Ch02-2016.pdf

Chapter 2: Atomic Structure & Interatomic Bonding 原子結構與原子間的鍵結 ISSUES TO ADDRESS... • What promotes bonding? • What types of bonds are there? • What properties are inferred from bonding?

Chapter 2 - 1

Atomic Structure (原子結構) 2.2 Fundamental concepts • atom –

electrons 電子 – 9.11 x 10-31 kg protons 質子 -27 kg 1.67 x 10 neutrons 中子

}

• atomic number原子序 = # of protons in nucleus of atom = # of electrons in neutral species • atomic mass 原子質量 = Total mass of protons and neutrons in the nucleus of a specific atom 特定原子原 子核中的質子和中子的質量和 • atomic weight 原子量 = the weighted average of the atomic masses of the atom’s naturally occurring isotopes 自然存在的所有同位素，其原子質量之平均值 C H

12.011 1.008 etc.

Chapter 2 - 2

2.2 Fundamental concepts • Avogadro number 亞彿加厥數 In one mole of a substance, there are 6.0221023 atoms or moleculs. 一莫耳 (mole) 的物質中含有 6.0221023 個 ( 亞佛加厥數 ) 原子或分子。 • atomic mass unit 原子質量單位= amu = 1/12 mass of C. amu 是計算原子量的單位。1 amu的定義是：以最常見的 碳同位數 ── 即碳12(12C) 的原子質量 (A = 12.00000) 的 1/12 。 1 amu/atom = 1 g/mol

Chapter 2 - 3

Atomic Structure • Some of the following properties 1) 2) 3) 4)

Chemical Electrical Thermal Optical

are determined by electronic structure

Chapter 2 - 4

2.3 Electrons in atoms • During the latter part of the 19th century, it was found that many phenomena involving electrons in solids could not be explained by the classical mechanics ( 古典力學). • Quantum mechanics (量子力學) was established.

Chapter 2 - 5

2.3 Electrons in atoms • Bohr atomic model 波爾原子模型. • The energies of the electrons are quantized 電子的能量 呈現量子化. 電子只擁有特定之能量值。一個電子在改變能量時，可以從 原來之能量狀態跳躍到另一特定之高能量 ( 吸收能量 ) 或 低能量 ( 釋放能量 )，跳躍前後之能量差為定值。 電子能量以 能階 (energy levels) 或狀態 (states) 來 思考

Chapter 2 - 6

2.3 Electrons in atoms • Bohr atomic model has its limitations 波爾模型出現了許多限制，無法完全說 明電子的所有現象. • Wave-mechanical model波動 - 力學模 型. • Electron has both wave-like and particle-like characteristics. • Electron no longer moves in a discrete orbital; its position is considered to be the probability at various locations around the nucleus. 電子考慮成圍繞在原子核外面區域中 出現電子機率的位置。 Chapter 2 - 7

Electronic Structure • Electrons have wavelike and particulate properties. • Two of the wavelike characteristics are – electrons are in orbitals defined by a probability. – each orbital at discrete energy level is determined by quantum numbers 量子數.

Chapter 2 - 8

Electronic Structure • Four quantum numbers. • Shells are specified by a principal quantum number ( 主量子數 ), n. 殼層由主量子數 (principal quantum number) n來表 示，n 為由1開始之整數值；這些殼層也可用大寫字母 K,L,M,N,O等來表示，n = 1相當於 K；2相當於 L；3相 當於 M；4相當於 N；5相當於 O 等 – Quantum #

Designation

n = principal (energy level-shell) l = subsidiary (orbitals) ml = magnetic

K, L, M, N, O (1, 2, 3, etc.) s, p, d, f (0, 1, 2, 3,…, n-1) 1, 3, 5, 7 (-l to +l)

ms = spin

½ , -½ Chapter 2 - 9

Electronic Structure • Four quantum numbers. • Shells are specified by a principal quantum number (主量子 數 ), n. 殼層由主量子數 (principal quantum number) n來表示，n 為由 1開始之整數值；這些殼層也可用大寫字母 K,L,M,N,O等來表 示，n = 1相當於 K；2相當於 L；3相當於 M；4相當於 N；5相當 於O等 • Related to the size of an electron’s orbital (average distance from the nucleus) Quantum # Designation n = principal (energy level-shell) l = subsidiary (orbitals) ml = magnetic

