Actinides in Solution: Nuclear Waste, Strong Correlations, and Emergence

Size: px

Start display at page:

Download "Actinides in Solution: Nuclear Waste, Strong Correlations, and Emergence"

Meghan Rich
5 years ago
Views:

1 University of Toronto April 5, 2007 Actinides in Solution: Nuclear Waste, Strong Correlations, and Emergence Brad Marston Department of Physics Brown University Collaborator: Steve Horowitz Support: NSF DMR /

2 Migration of plutonium in ground water at the Nevada Test Site, A. B. Kersting et al. Nature 397, 56 (1999)

3 IPCC 2001

5 (a) Absorption of only one neutron per nuclear reaction leads to sustainable nuclear power. Neutron absorbed Neutrons emitted, energy released (b) Absorption of more than one neutron per nuclear reaction can lead to an exponentially increasing number of nuclear reactions and a powerful explosion.

Challenges in Plutonium Science Los Alamos Science Number 26, 2000 Lowenriched U Enrichment Fabrication of UO 2 fuel Lowenriched U Reactor Volume I Historical Introduction Condensed-Matter Natural

6 Challenges in Plutonium Science Los Alamos Science Number 26, 2000 Lowenriched U Enrichment Fabrication of UO 2 fuel Lowenriched U Reactor Volume I Historical Introduction Condensed-Matter Natural Physics U Plutonium Aging Conversion to UF 6 U mines and mills OPEN FUEL CYCLE Spent-fuel rods Volume II Plutonium Metallurgy Actinide Chemistry and the Environment The Yucca Mountain Project Spent-fuel waste repository

Neutron-radiative capture (10 16 s) Beta decay (23 min) 238 239 239 n + 92 U 92U* 92 U +! U X + e + $ 92 93 239 239 e 238 92U 239 92U* 239 92U 239 93X $ Slow neutron is absorbed.

7 Neutron-radiative capture (10 16 s) Beta decay (23 min) n + 92 U 92U* 92 U +! U X + e + $ e U U* U X $ Slow neutron is absorbed. Compound nucleus forms in an excited state. Compound nucleus cools down by radiating!-rays. Unstable uranium nucleus in its ground state #-decays to element 93. Cells (b) Tissue wall Charged alpha particle Neutral helium atom Alexander Litvinenko: 210 Po poisoning 30 µm

$tuff itself provides desirable containment characteristics, and the fracture zones in this area contain zeolites and other minerals that have a$ high sorption affinity for most of the actinides.

high sorption affinity for most of the actinides.

least 10,000 years to migrate to the water table (saturated zone).

8 Infiltration (a) Unsaturated rock (~600 m) Potential repository and engineered barrier system Saturated rock Flow of groundwater (b) (c) The tuff itself provides desirable containment characteristics, and the fracture zones in this area contain zeolites and other minerals that have a high sorption affinity for most of the actinides. Based on extensive field data and state-of-the-art modeling of worst-case scenarios, researchers have predicted that the waste would take at least 10,000 years to migrate to the water table (saturated zone). This prediction is consistent with experience at the nearby Nevada Test Site, which indicates that the mobility of radionuclides is generally very small that is, for the most part, the actinides injected into underground test holes from nuclear explosions have remained close to where they were deposited. However, recent

$Am Cs Pu Am Sorption to fracture minerals Mineral coating ROCK MATRIX F R A C T U$ waste Np U Am Sorption to different colloids Colloid transport Np Dissolving

waste Np U Am Sorption to different colloids Colloid transport Np Dissolving

9 Am Cs Pu Am Sorption to fracture minerals Mineral coating ROCK MATRIX F R A C T U R E Am Cs Tc Diffusion into solid matrix U Desorption from colloids Dissolving waste Np U Am Sorption to different colloids Colloid transport Np Dissolving solid Precipitate Np Different species Np Pu Solubility and speciation Sorption to tuff

10 Photo: LBL

11 Outline Actinides in solution Disproportionation and negative-u 5f orbitals are chemically active due to relativity Density functional theory calculations Inclusion of spin-orbit interaction & strong correlations Environmental chemistry of Yucca Mountain Conclusions and open questions

12 Reduction-Oxidation (Redox) Electrochemistry Primer H 2 (g) + F 2 (g) 2 H F 2H + (aq) + 2F (aq) oxidizing half-reactions reducing F 2 (g) + 2e 2 F (aq) 2.87 V 2 H + (aq) + 2e H 2 (g) 0 V Na + (aq) + e Na(s) V

13 Pu(VI) PuO V Pu(V) 1.04V 1.01V Pu(III) Pu(IV) PuO + 2 Pu 3+ Pu V Pu(0) 0.99V 1.25V IV 0.8 Fraction III Fraction IV III 0.2 VI 0.2 VI V Time (M s) V ph David Clark, The Chemical Complexities of Plutonium, in Los Alamos Science: Challenges in Plutonium Science Vol. II No. 26 (2000).

