Comprehensive nuclear materials 2 01 the actinides elements properties and characteristics

Comprehensive nuclear materials 2 01 the actinides elements properties and characteristics Comprehensive nuclear materials 2 01 the actinides elements properties and characteristics Comprehensive nuclear materials 2 01 the actinides elements properties and characteristics Comprehensive nuclear materials 2 01 the actinides elements properties and characteristics Comprehensive nuclear materials 2 01 the actinides elements properties and characteristics

2.01 The Actinides Elements: Properties and Characteristics R J M Konings, O Benesˇ, and J.-C Griveau European Commission, Joint Research Centre, Institute for Transuranium Elements, Karlsruhe, Germany ß 2012 Elsevier Ltd All rights reserved 2.01.1 2.01.2 2.01.2.1 2.01.2.2 2.01.2.3 2.01.2.4 2.01.3 2.01.3.1 2.01.3.2 2.01.3.3 2.01.4 2.01.4.1 2.01.4.2 2.01.4.3 2.01.4.4 2.01.4.5 2.01.4.6 2.01.4.7 2.01.4.8 2.01.5 References Introduction Crystallographic Properties Crystal Structure Effects of Pressure Effects of Temperature Effects of Radiation Thermodynamic Properties Heat Capacity and Entropy of the Crystalline State Heat Capacity of the Liquid State Heat Capacity and Entropy of the Gaseous State Thermophysical and Electronic Properties Thermal Expansion and Density of the Crystalline State Electrical Resistivity of the Crystalline State Thermopower of the Crystalline State Thermal Conductivity of the Crystalline State Thermal Conductivity of the Liquid State Density of the Liquid State Viscosity Surface Tension Summary and Outlook Abbreviations dhcp fcc IUPAC OECD/NEA Double hexagonal close-packed Face-centered cubic International Union of Pure and Applied Chemistry Organisation for Economic Cooperation and Development/ Nuclear Energy Agency 2.01.1 Introduction The actinides are the 15 elements with atomic numbers 89–103 in the periodic system The International Union of Pure and Applied Chemistry (IUPAC) has recommended that these elements are named actinoids (meaning ‘like actinium’), but this has never found general acceptance In these elements, the 5f electron subshell is progressively filled, leading to the generalized 2 7 10 11 12 12 12 14 15 17 18 18 18 18 19 [Rn 7s25f n ] configuration Unlike the lanthanides, in which the 4f electrons lie in the interior of the xenon core region and thus hardly contribute to the chemical bonds (called ‘localized’), the 5f electrons show a much more diverse character, particularly in the metallic state.1 The 5f electrons in the elements thorium to neptunium are placed in the valence shell (often called ‘itinerant’ or ‘delocalized’) and show substantial covalent bonding, whereas the 5f electrons in the elements americium to lawrencium are localized Plutonium and americium have a transition position, showing both localized and delocalized behavior depending on temperature, pressure, and magnetic field.2 The actinides are radioactive elements, their isotopes having strongly variable half-lives Owing to the short half-life, compared with the age of the earth, majority of the actinides have decayed and cannot be found in nature Only the long-lived isotopes 232Th, 235 U, and 238U are of primordial origin, and possibly 244 Pu Also, 231Pa is found in very low concentrations in natural minerals (e.g., pitchblende ores), but it is a The Actinides Elements: Properties and Characteristics product of the 235U (4n ỵ 3) decay chain.3 Most other actinides are man-made elements They were synthesized by nuclear reactions using reactors and accelerators in the period 1940 (Np) to 1961 (Lr) The metals from Th to Cm are available in gram quantities that have allowed experimental determination of (some of) their physicochemical properties; Bk and Cf metals have been prepared in milligram quantities and Es in microgram quantities and therefore only limited investigations have been possible The metals Fm and beyond have not been prepared in pure form The main technological relevance of the actinides is their use as fuel for nuclear fission reactors, particularly the nuclides 233U, 235U, and 239Pu, which fission with thermal neutrons 235U and 239Pu occur in the so-called U/Pu fuel cycle 235U is present in 0.7% in natural uranium; 239Pu is formed when uranium is irradiated in a reactor as a result of neutron capture by 238U 233U is formed by neutron capture of 232Th in the Th/U fuel cycle The vast majority of nuclear power reactors use oxide fuel, but carbide and nitride as well metallic alloys fuels have been studied since the early days of reactor development.4 Table Ac Th Pa U Np Pu Am Cm Bk Cf Es a a a b a b a b g a b g a b g d d0 e a b g a b a a a In this chapter, we discuss the physicochemical properties of the actinide metals, with emphasis on the elements Th to Cm for which experimental data on bulk samples generally exist The trends and systematics in the properties of the actinide series will be emphasized and compared with those of the 4f series These physicochemical data are essential for understanding and describing the properties of multielement alloys (see Chapter 2.05, Phase Diagrams of Actinide Alloys) and actinide containing compounds (Chapter 2.02, Thermodynamic and Thermophysical Properties of the Actinide Oxides) 2.01.2 Crystallographic Properties 2.01.2.1 Crystal Structure The stable crystallographic modifications of the actinides at atmospheric pressure are listed in Table Compared to the lanthanide series in which the hexagonal close-packed (hcp) and the face-centered cubic (fcc) structures dominate, the actinide metals show a remarkable variation in the structural The crystal structure of the actinide metals Structure Space group a (pm) Cubic Cubic Cubic Tetragonal Cubic Orthorhombic Tetragonal Cubic Orthorhombic Tetragonal Cubic Monoclinic Monoclinic Orthorhombic Cubic Tetragonal Cubic Hexagonal Cubic Cubic Hexagonal Cubic Hexagonal Hexagonal Cubic Fm m Fm m Im m I4/mmm Fm m Cmcm Im m Pnma P42 Im m P21/n I2/m Fddd Fm m I4/mmm Im m P63/mmc Fm m 531.5 508.42 411 392.1 501.8 285.4 565.6 352.4 666.3 489.7 351.8 618.3 928.4 315.9 463.71 334 363.61 346.81 489.4 P63/mmc Fm m P63/mmc P63/mmc Fm m 349.6 503.9 341.6 338.4 575 a b (pm) c (pm) Angle(s) 323.5 587.0 495.5 1075.9 472.3 488.7 338.8 482.2 1046.3 576.8 1096.3 785.9 1016.2 b ¼ 101.79 b ¼ 93.13 444 1124.1 g ¼ 120 1113.3 g ¼ 120 1106.9 1104.0 g ¼ 120 g ¼ 120 Vm (cm3 molÀ1) r (g cmÀ3) 22.59 