SlideShare ist ein Scribd-Unternehmen logo
1 von 76
Downloaden Sie, um offline zu lesen
1
Dr. Nitin H. Bansod
Department of Chemistry,
Shri Shivaji Science College,
Amravati.
2
CONTENTS
 Types of solids
 Types of structures adopted by solids
3
SOLIDS
can be divided into two catagories.
 Crystalline
 Amorphous
Crystalline has long range order
Amorphous materials have short range order
Effect of Crystallinity on Physical properties - ex. Polyethylene
4
Crystal
Type
Particles Interparticle
Forces
Physical Behaviour Examples
Atomic
Molecular
Metallic
Ionic
Network
Atoms
Molecules
Atoms
Positive and
negative
ions
Atoms
Dispersion
Dispersion
Dipole-dipole
H-bonds
Metallic bond
Ion-ion
attraction
Covalent
• Soft
• Very low mp
• Poor thermal and electrical
conductors
 Fairly soft
 Low to moderate mp
 Poor thermal and electrical
conductors
 Soft to hard
 Low to very high mp
 Mellable and ductile
 Excellent thermal and
electrical conductors
 Hard and brittle
 High mp
 Good thermal and electrical
conductors in molten condition
• Very hard
• Very high mp
• Poor thermal and electrical
conductors
Group 8A
Ne to Rn
O2, P4, H2O,
Sucrose
Na, Cu, Fe
NaCl, CaF2,
MgO
SiO2(Quartz)
C (Diamond)
TYPES OF CRYSTALLINE SOLIDS
5
Molecular Solids Covalent Solids Ionic solids
Metallic solids
Na+
Cl-
STRUCTURES OF CRYSTALLINE SOLID TYPES
6
DIAMOND QUARTZ
GRAPHITE
7
CRYSTAL STRUCTURE
Crystal structure is the periodic arrangement of atoms in the
crystal. Association of each lattice point with a group of
atoms(Basis or Motif).
Lattice: Infinite array of points in space, in which each point has
identical surroundings to all others.
Space Lattice  Arrangements of atoms
= Lattice of points onto which the atoms are hung.
Elemental solids (Argon): Basis = single atom.
Polyatomic Elements: Basis = two or four atoms.
Complex organic compounds: Basis = thousands of atoms.
+
Space Lattice + Basis = Crystal Structure
=
• • •
• • •
• • •
8
ONE DIMENTIONAL LATTICE
ONE DIMENTIONAL UNIT CELL
a
a
UNIT CELL : Building block, repeats in a regular way
a
9
TWO DIMENTIONAL LATTICE
10
a
b
a  b,   90°
a  b,  = 90°
a
b
a = b,  = 90°
a
a
a  b,  = 90°
a
b
a = b,  =120°
a
a
TWO DIMENTIONAL UNIT CELL TYPES
11
EXAMPLE OF TWO DIMENTIONAL UNIT CELL
12
TWO DIMENTIONAL UNIT CELL POSSIBILITIES OF NaCl
Na+
Cl-
13
The “unit cell” is the basic repeating unit of the
arrangement of atoms, ions or molecules in a
crystalline solid.
The “lattice” refers to the 3-D array of particles in a
crystalline solid. One type of atom occupies a
“lattice point” in the array.
Examples of Unit Cells
16
THREE DIMENTIONAL UNIT CELLS / UNIT CELL SHAPES
1
2
3
4
5
6
7
17
Primitive ( P ) Body Centered ( I )
Face Centered ( F ) C-Centered (C )
LATTICE TYPES
18
BRAVAIS LATTICES
7 UNIT CELL TYPES + 4
LATTICE TYPES = 14
BRAVAIS LATTICES
19
COUNTING ATOMS IN THE THREE DIMENTIONAL
UNIT CELL
 Vertex(corner) atom shared by 8 cells  1/8 atom per cell
 Edge atom shared by 4 cells  1/4 atom per cell
 Face atom shared by 2 cells  1/2 atom per cell
 Body unique to 1 cell  1 atom per cell
Atoms in different positions in a cell are shared by
differing numbers of unit cells
. A: Body-centered cubic (bcc) B: Simple cubic (sc)
Contributions of Atoms to Cubic Unit Cells
Position of Atoms
in Unit Cell
Contribution to
Unit Cell
Unit-Cell Type
Center 1 bcc
Face 1/2 Fcc
Corner 1/8
fcc, bcc, simple
cubic
How many total atoms are found in a simple cubic
unit cell? Face centered cube? Body centered cube?
22
Number of Atoms per unit cell in cubic
crystal system(z)
1.For SCC( Simple Cubic Crystal Lattice)
Vertex(corner) atom shared by 8 cells  1/8 atom per cell
Z = 1/8 × 8 = 1
2. For FCC (Face Centred Cubic lattice)
Vertex(corner) atom shared by 8 cells  1/8 atom per cell
Face atom shared by 2 cells  1/2 atom per cell
Z = 1/8 × 8 + 1/2 × 6 = 1+3 = 4
Unit Cells
 A body-centered
cubic (bcc) unit cell
has atoms at the 8
corners of a cube and
at the center of the
cell
 A simple cubic unit
cell has atoms only at
the 8 corners of a
cube.
Number Atoms in a Unit Cell
 In the simple cubic cell
there are only the 8
atoms at the corners.
 1/8 x 8 = 1 atom in cell
 In bcc, 8 atoms at the
corners and 1 in center.
 1/8 x 8 + 1 x 1 = 2 atoms
in the cell
25
3.For BCC(Body Centred Cubic lattice)
Vertex(corner) atom shared by 8 cells  1/8 atom per cell
And Body unique to 1 cell  1 atom per cell
Z = 1/8 × 8 + 1 × 1 = 1+1 = 2
26
Density of crystal matter (D)
Density = Mass of the Unit cell
………………………………
Volume of the Unit cell
Mass of unit cell = Z × mass of each atom
= Z × M/N0
Volume of unit cell = a3 = where a is edge length is in pm
1pm = 10-12 m.
D = Z × M where M –molecular weight
……….
No × a3 No- Avogadro's Number(6.023×10-23
27
Numerical problem:
1.The length of side of unit cell of a cubic crystal is 4×10-3 m.
the density of crystal matter is 1.2× 10-3 kg m-3.if molar mass
is 2.4×10-2 mole-1 then find out i) type of lattice ii) number of
atoms in each unit cell
Solution :
28
Numerical problem:
1. The corner of a face centred cubic Crystal has atoms
of elements X while at centre of face has of element
Y. find out the formula of crystal compound.
The Chemistry of Solids
Miller Indices (l,m,n) are a
way of denoting planes in
crystal lattices.
Types of planes of cubic Crystal or indexing the planes
(110) planes (130) planes
a
b
(-210) planes
[010]
[100]
[001]
[110]
[101]
[011]
[110]
[111]
• Coordinates of the final point  coordinates of the initial point
• Reduce to smallest integer values
Intercepts → 1  
Plane → (100)
Family → {100} → 3
Intercepts → 1 1 
Plane → (110)
Family → {110} → 6
Intercepts → 1 1 1
Plane → (111)
Family → {111} → 8
(Octahedral plane)
The (111) planes:
Planes in Lattices and Miller Indices
(100) face
[100] vector
(100) planes
(-100) face
(100 Planes)
Copy of solid state fff 2013
37
Law of crystallography :
1. Law of constancy of interfacial angles:
2. Law of symmetry :
3. Law of rational indices
Face intercepts I
Crystal faces are defined by indicating their intercepts on the crystallographic axes. The
units along the axes is determined by the periodicity along theses axes:
- c
- b
- a
Intercepts: 5a : 3b : 2c = 5 : 3 : 2
+ c
+ b
+ a
2c
3b
5a
Face intercepts II
Faces parallel to an axis have an intercept with that axis at infinity
+ c
- c
+ b- b
+ a
- a
a
Intercepts: 3a : b : c = 3 :  : 
 c
 b
Face intercepts III
Intercepts are always given as relative values, e.g. they are divided until they have no common fac
Parallel faces in the same quadrant have, therefore, the same indices
+ c
+ b- b
+ a
- a
a
4c
2b1b
2a
2c
Intercepts: 4a : 2b : 4c = 4 : 2 : 4
div. by 2
 2 : 1 : 2
- c
Intercepts: 2a : 1b : 2c = 2 : 1: 2
Intercept ratios are called Weiss indices
MILLER INDICES
 PLANES
 DIRECTIONS
Miller indices I
The Miller indices of a face are derived from the Weiss indices by inverting the latter
and, if necessary, eliminating the fractions.
Reason for using Miller indices:- avoiding the index 
- simplifies crystallographic calculations
- simplifies the interpretation of x-ray diffraction
Example:
Weiss indices Miller indices
1 1 1
1  1 1 0 0
1 1 1
1 2 3 1 2 3 1 0.5 0.333 x 6 6 3 2
Miller indices are placed in round brackets, e.g. (1 0 0). Commas are only used, if two
digit indices appear, e.g. (1,14,2)
Negative intercepts are indicated by a bar above the number, e.g. (1 0 0).
Indices, which are not precisely known, are replaced by the letters h, k, l. This system
is also used to indcate indices of faces with common orientation properties e.g.
(0, k, 0) all faces parallel to the a- and c-axis
(0, k, l) all faces parallel to the a- axis
 Find intercepts along axes → 2 3 1
 Take reciprocal → 1/2 1/3 1
 Convert to smallest integers in the same ratio → 3 2 6
 Enclose in parenthesis → (326)
(2,0,0)
(0,3,0)
(0,0,1)
Miller Indices for planes
                