K, L, M, N, O (1, 2, 3, etc.) s, p, d, f (0, 1, 2, 3,…, n-1) 1, 3, 5, 7 (-l to +l)

ms = spin

½ , -½ Chapter 2 - 10

Electronic Structure • Second quantum number (第二量子數), l, designates the subshell (副殼層). l=0 to l=n-1. 第二 ( 或稱方位角 ) 量子數 l表示副殼層，l 的值由 n 值所 限制，為自 l = 0 到 l = (n – 1) 範圍的整數值。每一副殼層 對應上述整數值，以小寫字母 ── s,p,d 或 f 來標示。 – Quantum # Designation n = principal (energy level-shell) l = subsidiary (orbitals) ml = magnetic

K, L, M, N, O (1, 2, 3, etc.) s, p, d, f (0, 1, 2, 3,…, n-1) 1, 3, 5, 7 (-l to +l)

ms = spin

½ , -½

Chapter 2 - 11

Electronic Structure • Second quantum number (第二量子數), l, designates the subshell (副殼層). l=0 to l=n-1. • Electron orbital shapes depend on l.  s subshell: spherical and centered on the nucleus.  p subshell: dumbbell shape

Chapter 2 - 12

Electronic Structure • Third quantum number (第三量子數), ml, • Also called magnetic quantum number 磁量子數 • Determine the number of electron orbitals for each subshell.每一副殼層中的電子軌域數目由第三量子數 ml 來決定 • ml : integers between –l and l, including 0. 介於 -l 與 +l 之間包含0之整數。 – Quantum #

Designation

n = principal (energy level-shell) l = subsidiary (orbitals) ml = magnetic

K, L, M, N, O (1, 2, 3, etc.) s, p, d, f (0, 1, 2, 3,…, n-1) 1, 3, 5, 7 (-l to +l)

ms = spin

½ , -½ Chapter 2 - 13

Electronic Structure • Fourth quantum number (第四量子數), ms, • Spin moment 電子自轉動量 • Spin up (自旋向上): 1/2 or Spin down 和(自旋向下):-1/2。 – Quantum # Designation n = principal (energy level-shell) l = subsidiary (orbitals) ml = magnetic

K, L, M, N, O (1, 2, 3, etc.) s, p, d, f (0, 1, 2, 3,…, n-1) 1, 3, 5, 7 (-l to +l)

ms = spin

½ , -½

Bohr model was refined by wave mechanics by introducing three new quantum # (l, ml, ms)

Chapter 2 - 14

Electronic Structure

Chapter 2 - 15

Electron Energy States Electrons...

• have discrete energy states • tend to occupy lowest available energy state. 4d 4p 3d 4s

Energy

N-shell n = 4 Adapted from Fig. 2.6, Callister & Rethwisch 9e. (From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering, p. 22. Copyright © 1976 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)

3p 3s

M-shell n = 3

2p 2s

L-shell n = 2

1s

K-shell n = 1 Chapter 2 - 16

Table_02_01

Chapter 2 - 17

Electron Configurations 電子組態 • Valence electrons 價電子– those in unfilled shells 未填滿殼層中的電子，通常為原子最外 層sp能階上的電子數。 • Valence electrons are most available for bonding and tend to control the chemical properties 原子內參與鍵結合或化學反應的電子數， 原子的價電子數反映出原子與其他元素起化學反應的 能力，許多固體的物理和化學性質與價電子有密切的關 係。

Chapter 2 - 18

Electron Configurations 電子組態 example: Na (atomic number = 11) 1s22s22p6 3s1 valence electrons

Chapter 2 - 19

Electron Configurations 電子組態 • • • • •

Filled shells more stable H: 1s1 He: 1s2 Na: 1s22s22p6 3s1 惰性氣體 ( 氦、氖、氬、氪 ) 等元素，它們在最外殼層的 s 和 p 狀態，都被電子完全填滿，故呈現出化學惰性 ( 不容易發生化學反應 )。

Chapter 2 - 20

SURVEY OF ELEMENTS • Most elements: Electron configuration not stable. Element Hydrogen Helium Lithium Beryllium Boron Carbon ...

