Crystal defects are results of thermaldynamic equilibrium contributed also by the increase in entropy T S term of the Gibb's free energy:
On the other hand, some solid-like structure called flickering clusters also exist in a liquid. For example, the density of water is the highest at 277 K. The flickering clusters increase as temperature drops below 277 K, and the water density decreases as a result.
Solids are important for many technologies, and this link gives a well organized presentation.
Crystal defects occur as points, along lines, or in the form of a surface, and they are called point, line, or plane defects respectively.
Point defects are common in crystals with large anions such as AgBr, AgI, RbAgI4. Due to the defects, the ions have some freedom to move about in crystals, making them relatively good conductors. These are called ionic conductors, unlike metals in which electrons are responsible for electric conductivity.
Recently, ionic conductors have attracted a lot of attention because the fuel cell and battery technologies require conducting solids to separate the electrodes.
A dislocation is characterized by its Burgers vector: If you imagine going around the dislocation line, and exactly going back as many atoms in each direction as you have gone forward, you will not come back to the same atom where you have started. The Burgers vector points from start atom to the end atom of your journey (This "journey" is called Burgers circuit in dislocation theory).
In this electronmicroscope image of the surface of a crystal, you see point defects and a Burger journey around an edge dislocation. The dislocation line is in the crystal, and the image shows its ending at the surface. A Burger vector is approximately perpendicular to the dislocation line, and the missing line of atoms is somehwere within the block of the Buerger journey.
If the misalignment shifts a block of ions gradually downwards or upwards causing the formation of a screw like deformation, a screw dislocation is formed. The diagram here shows the idealized screw dislocation. This diagram is from the above link, which also shows an electromiscopic images of screw dislocations.
Line defects weakens the structure along a one-dimensional space, and the defects type and density affects the mechanical properties of the solids. Thus, formation and study of dislocations are particularly important for structural materials such as metals. This link gives some impressive images of dislocations. Chemical etching often reveal pits which are visible under small magnifications.
Actually, most of the required values have been listed in the table, but their evaluations illustrate the methods. These values are evaluated below:
rNi+rO = a / 2
X-ray density = 4*(58.69+16.00) / (6.023*1023*72.88*10-24)
= 6.806 g / cm3,
Compared to the observed density = 6.67 g / cm3.
The molar volumes (58.69+16.00) / density are thus
74.69 / 6.806 = 10.97 cm3; and 74.69 / 6.67 = 11.20 cm3
The vacancy rate = 6.806 - 6.67 / 6.806
= 0.02 (or 2%)
These methods are hints to assignments.
From the given conditions, we cannot calculate individual radii of Ni and O, but their sum is calculable.
Another surface defects are along the grain boundaries. A grain is a single crystal. If many seeds are formed when a sample starts to crystallize, each seed grow until they meet at the boundaries. Properties along these boundaries are different from the grains.
A third plane defects are the stacking faults. For example, in the close packing arrangement, the adjancent layers always have the AB relationship. In a ccp (fcc) close packing sequence, ...ABCABC..., one of the layer may suddenly be out of sequence, and become ..ABABCABC.... Similarly, in the hcp sequence, there is a possibility that one of the layer accidentally startes in the C location and resulting in the formation of a grain boundary.
The stacking fault of fullerene crystals have been studied by high resolution electron microscopy, and the images are shown in this link.
Perhaps the most demanding of purity is in the electronic industry. Silicon crystals of 99.999 (called 5 nines) or better are required for IC chips productions. These crystal are doped with nitrogen group elements of P and As or boron group elemnts B, Al etc to form n- aand p-type semiconductors. In these crystals, the impurity atom substitute atoms of the host crystals.
Presence minute foreign atoms with one electron more or less than the valence four silicon and germanium host atoms is the key of making n- aand p-type semiconductors. Having many simiconductors connected in a single chip makes the integrated circuit a very efficient information processor. The electronic properties change dramatically due to these impurities. This is further described in Inorganic Chemistry by Swaddle.
In other bulk materials, the presence of impurity usually leads to a lowering of melting point. For example, Hall and Heroult tried to electorlyze natural aluminum (aluminium) compounds. They discovered that using a 5% mixture of Al2O3 (melting point 273 K) in cryolite Na3AlF6 (melting point 1273 K) reduced the melting point to 1223 K, and that enabled the production of aluminum in bulk. Recent modifications lowered melting temperatures below 933 K.
Some types of glass are made by mixing silica (SiO2), alumina (Al2O3), calcium oxide (CaO), and sodium oxide (Na2O). They are softer, but due to lower melting points, they are cheaper to produce.
For example, a diamond with C vacancies (missing carbon atoms) absorbs light, and these centers give green color as shown here. Replacement of Al3+ for Si4+ in quartz give rise to the color of smoky quartz.
A high temperature phase of ZnOx, (x < 1), has electrons in place of the O2- vacancies. These electrons are color centers, often referred to as F-centers (from the German word farben meaning color). Similarly, heating of ZnS to 773 K causes a loss of sulfur, and these material fluoresces strongly in ultraviolet light.
Some non-stoichiometric solids are engineered to be n-type or p-type semiconductors. Nickel oxide NiO gain oxygen on heating in air, resulting in having Ni3+ sites acting as electron trap, a p-type semiconductor. On the other hand, ZnO lose oxygen on heating, and the excess Zn metal atoms in the sample are ready to give electrons. The solid is an n-type semiconductor.