The boron coefficient is defined as the change in reactivity per the change in the boron concentration.
αB = dρ⁄dg/kg
It is expressed in units of pcm/g.kg-1. The value of boron coefficient in PWRs is usually ranges from about -1000 pcm/g.kg-1 to about -2000 pcm/g.kg-1. The boron coefficient usually decreases (becomes more negative) as the fuel burnup increases.
This coefficient does not represent any reactivity feedback. Still, it is commonly used by reactor operators because it describes the influence of changes in the boron concentration on the reactor’s reactivity.
See also: Boron 10
Natural boron consists primarily of two stable isotopes, 11B (80.1%) and 10B (19.9%). In nuclear industry boron is commonly used as a neutron absorber due to the high neutron cross-section of isotope 10B. Its (n,alpha) reaction cross-section for thermal neutrons is about 3840 barns (for 0.025 eV neutron). Isotope 11B has absorption cross-section for thermal neutrons about 0.005 barns (for 0.025 eV neutron). Most of (n,alpha) reactions of thermal neutrons are 10B(n,alpha)7Li reactions accompanied by 0.48 MeV gamma emission.
Moreover, isotope 10B has a high (n, alpha) reaction cross-section along the entire neutron energy spectrum. The cross-sections of most other elements become very small at high energies, as in the case of cadmium. The cross-section of 10B decreases monotonically with energy. For fast neutrons, its cross-section is on the order of barns.
Boron, as the neutron absorber, has another positive property. The reaction products (after a neutron absorption), helium and lithium, are stable isotopes. Therefore there are minimal problems with decay heating of control rods or burnable absorbers used in the reactor core.
Theory of Boron Coefficient
↑boron ⇒ ↓keff = η.ε.p. ↓f .Pf.Pt
The concentration of boric acid diluted in the primary coolant influences the thermal utilization factor. For example, an increase in the concentration of boric acid (chemical shim) causes the addition of new absorbing material into the core, and this causes a decrease in the thermal utilization factor.
The thermal utilization factor for heterogeneous reactor cores must be calculated in terms of reaction rates and volumes, for example, by the following equation:
where Σa is the macroscopic absorption cross-section, which is the sum of the capture cross-section and the fission cross-section, Σa = Σc + Σf. The superscripts U, M, P, CR, B, BA, and O, refer to uranium fuel, moderator, poisons, control rods, boric acid, burnable absorbers, etc. The presence of control rods, boric acid, or poisons causes a decrease in neutron utilization, which, in turn, causes a decrease in the multiplication factor.
Compared with burnable absorbers (long-term reactivity control) or with control rods (rapid reactivity control), the boric acid avoids the unevenness of neutron-flux density in the reactor core because it is dissolved homogeneously in the coolant in the entire reactor core. On the other hand, high concentrations of boric acid may lead to a positive moderator temperature coefficient, which is undesirable. In this case, more burnable absorbers must be used.
Moreover this method is slow in controlling reactivity. Normally, it takes several minutes to change the concentration (dilute or borate) of the boric acid in the primary loop. For rapid changes of reactivity control rods must be used.
