave distinctive symmetry
and unit cell dimensions
Close Packed Array of SpheresClose Packed Array of Spheres
The gray spheres represent a 2DThe gray spheres represent a 2DClose Packed Array.Close Packed Array.
AABB StackingStacking AACC StackingStacking
In 3D the next layer of spheresIn 3D the next layer of spherescould sit on the depressionscould sit on the depressionsmarked inmarked in red (B)red (B) or thoseor those
marked inmarked in blue (C)blue (C)..
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Cubic and Hexagonal Close PackingCubic and Hexagonal Close Packing
Hexagonal Close PackingHexagonal Close Packing(ABAB(ABAB))
AABBAABB StackingStacking
AABBCCAABBCC StackingStacking
Cubic Close PackingCubic Close Packing(ABCABC(ABCABC))
Close Packed SpheresClose Packed Spheres
Hexagonal Close PackingHexagonal Close Packing(ABAB(ABAB))
Cubic Close PackingCubic Close Packing(ABCABC(ABCABC))
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Hexagonal CloseHexagonal ClosePackingPacking
Cubic CloseCubic ClosePackingPacking
Body CenteredBody Centered
Cubic PackingCubic Packing
Cubic or Hexagonal Close PackingCubic or Hexagonal Close PackingCoordination Number = 12Coordination Number = 12Packing Efficiency = 74%Packing Efficiency = 74%
Body Centered Cubic PackingBody Centered Cubic PackingCoordination Number = 8Coordination Number = 8Packing Efficiency = 68%Packing Efficiency = 68%
CsClCsCl StructureStructure
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EutacticEutactic StructuresStructures
Many ionic structure types can be described as aclose packing of anions with cations filling voidsor holes in the structure. Generally we willconsider two types of holes (for the cations)
Octahedral holes - Voids are surrounded by 6 anions andlead to octahedral coordination of the cation
Tetrahedral holes - Voids are surrounded by 4 anionsand lead to tetrahedral coordination of the cation
Octahedral HolesOctahedral HolesStart with a close packed layer of anions (A)Start with a close packed layer of anions (A)
Insert cations in the triangular depressions (c)Insert cations in the triangular depressions (c)
Add another anion layer (B)Add another anion layer (B)
The resulting cation coordination is an octahedronThe resulting cation coordination is an octahedron
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Tetrahedral HolesTetrahedral HolesStart with a close packed layer of anions (A)Start with a close packed layer of anions (A)
Insert cations in the triangular depressions (b)Insert cations in the triangular depressions (b)
Add another anion layer (B)Add another anion layer (B)
The resulting cation coordination is a tetrahedronThe resulting cation coordination is a tetrahedron
EutacticEutactic StructuresStructures
hcphcp2/32/3AlAl22OO33
hcphcp1/21/2TiOTiO22
hcphcp1/21/2CdICdI22
ccpccp1/21/2CdClCdCl22
hcphcp11NiAsNiAs
ccpccp11NaClNaCl
PackingPackingFractionFraction
HolesHolesFilledFilled
StructureStructure
hcphcp1/21/2WurtziteWurtzite
ccpccp1/21/2SphaleriteSphalerite
ccpccp11FluoriteFluorite
PackingPackingFractionFraction
HolesHolesFilledFilled
StructureStructure
Structures obtained byfilling Octahedral Holes
Structures obtained byfilling Tetrahedral Holes
In fluorite (i.e. CaFIn fluorite (i.e. CaF22) the cations are) the cations areclose packed and the anions fill theclose packed and the anions fill the
tetrahedral holes. The opposite is truetetrahedral holes. The opposite is trueof theof the antifluoriteantifluorite structure (Nastructure (Na22O)O)
TheThe hcphcp anion layers are buckled inanion layers are buckled in rutilerutile..
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Cubic close packed (CCP) anion arrayCubic close packed (CCP) anion array
Space GroupSpace Group = Fm3m= Fm3mAtomAtom Site x y zSite x y zAnionAnion 4a4a 0 0 00 0 0TetrTetr HoleHole 8c8c
Rock salt structure (Rock salt structure (NaClNaCl))(Octahedral Holes)(Octahedral Holes)
Space GroupSpace Group = Fm3m= Fm3mAtomAtom Site x y zSite x y zAnionAnion 4a4a 0 0 00 0 0Oct HoleOct Hole 4b4b
AntifluoriteAntifluorite structure (Nastructure (Na22O)O)
(Tetrahedral Holes)(Tetrahedral Holes)
CCP Anion Array & Tetrahedral HolesCCP Anion Array & Tetrahedral Holes
Space GroupSpace Group = Fm3m= Fm3mAtomAtom Site x y zSite x y zAnionAnion 4a4a 0 0 00 0 0TetrTetr HoleHole 8c8c
ZincZinc BlendeBlende Structure (Structure (ZnSZnS))(50% Tetrahedral Holes)(50% Tetrahedral Holes)
Space GroupSpace Group = F43m= F43mAtomAtom Site x y zSite x y zAnionAnion 4a4a 0 0 00 0 0TetrTetr HoleHole 4b4b
AntifluoriteAntifluorite structure (Nastructure (Na22O)O)(100% Tetrahedral Holes)(100% Tetrahedral Holes)
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SphaleriteSphalerite ((ZnSZnS))((ccpccp, 50%, 50% TetrTetr. Holes Filled). Holes Filled)
Space GroupSpace Group = F= F--43m43mAtomAtom Site x y zSite x y z
ZnZn 4a4a 0 0 00 0 0SS 4c4c
CationCation CoordCoord.. TetrahedronTetrahedronAnionAnion CoordCoord.. TetrahedronTetrahedronConnectivityConnectivity Corner sharing Oct.Corner sharing Oct.
