ME 381R Fall 2003 Micro-Nano Scale Thermal-Fluid Science and Technology Lecture 3: Microstructure of Solids

1. 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 78712 www.me.utexas.edu/~lishi lishi@mail.utexas.edu

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

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

6. Crystal: Periodic Arrays of Atoms a3 Translation Vectors a2 a1, a2 ,a3 Atom a1 • Primitive Cell: • Smallest building block for • the crystal structure. • Repetition of the primitive cell •  crystal structure

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. Add one atom at the center of each face Add one atom at the center of the cubic 2. Body-Centered Cubic (BCC) 3. Face-Centered Cubic (FCC) Three Cubic Lattices 1. Simple Cubic (SC) a1=a2 =a3 a1 a2 a3 Conventional Cell= Primitive Cell a3 a2 a1 Conventional Cell  Primitive Cell

9. Primitive Translation Vectors: • Kittel, p. 13 Primitive Cell of BCC • Rhombohedron primitive cell 0.53a 109o28’

10. Primitive Cell of FCC • Kittel, P. 13 • Angle between a1, a2, a3: 60o

11. Kittel p. 12

12. Diamond Structure C, Si, Ge, a-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. Crystal Structures of Elements Kittel, pg. 23 Notice: hcp vs. fcc in same column

15. Index System for Crystal Planes (Miller Indices) 1) Find the intercepts on the axes in terms of the lattice constants a1, a2, a3. 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.

16. Crystal Planes

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

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

19. van der Waals bond • Bonding energy: • ~0.01 eV (weak) • Compared to thermal • vibration energy kBT ~ • 0.026 eV at T = 300 K • Examples: inert gases Ar Ar + Ar - + Ar - Dipole-dipole interaction

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

21. Hydrogen bond • The electron of the H atom is • pulled toward the other atom • Ionic in nature • Bonding energy: ~kBT (weak) • Examples: DNA; • intermolecular bond between • water and ice F- F- H+ HF2- molecule

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

23. + H H H H Covalence bond C C • Two atoms share a pair of electrons • Bonding energy: ~1-10 eV (strong) • Examples: C, Ge, Si, H2 C C C

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