19.79 20.90 14.98 19.02 12.50 12.95 13.18 11.58 11.79 13.11 12.04 13.50 13.94 15.01 14.91 14.48 17.63 17.65 10.05 11.73 11.10 15.43 12.15 19.05 18.37 18.06 20.48 20.11 18.08 19.85 17.71 17.15 15.92 16.03 16.51 13.67 13.66 17.74 19.26 16.84 16.48 28.62 13.76 12.67 14.79 15.23 8.88 P42/mnm, P42/nm or P4n2 Source: Edelstein, N M.; Fuger, J.; Katz, J J.; Morss, L R In The Chemistry of the Actinide and Transactinide Elements; Morss, L R., Edelstein, N., Fuger, J., Katz, J J., Eds.; Springer Verlag, 2006; Chapter 15, pp 1753–1835 The Actinides Elements: Properties and Characteristics properties at room temperature, as shown in Figure Particularly, the elements Pa–Pu have unusual low symmetry (distorted) crystal structures a-Pa is body-centered tetragonal, and a-U and a-Np are orthorhombic but with slightly different space groups a-Pu has a monoclinic crystal structure with 16 atoms in the unit cell at room temperature Plutonium is unique in the periodic table of the elements with six allotropes at atmospheric pressure and one more at elevated pressure This complexity of the structural properties of the actinides is also evident from Figure 2, which shows the variation of the molar volume of the a-phases of the actinides at room temperature and atmospheric pressure, indicating that the actinides Pa to Pu follow the trend in the (itinerant) d-transition (a) metals, whereas the actinides Am to Bk follow that of the (localized) 4f metals It is generally accepted that this complex behavior is due to the active role of the f-electron in the metallic bond and the changes in temperature and pressure by which the f-electron bonding character is affected Experimental observations and electronic structure calculations have indeed shown that the bonding in the transition metals is dominated by d-electron contributions, that in the lanthanides there is a lack of f-electron contribution, and that the actinides fall in between.5 2.01.2.2 Effects of Pressure Pressure is expected to drive the atoms in the crystal lattice closer to each other, forcing the electrons to (b) (c) (d) (e) (f) Figure The crystal structures of the actinides at room temperatures: (a) a-Th, (b) a-Pa, (c) a-U, (d) a-Np, (e) a-Pu, (f) a-Am Vm(cm3 mol−1) 40 Y Zr Nb Mo Tc Ru Rh Pd Ag Cd La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu 30 20 10 Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Figure The molar volume of the actinide elements () compared with that of the lanthanides (○) and the 4d transition metals (□) 4 The Actinides Elements: Properties and Characteristics participate in the binding (delocalization),6 which particularly affects the heavy actinides with localized f-electron behavior at ambient pressure Recent studies using diamond anvil cells coupled to synchrotron radiation have provided strong evidence for that As discussed by Heathman et al.,7 americium shows a remarkable decrease in volume with increasing pressure (at ambient temperature) with three transitions up to 100 GPa (Figure 3) Its structure changes from hcp (Am-I) through fcc (Am-II) to orthorhombic (Am-III and Am-IV), indicating the appearance of the itinerant character 5f electrons This behavior is also observed in curium, with a puzzling supplementary magnetically stabilized Cm-III structure at 40–60 GPa.8 Uranium shows a comparatively straightforward behavior and the a-structure is stable up to 100 GPa, with a much smaller volume decrease.6 A similar behavior has been found for protactinium, its a-form being stable up to 80 GPa This is clearly reflected in the isothermal bulk modulus (Table 2), which is around 100 GPa for the elements Pa to Np but around 30–40 GPa for Am and Cm The Am-IV phase shows a large bulk modulus (more similar to that of uranium), as expected for a metal with appreciable 5f-electron character in its bonding This is also evident from the comparison of the actinide and lanthanide metals (Figure 4) Uncertainty still exists about the bulk modulus of a-plutonium As discussed by Ledbetter et al.,12 the published B0 values at ambient range show a large variation, as the theoretical calculations The most accurate results for the isothermal bulk modulus vary between 51(2) GPa13 and 43(2) GPa.14 2.01.2.3 Effects of Temperature Detailed studies show that the crystal lattice of most actinide metals expands with increasing temperature 1.00 0.95 0.90 Cm I 0.85 α-U Am I 0.80 Cm II 2% V/Vo 0.75 Am II 0.70 Cm III Am III 0.65 Pa I 4.5 % 7% Pa II Cm IV 0.60 0.55 Cm V Am IV 0.50 11.7 % 0.45 10 20 30 40 50 60 70 80 90 100 Pressure (GPa) Figure The relative volumes as a function of pressure of several actinide metals Table B0 (GPa) B0 References The isothermal bulk modulus (B0) and its pressure derivative (B0 ) of the actinide elements at ambient temperature a-Th a-Pa a-U a-Np a-Pu a-Am a-Cm 58(1) 4.2(3) 118(2) 3.3(2) 104(2) 6.2(2) 118(2) 6.6(6) 10 49 12.4 11 29.8(2) 3.6(2) 36.5(3) 4.6(2) The Actinides Elements: Properties and Characteristics La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu 150 B0 (GPa) 100 50 Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Figure The isothermal bulk modulus (B0) of the actinide elements (○) compared with that of the lanthanides () δ ε DL/L (%) δЈ γ Liquid β α 300 500 700 T (K) 900 1100 Figure The thermal expansion of Pu Made after Schonfeld, F W.; Tate, R E Los Alamos National Laboratory, Technical Report LA-13034-MS; 1996 Moreover, the stability of the crystalline state of the actinide metals varies significantly The melting temperature is high for thorium, similar to that of the transition metals in group IVB, and low for Np and Pu (Figure 6) When applying high temperature as well as high pressure to the actinides, phase changes can be suppressed, as is shown in Figure For example, the triple point for the a–b–g equilibrium in uranium is found at about 1076 K and 31.5 kbar; above this pressure, orthorhombic a-U directly transforms in fcc g-U.17 In plutonium, the g-, d-, and d0 -phases disappear at relatively low pressure and are replaced by a new phase designated z In contrast to the other actinides, plutonium shows a negative slope for the liquidus down to the b-z-liquid triple point (773 K, 27 kbar) reflecting the increase in density upon melting.17 2.01.2.4 and evolves to a simple cubic arrangement close to their melting temperature, similar to the lanthanide elements (For numerical data on the thermal expansion, see