                
                
                
                
                
                
                
                
                
5a + 3b
a
b
Miller indices → [53]
(0,0)
(4,3)
Miller Indices for directions
 Interplaner Distances for Cubic Crystal or Spacing of planes
222
lkh
a
dhkl


Here a = length of any side of a cube in Angstrom (A0 )
h – intercept made by plane on x- axis
k- – intercept made by plane on y- axis
l - – intercept made by plane on z- axis
Index
Number of
members in a
cubic lattice
dhkl
(100) 6
(110) 12 The (110) plane bisects the
face diagonal
(111) 8 The (111) plane trisects the
body diagonal
(210) 24
(211) 24
(221) 24
(310) 24
(311) 24
(320) 24
(321) 48
100d a
110 / 2 2 / 2d a a 
111 / 3 3 /3d a a 
Copy of solid state fff 2013
NanoLab/NSF NUE/Bumm
X-ray Diffraction
 Bragg’s Law
very small wavelengths of
radiation.
 Why are electrons go for studying matter?
 Why are electrons not ideal?
 What could be used instead?
 Xrays made by slamming electrons into metals.
Bragg’s Law
nλ = 2 d sin θ
 Constructive interference only occurs for certain θ’s
correlating to a (hkl) plane, specifically when the path
difference is equal to n wavelengths.
A simple explanation of what the Braggs realised.
path difference=nλ give constructive
interference.
Path difference depends on distance
between lattice planes d
d
path difference=nλ give constructive
interference.
let’s look at different angle rays.
path difference=nλ give constructive
interference.
for different angles path difference varies. Some angles give constructive some
destructive.
Braggs Law Path difference =2dsinθ=nλ
The Braggs realised that by sending the X rays in at different angles they should get periods of constructive
and destructive interference.
X ray tube target
Turntable
Collimating
Slits
The Bragg Spectrometer
This would help them
determine the lattice
structure including d.
In two dimensions this type of
pattern is produced.
 typical lattice diffraction pattern for iron
57
a) ROCK SALT STRUCTURE (NaCl)
• CCP Cl- with Na+ in all Octahedral
holes
• Lattice: FCC
• Motif: Cl at (0,0,0); Na at (1/2,0,0)
• 4 NaCl in one unit cell
• Coordination: 6:6 (octahedral)
• Cation and anion sites are topologically
identical
STRUCTURE TYPE - AX NaCl
CLOSE PACKED STRUCTURES
58
• CCP S2- with Zn2+ in half Tetrahedral holes ( T+ {or T-}
filled)
• Lattice: FCC
• 4 ZnS in one unit cell
• Motif: S at (0,0,0); Zn at (1/4,1/4,1/4)
• Coordination: 4:4 (tetrahedral)
• Cation and anion sites are topologically identical
b) SPHALERITE OR ZINC BLEND (ZnS) STRUCTURE
59
• HCP with Ni in all Octahedral holes
• Lattice: Hexagonal - P
• Motif: 2Ni at (0,0,0) & (0,0,1/2) 2As at (2/3,1/3,1/4)
& (1/3,2/3,3/4)
• 2 NiAs in unit cell
• Coordination: Ni 6 (octahedral) : As 6 (trigonal
prismatic)
c) NICKELARSENIDE (NiAs)
60
• HCP S2- with Zn2+ in half Tetrahedral holes ( T+ {or T-}
filled )
• Lattice: Hexagonal - P
• Motif: 2 S at (0,0,0) & (2/3,1/3,1/2); 2 Zn at (2/3,1/3,1/8) &
(0,0,5/8)
• 2 ZnS in unit cell
• Coordination: 4:4 (tetrahedral)
d) WURTZITE ( ZnS )
61
COMPARISON OF WURTZITE AND ZINC BLENDE
62
STRUCTURE TYPE - AX
NON – CLOSE PACKED STRUCTURES
CUBIC-P (PRIMITIVE) ( eg. Cesium Chloride ( CsCl ) )
• Motif: Cl at (0,0,0); Cs at (1/2,1/2,1/2)
• 1 CsCl in one unit cell
• Coordination: 8:8 (cubic)
• Adoption by chlorides, bromides and iodides of larger cations,
• e.g. Cs+, Tl+, NH4
+
63
• CCP Ca2+ with F- in all Tetrahedral holes
• Lattice: fcc
• Motif: Ca2+ at (0,0,0); 2F- at (1/4,1/4,1/4) & (3/4,3/4,3/4)
• 4 CaF2 in one unit cell
• Coordination: Ca2+ 8 (cubic) : F- 4 (tetrahedral)
• In the related Anti-Fluorite structure Cation and
Anion positions are reversed
STRUCTURE TYPE - AX2
CLOSE PACKED STRUCTURE eg. FLUORITE (CaF2)
64
• CCP Ca2+ with F- in all Tetrahedral holes
• Lattice: fcc
• Motif: Ca2+ at (0,0,0); 2F- at (1/4,1/4,1/4) & (3/4,3/4,3/4)
• 4 CaF2 in one unit cell
• Coordination: Ca2+ 8 (cubic) : F- 4 (tetrahedral)
• In the related Anti-Fluorite structure Cation and
Anion positions are reversed
STRUCTURE TYPE - AX2
CLOSE PACKED STRUCTURE eg. FLUORITE (CaF2)
65
ALTERNATE REPRESENTATION OF FLUORITE
STRUCTURE
Anti–Flourite structure (or Na2O structure) – positions of
cations and anions are reversed related to Fluorite structure
66
RUTILE STRUCTURE, TiO2
• HCP of O2- ( distorted hcp or Tetragonal)
• Ti4+ in half of octahedral holes
67
• HCP of Iodide with Cd in Octahedral holes of alternate layers
• CCP analogue of CdI2 is CdCl2
STRUCTURE TYPE - AX2
NON-CLOSE PACKED STRUCTURE
LAYER STRUCTURE ( eg. Cadmium iodide ( CdI2 ))
68
COMPARISON OF CdI2 AND NiAs
69
HCPANALOGUE OF FLOURITE (CaF2) ?
• No structures of HCP are known with all Tetrahedral sites (T+
and T-) filled. (i.e. there is no HCP analogue of the Fluorite/Anti-
Fluorite Structure).
• The T+ and T- interstitial sites above and below a layer of close-
packed spheres in HCP are too close to each other to tolerate the
coulombic repulsion generated by filling with like-charged species.
Unknown HCP
analogue of FluoriteFluorite
70
HOLE FILLING IN CCP
71
Formula Type and fraction of sites
occupied
CCP HCP
AX All octahedral
Half tetrahedral (T+ or T-)
Rock salt (NaCl)
Zinc Blend (ZnS)
Nickel Arsenide (NiAs)
Wurtzite (ZnS)
AX2 All Tetrahedral
Half octahedral (ordered
framework)
Half octahedral (Alternate
layers full/ empty)
Fluorite (CaF2),
Anti-Fluorite (Na2O)
Anatase (TiO2)
Cadmium Chloride
(CdCl2)
Not known
Rutile (TiO2)
Cadmium iodide (CdI2)
A3X All octahedral & All
Tetrahedral
Li3Bi Not known
AX3 One third octahedral YCl3 BiI3
SUMMARY OF IONIC CRYSTAL STRUCTURE TYPES
72
Rock salt(NaCl) – occupation of all octahedral holes
• Very common (in ionics, covalents & intermetallics )
• Most alkali halides (CsCl, CsBr, CsI excepted)
• Most oxides / chalcogenides of alkaline earths
• Many nitrides, carbides, hydrides (e.g. ZrN, TiC, NaH)
Fluorite (CaF2) – occupation of all tetrahedral holes
• Fluorides of large divalent cations, chlorides of Sr, Ba
• Oxides of large quadrivalent cations (Zr, Hf, Ce, Th, U)
Anti-Fluorite (Na2O) – occupation of all tetrahedral holes
• Oxides /chalcogenides of alkali metals
Zinc Blende/Sphalerite ( ZnS ) – occupation of half tetrahedral holes
• Formed from Polarizing Cations (Cu+, Ag+, Cd2+, Ga3+...) and
Polarizable Anions (I-, S2-, P3-, ...)
e.g. Cu(F,Cl,Br,I), AgI, Zn(S,Se,Te), Ga(P,As), Hg(S,Se,Te)
Examples of CCP Structure Adoption
73
Examples of HCP Structure Adoption
Nickel Arsenide ( NiAs ) – occupation of all octahedral holes
• Transition metals with chalcogens, As, Sb, Bi e.g. Ti(S,Se,Te);
Cr(S,Se,Te,Sb); Ni(S,Se,Te,As,Sb,Sn)
Cadmium Iodide ( CdI2 ) – occupation half octahedral (alternate) holes
• Iodides of moderately polarising cations; bromides and chlorides of
strongly polarising cations. e.g. PbI2, FeBr2, VCl2
• Hydroxides of many divalent cations. e.g. (Mg,Ni)(OH)2
• Di-chalcogenides of many quadrivalent cations . e.g. TiS2, ZrSe2, CoTe2
Cadmium Chloride CdCl2 (CCP equivalent of CdI2) – half octahedral holes
• Chlorides of moderately polarising cations e.g. MgCl2, MnCl2
• Di-sulfides of quadrivalent cations e.g. TaS2, NbS2 (CdI2 form as well)
• Cs2O has the anti-cadmium chloride structure
74
PEROVSKITE STRUCTURE
 Formula unit – ABO3
CCP of A atoms(bigger) at the corners
 O atoms at the face centers
 B atoms(smaller) at the body-center
75
• Lattice: Primitive Cubic (idealised structure)
• 1 CaTiO3 per unit cell
• A-Cell Motif: Ti at (0, 0, 0); Ca at (1/2, 1/2, 1/2);
3O at (1/2, 0, 0), (0, 1/2, 0), (0, 0, 1/2)
• Ca 12-coordinate by O (cuboctahedral)
• Ti 6-coordinate by O (octahedral)
• O distorted octahedral (4xCa + 2xTi)
PEROVSKITE
• Examples: NaNbO3 , BaTiO3 ,
CaZrO3 , YAlO3 , KMgF3
• Many undergo small distortions:
e.g. BaTiO3 is ferroelectric
76
SPINEL STRUCTURE
 Formula unit AB2O4 (combination of Rock Salt
and Zinc Blend Structure)
 Oxygen atoms form FCC
 A2+ occupy tetrahedral holes
 B3+ occupy octahedral holes
INVERSE SPINEL
 A2+ ions and half of B3+ ions
occupy octahedral holes
 Other half of B3+ ions occupy
tetrahedral holes
 Formula unit is B(AB)O4

