Frenkel pairs

A Frenkel pair is a type of point defect observed in crystalline materials. In this defect, an atom or ion departs from its regular lattice site and occupies an interstitial position within the crystal; the original site left behind becomes a vacancy. As a result, a vacancy and an interstitial atom form a paired entity that balances each other, known as a “Frenkel pair” (Figure 1). The Frenkel defect is a stoichiometric defect, meaning it does not alter the overall composition or electrical neutrality of the material; it only creates a local disorder in atomic positions. Frenkel defects are more common in ions of small size, such as cations in ionic crystals, because they can more easily move within the lattice and occupy interstitial sites.

History

The concept of Frenkel pairs was first proposed in 1926 by Russian physicist Yakov Frenkel. Frenkel suggested that atoms in crystals could be displaced from their lattice positions (atomic disorder) to explain phenomena such as ionic conductivity and diffusion. This work laid the foundation for the theory of point defects in solid-state physics and later inspired scientists like Schottky in the 1930s to identify other types of defects. In honor of Frenkel, this type of point defect is named the Frenkel defect or Frenkel pair.

Figure 1: Comparative illustration of a perfect crystal structure and the Frenkel defect (Figure: Sude Altınçekiç)

Effect on Crystal Structure

The formation of a Frenkel pair induces local strains and distortions in the crystal lattice. The atom occupying the interstitial site pushes against neighboring atoms, causing local expansion and stress in the lattice, while the vacant site may lead to a slight contraction or tensile effect in its vicinity (Figure 2). In particular, in closely packed crystal structures, the strain and volume increase caused by the interstitial atom often dominate over the volume reduction from the vacancy, resulting in a net decrease in material density. Thus, the accumulation of numerous Frenkel defects can lead to an overall increase in crystal volume (swelling) and a corresponding reduction in density. Moreover, these point defects can diffuse through the lattice and cluster together. Such microstructural changes directly affect lattice parameters and dimensional stability.

Figure 2: Stressed region in the lattice due to a Frenkel defect (Figure: Sude Altınçekiç)

Effect on Mechanical Properties

Frenkel pairs can significantly influence the mechanical behavior of materials. In materials with a high concentration of Frenkel defects, clusters of these defects act as obstacles that impede the motion of dislocations, behaving similarly to pinning points. As a result, the material exhibits hardening (precipitation hardening): its yield strength and hardness increase, but its ductility decreases. In other words, the accumulation of Frenkel defects makes the material more resistant to high stresses while reducing its ability to undergo plastic deformation, leading to embrittlement. This occurs because the movement of dislocations — line defects responsible for plastic deformation — is restricted by these clusters of point defects. When dislocations cannot move freely, the material behaves elastically up to the yield stress, and beyond this point, the tendency for cracking or fracture increases. In metallic materials exposed to radiation such as neutron bombardment, where large numbers of Frenkel pairs are generated, radiation hardening and embrittlement are widespread problems.

Examples

Frenkel defects have been observed in both ionic crystals and metallic systems. In some ionic solids, thermally generated Frenkel defects play a significant role, particularly when ion radii and coordination numbers are favorable. For instance, compounds such as zinc sulfide (ZnS) and silver(I) chloride (AgCl) exhibit Frenkel-type defects due to the relatively small size of their cations (Figure 3). These defects can alter the electrical conductivity or optical properties of these materials, such as by creating color centers.

Figure 3: Frenkel defect in the AgCl structure (Figure: Sude Altınçekiç)

In metallic materials and pure elemental crystals, Frenkel pairs do not form spontaneously in significant numbers under equilibrium conditions because their formation energy is typically high. Instead, Frenkel defects in metals are primarily induced by high-energy radiation. For example, zirconium alloys or stainless steels in nuclear reactors accumulate large numbers of Frenkel pairs under neutron bombardment. This leads to undesirable changes such as swelling, hardening, and embrittlement. Consequently, the formation and effects of Frenkel defects are a critical research and design consideration for materials used in radiation environments.