Section 2.01.4.1) As the atoms move away from each other, the electrons in the 5f metals tend to favor a localized state As discussed by Vohra and Holzapfel,15 this is particularly important for Np and Pu, which are on the threshold of localization/ itinerancy The case for plutonium is much more complex, as shown in Figure The crystal lattice of plutonium expands for the a-, b-, g-, and e-phases, and the g- to d-transition has a positive expansion The d- and d0 -phases have negative thermal expansion and the d- to d0 - and d0 - to e-transitions show a negative volume change, as is the case upon melting Dynamic mean field calculations show that the monoclinic a-phase of Pu is metallic, whereas fcc d is slightly on the localized side of the localization– delocalization transition.16 Effects of Radiation The a-decay of the actinides taking place in the crystal lattice creates an alpha particle and a recoil atom The recoil atom produced has a range of about 12 nm and causes a dense collision cascade with typically about 2300 displacements (Frenkel pairs) within a short distance, around 7.5 nm in size The a-particle has a path of about 10 mm, with a cascade of about 265 displacements at the end of its range.18 Although recombination will take place, point defects and eventually extended defects (dislocations, dislocation loops) will survive in the crystal lattice, resulting in changes in the properties of the materials Computer simulations of the radiation effects in fcc plutonium have shown that the defect recombination stage is much longer than that in other metals and that the vacancies not seem to form clusters.19 In addition to the radiation damage, helium ingrowth takes place As discussed by Hecker and Martz,20 the expansion of the lattice of a-Pu is significant due to The Actinides Elements: Properties and Characteristics La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu 2500 Tfus (K) 2000 1500 1000 500 Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Figure The melting point of the lanthanide () and actinide (○) metals The estimated values are indicated by  1100 1200 γ β α 800 γ 900 T (K) T (K) 1000 Liquid 1000 800 Neptunium β 700 600 Uranium 600 400 10 20 30 500 40 α 10 15 P (kbar) 25 30 35 1600 1000 900 δЈ ζ 600 γ γ 1400 T (K) 700 Liquid 1500 Liquid ε 800 T (K) 20 P (kbar) δ 1300 β 500 β 400 300 1200 Plutonium α 10 20 30 40 50 60 70 P (kbar) 1100 Americium 10 15 20 25 30 P (kbar) Figure The pressure–temperature phase diagrams for U, Pu, Np, and Am Reproduced from Lee, J A.; Waldron, M B Contemp Phys 1972, 13, 113–133 self-irradiation, when held at cryogenic temperatures, saturating at about 10 vol.% In contrast, the (Ti-stabilized) b-phase shows a slight contraction and the (Al-stabilized) d-phase a substantial contraction, the latter saturating at 15 vol.% Of course this is also reflected in other properties such as electrical resistivity.21,22 The radiation effects recover upon annealing to room temperature, a few percent of the damage remaining Gorbunov and Seleznev23 observed that a-Pu containing predominantly 239Pu retains its crystal structure after prolonged storage at room temperature A sample of predominantly shorter lived 238Pu (t1/2 ¼ 87.74 years) contains both the a- and b-forms at immediate examination and additionally the g-, Z-, and e-phases after a similar storage period Chung et al.24 showed by X-ray diffraction and dilatometry measurements on 238 Pu-doped d-phase plutonium samples that the lattice expansion by self-irradiation appears to be the primary cause for dimensional changes during The Actinides Elements: Properties and Characteristics the initial 23 years of aging Following the initial transient, the density change is primarily caused by a constant helium ingrowth rate as a result of particle decay The two effects were combined in an equation for the expansion DL/L with an exponential (radiation damage) and a linear (helium ingrowth) part: DL=L Aẵ1 expBt ị ỵ Ct ẵ1 where A, B, and C are constants and t is time The self-irradiation is one of the main causes that complicates the study of the heavy actinide metals For example, berkelium metal (t1/2 ¼ 314 days; $0.2% 249 Cf growth per day) shows signs of amorphization (weak and diffuse X-ray spectra) at room temperature, which improved after annealing and thermal cycling, and the samples were found to contain two crystallographic structures at room temperature, double hexagonal close-packed (dhcp) and fcc, of which the former is the stable form.25 An extreme case is Es; its crystal structure has been resolved only by rapid electron diffraction of thin film material due to the very short half-life of the isotope used.26 2.01.3 Thermodynamic Properties Many critical reviews of the thermodynamic properties of the actinide metals have been made since the 1960s The first milestone was the review by Oetting and coworkers,27 which gave recommended values for Th to Cm Ward et al.28 treated the same elements but also gave recommendations for Cf and Es In addition, the room temperature thermodynamic properties for the major actinides Th and U have been reviewed by the CODATA team for key values for Thermodynamics,29 while Th, U, Np, Pu, and Am have been reviewed by the OECD/NEA team.30–33 The most recent evaluation was made by Konings and Benesˇ,34 with emphasis on the high-temperature properties There are no large differences between these studies for the major actinides and it is thus clear that the recommendations given in this chapter rely heavily on these studies (Tables and 4) 2.01.3.1 Heat Capacity and Entropy of the Crystalline State The low-temperature heat capacity has been measured for the actinides Th through Am, in most cases showing anomalies The origin of these anomalies has generally not been explained adequately35 but is likely related to ordering phenomena and f-electron promotion The measurements for the major actinides Th, U, and Pu in the a-structure were made on gram-scale quantities, and the results should thus be of an acceptable accuracy However, although the low-temperature heat capacity of plutonium was measured by a remarkably large number of authors,36–42 there is considerable scatter among the results above 100 K (see Figure 8), probably due to self-heating and radiation damage But even the results for 242Pu samples from the same batch,40,41 which are affected less due to its much longer half-life, differ considerably The differences in the heat capacity have a pronounced effect on the standard entropy at T ¼ 298.15 K: 56.03 J KÀ1 molÀ1,39 56.32 J KÀ1 molÀ1,40 54.46 J KÀ1 molÀ1,41 and 57.1 J KÀ1 molÀ1.42 Especially, the results of Lashley et al.42 indicate a very different shape of the heat capacity curve of a-Pu, rising much steeper up to T ¼ 100 K and saturating at a lower value near room temperature Although the relaxation method used in that study is less accurate (Ỉ1.5% as claimed by the authors) than the traditional adiabatic technique used in the other studies, the difference is significant Lashley et al.42 attributed this to the buildup of radiation damage at the lowest temperatures, which they tried to avoid by measuring upon cooling, and below T ¼ 30 K by intermediate annealing at room temperature However, other authors also addressed this issue For example, Gordon et al.41 performed a heating run from room temperature to T ¼ 373 K before each low-temperature run Moreover, no substantial difference between the results for 239Pu and 242Pu was observed in that study The electronic Sommerfeld heat capacity coefficient (ge), a property proportional to the density of states at the Fermi level, varies strongly in the actinide series (Table 5) It increases steadily up to Pu but is very low for Am For d-Pu the electronic heat capacity coefficient ge is even three times higher than that of a-Pu This corresponds well with the results of photoemission spectra48 that show a-Th has a small density of states at the Fermi level compared with that of a-U, a-Np, and a-Pu (Figure 9) In a-Am, the valence band is well removed from the Fermi level The low-temperature heat capacity of other modifications of plutonium has been measured recently Specifically, the d-structure stabilized by Am or Ce doping shows clearly enhanced values of the electronic heat capacity coefficient ge at very low temperature.50,51 The standard entropies derived from the lowtemperature heat capacity data are given in Table 3, Recommended entropy (J KÀ1 molÀ1) and the heat capacity (J KÀ1 molÀ1) of actinide elements in the solid and liquid phase Phase Th Pa U Np Pu Am Cm a b Liquid a b Liquid a b g Liquid a b g Liquid a b g d d0 e Liquid a b g Liquid a b Liquid S0 (298.15) 51.8 Ỉ 0.50 – – 51.6 Ỉ 0.80 – – 50.20 Ỉ 0.20 – – – 50.45 Æ 0.40 – – – 54.46 Æ 0.80 – – – – – – 55.4 Ỉ 2.0 – – – 70.8 ặ 3.0 Cp ẳ A ỵ B T (K) ỵ C T2 (K) ỵ D T3 (K) ỵ E T2 (K) A B 23.435 15.702 46 21.6522 39.7 47.3 28.4264 47.12 61.6420 46.45 30.132 40 36 46 17.6186 27.4160 22.0233 28.4781 35.56 33.72 42.80 30.0399 8.4572 43 52 28.409 28.2 37.2 8.945  10À3 11.950  10À3 Source: Konings, R J M.; Benesˇ, O J Phys Chem Ref Data 2010, 39, 043102 C D or E E ¼ À1.140  104 12.426  10À3 À6.9587  10À3 29.8744  10À6 E ¼ À1.1888  105 E ¼ À33.1644  106 À36.2372  10À3 1.1589  10À4 45.5523  10À3 13.060  10À3 22.959  10À3 10.807  10À3 À29.053  10À3 33.167  10À3 5.2026  10À5 À7.587  10À6 À4.142  10À4 3.280  10À6 D ¼ À1.8961  10À8 Temperature range (K) 298–1650 1650–2020 2020–2500 298–1443 1443–1843 1843–2500 298–941 941–1049 1049–1407 1407–2500 298–553 553–850 850–913 913–2500 298–399 399–488 488–596 596–741 741–759 759–913 913–2500 298–1042 1042–1350 1350–1449 1449–2500 298–1569 1569–1619 1619–2500 The Actinides Elements: Properties and Characteristics Table The Actinides Elements: Properties and Characteristics Table Recommended transition temperatures (K), enthalpies (kJ molÀ1), and entropies (J KÀ1 molÀ1) of the actinide metals Th Pa U Np Pu Am Cm Transition Ttrs (K) DtrsH DtrsS a!b b!liq a!b b!liq a!b b!g g!liq a!b b!g g!liq a!b b!g g!d d!d0 d0 !E e!liq a!b b!g g!liq a!b b!liq 1650 Ỉ 15 2020 Ỉ 10 1443 Ỉ 50 1843 Ỉ 50 941 Ỉ 1049 Ỉ 1407 Ỉ 553 Ỉ 850 Æ 913 Æ 399 Æ 488 Æ 596 Ỉ 741 Ỉ 759 Ỉ 913 Ỉ 1042 Ỉ 10 1350 Ỉ 1449 Æ 1569 Æ 50 1619 Æ 50 3.5 Æ 0.1 13.8 Ỉ 1.3 6.6 Ỉ 2.0 12.3 Ỉ 2.0 2.85 Ỉ 0.15 4.62 Ỉ 0.50 8.47 Ỉ 1.00 4.7 Æ 0.5 3.0 Æ 0.5 3.2 Æ 0.5 3.706 Æ 0.030 0.478 Ỉ 0.020 0.713 Ỉ 0.050 0.065 Ỉ 0.020 1.711 Ỉ 0.050 2.766 Ỉ 0.1 0.34 Ỉ 0.10 3.8 Æ 0.4 8.0 Æ 2.0 4.5 Æ 0.5 11.7 Æ 1.0 2.12 6.83 4.57 6.67 3.03 4.40 6.02 8.50 3.53 3.50 9.29 0.98 1.20 0.09 2.25 3.03 0.33 2.81 5.52 0.29 7.23 Source: Konings, R J M.; Benesˇ, O J Phys Chem Ref Data 2010, 39, 043102 40 Cp (J K–1 mol–1) 30 20 35 30 10 25 100 100 200 200 T (K) 300 400 300 400 Figure The low-temperature heat capacity of plutonium; ◊,37; È,38; È,39; r,40; D,41; ,42; ○,43 Table and the variation along the actinide metal series is shown in Figure 10 The entropies of the elements Th to Am are close to the lattice entropies of the corresponding lanthanides, showing the absence of magnetic contributions The entropies of the other actinide elements must be derived from estimations, as experimental studies not exist To this purpose Ward et al.28 suggested a general formula by correlating the entropy with metallic radius (r), atomic weight (M), and magnetic entropy (Sm): ru Mu Su 298:15K ị ẳ Sk 298:15K ị ỵ R ln þ Sm rk Mk ½2Š where u refers to the unknown (lanthanide or actinide) element and k refers to the known element Sm is taken equal to Sspin ¼ (2J ỵ 1), where J is the total angular momentum quantum number The entropy of Cm thus obtained is significantly higher than that of the preceding elements, showing its magnetic character The heat capacity of the actinide metals from room temperature up to the melting temperature has been reported for Th, U, and Pu with reasonable accuracy and for Np for the a-phase only The values for the other metals are based on estimations For example, Konings52 estimated the heat capacity of americium metal from the harmonic, dilatation, electronic, and magnetic contributions, Cp ẳ Char ỵ Cdil ỵ Cele ỵ Cmag, whereas the heat capacity of g-americium was obtained from the trends in the 4f and 5f series The high-temperature heat capacity data for the actinide metals was analyzed in detail by Konings and Benesˇ,34 who gave recommendations for the elements Ac to Fm The results for the elements Th to Cm are summarized in Table Figure 11 shows the variation of the sum of the transition entropies from the crystalline room temperature phase to the liquid phase for the lanthanide and actinide series This value is about constant in the lanthanide series but shows large variation in the actinide series, particularly for the elements U–Np–Pu The deviation from the baseline The electronic heat capacity coefficient (ge) and Debye temperature (YD) of the actinide elements Th À2 À1 ge (mJ K mol ) YD (K) References 4.3(0.05) 163.3(0.7) 44 Pa 5.0(0.5) 185(5) 45 U a 9.1 256a 46 Np Pu Am 13.7(0.7) 240(4) 41 17(1) 153(2) 42 1(1) 120(20) 47 These values are for single crystal material, ge ¼ 9.9 mJ KÀ2 molÀ1 and YD ¼ 184 K for polycrystalline material a 10 The Actinides Elements: Properties and Characteristics correlates well with the atomic volume of the metals that is also anomalous for these elements, indicating that the itinerant behavior of the 5f electrons and the resulting lowering of the room temperature crystal symmetry require additional entropy to reach a similar disordered liquid state a-Th Intensity (arb units) a-U a-Np 2.01.3.2 a-Pu a-Am a-Cm 10 Energy below Ef (eV) Figure Valence-band photoemission spectra of the actinide metals Modified from Moore, K T.; van der Laan, G Rev Mod Phys 2009, 81, 235–298 by adding the results for a-Cm by Gouder et al.49 Note that the spectrum for a-Th is scaled up compared to the other spectra so that it is easily visualized In reality, it is much lower in intensity due to a small f density of states at the Fermi level Heat Capacity of the Liquid State The heat capacity of the actinide elements in the liquid state is relatively poorly known Experimental data exist for Th, U, and Pu, and only the values for Th and U are known with an acceptable accuracy They were measured by drop calorimetric techniques in a reasonable wide temperature range Semi-empirical models for liquid uranium suggest a large electronic contribution to the heat capacity of this element.53 The data for Pu, also obtained by calorimetry, are scattered and measured in a limited temperature range and the heat capacity value for the liquid of this element is thus uncertain Figure 12 also shows the estimated values for Am and Cm, based on assumptions considering the electron configurations.52,54 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu SЊ(M) (J K–1 mol–1) 100 80 60 40 Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Figure 10 The standard entropies of lanthanide () and actinide (○) metals at T ¼ 298.15 K; estimated values are indicated by () S (DtrsS) (J K–1 mol–1) 25 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Th Pa U Er Tm Yb Lu 20 15 10 Ac Np Pu Am Cm Bk Cf Es Fm Md No Lr Figure 11 The sum of the transition entropies of the lanthanide () and actinide (○) metals The estimated values are indicated by  The Actinides Elements: Properties and Characteristics Cp (liq) (J K–1 mol–1) 60 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho 11 Er Tm Yb Lu 50 40 30 Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Figure 12 The heat capacity of the lanthanide () and actinide (○) metals in the liquid phase Estimated values are indicated by () 2.01.3.3 Heat Capacity and Entropy of the Gaseous State The heat capacity and standard entropy for the ideal gas can be calculated from the atomic energy levels up to about 2000 K with reasonable accuracy using statistical thermodynamic methods34 from the atomic energy levels As discussed in detail by Brewer,55 the electronic states of the gaseous actinide elements are complete (through experiments and estimations) to about 15000 cmÀ1 The energies of the lowest electronic states for the elements Th to Cm are listed in Table Figure 13 shows a schematic representation of the atomic spectra of the actinide elements, based on the most recent assessments.56,57 The derived room temperature values for the entropy and the high-temperature heat capacity equations are shown in Table and are taken from the assessment by Konings and Benesˇ.34 The vapor pressure has been measured for all actinide metals except Md, No, and Lr The majority of the results deal with the elements Th–Am Measurements have also been made for Ac58 but they are of a very approximate nature The vapor pressure measurements for Es59 and Fm60 have been made on samples containing 10À5–10À7at.% of the actinides in rare earth alloys in combination with Henry’s law for dilute solutions These measurements have been carefully reviewed by Konings and Benesˇ34 and the recommended enthalpies of sublimation derived from these studies are listed in Table The assessed vapor pressure curves (ln(p) vs 1/T) are shown in Figure 14, indicating that the vapor pressure of the actinide metals varies strongly within the series It roughly increases with the atomic number but with prominent exceptions For example, americium is much more volatile than the neighboring Pu and Cm The enthalpies of sublimation of the actinides are plotted in Figure 15 together with the values Table Spectroscopic characteristics of the ground state and the lowest lying electronic states of the actinide elements Th Pa U Np Pu Am Cm State Spectroscopic term Energy level (cmÀ1) 6d27s2 6d27s2 6d27s2 6d27s2 6d27s2 5f26d7s2 5f26d7s2 5f26d7s2 5f6d27s2 5f26d7s2 5f36d7s2 5f36d7s2 5f36d7s2 5f36d7s2 5f36d7s2 5f46d7s2 5f46d7s2 5f46d7s2 5f46d7s2 5f46d7s2 5f67s2 5f67s2 5f67s2 5f67s2 5f56d7s2 5f77s2 5f66d7s2 5f66d7s2 5f76d7s 5f77s2 5f76d7s2 5f76d7s2 5f76d7s2 5f76d7s2 5f76d7s2 2558.06 2869.26 3687.99 3865.48 825.42 1618.325 2659.405 2966.53 620.323 3800.830 3868.486 4453.419 2033.94 3450.995 3502.855 6643.51 2203.61 4299.659 6144.515 6313.866 10684 12974 14000 14258 302.15 815.655 1764.268 3809.358 F2 P0 F3 P2 P1 K11/2 I9/2 G5/2 I9/2 H7/2 o L6 o K5 o L7 o H3 o I4 L11/2 L9/2 I7/2 L13/2 I9/2 F0 F1 F2 F3 K4 S7/2 H3/2 H5/2 10 D5/2 P7/2 o D2 o D3 o D4 o D5 o D6 Source: Blaise, J.; Wyart, J F http://www.lac.u-psud.fr/Database/ Contents.html, 2009; Worden, E F.; Blaise, J.; Fred, M.; Trautmann, N.; Wyart, J F In The Chemistry of the Actinide and Transactinide Elements; Morss, L R.; Edelstein, N.; Fuger, J.; Katz, J J., Eds.; Springer Verlag, 2006; Chapter 16, pp 1836–1892 12 The Actinides Elements: Properties and Characteristics 50 000 Energy (cm–1) 40 000 30 000 20 000 10 000 Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Figure 13 Schematic representation of the atomic spectra of the actinide elements for lanthanide metals The trend in the latter series shows a typical pattern, with La, Gd, and Lu forming an approximate linear baseline from which the others systematically deviate This trend can be understood from the electronic states of the condensed and gaseous atoms, as discussed by Nugent et al.61 These authors argued that the values for La, Gd, and Lu are almost identical, due