Atomic Structure of Elements
Atoms, the building block of elements, consist of a nucleus surrounded by a cloud of orbiting electrons. The nucleus consists of positively charged protons and neutral neutrons, and so has a net positive charge that holds the negatively charged electrons, which revolve around it, in position by an electrostatic attraction.
The charges on the proton and electron are equal and opposite (1.602 × 10−19 coulombs) and the number of electrons and protons are equal and so the atom overall is electrically neutral. Protons and neutrons have approximately the same mass, 1.67 × 10−27 kg, whereas an electron has a mass of 9.11 × 10−31 kg, nearly 2000 times less.
These relative densities mean that the size of the nucleus is very small compared to the size of the atom. Although the nature of the electron cloud makes it difficult to define the size of atoms precisely, helium has the smallest atom, with a radius of about 0.03 nanometers, while caesium has one of the largest, with a radius of about 0.3 nanometres.
An element is characterised by:
- the atomic number, which is the number of protons in the nucleus, and hence is also the number of electrons in orbit;
- the mass number, which is sum of the number of protons and neutrons. For many of the lighter elements these numbers are similar and so the mass number is approximately twice the atomic number, though this relationship breaks down with increasing atomic number. In some elements the number of neutrons can vary, leading to isotopes; the atomic weight is the weighted average of the atomic masses of an element’s naturally occurring isotopes.
Another useful quantity when we come to consider compounds and chemical reactions is the mole, which is the amount of a substance that contains 6.023 × 1023 atoms of an element or molecules of a compound (Avogadro’s number).
This number has been chosen because it is the number of atoms that is contained in the atomic mass (or weight) expressed in grams. For example, carbon has an atomic weight of 12.011, and so 12.011 grams of carbon contain 6.023 × 1023 atoms.
The manner in which the orbits of the electrons are distributed around the nucleus controls the characteristics of the element and the way in which atoms bond with other atoms of the same element and with atoms from different elements.
For our purposes it will be sufficient to describe the structure of the so-called Bohr atom, which arose from developments in quantum mechanics in the early part of the 20th century. This overcame the problem of explaining why negatively charged electrons would not collapse into the positively charged nucleus by proposing that electrons revolve around the nucleus in one of a number of discrete orbitals or shells, each with a defined or quantised energy level.
Any electron moving between energy levels or orbitals would make a quantum jump with either emission or absorption of a discrete amount or quantum of energy.
Each electron is characterised by four quantum numbers:
- the principal quantum number (n = 1, 2, 3, 4 . . .), which is the quantum shell to which the electron belongs, also denoted by K, L, M, N . . . , corresponding to n = 1, 2, 3, 4 . . . ;
- the secondary quantum number (l = 0, 1, 2 . . . n − 1), which is the sub-shell to which the electron belongs, denoted by s, p, d, f, g, h for l = 1, 2, 3, 4, 5, 6, according to its shape;
- the third quantum number (ml ), which is the number of energy states within each sub-shell, the total number of which is 2l +1;
- the fourth quantum number (ms) which describes the electron’s direction of spin and is either +1/2 or −1/2.
The number of sub-shells that occur within each shell therefore increases with an increase in the principal quantum number (n), and the number of energy states within each sub-shell (ml ) increases with an increase in the secondary quantum number (l).
Table 1 shows how this leads to the maximum number electrons in each shell for the first four shells. Each electron has a unique set of quantum numbers and with increasing atomic number, and hence increasing number of electrons, the shells and sub-shells fill up progressively, starting with the lowest energy state.
Atomic Structure of Elements
The one electron of hydrogen is therefore in the only sub-shell in the K shell (denoted as 1s1 ), the two electrons of helium are both in this same shell (denoted as 1s2 ) and in lithium, which has three electrons, two are in the 1s1 shell and the third is in the 2s1 shell.
By convention, the configuration of lithium is written as 1s2 2s1 . The configuration of subsequent elements follows logically (for example, sodium with 11 electrons is 1s2 2s2 2p6 3s1 ). The structures of these elements are illustrated in Fig. 1.
An extremely important factor governing the properties of an element is the number of electrons in the outermost shell (known as the valence electrons), since it is these that are most readily available to form bonds with other atoms.
