§ 2 Atomic structure and bonding in solids
§ 2.5 Bonding force & energies
Take ionic solids as an example
z1
z2
r
(a) Attractive force (coulombic force) F A
錯誤! 尚未定義書籤。
FA = − k
Electronic Repulsive Force F R
FR = −
bnn
r n +1
( z1 q )( z 2 q )
， k 0 = 9×109 Vm/c
r2
(b) Bonding energy E 0
E = − ∫ Fdr
，
r
r
∞
∞
E = ∫ FA dr + ∫ FR dr = E A + E R
At equilibrium, there is no net force
FA + FR = 0
γ = γ 0 γ 0 :equilibrium spacing
for many atoms , γ 0 ~ 3A
△ Three MSE properties can be obtained this cure:
(1) bonding energy
(2) CTE
(3) Yong’s modulus
(1) Bonding energy : deep & narrow trough
→Large bonding energy
→Higher melting point
(2) CTE
Deep & narrow → higher degree of symmetry of
the curve
∵ CTE = f (degree of symmetry of the curve)
= f (depth of the trough)
曲線越陡(深) 越對稱
∵ 若 越 symmetry ,
(3) Young’s modulus
F
σ = Eε
σ=
A0
ε=
→ 底 CTE
平均 → 抵消
剛性
，A 0 is constant
l − l 0 r − r0
r
=
= −1
l0
r0
r0
∂σ
∂F ∂ 2U
=E∝
∝ 2
∂ε
∂r
∂r
§ 2.6 Primary Interatomic Bonds
三種主要原子間的鍵結
1. 離子鍵 ionic bonding
Compounds composed of both metallic &
non-metallic elements
Bonding force: coulombic force
Attractive energy:
Repulsive energy:
Ex. NaCl, MgO
Bonding energy 600~1500 KJ/mole
Bond itself is non-directional, but properties are anisotropic
2. 共價鍵 Covalent Bonding
Sharing of es between adjacent atoms
Each atoms contributes at least one electron to the
bond .
Non-metallic element molecules (H 2 , Cl 2 ) &
molecules containing dissimiless atoms.
Ex. CH 4 Cl 2 H 2 O
Bonding energy : Si 450
C diamond 713
3. Metallic bonding
- metals & their alloys (合金)
-
e’s are free to drift throughout the entire metal
“forming sea of e’s”, or “electron cloud”
68~850 KJ/mole
§ 2.7 Secondary Bonding or Van Der Waals Bonding
Secondary bonding arises from Dioples
Hydrogen bonding 氫鍵
(a) Fluctuating induced dipole bonds
(b) Polar molecule – induces dipole bonds
Asymmetrical arrangement
本身
幾何上的不對稱
(c) permanent dipole bonds
HF – HF
H2O – H2O
H-F, H-O, H-N
Typical 10KJ/mole
H2O
~ 51KJ/mole
Bonding energy of (c) ＞ (b), (a)
★ Read § 3.1 ~ 3.3
1.8 ~ 3.11