A wealth of information can be garnered by looking at the structure of a material. Though there are many levels of structure (e.g., atomic or macroscopic), many physical properties of a material can be related directly to the arrangement and types of bonds that make up that material. To help introduce these "building blocks" of materials, this chapter is divided into the following general topics:
The Elements
Types of Bonds
Intermolecular Forces and Bonding
Covalent Bonding
More advanced concepts like crystal structures and polymer morphology are best dealt with using specific material classes, i.e., an introduction to crystal structures is given using metals, whereas structural defects most often occur in ceramics. After reading this introductory material, you may want to go to the structures section under each of the following class of materials:
Metals and Alloys: Structure
Ceramics and Glasses: Structure
Polymers: Structure
Composites: Structure
Let's be fair. Elements are materials, too. Often times this fact is overlooked. Think about all the materials from our daily lives that are elements: Gold and Silver for our jewelry; Aluminum for our soda cans and Copper for our plumbing; Carbon, both as a beautiful diamond and a mundane pencil lead, Mercury for our thermometers; and Tungsten for our light bulb filaments. Most of these elements, however, are of little importance in the grand scheme of things. A table of the relative abundance of elements shows that most of our universe is made up of Hydrogen and Helium. A little closer to home, things are much different. A similar table of relative abundance shows that Helium on earth is relatively scarce, while Oxygen dominates our planet. Just think how much molecular oxygen, water and aluminosilicate rocks are contained in the earth's crust. But those are molecules. Elements are still of vital importance on earth, and the ones we use most often are primarily in the solid form.
Recall from freshman chemistry that the elements can be systematically arranged in a periodic table (see above) according to their electronic structure. A quick look at the periodic table at room temperature clearly shows us that many elements are solids. The fact that many of these elements remain solid well above ambient temperatures is also important. As we heat up to 1000°C, note that many of the IIIA-VA elements have melted, but most of the transition elements are still solids. At 2000°C, the alkali earths are molten, and many of the transition elements have begun to melt, too. Any guess as to what the highest melting point element is? Check out the periodic table at 3500°C. (Keep in mind that this is in an inert atmosphere. What should happen to this element in the presence of oxygen?) Such elements as Tungsten, Platinum, Molybdenum and Tantalum have exceptional high-temperature properties. Later on we'll investigate why this is so.
In addition, many elements are in-and-of themselves materials of construction. Aluminum and Copper are just a few examples of elements that are used extensively for fabricating mechanical parts. Elements have special electrical characteristics, too. Silver and Gold are not just used for jewelry, but for a wide variety of electrical components. We'll see that many of these properties are a direct result of the electronic structure of the elements. Hence, this section on "structure" will begin by reviewing what you learned in introductory chemistry courses about the electronic structrue of atoms.
Before going into specifics, let's look at some interesting trends in the periodic table.
This is sometimes referred to as the "ionization potential".
It is the energy required to remove the most weakly bound (usually outermost)
electron from an isolated gaseous atom:
and can be calculated using the energy of the outermost electron as
given by the Bohr model and Schroedinger's equation (in eV):
The general trend in the periodic table is for the ionization energy to increase from bottom to top, and left to right. Why?
A related quantity is the work function. The work function is the energy necessary to remove an electron from the metal surface in thermoelectric or photoelectric emission. We'll talk more about this later when we discuss eletronic properties of materials.
Electron affinity is the reverse process to the ionization energy; it is the energy change (often expressed in eV) associated with an isolated gaseous atom accepting one electron:
Unlike the ionization energy, however, EA can have either a negative or positive value. The EA is positive if energy is released upon formation of the negative ion. If energy is required, EA is negative. The general trend in the periodic table is again toward an increase in EA as we go from the bottom to top, and left to right, though this trend is much less uniform than for the IE.
In general, positive ions are smaller than neutral atoms, while negative ions are larger. (Why?) The trend in ionic and atomic radii is opposite to that of IE and EA. In general, there is an increase in radius from top to bottom, right to left. In this case, the effective nuclear charge increases from left to right, the inner electrons cannot shield as effectively and the outer electrons are drawn close to the nucleus, reducing the atomic radius. Note that the radii are only approximations because the orbitals, in theory, extend to infinity.
The ionization energy and electron affinity are characteristics of isolated atoms; they say very little about how two atoms will interact. It would be nice to have an independent measure of the attraction an atom has for electrons in a bond formed with another atom. Electronegativity is such a quantity. It is represented by the greek letter "chi", . Values can be calculated in one of several ways. They are always relative to one another, and values from one method should not be used with values from another method.