Groups of elements with similar properties are obtained with varying atomic number but with the same number of outer shell electrons. For example, the ‘alkali metals’ lithium, sodium, potassium, rubidium and caesium all have one electron in their outermost shell, and all are capable of forming strong alkalis.
A further factor relating to this is that when the outermost electron shell is completely filled the electron configuration is stable. This normally corresponds to the s and p states in the outermost shell being filled by a total of eight electrons; such octets are found in neon, argon, krypton, xenon etc., and these ‘noble gases’ form very few chemical compounds for this reason.
The exception to the octet rule for stability is helium; the outermost (K) shell only has room for its two electrons.
The listing of the elements in order of increasing atomic number and arranging them into groups of the same valence is the basis of the periodic table of the elements, which is an extremely convenient way of categorising the elements and predicting their likely properties and behaviour.
As we will see in the next section, the number of valence electrons strongly influences the nature of the interatomic bonds.
Ionic Bonding of Atoms
If an atom (A) with one electron in the outermost shell reacts with an atom (B) with seven electrons in the outermost shell, then both can attain the octet structure if atom A donates its valence electron to atom B.
However, the electrical neutrality of the atoms is disturbed and B, with an extra electron, becomes a negatively charged ion (an anion), whereas A becomes a positively charged ion (a cation). The two ions are then attracted to each other by the electrostatic force between them, and an ionic compound is formed. The number of bonds that can be formed with other atoms in this way is determined by the valency.
Sodium has one electron in its outer shell; it is able to give this up to form the cation whereas chlorine, which has seven electrons in its outer shell, can accept one to form the anion, thus sodium chloride has the chemical formula NaCl (Fig. 1.).
Oxygen, however, has six valence electrons and needs to ‘borrow’ or ‘share’ two; since sodium can only donate one electron, the chemical formula for sodium oxide is Na2O.
Magnesium has two valence electrons and so the chemical formula for magnesium chloride is MgCl2 and for magnesium oxide MgO.
Thus, the number of valence electrons determines the relative proportions of elements in compounds.
The strength of the ionic bond is proportional to eAeB/r where eA and eB are the charges on the ions and r is the interatomic separation.
The bond is strong, as shown by the high melting point of ionic compounds, and its strength increases, as might be expected, where two or more electrons are donated.
Thus the melting point of sodium chloride, NaCl, is 801°C; that of magnesium oxide, MgO, where two electrons are involved, is 2640°C; and that of zirconium carbide, ZrC, where four electrons are involved, is 3500°C.
Although ionic bonding involves the transfer of electrons between different atoms, the overall neutrality of the material is maintained.
The ionic bond is always non-directional; that is, when a crystal is built up of large numbers of ions, the electrostatic charges are arranged symmetrically around each ion, with the result that A ions surround themselves with B ions and vice versa, with a solid being formed.
The pattern adopted depends on the charges on, and the relative sizes of, the A and B ions, i.e. how many B ions can be comfortably accommodated around A ions whilst preserving the correct ratio of A to B ions.
Covalent Bonding of Atoms
An obvious limitation of the ionic bond is that it can only occur between atoms of different elements, and therefore it cannot be responsible for the bonding of any of the solid elements. Where both atoms are of the electron-acceptor type, i.e. with close to 8 outermost electrons, octet structures can be built up by the sharing of two or more valence electrons between the atoms, forming a covalent bond.
For example, two chlorine atoms, which each have seven valence electrons, can achieve the octet structure and hence bond together by contributing one electron each to share with the other (Fig. 2a). Oxygen has six valence electrons and needs to share two of these with a neighbour to form a bond (Fig. 2b).
In both cases a molecule with two atoms is formed (Cl2 and O2), which is the normal state of these two gaseous elements and a few others. There are no bonds between the molecules, which is why such elements are gases at normal temperature and pressure.
Covalent bonds are very strong and directional; they can lead to very strong two- and three-dimensional structures in elements where bonds can be formed by sharing electrons with more than one adjacent atom, i.e. which have four, five or six valence electrons.
Carbon and silicon, both of which have four valence electrons, are two important examples. A structure can be built up with each atom forming bonds with four adjacent atoms, thus achieving the required electron octet. In practice, the atoms arrange themselves with equal angles between all the bonds, which produces a tetrahedral structure (Fig. 3). Carbon atoms are arranged in this way in diamond, which is one of the hardest materials known and also has a very high melting point (3500°C).