the fact that they have the same number of valence electrons in the ground states of the gaseous metal atom and the crystal In between, the enthalpy of sublimation decreases regularly because of a corresponding increase in stability of the divalent ground states in the gaseous metal atoms A similar explanation can be applied to the actinide series, although Th, Pa, U, Np, and Pu deviate from this trend due to unusually large cohesive energies of the crystalline metals, resulting from the large number of valence electrons in the metal 2.01.4 Thermophysical and Electronic Properties 2.01.4.1 Thermal Expansion and Density of the Crystalline State The thermal expansion of a number of actinide metals has been studied, particularly for uranium and plutonium The 1975 review by Touloukian et al.62 lists 48 studies for uranium, including single crystal and polycrystalline materials The data show that a-uranium has a different expansion along the three crystallographic axes; the a- and c-axis expand whereas the b-axis shrinks with increasing temperature (Figure 16) Also, a-Pa shows distinct different expansion along the crystallographic axes (Figure 16) a-Np, in contrast, expands along the three axes of the crystal The complex thermal expansion behavior of plutonium has already been discussed in Section 2.01.2.4 and is shown in Figure Schofeld and Tate63 reviewed the wealth of data for the various plutonium modifications and the recommended values from their work are listed in Table a-Pu expands along all three axes of the crystal, and the lattice expansion continues for the b- and g-phases, but the cell parameter of the cubic d and d0 modifications decreases Americium, the last actinide for which thermal expansion data exist, shows a regular thermal expansion in both crystallographic directions.68 Table summarizes the linear thermal expansion (DL/L0) for the actinide metals The density can be calculated from these data using the formula: rT ị ẳ M Vo ỵ 3DL=L0 T ịị ẵ3 where M is the atomic mass, and V0 is the molar volume at the reference temperature (see Table 1) Note that the linear thermal expansion corresponds to the average of the thermal expansion along the three crystallographic axes 2.01.4.2 Electrical Resistivity of the Crystalline State The electrical resistivity (r) of the elements Th to Cm has been measured in the cryogenic temperature range and the values up to 300 K are shown in Table The enthalpy of formation (kJ molÀ1), the absolute entropy (J KÀ1 molÀ1), and the heat capacity (J KÀ1 molÀ1) of lanthanide and actinide gas phases Df H0(298.15) S0 (298.15) Cp ¼ A þ B  T (K) þ C  T2 (K) þ D  T3 (K) þ E  T4 (K) þ F  TÀ2 (K) A Pa U Np Pu Am Cm 602 Ỉ – 548 Ỉ 26 – 533 Ỉ – 470 Ỉ – 348.9 Ỉ 3.0 – 285.5 Ỉ 3.0 – – 389 Ỉ 10 – 190.171 Ỉ 0.050 – 198.11 Ỉ 0.10 – 199.79 Æ 0.10 – 197.72 Æ 0.10 – 177.19 Æ 0.10 – 194.66 Ỉ 0.20 – – 197.58 Ỉ 0.20 – 28.7108 29.8483 21.3965 25.7107 35.1688 4.9298 28.7334 68.4689 24.2954 À112.0172 20.786 19.9856 268.8101 26.1234 22.3529 C À3 À33.4618  10 9.3756  10À3 8.1883  10À3 15.7656  10À3 À32.2466  10À3 10.4892  10À3 À41.2476  10À3 À48.7544  10À3 À37.0413  10À3 187.5714  10À3 – 0.0434  10À3 À179.4359  10À3 24.8448  10À3 1.7417  10À3 Source: Konings, R J M.; Benesˇ, O J Phys Chem Ref Data 2010, 39, 043102 D À6 45.7409  10 À2.1081  10À6 1.8634  10À6 À5.6052  10À6 27.0474  10À6 3.7043  10À6 76.2347  10À6 28.4161  10À6 95.1224  10À6 À86.6780  10À6 – 1.6974  10À6 45.9178  10À6 À45.9572  10À6 À0.4385  10À6 À9 À14.1005  10 0.2225  10À9 À1.0847  10À9 0.5709  10À9 À5.3433  10À9 À0.7598  10À9 À45.8415  10À9 À6.1153  10À9 À65.8404  10À9 18.8245  10À9 – À1.5984  10À9 À3.5637  10À9 21.6951  10À9 0.2286  10À9 E F – – – – – – 9.9079  10À12 4.4618  10À13 16.2344  10À12 À1.5431  10À12 – 4.4407  10À13 – – – À1.4548  105 À1.3137  107 À9.4644  104 À1.1144  107 À3.6652  105 6.8108  106 À1.1134  105 À1.6109  107 6.7865  104 2.7817  107 – 2.1403  105 À1.7767  108 À1.7020  104 2.6514.106 298–1400 1400–4000 298–1800 1800–4000 298–1800 1800–4000 298–1400 1400–4000 298–1400 1400–4000 298–900 900–2400 2400–4000 298–1000 1000–4000 The Actinides Elements: Properties and Characteristics Th B Temperature range (K) 13 The Actinides Elements: Properties and Characteristics Figure 17, which reveals a strong variation Th, Pa, U, Np, and Am show a regular increase from K to room temperature, typical for nonmagnetic metals in which transport carriers (electrons) are scattered by phonons (lattice vibrations) Pu and Cm show, however, a different behavior The electrical resistivity of a-Pu has a maximum of about 150 mO cm at about 100 K Boring and Smith71 argue that this high value is an indication of enhanced scattering of conduction electrons caused by electron correlations involving spin and charge interactions Curium is the first actinide metal that is magnetic a-Cm orders antiferromagnetically below 65 K,72 while its high-temperature phase, b-Cm with fcc structure, presents ferromagnetic order above 200 K similarly to Gd, its 4f counterpart The change in the resistivity curve occurs around the ordering temperature, which is similar to that in magnetic rare earth metals and especially Gd The electrical resistivity of the actinide metals above ambient temperature is well known for the major actinides Chiotti and coworkers73 showed that this property is very sensitive to impurities in the samples, Fm Cf –10 2.01.4.3 Thermopower of the Crystalline State The thermopower (S) has been reported for the elements Th to Pu in the cryogenic range and up to 300 K.74 Figure 19 shows the values and the sign of S for the a-phase of these actinide elements It can be observed that it varies from Th to Pu and depends strongly on temperature range As no carrier is available at K, S is reduced when approaching very low temperatures The thermopower of U and Np at high temperature shows discontinuities at the structural phase transition (a–b and consecutive).65 The hightemperature thermopower of Pu is not well known and is very sensitive to impurities Experimental Am Bk Pu Ac Np Pa Cm DL/L (%) –30 –40 –20 lnp (bar) Es particularly carbon Sahu et al.64 reported measurements for high purity a-Th in a wide temperature range, and Arajs et al.65 for uranium up to 1000 K, covering the a-, b, and g-phases Sandenaw and Gibby67 reported measurements for plutonium from 27 to 800 K, covering all allotropes A large decrease was observed for the a- to b-transition, as