conduction in solid, electrical Flow of free electrons under the influence of an electric field. Free electrons are not attached to any atom of the solid. They exist in the conduction band. Such solids are called conductors. The  Ohms law is the most fundamental, which gives the current, for voltage difference V across a conductor,

I  =  V/R  

where  R is the resistance of the conductor. This law is also written as

j = s E

where j is called the current density (current flowing normally / unit  area),  E the electric field and s the electrical conductivity  of  the conductor. For some materials (e.g. single crystals) s  depends  on the direction of the current, that is, it is a tensor. For polycrystalline material the above equation is valid.

The  quantity resistivity, r is more frequently used which is reciprocal  of conductivity. The  resistivity of a material is resistance  offered by a cube (1 m´ 1 m´ 1m) of the material, when  current  flows perpendicular to any two opposite faces. SI unit  of resistivity is ohm-metre ( W .m); unit of conductivity is sometime written as mho.m^-1.

The most remarkable feature of electrical resistivity is that it varies over  25  orders magnitude.  Table  CIII  lists  the electrical resistivity,  at  room  temperature,  of a number of industrially important materials.

                          Table - CIII. Resistivity of some materials

Conductivity of pure metals: The free electrons in a metal move continuously  in  a random  fashion.  When  external  field  is applied,  the  free  electrons  gain  kinetic energy,  along the direction  of  the field. Due to the collision with the positive ions, the  electrons  lose most of their kinetic energy, and the average  velocity  of  the electrons  alters  only slightly. The average  increase  in  its  velocity  component parallel  to the applied  field  direction  is  called  drift  velocity,  v_d. The average distance an electron travels between two consecutive collisions is called mean  free path,  l. The electron's acceleration due to field is proportional  to  its charge e, and inversely proportional to its mass m. The conductivity or resistivity of the material is given by,

r = s ^-1 =(m v_d)/(n_e e² l)

where n_c is the number of conduction electrons per m³.

The  vibration  of  ions in the material increases with the increasing  temperature.  This has  the  effect  of  increasing probability  of  electron ion collision or of decreasing the mean free   path.   Therefore   with   the  increase  of  temperature conductivity decreases.  Note  that  if temperature  is reduced to zero,  the  mean  free path tends to infinity. This implies that the  resistivity  should  tend  to zero as temperature approaches zero.  This  is  found  to  be  true  experimentally  (see super conductivity).

Alloying of a metal by adding another metal, results in the decrease of the mean free path of the electrons. It is because of the increase   of  number  of scattering centers  caused  by  local inhomogeneities  in the crystal structure.

The  collisions  of free electrons result in the production of  heat  in the conductor. The heat developed per m³ per second in  a  conductor  carrying  a current density, j as a result of an applied field E is given by

H = jE = s E²

j  is  in  A/m², E in V/m, and H in W/m³. If R is the resistance  of  the conductor,  and i is the current, heat developed per second is also given by,

H = i² R

(For electrical conduction in semiconductors see semiconductors)