Primary bonding. ionic. covalent. polar covalent. metallic. Examples of Substances with Different Types of Interatomic Bonding.

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Erick Benson
6 years ago
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1 Bonding

2 Primary bonding Table 1.5 Examples of Substances with Different Types of Interatomic Bonding Type of Bond Substance Bond Energy, kj/mol Melting Point, ( C) Characteristics ionic covalent polar covalent metallic Ionic CaCl Low electrical conductivity, NaCl transparent, brittle, high LiF melting point CuF Al 2 O 3 15, Covalent Ge Low electrical conductivity, GaAs very hard, very high Si melting point SiC Diamond Metallic Na High electrical and thermal Al conductivity, easily Cu deformable, opaque Fe W van der Waals Ne Weak binding, low melting Ar and boiling points, very CH compressible Kr Cl Hydrogen bonding HF Higher melting point than van H 2 O 50 0 der Waals bonding, tendency to form groups of many molecules

3 Electronegativity and its effect on bonding electronegativity is very useful quantity to categorise bonds. It provides a measure of the excess binding energy between atoms A and B ΔA-B = 96.5(χA-χB) 2. bond dissociation energy between two atoms DEij. The bond dissociation energy is the energy required to separate two bonded atoms. ΔA-B = DEAB - [(DEAA)(DEBB)] 1/2.

4 Ionic (hetropolar) results from the transfer of electrons from a more electropositive atom to an electronegative atom. Ionic bonds usually result when the difference in electronegativity is greater than 2.0, because of this large discrepancy in the electronegativity one atom will loose an electron while one will gain. This is favourable for both atoms as they can attain a noble gas configuration

5 Covalent (homopolar) Arises when electrons are shared between atoms. This would happen if the electronegatvies are not greatly different. Purely covalent bond when the differences in electronegativity is 0.4 or less. At differences in electronegativity from 0.4 -> 2.0, then we have a polar covalent bond. This is a hybrid between the two forms of bonds.

7 Ionisation energy

8 Calculate the ionic character % ionic character = 100[1-exp[-0.25(χA-χB) 2 ]]

9 Question What is the percent ionic character of H-F? 55%

10 Metallic bond Bonding electrons become delocalised. Formed by atoms of low electronegativity. Model first proposed by Lorentz, uses a sea of electrons known as an electron gas

11 ¼ Type of interaction Interaction energy w(r) Covalent, metallic Complicated, short range Charge charge þq 1 Q 2 /4p3 0 r (Coulomb energy) Charge dipole Qu cos q/4p3 0 r 2 Q 2 u 2 /6(4p3 0 ) 2 ktr 4 Dipole dipole u 1 u 2 [2 cos q 1 cos q 2 sin q 1 sin q 2 cos f]/4p3 0 r 3 u 2 1 u2 2 =3ð4p3 0Þ 2 ktr 6 ðkeesom energyþ Charge non-polar Q 2 a/2(4p3 0 ) 2 r 4 Dipole non-polar u 2 a(1 þ 3 cos 2 q)/2(4p3 0 ) 2 r 6 u 2 a/(4p3 0 ) 2 r 6 (Debye energy) Two non-polar molecules 3 4 hva 2 ð4p3 0 Þ 2 ðlondon dispersion energyþ r6 Hydrogen bond Complicated, short range, energy roughly proportional to 1/r 2 a w(r) is the interaction free energy or pair-potential (in J); Q, electric charge (C); u, electric dipole moment (C m); a, electric polarizibility (C 2 m 2 J 1 ); r, distance between the centers of the interacting atoms or molecules (m); k, Boltzmann constant ( JK 1 ); T, absolute temperature (K); h, Planck s constant ( J s); n, electronic absorption (ionization) frequency (s 1 ); 3 0, dielectric permittivity of free space ( C 2 J 1 m 1 ). The force F(r) is obtained by differentiating the energy w(r) with respect to distance r: F ¼ dw/dr. The stabilizing repulsive Pauli Exclusion interactions (not shown) usually follow an exponential function w(r)f exp( r/r 0 ), but for simplicity they are usually modeled as power laws: w(r)fþ1/r n (where n ¼ 9 12).