shown in Figure 18 Neptunium shows a similar behavior as Pu The recommended values are summarized in Table U Th (100) (001) DL/L (%) 14 (001) –50 (100) (010) –1 –60 0.0005 0.0006 0.0007 0.0008 0.0009 0.0010 1/T (K–1) DsubHЊ(298.15 K) (kJ mol–1) 500 700 900 300 T (K) Figure 14 The vapor pressure of the actinide elements, calculated from assessed thermochemical data 800 –1 300 600 900 1200 T (K) Figure 16 The thermal expansion of U (left) and Pa (right) along the different crystallographic axes La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu 600 400 200 Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Figure 15 The sublimation enthalpy at T ¼ 298.15 K of the lanthanide () and actinide (○) metals The estimated values are indicated by  The Actinides Elements: Properties and Characteristics Table Linear thermal expansion (DL/L0) of the actinide metals; L0 refers to 293 K DL/L0 (T) ẳ a ỵ b T (K) ỵ c T2 (K) ỵ d T3 (K) Th Pa U a a a b g a b a b g d d0 e liquid a a Np Pu Am Cm Table References a b c d À2.80Â10À3 À3.745Â10À3 À3.79Â10À3 8.04Â10À5 À1.49Â10À3 À8.381Â10À3 À1.258Â10À2 À9.291Â10À3 2.561Â10À3 3.279Â10À2 7.437Â10À2 0.1189 5.241Â10À2 2.912Â10À2 À2.315Â10À3 À3.262Â10À3 8.190Â10À6 1.555Â10À5 1.264Â10À5 1.729Â10À5 1.775Â10À5 2.848Â10À5 5.282Â10À5 1.266Â10À5 4.249Â10À5 3.469Â10À3 1.208Â10À6 À6.510Â10À3 1.325Â10À3 3.010Â10À3 6.965Â10À6 1.094Â10À5 5.286Â10À9 À1.144Â10À8 À8.982Â10À10 À1.432Â10À12 6.794Â10À12 6.844Â10À12 4.382Â10À11 À1.239Â10À12 7.498Â10À8 À1.048Â10À7 À2.952Â10À11 1.608Â10À8 1.782Â10À9 5.926Â10À12 3.176Â10À9 U Np Pu a a a b g a b g a b g d d0 e 61 61 61 61 61 68 68 62 62 62 62 62 62 62 69 53 Electrical resistivity of the actinide metals r (mV cm) ẳ a ỵ b T (K) ỵ c T2 (K) ỵ d T3 (K) ỵ e T4 (K) Th 15 a b c d À1.8305 À18.312 22.455 16.971 67.819 86 À94 110 158.09 117.18 108.87 90.22 À75.08 106.4 0.0593 0.1064 À4.5806Â10À2 8.6655Â10À2 À3.1502Â10À2 0.415 0.7217 À3.3116À3 3.2797Â10À4 À3.8929Â10À9 À4.6720Â10À5 1.8947Â10À5 À1.5Â10À4 3.333Â10À7 À8.5Â10À4 À0.0411 À0.0245 À0.0089 0.0072 0.2315 results indicate that the actinide metals have thermopower values close to those of the lanthanides75 but larger than the transition metals This essentially can be related to large band structures and a huge density of states at the Fermi level 2.01.4.4 Thermal Conductivity of the Crystalline State The thermal conductivity of the actinide metals varies strongly within the series This is particularly true at low temperatures for which the data for a-Th and a-Pu differ by two orders of magnitude, Temperature range (K) References e 1.4372Â10À10 300–800 800–1300 300–941 941–1049 1049–1400 300–553 553–850 850–900 300–399 399–488 488–596 596–741 741–759 759–913 63 63 64 64 64 65 65 65 66 66 66 66 66 66 as shown in Figure 20 This trend is opposite to that for the electrical conductivity and is in line with the Wiedemann–Franz law that states that the ratio between thermal conductivity and electrical conductivity (s ¼ 1/r) is a constant for any temperature (l=s ¼ LT , where L is the Lorenz number, 2.44 Â10À8 W O KÀ2) One can notice that thermal conductivity of Pu at 100 K is the lowest reported for any pure metal (3.5WmÀ1KÀ1) Experimental data for high temperatures are known only for the major actinides Th, U, and Pu in a reasonable temperature range, whereas the measurement for Np is made close to room temperature 16 The Actinides Elements: Properties and Characteristics 15 160 Pu α-Pu 140 Cm α-U Np 100 80 Am S (μV K–1) r (μΩ cm) 120 10 60 40 U α-Np Pa Th 20 α-Th –5 50 100 150 200 250 300 –10 50 100 150 200 250 300 350 T (K) T (K) Figure 17 The low-temperature electrical resistivity of the actinide elements Reproduced from Schenkel, R Solid State Comm 1977, 23, 389–392 Figure 19 The thermopower below 300 K of the actinide elements Reproduced from Meaden, G T Proc Roy Soc Lond 1963, 276A, 553–570 500 300 180 100 140 α-Np β-Np r (μΩ cm) 120 l (W m–1 K–1) 160 γ-Np 100 80 a-Th 50 a-U 30 10 β-U α-U 60 a-Np γ-U 40 a-Pu 20 400 600 800 T (K) (a) 1000 1200 1400 α-Pu r (μΩ cm) β-Pu 100 ε-Pu γ-Pu δ-Pu δЈ-Pu 80 60 α-Th 40 20 (b) 40 60 80 100 Figure 20 The low-temperature thermal conductivity of the actinide elements Reproduced from Lee, J A.; Waldron, M B Contemp Phys 1972, 13, 113–133 140 120 20 T (K) 180 160 400 600 800 T (K) 1000 1200 Figure 18 The high-temperature electrical resistivity of the actinide elements (Figure 21) The recommended equations are given in Table 10 The values for Th, taken from the assessment by Touloukian and coworkers,76 show a slight increase with temperature It should be noted that our graphs show a discrepancy between the lowand high-temperature data near T ¼ 300 K, which is probably related to the purity of the samples, as it is known that the properties of thorium metal are highly sensitive to carbon impurities.73 The values for U, also from the assessment by Touloukian and coworkers,76 are based on a set of several concordant The Actinides Elements: Properties and Characteristics measurements and cover the temperature range for the a-, b-, and g-phases but not show distinct differences Thermal conductivity data above ambient temperature exist for all crystal phases of plutonium The data for a-Pu from 100 to about 400 K were reported by Sandenaw and Gibney.40 However, the agreement with other values at ambient temperature is poor, which might be due to the differences in purity and to the accumulated radiation damage Wittenberg and coworkers77,78 measured the thermal diffusivity (D) of the d, d0 , and e phases from which they derived the thermal conductivity, which was found to be constant in all three cases However, the numbers in the early publication78 for the thermal diffusivity are different from those in the later publication.77 The values in Table 10 are taken from the latter work, which we consider to be the final results Note that only the early values are cited in the 60 β-U γ-U l (W m–1K–1) 40 α-U 30 δЈ-Pu 20 γ-Pu δ-Pu ε-Pu β-Pu 10 Pu-liq α-Pu Np 100 200 300 400 500 600 T (K) 700 800 900 1000 1100 Figure 21 The thermal conductivity of the actinide elements Table 10 2.01.4.5 Thermal Conductivity of the Liquid State Only data available for the thermal diffusivity and conductivity of the liquid state of plutonium have been reported Wittenberg and coworkers77,78 measured the thermal diffusivity (D) from which they derived the thermal conductivity, which is constant in the measured range (973 to 1073 K) As discussed above, the two publications by these authors are not consistent In the early one,78 Wittenberg gave 0.017–0.021 and 0.022–0.023 cm2 sÀ1 for the thermal diffusivity in two experiments with different heating Thermal conductivity (W mÀ1KÀ1) of the actinide metals above room temperature Phase Th U Np Pu Gmelin review from 1976.66 As discussed by Wittenberg, the data indicate that the thermal conductivity of the g- and d-phases are nearly the same (13 Ỉ 1) WmÀ1 KÀ1 These trends are in qualitative agreement with the electrical resistivity measurements, as discussed in Section 2.01.4.2 Wittenberg also noted that the large decrease in the thermal conductivity of the e-phase is not expected to be comparable with the electrical resistivity measurements, and he suggested that this value may be too low as a result of the difficulty in maintaining good thermal contact after the volume contraction during the d- to e-phase transformation Although the Wiedemann–Franz law states that the ratio between thermal conductivity and electrical conductivity is almost constant for metals, it was shown that the value for l/sT at T ¼ 298 K varies regularly in the lanthanide series, as shown in Figure 22 The values for Th, U, and Np are close to the Lorenz value, and that of Pu is slightly higher The values for Am and Cm in this figure are suggestions,79 assuming that the thermal conductivity of Cm is close to that of Gd α-Th 50 17 a b g d, d0 e Liquid l ẳ a ỵ b T (K) ỵ c T2 (K) ỵ d T3 (K) a b c d 48.101 19.019 4.18 2.264 15.4 3.54 6.94 0.44 16.5 0.00336 0.03256 À1.8235Â10À5 1.0343Â10À5 0.00696 2.5332Â10À5 0.02 0.01 0.01 T (K) References 100–1000 100–100 300 100–399 399–488 488–596 596–759 759–913 913–1073 75 75 75 75 66 76 76 76 76 18 The Actinides Elements: Properties and Characteristics La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu (l/sT) ϫ 108 (WW K−2) Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Figure 22 The variation of l/sT of the actinide (○) and lanthanide () metals The estimated values are indicated by  rates, yielding to l ¼ 5.4 WmÀ1 KÀ1 and 6.3 WmÀ1 KÀ1, respectively In the later publication,77 Wittenberg reports D ¼ 0.057–0.056 cm2 sÀ1 for the temperature range 948 to 1073 K, yielding l ẳ (17ặ1) Wm1 K1 This latter value is recommended here 2.01.4.6 Density of the Liquid State The density of liquid uranium was measured by Grosse et al.,80 Rohr and Wittenberg,81 and Shpil’rain et al.82 The results of the latter two studies are in very good agreement but deviate significantly from the results of Grosse et al., which has been explained by errors caused by surface tension forces in the hydrostatic weighing method used in that work.83 We have therefore selected the combined results from Rohr and Wittenberg81 and Shpil’rain et al.,82 as recommended by the latter authors: rkg m3 ị ẳ 20332 2:146T Kị ẵ4 The density of liquid plutonium was measured by Olsen et al.84 and Serpan and Wittenberg.85 The results are very close and the average of the two equations is recommended: rkg m3 ị ẳ 18004 1:486T Kị 2.01.4.7 ½5Š The viscosity of liquid plutonium was reported in several studies, and the following equation is the recommended representation of the results87: log10 ZcPị ẳ 672=T Kị ỵ 0:037 ẵ7 These equations give for the viscosity at the melting point 6.5 cP for uranium and 6.0 cP for plutonium These values are somewhat higher than the values predicted by Grosse,88 who used an empirical relationship between the activation energy for viscosity for liquid metals and their melting points, to obtain 5.9 cP for U, 4.5 cP for Pu, and 5.0 cP for Th at the melting point 2.01.4.8 Surface Tension The surface tension of liquid uranium was measured by Cahill and Kirshenbaum89 from 1406 to 1850 K The results can be represented by the equation: sN m1 ị ẳ 1:747 0:14103 T Kị ẵ8 This equation yields 1.55 Nm1 at the melting point The surface tension of plutonium was reported by Olsen et al.84 These authors obtained s(N mÀ1) ¼ 1.29À0.967Â10À3 T(K), yielding 0.40 N mÀ1 at the melting point It has been suggested that this value is too low because of dissolved tantalum Spriet49 reported the surface tension of liquid plutonium to be 0.55 N mÀ1, which is generally accepted Viscosity The viscosity of liquid uranium and plutonium has been measured using a direct oscillating method by researchers at the Mound Laboratory in the 1960s These data are still the only available to date For liquid uranium, Ofte86 reported: log10 ZcPị ẳ 1587:7=T K1 ị 0:3243 ẵ6 2.01.5 Summary and Outlook The actinide elements pose a very interesting paradox Uranium and especially plutonium are materials that are very difficult to handle because of their radioactive nature, but they are among the most The Actinides Elements: Properties and Characteristics extensively studied elements in the periodic table This is of course due to the importance of these two elements in nuclear technology The properties of the other actinides are relatively poorly known and are generally obtained from estimations However, due to the changes in the electronic properties of the 5f electrons, varying from delocalized to localized, going from Th to Am, the systematics in the properties of the actinides are difficult to predict, and analogies with the 4f lanthanides are not (always) obvious Theoretical predictions based on atomistic calculations could help to solve this, but the predictive potential of such calculations is still being explored Clearly, more experimental studies are needed, particularly on the minor actinides 21 22 23 24 25 26 27 28 29 References 10 11 12 13 14 15 16 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333–339 Cahill, J A.; Kirshenbaum, A D J Inorg Nucl Chem 1965, 27, 73–76 Spriet, B Mem Etud Sci Rev Met 1963, 60, 531  ... states of the actinide elements Th Pa U Np Pu Am Cm State Spectroscopic term Energy level (cmÀ1) 6d27s2 6d27s2 6d27s2 6d27s2 6d27s2 5f26d7s2 5f26d7s2 5f26d7s2 5f6d27s2 5f26d7s2 5f36d7s2 5f36d7s2 5f36d7s2... 5f36d7s2 5f36d7s2 5f36d7s2 5f46d7s2 5f46d7s2 5f46d7s2 5f46d7s2 5f46d7s2 5f67s2 5f67s2 5f67s2 5f67s2 5f56d7s2 5f77s2 5f66d7s2 5f66d7s2 5f76d7s 5f77s2 5f76d7s2 5f76d7s2 5f76d7s2 5f76d7s2 5f76d7s2 25 58.06... (K) A B 23 .435 15.7 02 46 21 .6 522 39.7 47.3 28 . 426 4 47. 12 61.6 420 46.45 30.1 32 40 36 46 17.6186 27 .4160 22 . 023 3 28 .4781 35.56 33. 72 42. 80 30.0399 8.45 72 43 52 28.409 28 .2 37 .2 8.945  10À3 11.950