Covalent bonds are also formed between atoms from different elements to give compounds. Methane (CH4) is a simple example; each hydrogen atom achieves a stable helium electron configuration by sharing one of the four atoms in carbon’s outer shell and the carbon atom achieves a stable octet figuration by sharing the electron in each of the four hydrogen atoms (Fig. 4).
It is also possible for carbon atoms to form long chains to which other atoms can bond along the length, as shown in Fig. 5. This is the basis of many polymers, which occur extensively in both natural and manufactured forms.
A large number of compounds have a mixture of covalent and ionic bonds, e.g. sulphates such as Na2SO4 in which the sulphur and oxygen are covalently bonded and form sulphate ions, which form an ionic bond with the sodium ions.
In both the ionic and covalent bonds the electrons are held fairly strongly and are not free to move far, which accounts for the low electrical conductivity of materials containing such bonds.
Metallic Bonding of Atoms
Metallic atoms possess few valence electrons and thus cannot form covalent bonds between each other; instead they obey what is termed the free-electron theory. In a metallic crystal the valence electrons are detached from their atoms and can move freely between the positive metallic ions (Fig. 6).
The positive ions are arranged regularly in a crystal lattice, and the electrostatic attraction between the positive ions and the free negative electrons provides the cohesive strength of the metal. The metallic bond may thus be regarded as a very special case of covalent bonding, in which the octet structure is satisfied by a generalised donation of the valence electrons to form a ‘cloud’ that permeates the whole crystal lattice, rather than by electron sharing between specific atoms (true covalent bonding) or by donation to another atom (ionic bonding).
Since the electrostatic attraction between ions and electrons is non-directional, i.e. the bonding is not localised between individual pairs or groups of atoms, metallic crystals can grow easily in three dimensions, and the ions can approach all neighbours equally to give maximum structural density.
The resulting structures are geometrically simple by comparison with the structures of ionic compounds, and it is this simplicity that accounts in part for the ductility (ability to deform non-reversibly) of the metallic elements.
Metallic bonding also explains the high thermal and electrical conductivity of metals. Since the valence electrons are not bound to any particular atom, they can move through the lattice under the application of an electric potential, causing a current flow, and can also, by a series of collisions with neighbouring electrons, transmit thermal energy rapidly through the lattice.
Optical properties can also be explained. For example, if a ray of light falls on a metal, the electrons (being free) can absorb the energy of the light beam, thus preventing it from passing through the crystal and rendering the metal opaque. The electrons that have absorbed the energy are excited to high energy levels and subsequently fall back to their original values with the emission of the light energy.
In other words, the light is reflected back from the surface of the metal, which when polished is highly reflective. The ability of metals to form alloys (of extreme importance to engineers) is also explained by the free-electron theory.
Since the electrons are not bound, when two metals are alloyed there is no question of electron exchange or sharing between atoms in ionic or covalent bonding, and hence the ordinary valence laws of combination do not apply.
The principal limitation then becomes one of atomic size, and providing there is no great size difference, two metals may be able to form a continuous series of alloys or solid solutions from 100% A to 100% B. The rules governing the composition of these solutions are discussed in next articles.
Van Der Waals Bonds and the Hydrogen Bond
Ionic, covalent and metallic bonds all occur because of the need for atoms to achieve a stable electron configuration; they are strong and are therefore sometimes known as primary bonds.
However, some form of bonding force between the resulting molecules must be present since, for example, gases will all liquefy and ultimately solidify at sufficiently low temperatures.
Such secondary bonds of forces are known as Wan der Waals bonds or Wan der Waals forces and are universal to all atoms and molecules; they are however sufficiently weak that their effect is often overwhelmed when primary bonds are present. They arise as follows.
Although in Fig. 1 of previous article, we represented the orbiting electrons in discrete shells, the true picture is that of a cloud, the density of the cloud at any point being related to the probability of finding an electron there. The electron charge is thus ‘spread’ around the atom, and, over a period of time, the charge may be thought of as symmetrically distributed within its particular cloud.
