1. crystallogeaphy

3. Empirical Formula
C19H19N3O10
Formula weight
449.37
Temperature
100(2) K
Wave length Å
Crystal system
Triclinic
Space group Pī
Unit cell dimensions
a = (9) Å a= (5)°.
b = (12) Å b= (5)°.
c = (2) Å g = (5)°.
Volume
973.1(2) Å 3 Z 2
Density(calculated)
1.534 Mg/m3
Absorption coefficient
0.126 mm-1
F(000)
468
Crystal size
0.30×0.25×0.25 mm3
Theta range for data collection
1.78 to 29.00°
Index ranges
-11<=h<11,-14<=k<=14,-16<=1<=16
Reflections collected
11866
Independent reflecions
5169 [R(int)=0.0263]
Completmeness to theta=29.00°
99.8%
Refinement method
Full-matrix least-squares on F2
Data / restraints / parameters
5169 / 0 / 289
Goodness-of-fit on F2
1.003
Final R indices [for 4098 rfln with I>2sigma(I)]
R1= , wR2=0.0993
R indices (all data)
R1=0.0552, wR2=0.1088
Larges diff. peak and hole
0.388 and e. Å -3

4. جدول3-2 برخی از طول(Å)،زاویه های پیوندی(°) و زاویه های پیچشی(°)ترکیب هم بلور pydcH2).4H2O)( ( phen-dione
N(1)-C(2)
1.3403(17)
N(3)-C(17)
1.3342(17)
N(1)-C(1)
1.3439(16)
N(3)-C(13)
1.3378(17)
O(1)-C(6)
1.2165(16)
O(3)-C(18)
1.3181(17)
C(1)-C(12)
1.4873(18)
O(4)-C(18)
1.2176(17)
N(2)-C(11)
O(5)-C(19)
1.2134(17)
N(2)-C(12)
1.3411(17)
O(6)-C(19)
1.3175(17)
O(2)-C(7)
1.2127(16)
C(13)-C(18)
1.5027(19)
C(6)-C(7)
1.5399(19)
C(17)-C(19)
1.5060(18)
C(2)-N(1)-C(1)
117.83(12)
O(2)-C(7)-C(8)
123.50(13)
N(1)-C(1)-C(5)
121.74(12)
O(2)-C(7)-C(6)
118.64(12)
N(1)-C(1)-C(12)
117.27(11)
N(2)-C(11)-C(10)
123.86(13)
C(11)-N(2)-C(12)
117.65(11)
N(2)-C(12)-C(8)
122.48(12)
N(1)-C(2)-C(3)
124.03(12)
N(2)-C(12)-C(1)
116.67(11)
O(1)-C(6)-C(5)
122.90(12)
C(17)-N(3)-C(13)
117.54(11)
O(1)-C(6)-C(7)
118.75(12)
N(3)-C(13)-C(18)
115.52(12)
C(5)-C(6)-C(7)
118.32(11)
N(3)-C(17)-C(19)
114.09(11)
C(2)-N(1)-C(1)-C(5)
-0.34(19)
C(7)-C(8)-C(12)-N(2)
(12)
C(2)-N(1)-C(1)-C(12)
(12)
N(1)-C(1)-C(12)-N(2)
-1.89(18)
C(1)-N(1)-C(2)-C(3)
1.1(2)
C(5)-C(1)-C(12)-N(2)
178.79(12)
N(1)-C(2)-C(3)-C(4)
-0.5(2)
N(1)-C(1)-C(12)-C(8)
178.11(12)
N(1)-C(1)-C(5)-C(4)
-1.1(2)
C(17)-N(3)-C(13)-C(14)
0.2(2)
N(1)-C(1)-C(5)-C(6)
177.60(12)
C(17)-N(3)-C(13)-C(18)
179.95(12)
C(4)-C(5)-C(6)-O(1)
4.8(2)
N(3)-C(13)-C(14)-C(15)
C(1)-C(5)-C(6)-O(1)
(13)
C(13)-N(3)-C(17)-C(16)
-0.3(2)
O(1)-C(6)-C(7)-O(2)
-0.8(2)
C(13)-N(3)-C(17)-C(19)
(12)
C(5)-C(6)-C(7)-O(2)
(13)
C(15)-C(16)-C(17)-N(3)
-0.1(2)
O(1)-C(6)-C(7)-C(8)
177.16(12)
N(3)-C(13)-C(18)-O(4)
173.28(13)
O(2)-C(7)-C(8)-C(9)
-2.8(2)
C(14)-C(13)-C(18)-O(4)
-7.0(2)
O(2)-C(7)-C(8)-C(12)
174.42(13)
N(3)-C(13)-C(18)-O(3)
-6.35(19)
C(12)-N(2)-C(11)-C(10)
0.4(2)
C(14)-C(13)-C(18)-O(3)
173.38(13)
C(9)-C(10)-C(11)-N(2)
1.4(2)
N(3)-C(17)-C(19)-O(5)
2.7(2)
C(11)-N(2)-C(12)-C(8)
-1.96(19)
C(16)-C(17)-C(19)-O(5)
(14)
C(11)-N(2)-C(12)-C(1)
178.03(12)
N(3)-C(17)-C(19)-O(6)
(12)
C(9)-C(8)-C(12)-N(2)
1.8(2)
C(16)-C(17)-C(19)-O(6)
2.98(19)