Zeff = effective nuclear charge and r is the atomic radius.
n = number of valence electrons
c = any formal valence charge on the atom and the sign corresponding
to it
r = covalent radius
Electronegativity is a very useful quantity to help categorize bonds, because it provides a measure of the excess binding energy between atoms:
is the excess binding energy between atoms A and B in KJ/mol
The excess binding energy, in turn, is related to a measurable quantity, namely the bond dissociation energy between two atoms, DEii:
DE is the energy required to separate two bonded atoms. These descriptions are emperical.
The greater the electronegativity difference, the greater the excess binding energy. These quantities give us a method of characterizing bond types. First, let's review the bond types and characteristics, then we'll discuss each in more detail.
Also known as "strong bonds", primary bonds arise from direct exchange or sharing of electrons between atoms. The more electrons per atom that take place in this process, the higher the bond "order"; e.g., single-, double-, or triple-bond, and the stronger the connection between atoms.
These types of associations between atoms occur when the electronegativity difference between the atoms is greater than about 2.0. Because of the large discrepancy in electronegativies, one atom will generally gain an electron, while the other atom in a diatomic molecule will lose an electron. Both atoms tend to be "satisfied" with this arrangement because they often times end up with noble gas electron configurations, i.e., fill electonic orbitals. The classic example of an ionic bond is NaCl, but CaF2, and MgO are also examples of molecules in which ionic bonding dominates.
In contrast to the ionic bond, in which electrons are directly donated or accepted by an atom, covalent bonding is characterized by the sharing of electrons. This means that a binding electron in a covalent diatomic molecule such as H2 has equal likelihood of being found around either hydrogen atom. Dissimilar atoms can also form covelently-bonded molecules. In water, the electrons on oxygen can be shared by two hydrogen atoms to create a stable, covalently-bound molecule.
This type of bond can be thought of as a cross between ionic and covalent bonds. Though there is significant sharing of the electrons, some charge distribution exists that results in a polar or "partial ionic character" to the bond. The percent ionic charcter of the bond can again be related to the electronegativities of the individual atoms:
The larger the electronegativity difference, the more ionic character the bond has. Of course, if the electronegativity difference is greater than about 2.0, we know that an ionic bond should result.
Metallic bonds occur when elements of low electronegativy (usually found in the lower left region of the periodic table) bond with each other to form a class of materials we call metals. Typical metals are Sodium, Copper and Aluminum. Metals tend to have common characteristics such as ductility, luster, and high thermal and electrical conductivity. All of these characteristics can to some degree be accounted for by the nature of the metallic bond. The model of a metallic bond, first proposed by Lorentz, consists of an assembly of positively-charged ion cores surrounded by free electrons or an "electron gas". We will see later on, when we discuss intermolecular forces and bonding, that the electron cloud does indeed have "structure" in the quantum mechanical sense, which accounts nicely for the observed electrical properties of these materials.
This is the weakest kind of secondary bonding. It occurs mostly between inert gases where fluctuating electric dipoles create momentary attractions between atoms. van der Waals forces exist between all atoms, but their contribution is so small in polar compounds as to be considered negligible.
Hydrogen bonding is so named because it involves the interaction of a hydrogen atom with another atom. The hydrogen atom is typically bound to a strongly electronegative atoms, such as Oxygen or Fluorine. As electrons are pulled toward the electronegative atoms, a net positive charge on the bound Hydrogen results. This positive portion of the molecule can interact with other negative portions of adjacent atoms, such as the electron-withdrawing groups of the very same compound. Although this type of bonding is of the same order of magnitude in strength as van der Waals bonding, it can have a profound influence on the properties of a material, such as boiling and melting points. Hydrogen bonding is responsible, in part, for the high density of water relative to the solid state (ice). Think about the density of most solids relative to their liquid state, and you will realize that is is highly unusual that ice is able to float atop water. Just image what would happen if lakes and ponds froze from the bottom up! What an enormous impact this would have on the ability of aquatic life to survive the winter.
Dipole-dipole interactions arise when the positive portion of a dipoloar molecule is attracted to the negative portion of another dipolar molecule. Hydrogen bonding is a specific type of dipole-dipole interaction, but the concept is the same. A dipolar molecule like ammonia, NH3, is able to dissolve other polar molecules, like water, due to dipole-dipole interactions. In the case of NaCl in water, the dipole-dipole interactions are so strong as to break the intermolecular forces within the molecular solid.
