Interatomic Bonding (or Binding) Each bonding mechanism between 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 Total Energy than any other configuration of these particles (including infinite separation of the atoms).

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 Energies in solids range from ~ 0.1 eV/atom for solids with only the weak Van der Waals interaction to ~ 7 eV/atom or greater in some covalent & some ionic compounds & some metals.

Interaction Energies Between Atoms The energy 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 NaCl is much more stable than a collection of free Na & Cl atoms Crystalline NaCl Na + Cl

R R2R2 R1R1 V(R) 0  R0 R0 Repulsive Attractive 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 equilibrium distance R 0 : At R 0, F(R 0 ) = 0. R = R 1 + R 2 For R > R 0, V(R) increases gradually with increasing R. V(R)  0 as R  ∞ The force F(R) is attractive in this region. For R < R 0 : V(R) increases rapidly with decreasing R. V(R)  ∞ as R  0 The force F(R) is replusive in this region.

Mathematically, V has the general empirical form (R  r): V= Sum of 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. The potential energy V of either atom is given by:

Table 3.1: Cohesive Energies of Elemental Solids

Table 3.2: Melting Points of Elemental Solids

Table 3.3: Isothermal Bulk Moduli & Compressibilities of Elemental Solids

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.derivative

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.

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 m.

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

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

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??

Atomic and Ionic Radii Need one pure element first Native Cu. Atomic radius = 1/2 bond length Metals usually FCC or BCC a a X-ray d 100  a Ionic radius = a

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: 1)Variations in related to % ionic or covalent character 2) Variations in # of closest neighbors (coordination #)

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.moleculecrystal

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.

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

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.

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.

Effective Nuclear Charge What keeps electrons from simply flying off into space? Effective nuclear charge is the pull that an electron “feels” from the nucleus. 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.

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.

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.

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.

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

Electron Affinity What does the word ‘affinity’ mean? Electron affinity is the energy change 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.

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.

Electron Affinity Your help sheet should look like this: ++

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

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

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

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

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?

Electronegativity Your help sheet should look like this: 0

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.

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

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

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 Cs0.7

Overall Reactivity Your help sheet will look like this: 0

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.

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.

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.

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

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

Most ionic compounds are brittle; a crystal will shatter if we try to distort it. This happens because distortion cause ions of like charges to come close together then sharply repel. Brittleness 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. Hardness Solid ionic compounds do not conduct electricity when a potential is applied because there are no mobile charged particles. No free electrons causes the ions to be firmly bound and cannot carry charge by moving. Electrical conductivity 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. Melting point & boiling point ExplanationProperty Ionic Materials