# Solid

solid is a state of matter in which atoms or molecules are tightly bound together by powerful forces thereby creating a rigid body (with a defined geometric shape and volume). In other words, a solid is a material object that is in a condensed state characterized by resistance to deformation and changes in volume. The branch of physics that deals with solids is called solid-state physics, while solid-state chemistry focuses primarily on the nature and chemical and physicochemical properties of solids. The study of solid materials falls under Materials Science and Materials Technology. The study of the mechanical behavior of the solid body is the subject of solid mechanics.

The formation of a solid occurs with the establishment of bond forces between the atoms, of such intensity as to overcome the energy of thermal agitation. These bonding forces are five, of which three are strong (ionic, covalent, and metallic bond) and two weak (hydrogen bond and Van der Waals molecular forces). All these forces are attractive until the distance between the atoms is slightly less than the diameter of the atoms themselves, and they become violently repulsive for distances between the lower atoms; for this reason, the solids are difficult to compress.

## Categories and classification of solids

In most cases, the atoms bind themselves according to a crystal lattice or amorphously, without the possibility of moving in space, except for vibration motions (caused by thermal energy). Most of the substances existing in nature are found in the solid crystalline state. Solids that do not have a crystalline structure are called amorphous solids.

The differences between the types of solid derive from the differences between their bonds; consequently, we can classify the solids into two main categories:

• crystalline solids (ionic solid, molecular solid, covalent network solids, and metallic solid);
• amorphous solids (such as common glass) based on how the particles are arranged.

## Crystalline solids

Crystalline solids consist of atoms, ions and molecules arranged in a definite and repeating three-dimensional pattern in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions in a definite repeating pattern.

Unlike amorphous solids that melt at a range of temperatures, crystalline solids have definite melting points. Crystalline solids include metallic, ionic, network atomic and molecular solids, and true solids are crystalline.

### Characteristics of crystalline solids

The main characteristics of crystalline solids are mentioned as below:

• Crystalline solids show a regular structure and have a definite geometrical shape.
• The sharp freezing point is found in crystalline solids. This is because the distance between the same atoms/molecules or ions is the same and remains constant, unlikely from amorphous solids.
• The heat of fusion is definite and fixed as the regularity in crystal lattice remains the same and is ideal.
• Crystalline solids are also known as true solids as they don’t tend to flow like pseudo-solids.
• When we cut a crystal solid with a knife, we obtain a flat and smooth surface.
• The nature of crystalline solid is anisotropic; that is, the properties turn out to be different in a different direction.
• Crystalline solids depict both long-range and short-range order.

A single macroscopic crystal is usually identifiable by their geometrical shape, consisting of flat faces with specific, particular orientations.

The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification.

### Determination of the dynamic behavior of free electrons in the crystal lattice

Quantitatively, the dynamical behavior of free electrons in the crystal lattice is determined by a wave function satisfying the Schrödinger equation which, given the characteristics of the potential created by the lattice atoms, is very complex (W. Pauli, 1927; A. Sommerfeld, 1928; F. Bloch, 1928). Therefore, simplified models of the potential are generally introduced.

If a crystal lattice is considered one-dimensional, the solution of Schrödinger’s equation shows that electrons can have only energies of value within well-defined intervals, called allowed bands, separated by forbidden energy bands, called precisely forbidden bands. In a representation in which the electron energy is expressed as a function of the wave number, that is the inverse of the wavelength associated with the electron, these bands are called Brillouin zones.

Similar results are obtained for a three-dimensional crystal lattice if you consider the wave number as a vector quantity. Within each band, electrons can only take on a certain number of discrete energy values, each of which constitutes an energy level. Given a band with N levels, this, for the Pauli exclusion principle, can contain 2N electrons.

In complete bands, i.e. containing 2N electrons, the average velocity of these electrons is zero and therefore they do not contribute to the current circulating in the body; in bands occupied only partially the absence of an electron is equivalent to the presence of an identical charge, but of opposite sign, i.e. positive, called hole.

The distribution of electrons in a band is regulated by Fermi-Dirac statistic and in it is fundamental the Fermi level, which corresponds to the maximum value of energy that can be reached by electrons at a temperature of 0 K.

### Electron distribution in a band according to fermi-dirac statistics

When the Fermi level corresponds to a permitted band, this band is only partially occupied and therefore, by applying a potential difference, an electric current is produced and the solid is a conductor. In insulators, instead, the Fermi level is a forbidden band.

At 0 K the allowed bands below this level are completely occupied and the upper ones are completely empty; therefore, in no case, electric current is produced. At temperatures other than 0 K, due to thermal agitation, some electrons may jump into a permitted band, but the energy required is high and the probability of such a jump occurring is low; therefore, in each case, the corresponding electric current is very weak.

When the forbidden band containing the Fermi level is very narrow this probability is greater and the corresponding current can appreciate. The types of solids that fall into this pattern are called intrinsic semiconductors.

## Ionic solids

The crystal lattice of ionic solids consists of monoatomic or polyatomic ions held together by intense electrostatic interactions of the Coulomb type. These, by their nature, are not directional and therefore the ions of opposite charge are attracted independently of their spatial location: therefore, no single molecular units are recognizable.

