Ion Transport

Ion transport is measured in terms of the ionic diffusion coefficients. In general, the diffusion in solids is much slower than in liquids and gases, but there are important exceptions, when certain compounds can have very high ionic diffusion coefficients. This has a large effect on the conductivity of those compounds.

Diffusion is an activated process, governed by an Arrhenius expression,

D = D0e-Ea/RT

and anything which serves to decrease the height of the activation barrier, Ea, will increase the diffusion coefficient.

Defects allow increased motion of ions in a crystal. When defects are introduced, they can change the mechanism by which ionic motion may occur, and so lower the barriers towards that motion and increase the magnitude of diffusion.

The defects allow different types of motion, such as cation migration, anion migration, and also vacancy migration.

Mechanisms of ionic motion involving defects
Vacancy Mechanism Interstitial Mechanism

In the vacancy mechanism, an ion jumps from its normal position on the lattice to a neighboring, vacant, lattice site (it is called the vacancy mechanism as it can also be seen as the hop of the vacancy from site to site, in a rightwards direction as shown in the diagram). This mechanism is aided by the presence of Schottky defects, which introduce vacancies.

In the interstitial mechanism, the motion involves the jump of an ion from an interstitial lattice point to a neighboring interstitial site. This mechanism is aided by the presence of Frenkel defects which introduce ions into interstitial sites.

In these descriptions of the motion, an ion or vacancy is described as jumping from one site to an adjacent site, so the motion is only over a short length scale. Diffusion over larger length scales proceeds via a series of such jumps. Whilst there may be more complicated cooperative diffusion mechanisms, involving the motion of many ions simultaneously, many diffusive mechanisms are understood well in terms of this simple jumping model, or hopping model.

Fast Ion Conductors

As the diffusion coefficient increases due to the motion of defects, so too does the electrical conductivity of the solid (the conductivity is proportional to the diffusivity).

Typical electrical conductivity values
Material Conductivity (Sm-1)
Ionic Conductors Ionic crystals <10-16 – 10-2
Solid Electrolytes 10-1 – 103
Strong (liquid) electrolytes 10-1 – 103
Electronic Conductors Metals 103 – 107
Semiconductors 10-3 – 104
Insulators <10-10

In general there is a gradual increase in the diffusion coefficient with temperature, following the Arrhenius law, and so a gradual increase in conduction, until the material melts and there is a jump in diffusivity and conductivity.

However, some compounds exhibit a discontinuous variation of the diffusivity with temperature, and also display much higher values for the diffusion coefficients. These compound are known as fast ion conductors, and a good example is silver iodide, AgI.

Silver Iodide

Below 146 oC there are two phases of AgI, both based on a close packed array of iodide anions with silver ions in half the tetrahedral holes (γ-AgI has the zinc blende structure and β-AgI has a wurtzite structure).

Above 146 oC, a new structure, α-AgI, is adopted with the iodide ions in a body centered cubic lattice, and here the conductivity is 131 Sm-1, a very high value, and 104 times the conductivity in β-AgI or γ-AgI.

The reason for this dramatic change in conductivity is due to the change in structure. In the open body centered cubic lattice, there are many sites available for the silver ion to occupy, most of them interstitial sites of a range of geometries. In the unit cell there are two Ag+ ions, but there are 12 tetrahedral interstitial sites, and structure determinations show that the Ag+ ions are distributed over all of these sites.

The motion of the Ag+ ions in the α-AgI phase is therefore very easy by a interstitial migration mechanism: there are very many vacant sites for each Ag+ ion, and furthermore the open structure means that there is a low barrier towards migration between these sites. The rapid motion of Ag+ ions through the network of tetrahedral vacancies leads to the idea of a molten sublattice of Ag+ ions,

ie. the huge increase in conductivity is due to the fact that the cation sublattice melts, but the structure retains its integrity because the anion sublattice remains solid, and so we get a solid phase with high conductivity.

Silver Iodide is particularly suitable for this kind of behaviour because it satisfies a range of conditions, all of which contribute to the hopping pathways being plentiful and low in energy:

The charge on the ions is low (the mobile Ag+ ions are monovalent)

The coordination number of the ions is low, so that the hops involve pathways where there is little change in coordination, and hence a low activation barrier

The anion sublattice is polarizable, and so it can distort to stabilize the cations in high energy positions, also meaning that there is a low activation barrier

There is a large number of vacant sites available for the cation motion.