We will concentrate on the primary bond types because they correlate directly with physical properties. Be aware that the secondary forces exist, though. They play a larger role in liquids and gases.
We've discussed the different types of primary bonds, but how do these bonds form in the first place? What is it that causes a sodium ion and a chloride ion to form a compound, and what is it that prevents the nuclei from fusing togother to form one element? These questions all lead us to the topic of intermolecular forces and bond formation. We know that atoms approach each other only to a certain distance, and then, if they form a compound, will maintain some equilibrium distance known as the "bond length." Hence, we expect that there is some attractive force that brings them together, and some repulsive force that keeps the atoms a certain distance apart.
Also known as "chemical affinity", the attractive force between
atoms is what causes them to approach each other. This attraction is due
to the electrostatic force between the nucleus and electron clouds of the
separate atoms. It should make sense to you that the attractive energy (UA)is inversely proportional to the separation distance (r);
that is, the further the atoms are apart, the weaker the attraction:
Once the atoms begin to approach each other, they can only come so close together due
to impenetrability of matter. The result is a repulsive energy, which
we assign a positive value, again, by convention. The primary consituents
of this repulsive energy are nucleus/nucleus and electron/electron repulsions.
As with the attractive energy, the repulsive energy is inversely proportional to the separation distance; the closer the atoms are, the more they repel each other:
The total, or potential energy of the system is then the sum of the
attractive and repulsive components:
The result is the well-known "Potential Energy Well":
It is often times useful to know the forces involved, as well as the energy. How do we get a mathematical expression for the attractive and repulsive forces? Recall that energy (U) and force (F) are related:
This is not the same thing as the maximum attractive force, which we get by maximizing F:
The forces are equal when the potential energy is a minimum and the separation distance is at the bond length, r0. Differentiation of equation 9 and solving for r0 in terms of a, b, n and m gives:
Let's use sodium chloride as an example to see how we can get a bond energy for the formation and the force components of a compound using the potential energy approach. The potential energy is given by equation 9, but we must also take into account the energy required to form ions from sodium and chlorine atoms. So, our energy expression looks like this:
Let's look at each of the three energies individually.
The electrostatic potential energy, UA, is the energy released by bringing the ions to their equilibrium separation, r0, from infinity:
= permittivity = 8.854 x 10-12 C2/N2 m2
e = charge of electron = 1.6 x 10-19 C
Z = respective numbers of charge of positive and negative ions (Z1 = Z2 = 1)
Substituting:
The attractive energy is then obtained by integrating the force expression:
Note the similarity in form of this expression for the attractive energy with that described in equation 7. The exponent on r is one, as it should be for ions (m=1), and the other parameters can be grouped to form the constant, a.
so that the repulsive energy is given by:
Try to derive the energy expression from the force yourself. Click here to see the complete derivation.
Inserting UA and UR into the main expression gives:
Simplifying:
Inserting values as given above for r0 and constants, and using n=8 (why?):
When we have a lattice, or more than one bond of a certain type, we
have to account for interactions with adjacent atoms that result in an increased interionic spacing compared to an isolated atom. We do this with the
Madelung constant, M or . This parameter depends on the structure of the ionic crystal, the charge on the ions and the relative size of the ions. The Madelung constant fits directly into the energy expression:
For NaCl, M = 1.75 so UL = -811 KJ/mol. Click here to see typical values of the Madelung constant.
In general, the lattice energy increases (becomes more negative) with decreasing interionic distance for ions with the same charge. This increase in lattice energy translates directly into an increased melting point. For example, if we replace the chlorine in sodium chloride with other halogens, while retaining the cubic structure, the interionic spacing should change, as well as the melting point.We could also account for additional van der Waals interactions, but this effect is relatively small in lattices.
We can also us the potential energy diagram to show how orbitals form as atoms approach each other.
For atoms with p and d orbitals, diagrams become more complex but are essentially the same:
We can construct a molecular energy level diagram for the general case of molecule AB where B is more electronegative than A. The molecular orbitals in molecule AB where B is more electronegative than A look like this:
Molecular orbitals don't explain everything, however, and they become increasingly more difficult to draw with more than two atoms. We use hybridization to explain other effects, particularly in carbon compounds.
Hybridization gives us a simple model for determining the correct geometry in simple molecules. It also provides us with a rationalization for multiple bonds.
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