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What are point defects?

Point defects are imperfections or irregularities that occur in the crystalline lattice of a solid, and that deviate the crystalline structure from its perfect state. They are said to have no (0) dimension because they are only points on the crystalline lattice; this point can be an atom, ion, molecule, clusters, etc.

Solids at a temperature of 0 K (absolute zero) exhibit perfect structures, since in theory their components are immobilized, frozen. However, as soon as the temperature rises, the atoms start to vibrate, which sooner or later ends up causing them to move out of their corresponding places.

Let’s see the image above as an example. In a perfect and orderly crystalline structure, all the bluish points should be aligned. However, some of the bluish spots may be absent, which is observed by the presence of an empty space or a vacancy.

If the formation of said vacancy is due to the displacement of a bluish point from its original place, we will have a Frenkel pair, one of the main types of point defects that exist. The mobilized bluish point is now in an interstitial position (colored green).

Point defects are essential to understanding other defects that project into other dimensions of the glass.

Intrinsic point defects

When defining a crystalline structure, it is always done from ideality. But in nature, defects are inevitable, no matter how small. Thus, solids have a natural predisposition to present specific defects in their structures, whose interaction and summation affect or modify their chemical and physical properties. So-called intrinsic point defects occur in “pure” materials.

This natural predisposition is due to thermodynamic and kinetic factors. The introduction of the defects increases the entropy of the solid, which in turn increases with temperature. Then, at a certain temperature, any solid will have a state with a minimum configuration of point defects.

As the temperature increases there will be even more defects, with the maximum possible quantity in the vicinity of the melting point. All of this makes sense considering that the higher the thermal vibrations, the greater the chances that the atoms will leave their respective lattice positions.

Extrinsic point defects

Unlike intrinsic point defects, extrinsic defects occur due to the incorporation of impurities. No solid in nature is 100% pure, so it will always manifest these types of defects, in addition to the intrinsic ones.

Depending on the characteristics of the dopant and the selected material, defects are deliberately incorporated into the solid, which affects its chemical and physical properties. Such is the case with semiconductor formulation, for example GaAs.

On the other hand, extrinsic point defects also refer to those that modify the composition of materials or solids. That is, they lose their stoichiometry to become non-stoichiometric solids.

Point defects in metals

In metals we have crystals that, in principle, lack electrical charges; that is, there are no cations or anions present, only neutral metal atoms. Then, the defects that may exist in the metals would not affect their neutrality, so no mechanism would take place to compensate for these defects.

Intrinsic point defects in crystals of a hypothetical metal. Source: Gabriel Bolívar.

In the image above we have a perfect crystal and two others with defects. Atoms can be located in interstitial positions, which messes up the positions of neighboring atoms and is known as a self-interstitial defect (bottom center). Meanwhile, some atoms are capable of leaving their respective sites in the crystal array to generate vacancies (right).

Therefore, in pure metals the existence of intrinsic vacancy and auto-interstitial defects is possible. The more vacancies there are, the density of the substance decreases; a fact that is consistent with the increase in the number of defects with temperature.

When, on the other hand, the metal is doped with atoms of another element, they cause substitutions or seek to locate themselves in the interstices. In such cases, the density of the metal increases to a maximum value, after which it begins to decline dramatically.

Point defects in crystalline structures

In crystalline structures, encompassing other solids in addition to the aforementioned metals, we have two main types of point defects: those of Frenkel, and those of Schottky. Both can occur in the same regions of a crystal, and it is also quite possible that they are present together with void defects or interstitial occupancies.

When we talk about salts, oxides, sulfates, etc., there will be cations and anions that define a crystal by their electrostatic interactions. Therefore, if we remove a cation, the negative charges of the anions will predominate, and the crystal will become negatively charged. This is impossible to happen because it would violate the principle of electroneutrality.

Thus, the defects in this type of crystals generate electrical charges, which through a mechanism must be equalized again. However, the Frenkel and Schottky defects do not produce this imbalance of electric charges.

Frenkel

Representation of the Frenkel point defect. Source: Gabriel Bolívar.

