Bonding in Solids. What is the chemical bonding? Bond types: Ionic (NaCl vs. TiC?) Covalent Van der Waals Metallic

Size: px

Start display at page:

Download "Bonding in Solids. What is the chemical bonding? Bond types: Ionic (NaCl vs. TiC?) Covalent Van der Waals Metallic"

Anabel Nash
5 years ago
Views:

1 Bonding in Solids What is the chemical bonding? Bond types: Ionic (NaCl vs. TiC?) Covalent Van der Waals Metallic 1

2 Ions and Ionic Radii LiCl 2

3 Ions (a) Ions are essentially spherical. (b) Ions may be regarded as composed of two parts: a central core in which most of the electron density is concentrated and an outer sphere of influence which contains very little electron density. (c) Assignment of radii to ions is difficult; even for ions which are supposedly in contact, it is not obvious where one ion ends and another begins. 3

4 Where is the border bet. M + and N -? 1. Ions are charged, but they cannot be regard as hard sphere. 2. The e- density does not decrease abruptly to zero. 4

5 Ions in Crystal 1.Similar to Pauling & Goldschmidt s table. 2. Based on r(o 2- ) and r(f - ). 3. Obtained from X- ray electron density map. 5

6 Ionic Radii a) s- and p-block elements: radii increase with atomic number for vertical group b) For isoelectronic cations, radii decrease with increassing charge. c) For element which can have > +1 oxidation state, the radius decreases with increasing oxidation state, e.g. V 2+, V 3+, V 4+, V 5+. d) For an element which can have various coordination numbers, the cationic radius increases with increasing coordination number. 6

7 Ionic Radii cont. e) Lanthanide contraction (due to ineffective shielding of the nuclear charge by the d and, especially, f electrons), e.g. La 3+ (1.20 A) --Eu 3+ (1.09 A)--Lu 3+ (0.99 A). f) The radius of a particular transition metal ion is smaller than that of the corresponding main group ion for the reasons given in (e), e.g. octahedral radii, Rb + (1.63 A) and Ag + (1.29 A) or Ca 2+ (1.14 A) and Zn 2+ (0.89 A). g) Diagonal relationship: Li + (0.88 A) and Mg +2 (0.86 A). 7

8 2.3 Ionic Structure a) Ions are charged, elastic and polarizable spheres. b) Ionic structures are held together by electrostatic forces and are arranged so that cations are surrounded by anions, and vice versa. c) To maximize the net electrostatic attraction between ions (i.e. the lattice energy), coordination numbers are as high as possible, provided that the central ion 'maintains contact' with its neighboring ions of opposite charge. 8

9 Ionic Structure cont. (d) Next nearest neighbor interactions are of the anion-anion and cation - cation type and are repulsive. Like ions arrange themselves to be as far apart as possible and this leads to structures of high symmetry with a maximized volume. (e) The valence of an ion is equal to the sum of the electrostatic bond strengths between it and adjacent ions of opposite charge. (Pauling s electrostatic valence rule.) 9

10 Rutile 10

11 Electrostatic bond strength For a cation M m+ surrounded by n anions, X x- ebs = m/n (m/n) = x MgAl 2 O 4 :Mg 2+ (T d site) ebs = 2/4 = ½ Al 3+ (O h site) ebs = 3/6 = ½ Oxygen charge ebs(3al Mg 2+ ) = 2 (Each O atom is surrounded by three Al 3+ and one Mg 2+ cations, the observed charge is equal to oxygen s charge) 11

12 SiO 4 cannot share a common corner in silicate structures: Si 4+ : ebs = 4/4 = 1 Two Td corner: ebs = 2 (O atom connect to two Si atoms) Three Td corner: ebs = 3 (unreasonable) 12

13 13

14 The radius ratio rule (2r x ) 2 + (2r x ) 2 =[2(r M +r x )] 2 2rx 2 = 2 (r M +r x ) r M /r x =

15 15

16 A cation must be in contact with its anionic neighbors. Neighboring anions may or may not be in contact. 16

17 17

18 Borderline Radius & Distorted Structures V 2 O 5 Orthorhombic, Pnma 18

19 ZrO Orthorhombic, Pnam 19

20 PbTiO 3 Tetragonal, P4mm 20

21 Lattice Energy NaCl(s) Na + (g) + Cl - (g) ΔH = U a) Electrostatic forces attraction V = - (Z + Z - e 2 )/r b) Short-range repulsive forces V = B/r n V = r Fdr = Z + Z r 21 e 2

22 Madelung constant N : M constant 22

23 2.6 Lattice Energy 23

24 Lattice Energy I Therefore, 2 Z + Z e NA U = + r du dr Z Z e r NA BN n r nbn r 2 + = n + 1 du when = 0 dr then B = Z + Z e NAr n 2 n 1 and therefore U Z + Z e = r e 2 NA (1 1 n ) 24

25 Lattice Energy II Van der Waals or London forces, zero-point energy, correction for heat capacity 25

26 Kapustinskii s eq. U VZ r + r + = c a Z r + r c a -1 kj mol V: # of ions per formula unit 26

27 27

28 Born-Haber Cycle ΔH f = S + (1/2)D + IP + EA + U (could be estimated) = (-356) + (-764.4) = kj mol -1 28

29 The Synthesis of XePtF 6 XePtF 6 was first synthesized by Barlett at The idea for this compound is from the formation of O 2 PtF 6 (O 2 ) + (PtF 6 ) - The 1st IE of O 2 (1169 kj/mol) and Xe (1176 kj/mol) are similar! 29