WurtziteWurtzite (ZnO)(ZnO)((hcphcp, 50%, 50% TetrTetr. Holes Filled). Holes Filled)
Space GroupSpace Group = P6= P633mcmcAtomAtom Site x y zSite x y z
ZnZn 2b2b 1/3 2/3 01/3 2/3 0OO 2b2b 1/3 2/3 0.381/3 2/3 0.38
CationCation CoordCoord.. TetrahedronTetrahedronAnionAnion CoordCoord.. TetrahedronTetrahedronConnectivityConnectivity Corner sharing Oct.Corner sharing Oct.
Space GroupSpace Group = P6= P633/mmc/mmcAtomAtom Site x y zSite x y zAnionAnion 2c2c 1/3 2/3 1/41/3 2/3 1/4Oct HoleOct Hole 2a 0 0 02a 0 0 0
Hexagonal Close Packed Anion ArrayHexagonal Close Packed Anion Array
Nickel Arsenide Structure (Octahedral Holes)Nickel Arsenide Structure (Octahedral Holes)
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Space GroupSpace Group = P6= P633/mmc/mmcAtomAtom Site x y zSite x y zAnionAnion 2c2c 1/3 2/3 1/41/3 2/3 1/4TetrTetr HoleHole 4f4f 1/3 2/3 z1/3 2/3 z
z ~ 0.632z ~ 0.632
HCP Anion ArrayHCP Anion Array -- Tetrahedral HolesTetrahedral HolesNo such structure existsNo such structure exists
XX--ray Diffractionray Diffraction
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Diffraction DemoDiffraction Demo
Take home messageTake home message The diffraction pattern isThe diffraction pattern is
related but not equal to therelated but not equal to thegrid patterngrid pattern
Diffraction is most effectiveDiffraction is most effectivefor monochromatic light whosefor monochromatic light whosewavelength is similar to thewavelength is similar to thespacing ofspacing of slitsslits
For crystals XFor crystals X--rays have arays have awavelength comparable towavelength comparable to
spacingsspacings of atomsof atoms
PowderPowder DiffractometerDiffractometer
HorizontalDiffraction
Circle
DivergentX-ray
Source
Detector
DivergenceSlit
AntiscatterSlit
Receiving Slit
HorizontalSoller Slits
Sample (VerticalFlat Plate)
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Single CrystalSingle CrystalDiffractionDiffraction
IncidentIncidentBeamBeam
DiffractedDiffractedBeamBeam
IncidentIncidentBeamBeam
DiffractedDiffractedBeamBeam
PowderPowderDiffractionDiffraction
In powder diffraction only asmall fraction of the crystals(shown in blue) are correctly
oriented to diffract.
BraggBraggs Laws Law
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XX--ray Powder Patternray Powder Pattern
Bond Distance from XRD PatternBond Distance from XRD Pattern
(Ex.(Ex. PbSPbS, Rock Salt Structure), Rock Salt Structure)
Braggs Law = 2dhkl sin hkl
1. Determine the 2-theta value, 2, and hkl values for a diffractionpeak
20 25 30 35 40 45 50 55 60 652Theta
0
0
0
0
0
0
0
Int.
2 = 38.7
h=2, k=2, l=0
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Bond Distance from XRD (Cont.)Bond Distance from XRD (Cont.)(Ex.(Ex. PbSPbS, Rock Salt Structure), Rock Salt Structure)
2. Use Braggs Law and the wavelength of radiation (typically =1.541 ) to calculate dhkl
= 2dhkl sin hkldhkl = /(2 sin hkl)
dhkl = 1.541 /{2 sin (38.7/2)} = 2.10
3. The interplanar spacing, dhkl, is related to the unit cell size. For acubic crystal:
a = (h2 + k2 + l2)1/2 dhkl
a = (22 + 22 + 02)1/2(2.10 ) = 5.94
Bond Distance from XRD (Cont.)Bond Distance from XRD (Cont.)
(Ex.(Ex. PbSPbS, Rock Salt Structure), Rock Salt Structure)
4. Now that we know the unit cell size, the Pb-S distance can bedetermined from the unit cell using simple geometry.
dist (Pb-S) = a/2
dist (Pb-S) = 5.94 /2
dist (Pb-S) = 2.97
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Peak PositionsPeak Positions
Braggs Law = 2dhkl sin hklThe distance between different planes of atoms in a crystal, dhkl,where h, k and l are integers that correspond to different planesCubic:
1/d2 = (h2 + k2 + l2)/a2
Tetragonal:
1/d2 = {(h2 + k2)/a2} + (l2/c2)
Orthorhombic:
1/d2 = (h2/a2) + (k2/b2) + (l2/c2)
Hexagonal:
1/d2 = (4/3){(h2 + hk + k2)/a2} + (l2/c2)