However, the electronic charge is moving, and this means that on a scale of nanoseconds the electrostatic field around the atom is continuously fluctuating, resulting in the formation of a dynamic electric dipole, i.e. the centres of positive charge and negative charge are no longer coincident.
When another atom is brought into proximity, the dipoles of the two atoms may interact cooperatively with one another (Fig. 7) and the result is a weak non-directional electrostatic bond. As well as this fluctuating dipole, many molecules have permanent dipoles as a result of bonding between different types of atom.
These can play a considerable part in the structure of polymers and organic compounds, where side-chains and radical groups of ions can lead to points of predominantly positive or negative charges. These will exert an electrostatic attraction on other oppositely charged groups.
The strongest and most important example of dipole interaction occurs in compounds between hydrogen and nitrogen, oxygen or fluorine. It occurs because of the small and simple structure of the hydrogen atom and is known as the hydrogen bond.
When, for example, hydrogen links covalently with oxygen to form water, the electron contributed by the hydrogen atom spends the greater part of its time between the two atoms. The bond acquires a definite dipole with the hydrogen becoming virtually a positively charged ion (Fig. 8a).
Since the hydrogen nucleus is not screened by any other electron shells, it can attract to itself other negative ends of dipoles, and the result is the hydrogen bond. It is considerably stronger (about 10 times) than other Van der Waals linkages, but is much weaker (by 10 to 20 times) than any of the primary bonds.
Figure 8b shows the resultant structure of water, where the hydrogen bond forms a secondary link between the water molecules, and acts as a bridge between two electronegative oxygen ions. Thus, this relatively insignificant bond is one of the most vital factors in the evolution and survival of life on Earth.
It is responsible for the abnormally high melting and boiling points of water and for its high specific heat, which provides an essential global temperature control. In the absence of the hydrogen bond, water would be gaseous at ambient temperatures, like ammonia and hydrogen sulphide, and we would not be here.
The hydrogen bond is also responsible for the unique property of water of expansion during freezing i.e. a density decrease. In solid ice, the combination of covalent and strongish hydrogen bonds result in a three-dimensional rigid but relatively open structure, but on melting this structure is partially destroyed and the water molecules become more closely packed, i.e. the density increases.
Energy and Entropy
The bonds that we have just described can occur between atoms in gases, liquids and solids and to a large extent are responsible for their many and varied properties.
Although we hope construction materials do not change state whilst in service, we are very much concerned with such changes during their manufacture, e.g. in the cooling of metals from the molten to the solid state.
Some knowledge of the processes and the rules governing them are therefore useful in understanding the structure and properties of the materials in their ‘ready-to use’ state. As engineers, although we conventionally express our findings in terms of force, deflection, stress, strain and so on, these are simply a convention. Fundamentally, we are really dealing with energy.
Any change, no matter how simple, involves an exchange of energy. The mere act of lifting a beam involves a change in the potential energy of the beam, a change in the strain energy held in the lifting cables and an input of mechanical energy from the lifting device, which is itself transforming electrical or other energy into kinetic energy.
The harnessing and control of energy are at the heart of all engineering. Thermodynamics teaches us about energy, and draws attention to the fact that every material possesses an internal energy associated with its structure. So we are discussing some of the thermodynamic principles that are of importance to understanding the behaviour patterns.
Stable and Metastable Equilibrium
We should recognise that all systems are always seeking to minimise their energy, i.e. to become more stable. However, although thermodynamically correct, some changes toward a more stable condition proceed so slowly that the system appears to be stable even though it is not. For example, a small ball sitting in a hollow at the top of a hill will remain there until it is lifted out and rolled down the hill. The ball is in a metastable state and requires a small input of energy to start it on its way down the main slope.
Figure 1 shows a ball sitting in a depression with a potential energy of P1. It will roll to a lower energy state P2, but only if it is first lifted to the top of the hump between the two hollows. Some energy has to be lent to the ball to do this, which the ball returns when it rolls down the hump to its new position. This borrowed energy is known as the activation energy for the process. Thereafter it possesses free energy as it rolls down to P2. However, it is losing potential energy all the time and eventually (say, at sea level) it will achieve a stable equilibrium.