In ionic solids, cations and anions are located on the nodes of the crystal lattice; these ions are joined together by intense Coulombian-type forces, therefore, the lattice energy of these crystals is very high and so is their melting point. All halides of alkali metals, zinc sulfide, calcium fluoride, lithium, calcium, titanium oxides, etc. form ionic solids.

Because of the strong attraction between opposite charges, it takes a lot of energy to overcome ionic bonds (the attractions between full charges are much larger than those between the partial charges in polar molecular compounds). This means that ionic compounds have very high melting points, often between 300÷1000 °C. The common characteristics of these substances are:

• high melting and boiling point: due to the strong electrostatic attractions between the ions of opposite sign, high energy is needed to separate them. The difference in behavior between the various ionic solids depends on the number of charges present in the ion. In fact, magnesium oxide has a higher melting point and boiling point than sodium chloride (the Mg2+ and O2- ions having charge +2 and -2 respectively, attract each other more than the ions Na+ and Cl which have charge +1 and -1 respectively). Another factor influencing the melting and boiling temperature is given by the size of the ions: if the ions are very small they will be closer and the electrostatic attraction is greater. For example, rubidium iodide has lower melting and boiling temperatures than sodium chloride since both the Rb+ ion and the I ion have significantly larger dimensions than Na+ and Cl therefore the attractions between rubidium ion and iodide ion are low and less energy is required to separate them.
• hardness and at the same time fragility given their easy flaking (they shatter rather than bend),
• solubility in polar solvents: many ionic solids are insoluble in almost all apolar or low-polar solvents due to the high reticular energy. When the energy released by the solvation of the ions exceeds the lattice energy these compounds can be soluble: this usually occurs in water. Most of the ionic solids are soluble in water and the positive ions are attracted by the solitary electronic doublet present on the oxygen with the formation of a dative bond. Furthermore, water molecules can form hydrogen bonds with negative ions. Many simple compounds formed by the reaction of a metallic element with a nonmetallic element are ionic;
• furthermore, since there are no free electrical charges, their conductivity is low; however, they do conduct when molten or dissolved because undergo electrolysis and their ions are free to move (the positive ion migrates towards the negative electrode while the negative ion migrates towards the positive electrode).

Ionic conduction (denoted by λ-lambda) is the movement of an ion from one site to another through defects in the crystal lattice of a solid or aqueous solution.

The ionic solids have a more complex structure than that of metals as they are made up of ions that have different ionic rays and also if on the one hand there is an attraction between ions of opposite charge on the other there is a repulsion between ions having the same charge. Furthermore, polyatomic ions such as, for example, the nitrate ion and the carbonate ion, cannot be assimilated to spheres.

## Molecular solids

Molecular solids are composed of discrete molecules. The cohesive forces that bind the molecules together are van der Waals forces, dipole-dipole interactions, quadrupole interactions, π-π interactions, hydrogen bonding, halogen bonding, London dispersion forces, and in some molecular solids, coulombic interactions.

The strengths of the attractive forces between the units present in different crystals vary widely, as indicated by the melting points of the crystals. Small symmetrical molecules (nonpolar molecules), such as H2, N2, O2, and F2, have weak attractive forces and form molecular solids with very low melting points (below -200 °C). Substances consisting of larger, nonpolar molecules have larger attractive forces and melt at higher temperatures. Molecular solids composed of molecules with permanent dipole moments (polar molecules) melt at still higher temperatures.

Most molecular solids are nonpolar. These nonpolar molecular solids will not dissolve in water but will dissolve in a nonpolar solvent, such as benzene and octane. Polar molecular solids, such as sugar and salt, dissolve easily in water. Molecular solids are nonconductive.

## Covalent network solids

Covalent network solids there are no individual molecules, the atoms in the crystal lattice are all directly linked by covalent bonds, so that in the crystal no single molecules can be identified (the crystal can be seen as a single macromolecule); are included crystals of diamond, silicon, some other nonmetals, and some covalent compounds such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds to all the surrounding atoms in a continuous network, resulting in huge crystals.

To break or to melt a covalent network solid, covalent bonds must be broken. Because covalent bonds are relatively strong, covalent network solids are typically characterized by hardness, strength, and high melting points. They do not dissolve in water, nor do they conduct electricity.

## Metallic solids

Metallic solids (consisting of a metallic bond) are formed exclusively by electropositive atoms (for example sodium, copper, aluminum), tending to give up their electrons which, however, having no electronegative atoms to join with, remain free.

The set of properties of metals suggests a structure in which the crystalline solid is made up of metal cations, obtained by the release of electrons from the valence shell — oscillating around the nodes of the crystal lattice, while the released electrons move in the entire lattice behaving as a kind of “electronic gas” (that permeates the entire crystal and is responsible for the stability of the crystal structure).

