Residual-resistivity ratio (also known as Residual-resistance ratio or just RRR) is usually defined as the ratio of the
resistivity of a material at room temperature and at
0 K. Of course, 0 K can never be reached in practice so some estimation is usually made. Since the RRR can vary quite strongly for a single material depending on the amount of impurities and other
crystallographic defects
A crystallographic defect is an interruption of the regular patterns of arrangement of atoms or molecules in crystalline solids. The positions and orientations of particles, which are repeating at fixed distances determined by the unit cell param ...
, it serves as a rough index of the purity and overall quality of a sample. Since resistivity usually increases as defect prevalence increases, a large RRR is associated with a pure sample. RRR is also important for characterizing certain unusual low temperature states such as the
Kondo effect
In physics, the Kondo effect describes the scattering of conduction electrons in a metal due to magnetic impurities, resulting in a characteristic change i.e. a minimum in electrical resistivity with temperature.
The cause of the effect was fir ...
and
superconductivity
Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
. Note that since it is a unitless ratio there is no difference between a residual resistivity and residual-resistance ratio.
Background
Usually at "warm" temperatures the resistivity of a
metal varies linearly with temperature. That is, a plot of the resistivity as a
function of temperature is a straight line. If this straight line were extrapolated all the way down to absolute zero, a theoretical RRR could be calculated
:
In the simplest case of a good metal that is free of scattering mechanisms one would expect ρ
(0K) = 0, which would cause RRR to diverge. However, usually this is not the case because defects such as
grain boundaries, impurities, etc. act as scattering sources that contribute a temperature independent ρ
0 value. This shifts the intercept of the curve to a higher number, giving a smaller RRR.
In practice the resistivity of a given sample is measured down to as cold as possible, which on typical laboratory instruments is in the range of 2 K, though much lower is possible. By this point the linear resistive behavior is usually no longer applicable and by the low temperature ρ is taken as a good approximation to 0 K.
Special Cases
* For
superconducting materials, RRR is calculated differently because ρ is always exactly 0 below the critical temperature, ''T''
c, which may be significantly above 0 K. In this case the RRR is calculated using the ρ from just above the superconducting transition temperature instead of at 0 K. For example, superconducting
Niobium–titanium
Niobium–titanium (Nb-Ti) is an alloy of niobium and titanium, used industrially as a type II superconductor wire for superconducting magnets, normally as Nb-Ti fibres in an aluminium or copper matrix.
Its critical temperature is about 10 kelvin ...
wires have a RRR defined as
.
*In the
Kondo effect
In physics, the Kondo effect describes the scattering of conduction electrons in a metal due to magnetic impurities, resulting in a characteristic change i.e. a minimum in electrical resistivity with temperature.
The cause of the effect was fir ...
the resistivity begins to increase again with cooling at very low temperatures, and the value of RRR is useful for characterizing this state.
Examples
* The RRR of
copper wire is generally ~ 40–50 when used for
telephone lines, etc.
References
Bibliography
*Ashcroft, Neil W.; Mermin, N. David (1976). Solid State Physics. Holt, Rinehart and Winston. .
Electrical resistance and conductance
Cryogenics
Superconductivity
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