14 Formal Oxidation States Table I. Oxidation States of Light Actinides a Th Pa U Np Pu Am Cm III III III III III III III IV IV IV IV IV IV IV V V V V V VI VI VI VI VII VII a The environmentally most important oxidation states are bolded. W. Runde, The Chemical Interactions of Actinides in the Environment, in Los Alamos Science: Challenges in Plutonium Science Vol. II No. 26 (2000).

15 Disproportionation Reactions 2 E n+ E (n+1)+ + E (n 1)+ 2Pu H 2 O Pu 3+ + PuO H + Pu 4+ + PuO 2 + Pu 3+ + PuO2 2+ 2PuO H + Pu 4+ + PuO H 2 O

16 Ionization levels and negative-u Atomic limit of Hubbard model Ĥ eff = ɛ a n + Un n 0, n = 0 E 0 = ɛ a, n = 1 2ɛ a + U, n = Na(gas) (U > 0) Na in NH3 (U < 0) Na 0 Na 0 2 Na + Na -

17 Examples of negative-u Alkali metals in liquid ammonia Other metal ions in aqueous solution: In 2+ and Sn 3+ Doped chalcogenide glasses [P. W. Anderson 1975] Indium in lead telluride Interstitial boron or vacancies in silicon (Watkins) G. D. Watkins, Negative-U properties for defects in solids Festkörperprobleme (Advances in Solid State Physics) XXIV, p.163 P. Grosee (ed.) (Vieweg, Braunschweig 1984).

18 Alkali metals Alkali-earth metals d-block elements Nonmetals Semimetals Noble gases Lanthanides Actinides H Li Na K Rb Cs Fr s d p 2 Be Mg Ca Sr Ba Ra Sc Y La Ac Lanthanides Actinides Ti Zr Hf V Nb Ta Cr 42 Mo 74 W Mn 43 Tc 75 Re Fe Ru Os Co Rh Ir Ni Pd Pt Cu Ag Au Rf Ha Sg Ns Hs Mt Ce Pr f Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Zn Cd Hg B Al Ga In Tl C Si Ge Sn Pb N P As Sb Bi O S Se Te Po F Cl Br I At He Ne Ar Kr Xe Rn Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

19 Actinide Configuration Ac actinium 6d 1 7s 2 Th thorium 6d 7s 2 Pa protactinium 5f 2 6d 1 7s 2 U uranium 5f 3 6d 1 7s 2 Np neptunium 5f 4 6d 1 7s 2 Pu plutonium 5f 6 7s 2 Am americium 5f 7 7s 2 Cm curium 5f 7 6d 1 7s 2 Bk berkelium 5f 9 7s 2 Cf californium 5f 10 7s 2 Es einsteinium 5f 11 7s 2 Fm fermium 5f 12 7s 2 Md mendelevium 5f 13 7s 2 No nobelium 5f 14 7s 2 Lr lawrencium 5f 14 6d 1 7s 2

20 (a) 1.2 Sm f Relativistic Nonrelativistic P(R) 0.6 5d 6s 0.4 6p (b) f Pu 3+ a 0 = h2 me d Relativistic Nonrelativistic P(R) 7s 0.4 7p Radius (Å) 3 4

21 Approximate treatment of 5f-systems with partial localization due to intraatomic correlations, E. Runge, P. Fulde, et al., Phys. Rev. B69, (2004) Disproportionation in a Model of Partially Localized 5f Electrons

22 XAFS = X-ray Absorption Fine Structure (a) Pu(III,IV): Cube Pu(III,IV): Square antiprism Pu(III,IV): Dodecahedron (b) Pu(III,IV): Tricapped trigonal prism (c) Pu(V,VI): Pentagonal bipyramid (d) Pu(VII): Tetragonal bipyramid

23 O=An=O Actinyl Ion Self-Consistent Picture Antibonding molecular orbital (not filled) Oxygen 2p z atomic orbital Uranium 5f z atomic orbital 3 U 6+ O 2 O Oxygen 2p z atomic orbital Electron pair Bonding molecular orbital (filled) U O! u molecular orbital of O=U=O P. J. Hay and R. L. Martin, Computational Studies of Actinide Chemistry, in Los Alamos Science: Challenges in Plutonium Science Vol. II No. 26 (2000).

