《固体物理学》课程教学课件（PPT讲稿）Chapter 3 Interatomic Bonding 3（Supplement - Rules of crystal binding）

3-1 supplement:Rules of crystal binding Electronegative:used to characterize the ability of losing or getting electrons.In the periodical tables,the Electronegativity is increased from the left to right in the same period,and is reduced from the top to down Mulliken definition: Electronegativity=0.18 (ionization energy+electron affinity)

3-1 supplement：Rules of crystal binding Electronegative：used to characterize the ability of losing or getting electrons. In the periodical tables, the Electronegativity is increased from the left to right in the same period, and is reduced from the top to down Mulliken definition： Electronegativity＝0.18（ionization energy＋electron affinity）

Similar Regularity Electronegativity values H H He 2.30 2.304.16 Be B C N 0 F Ne 0.91 1.58 2.052.543.073.61 4.194.79 Na Si P Ar 0.87 1.611.922.252.592.873.24 K Ca Sc Ti Mn Fe Co Ni Cu Ga Ge As Se Br Kr 0.73 1.03 1.2 1.3 1.4 .5 1.6 1.8 1.9 1.8 1.6 1.76 1.99 2.212.42 2.692.97 Rb Sr Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 0.71 0.96 1.0 1.1 1.3 1.4 1.5 1.7 1.8 1.9 2.0 1.5 1.66 1.82 1.982.162.362.58 Cs Ba Ha 0.660.88 1.76 Figure by MIT OCW

Similar Regularity

离能 资料来源：National Bureau of Standards Circular467). He 24.58 78.98 B c N 0 Ne 8.30 11.26 14.54 13.61 1742 21.56 33.45 35.64 44.14 48.76 52.40 62.63 Si CI Ar 5.98 8.15 10.55 10.38 1301 15.76 24.80 24.49 30.20 34.0 36.81 43.38 Cited from Kittel p42 Cu Zn Ga Ge AS Se Br Kr 3 7.72 9.39 6.00 7,88 9.81 9.75 11.84 14.00 5.78 27.93 27.35 26.51 23.81 30.0 312 33.4 38.56 Ag Cd In Sn Sb Xe 33 7.57 899 578 7.34 8.64 9.01 10.45 12.13 775 29.05 25.89 24.64 21.97 25.1 27.6 29.54 33.3 Au Hg Pb Po At Rn 96 922 10.43 6.11 7.41 729 8.43 10.74 7.52 29.7 29.18 26.53 22.44 23.97 Gd Tb Dy Ho Er Tm Yb 6.16 6.74 6.82 82 5.0 Cm Bk Fm Md No

Cited from Kittel p42

General rules for crystal binding lowest electronegativity for alkali metal,liable to lose elctrons *IV-VI elements possess a higher electronegativity,and strong ability to obtain electrons,liable to form covalent bonds.IVelements are typical example.C (diamond)have biggest electronegativity, and have a strong covalent bond,while Pb is weakly electronegative and is a mental The value of electronegativity for elements at both end of the periodical tables have a big differnce,so,I -VII elements are lible to form ionic crystal,for example,NaCl,CsCl. With the reduction of the electronegativity difference,the ionic binding gradually is tranformed to covalent bingding

★ The value of electronegativity for elements at both end of the periodical tables have a big differnce, so , Ⅰ－Ⅶ elements are lible to form ionic crystal , for example, NaCl,CsCl. ★ With the reduction of the electronegativity difference，the ionic binding gradually is tranformed to covalent bingding. 。 General rules for crystal binding ★ lowest electronegativity for alkali metal, liable to lose elctrons ★ Ⅳ－Ⅵ elements possess a higher electronegativity, and strong ability to obtain electrons, liable to form covalent bonds. Ⅳelements are typical example. C（diamond) have biggest electronegativity, and have a strong covalent bond, while Pb is weakly electronegative and is a mental

3-2 supplement:Madelung常数的计算 Evjen中性组合法 ⊕ O⊕ 选取一个负离子为原点，用中性 ⊕ ⊕ o ⊕ ⊕ 组合法来计算Madelung常数，可以收 ⊕ ⊕ ⑧ 到快速收敛的效果。 ⊕ ⊕ ⊕ 以二维情况为例： ⊕ 4=4)4161293 ⊕ 214√2 2=446-4+851-411 -4-+8 迈42225中422 ≈1.607 03≈1.6105 式中同性电荷取负值异性 电荷取正值

3-2supplement :Madelung常数的计算 ——Evjen中性组合法 选取一个负离子为原点，用中性 组合法来计算Madelung常数，可以收 到快速收敛的效果。 以二维情况为例： 1 1 1 1 1 4 4 1.293 2 1 4 2  =   −    2 1 1 1 1 1 1 1 4 4 4 8 4 1.607 2 5 2 2 2 2 2 4  = −  −   +   −    3  1.6105 1 j ij a  =   式中同性电荷取负值异性 电荷取正值

NaCl结构Madelung常数的计算： 参考二维做法，一层一层计算，逐步扩大，收敛很快。 002 012 022 10 111 001 011 021 000 010 020 Na* OC

NaCl结构Madelung常数的计算： 参考二维做法，一层一层计算，逐步扩大，收敛很快。 000 010 020 001 011 002 021 111 012 022 101

原子坐标 相同个数 距离 对势能的贡献 100 6 1 +6.00 110 12 2 -1%2-8485 111 8 万460 200 6 √4 -4=-300 210 24 5 2以5=+10730 211 24 6 ☐26-9800 220 12 V⑧ 84244 -12/ 221 24 √ 245=+80 222 8 √2 -82-2310

原子坐标 相同个数 距离 对势能的贡献 100 6 1 ＋6.00 110 12 111 8 200 6 210 24 211 24 220 12 221 24 222 8 2 12 8.485 2 − = − 3 8 4.600 3 = + 4 5 6 8 9 12 6 3.000 4 − = − 24 10.730 5 = + 24 9.800 6 − = − 12 4.244 8 − = − 24 8.000 9 = + 8 2.310 12 − = −

一个晶胞范围内和加倍范围后的数值： 6.08.485.4.62 =1.456 248 6.0-8.485+4.62- 3,10.739.84.244,8.02. 1=1.751 22 2 48 结构 a 氯化钠(NaCl) 1.747565 氯化铯(CsCI) 1.762675 闪锌矿（立方ZnS) 1.6381 纤锌矿（六方ZnS) 1.641 萤石(CaF2) 5.039 金红石（Ti02) 4.816

6.0 8.485 4.62 1.456 2 4 8 3 10.73 9.8 4.244 8.0 2.31 6.0 8.485 4.62 1.751 2 2 2 4 4 8 − + = − + − + − − + − = 一个晶胞范围内和加倍范围后的数值： 纤锌矿（六方ZnS） 1.641 萤 石（CaF2） 5.039 金红石（TiO2） 4.816