1. Materials Engineering
Lecture 3:
Aggregation states.
Crystallines

2. Aggregation states Gas, Liquid and Solid. The main factors are:
the distance between particles;
the motion of the particles.
Particles can be molecules, atoms or ions.

3. Order and disorder of Particles
Order is the regularity of position, when according to a few particles it is possible to foretell the position of another particle.
Far order covers the entire body (or, at least, much more that ~ 100 particles)
Close order covers only the close vicinity of a particle (less than ~ 100 particles).

4. Gas
Very large distances (e.g. at 25oC ant 1 atm the distance is ~30 nm, that is about 100 times the size of a molecule)
Very high molecular velocities (e.g. at 25oC and 1 atm the mean molecular velocity is m/sec)
Complete disorder
Brownian motion

5. Liquid The distances are moderate (~ as 1-10 molecular sizes)
The velocities are lower
Van der Waals forces act
Close order
Liquid water structure

6. Solid 1. Crystalline Crystallites are true solids Close packing
Only vibrational motion
Far order (lattice)
Quartz crystal
Spinel crystal

7. Solid 2. Amorphous Only close order (as liquids) Small distances
Not only vibrations
a. Crystalline b. Amorphous
Amorphous state can be defined as a very viscose overcooled liquid. And still, it is solid.

8. Changes of State of Aggregation

9. Platinum surface (STM image)
Basics of crystals
Crystalline material is one in which the atoms are situated in repeating or periodic order over large atomic distance (long-range order).
Lattice (סריג): 3D array of points coinciding with atom positions
Platinum surface (STM image)
Diamond crystal
(animation)

10. Lattice and Unit Cell
A convenient way to visualize an infinite (or very large) lattice is unit cell.
Unit cell: The smallest building block of a crystal, consisting of atoms, ions, or molecules, whose geometric arrangement defines a crystal's characteristic symmetry and whose repetition in space produces a crystal lattice.
A high resolution image of the crystal lattice of an oxide ceramic (Ba45Nd95Ti18O54)

11. Some Important Unit Cells

12. Some metal cells
Metallic bonding is not directional => no restrictions for the number and position of neighboring atoms.
FСС: Al, Cu, Au, Pb, Pt, Ag
BСС: a-Fe, W, Cr
HCP: a-Ti, Zn, Mg

13. Coordination number and atomic packing factor
Coordination number: the number of nearest neighbors.
Atomic Packing Factor (APF):
Example: FCC cell
Coordination Number = 12 
Finding APF is a bit more complicated:

14. Comparison of unit cells
HCP
FCC
BCC PC 12 8 6 CN
74%
68%
52%
APF

15. Polymorphism and Allotropy
When a substance can have more than one crystal structure: polymorphism (for elements: allotropy)
Some examples:
C: graphite  (high pressure) diamond
Fe: a-Fe (BCC)  (T >912ºC) g-Fe (FCC)
Sn: a-Sn (white)  (T < -34ºC) b-Sn (grey)

16. Allotropy of carbon Graphite Diamond Properties: Color: black-silver
Specific Gravity: 2.2
Hardness (Mohs): 2
Electric conductivity: good
Properties:
Color: colorless
Specific Gravity: 3.5
Hardness (Mohs): 10
Electric conductivity: insulator

17. Crystal Systems (Syngonies)

18. Lattice Parameters

19. Crystallographic Directions

20. Miller indexes
מציאת אינדקסי מילר:
מצא את החיתוכים של המישור הרצוי על צירי X, Y ו-Z. לדוגמא: (∞1∞) עבור המישור בציור עליון שמאלי ב-"Fig.20"
קח את ההיפוך של כל מספר שבסוגריים בסעיף 1: (010). במידה ומתקבלים ערכים לא-שלמים, הכפל את כל הערכים למספר קטן כך שיתקבלו רק שלמים. דוגמא: (1 ½ 1)  (212)
אם בסעיף 1 התקבלו ערכים שליליים, רשום אותם מעל האינדקס.
1.      Find the intercepts on the axes in terms of the lattice constants a1, a2, and a3. The axes may be those of a primitive or non-primitive cell.
2.      Take the reciprocals of these numbers and then reduce to three integers having the same ratio, usually the smallest three integers. The result, enclosed in parenthesis (hkl), is called the index of the plane.
3.      The indices (hkl) may denote a single plane or a set of parallel planes.
4.      If a plane cuts an axis on the negative side of the origin, the corresponding index is negative, indicated by the minus sign (or bar) above index:

21. Miller-Bravais indexes

22. Single crystals and polycrystalline materials
Polycrystalline is formed by many small single crystals (grains).

23. Anisotropy Modulus of Elasticity )GPa) [111] [110] [100] 76.5 72.6
Anisotropy is the directionality of properties depending on the crystallographic direction.
Example:
Modulus of Elasticity )GPa)
[111]
[110]
[100]
76.5
72.6
63.7 Al
191.1
130.3
66.7 Cu
272.7
210.5
125.0 Fe
384.6 W

24. Musts of this lecture
You have to be able to characterize the three states of aggregation.
You have to understand, what the amorphous state is.
The most important unit cells: PC, BCC, FCC, HCP.
Isomorphism and allotropy
Lattice Parameters of different Crystal Systems
Crystallographic directions and planes.
Miller and Miller-Bravais indexes.
Single crystals and polycrystallites.
Anisotropy.