Born ForcesBorn forces are one type of force that acts upon atoms in an ionic lattice. In simplest terms, because ions have some

finite size, electron-electron and nucleus-nucleus interactions occur and give rise to repulsion forces and electrostatic

potential, both called Born forces.

IntroductionLattice energy is the energy released when gaseous cations and anions bond to form a solid ionic compound. With

the Born-Lande equation one can calculate the lattice energy of a crystalline ionic compound. Born and Lande

theorized around the turn of the century, that lattice energy of a crystalline ionic compound could be found by

calculating terms of electrostatic potential and a repulsive potential.

Table 1: Born Forces Defined Mathematically

The first potential is the force of attraction.  It is a negative value because it pulls the two atoms closer together, and

the forming of a bond is energetically favorable. In English it reads, the negative value of Avogadro’s

number (6.022x1023) times a Madelung Constant (varies) times the absolute value of the charge of the cation times

the absolute value of the charge of the anion, times the charge of an electron (1.6022x10 -19 C) all over four times pi

times the emissivity of space times the ion radius. The second equation is the repulsive force.   It found by

multiplying Avogadro’s number (6.022x1023) by a repulsion coefficient, and dividing that by the ionic radius raised to

the power of a Born exponent (some number between 5 and 12).

Implications of Born ForcesAttractive forces are affected by the charge of the ions and their radii.  Ions with large charges (like Mg7+ or O2-) have

greater attractive potential than those with smaller charges (like Na1+ or F1-).  Smaller ions (like Li+ or Cl-) also have

greater electrostatic potential than larger ions (like I- or Cs+).  The Madelung constant is dependent on the crystal

structure type.  This value is found in tables online or in a text, but in general can be thought of as large with larger

cation-cation distances and anion-anion distances.  A structure with fluorite geometry has a relatively large A value,

whereas rock salt crystals have a much lower A value.  

Repulsive forces are mainly determined by the born exponent.  The Born exponent is dictated by the electronic

configuration of the noble gas in the row above it on the periodic table (a closed shell).