Interatomic B o nding (or Binding)

1. Interatomic Bonding(or Binding) Each bonding mechanismbetween the atoms in a solid is a result of the electrostatic interactions between the nuclei & the electrons. The differing bond strengths & differing bond types are determined by the electronic structures of the atoms involved. The existence of a stable bonding arrangement implies that the spatial configuration of positive ion cores & outer electrons has a smaller Quantum Mechanical TotalEnergy than any other configuration of these particles (including infinite separation of the atoms).

2. In a particular solid, the energy difference of the configuration of atoms compared with that of the isolated atoms is called The Cohesive Energy Cohesive Energiesin solids range from ~ 0.1 eV/atomfor solids with only the weak Van der Waals interaction to ~ 7eV/atomor greater in some covalent &some ionic compounds & some metals.

3. Interaction Energies Between Atoms Theenergy of a crystal is lower than that of the free atoms by an amount equal to the energy required to pull the crystal apart into a set of free atoms. This is called the crystal Binding(Cohesive)Energy. Example Crystalline NaClis much more stable than a collection of free Na & Cl atoms + Crystalline NaCl Cl Na

4. For a pair of atoms, a typical potential energy curve V(R) as a function of interatomic separation R looks qualitatively as shown. The force is F(R) = - (dV/dR). At equlibrium, the repulsive part of the force exactly equals the attractive part. The V(R) curve has a minimum at equilibriumdistance R0: At R0, F(R0) = 0. R0 V(R) Repulsive 0 Attractive R1 R2 R R = R1 + R2 For R > R0, V(R) increases gradually with increasingR. V(R)  0 as R  ∞ The force F(R)is attractive in this region. For R < R0: V(R)increases rapidly with decreasing R. V(R) ∞as R  0 The force F(R)is replusive in this region.

5. Mathematically, Vhas the general empirical form (R  r): • The potential energy Vof either atom is given by: V= Sumof an Attractive Term which decreases with increasing separation & a Repulsive Term which increases with decreasing separation. V(r) = Net potential energy of interaction as a function of r r =Distance between atoms, ions, or molecules a,b =Proportionality constants m, n =Constants characteristic of bond type & structure type.

6. Table 3.1:Cohesive Energies of Elemental Solids

7. Table 3.2:Melting Points of Elemental Solids

8. Table 3.3: Isothermal Bulk Moduli & Compressibilities of Elemental Solids

9. Isothermal bulk modulus • The  isothermal bulk modulus is the bulk modulus (  or  ) of a substance measures the substance's resistance to uniform compression • The bulk modulus   can be formally defined by the equation • where P is pressure,V is volume, and    denotes the derivative of pressure with respect to volume.

10. Atomic Radius • There are several important atomic characteristics that show predictable trends that you should know. • The first and most important is atomic radius. • Radius is the distance from the center of the nucleus to the “edge” of the electron cloud.

11. Atomic Radius • Since a cloud’s edge is difficult to define, scientists use define covalent radius, or half the distance between the nuclei of 2 bonded atoms. • Atomic radii are usually measured in picometers (pm) or angstroms (Å). An angstrom is 1 x 10-10 m.

12. Ionic Radius • The ionic radius of an element is the element’s share of the distance between neighboring ions in an ionic solid. • Generally: • Cations are smaller than their parent atoms • Anions are larger than their parent atoms

13. 2.86Å 1.43 Å 1.43 Å Covalent Radius • Two Br atoms bonded together are 2.86 angstroms apart. So, the radius of each atom is 1.43 Å.

14. Atomic and Ionic Radii Can't absolutely determine: e- cloud is nebulous & based on probability of encountering an e- In crystalline solids the center-to-center distance = bond length & is accepted to = sum of ionic radii How get ionic radius of X & Y in XY compound??

15. Need one pure element first • Native Cu. Atomic radius = 1/2 bond length • Metals usually FCC or BCC X-ray d100a Ionic radius = a 2 2 a a 4 Atomic and Ionic Radii

16. Atomic and Ionic Radii • If can look up lattice type (really space group) • BCC uses body diagonal rather than face • With compounds, don't know what % of bond • However there are variations: • Variations in related to % ionic or covalent character • 2) Variations in # of closest neighbors (coordination #)

17. Atomic and Ionic Radii • True radius will vary with actual bond-type, resonance (1x  2x in covalent), structural causes (Na in Ab), & coordination # • Purpose of all this radii stuff: • To understand & predict behavior of atoms in crystalline solids • Particularly Coordination Number • -of a central atom in a molecule or crystal is the number of its nearest neighbours.

18. Atomic Radius • The trend for atomic radius in a vertical column is to go from smaller at the top to larger at the bottom of the family. • Why? • With each step down the family, we add an entirely new Principle Energy Levels (PEL) to the electron cloud, making the atoms larger with each step.

19. Atomic Radius • Here is an animation to explain the trend. • On your help sheet, draw arrows like this:

20. Atomic Radius • The trend across a horizontal period is less obvious. • What happens to atomic structure as we step from left to right? • Each step adds a proton and an electron (and 1 or 2 neutrons). • Electrons are added to existing PELs or sublevels.

21. Atomic Radius • The effect is that the more positive nucleus has a greater pull on the electron cloud. • The nucleus is more positive and the electron cloud is more negative. • The increased attraction pulls the cloud in, making atoms smaller as we move from left to right across a period.