Weitere ähnliche Inhalte

Was ist angesagt?

Crystal Structure, BCC ,FCC,HCP
Crystal Structure, BCC ,FCC,HCPCrystal Structure, BCC ,FCC,HCP
Crystal Structure, BCC ,FCC,HCPBSMRSTU
 
Crystal structure notes
Crystal structure notesCrystal structure notes
Crystal structure notesPraveen Vaidya
 
Space lattice and crystal structure,miller indices PEC UNIVERSITY CHD
Space lattice and crystal structure,miller indices PEC UNIVERSITY CHDSpace lattice and crystal structure,miller indices PEC UNIVERSITY CHD
Space lattice and crystal structure,miller indices PEC UNIVERSITY CHDPEC University Chandigarh
 
Lect3 Tinh thể
Lect3 Tinh thểLect3 Tinh thể
Lect3 Tinh thểdayhoahoc
 
MATERIAL SCIENCE-CRYSTALLOGRAPHY (ATOMIC RADIUS,APF,BONDING ENERGY)
MATERIAL SCIENCE-CRYSTALLOGRAPHY (ATOMIC RADIUS,APF,BONDING ENERGY)MATERIAL SCIENCE-CRYSTALLOGRAPHY (ATOMIC RADIUS,APF,BONDING ENERGY)
MATERIAL SCIENCE-CRYSTALLOGRAPHY (ATOMIC RADIUS,APF,BONDING ENERGY)Abhilash kk
 
Space lattices
Space latticesSpace lattices
Space latticesjo
 
Materiales the science and engineering of materials - Solution Manual
Materiales   the science and engineering of materials - Solution ManualMateriales   the science and engineering of materials - Solution Manual
Materiales the science and engineering of materials - Solution ManualMeylis Hydyrow
 
Nridul sinha's bravais lattice
Nridul sinha's bravais latticeNridul sinha's bravais lattice
Nridul sinha's bravais latticeNridul Sinha
 
Crystal Systems
Crystal SystemsCrystal Systems
Crystal SystemsRionislam
 
Unit i-crystal structure
Unit i-crystal structureUnit i-crystal structure
Unit i-crystal structureAkhil Chowdhury
 
Crystal structure
Crystal structureCrystal structure
Crystal structureParth Patel
 
Solid state physics lec 1
Solid state physics lec 1Solid state physics lec 1
Solid state physics lec 1Dr. Abeer Kamal
 
