LETTERS PUBLISHED ONLINE: 6 SEPTEMBER 2009 | DOI: 10.1038/NMAT2528
Nanoscale manipulation of the properties of solids at high pressure with relativistic heavy ions Maik Lang1 , Fuxiang Zhang1 , Jiaming Zhang1 , Jianwei Wang1 , Beatrice Schuster2 , Christina Trautmann2 , Reinhard Neumann2 , Udo Becker1 and Rodney C. Ewing1 * High-pressure and high-temperature phases show unusual physical and chemical properties, but they are often difficult to ‘quench’ to ambient conditions1 . Here, we present a new approach, using bombardment with very high-energy, heavy ions accelerated to relativistic velocities, to stabilize a high-pressure phase. In this case, Gd2 Zr2 O7 , pressurized in a diamond-anvil cell up to 40 GPa, was irradiated with 20 GeV xenon or 45 GeV uranium ions, and the (previously unquenchable) cubic high-pressure phase was recovered after release of pressure. Transmission electron microscopy revealed a radiation-induced, nanocrystalline texture. Quantummechanical calculations confirm that the surface energy at the nanoscale is the cause of the remarkable stabilization of the high-pressure phase. The combined use of high pressure and high-energy ion irradiation2,3 provides a new means for manipulating and stabilizing new materials to ambient conditions that otherwise could not be recovered. Investigations of the properties of materials at high pressures have been essential to understanding the internal structure of the Earth4,5 . Most recently, materials scientists have begun to take advantage of high pressures to fabricate materials with unique properties1,6–8 . For example, super-hard materials have been discovered9,10 and elementary high-temperature superconductors have been produced under pressures as high as 200 GPa (ref. 11). The development of next-generation high-pressure devices12 , coupled with state-of-the-art analytical techniques, will extend the possibilities for the synthesis and in situ characterization of unique solids under extreme conditions1 . A serious drawback of these efforts is that many of the unusual materials are stable only at high pressure, that is, they rapidly transform to the low-pressure phase on the release of pressure and cannot be examined ex situ or used in special applications. Here, we describe a new strategy for the recovery of such high-pressure phases to ambient conditions. The approach is based on a recently developed method2,3 using swift heavy ions to manipulate directly the structure of a solid at high pressures and to induce nanoscale modifications that result in stabilization of the high-pressure phase. The irradiation is carried out with relativistic projectiles (v/c ∼ 0.5) produced by one of the world’s largest ion accelerators. The high velocity (kinetic energy) of the ion beam is required because it first has to traverse the millimetre-thick diamond anvil of the high-pressure cell before reaching the pressurized sample. As the projectiles slow down along their trajectory, they induce intense electronic excitations and ionizations (electronic energy loss, dE/dx), which finally trigger complex processes within the solid. A cylindrical zone of ∼10 nm diameter is formed in which the deposited energy