Atomic # 1 2 3 4 5 6

Electron configuration 1s 1 1s 2 (stable) 1s 2 2s 1 1s 2 2s2 1s 2 2s 2 2p 1 1s 2 2s 2 2p 2 ...

Adapted from Table 2.2, Callister & Rethwisch 9e.

Neon Sodium Magnesium Aluminum ...

10 11 12 13

1s 2 2s 2 2p 6 (stable) 1s 2 2s 2 2p 6 3s 1 1s 2 2s 2 2p 6 3s 2 1s 2 2s 2 2p 6 3s 2 3p 1 ...

Argon ... Krypton

18 ... 36

1s 2 2s 2 2p 6 3s 2 3p 6 (stable) ... 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

• Why? Valence (outer) shell usually not filled completely. Chapter 2 - 21

Electronegativity 電負度(陰電性) • Capability to accept electrons 吸引電子的能力 • Ranges from 0.9 to 4.1, Large values: tendency to acquire electrons.

Smaller electronegativity

Larger electronegativity

Chapter 2 - 22

The Periodic Table

give up 1egive up 2egive up 3e-

accept 2eaccept 1einert gases

• Columns: Similar Valence Structure

K Ca Sc

Se Br Kr

H

He

Li Be

O

F Ne

Na Mg

S

Cl Ar

Rb Sr

Y

Cs Ba

Te

I

Adapted from Fig. 2.8, Callister & Rethwisch 9e.

Xe

Po At Rn

Fr Ra

Electropositive elements: Readily give up electrons to become + ions.

Electronegative elements: Readily acquire electrons to become - ions. Chapter 2 - 23

原子安定性與陰電性 Atomic stability and electronegativity 若一原子的價電子數=0，則無電子可參與反應，稱謂惰性(inert)，例如氬氣(Ar) 1s2 2s2 2p63s2 3p6 其他的元素喜歡把他們的最外層的sp能階完全由8個電子填滿，或完全空缺。 Al: 1s2 2s2 2p6 3s2 3p1 Cl: 1s2 2s2 2p63s2 3p5 鋁原子很容易付出期外側的3個電子，使其3sp能階完全空缺； 氯原子在其外側3sp能階有7個電子，所以容易吸收一個電子將能階填滿

陰電性 Electronegativity

原子獲得電子的趨勢 Tendency of an atom to gain an electron

陽電姓 Electropositive

當陰電性較低時，可用陽電性來表示 Elements with low electronegativity i.e.,<2.0

2 - 24 © 2011 Cengage Learning Engineering. All Rights Reserved.

Atomic bonding in solids 原子鍵結 2.5 Bonding forces and energies 鍵結力與鍵結能 Force •Attractive force (吸引力, FA) and Repulsive force (排斥力 FR) •Net Force (淨力, FN)

FN  FA  FR

•State of equilibrium 平衡狀態

FA  FR  0

•此時兩原子之間保持一定的間 距: equilibrium spacing 平衡間 距, r0

Atomic bonding in solids 原子鍵結 2.5 Bonding forces and energies 鍵結力與鍵結能 Energy •Attractive energy (吸引能, EA) and Repulsive Energy (排斥能 ER) •Net Energy (淨位能, EN)

E N  E A  ER

•State of equilibrium 平衡狀態: EN 曲線最小值處 •此時兩原子之間的能量為E0 : 鍵結能 (bonding energy) • 鍵結能代表將這兩個緊密結合之原子分 開到無窮遠距離所需之能量。

Atomic bonding in solids 原子鍵結 Figure 2.18

打破鍵結所需之能量

束縛能

Interatomic space 原子的平衡距離，由斥 力和吸力平衡造成的。

原子間距 F=0 © 2011 Cengage Learning Engineering. All Rights Reserved.

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2 - 27

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ed. 2011.