12 Ionic in more depth

13 The Ionic Bond. To form an ionic bond, we must account for the complete transfer of electrons from one atom to the other. The easiest approach is to first transfer the electrons to form ions, then bring the two ions together to form a bond. Sodium chloride is a simple example that allows us to obtain both the bond energy and equilibrium bond distance using the potential energy approach. For this case, the potential energy, U, not only is the sum of the attractive and repulsive energies, UA and UR, respectively, but must also take into account the energy required to form ions from sodium and chlorine atoms, E ions. So, our energy expression looks like:

14 For NaCl

15 Ionic in more depth If we take a single charge, the field is given by

16 The Force between two ions

17 Work done attractive

18 Example The charge on an Ion is dependent on the number of lost or gained electrons. lets use Na + Cl -, sodium chloride. For now we will ignore the medium so E 0 =1. r is the sum of the two atomic radii =0.276 nm. W(r)= (1-)*(1)(1x10^-19)^ = -8.4 x 10 ^-19 Joules 4*pi*(8.85X10^-12)*(0.276x10^-9)

19 What does -8.4 x J means. Thermal energy is kt = 4.1 x at room temp The bond strength is about 200 times room temp

20 Question Thermal energy is kt = 4.1 x at room temp At what separation would the bond strength be equivalent to thermal energy? 58 nm

21 Question What is the force required to break an ionic bond?

22 What do we know now? Ionic bonds much stronger than thermal energy Non-Directional (why is this important) Quite long range (again why is this important)

23 Ionic Crystals

24 Ca Na Ca Na Ca Na Ca Na Ca Na Ca Na Ca Na Ca Na Ca Na Ca Na Ca Ca Na Ca Ca Na Ca Na Ca Na r Na Ca Na Ca Na Na Ca Na Ca Na Ca r Na Ca Na Ca Na

25 Madelung Constant Different for differing crystal structures. Varies from > Very difficult to calculate. crystals are more stable

26 molar lattice energy Some time called the cohesive energy. U = -Nou i = (6.02 X10 23 )(1.46X10-18 ) = 880 kj mol-1

27 Reference states Any value for the energy is not meaningful unless referenced to some state with which it is being compared. For example we took r to be infinity and epsilon to be 1. But ions don t really exist at infinity and epsilon will change as we enter the solid state.

29 Born Energy of an Ion So what is the energy of an Ion with respect to that of an atom

30 Born energy The Born energy gives the electrostatic free energy of an ion. In the medium of dielectric constant epsilon. It is always +ve because it is an unfavourable state

31 Epsilon The Born energy allows us to think about moving our Ions out o vacuum and in to a more realistic medium. Joules KJ per mol

32 Moving an ion from Vacuum in to water

33 Boltzmann

34 One last thing

35 þ 1 Methyl formamide Dielectric constant Work out the inter ionic spacing for NaCl 10 1 Formamide Water Ethylene glycol Solubility X s (mole fraction) Formamide Glycine Ethanolamine Methanol NaCl Ethanol 10 4 Methanol Propanol Butanol Pentanol 10 5 Ethanol Butanol /

36 Covalent Bonding In covalent bonding stable electron configurations are assumed by the sharing of electrons between adjacent atoms. Two atoms that are covalently bonded will each contribute at least one electron to the bond, and the shared electrons may be considered to belong to both atoms. Covalent bonding is schematically illustrated in Figure below for a molecule of methane (CH4). The carbon atom has four valence electrons, whereas each of the four hydrogen atoms has a single valence electron. Each hydrogen atom can acquire a helium electron configuration (two 1s valence electrons) when the carbon atom shares with it one electron. The carbon now has four additional shared electrons, one from each hydrogen, for a total of eight valence H Shared electron from hydrogen Shared electron from carbon H C H H

37 Covalent 1s Anti bonding orbital σ* σ bonding orbital 1s

38 Hydrogen Antibonding molecular orbital s* Energy Atomic orbital 1s Atomic orbital 1s Atom A Bonding molecular orbital s Molecule Atom B

39 Atomic orbitals Molecular orbitals (a) A + B s bonding + + 2s 2s A B + s* antibonding (b) + + A + B s bonding 2p x 2p x A B + s* antibonding (c) + + A + B p bonding 2p y 2p y + A B + p* antibonding 1.5

