chemical thermodynamics of neptunium and plutonium - U.S. ...

6.1 Neptunium crystal and liquid 87Table 6.3: Enthalpies of transformation for neptunium allotropesReference trs H(α → β) trs H(β → γ ) trs H(β → 1)kJ·mol −1 kJ·mol −1 kJ·mol −1[59EVA/MAR] 8.37[70WIT/VAU] 5.607 5.272 5.188[90FOL] 4.73 2.99 3.19Calculated from (5.04 ± 0.51) (5.4 ± 0.8) —high pressure measurementsSelected (5.607 ± 1.000) (5.272±1.000) (5.188±1.000)Cp,m ◦ (Np,α,T) = (−4.0543 + 8.2555 × 10−2 T+805714T −2 ) J·K −1·mol −1 (298.15 K to 553 K)which joins smoothly with the low-temperature data of Lee et al. [70LEE/MEN] at298.15 K. Lacking any experimental data for the β and γ allotropes, we have estimatedthe heat capacity of tetragonal β-Np to be 39.33 J·K −1·mol −1 , the average ofthe values for the tetragonal phases β-U and δ ′ -Pu and the heat capacity of bcc γ -Npto be 36.40 J·mol −1 K −1 , the average bcc γ -U and ε-Pu. The heat capacity of theliquid is also estimated from U(l) and Pu(l). The totality of the estimated heat capacitiesand enthalpies of transition were also selected to make vap S(1840 K) closeto 99.5 J·K −1·mol −1 , as measured by [75ACK/RAU] (see below). If the appreciablylower enthalpies of transition given by [90FOL] are used, the required heat capacitiesfor β, γ and liquid Np all have to be near (but not beyond) their reasonable upperbounds.The experimental data on the enthalpies of transition are summarised in Table 6.3.Wittenberg et al.[70WIT/VAU] used differential thermal analysis of a 7.3 g sampleof a metal containing less than 0.35 wt% impurities. They reported enthalpies of 5607J·mol −1 for the α to β transition and 5272 J·mol −1 for the β to γ transition, and5188 J·mol −1 for the enthalpy of fusion. More recently Foltyn [90FOL] reported ratherdifferent values of 4700, 3000 and 3200 J·mol −1 , again using differential analysis, butof a much smaller (0.1 g), but purer (99.97 wt%) sample of Np. In view of the largedifferences in these enthalpies of transition, approximate values were calculated fromthe molar volumes of the phases, calculated from Zachariasen’s data [52ZAC] andthe variation of the transition temperatures with pressure, given by Stephens [66STE].There is an appreciable uncertainty in the calculated value for the β → γ transition,since the thermal expansion of the phases is not well-defined at these temperatures. Themolar volumes (cm 3· mol −1 ) used at the given transition temperatures were: α(553 K)11.838; β(553 K) 12.165; β(849 K) 12.75 ± 0.03; γ (849 K) 13.09 ± 0.04. However,the calculated data indicate that the measurements of [70WIT/VAU] are to be preferred.The higher enthalpies of transition also lead to better consistency with the entropy ofvaporisation, as discussed below.