Solid state__physics (1)by D.Udayanga.
Solid  state__physics (1)by D.Udayanga.Solid  state__physics (1)by D.Udayanga.
Solid state__physics (1)by D.Udayanga.damitha udayanga
 
Crystal structures & Packing Fraction
Crystal structures & Packing FractionCrystal structures & Packing Fraction
Crystal structures & Packing Fractionbagga1212
 

Was ist angesagt? (20)

Engineering Physics - Crystal structure - Dr. Victor Vedanayakam.S
Engineering Physics - Crystal structure - Dr. Victor Vedanayakam.SEngineering Physics - Crystal structure - Dr. Victor Vedanayakam.S
Engineering Physics - Crystal structure - Dr. Victor Vedanayakam.S
 
Crystal structure
Crystal structureCrystal structure
Crystal structure
 
Crystal Structure, BCC ,FCC,HCP
Crystal Structure, BCC ,FCC,HCPCrystal Structure, BCC ,FCC,HCP
Crystal Structure, BCC ,FCC,HCP
 
Crystal structure notes
Crystal structure notesCrystal structure notes
Crystal structure notes
 
Space lattice and crystal structure,miller indices PEC UNIVERSITY CHD
Space lattice and crystal structure,miller indices PEC UNIVERSITY CHDSpace lattice and crystal structure,miller indices PEC UNIVERSITY CHD
Space lattice and crystal structure,miller indices PEC UNIVERSITY CHD
 
Crystal Physics
Crystal PhysicsCrystal Physics
Crystal Physics
 
Lect3 Tinh thể
Lect3 Tinh thểLect3 Tinh thể
Lect3 Tinh thể
 
MATERIAL SCIENCE-CRYSTALLOGRAPHY (ATOMIC RADIUS,APF,BONDING ENERGY)
MATERIAL SCIENCE-CRYSTALLOGRAPHY (ATOMIC RADIUS,APF,BONDING ENERGY)MATERIAL SCIENCE-CRYSTALLOGRAPHY (ATOMIC RADIUS,APF,BONDING ENERGY)
MATERIAL SCIENCE-CRYSTALLOGRAPHY (ATOMIC RADIUS,APF,BONDING ENERGY)
 
Space lattices
Space latticesSpace lattices
Space lattices
 
Materiales the science and engineering of materials - Solution Manual
Materiales   the science and engineering of materials - Solution ManualMateriales   the science and engineering of materials - Solution Manual
Materiales the science and engineering of materials - Solution Manual
 
CRYSTAL STRUCTURE
CRYSTAL STRUCTURE CRYSTAL STRUCTURE
CRYSTAL STRUCTURE
 
Nridul sinha's bravais lattice
Nridul sinha's bravais latticeNridul sinha's bravais lattice
Nridul sinha's bravais lattice
 
Solid state chemistry
Solid state chemistrySolid state chemistry
Solid state chemistry
 
Crystal Systems
Crystal SystemsCrystal Systems
Crystal Systems
 
Unit i-crystal structure
Unit i-crystal structureUnit i-crystal structure
Unit i-crystal structure
 
Crystal structure
Crystal structureCrystal structure
Crystal structure
 
Solid state physics lec 1
Solid state physics lec 1Solid state physics lec 1
Solid state physics lec 1
 
Solid state__physics (1)by D.Udayanga.
Solid  state__physics (1)by D.Udayanga.Solid  state__physics (1)by D.Udayanga.
Solid state__physics (1)by D.Udayanga.
 
Phys 4710 lec 3
Phys 4710 lec 3Phys 4710 lec 3
Phys 4710 lec 3
 
Crystal structures & Packing Fraction
Crystal structures & Packing FractionCrystal structures & Packing Fraction
Crystal structures & Packing Fraction
 

Ähnlich wie Copy of solid state fff 2013

Ähnlich wie Copy of solid state fff 2013 (20)

Crystal Structure.ppt
Crystal Structure.pptCrystal Structure.ppt
Crystal Structure.ppt
 
4353486.ppt
4353486.ppt4353486.ppt
4353486.ppt
 
Module2
Module2Module2
Module2
 
Phy351 ch 3
Phy351 ch 3Phy351 ch 3
Phy351 ch 3
 
Phy351 ch 3
Phy351 ch 3Phy351 ch 3
Phy351 ch 3
 
Miller indecies
Miller indeciesMiller indecies
Miller indecies
 
Solid state physics unit 1.pdf
Solid state physics unit 1.pdfSolid state physics unit 1.pdf
Solid state physics unit 1.pdf
 
Packing density
Packing densityPacking density
Packing density
 
Crystallography SP.pptx
Crystallography SP.pptxCrystallography SP.pptx
Crystallography SP.pptx
 
Atoms and molecules
Atoms and moleculesAtoms and molecules
Atoms and molecules
 
Chapter 3 - crystal structure and solid state physics
Chapter 3 - crystal structure and solid state physicsChapter 3 - crystal structure and solid state physics
Chapter 3 - crystal structure and solid state physics
 
Solid state physics by Dr. kamal Devlal.pdf
Solid state physics by Dr. kamal Devlal.pdfSolid state physics by Dr. kamal Devlal.pdf
Solid state physics by Dr. kamal Devlal.pdf
 
Crystal structure
Crystal structureCrystal structure
Crystal structure
 
Ch 27.2 crystalline materials & detects in crystalline materials
Ch 27.2 crystalline materials & detects in crystalline materialsCh 27.2 crystalline materials & detects in crystalline materials
Ch 27.2 crystalline materials & detects in crystalline materials
 
X-Ray Topic.ppt
X-Ray Topic.pptX-Ray Topic.ppt
X-Ray Topic.ppt
 
Crystal Structure
Crystal StructureCrystal Structure
Crystal Structure
 
Crystallography
CrystallographyCrystallography
Crystallography
 
Lecture3
Lecture3Lecture3
Lecture3
 
Bell 301 unit II
Bell 301 unit IIBell 301 unit II
Bell 301 unit II
 
inmperfections in crystals
 inmperfections in crystals inmperfections in crystals
inmperfections in crystals
 

Mehr von Nitin Bansod

Evolution of ncc ppt nhb
Evolution of ncc ppt nhbEvolution of ncc ppt nhb
Evolution of ncc ppt nhbNitin Bansod
 
Inner Transition Element by Dr.N.H.Bansod
Inner Transition Element  by Dr.N.H.BansodInner Transition Element  by Dr.N.H.Bansod
Inner Transition Element by Dr.N.H.BansodNitin Bansod
 
Extraction of elements
Extraction of elements Extraction of elements
Extraction of elements Nitin Bansod
 
Colligative properties ppt ssc,amt
Colligative properties ppt ssc,amtColligative properties ppt ssc,amt
Colligative properties ppt ssc,amtNitin Bansod
 

Mehr von Nitin Bansod (6)

Evolution of ncc ppt nhb
Evolution of ncc ppt nhbEvolution of ncc ppt nhb
Evolution of ncc ppt nhb
 
Inner Transition Element by Dr.N.H.Bansod
Inner Transition Element  by Dr.N.H.BansodInner Transition Element  by Dr.N.H.Bansod
Inner Transition Element by Dr.N.H.Bansod
 
ACID BASE THEORY
ACID BASE THEORY ACID BASE THEORY
ACID BASE THEORY
 
Extraction of elements
Extraction of elements Extraction of elements
Extraction of elements
 
Colligative properties ppt ssc,amt
Colligative properties ppt ssc,amtColligative properties ppt ssc,amt
Colligative properties ppt ssc,amt
 