density may exceed the average binding energy of the target atoms. Depending on the material, many different structural modifications have been observed for irradiations at ambient pressure, ranging from isolated point defects to substantial amorphization or crystalline-to-crystalline phase transitions13 . The first experiments combining high pressure and ion irradiation have already revealed novel effects, which include the formation of large amorphous domains, decomposition into nanocrystals and nucleation of high-pressure phases2 . In this investigation, pyrochlore (Gd2 Zr2 O7 ) was simultaneously exposed to swift heavy ions and to pressures up to ∼40 GPa. The isometric pyrochlore structure has a general formula of A2 B2 O7 with over 500 different compositions that have a remarkable range of physical, chemical and electronic properties with a number of significant technological applications (for example, catalysts and oxygen conductors in fuel cells)14,15 . Zirconate pyrochlores, specifically Gd2 Zr2 O7 , are important candidates for nuclear-waste forms and inert matrix nuclear fuels owing to their exceptional resistance to radiation-induced amorphization16 . The radiation response is mainly characterized by a unique transformation from the ordered pyrochlore structure to the disordered, defect-fluorite structure17–19 . Both structures are closely related to the idealfluorite structure (AX2 ), except that there are two cation sites (ordered for pyrochlore and disordered for defect fluorite) and one-eighth fewer anions (ordered anion vacancies for pyrochlore and disordered for defect fluorite)14 . Interestingly, the same order– disorder transition has a key role for the high-pressure behaviour of Gd2 Zr2 O7 , as well as for many other pyrochlore compositions20 . At room temperature and Pc = ∼17 GPa, the cubic pyrochlore transforms to an orthorhombic, cotunnite-like high-pressure phase20 . This polymorph cannot be recovered, because on pressure release Gd2 Zr2 O7 transforms to the disordered, defect-fluorite structure at ambient conditions. Here, we demonstrate that the simultaneous exposure to high pressure and ion irradiation creates new possibilities that allow the stabilization of a high-pressure phase to ambient conditions, which has never been achieved previously. To characterize the new phase, synchrotron X-ray diffraction (XRD) and transmission electron microscopy (TEM) were used. Quantum-mechanical calculations of the different structure types provide the theoretical basis for understanding this remarkable stabilization process. The inner parts of the two-dimensional XRD images together with the integrated patterns of irradiated and non-irradiated Gd2 Zr2 O7 are shown in Fig. 1 for different pressures (see figure caption for details). In agreement with earlier studies20 , we found the initial pyrochlore (Fig. 1a) transformed to the cotunnitelike high-pressure phase at pressures in excess of ∼17 GPa
1 Department of Geological Sciences, University of Michigan, 1100 N University Avenue, Ann Arbor, Michigan 48109-1005, USA, 2 GSI Helmholtzzentrum für Schwerionenforschung, Planckstr. 1, 64291 Darmstadt, Germany. *e-mail:
[email protected].
NATURE MATERIALS | VOL 8 | OCTOBER 2009 | www.nature.com/naturematerials
© 2009 Macmillan Publishers Limited. All rights reserved.
793
NATURE MATERIALS DOI: 10.1038/NMAT2528
LETTERS a
6
8
10
b
2θ (°) 12 14
16
18
c
6
8
2θ (°) 10 12 14
16
18
d
6
8
10
2θ (°) 12 14
16
18
6
8
10
2θ (°) 12 14
16
18
e
6
8
2θ (°) 10 12 14
16
18
Figure 1 | Synchrotron XRD images and integrated patterns of Gd2 Zr2 O7 obtained at different combinations of pressure and irradiation. a–e, Pyrochlore-structured Gd2 Zr2 O7 starting material (a) on releasing pressure without (b,d) and with (c,e) irradiation ((c) 4 GeV xenon and (e) 7-GeV uranium ions of fluence 3 × 1012 cm−2 ). The sample structure at the specific pressure is cotunnite-like high-pressure phase at 20.2 GPa (b), cotunnite-like high-pressure phase at 21.5 GPa (c), defect-fluorite structure with some remnants of X-Phase (arrow) 10 h after quenching (d) and pure X-phase 50 h after quenching (e).
(Fig. 1b). Ion-beam exposures at ∼40 GPa (not shown here) and 21.5 GPa did not result in any obvious structural modification (for example, amorphization) and the diffraction pattern of the irradiated cotunnite-like phase (Fig. 1c) is very similar to the non-irradiated reference sample (Fig. 1b), indicative of the enhanced radiation resistance of the high-pressure phase. The slight broadening of the intense inner diffraction maximum after irradiation (Fig. 1c) may be related to the formation of nanocrystals; however, there is already an initial stress-induced broadening at high pressure for the non-irradiated sample (Fig. 1b), which complicates the interpretation. Although in situ XRD did not demonstrate significant radiation effects under pressure, the results are surprisingly different for the recovered samples at ambient conditions. Ten hours after release of pressure, the diffraction image and pattern of the unirradiated pyrochlore shows the typical maxima of the defect-fluorite structure (Fig. 1d), whereas a new phase of unknown structure, here denoted as the ‘X-phase’, was observed in the irradiated sample directly (not shown here) and 50 h after quenching (Fig. 1e). This Xphase is also evident before pressure release and is gradually formed from the cotunnite-like phase during decompression. 794
This transformation, which is complete at ∼3 GPa, together with structural similarities, suggests that the X-phase is a further highpressure phase of Gd2 Zr2 O7 . The new structure was also observed during the quenching process of non-irradiated pyrochlore, but some fraction of the cotunnite-like phase persists even to 1 bar. On complete pressure release, the X-phase transformed rapidly to the defect-fluorite structure, except for some remnants that were still detected after 10 h (arrow in Fig. 1d). The occurrence of this metastable X-phase together with the known cotunnite-like phase was also noticed in an earlier investigation20 ; however, owing to the incomplete transformation and its highly unstable character, this high-pressure polymorph could not be investigated. The ion–matter interactions in the cotunnite-like structure have obviously accelerated the transformation to the X-phase during pressure release and, more importantly, have triggered a remarkable stabilization of this unusual structure. Even two weeks after pressure release, XRD measurements showed no change but confirmed the presence of the pure X-phase. Interestingly, ion-beam irradiation of Gd2 Zr2 O7 at 10 GPa (Xe-ions), which is well below the critical pressure, Pc = ∼17 GPa, for the pyrochlore-to-cotunnite-like phase transformation20 , did not result in the stabilization of the X-phase.
NATURE MATERIALS | VOL 8 | OCTOBER 2009 | www.nature.com/naturematerials © 2009 Macmillan Publishers Limited. All rights reserved.
NATURE MATERIALS DOI: 10.1038/NMAT2528
LETTERS a (022)
6
8
10
12
(220)
4
(211)
(110)
(200)
Intensity (arb.units)
(002) (111)
14
16
2θ (°)
b (211)
Figure 2 | Synchrotron XRD pattern of the X-phase recovered from 20 GPa after irradiation with 7-GeV uranium ions. (See the corresponding XRD image in Fig. 1e.) Measured diffraction maxima (open circles) can be fully reproduced by the calculated pattern (line) of a cubic Gd2 Zr2 O7 ¯ structure (Im3m). Inset: The crystal structure of the new phase for mixed cation occupancy (large spheres) and fully occupied anions (small spheres).
In this case, the pyrochlore was almost completely transformed to the defect-fluorite structure, as is the case for ambientpressure irradiation17–19 . The indexed sequence of diffraction maxima of the quenched irradiated sample suggests a body-centred-cubic lattice for the X-phase. The structure may be isostructural with the cubic hightemperature phase of Gd2 O3 (ref. 21) and the observed XRD pattern (circles, Fig. 2) can be well refined with this structure model (solid line, Fig. 2). Similar to the defect-fluorite structure, Gd and Zr are fully disordered over the cation sites and the anion sites are not fully occupied. The crystal structure of the X-phase is illustrated in the inset of Fig. 2, with large and small spheres representing the cations and anions (without anion vacancies), respectively. The symmetry ¯ (Im3m) is different from the face-centred-cubic crystal structure ¯ of pyrochlore (Fd 3m) and defect-fluorite (Fm3m). The unit-cell constant of the X-phase is smaller (4.107(2) Å) than both of the ambient-pressure polymorphs (pyrochlore: 10.53 Å, defect-fluorite: 5.27 Å), resulting in a calculated increase of density of ∼5%. On the basis of the chemical composition and the crystal symmetry, the oxygen occupancy of the anion site in the X-phase is ∼0.6, significantly lower than the 7/8 in pyrochlore and defect-fluorite14 . This larger number of oxygen vacancies may lead to an increase in the intrinsic ionic conductivity of Gd2 Zr2 O7 , which has the highest value of any pyrochlore composition22 and it is comparable to that of yttria-stabilized zirconia—the electrolyte most commonly investigated for the development of solid-oxide fuel cells23 . TEM provides the direct experimental evidence for the cause of the stabilization of the high-pressure phase. The high-resolution images (HRTEM) of an irradiated and unirradiated sample, recovered from 40 and 43 GPa experiments, respectively, (Fig. 3) show the formation of nanocrystals in the irradiated sample. The application of only pressure does not significantly affect the sample texture and the micrometre-sized crystals of the starting material were essentially the same as those observed in the recovered
(200) (110)
Figure 3 | High-resolution TEM images of Gd2 Zr2 O7 recovered from ∼40 GPa. a,b, Note, the polycrystalline texture for the non-irradiated sample (a) versus the presence of nanocrystals in the irradiated material (b). SAED patterns confirm the defect-fluorite structure as a quench product for only pressure (inset a) and the X-phase as the final state for the sample irradiated under pressure with 4 GeV Xe ions (inset b). Scale bars: 2 nm.
specimen (Fig. 3a). The selected-area electron diffraction (SAED) pattern is typical of the defect-fluorite structure24 and the discrete spots are due to the large grain size (inset of Fig. 3a). On the other hand, HRTEM images clearly demonstrate that the quenched irradiated pyrochlore consists of nanometre-sized crystals (Fig. 3b). The corresponding SAED pattern (inset of Fig. 3b) is very similar to the XRD pattern of the quenched X-phase (Fig. 2). The distinct ring-like pattern is indicative of a nanocrystalline sample; however, orientation and strain effects may be responsible for the distortion and separation of individual spots. The most prominent difference in the SAED patterns of the irradiated and unirradiated sample is the order of rings for specific orientations: the first (110) and second (200) diffraction rings of the X-phase are well separated,
NATURE MATERIALS | VOL 8 | OCTOBER 2009 | www.nature.com/naturematerials
© 2009 Macmillan Publishers Limited. All rights reserved.
795
NATURE MATERIALS DOI: 10.1038/NMAT2528
LETTERS Relative potential energy (eV)
3
2
Cotunnite-like
1
X-phase Defect fluorite Pyrochlore
0
0
0.5
1.0
1.5
2.0
2.5
1/H (nm¬1)
Figure 4 | Quantum-mechanical calculations of the potential energy of different Gd2 Zr2 O7 structure types as a function of grain size, H. All calculated energies are relative to the potential energy of bulk pyrochlore. The pyrochlore structure is energetically favoured for bulk material; in contrast, the X-phase has the lowest energy for nanocrystals with a grain size of ∼1 nm.
which is not the case for the defect-fluorite structure with the two closely spaced inner rings (111) and (002). Thus, the TEM data confirm the XRD results. The irradiation under high pressure allows quenching of the high-pressure X-phase. The formation of nanocrystals evidently has a key role in this stabilization process. This hypothesis is supported by quantum-mechanical calculations of the enthalpy of formation as a function of crystal size for the different Gd2 Zr2 O7 structures (Fig. 4). For the calculations, a slab model was applied, which describes the sample as a two-dimensional infinite plane of thickness, H . For bulk materials (H → ∞), the pyrochlore structure has the lowest energy and the sequence of the energies provides a qualitative description of the observed phase-transformation behaviour of the different phases with increasing pressure (pyrochlore → cotunnite-like phase) and pressure release (cotunnite-like phase → X-phase → defect-fluorite). Materials consisting of nanometre-sized crystals follow different thermodynamic pathways, as compared with that of the bulk material, which is generally ascribed to the dominant influence of surface-energy modifications of the electronic structure and defect behaviour25–27 . According to these calculations, the surface energy becomes an important contribution to the total energy for nanometre-sized pyrochlore structure types and accounts for substantial modifications in the relative potential energies (Fig. 4). Below a critical grain size of ∼1 nm, an energetic crossover occurs and the X-phase becomes energetically most favourable, a qualitative trend that provides the basis for a theoretical description of the observed stabilization process: the high-dose irradiation of the highpressure cotunnite-like phase causes the formation of nanocrystals, which is in agreement with earlier irradiation studies at ambient28 and high pressure2 and these results demonstrate that ion–matter interactions can induce the formation of nanocrystals. Sluggish kinetics prevent a direct transformation from the cotunnite-like structure to the X-phase; however, on pressure release, the nanomaterial transforms completely to the X-phase. As the nanocrystalline X-phase is energetically the most favourable, no further transformations occur (for example, to the defect-fluorite structure) and the X-phase is stabilized at ambient pressure conditions. The issue of whether the irradiation causes the fragmentation of the cotunnitelike phase directly into a nanomaterial—as indicated by the slight broadening of diffraction maxima (Fig. 1c)—or whether this occurs during pressure release, for example, as a result of ion-induced strain, cannot be fully resolved. However, the irradiated sample 796
does consist of nanometre-sized crystals at ambient pressure and these are consistently present, as demonstrated by the distinct broad XRD maxima (Fig. 1e) and the TEM measurements. The quantitative discrepancy of the calculated (Fig. 4) and measured (Fig. 3b) X-phase nanoparticle size may originate from both the calculations (‘zero-temperature’, slab model, neglected grain-boundary energy and the calculation of enthalpy instead of the free energy) and the use of TEM to determine the average crystal size (an overestimation of average grain size due to the limited number of crystals that were measured). Nanoscale manipulation by energetic projectiles and in particular, the formation of radiation-induced nanocrystals, is a unique tool for in situ modification of the thermodynamic pathways on pressure release. The application of high pressure simultaneously with the deposition of large energy densities provides a new strategy for the recovery of unique, high-pressure structures that are otherwise inaccessible.
Methods Powdered Gd2 Zr2 O7 samples of a few micrometres in size were loaded into symmetric-type diamond-anvil cells and pressurized at room temperature. A mixture of methanol, ethanol and H2 O (16:3:1) was used as the pressure-transmitting medium. Pressures of about 10, 20 and 40 GPa were applied and measured by means of the fluorescence of several small ruby grains distributed throughout the sample chamber29,30 . The diamond-anvil cells were irradiated at the heavy-ion synchrotron (SIS) of the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt, Germany. Samples were exposed to either 132 Xe or 238 U ions accelerated to relativistic energies of about 20 GeV (xenon) and 45 GeV (uranium). The ion beam, as delivered by the SIS, is pulsed (pulse length > 50 ms, rate ∼1 Hz) and has a spot size of ∼0.3 cm2 . To induce substantial structural modifications in the samples, the irradiation fluence was maximized to about 3 × 1012 ions cm−2 for all irradiations. After passing through the first ∼2-mm-thick diamond anvil, the ions were slowed down to about 4 GeV (xenon) and 7 GeV (uranium), respectively, as they reached the pressurized pyrochlore31,32 . This reduced energy is still sufficient that the ions pass completely through the sample and deposit an almost constant energy per unit path length of approximately 19 keV nm−1 (xenon) and 42 keV nm−1 (uranium)32 across the entire sample thickness. Irradiated and non-irradiated reference samples were characterized by in situ XRD carried out at the beam line X17C of the National Synchrotron Light Source, Brookhaven National Laboratory. Using powder XRD with a monochromatic beam of 30.5 keV and a spot size of ∼25 µm, the pressurized pyrochlores were characterized as a function of decreasing pressure. The Debye diffraction rings were recorded with a Mar CCD (charge-coupled device) detector and the integrated two-dimensional patterns were produced with the software Fit 2d (ref. 33). Structural details of the X-phase were obtained by Rietveld refinement of the XRD patterns34 . Finally, fine powder of the quenched samples was deposited onto holey-carbon TEM grids and analysed using a JEOL 2010F by means of high-resolution images (HRTEM) and SAED patterns. Quantum-mechanical calculations were carried out using the density functional theory framework and plane-wave basis sets as implemented in the Vienna Ab initio Simulation Package35–37 . The projector-augmented wave method and exchange–correlation as parameterized by the Perdew–Wang 91 functional were applied in the generalized gradient approximation.
Received 31 May 2009; accepted 6 August 2009; published online 6 September 2009
References 1. McMillan, P. F. New materials from high-pressure experiments. Nature Mater. 1, 19–25 (2002). 2. Glasmacher, U. A. et al. Phase transitions in solids stimulated by simultaneous exposure to high pressure and relativistic heavy ions. Phys. Rev. Lett. 96, 195701 (2006). 3. Lang, M. et al. Fission tracks simulated by swift heavy ions at crustal pressures and temperatures. Earth Planet. Sci. Lett. 274, 355–358 (2008). 4. Liu, L. G. & Bassett, W. A. Elements, Oxides, and Silicate: High-Pressure Phases with Implications for the Earth’s Interior 134 (Oxford Univ. Press, 1986). 5. Murakami, M., Hirose, K., Kawamura, K., Sata, N. & Ohishi, Y. Post-perovskite phase transition in MgSiO3 . Science 304, 855–858 (2004). 6. Hemley, R. J. & Ashcroft, N. W. The revealing role of pressure in the condensed matter sciences. Phys. Today 51, 26–32 (1998). 7. Liu, H. et al. Anomalous high-pressure behaviour of amorphous selenium from synchrotron X-ray diffraction and microtomography. Proc. Natl Acad. Sci. 105, 13229–13234 (2008). 8. Ahart, M. et al. Origin of morphotropic phase boundaries in ferroelectrics. Nature 451, 545–548 (2008).
NATURE MATERIALS | VOL 8 | OCTOBER 2009 | www.nature.com/naturematerials © 2009 Macmillan Publishers Limited. All rights reserved.
NATURE MATERIALS DOI: 10.1038/NMAT2528 9. Chung, H.-Y. et al. Synthesis of ultra-incompressible superhard rhenium diboride at ambient pressure. Science 316, 436–439 (2007). 10. Mao, W. L. et al. Bonding changes in compressed superhard graphite. Science 302, 425–427 (2003). 11. Shimizu, K. New superconductors under very high pressure. J. Phys. Condens. Matter 19, 125207 (2007). 12. Hemley, R. J., Chen, Y.-C. & Yan, C.-S. Growing diamond crystals by chemical vapor deposition. Elements 1, 105–108 (2005). 13. Sigmund, P. (ed.) Ion Beam Science: Solved and Unsolved Problems (The Royal Danish Academy of Sciences and Letters, 2006). 14. Subramanian, M. A., Aravamudan, G. & Subba Rao, G. V. Oxide pyrochlores—a review. Prog. Solid State Chem. 15, 55–143 (1983). 15. Chakoumakos, B. C. Systematics of the pyrochlore structure type, ideal A2 B2 X6 Y. J. Solid State Chem. 53, 120–129 (1984). 16. Ewing, R. C., Weber, W. J. & Lian, J. Nuclear waste disposal—pyrochlore (A2 B2 O7 ): Nuclear waste form for the immobilization of plutonium and minor actinides. J. Appl. Phys. 95, 5949–5971 (2004). 17. Lian, J. et al. The order–disorder transition in ion-irradiated pyrochlore. Acta Mater. 51, 1493–1502 (2003). 18. Lang, M. et al. Structural modifications of Gd2 Zr2−x Tix O7 pyrochlore induced by swift heavy ions: Disordering and amorphization. J. Mater. Res. 24, 1322–1334 (2009). 19. Lang, M. et al. Single-ion tracks in Gd2 Zr2−x Tix O7 pyrochlore irradiated with swift heavy ions. Phys. Rev. B 79, 224105 (2009). 20. Zhang, F. X. et al. Phase stability and pressure dependence of defect formation in Gd2 Ti2 O7 and Gd2 Zr2 O7 pyrochlores. Phys. Rev. Lett. 100, 045503 (2008). 21. Zinkevich, M. Thermodynamics of rare earth sesquioxides. Prog. Mater. Sci. 52, 597–647 (2007). 22. Burggraaf, A. J., Van Dijk, T. & Verkerk, M. J. Structure and conductivity of pyrochlore and fluorite type solid solutions. Solid State Ion. 5, 519–522 (1981). 23. Goodenough, J. B. Ceramic technology: Oxide-ion conductors by design. Nature 404, 821–823 (2000). 24. Zhang, J. et al. Liquid-like phase formation in Gd2 Zr2 O7 by extremely ionizing irradiation. J. Appl. Phys. 105, 113510 (2009). 25. Navrotsky, A. Thermochemistry of nanomaterials. Rev. Miner. Geochem. 44, 73–103 (2001). 26. San-Miguel, A. Nanomaterials under high-pressure. Chem. Soc. Rev. 35, 876–889 (2006). 27. Swamy, V. et al. Size-dependent pressure-induced amorphization in nanoscale TiO2 . Phys. Rev. Lett. 96, 135702 (2006).
LETTERS 28. Boccanfuso, M. et al. Heavy-ion induced damage in fluorite nanopowder. Nucl. Instrum. Methods B 175–177, 590–593 (2001). 29. Mao, H.-K., Xu, J. & Bell, P. M. Calibration of the ruby pressure gauge to 800 kbar under quasihydrostatic conditions. Geophys. Res. 91, 4673–4676 (1986). 30. Holzapfel, W. B. Refinement of the ruby luminescence pressure scale. J. Appl. Phys. 93, 1813–1818 (2003). 31. Lang, M. et al. Energy loss of 50-GeV uranium ions in natural diamond. Appl. Phys. A 80, 691–694 (2005). 32. SRIM. (2006). 33. Hammersley, A. P., Svensson, S. O., Hanfland, M., Fitch, A. N. & Häussermann, D. Two-dimensional detector software: From real detector to idealized image or two-theta scan. High Press. Res. 14, 235–248 (1996). 34. Rodriguez-Carvajal, J. Fullprof 2k, 2001, France. 35. Hafner, J. Materials simulations using VASP—a quantum perspective to materials science. Comput. Phys. Commun. 177, 6–13 (2007). 36. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994). 37. Perdew, J. P. & Wang, Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B 45, 13244–13249 (1992).
Acknowledgements This work was supported by the Office of Basic Energy Sciences, USDOE, under grant DE-FG02-97ER45656. The use of the National Synchrotron Light Source at X17C station is supported by NSF COMPRES EAR01-35554 and by USDOE contract DE-AC02-10886. This research was supported in part by the National Science Foundation through TeraGrid resources provided by NCSA and NICS. Further support was provided by the German Science Foundation DFG (grant to M.L.).
Author contributions M.L., F.X.Z. and R.C.E conceived and designed the experiments. C.T., B.S. and R.N. participated in the high-energy irradiations at GSI. M.L. and F.X.Z. analysed the samples by synchrotron XRD. J.Z. completed the TEM analysis and measurements. J.W. and U.B. carried out the quantum-mechanical calculations. All authors have reviewed, discussed and approved the results and conclusions of this letter.
Additional information Reprints and permissions information is available online at http://npg.nature.com/ reprintsandpermissions. Correspondence and requests for materials should be addressed to R.C.E.
NATURE MATERIALS | VOL 8 | OCTOBER 2009 | www.nature.com/naturematerials
© 2009 Macmillan Publishers Limited. All rights reserved.
797
