Frenkel & Schottky Point Defects — 2D Lattice View

Defect Type

Conditions

Temperature T 900 K

Formation energy E_f 1.20 eV

Relaxation speed 1.0×

Live State

n/N = exp(−E_f / k_BT)

Equilibrium n/N

0.0%

Defect count

0 / 400

k_BT

0.078 eV

E_f / k_BT

15.4

Drag the lattice to pan, scroll/pinch to zoom.

How it works

A crystal is never a perfect lattice at T > 0 — thermal agitation constantly creates and destroys point defects. The equilibrium number present at a given temperature is set purely by minimising free energy F = E − TS: making n defects costs energy nE_f but gains configurational entropy from the huge number of ways to arrange them among the N available sites, and balancing dF/dn = 0 gives an Arrhenius law. That combinatorial argument never uses the lattice's dimensionality, so the same law governs the 2D cross-section drawn here as it does the full 3D crystal.

Schottky vacancy:
  n/N = exp(−E_f / k_BT)

Frenkel pair (vacancy + interstitial):
  n_F = √(N·N_i) · exp(−E_f / 2k_BT)

k_B = 8.617×10⁻⁵ eV/K

Schottky — an atom leaves its lattice site entirely (migrates to the surface/grain boundary), leaving one empty site (red wire ring) per defect.
Frenkel — an atom is displaced into a nearby interstitial gap instead of leaving the crystal, so a vacancy (ring) and an interstitial atom (orange dot, off-lattice) always appear together. The extra freedom of "which interstitial site" halves the effective exponent, so at equal E_f Frenkel pairs are always more numerous than Schottky vacancies.
The lattice relaxes the live defect count toward whichever equilibrium value the sliders currently predict — exactly the kinetic process (vacancy diffusion driven by the same Boltzmann factor) that lets a real crystal re-equilibrate after a temperature change. The relaxation-speed slider only changes how fast it visibly catches up, not the target it is chasing.
The Arrhenius panel plots ln(n/N) against 1000/T for both defect types at the current E_f; the highlighted dot is where your sliders currently sit on that line.

This is why quenching a metal from high temperature "freezes in" excess vacancies, and why ionic crystals (which favour Frenkel/Schottky disorder depending on the ion size ratio) become significantly more conductive as they approach their melting point.

Lattice atom Vacancy Interstitial atom

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Arrhenius plot

Defect count history