24 Redox Reactions PuO 2 (H 2 O) 2+ 5 (VI) H 2(g) + H 2 O PuO 2 (H 2 O) + 5 (V) + H 3O + Pu(H 2 O) 4+ 8 (IV) H 2(g) +H 2 O Pu(H 2 O) 3+ 8 (III) + H 3O + PuO 2 (H 2 O) + 5 (V) + 3 H 3O H 2(g) Pu(H 2 O) 4+ 8 (IV) + 2 H 2O

25 Density Functional Theory (DFT) Ĥ Ψ 0 = E 0 Ψ 0 n( r) = N Ψ( r, r 2,..., r N ) 2 d 3 r 2 d 3 r 3 d 3 r N E[n( r)] = Ψ Ĥ Ψ

26 DFT Ingredients Use ADF ( with n=4 frozen cores Scalar ZORA relativity (spin orbit included later) Unrestricted spin Revised Perdew-Burke-Ernzerhof (RPBE) exchange-correlation functional Geometry relaxation Vibrational modes contribute to free energy First solvation sphere treated quantum mechanically Beyond first solvation sphere: use conductor-like screening (COSMO) solvation model

27 Zero Order Regular Approximation (ZORA) E = m 2 0 c4 + p 2 c 2 + V ( r) Ẽ E m 0 c 2 = m 0 c 2 ( p 2 2m p2 m 2 0 c2 1 p4 8m 3 0 ) c V ( r) + V ( r) p < m 0 c

28 Ẽ = = = = E < 2m 0 c 2 V ( r) V ( r) Ze2 r m 2 0 c4 + p 2 c 2 m 0 c 2 + V ( r) p 2 c 2 m 0 c 2 + m 2 0 c4 + p 2 c 2 + V ( r) 2m 0 c 2 + p 2 c 2 Ẽ V ( r) + V ( r) p 2 c ( 2 (2m 0 c 2 V ( r)) 1 + ) + V ( r) Ẽ 2m 0 c 2 V ( r) Ẽ ZORA p 2 c 2 2m 0 c 2 V ( r) + V ( r)

29 Pu(H2O)83+ PuO2(H2O)52+

30 Oxidation State DFT Results Pu-O distance (Angstroms) Hay, Martin, & Schreckenbach This work Experiment (XAFS) V VI Pu-OH2 distance (Angstroms) Oxidation Hay, Martin, & State Schreckenbach This work Experiment (XAFS) III IV V VI

31 DFT Results (cont.) Reduction-Oxidation Potentials (volts) -- No spin orbit Reduction Reaction Hay, Martin, & Schreckenbach This work Experiment VI to V V to IV IV to III P. J. Hay, R. L. Martin, and G. Schreckenbach, Theoretical studies of the properties and solution chemistry of AnO2 2+ and AnO2 + aquo complexes for An = U, Np, and Pu, J. Phys. Chem. A 104, (2000).

32 Spin-Orbit Interaction from ZORA Ĥ SO = λ SO l s + α { 0.1 ev, j = 5/2 E 0.9 ev, j = 7/2 Redox Potentials (volts) With Spin-Orbit Interaction Reduction Reaction Hay, Martin, & Schreckenbach This work Experiment VI to V V to IV IV to III

33 Shamov and Schreckenbach, J. Phys. Chem. A 109, (2005). Figure 4. Calculated and experimental [AnO 2 (H 2 O) 5 ] 2+ /[AnO 2 - (H 2 O) 5 ] 1+ reduction potentials according to Table 10. Calculated values without and with the inclusion of spin-orbit and multiplet corrections are shown; see text. (Dark red diamonds) LC-ECP-B3LYP values from ref 20; (red circles and blue triangles) SC-ECP-B3LYP and Priroda- PBE values without the corrections; (orange stars and light blue crosses) SC-ECP B3LYP and Priroda PBE values with the corrections applied, correspondingly; (green squares) experimental values 87 as cited from ref 20.

35 Toy Model of Strong Correlations Ĥ = e f σ f σ t (f σ c σ + H.c.) + U f f f f c t f U, e Uf f f f = Un n U ( n n + n n n n ) U HF ( n, n) = U 2 n n U 4 n 2

36 t = 1, e = -8 Ground State Energy Calculation Exact Hartree-Fock -8 Energy U

37 Strong Correlations Between 5f Electrons M. X. LaBute, R. G. Endres, and D. L. Cox, An Anderson impurity model for efficient sampling of adiabatic potential energy surfaces of transition metal complexes, J. Chem. Phys. 121, 8221 (2004). Ĥ el el = I m1,m 2,m 3,m 4 f m σ1 1 f σ 2 m 2 f m3,σ 2 f m4,σ 1 m 1 m 2 m 3 m 4 m 1 +m 2 =m 3 +m 4 I m1,m 2,m 3,m 4 = L=0,2,4,6 Gaunt coefficients F L c (L) (m 1, m 4 ) c (L) (m 2, m 3 ) Slater-Condon parameters

