Everything starts with atomic structure and bonding

Transcription

1 Everything starts with atomic structure and bonding not all energy values can be possessed by electrons; e- have discrete energy values we call energy levels or states. The energy values are quantized and not continuous Convention: we take the zero reference energy to represent the situation of a fully unbound, or free e-. Hence, relative to this condition, a fully bound electron in an orbital requires a certain input of positive energy to reach a free condition of zero energy. Thus bound e- are taken to have negative energy wrt the free state. This is the BOHR ATOMIC MODEL BUT, the Bohr Model does NOT predict reality! Why? Because it states that both the energy value And radial position of the e- are known simultaneously! l This violates the Heisenberg Uncertainty Principle (later)

2 Wave Mechanical (quantum mechanical) model of an atom energy levels of individual electrons are discrete and every e- is in a different energy configuration that t we describe by quantum numbers to characterize size, shape and spatial orientation of the PROBABILITY DENSITY of an e-. in chemistry you ll remember that these are called PQN (principle quantum number), electron shell, electron subshell, and electron spin! we will re-visit QM for real when we describe solids instead of atoms! Quantum # Designation n = principal i (energy level-shell) l ll) K, L, M, N, O (1, 2, 3, etc.) l = subsidiary (orbitals) s, p, d, f (0, 1, 2, 3,,, n -1) ml = magnetic 1, 3, 5, 7 (-l to +l) ms = spin ½, -½

3 Electron Energy States Electrons... have discrete energy states tend to occupy lowest available energy state. 4d 4p N-shell n = 4 3d 4s Energy 3p M-shell n = 3 3s 2p 2s Adapted from Fig. 2.4, Callister 7e. L-shell n = 2 1s K-shell n = 1

4 Atomic Bonds in Solids bonding represents the balance between attractive and repulsive forces involving e- and positively charged ions when the net force between attraction and repusion is zero, F A + F R = 0. In terms of energy, we have a stable bond when the potential energy of the system is at a minimum, de N /dr = 0, E N is the net energy r = r o in this condition, which is the equilibrium bond length E N = E o in this condition, which is the bond energy E N = E A + E R = A r B n r Repulsive energy E R Interatomic separation r Net energy E N Attractive energy E A

5 Primary Atomic Bonds in Solids Ionic bonding occurs between elements with large differences in electronegativity e.g. NaCl non-directional bonding (i.e. bond strength is very similar in all directions) electron transfer enables a closed shell stable configuration ionic compounds are relatively stable, hard, electrically and thermally insulating in PURE STATE (later, we will see that t there are ionic i semiconductors and conductors that are not pure) Na (metal) unstable Na (cation) stable electron + - Coulombic Attraction Cl (nonmetal) unstable Cl (anion) stable Covalent bonding: neighboring atoms share e- to complete a shell examples: CH 4, Silicon, diamond can be strong or weak very directional i bonding!! Very important for semiconductor technology!

6 Primary Atomic Bonds in Solids Metallic Bond -- delocalized electrons as electron cloud Ionic-Covalent Mixed Bonding % ionic character = 1 e (X A X B ) 4 x (100 where XA &XB are Pauling electronegativities 2 %) Ex: MgO X Mg = 1.3 X O = 3.5 (3.5 % ionic character = 1 e 4 1.3) 2 x (100%) = 70.2% ionic

7 Summary: Bonding Type Ionic Bond Energy Large! Comments Nondirectional (ceramics) Covalent Variable large-diamond small-bismuth Directional (semiconductors, ceramics polymer chains) Metallic Secondary Variable large-tungsten small-mercury smallest Nondirectional (metals) Directional inter-chain (polymer) inter-molecular

8 Properties From Bonding: T m Bond length, r r Melting Temperature, T m Energy Bond energy, E o r o r Energy unstretched length r o r E o = bond energy smaller T m larger T m T m is larger if E o is larger.

9 Properties From Bonding : α Coefficient of thermal expansion, α length, Lo unheated, T1 heated, T2 ΔL coeff. thermal expansion ΔL Lo = α (T 2 -T 1 ) α ~ symmetry at r o Energy E o E unstretched length r o larger α smaller α r α Follows E vs r slope α is usually larger if E o is smaller. o

10 Crystal Structures Not everything is a crystal!!! We have amorphous and polycrystalline materials. These all can be big, thick blocks, or ultra-thin layers. Former we refer to as bulk materials, latter as thin films. crystalline materials: possess long range periodic order, in which identical unit cells are repeated in all dimensions in perfection. We call these type of materials single crystals in electronic materials technology polycrystalline materials: most crystalline solids are actually composed of collections of smaller crystals or grains, with each grain or crystal separated by a grain-boundary, which is a 2-dimentional interface. Most solar cells today are polycrystalline silicon!! non-crystalline materials have no systematic and regular atomic arrangement over relatively large atomic distances. These are called amorphous materials. Amorphous silicon is a mainstay of several device technologies, and its electronic, optical and structural properties are COMPLETELY DIFFERENT from crystalline forms of silicon demonstrates how structure dictates properties, even for the same element!

11 Single crystal polycrystalline Crystalline silocon dioxide and amorphous SiO 2

12 Crystalline Structures: Definitions Lattice: periodic arrangment of points in 3-dimensions. defined by a lattice vector T = pa + qb +sc. basically a translation vector to map out all of space in terms of lattice points Around each lattice point there are atoms. An atom can be right on a lattice point or atoms can be arranged around a lattice point. The way in which atoms are arranged around a lattice point is called the basis and there is a 3-D basis vector, r, that describes this arrangement. So, crystal structure = lattice + basis

13 Crystalline Structures: Definitions Unit Cell: a region of a crystal that can be translated through space to any lattice point to completely build the crystal structure. the unit cell is essentially a building block and is fundamental to the prediction of all electronic and optical properties of electronic materials Primitive Cell: is the smallest possible unit cell that can still be translated by lattice vectors to create a crystal. Tend to be less convenient to use, except for the simplest of crystal structures.

14 7 Unique Crystal Systems

15 Cubic Crystal Structures α, β, γ = 90 degrees a = b = c = lattice constant for cubic materials Simple cubic (SC) Body centered cubic (BCC) Face centered cubic (FCC)

16 7 Unique Crystal Systems