40 Oxygen s*2p 2p p*2p p2p 2p 2s s2p s*2s s2s 2s (a) (b) Atomic orbitals + + 2s 2s + + A A A Molecular orbitals + + B B B + s bonding s* antibonding s bonding O O 2 O (c) 2p x 2p x + + A A + B B + s* antibonding p bonding 2p y 2p y + A B + p* antibonding

41 Question Can you do the same for nitrogen

42 Take Home Ionic strong, non direction Covalent can be strong but are directional

43 Mie Potential

44 Attraction An attractive force can be written as Energy Distance

45 Repulsion A repulsive force can be written as

46 Total energy of a system Therefore the total energy of a system is simply

47 Mei Potential Energy Distance

48 u = b r n a r m du dr = b r n a 0 r m = b 0 r n a r m 0 =(br n ) 0 (ar m ) 0 = nbr n 1 + mar m 1 du dr = 0 nbr n 1 + mar m 1 = 0 nbr n 1 = mar m 1 nb ma = r m 1 r n 1 nb ma = r m 1 r n+1 nb ma = r m nb ma = r n r n 1+n+1 m m = nb ma n,m are positive integer numaers, so we can take the (n r = m) th root: nb n m r nb = n m ma ma

50 + Attractive force F A Attraction Force F 0 Interatomic separation r Repulsion r 0 Repulsive force F R Net force F N (a) + Repulsive energy E R Potential energy E Attraction Repulsion 0 E 0 Net energy E N Interatomic separation r Attractive energy E A (b)

51 blue 15 6 potential, red 12 6 Mie potential

(a) (c) (e) (b) (d) quality factor and stiffness are described in detail elsewhere Briefly, we recorded Q factors of between 1000 and 50 0 at 5 K with resonance frequencies of between 22 and 25 kh

We then performed dynamic ST (dstm) (i.e., tunnel-current-based feedback with an os lating tip) and transferred to constant f (i.e., FM-AF feedback and subsequently reduced the tip bias to 0 V.

In some cases we immediat obtained atomic resolution after transferring from dst in other cases it was necessary to perform small control contacts with the surface to alter the tip state.

52 (a) (c) (e) (b) (d) quality factor and stiffness are described in detail elsewhere Briefly, we recorded Q factors of between 1000 and 50 0 at 5 K with resonance frequencies of between 22 and 25 kh and tuning fork stiffness of k = 2600 N/m (±400 N/m). 28 The sensors were prepared using standard STM techniq (e.g., voltage pulsing, controlled tip crashes) until atom resolution was obtained. We then performed dynamic ST (dstm) (i.e., tunnel-current-based feedback with an os lating tip) and transferred to constant f (i.e., FM-AF feedback and subsequently reduced the tip bias to 0 V. would then increase the frequency shift set point until we beg to observe atomic resolution. In some cases we immediat obtained atomic resolution after transferring from dst in other cases it was necessary to perform small control contacts with the surface to alter the tip state. As a consequen of our tip preparation techniques (and evidence from scann electron microscope measurements on similarly prepared ST tips 28 )weexpecttheapexofthetiptobesiliconratherth tungsten terminated. The reduction of the tip bias to 0 V essential both in order to remove the possibility of electro crosstalk from the I t channel 30 and, critically, to also elimin the effect of tunneling electrons. As a consequence, we not null out any contact potential difference (CPD) betwe tip and surface, and as such a large electrostatic backgrou may be present. Nonetheless, we routinely observed atom resolution even with relatively blunt tips (e.g., tips t experienced surface indentations in excess of 1000 nm co still produce atomic resolution), most likely because operat with small oscillation amplitudes increases our sensitivity the short-range chemical force p(2x2) c(4x2) 'three in a row' 'phason'

PHYSICAL REVIEW B 84,085426(2011) f(hz) -20-40 -60-80 (a) α Flip type i App. Flip type i Ret. up atom App. up atom Ret. f(hz) -20-40 -60-80 (b) α β Fail flip type i App.

rst, the ata stiific (c) (e) (d) (f) (h) f(hz) -140-20 -40-60 -80-100 -120-140 (c) -2.5-2.0-1.5-1.0-0.5 0.00 0.5 α Z (Å) Fail flip type ii App. Fail flip type ii Ret.