In the Frenkel-type point defect, in honor of Yakov Frenkel, a lattice point leaves its original position to end in a gap. That is, an atom, molecule or ion passes into an interstitial position leaving behind a vacancy.

See the example in the image above. On the left we have the perfect crystal made up of two ions: a green one, which usually represents the anion (larger), and a purple one, which is the cation (smaller).

When one of the purple cations leaves its position in the crystal array, it leaves behind a vacancy. Note on the left the direction in which the black arrow points, indicating that the cation is now located in a gap.

Because the Frenkel defect consists of cation (or anion) shifts, the crystal remains neutral. Likewise, the composition of the crystal remains constant, since the ions in the lattice are changing positions: they are not leaving it, nor are others joining it.

Schottky

Representation of the Schottky defect. Source: Gabriel Bolívar.

In the point defect of the Schottky type we have two simultaneous vacancies: one corresponding to the cation, and another corresponding to the anion. For example, now it is not a question of a cation jumping to an interstitial position, but rather that it “disappears” accompanied by an anion (right of the upper image).

Again, by creating two vacancies at the same time, one cationic (which will behave like an anion), and one anionic (which will behave like a cation), the composition of the crystal remains unchanged. This is the case as long as this type of defect is discussed, and not arbitrary vacancies caused by external or internal agents.

From all the aforementioned, it is concluded that the Frenkel and Shottky defects are intrinsic point defects of a stoichiometric type, since they do not alter the composition or stoichiometry of the solids.

Specific defects in ceramic materials

Ceramics are materials whose ionic character is highly oscillating. Some have a marked covalent character, as occurs with silica, SiO 2 , or with aluminum nitride, AlN.

Therefore, we must consider two other types of point defects that can occur as a product of the covalent character of ceramics: the antisite and the unsaturated bond.

Antisite

As its name suggests, it is the defect that occurs when two atoms change places, finding themselves in opposite positions to that of the original crystalline lattice. For example, in SiC it may happen that there are CC or Si-Si links where there should not be. This type of point defect is very common also in alloys:

Specific antisite defect in an Au-Cu alloy. Source: Gabriel Bolívar.

Note that the copper and gold atoms in the Au-Cu alloy are neutral. No matter how they move, the neutrality of the crystal is not disturbed. Therefore, the fact that two atoms change places in the crystal, as in the right of the image above, does not affect the neutrality of the alloy.

In ceramics that have more than one cation, as in spinels, two cations with the same valences can exchange places (for example Al 3+ and Cr 3+ ) without unbalanced electrical charges.

Unsaturated link

The unsaturated bond (dangling bond in English) interrupts the order in the crystals of covalent ceramics, since the atom that forms the bond is absent, leaving a pair of free electrons.

In ceramics, not only antisite and unsaturated bonding defects occur, but also all intrinsic and extrinsic defects, so it is difficult to analyze their real, not perfect structures.

Examples of point defects

Throughout the article some examples of materials and their specific defects have been mentioned. Next, and finally, other materials will be listed, accompanied by the type of defect that they usually present.

Silver halides

Silver halides, such as AgCl or AgBr, have Frenkel defects where the Ag + cation moves to interstitial positions.

Alkali halides

Alkali halides, such as NaCl, exhibit Schottky defects, whose anion gaps are filled with electrons when their crystals are heated in the presence of metallic sodium or potassium vapors.

Thorium dioxide

In ThO 2 the Th 4+ cation is more voluminous than the O 2- anion . Therefore, this oxide presents a Frenkel defect where it is the O 2 that moves to interstitial positions.

Palladium sponge

Palladium is capable of absorbing hydrogen, behaving like a sponge that retains it in the interstitial positions of its crystals.

Steels

In a similar way as between palladium and hydrogen, iron can incorporate carbon atoms in its interstices, which gives rise to the formation of steels.

Titanium alloys

The punctual substitutional defect, although it has not been explained like the other defects, is nothing more than the substitution of one atom for another, which breaks with the order established by the crystal.

Thus, for example, the atoms of a titanium crystal can be replaced by other (metallic) atoms to give rise to a family of titanium alloys.

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