5. Objectives By the end of this section you should:
be able to identify a unit cell in a symmetrical pattern
know that there are 7 possible unit cell shapes
be able to define cubic, tetragonal, orthorhombic and hexagonal unit cell shapes
Crystal Structure

6. LIQUIDS and LIQUID CRYSTALS
matter
Matter
GASES
LIQUIDS and LIQUID CRYSTALS
SOLIDS
Crystal Structure

7. Gases
Gases have atoms or molecules that do not bond to one another in a range of pressure, temperature and volume.
These molecules haven’t any particular order and move freely within a container.
Crystal Structure

8. Liquids and Liquid Crystals
Similar to gases, liquids haven’t any atomic/molecular order and they assume the shape of the containers.
Applying low levels of thermal energy can easily break the existing weak bonds.
Liquid crystals have mobile molecules, but a type of long range order can exist; the molecules have a permanent dipole. Applying an electric field rotates the dipole and establishes order within the collection of molecules.
+ -
Crystal Structure

9. Crytals
Solids consist of atoms or molecules executing thermal motion about an equilibrium position fixed at a point in space.
Solids can take the form of crystalline, polycrstalline, or amorphous materials.
Solids (at a given temperature, pressure, and volume) have stronger bonds between molecules and atoms than liquids.
Solids require more energy to break the bonds.
Crystal Structure

10. ELEMENTARY CRYSTALLOGRAPHY
Crystal Structure

11. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Crystal Geometry
Crystals
Lattice
Lattice points, lattice translations
Cell--Primitive & non primitive
Lattice parameters
Crystal=lattice+motif
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

12. Types of Solids
Single crsytal, polycrystalline, and amorphous, are the three general types of solids.
Each type is characterized by the size of ordered region within the material.
An ordered region is a spatial volume in which atoms or molecules have a regular geometric arrangement or periodicity.
Crystal Structure

13. Crystalline Solid
Crystalline Solid is the solid form of a substance in which the atoms or molecules are arranged in a definite, repeating pattern in three dimension.
Single crystals, ideally have a high degree of order, or regular geometric periodicity, throughout the entire volume of the material.
Crystal Structure

14. Crystalline Solid
Single crystal has an atomic structure that repeats periodically across its whole volume. Even at infinite length scales, each atom is related to every other equivalent atom in the structure by translational symmetry
Single Pyrite
Crystal
Amorphous
Solid
Single Crystal
Crystal Structure

15. Polycrystalline Solid
Polycrystal is a material made up of an aggregate of many small single crystals (also called crystallites or grains).
Polycrystalline material have a high degree of order over many atomic or molecular dimensions.
These ordered regions, or single crytal regions, vary in size and orientation wrt one another.
These regions are called as grains ( domain) and are separated from one another by grain boundaries. The atomic order can vary from one domain to the next.
The grains are usually 100 nm microns in diameter. Polycrystals with grains that are <10 nm in diameter are called nanocrystalline
Polycrystalline
Pyrite form
(Grain)
Crystal Structure

16. Amorphous Solid
Amorphous (Non-crystalline) Solid is composed of randomly orientated atoms , ions, or molecules that do not form defined patterns or lattice structures.
Amorphous materials have order only within a few atomic or molecular dimensions.
Amorphous materials do not have any long-range order, but they have varying degrees of short-range order.
Examples to amorphous materials include amorphous silicon, plastics, and glasses.
Amorphous silicon can be used in solar cells and thin film transistors.
Crystal Structure