Boron family new
Boron family  newBoron family  new
Boron family new
 

Kürzlich hochgeladen

Pests of Redgram_Identification, Binomics_Dr.UPR
Pests of Redgram_Identification, Binomics_Dr.UPRPests of Redgram_Identification, Binomics_Dr.UPR
Pests of Redgram_Identification, Binomics_Dr.UPRPirithiRaju
 
Pests of tenai_Identification,Binomics_Dr.UPR
Pests of tenai_Identification,Binomics_Dr.UPRPests of tenai_Identification,Binomics_Dr.UPR
Pests of tenai_Identification,Binomics_Dr.UPRPirithiRaju
 
IB Biology New syllabus B3.2 Transport.pptx
IB Biology New syllabus B3.2 Transport.pptxIB Biology New syllabus B3.2 Transport.pptx
IB Biology New syllabus B3.2 Transport.pptxUalikhanKalkhojayev1
 
Basic Concepts in Pharmacology in molecular .pptx
Basic Concepts in Pharmacology in molecular  .pptxBasic Concepts in Pharmacology in molecular  .pptx
Basic Concepts in Pharmacology in molecular .pptxVijayaKumarR28
 
Shiva and Shakti: Presumed Proto-Galactic Fragments in the Inner Milky Way
Shiva and Shakti: Presumed Proto-Galactic Fragments in the Inner Milky WayShiva and Shakti: Presumed Proto-Galactic Fragments in the Inner Milky Way
Shiva and Shakti: Presumed Proto-Galactic Fragments in the Inner Milky WaySérgio Sacani
 
Pests of cumbu_Identification, Binomics, Integrated ManagementDr.UPR.pdf
Pests of cumbu_Identification, Binomics, Integrated ManagementDr.UPR.pdfPests of cumbu_Identification, Binomics, Integrated ManagementDr.UPR.pdf
Pests of cumbu_Identification, Binomics, Integrated ManagementDr.UPR.pdfPirithiRaju
 
Pests of ragi_Identification, Binomics_Dr.UPR
Pests of ragi_Identification, Binomics_Dr.UPRPests of ragi_Identification, Binomics_Dr.UPR
Pests of ragi_Identification, Binomics_Dr.UPRPirithiRaju
 
Applied Biochemistry feedback_M Ahwad 2023.docx
Applied Biochemistry feedback_M Ahwad 2023.docxApplied Biochemistry feedback_M Ahwad 2023.docx
Applied Biochemistry feedback_M Ahwad 2023.docxmarwaahmad357
 
Contracts with Interdependent Preferences (2)
Contracts with Interdependent Preferences (2)Contracts with Interdependent Preferences (2)
Contracts with Interdependent Preferences (2)GRAPE
 
Physics Serway Jewett 6th edition for Scientists and Engineers
Physics Serway Jewett 6th edition for Scientists and EngineersPhysics Serway Jewett 6th edition for Scientists and Engineers
Physics Serway Jewett 6th edition for Scientists and EngineersAndreaLucarelli
 
RCPE terms and cycles scenarios as of March 2024
RCPE terms and cycles scenarios as of March 2024RCPE terms and cycles scenarios as of March 2024
RCPE terms and cycles scenarios as of March 2024suelcarter1
 
M.Pharm - Question Bank - Drug Delivery Systems
M.Pharm - Question Bank - Drug Delivery SystemsM.Pharm - Question Bank - Drug Delivery Systems
M.Pharm - Question Bank - Drug Delivery SystemsSumathi Arumugam
 
Application of Foraminiferal Ecology- Rahul.pptx
Application of Foraminiferal Ecology- Rahul.pptxApplication of Foraminiferal Ecology- Rahul.pptx
Application of Foraminiferal Ecology- Rahul.pptxRahulVishwakarma71547
 
TORSION IN GASTROPODS- Anatomical event (Zoology)
TORSION IN GASTROPODS- Anatomical event (Zoology)TORSION IN GASTROPODS- Anatomical event (Zoology)
TORSION IN GASTROPODS- Anatomical event (Zoology)chatterjeesoumili50
 
THE HISTOLOGY OF THE CARDIOVASCULAR SYSTEM 2024.pptx
THE HISTOLOGY OF THE CARDIOVASCULAR SYSTEM 2024.pptxTHE HISTOLOGY OF THE CARDIOVASCULAR SYSTEM 2024.pptx
THE HISTOLOGY OF THE CARDIOVASCULAR SYSTEM 2024.pptxAkinrotimiOluwadunsi
 
Krishi Vigyan Kendras - कृषि विज्ञान केंद्र
Krishi Vigyan Kendras - कृषि विज्ञान केंद्रKrishi Vigyan Kendras - कृषि विज्ञान केंद्र
Krishi Vigyan Kendras - कृषि विज्ञान केंद्रKrashi Coaching
 
3.2 Pests of Sorghum_Identification, Symptoms and nature of damage, Binomics,...
3.2 Pests of Sorghum_Identification, Symptoms and nature of damage, Binomics,...3.2 Pests of Sorghum_Identification, Symptoms and nature of damage, Binomics,...
3.2 Pests of Sorghum_Identification, Symptoms and nature of damage, Binomics,...PirithiRaju
 
Substances in Common Use for Shahu College Screening Test
Substances in Common Use for Shahu College Screening TestSubstances in Common Use for Shahu College Screening Test
Substances in Common Use for Shahu College Screening TestAkashDTejwani
 

Kürzlich hochgeladen (20)

Pests of Redgram_Identification, Binomics_Dr.UPR
Pests of Redgram_Identification, Binomics_Dr.UPRPests of Redgram_Identification, Binomics_Dr.UPR
Pests of Redgram_Identification, Binomics_Dr.UPR
 
Pests of tenai_Identification,Binomics_Dr.UPR
Pests of tenai_Identification,Binomics_Dr.UPRPests of tenai_Identification,Binomics_Dr.UPR
Pests of tenai_Identification,Binomics_Dr.UPR
 
IB Biology New syllabus B3.2 Transport.pptx
IB Biology New syllabus B3.2 Transport.pptxIB Biology New syllabus B3.2 Transport.pptx
IB Biology New syllabus B3.2 Transport.pptx
 
Basic Concepts in Pharmacology in molecular .pptx
Basic Concepts in Pharmacology in molecular  .pptxBasic Concepts in Pharmacology in molecular  .pptx
Basic Concepts in Pharmacology in molecular .pptx
 
Shiva and Shakti: Presumed Proto-Galactic Fragments in the Inner Milky Way
Shiva and Shakti: Presumed Proto-Galactic Fragments in the Inner Milky WayShiva and Shakti: Presumed Proto-Galactic Fragments in the Inner Milky Way
Shiva and Shakti: Presumed Proto-Galactic Fragments in the Inner Milky Way
 
Data delivery from the US-EPA Center for Computational Toxicology and Exposur...
Data delivery from the US-EPA Center for Computational Toxicology and Exposur...Data delivery from the US-EPA Center for Computational Toxicology and Exposur...
Data delivery from the US-EPA Center for Computational Toxicology and Exposur...
 