Interatomic bonds 原子鍵結 • Three types of primary or chemical bonds in solids.三種主鍵結  Ionic bond 離子鍵  Covalent bond 共價鍵  Metallic bond 金屬鍵  Bonding involves the valence electrons每一 種鍵結均涉及價電子 •Secondary bond 次鍵結 or physical forces

Chapter 2 - 28

Ionic bond 離子鍵 metal 金屬 + nonmetal 非金屬 donates electrons

ex: MgO

Mg

1s2 2s2 2p6 3s2 [Ne] 3s2

Mg2+ 1s2 2s2 2p6 [Ne]

accepts electrons

O

1s2 2s2 2p4

O2- 1s2 2s2 2p6 [Ne]

Chapter 2 - 29

Ionic bond – metal

+

donates electrons

nonmetal accepts electrons

Dissimilar electronegativities e.g., NaCl

Chapter 2 - 30

• • • •

Ionic Bonding

Occurs between + and - ions. Requires electron transfer. Large difference in electronegativity required. Example: NaCl

Na (metal) unstable

Cl (nonmetal) unstable

electron Na (cation) stable

-

+ Coulombic Attraction 庫倫吸引力

Cl (anion) stable

Chapter 2 - 31

Ionic Bonding • Energy – minimum energy most stable – Energy balance of attractive and repulsive terms

A B EN = EA + ER = + n r r Repulsive energy ER

Interatomic separation r Net energy EN Adapted from Fig. 2.10(b), Callister & Rethwisch 9e.

Attractive energy EA Chapter 2 - 32

Ionic Bonding

• Predominant bonding in Ceramics NaCl MgO CaF 2 CsCl

Give up electrons

Acquire electrons

Chapter 2 - 33

Ionic Bonding • Nondirectional 無方向性: magnitude of the bond is equal in all direction around an ion. 離子鍵結沒有方向性；也就 是說，一離子周圍所有方向的鍵結大小都相同。 • Bonding energy is relatively large (600~1500 kJ/mol)  high melting temperature 離子鍵之鍵能相當大，因而顯示 出高熔點。

Chapter 2 - 34

Table_02_03 Chapter 2 - 35

Ionic Bonding • Energy – minimum energy most stable – Energy balance of attractive and repulsive terms

A B EN = EA + ER = + n r r Repulsive energy ER

Interatomic separation r Net energy EN Adapted from Fig. 2.10(b), Callister & Rethwisch 9e.

Attractive energy EA Chapter 2 - 36

Examples: Ionic Bonding

• Predominant bonding in Ceramics NaCl MgO CaF 2 CsCl

Give up electrons

Acquire electrons

Chapter 2 - 37

Covalent Bonding 共價鍵 • similar electronegativity相近的電負度  share electrons電 子共用 • bonds determined by valence – s & p orbitals dominate bonding H2 • Example: H2 Each H: has 1 valence e-, needs 1 more

H

H

Electronegativities are the same. shared 1s electron from 1st hydrogen atom

shared 1s electron from 2nd hydrogen atom

Fig. 2.12, Callister & Rethwisch 9e. Chapter 2 - 38

共價鍵 Covalent bonds  兩個或兩個以上的原子，彼此間共用價電子而產生的鍵結

1s2 2s2 2p63s2 3p2 Valance=4

For each Si atom, it need 4 atoms to share their electrons →4 covalent bonds

1s2 2s2 2p63s2 3p2  1s2 2s2 2p6 3s23p6 Fill 8 electrons in the outer sp orbit

四面體 Tetrahedron

Askland et al. The science and engineering of materials. 6th ed. 2011. © 2011 Cengage Learning Engineering. All Rights Reserved.

2 - 39

 共價鍵 Covalent bonds  非金屬元素構成的分子 ( 如 Cl2,F2 等 ) 和不同類非金屬 元素構成的分子 ( 如 CH4 , H2O , HNO3 和HF等 )，都 具有共價鍵結。  原子的平均陰電性≥4  共價鍵具有方向性 directional relationship  在具共價鍵的材料中，因為原子要重新排列形成鍵結，因 此鍵與鍵之鍵會形成特定的夾角，夾角大小視材料種類而 定。  共價鍵很強，所以此方式結合的材料一般有高的熔點 (BN, SiC)。  共價鍵有方向性，因以此方式結合的材料延展性不佳。  大部分以共價鍵結合的材料之導電性不高，因為可用的價 電子被固定在特定的位置上。 © 2011 Cengage Learning Engineering. All Rights Reserved.

2 - 40

Bond Hybridization 鍵結混成 • Carbon can form sp3 hybrid orbitals

Fig. 2.14, Callister & Rethwisch 9e. (Adapted from J.E. Brady and F. Senese, Chemistry: Matter and Its Changes, 4th edition. Reprinted with permission of John Wiley and Sons, Inc.)