The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. In a metallic bond, the valence electrons are not donated or shared as they are in ionic and covalent bonding. Rather, the electron clouds of adjacent atoms overlap so that electrons become delocalized. The electrons move with relative freedom from one atom to another throughout the crystal. This electron mobility means that metals are highly conductive of heat and electricity.

Metallic solids are opaque, lustrous solids that are both malleable and ductile. Malleable means they are soft and can be shaped or pressed into thin sheets, while ductile means they can be pulled into wires.

Metals tend to have high melting points, though notable exceptions are mercury.

## Amorphous solids

In amorphous solids (literally “solids without form” or non-crystalline solids) the particles do not have a repeating lattice pattern. They are also called “pseudo solids.” Amorphous materials have an internal structure made of interconnected structural blocks. These blocks can be similar to the basic structural units found in the corresponding crystalline phase of the same compound.

The amorphous solids are formed due to particular conditions during the solidification process (for example by increasing the cooling speed), which do not allow the atoms to stabilize thermodynamically in an ordered condition, thus preventing the formation of a periodic crystal structure. Amorphous solids are isotropic.

Examples of amorphous solids include glass, rubber, gels, and most plastics. An amorphous solid does not have a definite melting point; instead, it melts gradually over a range of temperatures, because the bonds do not break all at once. This means an amorphous solid will melt into a soft, malleable state (think candle wax or molten glass) before turning completely into a liquid.

Amorphous solids have no characteristic symmetry, so they do not have regular planes of cleavage when cut; the edges may be curved. They are called isotropic because properties such as refractive index, conductivity and tensile strength are equal regardless of the direction in which a force is applied.

### Characteristics of amorphous solids

An amorphous solid depicts the following properties, which are as follows:

• The constituent particles of matter inside a solid are arranged randomly, that is, the position of atoms and molecules is not fixed and varies from one solid to another.
• Amorphous Solids don’t have definite shape or geometry due to the random arrangement of atoms and molecules inside the solid lattice.
• Short-range order (arrangement of atoms) is found in amorphous solids; due to the absence of long-range order, the amorphous solids present X-ray diffraction without peaks. Compared to liquids, the amorphous state has closer atoms and a lower free volume.
• Amorphous solids are also called pseudo-solids or supercooled Liquids because they don’t form crystalline structure and can flow.
• The nature of amorphous solids is isotropic in nature that is, the properties measured in all directions come out to be the same (in other words their physical properties do not depend on the direction in which the sample is analyzed), for example, the refractive index of amorphous solids is the same.
• Amorphous solids don’t show a sharp melting point, this is because of the irregular packing of amorphous solids (in other words the melting of an amorphous solid does not occur at a constant temperature since the bonds present in the solid do not all break at the same temperature).
• When we cut an amorphous solid, we find the broken constituent particles to be irregular in shape and geometry.
• Amorphous solids are unsymmetrical in nature, due to the irregular packing of atoms and molecules inside the solid lattice.
• Amorphous solids don’t have fixed heat of fusion because of the absence of a sharp melting point.
• The Amorphous solid-state has a metastable structure that can be transformed into crystalline structures only under certain thermodynamic and kinetic conditions.
• As the temperature increases, the viscosity of the amorphous solids decreases exponentially.
• They can exist in two distinct phases: the gummy one and the glassy one.

## Physical properties of solids

### Mechanical

Mechanical properties of solids include:

• elasticity;
• plasticity;
• viscoelasticity;
• tensile strength;
• compression strength;
• shear strength;
• fracture toughness;
• ductility (low in brittle materials);
• indentation hardness.

### Thermal

Thermal properties of solids include thermal conductivity, which is the property of a material that indicates its ability to conduct heat. Solids also have a specific heat capacity, which is the capacity of a material to store energy in the form of heat (or thermal lattice vibrations).

Thermal volume expansion of solids. When a certain amount of heat is administered to a solid, this effect affects a volume expansion (i.e., three-dimensional), due to the thermal effect of the temperature increase. Vice versa, if heat is removed, the solid will shrink due to the decrease in temperature.

The expansion is not always uniform in all dimensions, but some may be more evident than others depending on the geometric shape of the solid. For example, a beam will undergo a more evident longitudinal expansion (along with its prevailing dimension: i.e., the length) rather than transversely (i.e., in thickness).

The physical law that regulates this thermal expansion is the following:

$V = V_0(1 + \alpha\Delta T)$

where: V is the final volume, V0 is the initial volume, α is the coefficient of volume expansion of the body, ΔT is the temperature variation during the expansion process.

### Electrical

Electrical properties of solids include:

• conductivity;
• resistance;
• impedance;
• capacitance;
• piezoelectricity (electro-mechanical).

Electrical conductors such as metals and alloys are contrasted with electrical insulators such as glasses and ceramics. Semiconductors behave somewhere in between. Whereas electrons cause conductivity in metals, both electrons and holes contribute to the current in semiconductors. Alternatively, ions support electric current in ionic conductors.

### Optical

Solid materials can transmit or reflect visible light (many materials can transmit some wavelengths while blocking others). This property is used for frequency-selective optical filters, which can alter the color of the incident light.

## Insights

• Solid state physics
• Solid state chemistry