Pests of cumbu_Identification, Binomics, Integrated ManagementDr.UPR.pdf
Pests of cumbu_Identification, Binomics, Integrated ManagementDr.UPR.pdfPests of cumbu_Identification, Binomics, Integrated ManagementDr.UPR.pdf
Pests of cumbu_Identification, Binomics, Integrated ManagementDr.UPR.pdf
 
Pests of ragi_Identification, Binomics_Dr.UPR
Pests of ragi_Identification, Binomics_Dr.UPRPests of ragi_Identification, Binomics_Dr.UPR
Pests of ragi_Identification, Binomics_Dr.UPR
 
Applied Biochemistry feedback_M Ahwad 2023.docx
Applied Biochemistry feedback_M Ahwad 2023.docxApplied Biochemistry feedback_M Ahwad 2023.docx
Applied Biochemistry feedback_M Ahwad 2023.docx
 
Contracts with Interdependent Preferences (2)
Contracts with Interdependent Preferences (2)Contracts with Interdependent Preferences (2)
Contracts with Interdependent Preferences (2)
 
Applying Cheminformatics to Develop a Structure Searchable Database of Analyt...
Applying Cheminformatics to Develop a Structure Searchable Database of Analyt...Applying Cheminformatics to Develop a Structure Searchable Database of Analyt...
Applying Cheminformatics to Develop a Structure Searchable Database of Analyt...
 
Physics Serway Jewett 6th edition for Scientists and Engineers
Physics Serway Jewett 6th edition for Scientists and EngineersPhysics Serway Jewett 6th edition for Scientists and Engineers
Physics Serway Jewett 6th edition for Scientists and Engineers
 
RCPE terms and cycles scenarios as of March 2024
RCPE terms and cycles scenarios as of March 2024RCPE terms and cycles scenarios as of March 2024
RCPE terms and cycles scenarios as of March 2024
 
M.Pharm - Question Bank - Drug Delivery Systems
M.Pharm - Question Bank - Drug Delivery SystemsM.Pharm - Question Bank - Drug Delivery Systems
M.Pharm - Question Bank - Drug Delivery Systems
 
Application of Foraminiferal Ecology- Rahul.pptx
Application of Foraminiferal Ecology- Rahul.pptxApplication of Foraminiferal Ecology- Rahul.pptx
Application of Foraminiferal Ecology- Rahul.pptx
 
TORSION IN GASTROPODS- Anatomical event (Zoology)
TORSION IN GASTROPODS- Anatomical event (Zoology)TORSION IN GASTROPODS- Anatomical event (Zoology)
TORSION IN GASTROPODS- Anatomical event (Zoology)
 
THE HISTOLOGY OF THE CARDIOVASCULAR SYSTEM 2024.pptx
THE HISTOLOGY OF THE CARDIOVASCULAR SYSTEM 2024.pptxTHE HISTOLOGY OF THE CARDIOVASCULAR SYSTEM 2024.pptx
THE HISTOLOGY OF THE CARDIOVASCULAR SYSTEM 2024.pptx
 
Krishi Vigyan Kendras - कृषि विज्ञान केंद्र
Krishi Vigyan Kendras - कृषि विज्ञान केंद्रKrishi Vigyan Kendras - कृषि विज्ञान केंद्र
Krishi Vigyan Kendras - कृषि विज्ञान केंद्र
 
3.2 Pests of Sorghum_Identification, Symptoms and nature of damage, Binomics,...
3.2 Pests of Sorghum_Identification, Symptoms and nature of damage, Binomics,...3.2 Pests of Sorghum_Identification, Symptoms and nature of damage, Binomics,...
3.2 Pests of Sorghum_Identification, Symptoms and nature of damage, Binomics,...
 
Substances in Common Use for Shahu College Screening Test
Substances in Common Use for Shahu College Screening TestSubstances in Common Use for Shahu College Screening Test
Substances in Common Use for Shahu College Screening Test
 