Fig. 2.13, Callister & Rethwisch 9e. Chapter 2 - 41

Covalent Bonding: Carbon sp3 • Example: CH4 C: has 4 valence e-, needs 4 more H: has 1 valence e-, needs 1 more

Electronegativities of C and H are comparable so electrons are shared in covalent bonds.

Fig. 2.15, Callister & Rethwisch 9e. (Adapted from J.E. Brady and F. Senese, Chemistry: Matter and Its Changes, 4th edition. Reprinted with permission of John Wiley and Sons, Inc.)

Chapter 2 - 42

Metallic bond 金屬鍵 • Metallic Bond -- delocalized as electron cloud 價電 子生成電子海 • 價電子並非固定被固體中某個原子綁住，而是在金屬整 體中自由漂移。這些電子形成一”電子海”或”電子雲”，屬 於整體金屬所有。

Chapter 2 - 43

 Metallic bonds  陽電性的金屬元素付出它的 價電子，而形成一個圍繞著 原子(核心)的電子海。  這種原子的陰電性≤3  e.g. Al付出3個價電子，留 下帶3價正電的原子核及內層 電子所組成的核心。帶負電 的價電子成為游離價電子 (non-localized valence electron)，不再附屬於特定 的原子，可在電子海內自由 運動，且可同時附屬於好幾 個核心。帶正電的核心與電 子吸引而成為一體，產生金 屬鍵。

Metallic Bonds

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2.8 Mixed Bonding 混鍵 •Ionic-Covalent Mixed Bonding 離子-共價混合鍵 % ionic character =

x (100%)

where XA & XB are Pauling electronegativities Ex: MgO XMg = 1.3 XO = 3.5

Chapter 2 - 45

 混合的鍵結 Mixed bonding  



大部分的材料中，原子的鍵結是兩種或兩種以上鍵結的合成。 e.g. Fe的鍵結為金屬鍵和共價鍵的組合。 由兩種或多種金屬形成的化合物 (金屬間化合物 intermetallic compounds) ，可能會有混合的金屬鍵和離子鍵產生；尤其是 元素間存在著大的陰電性差異時。 在陶瓷與半導體中，材料的組成多為金屬和非金屬的結合，原 子間的鍵結為共價鍵(covalent)和離子鍵(ionic)的混合鍵結。

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2 - 46

 混合的鍵結 Mixed bonding

在週期表中的IIIA、IVA和VA族元素 ( 如硼、矽、鍺、砷、 銻、碲、釙和砈 ) 也會發生另一種混鍵。這些元素在原子 之間的混鍵屬於金屬與共價的混合，如圖所示為擬金屬 (metalloids) 或半金屬 (semi-metals)。

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2 - 47

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2 - 48

2.7 Secondary Bonding or Van Der Waals bonding 次要鍵結或凡得瓦鍵 • Weak in comparison to the primary bonds, 4-30 kJ/mol 比三種主要鍵結弱 • Secondary bonding forces arise from atomic or molecular dipoles (偶極)

Chapter 2 - 49

Fluctuating induced dipole bonds 擾動感應偶極鍵

Fig_02_21b Chapter 2 - 50

Polar-molecule-induced dipole bonds 極性分子-感應偶極鍵

Chapter 2 - 51

Permanent dipole bonds 永久電偶極

Chapter 2 - 52

Secondary Bonding Arises from interaction between dipoles • Fluctuating dipoles asymmetric electron clouds

+

-

+ secondary bonding

-

ex: liquid H 2 H2 H2

H H

H H secondary bonding

Adapted from Fig. 2.20, Callister & Rethwisch 9e.

• Permanent dipoles-molecule induced -general case: -ex: liquid HCl -ex: polymer

+

-

H Cl

secondary bonding

+

secondary bonding

H Cl

Adapted from Fig. 2.22, Callister & Rethwisch 9e.

secondary bonding Chapter 2 - 53

Secondary bonding • Involved in a number of natural phenomena and many products in our daily life. • Physical phenomena: surface tension, capillary action, viscocity • Apps: • Aadhesives 黏結. Two surfaces adhere to each other by van der waals force between them • Desiccants 乾燥劑: materials formed H bonds with water molecules (and thus remove moisture from the container)

