The electrical conductivity σ (= 1/ρ) of a material is not constant.
The factors which affect the value of conductivity σ of a material are: 1. Temperature 2. Alloying atoms 3. Mechanical stress 4. Age Hardening.
1. Effect of Temperature:
We know that the resistance of most of the conducting materials increases with temperature. The change in resistance of a material per ohm per degree change in temperature is known as temperature coefficient of resistance and is given by-
α = 1/R dR/dT
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Thus, the resistance of a conducting material changes with temperature according to the following expression-
Where, RT1 and RT2 are respectively the resistances of the material at temperature T1 and T2 and ΔT represent the difference of temperature i.e. ΔT = T2 – T1. The above expression implies that the resistance of material at any temperature T2 can be calculated if the resistance at T1 is known.
In accordance with above relation, the variation of resistivity ρ (= 1/σ) with temperature can be written as-
with the increase of temperature, the scattering of electrons increases and the mean free path decreases which in turn reduces the mobility of charge carriers and hence the resistivity of material increases (or electrical conductivity decreases).
2. Effect of Alloying Atoms:
Alloying is another factor which affects the resistivity of a material. By adding traces of some impurities to a metal, its resistivity increases. Alloys have higher resistivity than pure base metal e.g. pure copper has ρ = 1.7 × 10-8 Ωm while its alloy brass (60% Cu + 40% Zn) has ρ = 7 × 10-8 Ωm at room temperature. Alloying elements greatly increase the lattice imperfections that in turn increases the scattering of electrons and phonons and hence the resistivity of metal increases with alloying atoms.
The effect of impurity or alloying on resistivity may be determined by Nordien equation as-
ρA = ρm + Cρl
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where ρA, ρm and ρl are resistivities of alloy, base metal and alloying element. C is the concentration of alloying element in atomic percent. The above equation is applicable only for few binary solid solutions because it does not take into consideration the changes in the density of states with composition.
The increase in resistivity with alloying elements can be explained as:
(a) Atoms of different sizes cause a variation of lattice parameters which result into scattering of electrons.
(b) The valence difference between atoms of base metal and alloying metal introduces a local charge difference that increases the scattering.
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(c) Alloying element having different electron concentration than base element changes the position of Fermi energy and hence the resistivity of the material as per following relation-
3. Effect of Mechanical Stress:
Any mechanical process that increases the number of dislocations will result in an increase in the electrical resistivity. Although mechanical stressing increases the resistivity, annealing of the material restores the electrical resistivity by establishing the regularity in crystal structure.
4. Effect of Age Hardening:
The electrical resistivity of an alloy increases with age hardening. During this process crystal lattice undergoes distortion due to which electron mobility is decreased which in turn decreases the mean free path.