Copy of solid state fff 2013

  • 1. 1 Dr. Nitin H. Bansod Department of Chemistry, Shri Shivaji Science College, Amravati.
  • 2. 2 CONTENTS  Types of solids  Types of structures adopted by solids
  • 3. 3 SOLIDS can be divided into two catagories.  Crystalline  Amorphous Crystalline has long range order Amorphous materials have short range order Effect of Crystallinity on Physical properties - ex. Polyethylene
  • 4. 4 Crystal Type Particles Interparticle Forces Physical Behaviour Examples Atomic Molecular Metallic Ionic Network Atoms Molecules Atoms Positive and negative ions Atoms Dispersion Dispersion Dipole-dipole H-bonds Metallic bond Ion-ion attraction Covalent • Soft • Very low mp • Poor thermal and electrical conductors  Fairly soft  Low to moderate mp  Poor thermal and electrical conductors  Soft to hard  Low to very high mp  Mellable and ductile  Excellent thermal and electrical conductors  Hard and brittle  High mp  Good thermal and electrical conductors in molten condition • Very hard • Very high mp • Poor thermal and electrical conductors Group 8A Ne to Rn O2, P4, H2O, Sucrose Na, Cu, Fe NaCl, CaF2, MgO SiO2(Quartz) C (Diamond) TYPES OF CRYSTALLINE SOLIDS
  • 5. 5 Molecular Solids Covalent Solids Ionic solids Metallic solids Na+ Cl- STRUCTURES OF CRYSTALLINE SOLID TYPES
  • 7. 7 CRYSTAL STRUCTURE Crystal structure is the periodic arrangement of atoms in the crystal. Association of each lattice point with a group of atoms(Basis or Motif). Lattice: Infinite array of points in space, in which each point has identical surroundings to all others. Space Lattice  Arrangements of atoms = Lattice of points onto which the atoms are hung. Elemental solids (Argon): Basis = single atom. Polyatomic Elements: Basis = two or four atoms. Complex organic compounds: Basis = thousands of atoms. + Space Lattice + Basis = Crystal Structure = • • • • • • • • •
  • 8. 8 ONE DIMENTIONAL LATTICE ONE DIMENTIONAL UNIT CELL a a UNIT CELL : Building block, repeats in a regular way a
  • 10. 10 a b a  b,   90° a  b,  = 90° a b a = b,  = 90° a a a  b,  = 90° a b a = b,  =120° a a TWO DIMENTIONAL UNIT CELL TYPES
  • 11. 11 EXAMPLE OF TWO DIMENTIONAL UNIT CELL
  • 12. 12 TWO DIMENTIONAL UNIT CELL POSSIBILITIES OF NaCl Na+ Cl-
  • 13. 13
  • 14. The “unit cell” is the basic repeating unit of the arrangement of atoms, ions or molecules in a crystalline solid. The “lattice” refers to the 3-D array of particles in a crystalline solid. One type of atom occupies a “lattice point” in the array.
  • 16. 16 THREE DIMENTIONAL UNIT CELLS / UNIT CELL SHAPES 1 2 3 4 5 6 7
  • 17. 17 Primitive ( P ) Body Centered ( I ) Face Centered ( F ) C-Centered (C ) LATTICE TYPES
  • 18. 18 BRAVAIS LATTICES 7 UNIT CELL TYPES + 4 LATTICE TYPES = 14 BRAVAIS LATTICES
  • 19. 19 COUNTING ATOMS IN THE THREE DIMENTIONAL UNIT CELL  Vertex(corner) atom shared by 8 cells  1/8 atom per cell  Edge atom shared by 4 cells  1/4 atom per cell  Face atom shared by 2 cells  1/2 atom per cell  Body unique to 1 cell  1 atom per cell Atoms in different positions in a cell are shared by differing numbers of unit cells
  • 20. . A: Body-centered cubic (bcc) B: Simple cubic (sc)
  • 21. Contributions of Atoms to Cubic Unit Cells Position of Atoms in Unit Cell Contribution to Unit Cell Unit-Cell Type Center 1 bcc Face 1/2 Fcc Corner 1/8 fcc, bcc, simple cubic How many total atoms are found in a simple cubic unit cell? Face centered cube? Body centered cube?
  • 22. 22 Number of Atoms per unit cell in cubic crystal system(z) 1.For SCC( Simple Cubic Crystal Lattice) Vertex(corner) atom shared by 8 cells  1/8 atom per cell Z = 1/8 × 8 = 1 2. For FCC (Face Centred Cubic lattice) Vertex(corner) atom shared by 8 cells  1/8 atom per cell Face atom shared by 2 cells  1/2 atom per cell Z = 1/8 × 8 + 1/2 × 6 = 1+3 = 4
  • 23. Unit Cells  A body-centered cubic (bcc) unit cell has atoms at the 8 corners of a cube and at the center of the cell  A simple cubic unit cell has atoms only at the 8 corners of a cube.
  • 24. Number Atoms in a Unit Cell  In the simple cubic cell there are only the 8 atoms at the corners.  1/8 x 8 = 1 atom in cell  In bcc, 8 atoms at the corners and 1 in center.  1/8 x 8 + 1 x 1 = 2 atoms in the cell
  • 25. 25 3.For BCC(Body Centred Cubic lattice) Vertex(corner) atom shared by 8 cells  1/8 atom per cell And Body unique to 1 cell  1 atom per cell Z = 1/8 × 8 + 1 × 1 = 1+1 = 2
  • 26. 26 Density of crystal matter (D) Density = Mass of the Unit cell ……………………………… Volume of the Unit cell Mass of unit cell = Z × mass of each atom = Z × M/N0 Volume of unit cell = a3 = where a is edge length is in pm 1pm = 10-12 m. D = Z × M where M –molecular weight ………. No × a3 No- Avogadro's Number(6.023×10-23
  • 27. 27 Numerical problem: 1.The length of side of unit cell of a cubic crystal is 4×10-3 m. the density of crystal matter is 1.2× 10-3 kg m-3.if molar mass is 2.4×10-2 mole-1 then find out i) type of lattice ii) number of atoms in each unit cell Solution :
  • 28. 28 Numerical problem: 1. The corner of a face centred cubic Crystal has atoms of elements X while at centre of face has of element Y. find out the formula of crystal compound.
  • 29. The Chemistry of Solids Miller Indices (l,m,n) are a way of denoting planes in crystal lattices.
  • 30. Types of planes of cubic Crystal or indexing the planes (110) planes (130) planes a b (-210) planes
  • 31. [010] [100] [001] [110] [101] [011] [110] [111] • Coordinates of the final point  coordinates of the initial point • Reduce to smallest integer values
  • 32. Intercepts → 1   Plane → (100) Family → {100} → 3 Intercepts → 1 1  Plane → (110) Family → {110} → 6 Intercepts → 1 1 1 Plane → (111) Family → {111} → 8 (Octahedral plane)
  • 34. Planes in Lattices and Miller Indices
  • 35. (100) face [100] vector (100) planes (-100) face (100 Planes)
  • 37. 37 Law of crystallography : 1. Law of constancy of interfacial angles: 2. Law of symmetry : 3. Law of rational indices
  • 38. Face intercepts I Crystal faces are defined by indicating their intercepts on the crystallographic axes. The units along the axes is determined by the periodicity along theses axes: - c - b - a Intercepts: 5a : 3b : 2c = 5 : 3 : 2 + c + b + a 2c 3b 5a
  • 39. Face intercepts II Faces parallel to an axis have an intercept with that axis at infinity + c - c + b- b + a - a a Intercepts: 3a : b : c = 3 :  :   c  b
  • 40. Face intercepts III Intercepts are always given as relative values, e.g. they are divided until they have no common fac Parallel faces in the same quadrant have, therefore, the same indices + c + b- b + a - a a 4c 2b1b 2a 2c Intercepts: 4a : 2b : 4c = 4 : 2 : 4 div. by 2  2 : 1 : 2 - c Intercepts: 2a : 1b : 2c = 2 : 1: 2 Intercept ratios are called Weiss indices
  • 42. Miller indices I The Miller indices of a face are derived from the Weiss indices by inverting the latter and, if necessary, eliminating the fractions. Reason for using Miller indices:- avoiding the index  - simplifies crystallographic calculations - simplifies the interpretation of x-ray diffraction Example: Weiss indices Miller indices 1 1 1 1  1 1 0 0 1 1 1 1 2 3 1 2 3 1 0.5 0.333 x 6 6 3 2 Miller indices are placed in round brackets, e.g. (1 0 0). Commas are only used, if two digit indices appear, e.g. (1,14,2) Negative intercepts are indicated by a bar above the number, e.g. (1 0 0). Indices, which are not precisely known, are replaced by the letters h, k, l. This system is also used to indcate indices of faces with common orientation properties e.g. (0, k, 0) all faces parallel to the a- and c-axis (0, k, l) all faces parallel to the a- axis
  • 43.  Find intercepts along axes → 2 3 1  Take reciprocal → 1/2 1/3 1  Convert to smallest integers in the same ratio → 3 2 6  Enclose in parenthesis → (326) (2,0,0) (0,3,0) (0,0,1) Miller Indices for planes
  • 44.                                                                                                                                                                           5a + 3b a b Miller indices → [53] (0,0) (4,3) Miller Indices for directions