38 Tight-Binding Model of Pu(5f) and O(2p) Orbitals Kohn-Sham molecular orbitals may be expressed as a linear combination of (orthonormal) Lowdin atomic orbitals. Project onto 5f-2p subspace. Ĥ = z 3,xz 2,... i,j t σ σij ( f σ i ) f jσ + H.c. Pu(H2O)8: 14 independent-particle states PuO2(H2O)5: 26 independent-particle states Sparse matrices with up to 500 million matrix elements

39 Slater-Condon Parameter F0 = U Ionization Reaction Experiment (ev) DFT (ev) Pu 3+ to Pu 4+ + e PuO2 + to PuO e (4) 15.65

40 Slater-Condon Parameters F2, F4, and F6 M. Norman, Calculation of effective Coulomb interaction for Pr 3+, U 4+, and UPt3, PRB52, 1421 (1995) I. S. Poirot et al., Optical study and analysis of Pu 4+ in single crystals of ZrSiO4, PRB39, 6388 (1989)

41 Toy Model of System / Environment Ĥ = e f σ f σ t (f σ c σ + H.c.) + U f f f f c t f U, e Uf f f f = Un n U ( n n + n n n n ) U HF ( n, n) = U 2 n n U 4 n 2

42 E corrected 0 (n) = E HF 0 U HF ( n, n) + U 2 (n2 n) n = 1 + x E corrected 0 = (1 x)e corrected 0 (1) + xe corrected 0 (2) t = 1, e = -8 U Exact <n> HF E(1) E(2) E

43 Ground State Energy Calculation Exact Hartree-Fock Corrected Energy U

44 Strong Correlations Alter Redox Potentials f σ 1 m 1 f m3 σ 2 f σ 1 m 1 f m3 σ 2 f σ 1 m 1 f m3 σ 2 0 Ĥel el 0 = 0 Redox Potentials From Hubbard Model Model VI to V (volts) V to IV (volts) IV to III (volts) DFT + SO Hubbard (F0 = 3 ev) Experiment

45 Yucca Mountain

47 Complexation Follows Effective Ion Charge An 4+ (IV) > An 3+ (III) AnO 2+ 2 (VI) > AnO+ 2 (V) More Oxidizing Environment Redox potential, Eh (volts) PuO 2 F + 2+ PuF 2 Pu 3+ Pu(III) Pu(IV) Pu(V) Pu(VI) natural waters PuO 2 CO 3 (aq) 2 PuO 2 (CO 3 ) 2 4 PuO 2 (CO 3 ) 3 PuO + 2 PuO 2 (OH 2 ) 2 (aq) PuO 2 CO 3 PuO 2 OH(aq) Rain/streams Ocean Groundwater Pu(OH) 4 (aq) + PuOH 2 O H e 2 H 2 O 1.23 V 2 H 2 O + 2 e H OH V ph

NpO 2 (CO 3 ) 3 5 The Np(IV) species Np(H 2 O) 8 4+ Redox reactions change an actinide's oxidation state and help to establish equilibrium between species Redox Complexation Complexation with

48 NpO 2 (CO 3 ) 3 5 The Np(IV) species Np(H 2 O) 8 4+ Redox reactions change an actinide's oxidation state and help to establish equilibrium between species Redox Complexation Complexation with different ligands can stabilize actinides in solution and enhance their transport through the environment Transport Microbes can facilitate actinide redox processes, while sorption or uptake by the microbes may be a potential transport or immoblilzation mode. Bioavailability Actinides typically form large molecular complexes in solution. Neptunium assumes the Np(V) species, NpO 2 (H 2 O) 5 +, in many natural waters. Dissolution Precipitation Actinides can migrate by water transport or by sorption onto mobile particulates or colloids Solvated actinide species can precipitate, forming a solid that in turn determines the upper concentration limit for the solvated species. Np(V) complex sorbed to montmorillonite Sorption At low actinide concentrations, sorption onto particulates, clays, or rock surfaces determines the environmental behavior. Actinides can also diffuse into rock, or coprecipitate with natural ligands and become incorportated into minerals NaNpO 2 CO 3 (s)

49 Conclusions & Open Questions Relativistic DFT calculations of aqueous actinides have been carried out. Evidence of strong correlations. Can better quantitative agreement be achieved? Will the same approach explain neptunium and americium? Organizing principle at work? Application to complexation with carbonates, etc.?

The Periodic Table. Periodic Properties. Can you explain this graph? Valence Electrons. Valence Electrons. Paramagnetism

The Periodic Table. Periodic Properties. Can you explain this graph? Valence Electrons. Valence Electrons. Paramagnetism Periodic Properties Atomic & Ionic Radius Energy Electron Affinity We want to understand the variations in these properties in terms of electron configurations. The Periodic Table Elements in a column