ME 381R Fall 2003 Micro-Nano Scale Thermal-Fluid Science and Technology Lecture 3: Microstructure of Solids Dr. Li Shi Department of Mechanical Engineering The University of Texas at Austin Austin, TX

2 Outline  Kinetic Theory Crystalline Structure of Solids Crystal Bonding Reading: Kittel Ch1

3 Heat Conduction in Gases Heat conducted by gas molecules. K is determined by inter-molecular collisions, and can be predicted using kinetic theory Thermal Conductivity

4 If so, what are C, v, for electrons and crystal vibrations? Kinetic theory is valid for particles: can electrons and crystal vibrations be considered particles? Heat Conduction in Solids Heat is conducted by electrons and phonons. k is determined by electron-electron, phonon-phonon, and electron-phonon collisions. Hot Cold - Hot Cold p We will use the next 4 lectures to figure out C, v, and k of crystal vibrations, i.e. phonons.

5 Kittel pg. 2 The building blocks of these two are identical, but different crystal faces are developed Crystal Structure Cleaving a crystal of rocksalt

6 Crystal: Periodic Arrays of Atoms Atom Translation Vectors Primitive Cell: Smallest building block for the crystal structure. Repetition of the primitive cell  crystal structure a1a1 a3a3 a2a2 a 1, a 2,a 3

7 Common Lattice Types There are 14 lattice types Most common types (Kittel Table 3): Cubic: Li, Na, Al, K, Cr, Fe, Ir, Pt, Au etc. Hexagonal Closed Pack (HCP): Mg, Co, Zn, Y, Zr, etc. Diamond: C, Si, Ge, Sn (only four)

8 Three Cubic Lattices a1a1 a3a3 a2a2 a 1 = a 2 =a 3 a 1  a 2  a 3 1. Simple Cubic (SC) Add one atom at the center of the cubic 2. Body-Centered Cubic (BCC) Add one atom at the center of each face 3. Face-Centered Cubic (FCC) Conventional Cell= Primitive Cell Conventional Cell  Primitive Cell

9 Primitive Cell of BCC Primitive Translation Vectors: Rhombohedron primitive cell 0.5  3a 109 o 28 ’ Kittel, p. 13

10 Primitive Cell of FCC Angle between a 1, a 2, a 3 : 60 o Kittel, P. 13

11 Kittel p. 12

12 Diamond Structure C, Si, Ge,  -Sn Add 4 atoms to a FCC Tetrahedral bond arrangement Each atom has 4 nearest neighbors and 12 next nearest neighbors

13 Hexagonal Close Packing (hcp)

14 Kittel, pg. 23 Notice: hcp vs. fcc in same column Crystal Structures of Elements

15 1) Find the intercepts on the axes in terms of the lattice constants a 1, a 2, a 3. The axes may be those of a primitive or nonprimitive unit cell. 2) Take the reciprocals of these numbers and then reduce to three integers having the same ratio, usually the smallest three integers. The reulst enclosed in parethesis (hkl), is called the index of the plane. Index System for Crystal Planes (Miller Indices)

16 Crystal Planes

17 Types of Microstructures Single Crystalline Polycrystalline Amorphous TEM images of nanobelts by Prof. Z. L. Wang

18 van der Waals bond Ionic bond Hydrogen bond Metallic bond Covalence bond Crystal Bonding

19 van der Waals bond Ar + Ar - Ar Dipole-dipole interaction Bonding energy: ~0.01 eV (weak) Compared to thermal vibration energy k B T ~ eV at T = 300 K Examples: inert gases

20 Ionic Bond Na + Cl - The electron of the Na atom is removed and attached to the Cl atom Bonding energy: 1-10 eV (strong) Cl - Na +

21 Hydrogen bond F-F- F-F- H+H+ HF 2 - molecule The electron of the H atom is pulled toward the other atom Ionic in nature Bonding energy: ~k B T (weak) Examples: DNA; intermolecular bond between water and ice

22 Metallic Bond Na + Electron sea Positive ions in a sea of electrons Bonding energy: ~1-10 eV (strong)

23 Covalence bond Two atoms share a pair of electrons Bonding energy: ~1-10 eV (strong) Examples: C, Ge, Si, H 2 C CC C C H H+HH

24 Bonding Energy vs. Inter-atomic Distance 1-D Array of Spring Mass System