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Low Temperature Equations

        For temperatures below about 13,000°K, the numerical technique using equation (6.27) experiences convergence difficulties, as described previously for the uranium and hydrogen composition calculations. A different mathematical formulation is developed for the low temperature region. At low temperatures, all five hydrogen species are considered. For uranium, only the species U0 and U1+ are considered. The scaled reaction equations for the four hydrogen reactions and the uranium reaction U0 t U1+ + e are given by (6.7), (6.8), (6.9), (6.10), and (6.15-1). The total particle concentration is


                        5        13
                  C c+     d d +   Ci            (6.34)
                       i=l      i=1


The charge neutrality condition is
                    5           2

              COe =   Zi  d. +      1 .C.        (6.35)
                      i~l      i=l


Using the expression for Ci from (6.16-i) in equations (6.34) and (6.35) gives K*
                         51
               1   Ca +    d. + C1(1 +  1         (6.36)
                           i~l i I      e