30 30

31 Stabilities of Real and Hypothetical ionic compounds S 0.5D IP EA U ΔH f (calc) NaCl kj mol -1 KCl ArCl

32 Partial Covalent Bonding SrO HgO sp hybridization? 32

33 AlF 3, AlCl 3, AlBr 3, AlI 3 ionic covalent AlF 3 AlCl 3 AlBr 3 (Al 2 Br 3 unit) AlI 3 (Al 2 I 3 unit) 33

34 Sanderson s Model To calculate partial charge of atom To evaluate ionic and covalent bonding for total energy of ionic compounds Effective nuclear charge Atomic radii (r = r c -Bδ; δ = ΔS/S c ) Electronegativity and charged atoms 34

35 Effective Nuclear Charge The positive charge that would be felt by a foreign electron on arriving at the periphery of the atom. The valence electrons are not very effective in shielding the outside world from the positive charge on the nucleus. Therefore, any incoming e- feels a positive, attractive charge. 35

36 Screening constants The value of screening constants in different elements could be obtained theoretically. The valence electron experience an increasingly strong attraction to the nucleus on going from sodium (Na) to chlorine (Cl). 36

37 Atomic Radius Atomic radii vary considerably for a particular atom depending on bond type and CN. With increasing amount of partial positive charge, the radii become smaller Sanderson s model: r = r c -Bδ r c : non-polar covalent radius; δ: partial charge (estimated) 37

38 Electronegativity and Partially Charged Atoms The magnitude of the partial charge depends on the initial difference in electronegativity between the two atoms. Sanderson s model for electronegativity: S = D/D a D: electron density of the atom (atomic number/atomic volume) D a : expected electron density 38

39 39

40 Electronegativity Equalization When two or more atom initially different in electronegativity combine chemically, they adjust to have the same intermediate electronegativity within the compound. NaF: geometric mean of their χ S b = S S Na F =

41 Partial Charge The ratio of the change in electronegativity undergone by an atom on bond formation to the change it would have undergone on becoming completely ionic with charge + or -1. NaF: Assume 75% ionic S c = 2.08/S (changes in χ) Partial charge δ = S/ S c S = S - S b 41

42 Example: BaI 2 S Ba = 0.78; S I = 3.84 S b = 3 /S Ba S 2 I = 2.26 For Ba, S = = 1.48 For iodine S = = 1.58 S c : 1.93 (Ba), 4.08(I) (from tab. 2.10) δ Ba = 1.48/1.93 = 0.78 δ I = 1.58/4.08 = The result suggest BaI 2 is ~ 39% ionic 42

43 The radii of the partially charged atom: Ba: r Ba = r c -Bδ = x0.78 = 1.71 Å r I = 1.87 Å d(ba-i) = 3.58 Å (exp = 3.59 Å) 43

44 It is unrealistic and misleading to assign a radius to the chloride ion which is constant for all solid chlorides. 44

45 Calculations show that the actual charge carried by an oxygen never exceed -1 and is usually much less than

46 Mooser-Pearson plots and Ionicities 46

47 bcc fcc 47

48 Bond Valence and Bond Length Most molecular materials may be described satisfactorily using valence bond theory. For non-molecular inorganic materials, the VBT is not always fit. Pauling, Brown, Shannon, Donnay et. al. : Bond order (bond valence) in a structure. 48

49 Bond valences are defined empirically. Valence rule: V = bv i ij j V i : valence of atom I bv ij : bond valence between atom i and j 49

50 50

51 Applications To check the valence state of cation atom. To locate the position of H + To distinguish between Al 3+ and Si 4+ Transition metals in oxide compounds 51

52 Non-bonding electron effects d-electrons in transition metal compounds 52

53 53

54 54

55 Ca 2+ Mn 2+ Zn 2+ 55

56 Crystal Field Stabilization Energy 56

57 Jahn-Teller distortions d 9 (Cu 2+ ), d 7 (LS) and d 4 (HS, Cr 2+ ) 57

58 Cu 2+ (d 9 ), Cr 2+ (d 4 ) -MO oxides: Ti, V, Mn, Fe, Co, Ni: NaCl-type CuO: distorted CuO 6 octahedral CrO: NA MF 2 : -Ti, V, Mn, Fe, Cu, Ni, Zn: rutile -Cr, Cu: distorted rutile 58

59 Square plannar coordination d 8 ions: Ni 2+, Pd 2+, Pt 2+ Square planar coordination is more common with 4d and d transition elements. 59

60 Tetrahedral Coordination The magnitude of the splitting is generally less in a tetrahedral field. 60

61 61

62 Inert Pair Effect Heavy, post-transition metals: Tl, Sn, Pb, Sb, Bi These metals usually exhibit a valence state that is two less than the group valence. Inert pair effect Example: Pb +2 environment in PbTiO 3 62

63 PbTiO 3 Pb Tetragonal, P4mm 63

64 Non Linear Optic Materials Pb 6 Ti 2 Nb 8 O 30 Cm2m Chem. Mater. 2004, 16,

65 65

Ionic Bonding. Chem

Ionic Bonding. Chem Whereas the term covalent implies sharing of electrons between atoms, the term ionic indicates that electrons are taken from one atom by another. The nature of ionic bonding is very different than that