  • 45.  Interplaner Distances for Cubic Crystal or Spacing of planes 222 lkh a dhkl   Here a = length of any side of a cube in Angstrom (A0 ) h – intercept made by plane on x- axis k- – intercept made by plane on y- axis l - – intercept made by plane on z- axis
  • 46. Index Number of members in a cubic lattice dhkl (100) 6 (110) 12 The (110) plane bisects the face diagonal (111) 8 The (111) plane trisects the body diagonal (210) 24 (211) 24 (221) 24 (310) 24 (311) 24 (320) 24 (321) 48 100d a 110 / 2 2 / 2d a a  111 / 3 3 /3d a a 
  • 49. very small wavelengths of radiation.  Why are electrons go for studying matter?  Why are electrons not ideal?  What could be used instead?  Xrays made by slamming electrons into metals.
  • 50. Bragg’s Law nλ = 2 d sin θ  Constructive interference only occurs for certain θ’s correlating to a (hkl) plane, specifically when the path difference is equal to n wavelengths.
  • 51. A simple explanation of what the Braggs realised.
  • 52. path difference=nλ give constructive interference. Path difference depends on distance between lattice planes d d
  • 53. path difference=nλ give constructive interference. let’s look at different angle rays.
  • 54. path difference=nλ give constructive interference. for different angles path difference varies. Some angles give constructive some destructive. Braggs Law Path difference =2dsinθ=nλ
  • 55. The Braggs realised that by sending the X rays in at different angles they should get periods of constructive and destructive interference. X ray tube target Turntable Collimating Slits The Bragg Spectrometer This would help them determine the lattice structure including d.
  • 56. In two dimensions this type of pattern is produced.  typical lattice diffraction pattern for iron
  • 57. 57 a) ROCK SALT STRUCTURE (NaCl) • CCP Cl- with Na+ in all Octahedral holes • Lattice: FCC • Motif: Cl at (0,0,0); Na at (1/2,0,0) • 4 NaCl in one unit cell • Coordination: 6:6 (octahedral) • Cation and anion sites are topologically identical STRUCTURE TYPE - AX NaCl CLOSE PACKED STRUCTURES
  • 58. 58 • CCP S2- with Zn2+ in half Tetrahedral holes ( T+ {or T-} filled) • Lattice: FCC • 4 ZnS in one unit cell • Motif: S at (0,0,0); Zn at (1/4,1/4,1/4) • Coordination: 4:4 (tetrahedral) • Cation and anion sites are topologically identical b) SPHALERITE OR ZINC BLEND (ZnS) STRUCTURE
  • 59. 59 • HCP with Ni in all Octahedral holes • Lattice: Hexagonal - P • Motif: 2Ni at (0,0,0) & (0,0,1/2) 2As at (2/3,1/3,1/4) & (1/3,2/3,3/4) • 2 NiAs in unit cell • Coordination: Ni 6 (octahedral) : As 6 (trigonal prismatic) c) NICKELARSENIDE (NiAs)
  • 60. 60 • HCP S2- with Zn2+ in half Tetrahedral holes ( T+ {or T-} filled ) • Lattice: Hexagonal - P • Motif: 2 S at (0,0,0) & (2/3,1/3,1/2); 2 Zn at (2/3,1/3,1/8) & (0,0,5/8) • 2 ZnS in unit cell • Coordination: 4:4 (tetrahedral) d) WURTZITE ( ZnS )
  • 61. 61 COMPARISON OF WURTZITE AND ZINC BLENDE
  • 62. 62 STRUCTURE TYPE - AX NON – CLOSE PACKED STRUCTURES CUBIC-P (PRIMITIVE) ( eg. Cesium Chloride ( CsCl ) ) • Motif: Cl at (0,0,0); Cs at (1/2,1/2,1/2) • 1 CsCl in one unit cell • Coordination: 8:8 (cubic) • Adoption by chlorides, bromides and iodides of larger cations, • e.g. Cs+, Tl+, NH4 +
  • 63. 63 • CCP Ca2+ with F- in all Tetrahedral holes • Lattice: fcc • Motif: Ca2+ at (0,0,0); 2F- at (1/4,1/4,1/4) & (3/4,3/4,3/4) • 4 CaF2 in one unit cell • Coordination: Ca2+ 8 (cubic) : F- 4 (tetrahedral) • In the related Anti-Fluorite structure Cation and Anion positions are reversed STRUCTURE TYPE - AX2 CLOSE PACKED STRUCTURE eg. FLUORITE (CaF2)
  • 64. 64 • CCP Ca2+ with F- in all Tetrahedral holes • Lattice: fcc • Motif: Ca2+ at (0,0,0); 2F- at (1/4,1/4,1/4) & (3/4,3/4,3/4) • 4 CaF2 in one unit cell • Coordination: Ca2+ 8 (cubic) : F- 4 (tetrahedral) • In the related Anti-Fluorite structure Cation and Anion positions are reversed STRUCTURE TYPE - AX2 CLOSE PACKED STRUCTURE eg. FLUORITE (CaF2)
  • 65. 65 ALTERNATE REPRESENTATION OF FLUORITE STRUCTURE Anti–Flourite structure (or Na2O structure) – positions of cations and anions are reversed related to Fluorite structure
  • 66. 66 RUTILE STRUCTURE, TiO2 • HCP of O2- ( distorted hcp or Tetragonal) • Ti4+ in half of octahedral holes
  • 67. 67 • HCP of Iodide with Cd in Octahedral holes of alternate layers • CCP analogue of CdI2 is CdCl2 STRUCTURE TYPE - AX2 NON-CLOSE PACKED STRUCTURE LAYER STRUCTURE ( eg. Cadmium iodide ( CdI2 ))
  • 69. 69 HCPANALOGUE OF FLOURITE (CaF2) ? • No structures of HCP are known with all Tetrahedral sites (T+ and T-) filled. (i.e. there is no HCP analogue of the Fluorite/Anti- Fluorite Structure). • The T+ and T- interstitial sites above and below a layer of close- packed spheres in HCP are too close to each other to tolerate the coulombic repulsion generated by filling with like-charged species. Unknown HCP analogue of FluoriteFluorite
  • 71. 71 Formula Type and fraction of sites occupied CCP HCP AX All octahedral Half tetrahedral (T+ or T-) Rock salt (NaCl) Zinc Blend (ZnS) Nickel Arsenide (NiAs) Wurtzite (ZnS) AX2 All Tetrahedral Half octahedral (ordered framework) Half octahedral (Alternate layers full/ empty) Fluorite (CaF2), Anti-Fluorite (Na2O) Anatase (TiO2) Cadmium Chloride (CdCl2) Not known Rutile (TiO2) Cadmium iodide (CdI2) A3X All octahedral & All Tetrahedral Li3Bi Not known AX3 One third octahedral YCl3 BiI3 SUMMARY OF IONIC CRYSTAL STRUCTURE TYPES
  • 72. 72 Rock salt(NaCl) – occupation of all octahedral holes • Very common (in ionics, covalents & intermetallics ) • Most alkali halides (CsCl, CsBr, CsI excepted) • Most oxides / chalcogenides of alkaline earths • Many nitrides, carbides, hydrides (e.g. ZrN, TiC, NaH) Fluorite (CaF2) – occupation of all tetrahedral holes • Fluorides of large divalent cations, chlorides of Sr, Ba • Oxides of large quadrivalent cations (Zr, Hf, Ce, Th, U) Anti-Fluorite (Na2O) – occupation of all tetrahedral holes • Oxides /chalcogenides of alkali metals Zinc Blende/Sphalerite ( ZnS ) – occupation of half tetrahedral holes • Formed from Polarizing Cations (Cu+, Ag+, Cd2+, Ga3+...) and Polarizable Anions (I-, S2-, P3-, ...) e.g. Cu(F,Cl,Br,I), AgI, Zn(S,Se,Te), Ga(P,As), Hg(S,Se,Te) Examples of CCP Structure Adoption
  • 73. 73 Examples of HCP Structure Adoption Nickel Arsenide ( NiAs ) – occupation of all octahedral holes • Transition metals with chalcogens, As, Sb, Bi e.g. Ti(S,Se,Te); Cr(S,Se,Te,Sb); Ni(S,Se,Te,As,Sb,Sn) Cadmium Iodide ( CdI2 ) – occupation half octahedral (alternate) holes • Iodides of moderately polarising cations; bromides and chlorides of strongly polarising cations. e.g. PbI2, FeBr2, VCl2 • Hydroxides of many divalent cations. e.g. (Mg,Ni)(OH)2 • Di-chalcogenides of many quadrivalent cations . e.g. TiS2, ZrSe2, CoTe2 Cadmium Chloride CdCl2 (CCP equivalent of CdI2) – half octahedral holes • Chlorides of moderately polarising cations e.g. MgCl2, MnCl2 • Di-sulfides of quadrivalent cations e.g. TaS2, NbS2 (CdI2 form as well) • Cs2O has the anti-cadmium chloride structure
  • 74. 74 PEROVSKITE STRUCTURE  Formula unit – ABO3 CCP of A atoms(bigger) at the corners  O atoms at the face centers  B atoms(smaller) at the body-center
  • 75. 75 • Lattice: Primitive Cubic (idealised structure) • 1 CaTiO3 per unit cell • A-Cell Motif: Ti at (0, 0, 0); Ca at (1/2, 1/2, 1/2); 3O at (1/2, 0, 0), (0, 1/2, 0), (0, 0, 1/2) • Ca 12-coordinate by O (cuboctahedral) • Ti 6-coordinate by O (octahedral) • O distorted octahedral (4xCa + 2xTi) PEROVSKITE • Examples: NaNbO3 , BaTiO3 , CaZrO3 , YAlO3 , KMgF3 • Many undergo small distortions: e.g. BaTiO3 is ferroelectric
  • 76. 76 SPINEL STRUCTURE  Formula unit AB2O4 (combination of Rock Salt and Zinc Blend Structure)  Oxygen atoms form FCC  A2+ occupy tetrahedral holes  B3+ occupy octahedral holes INVERSE SPINEL  A2+ ions and half of B3+ ions occupy octahedral holes  Other half of B3+ ions occupy tetrahedral holes  Formula unit is B(AB)O4