Materials Engineering Lecture 3: Aggregation states. Crystallines

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.

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).

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 400-500 m/sec) Complete disorder Brownian motion

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

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

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.

Changes of State of Aggregation

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)

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)

Some Important Unit Cells

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

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:

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

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)

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

Crystal Systems (Syngonies)

Lattice Parameters

Crystallographic Directions

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:

Miller-Bravais indexes

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

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

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.