Detail the process of reactivity control in a micro reactor using control rods, focusing on the material properties of the rods and their impact on reactivity changes.

Reactivity control in a micro reactor, particularly using control rods, is essential for managing the nuclear chain reaction. Control rods are designed to absorb neutrons, thereby decreasing the reactor's reactivity and enabling operators to maintain a steady-state power level, shut down the reactor safely, and respond to unexpected changes in operating conditions. The effectiveness of control rods depends significantly on their material properties and their positioning within the reactor core.

The primary function of a control rod is to reduce the neutron population in the reactor core, which in turn reduces the rate of fission. This is achieved through the selection of materials with high neutron absorption cross-sections. These materials readily absorb neutrons without undergoing fission themselves, and therefore do not contribute to the chain reaction. Common control rod materials include boron, cadmium, hafnium, and silver-indium-cadmium alloys. Boron, typically in the form of boron carbide (B4C), is often used in thermal reactors due to its high absorption cross-section for thermal neutrons and its cost-effectiveness and the ease with which it can be integrated into a fuel assembly. For example, in a small thermal micro reactor, control rods might be fabricated from B4C and inserted into specific locations within the fuel assembly to manage reactivity. Cadmium is another effective absorber, but it has the drawback of becoming activated by neutron capture which results in radioactive isotopes, and so its use may require further consideration for its management.

Hafnium is a more expensive absorber but has excellent mechanical strength, high melting point, and resistance to corrosion and it is very effective at absorbing thermal and epithermal neutrons. Hafnium is used in applications where robust control is needed, and in reactors that have high neutron fluxes. Silver-indium-cadmium alloys are sometimes preferred for certain applications because of their high absorption properties across a broad range of neutron energies and their good mechanical properties. Their combination provides a more uniform reactivity change than other single elements might offer.

The material properties of control rods have a profound impact on reactivity changes. The absorption cross-section determines the probability that a neutron will be absorbed by a given nucleus. A higher absorption cross-section means a greater number of neutrons will be removed from the chain reaction for a given number of absorbing nuclei, thus a higher effectiveness at reducing reactivity. The material needs to maintain its absorption properties throughout the lifespan of the reactor, therefore burnable absorbers (such as boron) must be utilized judiciously in such applications where a change in absorption with time is acceptable. Another important property is the material's mechanical strength and resistance to corrosion. Control rods must be able to withstand high temperatures and pressures within the reactor core without deforming or degrading. Degradation of the control rod structure or material would alter its absorption capability and thereby reduce its overall effectiveness. Additionally, the expansion and contraction characteristics of the material due to temperature changes must be considered to ensure smooth and precise movement of the control rods. Thermal expansion may also lead to mechanical issues within the fuel assembly if the designs do not consider thermal expansion differences.

The way the control rods are deployed can also affect how much reactivity is controlled. Control rods are often shaped as rods or plates, and they can be inserted and withdrawn from the reactor core using mechanical drive mechanisms. The depth of insertion is crucial, with deeper insertion resulting in greater neutron absorption and greater reduction in reactivity. In a micro reactor, control rods may be positioned to provide both coarse and fine reactivity control. Coarse control rods are used for large changes in reactivity, such as during start-up or shut-down, while fine control rods are used for making precise adjustments to maintain a desired power level. In some reactor designs, additional control is provided by burnable absorbers mixed within the fuel itself to help manage excess reactivity and achieve a more even power distribution, although these are not considered control rods.

The effectiveness of control rods can also depend on their physical location within the reactor core. Rods located in regions of high neutron flux have a greater impact on reactivity than those in regions of low flux. Positioning control rods strategically to maximize their effectiveness in controlling the chain reaction is an important consideration. For example, positioning control rods near the center of the reactor core is an effective method of control since neutron fluxes are generally higher in these regions. The performance of control rods is further affected by their arrangement within the core: clustered control rods may provide more localized reactivity control while a wider arrangement of control rods would have more impact on the whole core.

In summary, the effectiveness of control rods in reactivity control is dependent upon the neutron absorption cross-section of the material, its mechanical properties under extreme reactor conditions, its chemical stability under operation and the positioning and distribution within the reactor core, all working together to ensure a safe and reliably controllable nuclear reaction.