Flip type ii Ret. up atom App. up atom Ret. FIG. 2. (Color online) Scan-induced phason manipulation FIG. 8. (Color and online) Representative examples of f (z) signatures.

(a) FM-AFM image wasshowing acquired using an a different tip apex and different parameters (A 0 = 250 pm) as this type of event was comparatively rare.

f (z) curves. (a) Successful flip type (i), defects (highlighted). f = 26 Hz; A 0 = 100 pm; showing V gap a= smooth 0V.

At higher set points we observe strong scan-induced similarity to the f (z) curve taken over an up atom. (b) Unsuccessful flip type (i).

jump back onto the approach curve is detected (β), indicating that the atom under the tip has dropped back into a down state. (c) Unsuccessful flip type (ii).

53 PHYSICAL REVIEW B 84,085426(2011) f(hz) (a) α Flip type i App. Flip type i Ret. up atom App. up atom Ret. f(hz) (b) α β Fail flip type i App. Fail flip type i Ret. up atom App. up atom Ret. the the (a) (b) (g) guns, EB nd the f a ate ith the ic ion his ges Å. rst, the ata stiific (c) (e) (d) (f) (h) f(hz) (c) α Z (Å) Fail flip type ii App. Fail flip type ii Ret. up atom App. up atom Ret Z (Å) f(hz) (d) α γ Z (Å) Z (Å) Flip type ii App. Flip type ii Ret. up atom App. up atom Ret. FIG. 2. (Color online) Scan-induced phason manipulation FIG. 8. (Color and online) Representative examples of f (z) signatures. (a) to (c) were acquired using the same tip apex (A 0 = 50 pm). (d) c(4 2)-to-p(2 1) transition. (a) FM-AFM image wasshowing acquired using an a different tip apex and different parameters (A 0 = 250 pm) as this type of event was comparatively rare. On each graph a unperturbed buckled surface structure and three native f (z) curve phason taken over an up atom with the same tip is plotted to aid comparison with the retract f (z) curves. (a) Successful flip type (i), defects (highlighted). f = 26 Hz; A 0 = 100 pm; showing V gap a= smooth 0V. increase followed by a sudden discontinuity (α) andsubsequentretractalongadifferentpath.theretractcurveexhibitsa (b) f = 27 Hz. At higher set points we observe strong scan-induced similarity to the f (z) curve taken over an up atom. (b) Unsuccessful flip type (i). Similar behavior as shown in (a) except that on phason motion, as previously reported (Ref. 28). (c) f the retract = 28 a sudden Hz. jump back onto the approach curve is detected (β), indicating that the atom under the tip has dropped back into a down state. (c) Unsuccessful flip type (ii). In this instance the jump on retract is in almost the same position as the initial jump, resulting in very little At still higher set points the position of some of the phasons becomes hysteresis in the f (z) curve. (d) Successful flip type (ii) taken from a different data set with a different long-range f (z) behavior. Here it difficult to identify (larger highlighted regions). (d) f = 29 Hz. appears that the flip has failed as the retract follows the same path as approach, but then suddenly jumps down onto the up atom curve (γ ).

54 Take home The Mie potential The Lennard-Jones is just a Mie potential

Complicated, short range. þq 1 Q 2 /4p3 0 r (Coulomb energy) Q 2 u 2 /6(4p3 0 ) 2 ktr 4. u 2 1 u2 2 =3ð4p3 0Þ 2 ktr 6 ðkeesom energyþ

Complicated, short range. þq 1 Q 2 /4p3 0 r (Coulomb energy) Q 2 u 2 /6(4p3 0 ) 2 ktr 4. u 2 1 u2 2 =3ð4p3 0Þ 2 ktr 6 ðkeesom energyþ Bonding ¼ Type of interaction Interaction energy w(r) Covalent, metallic Complicated, short range Charge charge þq 1 Q 2 /4p3 0 r (Coulomb energy) Charge dipole Qu cos q/4p3 0 r 2 Q 2 u 2 /6(4p3 0 ) 2