# Negative temperature coefficient

Negative temperature coefficient

A negative temperature coefficient (NTC) occurs when the thermal conductivity of a material rises with increasing temperature, typically in a defined temperature range. For most materials, the thermal conductivity will decrease with increasing temperature.

Materials with a negative temperature coefficient have been used in floor heating since 1971. The negative temperature coefficient avoids excessive local heating beneath carpets, bean bag chairs, mattresses etc., which can damage wooden floors, and may infrequently cause fires.

Most ceramics exhibit NTC behaviour, which is governed by an Arrhenius equation over a wide range of temperatures:
$R=A cdot e^\left\{frac\left\{B\right\}\left\{T$
where R = resistance A, B = constants T = absolute temperature (K)The constant B is related to the energies required to form and move the charge carriers responsible for electrical conduction – hence, as the value of B decreases, the material becomes insulating. Practical and commercial NTC resistors aim to combine modest resistance with a value of B that provides good sensitivity to temperature. Such is the importance of the B constant value, that it is possible to characterize NTC thermistors using the B parameter equation: R = r∞eB/T -(3)where r∞ = R0 e-B/T0 R0 = resistance at temperature T0Therefore, many materials that produce acceptable values of B include materials that have been alloyed or possess variable cation valence states and thus contain a high natural defect center concentration. The value of B strongly depends on the energy required to dissociate the charge carriers that are used for the electrical conduction from these defect centers.

NTC thermistors are generally manufactured from pressed die chip of semi-conducting material – often a sintered ceramic oxide – and are based on a conduction model. A semi conductor is intermediate between an insulator and a conductor, and behaves as an insulator as low temperatures and becomes more conducting as temperature increases.

One of the main reasons that semi-conductors are so useful for thermistors is that their electrical properties can be controlled and enhanced by ‘doping’ or alloying with impurities – either elements or compounds. A common commercially available NTC thermistor material is Mn3O4 which can be doped with varying amounts of NiO. Since the Ni2+ cation has less positive charges than the Mn3+ cation so to maintain charge neutrality a Mn3+ is converted to a Mn4+ cation for each of the substituted Ni2+ cations. The electrical conduction is therefore increase by an electron hopping mechanism between the Mn3+ and Mn4+ ions on equivalent sites in the crystal lattice. It is also possible to dope the Mn3O4 with other combinations of impurities such as CoO and CuO.

Due to these properties of semi-conductors, as the temperature increases, the energy of the electrons increases due to the increased thermal energy available and therefore enables them to be promoted to the conduction band. This results in a greater proportion of electrons being able to move around and carry charge – the more electrons that are mobile and can carry charge, the more current a material can conduct and therefore the resistivity has decreased – hence the NTC thermistors exhibit a decrease in resistivity with increasing temperature.

This phenomenon is also described by the change in the temperature coefficient of resistance: α = (1/R) dR /dT -(4) α = -B/T3 -(5)It is therefore clear that the temperature coefficient of resistance is inversely proportion to the temperature, and decreases when the temperature increases.

Negative temperature coefficient of reactivity

In a nuclear reactor, temperature changes can introduce reactivity changes. This property is called the "temperature coefficient of reactivity." In water-cooled nuclear reactors, the predominant reactivity changes are brought about by changes in the temperature of the coolant water. In this case the temperature coefficient is negative, which means that an increase in coolant temperature causes a decrease in reactivity, and vice-versa. A reactor with a negative temperature coefficient of reactivity is therefore inherently self-controlling and safe.

See also

* Thermistor
* Temperature coefficient
* Passive nuclear safety

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