Residual-resistivity ratio (also known as Residual-resistance ratio or just RRR) is usually defined as the ratio of the
resistivity
Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity i ...
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, 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 and
superconductivity
Superconductivity is a set of physical properties observed in superconductors: materials where Electrical resistance and conductance, electrical resistance vanishes and Magnetic field, magnetic fields are expelled from the material. Unlike an ord ...
. 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
A metal () is a material that, when polished or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, electricity and thermal conductivity, heat relatively well. These properties are all associated wit ...
varies linearly with temperature. That is, a plot of the resistivity as a
function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-orie ...
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
In materials science, a grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are two-dimensional crystallographic defect, defects in the crystal structure, and tend to decrease the ...
, 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
Superconductivity is a set of physical properties observed in superconductors: materials where electrical resistance vanishes and magnetic fields are expelled from the material. Unlike an ordinary metallic conductor, whose resistance decreases g ...
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 a ductile 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 1 ...
wires have an RRR defined as
.
*In the
Kondo effect 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
Copper is a chemical element; it has symbol Cu (from Latin ) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pinkish-orang ...
wire
file:Sample cross-section of high tension power (pylon) line.jpg, Overhead power cabling. The conductor consists of seven strands of steel (centre, high tensile strength), surrounded by four outer layers of aluminium (high conductivity). Sample d ...
is generally ~ 40–50 when used for
telephone line
A telephone line or telephone circuit (or just line or circuit industrywide) is a single-user circuit on a telephone communication system. It is designed to reproduce speech of a quality that is understandable. It is the physical wire or oth ...
s, etc.
See also
*
Wiedemann–Franz law
References
Bibliography
*Ashcroft, Neil W.; Mermin, N. David (1976). Solid State Physics. Holt, Rinehart and Winston. .
{{DEFAULTSORT:Residual Resistance Ratio
Electrical resistance and conductance
Cryogenics
Superconductivity