17. Departure From Perfect Crystal
Strictly speaking, one cannot prepare a perfect crystal. For example, even the surface of a crystal is a kind of imperfection because the periodicity is interrupted there.
Another example concerns the thermal vibrations of the atoms around their equilibrium positions for any temperature T>0°K.
As a third example, actual crystal always contains some foreign atoms, i.e., impurities. These impurities spoils the perfect crystal structure.
Crystal Structure

18. CRYSTALLOGRAPHY What is crystallography?
The branch of science that deals with the geometric description of crystals and their internal arrangement.
Crystal Structure

19. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Crystal?
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

20. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
A 3D translationally periodic arrangement of atoms in space is called a crystal.
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

21. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
A two-dimensional periodic pattern by a Dutch artist M.C. Escher
Air, Water and Earth
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

22. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Lattice?
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

23. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
A 3D translationally periodic arrangement of points in space is called a lattice.
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

24. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Crystal
Lattice
A 3D translationally periodic arrangement of atoms
A 3D translationally periodic arrangement of points
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

25. What is the relation between the two?
Crystal = Lattice + Motif
Motif or basis: an atom or a group of atoms associated with each lattice point
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

26. Crystal=lattice+basis
Lattice: the underlying periodicity of the crystal,
Basis: atom or group of atoms associated with each lattice points
Lattice: how to repeat
Motif: what to repeat
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

27. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Love Pattern =
Love Lattice
+ Heart +
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

28. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Space Lattice
A discrete array of points in 3-d space such that every point has identical surroundings
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

29. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Lattice
Finite or infinite?
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

30. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Nonprimitive cell
Primitive cell
Primitive cell
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

31. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Cells
A cell is a finite representation of the infinite lattice
A cell is a parallelogram (2D) or a parallelopiped (3D) with lattice points at their corners.
If the lattice points are only at the corners, the cell is primitive.
If there are lattice points in the cell other than the corners, the cell is nonprimitive.
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

32. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Lattice Parameters
Lengths of the three sides of the parallelopiped : a, b and c.
The three angles between the sides: , , 
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

33. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Convention
a parallel to x-axis
b parallel to y-axis
c parallel to z-axis
Angle between y and z
Angle between z and x
 Angle between x and y
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

34. The six lattice parameters a, b, c, , , 
The cell of the lattice
lattice
+ Motif
crystal
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

35. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

36. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

37. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
In order to define translations in 3-d space, we need 3 non-coplanar vectors
Conventionally, the fundamental translation vector is taken from one lattice point to the next in the chosen direction
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

38. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
With the help of these three vectors, it is possible to construct a parallelopiped called a CELL
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

39. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
The smallest cell with lattice points at its eight corners has effectively only one lattice point in the volume of the cell.
Such a cell is called PRIMITIVE CELL
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

40. Bravais Space Lattices
Conventionally, the finite representation of space lattices is done using unit cells which show maximum possible symmetries with the smallest size.
Symmetries: 1.Translation
2. Rotation
3. Reflection
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

41. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Considering
Maximum Symmetry, and
Minimum Size
Bravais concluded that there are only 14 possible Space Lattices (or Unit Cells to represent them). These belong to 7 Crystal Classes
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

42. Arrangement of lattice points in the unit cell
8 Corners (P)
8 Corners and 1 body centre (I)
8 Corners and 6 face centres (F)
8 corners and 2 centres of opposite faces (A/B/C)
Effective number of l.p.
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

43. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
5. Hexagonal unit cell has 12 corners of the hexagonal prism 2 centres of hexagonal faces
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

44. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Cubic Crystals
Simple Cubic (P)
Body Centred Cubic (I) – BCC
Face Centred Cubic (F) - FCC
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

45. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Tetragonal Crystals
Simple Tetragonal
Body Centred Tetragonal
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

46. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Orthorhombic Crystals
Simple Orthorhombic
Body Centred Orthorhombic
Face Centred Orthorhombic
End Centred Orthorhombic
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

47. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Hexagonal Crystals
Simple Hexagonal or most commonly HEXAGONAL
Rhombohedral Crystals
Rhombohedral (simple)
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

48. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Monoclinic Crystals
Simple Monoclinic
End Centred Monoclinic (A/B)
Triclinic Crystals
Triclinic (simple)
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

49. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi
Crystal Structure
Space Lattice + Basis (or Motif)
Basis consists of a group of atoms located at every lattice point in an identical fashion
To define it, we need to specify
Number of atoms and their kind
Internuclear spacings
Orientation in space
Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

50. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi