J. MATER. CHEM., 1991, 1(3), 415-421 Computer-simulation Study of Alkali-metal Insertion into a-lJ30, Richard G. J. Ball*"nb and Peter G. Dickens" a Inorganic Chemistry Laboratory, South Parks Road, Oxford OX1 3QR, UK Materials and Chemistry Division, AEA Technology, Harwell Laboratory, Oxfordshire OX1 1 ORA, UK Atomistic simulation techniques have been used to study the insertion of lithium and sodium into a-U,O,. Calculations for isolated guest ions predict that lithium will occupy five-co-ordinate trigonal bipyramidal sites whereas sodium will occupy nine-co-ordinate sites. The modelling of the stoichiometric phases MU,08 (M=Li, Na) reinforces these predictions. Calculations of ion migration are presented; lithium is demonstrated to be fairly mobile within the lattice whereas the diffusion of sodium is much more difficult. Keywords: Computer simulation; Uranium oxide; Intercalation; Defects; Interatomic potential 1.Introduction Over the last 40 years there has been considerable interest in the chemistry of the oxides of uranium, owing mainly to their importance in the nuclear industry. One area that has been under recent investigation is concerned with the insertion compounds of these Such compounds have a general formula A,UO, where A is an electropositive species, such as hydrogen or an alkali metal, which has been inserted into the host oxide UO, with minimal structural rearrange- ment. For such reactions to occur it is necessary for the host lattice to have suitable sites for the inserted species to occupy.In addition, it must be possible for the lattice to readily accommodate electrons from the guest, which is generally present as a cation. In both respects a-U308 is well suited to this type of reaction since it possesses a rather open pillared- layer structure, and uranium has a range of available oxidation states. In a recent paper we developed an atomistic model for simulating the structural and defect properties of a-U308e7 In the present work we extend this model to study the insertion of lithium and sodium into U308. Through these calculations we are able to investigate the possible sites occupied by the alkali metal and the various mechanisms for their migration through the host matrix. Similar computer- simulation studies have been reported for analogous insertion compounds of the transition-metal oxides Fe3048 and Wo3.' 2.Experimental At ambient temperatures a-U308 adopts a pseudo-hexagonal orthorhombic structure which consists of layers of edge- sharing U05 pentagons connected by -U-0-U-0- chains, which run perpendicular to the layers." At higher temperatures this polymorph undergoes a transition to the closely related hexagonal structure a'-U3O8.'' However, the difference between the a and a' forms of U308 is minimal and both are illustrated in Fig. 1, where the hexagonal unit cell of the a' form is shown by the dashed line. The pillared- layer nature of the structure of ar-U308 suggests that the intercalation of alkali metals between the layers should be reasonably facile.Indeed, both lithium and sodium insertion compounds of this oxide have been synthesized and the materials have been characterized in terms of their thermo- dynamic, structural and transport proper tie^.^* 9 '7' The U308structure is an archetype for a number of ternary -0-U-0-chain 0oxygen Fig. 1 The structure of cl-U308(z=O plane) layer structures consisting of planes of edge-sharing UO, and MO, polyhedra connected by metal-oxygen chains. Related structures are also to be found amongst non-uranium com- pounds; LiW309F,17'18 for example, consists of layers which are packed in a similar fashion to UNb3OI0. The insertion of lithium into UV05, UTi05 and LiW309F has recently been Thus, the study of alkali-metal inser- tion into U308 will be valuable for understanding insertion processes in a wide range of materials.2.1 Lithium Insertion The insertion of lithium into a-U308 has been studied by uranium oxide phases such as UVo5,l3 UTiOS, CUU~O~~'~ Dickens et u1.293*5Electrochemical measurements indicate that and UNb3010,15~16 all of which are thought to have pillared- single-phase regions for LixU308 exist for 0.78 <x <0.88 and 416 3.6 3.2 2a B2.L 2.0 1 . 2 1 - - I I I I 1 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2-1 x in Li,U,O, Fig. 2 Voltage versus composition curve for lithium insertion into a-U308 for 1.20 <x <1.26. A typical discharge curve is shown in Fig. 2, and consists of a number of plateaux, at which two phases coexist, separated by monophasic regions, where the emf changes smoothly with x.A pure phase of composition Lio.9U308 may be prepared chemically by lithiation with anhydrous LiI. X-Ray powder diffraction measurements on this phase show that there is very little structural rearrange- ment of a-U308 on insertion. The refined lattice parameters of Lio.9U308 are given in Table 1; the increase in the c lattice parameter is consistent with the accommodation of the lithium ions in interlayer sites. However, the precise location of the lithium ions cannot be determined by X-ray diffraction since the pattern is dominated by scattering from the heavy uranium ions. Fortunately, this problem does not arise with neutron diffraction and this technique has been used in a recent study to determine the intercalation sites in Lio.9U308.12 The enthalpy of insertion of lithium into a-U308 to form Lio.9U308 has been determined by solution calorimetry to be -298k4 kJ per mole of Li.’ This value is close to the Gibbs energy of insertion as obtained from electrochemical studies.’ Thermochemical measurements have also established that Lio.9U308 is stable with respect to disproportionation into Li2U3Ol0, U308 and U02.The thermodynamic stability is also supported by Kemmler-Sack and Riidorff” who have prepared materials (Li20);UO2 *U03 in the range 0.05 <x <0.45 (x =0.33 corresponding to the composition LiU308) at a temperature of 800 “C. These phases have lattice parameters that are close to those of either a- or a’-U308, depending on the value of x.The high-temperature phase discovered by Kemmler-Sack and Riidorff is likely to be closely related to the ambient temperature phase Lio.9U308 characterized by Dickens et The introduction of lithium ~1.~9~9’ ions into the a-U308 lattice and the consequent stabilization of the lattice has also been observed by Tsvigunov and Kuznetsov.22 Crude diffusion coefficients for lithium in Lio.9U308 have been measured by current pulse method^.^ The values Table 1 Experimental cell parameters of insertion compounds of a-U308 compound alA blA 4 reference a-U,o8 6.716 1 1.960 4.147 10 Li0.88u308 6.727 11.953 4.188 5 Na1.29U308 6.875 12.630 4.267 4 J.MATER. CHEM., 1991, VOL. 1 observed indicate a rapid lithium-ion transport, which is characteristic of the insertion compounds of layered materials. 2.2 Sodium Insertion The sodium insertion compound Na1.3U308 has been pre- pared4 and the X-ray diffraction pattern showed, as might be expected, that the increase in lattice parameters from the parent oxide is larger than that observed for lithium insertion (see Table 1). No thermochemical measurements have so far been carried out on Na,U308. 3. Insertion Calculations In the previous section it was seen that lithium and sodium can be inserted into a-U308 under ambient temperature conditions. Theoretical calculations can provide a valuable insight into these processes by examining the sites occupied by the guest species and the mechanisms for their migration through the host matrix.3.1 Theoretical Methodology The lattice simulation techniques employed in this work were described in detail in a previous paper.’ The defect calculations are based on a generalized Mott-Littleton procedure which divides the lattice into two regions: an inner region I, which incorporates the defect, and an outer region 11. In region I, the interactions between ions, as defined through interatomic pair potentials, are calculated explicitly, whereas in region I1 forces are calculated using a continuum model. Ions in region I are relaxed to zero force using a Newton-Raphson minimiz- ation procedure. An essential part of the procedure is the specification of the interatomic potentials.In this work short- range pairwise interactions are combined with long-range Coulombic interactions. The short-range repulsive interac- tions were calculated as a function of the interionic distance, r, by means of an electron-gas method.23 Each set of short- range interactions were then fitted to a Born-Mayer potential form: V”.‘*(r)=A exp (-r/p) to obtain the parameters A and p. The many-electron disper- sion interactions not accounted for in the electron-gas method were estimated using the Slater-Kirkwood formula24 and incorporated into the potential function as a -C/r6 term. The calculated interatomic potential parameters used in this study are given in Table 2. Alkali-metal-oxygen interatomic potentials have also been calculated by a similar method by Le~is,~’and Freeman and Catlow26 who obtained parameters which are close to the ones used in this work.Any slight differences between the two sets of potentials are attributable to the different oxide-ion densities used in the two studies. Ion polarization effects are taken into account by means of the shell This treats an ion as a massless shell of charge Y coupled to the core by means of a harmonic spring of force constant k. Shell-model parameters for the alkali metals were estimated from the free-ion polarizabilities, a, by assuming a shell charge of 1.0 atomic units and using the relationship: to obtain the force constants. The shell-model parameters used in this work are given in Table 3.Shell-model parameters for alkali-metal cations in the alkali-metal halides have also .~~been derived by Catlow et ~2 by empirical fitting techniques. J. MATER. CHEM., 1991, VOL. 1 Table 2 Potential parameters used in this study u5.33+ -ox 3023.3 1 0.33889 48.2 1 u5.33+ -0P 2963.89 0.34 165 48.2 1 u5+-ox 2866.86 0.34280 50.56 U~+-OP 2899.06 0.34184 50.56 ox-ox 154.30 0.43456 35.30 ox-OP 149.47 0.43842 35.30 OP-OP 144.78 0.44141 35.30 u5.33+ -u5.33+ 3 1002.05 0.24421 67.97 US+ -u5+ 27406.37 0.25 128 74.59 u5.33+-Li+ 3427.57 0.2 160 1 0.97 US+-Li+ 3282.06 0.21993 1.01 Li+ -OX 308.07 0.34619 0.63 Li+ -0P 322.80 0.34286 0.63U5.33+-Naf 11412.60 0.22198 3.86 U5+-Na+ 10452.24 0.22675 4.04 Na+-OX 876.08 0.33574 2.66 Na+ -0P 894.13 0.3 3465 2.66 NB OX denotes chain oxygens [0(1) and 0(2)] and OP denotes oxygens in the planes [0(3), O(4) and 0(5)].Table 3 Shell model and polarizability parameters u5.33+ 6.68 21 1.41 10.67 3.04 us+ 6.35 181.40 11.0 3.20 O2- -3.00 49.49 4.5 2.62 Li + I .oo 506.1 1 1.o 0.03" Na+ 1.oo 96.98 1.o 0.15" " Ref. 35. These alternative parameters were not used in the present work since, for lithium and sodium, they somewhat over- estimate the ionic polarizability which will be manifested in the C6van der Waals term of the interatomic potential. It should be noted, however, that a few test calculations were performed with the shell parameters of Catlow et al.but the results differed little from those presented in this paper. The model for U308 employs an average uranium-ion oxidation state of 53 to reproduce the nearly identical environ- ments observed around each uranium-ion site. The interac- tions calculated between isolated intercalated ions and the lattice therefore represent an average over the uranium sublat- tice. This is a valid approximation so long as the residence time of the guest ion in any one position is greater than the frequency of the charge transfer which is presumed to occur between the uranium ions. This is likely to be true of the guest ions when they are within their equilibrium sites but may not be true when they are migrating between sites. We therefore expect the calculation of structural properties to be more reliable than the calculation of the activation energies for migration.3.2 Intercalation Sites In the U308 structure we can identify two categories of site that may be occupied by the guest ions. With reference to Fig. 1, if the alkali metal sits directly between two oxygen ions in adjacent layers then it will occupy a distorted five-co- ordinate trigonal bipyramidal site as in Fig. 3. There is one such site above each of the three crystallographically distinct oxygen ions in the planes. The alternative site is the nine-co- ordinate position illustrated in Fig. 4. In this site the interca- lated ion sits centrally above the triangle of oxygen ions defined by O(4)-O(4)-O(3). Using the Madelung potentials calculated at the various intercalation sites and reported in 0 Po @ interstitial alkali metal Fig.3 Trigonal bipyramidal interstitial site uranium int erst it ial alkali metal Fig. 4 Nine-co-ordinate interstitial site Table4, it is clear that the Madelung energy favours the occupation of the trigonal bipyramidal sites by the intercalated cations. However, the Madelung energy does not provide a complete description of the processes involved in incorporat- ing the interstitial ion; we must also consider the effect of relaxation of the lattice around the guest ion. In Table 5 we present the results of calculations of the energy to bring an alkali-metal ion from infinity and place it at an interstitial site in the crystal.These results show that the smaller lithium ions will preferentially occupy the trigonal bipyramidal sites (which have a more favourable Madelung potential) rather than the nine-co-ordinate position. However, since the ener- gies for a lithium ion at each of the trigonal bipyramidal sites are rather similar, we predict that there will be no strong preference for the occupation of any particular trigonal bipyr- amidal site. This suggestion is supported by a recent neutron Table 4 Madelung potentials at the various intercalation sites site V,leV five-co-ordinate site apical oxygen O(3) -5.48 O(4) -5.45 O(5) -7.18 nine-co-ordinate site -2.86 Table 5 Formation energies of isolated alkali-metal ions" intercalation site calculated energies/eV lithium insertion five-co-ordinate site apical oxygen O(3) (44) O(5)nine-co-ordinate site -7.61 -7.63 -7.63 -7.36 sodium insertion five-co-ordinate site apical oxygen O(3) O(4)00)nine-co-ordinate site -3.81 -3.83 -3.21 -5.26 " Calculations performed with a region I size of ca.425 ions. diffraction study of Lio.gU308,12 which shows that if the insertion is carried out at room temperature, the lithium ions are randomly distributed over the trigonal bipyramidal sites. At higher temperatures, where there are fewer kinetic con- straints, the lithium ions were observed to occupy only the trigonal bipyramidal sites above the O(5)oxygen ions. This observation is also consistent with the calculated relative preference amongst the sites (see Table 5). In contrast to the results for lithium, the results in Table 5 indicate that isolated sodium ions would favour occupation of the nine-co-ordinate sites. This site is more able to accommo- date the larger sodium ion than the trigonal bipyramidal sites.We must be aware that calculations based on isolated intercalated ions may not be comparable with experimental measurements performed on phases containing a substantial concentration of guest ions. The preference for one ordering pattern over another, for example, could lead to different sites being occupied from those predicted above. It is therefore prudent to carry out additional calculations on the possible ordered phases of MU308 and to compare these with the available experimental observations. 3.3 Modelling of MU308 In MU308 we assume that all of the uranium ions have an equal oxidation state of I.: The structures of these phases can then be modelled by taking an initial structure, consisting of an unperturbed U308 framework with the alkali metals in the appropriate sites and with all uranium ions having a charge of 5+, and relaxing the configuration to a minimum lattice energy.This minimization occurs at constant pressure, allowing the alkali-metal insertion to cause a change in both the U308 cell volume and the lattice vectors. It should be noted that this procedure will not sample structures that are beyond an activation energy barrier from the initial structure.However, for our purposes this should not be a problem since we are mainly interested in topotactic processes, which involve relatively small perturbations to the U308 structure. For both LiU308 and NaU308, individual calculations were performed with the alkali metal ordered on each of the four sites. For LiU308 the lattice energies corresponding to the three structures in which the lithium ions order on the three sets of trigonal bipyramidal sites were very similar and significantly more negative than the structure in which the lithium ions occupy the nine-co-ordinate sites. This is in agreement with the conclusions of the previous section. The cell parameters and lattice energy for LiU308 with the lithium ions on the trigonal bipyramidal sites above the O(5)oxygen ions are given in Tables 6 and 7, respectively. Comparing the J.MATER. CHEM., 1991, VOL. 1 Table 6 Calculated cell parameters of insertion compounds of a-U308 a-U,O, 6.96 12.06 4.14 LiU,O, 7.10 12.19 4.25 NaU,O, 7.05 12.21 4.27 Table 7 Calculated lattice energies of insertion compounds of a-U30, compound HJeV a-U,O, -507.97' LiU,O, -465.74 NaU,O, -463.67 " Ref. 7. calculated cell parameters for LiU308 with the experimental cell parameters for Lio.88U308 given in Table 1, we predict a similar expansion for both the a and the c parameters. For NaU308 it was found that the lowest-energy configur- ations involved significant deviations from the U308 structure. This is contrary to experimental observations and the topotac- tic nature of the insertion reaction.For the cases in which the U308 structure is essentially preserved, the minimum lattice energy occurs for the structure having the sodium ions in the nine-co-ordinate sites. Furthermore, for the calculation with the sodium ions initially on the trigonal bipyramidal sites above the O(4) oxygen ions, all the sodium ions relaxed into the nine-co-ordiante sites. These results suggest that the sodium insertion compounds of U308 with compositions around NaU308 (which, at ambient temperatures, have been observed to occur with only a slight modification of the U308 structure) are metastable. However, in these metastable com- pounds we predict that the sodium ions will occupy the nine- co-ordinate sites and the calculated lattice parameters and lattice energy for this compound are given in Tables 6 and 7, respectively.The relaxed coordinates for the MU308 phases are reported in Table 8, along with those for a-U308 itself. It is clear that the internal structure of the U308 unit cell is essentially preserved during the insertion reaction. In most inorganic compounds the sum of the bond strengths around any particu- lar atom is expected to be within ca. 5% of the formal oxidation state of that atom.29 The bond strength can be calculated according to:30 Sij=(;) -N where sii is the bond strength between atoms i and j which are separated by rip N and ro are empirical parameters which are derived by fitting to a large range of structural data.The oxidation state, 6,for a particular atom is therefore estimated by summing the bond strengths over the nearest neighbours to the atom: This method can be used to check the structure of a particular compo~nd~~.~~or to assign oxidation states to the ions.33 It has been shown that the parameters ro and N vary little with oxidation and since few Uv-containing oxide struc- tures have been investigated, the values used here are those determined for the Uv' ion, rather than for the Uv ion. The oxidation states for the metal ions in U308, LiU308 and NaU308 calculated by this method are given in Table 9. For U308 itself the oxidation states are ca. 5% lower than the ones estimated by the same method but using the experimental J.MATER. CHEM., 1991, VOL. 1 Table 8 Comparison of calculated structures of a-U308 and MU308 (M =Li, Na) (space group C2rnm) a-U308 LiU308 NaU308 A, b= 12.21 A, ~=4.27A)(a=6.96 A, b= 12.06 A, ~=4.14A) (~=7.10A, b= 12.19A, ~=4.25A) (~7.05 atom symmetry xla Ylb zlc xla Ylb zlc xla Ylb ZIC 2a 0.961 0.000 0.000 0.961 0.000 0.000 0.96 1 0.000 0.000 4d -0.017 0.326 0.000 -.0.053 0.327 0.000 0.0 12 0.3 16 0.000 2b 0.934 0.000 0.500 0.925 0.000 0.500 0.97I 0.000 0.500 4e 0.996 0.3 13 0.500 0.992 0.316 0.500 1.007 0.321 0.500 2a 0.569 0.000 0.000 0.558 0.000 0.0o0 0.584 0.000 0.000 4d 0.179 0.130 0.000 0.173 0.131 O.OO0 0.200 0.128 0.000 4d 0.309 0.333 0.000 0.282 0.338 0.000 0.328 0.333 0.000 4e" ---0.274 0.326 0.500 2b ------0.328 0.000 0.500 " Half occupied.Table 9 Bond-strength calculations for U308 and MU308" U308 (calculated) around U( 1) around U(2) 2~ U(1)-0(1) 2.079 1.919 2 x U(2)-0(2) 2.078 1.923 2 x U(1)-0(4) 2.182 1.558 1 x U(2)-0(3) 2.182 0.779 2 x U(l)-0(5) 2.272 1.310 1x U(2)-0(4) 2.181 0.781 1 x U(1)-0(3) 2.728 0.298 1 x U(2)-0(4) 2.729 0.298 1 x U(2b--0(5) 2.271 0.656 ISij=5.09 LiU308 (calculated) around U( 1) around U(2) around Li 2 x U(1)-0(1) 2.139 1.698 2 x U(2)-0(2) 2.152 1.654 1 x Li-O(1) 2.380 0.108 2 x U(1)-0(4) 2.199 1.507 1 x U(2)-0(3) 2.254 0.678 2 x Li-0(2) 2.012 0.429 2 x U(1)-O(5) 2.352 1.129 1x U(2)-0(4) 2.883 0.235 2 x Li-O(5) 2.129 0.341 1 x U(1j-0(3) 2.870 0.240 1x U(2)-0(4) 2.018 1.090 1 x U(2)-O(5) 2.390 0.527 csij=4.57 1 x U(2)-O(5) 2.331 0.587 csij=4.77 ISij=0.88 NaUJ08 (calculated) around U( 1) around U(2) around Na 2 x U(1)-O(1) 2.138 1.701 2 x U(2)-0(2) 2.138 1.701 1 x Na-O(1) 2.516 0.152 2 x U( 1)-0(4) 2.298 1.247 1 x U(2)-0(3) 2.303 0.618 2 x Na-0(2) 2.523 0.301 2 x U( 1)-O(5) 2.241 1.389 1 x U(2)-0(4) 2.650 0.338 2 x Na-0(3) 2.797 0.193 1 x U( 1)-0(3) 2.657 0.334 1 x U(2)-0(4) 2.303 0.618 4 x Na-0(4) 2.797 0.386 1 x U(2)-O(5) 2.237 0.700 ISij== 1 x U(2)-O(5) 2.237 0.700 csij=4.68 CSij =1.03 Values of ro: U, 2.059 A; Li, 1.378 A; Na, 1.622 A.Values of N: U, 4.300; Li, 4.065; Na, 4.290. (See ref. 30) coordinate^.^ This reduction of the mean uranium oxidation and can be split up into several contributions: state reflects the expansion of the unit-cell volume, and therefore bond lengths, in going from the experimental to the calculated U308 structure.An expansion of this order is frequently observed when using electron gas potentials. Bear- ing this in mind, the changes in bond lengths, and therefore where HL(U3o8) and HL(MU3o8) are the lattice energies of oxidation states, on forming the MU308 phases are in good U308 and MU308 respectively, E,(M) is the enthalpy of agreement with the assumption of v and I oxidation states sublimation of M, Z,(M) is the first ionization energy of M for uranium and the alkali metal, respectively. The calculated and Ee,(U"+) is the gas-phase electron affinity of the U308structural changes are therefore in accordance with empirically uranium ions.However, calculating AinsH in this way isderived trends observed over a wide range of inorganic unreliable since we are taking the difference between twocompounds. large quantities [HL(U308)and HL(MU308)]. In our earlier Having calculated lattice energies for the phases MU308, paper' we noted that the experimental and calculated lattice we should now be in a position to calculate enthalpies of energies for U308 agreed to within 4%. This is a goodinsertion (AinsH).This enthalpy change corresponds to the agreement but, because of the large numbers involved, the process numerical difference amounts to some 20eV. Such problems M(s)+u308(s)--' MU308(S) are much less acute if we calculate instead the enthalpy change for the process Li+(g)+NaU,O,(s)-,Na+(g) +LiU,O,(s) In this case, there is some cancellation in the errors associated with the individual lattice-energy terms.From Table 7, the enthalpy change for this process is found to be -2.1 eV. This value is consistent with the value of -1.1 eV4 for the analogous process Li+(g)+NaUO,(s)-,Na+(g) +LiUO,(s) and reflects the greater difficulty in inserting the larger sodium ions into the host matrix. 3.4 Migration Mechanisms Having established the possible intercalation sites we now turn to the problem of alkali-metal migration through the host lattice. The insertion reaction depends very much on the availability of favourable diffusional routes for the guest ions in the host matrix. Since we predict that the lithium and sodium ions will occupy different sites in U308, their migration behaviour might also be quite different.For an alkali-metal ion occupying a trigonal bipyramidal site, an obvious mechanism for its migration is a direct jump to a neighbouring trigonal bipyramidal site. The saddle point for such a move will be approximately midway between the two sites, as shown in Fig. 5. From Fig. 1 we can see that there are four distinct jumps possible between neighbouring trigonal bipyramidal sites. If we label the sites by their apical oxygen ions then the four jumps are O(4) +0(4), 0(4)-+0(5), 0(5)+0(3) and 0(3)-,0(4). The calculated activation energy barriers for each of these jumps can be illustrated by plotting the energy profile for alkali-metal migration along the path 0(4)+0(4)+0(5)+0(3)-+0(4) as shown in Fig.6. The calcu- lated energy profiles for lithium and sodium migration are quite different. For lithium migration, the plot is simplified by the fact that the energies of the lithium ion at each site are very similar. The activation energies for lithium-ion migration are greatest for the 0(4)+0(4) and 0(3)+0(4) steps, reflecting the exposure to the uranium cation charge field that occurs along these direct routes. The energy barriers Q Q QI Q-1 J. MATER. CHEM., 1991, VOL. 1 -6 6(4) O(4) O(5) O(3) O(4) position of intercalated ion Fig. 6 Energy profile for alkali-metal migration between trigonal bipyramidal sites. (a)Sodium, (b)lithium for the 0(4)+0(4) and 0(3)+0(4) steps can, however, be reduced if the lithium ion migrates via the nine-co-ordinate position, an option that is not available for the 0(4)+0(5) and 0(5)+0(3) jumps.The energy profile for this route is shown in Fig. 7. It therefore appears from the calculations that the rate-determining activation energy for lithium migration will be ca. 0.7 eV. This activation energy is consist- ent with the high lithium mobility observed experimentally in U308e3 For sodium, the activation energies for direct migration between two trigonal bipyramidal sites (see Fig. 6) are lower than those for lithium owing to the release of steric forces when the sodium ion moves out of the trigonal bipyramidal position. The activation energies for these steps lie between 0.43 and 1.05 eV.The greatest barrier to sodium diffusion comes, however, from the activation energy of 1.52 eV for the -3.5 -,(iXTX\ 0.12-j ----x-\ X -4.0'-\ T-7/ 4.5 -1.52 "\ i -5.0 -% \ -6 -5.5 a a --6.0 @ migrating alkali metal I-8.0 IX trigonal bipyramidal O(3) 9-coordination site O(4) site position of intercalated ion Fig. 5 Saddle point for migration between two trigonal bipyramidal Fig. 7 Energy profile for alkali-metal migration between trigonal sites bipyramidal and nine-co-ordinate sites. (a)Sodium, (b)lithium J. MATER. CHEM., 1991,VOL. 1 421 migration of the ion out of the nine-co-ordiante site into a neighbouring trigonal bipyramidal site. Since the nine-co- ordinate sites are far apart, this step is always required and is therefore rate-determining.Consequently, the migration of isolated sodium ions in U308 is predicted to be much slower than that for lithium ions. 7 8 9 10 11 12 R. G. J. Ball and P. G. Dickens, J. Muter. Chem., 1991,1, 105. M. S.Islam and C. R.A. Catlow, J. Solid State Chem., 1988, 77, 180. J. C. Newton-Howes and A. N. Cormack, J. Solid State Chem., 1989, 79, 12. B. 0.Loopstra, Acta Crystallogr., 1964, 16, 651. B.0.Loopstra, J. Appl. Crystallogr., 1970,3, 94. P.G. Dickens and A.V. Powell, J. Solid State Chem., 1990,in 4. Conclusions 13 the press. R. G. J. Ball, P. G. Dickens, S. Patat and S. Hull, 1991,to be submitted. In this paper we have presented the results of a theoretical study of the insertion of alkali metals into ct-U308.Calcu- lations on the energetics of isolated alkali-metal ions suggest that lithium will preferentially occupy five-co-ordinate trigonal bipyramidal sites, whereas sodium will occupy nine-co-ordi- nate positions. In the lithium intercalate there does not appear 14 15 16 17 H. R. Hoekstra and R. H. Marshall, J. Znorg. Nucl. Chem., 1965, 27, 1947. R. Chevalier and M. Gasperin, C.R. Acad. Sci., 1968, C267,481. A. Deschanvres, L. Leparmentier and B. Raveau, Bull. SOC.Chim. Fr., 1971,3460. J. M. Moutou, M. Vlasse, M. Cervera-Marzal, J. P. Chaminade and M. Pouchard, J. Solid State Chem., 1984, 51, 190. to be a strong preference for one trigonal bipyramidal site over another. Simulation of the stoichiometric insertion com- pounds MU308 reinforces these predictions.The insertion process is demonstrated to occur with the preservation of the U30s structure but with a slight expansion in the lattice parameters. The sodium insertion compound prepared under ambient temperatures, however, does appear to be metastable. Calculations of the migration of isolated alkali-metal ions within the U308lattice predict that lithium will have a much higher mobility than sodium. 18 19 20 21 22 23 J.P. Chaminade, J.M. Moutou, G. Villeneuve, M.Couzi, M. Pouchard and P.Hagenmuller, J. Solid State Chem., 1986, 65, 27. P. G.Dickens, A. V. Powell and G. P. Stuttard, Proc. Znt. Con$ Electron. Ceram. Muter., Wyoming, USA, 1990,in the press. S. H. Chang, C. Delmas, J. P. Chaminade and P. Hagenmuller, Solid State Zonics, 1990, 39, 305.S. Kemmler-Sack and W. Rudorff, Z. Anorg. Allg. Chem., 1967, 354,255. A. N. Tsvigunov and L. M. Kuznetsov, Radiokhimiya, 1974, 16, 882. J. 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D. Lawrence and M.T. Weller, Muter. Res. Bull., 1985, 20, 635. P. G. Dickens, D. J. Penny and M. T. Weller, Solid State Zonics, P. G. Dickens, A. V. Powell and A. M. Chippindale, Solid State Zonics, 1988,28-30, 1123. P. G. Dickens, S. D. Lawrence, D. J. Penny and A. V. Powell, Solid State Zonics, 1989, 32-33, 77. 1986, 18-19, 778. 31 32 33 34 35 D. Altermatt and I. D. Brown, Acta Crystallogr. Sect. B, 1985, 41,240. A. M. Chippindale, P. G. Dickens and W. T. A. Harrison, J. Solid State Chem., 1989, 78, 256. I. D. Brown, J. Solid State Chem., 1989, 82, 122. E. H. P. Cordfunke and W. Ouweltjes, J. Chem. Thermodyn., 1981, 13, 187. P. W. Fowler and N. C. Pyper, Proc. R. SOC. London, A, 1985, 398,377. R. G. J. Ball, U.K.A.E.A. Harwell Report, 1989,AERE R-13396. Paper 0/05584K;Received 12th December, 1990