Chapter 2 - 54

Chapter 2: Atomic Structure

凡德瓦鍵 Van der Waals bond  Van der Waals bonding  當一個中性的原子置入在電場中，原子會產生極性，造成偶極子 的移動 (dipole movement)。When a neutral atom is exposed to an internal or external electric field, the atom becomes polarized. This creates or induces a dipole moment.  有些分子中，極性不需要被誘導而產生，而是自然的存在。In some molecules, the dipole moment does not have to be induced—it exists by virtue of the direction of bonds and the nature of atoms. These molecules are known as polarized molecules.  凡德瓦鍵是次鍵，但是存在分子中原子的結合可為共價鍵或離子 鍵。Van der Waal bonds are secondary bonds, but the atoms within the molecule are joined by strong covalent or ionic bonds. © 2011 Cengage Learning Engineering. All Rights Reserved.

2 - 55

Properties From Bonding: Tm • Bond length, r

• Melting Temperature, Tm Energy

r • Bond energy, Eo

ro

Energy

r smaller Tm

unstretched length ro

r

Eo = “bond energy”

larger Tm Tm is larger if Eo is larger.

Chapter 2 - 56

Chapter 2: Atomic Structure

2-6 鍵能和原子間距 Binding Energy and Interatomic Spacing 原子間距 Interatomic spacing

原子的平衡距離，由斥力和吸力平衡造成的。固態 金屬之原子平衡距離為原子直徑。 The interatomic spacing in a solid metal is approximately equal to the atomic diameter, or twice the atomic radius r.

束縛能 Binding energy

打破鍵結所需之能量 Minimum energy required to break the bond

彈性模數 Modulus of elasticity

The slope (E) of the stress strain curve in the elastic region

降伏強度 Yield strength

Level of stress at which the material begins to permanently deform

熱膨脹係數 Coefficient of thermal expansion

Denoted by α = (1/L)(dL/dT), where L is the length and T is temperature © 2011 Cengage Learning Engineering. All Rights Reserved.

2 - 57

Chapter 2: Atomic Structure

Figure 2.18

打破鍵結所需之能量

束縛能

Interatomic space 原子的平衡距離，由斥 力和吸力平衡造成的。

原子間距 F=0 © 2011 Cengage Learning Engineering. All Rights Reserved.

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ed. 2011.

Chapter 2: Atomic Structure

Property from bonding: melting point, Tm 彈性模數 高熔點

Energy 低熔點

Figure 2.19 © 2011 Cengage Learning Engineering. All Rights Reserved.

ro

r smaller Tm larger Tm

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Properties From Bonding: α • Coefficient of thermal expansion, α length, L o coeff. thermal expansion unheated, T1

ΔL = α (T2 -T1) Lo

ΔL

heated, T 2

• α ~ symmetric at ro Energy unstretched length ro

E o

E o

r

α is larger if Eo is smaller.

larger α smaller α Chapter 2 - 60

Chapter 2: Atomic Structure

Property from bonding:熱膨脹係數 (coefficient of thermal expansion)

(Interatomic energy)

鍵結較弱→加熱後位移較大→熱膨 脹係數較高 鍵結較強→加熱後位移較小→熱膨 脹係數較低

Figure 2.20

© 2011 Cengage Learning Engineering. All Rights Reserved.

Chapter 2 - 2 Askland et al. The science and engineering of materials. 6th ed. 2011.

Chapter 2: Atomic Structure

四種鍵結之束縛能比較

Askland et al. The science and engineering of materials. 6th ed. 2011.

© 2011 Cengage Learning Engineering. All Rights Reserved.

Chapter 2 - 2

Summary: Bonding Comments

Type

Bond Energy

Ionic

Large!

Nondirectional (ceramics)

Covalent

Variable large-Diamond small-Bismuth

Directional (semiconductors, ceramics polymer chains)

Metallic

Variable large-Tungsten small-Mercury

Nondirectional (metals)

Secondary

smallest

Directional inter-chain (polymer) inter-molecular Chapter 2 - 63

Summary: Primary Bonds Ceramics (Ionic & covalent bonding):

Metals (Metallic bonding):

Polymers (Covalent & Secondary):

Large bond energy large Tm large E small α

Variable bond energy moderate Tm moderate E moderate α

Directional Properties Secondary bonding dominates small Tm small E large α

Chapter 2 - 64