However, note two things. At P1, P2, etc. it is apparently stable, but actually it is metastable, as there are other more stable states available to it, given the necessary activation energy. Where does the activation energy come from?
In materials science it is extracted mostly (but not exclusively) from heat. As things are heated to higher temperatures the atomic particles react more rapidly and can break out of their metastable state into one where they can now lose energy.
If whisky and water are placed in the same container, they mix spontaneously. The internal energy of the resulting solution is less than the sum of the two internal energies before they were mixed. There is no way that we can separate them except by distillation, i.e. by heating them up and collecting the vapours and separating these into alcohol and water. We must, in fact, put in energy to separate them.
But, since energy can be neither be created nor destroyed, the fact that we must use energy, and quite a lot of it, to restore the status quo must surely pose the question ‘Where does the energy come from initially?’
The answer is by no means simple but, as we shall see, every particle, whether of water or whisky, possesses kinetic energies of motion and of interaction. When a system such as a liquid is left to itself, its internal energy remains constant, but when it interacts with another system it will either lose or gain energy.
The transfer may involve work or heat or both and the first law of thermodynamics, ‘the conservation of energy and heat’, requires that:
dE = dQ – dW …….(1)
where E = internal energy, Q = heat and W = work done by the system on the surroundings.
What this tells us is that if we raise a cupful of water from 20°C to 30°C it does not matter how we do it. We can heat it, stir it with paddles or even put in a whole army of gnomes each equipped with a hot water bottle, but the internal energy at 30°C will always be above that at 20°C by exactly the same amount. Note that the first law says nothing about the sequences of changes that are necessary to bring about a change in internal energy.
Classical thermodynamics, as normally taught to engineers, regards entropy, S, as a capacity property of a system which increases in proportion to the heat absorbed (dQ) at a given temperature (T). Hence the well known relationship:
dS ≥ dQ/T …….(2)
which is a perfectly good definition but does not give any sort of picture of the meaning of entropy and how it is defined. To a materials scientist entropy has a real physical meaning, it is a measure of the state of disorder or chaos in the system.
Whisky and water combine; this simply says that, statistically, there are many ways that the atoms can get mixed up and only one possible way in which the whisky can stay on top of, or, depending on how you pour it, at the bottom of, the water.
Boltzmann showed that the entropy of a system could be represented by:
S = k lnN ……(3)
where N is the number of ways in which the particles can be distributed and k is a constant (Boltzmann’s constant k = 1.38 × 10−23 J/K).
The logarithmic relationship is important; if the molecules of water can adopt N1 configurations and those of whisky N2 the number of possible configurations open to the mixture is not N1 + N2 but N1 × N2.
It follows from this that the entropy of any closed system not in equilibrium will tend to a maximum since this represents the most probable array of configurations.
This is the second law of thermodynamics, for which you should be very grateful. As you read these words, you are keeping alive by breathing a randomly distributed mixture of oxygen and nitrogen.
Now it is statistically possible that at some instant all the oxygen atoms will collect in one corner of the room while you try to exist on pure nitrogen, but only statistically possible. There are so many other possible distributions involving a more random arrangement of the two gases that it is most likely that you will continue to breathe the normal random mixture.
It must be clear that the fundamental tendency for entropy to increase, that is, for systems to become more randomised, must stop somewhere and somehow, i.e. the system must reach equilibrium. If not, the entire universe would break down into chaos.
As we have seen in the previous article, the reason for the existence of liquids and solids is that their atoms and molecules are not totally indifferent to each other and, under certain conditions and with certain limitations, will associate or bond with each other in a non-random way. As we stated above, from the first law of thermodynamics the change in internal energy is given by:
dE = dQ – dW
From the second law of thermodynamics the entropy change in a reversible process is:
TdS = dQ ……(4)
Hence: dE = TdS – dW …….(5)
In discussing a system subject to change, it is convenient to use the concept of free energy. For irreversible changes, the change in free energy is always negative and is a measure of the driving force leading to equilibrium.
Since a spontaneous change must lead to a more probable state (or else it would not happen) it follows that, at equilibrium, energy is minimised while entropy is maximised.
The Helmholtz free energy is defined as:
H = E – TS ……(6)
and the Gibbs free energy as:
G = pV + E – TS ……(7)
and, at equilibrium, both must be a minimum.