Physical Foundations of Materials Science

The development of new materials is considered a key technology on an international level. The capability of production, fabrication, and application of high performance materials is a prerequisite for novel, and internationally competitive products and processes and a crucial element for more efficient use of resources and for environmental protection.

When we buy a commercial product what we first note is its function and its appearence as, for example, the precious look of a noble metal, the engine of an automobile, the rope of a bridge, the wire of an electrical cable, the heat absorbing panes of a modern building, or the decorative ceramic and metallic parts of a modern bathroom. However, the usefulness of these items for their purpose and their life cycle will be determined by the properties of the material from which they were manufactured. Without any doubt we trust in the strength of the rope that suspends a large bridge, in the impact resistance of a ceramic hot plate in our kitchen or in the reliability of the little metallic buckets which provide the thrust of the turbine engine of an airplane at temperatures above 1000 °C. The properties of advanced materials are not so much affected by their overall chemical composition but rather by the specific arrangement of their constituents which we usually can not discriminate with our bare eye. The arrangement of the constituents of a material, i.e. the spatial distribution of elements, phases, orientations, and defects are subsumed under the term microstructure.

The structural elements of matter are the atoms, which consist of a nucleus and the atomic shell. The properties of solids are essentially determined by the electron shell structure. According to the Bohr model of an atom, the electrons occupy specific orbitals (Fig. 2.1) the configuration of which, i.e. number of electrons and their spatial arrangement, follows the laws of quantum mechanics. The most important electrons for the properties of a solid are the electrons in the outermost orbital, because they determine the interaction with other atoms. The dominant principle of atomic interaction is the tendency of an atom to have its outermost shell filled with eight electrons, i.e. the noble gas configuration. This simple principle is the foundation of chemical bonding. If an atom has already a complete outer shell with eight electrons, like the noble gases, then its tendency to interact with other atoms, i.e. for chemical bonding or even for solidification is very small. Helium has to be cooled to 0.1 K to make the interaction forces between the atoms sufficiently large compared to thermal vibrations to generate a solid. All elements which do not have a noble gas configuration have the tendency (since associated with an energy gain) to accept, to donate, or to share the outermost electrons, also referred to as valence electrons, when in contact with other atoms. From these principles we obtain the fundamental types of atomic bonding (Fig. 2.2):

Crystals are never free of defects. This is a fundamental consequence of equilibrium thermodynamics, as we will show in Section 3.2.2. Real crystals even have a defect structure far from thermodynamic equilibrium, due to the lack of mechanisms to establish thermodynamic equilibrium. We distinguish different kinds of crystal defects which are most easily classified according to their dimension; vacancies and interstitials (zero dimensional point defects), dislocations (one dimensional line defects), and grain and phase boundaries (two dimensional planar defects). Sometimes different phases are considered as three dimensional defects. However, these phases are constituents of the thermodynamic equilibrium and the real defect, the interface boundary, can be subsumed under the category of two dimensional defects.

Matter is known to occur in three different states as gas, liquid, or solid. Each element has a specific melting temperature T _m , which separates the solid and liquid temperature regimes and a boiling temperature T _b ,for the transition from liquid to gas. At T _m and T _b two states of matter are in thermodynamic equilibrium. Melting and boiling temperatures also depend on pressure p,although this dependency may be very mild as in metals.

Everybody is familiar with the experience that a drop of ink slowly dissolves in water or smoke spreads out in air. The reason for these phenomena is the motion of the molecules in a liquid or a gas. Although less obvious, atoms in a solid are also capable of leaving their lattice sites by thermal activation and to move through the crystal. This is referred to as solid state diffusion.

If a solid is exposed to external forces that try to change its shape, it remains coherent but resists by the generation of an internal stress (Fig. 6.1). For instance, if we pull on a solid it would separate into two parts, if it were cut through in the center. The forces that need to be exerted to keep the two parts in contact correspond to the internal forces in the loaded solid. Let us use a simple model in which we visualize the solid as being composed of hard spheres (atoms) that are connected by springs (interatomic potential, Fig. 6.2). External tensile forces imposed on the solid will stretch the springs until their reaction force, which is proportional to the elongation of the springs, balances the external forces. The state of the stressed springs represents the internal forces.

Many materials undergo a heat treatment during their processing that strongly impacts properties. During heat treatment subsequent to plastic deformation in particular the mechanical properties and the microstructure are strongly affected, while other physical properties (e.g. electrical resistivity) are scarcely influenced (Fig. 7.1).

In order to melt a metallic solid a certain amount of heat must be expended, the heat of melting. Different metals melt at different temperatures. This is related to the binding forces between the atoms. At the melting temperature, T _m , the thermal energy per mole (RT _m ) has to be of the same order of magnitude as the binding energy (heat of melting per mole, H _m ): H _m ≅RT _m (Richards rule).

The crystal structure of a metal is not necessarily stable at all temperatures below the melting temperature. This is due to the fact that the solid always assumes the crystal structure with the lowest Gibbs free energy, even if there are other crystal structures with a slightly higher free energy. This holds, in particular, for metals since the binding energy E ₀ of a metal depends relatively little on its atomic arrangement. For instance, the change of heat of fusion of sodium from the bcc to the hexagonal structure amounts to only E ₀/1000 (at 36 K). The major contributions to bonding are determined by the electronic structure, and small changes can cause an instability of the crystal structure, for instance by internal fields in ferromagnetic materials. The latter is the cause for the ferromagnetic bcc structure of iron (α-Fe) at low temperatures.

The properties of a solid mainly reflect the properties of the electronic structure of its atoms. The existence of a solid state as the stable low-temperature configuration of the atoms proves that there are attractive forces between the atoms. If two atoms are far apart, this attractive force is small and caused by the dipole moment of their electron structure. A dipole moment results from the fact that the centers of gravity of the positive charge (nucleus) and the negative charge (electrons) are never identical, because of fluctuations of the electron density distribution. A locally separated positive and negative charge forms an electrical dipole. The interaction among dipoles always is attractive and, therefore, causes atoms to approach each other (Fig. 10.1). The attractive force increases rapidly with decreasing distance between dipoles. If the atoms reach a distance where their outermost electrons interact, various outcomes can occur depending on the different types of chemical bonding as covered in Chapter 2. A further decrease of the atomic spacing causes the electron orbitals to overlap. According to the Pauli principle, two electrons cannot share the same energy state. Correspondingly, an overlap forces some electrons to change to “free” states, which are of higher energy. The corresponding rapid increase of electron energy results in a strong repulsive interatomic force. The sum of the attractive and repulsive forces constitutes the total interaction force between the atoms (Fig. 10.2). At the equilibrium spacing, repulsive and attractive forces balance, i.e., the sum of forces is zero. This simple concept of the formation of a two-atomic molecule can be generalized to a solid consisting of many atoms, where the same interactions determine the next neighbor arrangement, qualitatively.