22. Effective Nuclear Charge • What keeps electrons from simply flying off into space? • Effective nuclear charge is the pull that an electron “feels” from thenucleus. • The closer an electron is to the nucleus, the more pull it feels. • As effective nuclear charge increases, the electron cloud is pulled in tighter.

23. Shielding • As more PELs are added to atoms, the inner layers of electrons shield the outer electrons from the nucleus. • The effective nuclear charge (enc) on those outer electrons is less, and so the outer electrons are less tightly held.

24. Ionization Energy • This is the second important periodic trend. • If an electron is given enough energy (in the form of a photon) to overcome the effective nuclear charge holding the electron in the cloud, it can leave the atom completely. • The atom has been “ionized” or charged. • The number of protons and electrons is no longer equal.

25. Ionization Energy • The energy required to remove an electron from an atom is ionization energy. (measured in kilojoules, kJ) • The larger the atom is, the easier its electrons are to remove. • Ionization energy and atomic radius are inversely proportional. • Ionization energy is always endothermic, that is energy is added to the atom to remove the electron.

26. Ionization Energy (Potential) • Draw arrows on your help sheet like this:

27. Electron Affinity • What does the word ‘affinity’ mean? • Electron affinity is the energychange that occurs when an atom gains an electron (also measured in kJ). • Where ionization energy is always endothermic, electron affinity is usually exothermic, but not always.

28. Electron Affinity • Electron affinity is exothermic if there is an empty or partially empty orbital for an electron to occupy. • If there are no empty spaces, a new orbital or PEL must be created, making the process endothermic. • This is true for the alkaline earth metals and the noble gases.

29. + + Electron Affinity • Your help sheet should look like this:

30. Electron Affinity • A measure of how much an atom ‘wants’ an electron • A High electron affinity means that energy is released when an element gains an electron • A Low or negative electron affinity implies that energy must be supplied to ‘push’ the electron onto the atom

31. Metallic Character • This is simple a relative measure of how easily atoms lose or give up electrons. • Your help sheet should look like this:

32. Ionization Energies and Metallic Character • Low ionization energies account for metallic character of elements in the s, d and f blocks. • They readily lose electrons and can therefore exist as a metalic solid

33. Electronegativity: the ability of an atom in a bond to pull on the electron. (Linus Pauling)

34. Electronegativity • Electronegativity is a measure of an atom’s attraction for another atom’s electrons. • It is an arbitrary scale that ranges from 0 to 4. • The units of electronegativity are Paulings. • Generally, metals are electron givers and have low electronegativities. • Nonmetals are are electron takers and have high electronegativities. • What about the noble gases?

35. 0 Electronegativity • Your help sheet should look like this:

36. Overall Reactivity • This ties all the previous trends together in one package. • However, we must treat metals and nonmetals separately. • The most reactive metals are the largest since they are the best electron givers. • The most reactive nonmetals are the smallest ones, the best electron takers.

37. Electronegativity • When electrons are shared by two atoms a covalent bond is formed. • When the atoms are the same they pull on the electrons equally. Example, H-H. • When the atoms are different, the atoms pull on the electrons unevenly. Example, HCl

38. Trends in Electronegativity • Electronegativity generally decreases as you move down a group. • Electronegativity of the representativeelements (Group A elements) increases as you move across a period.

39. Electronegativities of Some Elements Element Pauling scale F 4.0 Cl 3.0 O 3.5 N 3.0 S 2.5 C 2.5 H 2.1 Na 0.9 Cs 0.7

40. 0 Overall Reactivity • Your help sheet will look like this:

41. The Octet Rule • The “goal” of most atoms (except H, Li and Be) is to have an octet or group of 8 electrons in their valence energy level. • They may accomplish this by either giving electrons away or taking them. • Metals generally give electrons, nonmetals take them from other atoms. • Atoms that have gained or lost electrons are called ions.

42. Ions • When an atom gains an electron, it becomes negatively charged (more electrons than protons ) and is called an anion. • In the same way that nonmetal atoms can gain electrons, metal atoms can lose electrons. • They become positively charged cations.

43. Ionic Radius • Cations are always smaller than the original atom. • The entire outer PEL is removed during ionization. • Conversely, anions are always larger than the original atom. • Electrons are added to the outer PEL.

44. Cation Formation Effective nuclear charge on remaining electrons increases. Na atom 1 valence electron Remaining e- are pulled in closer to the nucleus. Ionic size decreases. 11p+ Valence e- lost in ion formation Result: a smaller sodium cation, Na+

45. Anion Formation A chloride ion is produced. It is larger than the original atom. Chlorine atom with 7 valence e- 17p+ One e- is added to the outer shell. Effective nuclear charge is reduced and the e- cloud expands.

47. Property Explanation Melting point & boiling point The melting and boiling points of ionic compounds are high because a large amount of thermal energy is required to separate the ions which are bound by strong electrical forces. Electrical conductivity Solid ionic compounds do not conduct electricitywhen a potential is applied because there are nomobile charged particles. No free electrons causes the ions to be firmly bound and cannot carrycharge by moving. Hardness Most ionic compounds are hard; the surfaces of their crystals are not easily scratches. This is because the ions are bound strongly to the lattice and aren't easily displaced. Brittleness Most ionic compounds are brittle; a crystal willshatter if we try to distort it. This happens because distortion cause ions of like charges to come close together then sharply repel. Ionic Materials