Atomic Value Control Theory

• The Atomic Value Control Theory is a theory that states, as with general single crystal conduction theory, that when excessive electrons are produced in the crystal and electrons with different atom value enters, the excessive electrons receive electricity conduction and electricity flows.

• It is known that in high temperature, it shows behavior of P-type semi-conductor that has stoichiometric composition due to insufficient negative ions.

Dilution Theory

• The Dilution Theory is a theory that explains that when Fe₃O⁴ that conducts electricity and spinel that does not conduct are combined, it comes to have the characteristic value between the two types of spinel, thus holds conductive properties.
• For example, CO₃O₄ or Mn₃O₄ are Co²⁺[Co³⁺Co³⁺]O₄ and Mn²⁺[Mn³⁺Mn³⁺]O₄, forming normal spinel, and these to oxides carries out mutually full solid substitution as in the following.

• Therefore, amount of substitution of Co increases, the probability of electron hopping between Mn³⁺ and Mn⁴⁺ increase and resistance decreases. Also if CuO is added to Mn₃O₄, the Cu²⁺ ion is substituted in the bicovalent state with Mn²⁺ ion in A site. For this, in order to electrically maintain neutrality, Mn³⁺ and Mn⁴⁺ ,that are of the same quantity as Cu⁺, increase in hopping conduction with each other.
• In other words, by becoming Cu²⁺XMn²⁺1-X[Mn^3+2-xMn⁴⁺x]O₄, hopping conduction increases, and resistance significantly decreases. Therefore, for addition of Cu²⁺, Ni²⁺ the atom acts as control-type ion donor, and for addition of Co²⁺, Co³⁺ as dilution theory-type ion, changing the resistance value and B constant. Also, oxygen ion insufficiency comes to exist due to differences in plus ion due to heating temperature or atmosphere, and such oxygen insufficiency causes reduction in plus ion atom value, changing the yield, B constant and reliability of Thermistor, thus is very important.

Hopping Theory

• The Hopping Theory is one that considers that when an electrons is excited and moves to a nearby electron, electricity flows due to the movement of the electron.
• For example, Fe₃O₄ is known to have greater conductive properties compared to Mn₃O₄, CO₃O₄ having similar crystal composition with Fe₃O₄
• For Fe₃O₄, in the spinel composition, Fe³⁺ ion exists in A site, Fe²⁺ in B site, and Fe³⁺ and O4^2- in A site. In this, those that contributes to conduction are plus ions in B site, and plus ions in A site do not contribute at all. The reason is that the lattice gaps are significantly empty in A site, rendering electron hopping impossible, thus only the plus ions in B site hop.
• In B site, Fe has two types of ions namely Fe²⁺ and Fe³⁺, and differences in electric charge of electrons between bicovalent and tricovalent ions in the nearby B site, causing Fe³⁺ to change into Fe²⁺ and Fe²⁺ into Fe³⁺ ion, and such change in electric charge of ion is called hopping phenomenon, and this phenomenon continues to occur between nearby ions, causing movement in electrons.
• At this, when voltage is applied, it is organized and moves to the opposite direction of the flow and grain boundary of this electron, thus transforms into current. The easiness of electricity conduction is determined by the number of ions with the ability to be donor and acceptor of this moving electron.

• For 1 electron to escape from an Fe³⁺ ion surrounded by oxygen ions it requires the lowest energy, thus for the energy of the electron contributing to conduction, a higher energy is required, and this energy is obtained from external temperature. If the lowest energy required for hopping is expressed in energy as ΔE and rate of conduction as σ, it can be expressed as in the formula above. In this, σo expresses the total number of B site which is the rate of conduction, k the Boltzmann constant, and T the absolute temperature.
• The above formula is very similar to σ = σ∞exp (B/T) , the characteristic of Thermistor in which resistance functionally decreases as temperature increases, and if -ㅿE/2k=B is used, they become the same formula. Therefore, B constant is determined by the ingredients, and the activation energy is the constant that can be obtained in proportion to Boltzmann constant.
• Next, regarding the Mn^-Ni family mainly used as ingredients of Thermistor, it can be explained with conduction element of the same form. Mn₃O₄, as opposed to Fe₃O₄, is not conductive, but because when Ni is added to Mn²⁺(Mn³⁺Mn⁺³)O₄ in X amount , for the conduction element, bicovalent Ni²⁺ enters B site, in order for B site to maintain electrical neutraliaty, Mn³⁺ becomes Mn⁴⁺ in other words Nix²⁺Mnx⁴⁺Mn1-2x³+Mn³⁺ so that tricovalent and tetravalent Mn exists, causing hopping conduction.Here, Ni itself does not contribute to hopping but merely transforms the electrons of Mn ion.
• On the other hand, it is known that Ni²⁺ ion not only enters B site of Mn but also A site, and here the spinel composition becomes MnxNi1-x(Mn²-xNix)O₄
• Therefore, for Thermistor, grain with crystal and crystal with grain boundary cannot directly apply to this theory, but it is assumed that it carries out conduction for which the above 3 theories are combined.