School of Chemistry, The University of Sydney, Sydney, New South Wales 2006, Australia ... Howard and Stokes6 suggested possible pathways by which.
PHYSICAL REVIEW B
VOLUME 60, NUMBER 5
1 AUGUST 1999-I
High-temperature phase transitions in SrHfO3 Brendan J. Kennedy and Christopher J. Howard* School of Chemistry, The University of Sydney, Sydney, New South Wales 2006, Australia
Bryan C. Chakoumakos Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 共Received 12 January 1999兲 The crystal structure of SrHfO3 has been studied at high temperatures using powder neutron diffraction and the Rietveld method. From 300 K to approximately 670 K the structure of SrHfO3 is orthorhombic 共Pnma兲. By 870 K the material adopts a second orthorhombic structure 共Cmcm兲. The material then undergoes a further phase transition and is tetragonal (I4/mcm) from ⬃1000 to 1353 K. At higher temperatures 共⬎1360 K兲 the ¯ m). The angle of rotation of the oxygen octahedron in the structure is the ideal cubic perovskite ( Pm3 tetragonal phase is taken as the order parameter and its temperature variation is consistent with a second order phase transition. 关S0163-1829共99兲06229-3兴
INTRODUCTION
A number of ABO3 oxides that adopt the orthorhombic Pnma type perovskite structure under ambient conditions undergo structural transitions to the archetypal cubic perovskite structure at elevated temperatures.1 In both perovskite itself, CaTiO3, and SrZrO3 three phase transitions are observed as follows: Orthorhombic (Pnma)˜ orthorhombic (Cmcm)˜ tetragonal (I4/mcm)˜ ¯ m).2–5 Recent group theoretical analysis by cubic (Pm3 Howard and Stokes6 suggested possible pathways by which the phase transitions could occur. The analysis showed that ¯ m to I4/mcm and then to Cmcm the transitions from Pm3 could be continuous, however there is no continuous path for the transition from Cmcm to Pnma. Despite the importance of many perovskite type oxides under nonambient conditions, for example MgSiO3 as it occurs in the earth’s mantle, or CaTiO3 which is a key component of Synroc used to immobilize nuclear waste,7 there have been few systematic studies of the structural transformations of perovskites at high temperatures. Consequently further experimental data are needed to understand the thermal behavior of the structures of perovskites. Recently we reported details of the transition pathways between the orthorhombic ¯ m) structures in SrZrO and 共Pnma兲 and cubic ( Pm3 3 2,3 CaTiO3. In the present work we extend this study to the heaviest of the group III oxides, Hf. The present paper reports a high temperature study of the crystal structure of SrHfO3 using powder neutron diffraction and the Rietveld method for data analysis. EXPERIMENT
A polycrystalline sample of SrHfO3 was prepared by reacting HfO2 and SrCO3 to 1373 K for 72 h, with periodic regrinding. The neutron powder diffraction patterns were recorded using neutrons of wavelength 1.500 Å, in 0.05° steps over the range 11°⬍2 ⬍135° on the powder diffractometer on HB4 at the High Flux Isotope Reactor at Oak Ridge National Laboratory.8 The sample was placed in a thin-walled 0163-1829/99/60共5兲/2972共4兲/$15.00
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9-mm-diameter vanadium can that was housed in an ILL type vacuum furnace under a dynamic vacuum of around 10⫺6 torr. The data were collected first at room temperature and then at successively higher temperatures. The structural refinements were undertaken using the Rietveld program LHPM operating on a PC.9 The background was defined by a third-order polynomial in 2 and was refined simultaneously with the other profile parameters. A Voigt function was chosen to generate the line shape of the neutron diffraction peaks where the width of the Gaussian component was varied according to (FWHM) 2 ⫽U tan2 ⫹V tan ⫹W to describe instrumental and strain broadening and that of the Lorentzian component as sec to model broadening due to particle size. The 2 region near 38° affected by a peak from the furnace heating element was excluded from the refinements. RESULTS AND DISCUSSION Thermal behavior
Examination of the powder neutron diffraction data demonstrated the following sequence of phase transitions: orthorhombic (Pnma)˜ orthorhombic (Cmcm)˜ tetragonal ¯ m), where the tetragonal (I4/mcm) (I4/mcm)˜ cubic (Pm3 phase exists over a reasonably wide temperature range from about 1023 to 1353 K; see Table I. The temperature variations of the cell parameters and volume are shown in Fig. 1. The identification of the appropriate symmetry involved a careful examination of the various, weak, superstructure peaks that are a result of tilting of the octahedra. Figure 2 illustrates some of the weak reflections that are diagnostic of the different phases. The 141 reflection near 65° and the 143 reflection near 73° in the tetragonal phase are convenient indicators for this space group. The intensities of these reflections rapidly decrease above 1300 K, but they are still just discernible at 1353 K. The weakness of these reflections above 1300 K results in somewhat larger uncertainties in the refined structures in the temperature range 1300–1360 K. Orthorhombic structure „Pnma…
Under ambient conditions SrHfO3 is reported to be isostructural with the mineral perovskite and has a 冑2a⫻ 冑2a 2972
©1999 The American Physical Society
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TABLE I. Cell parameters and space groups for SrHfO3 as a function of temperature. The numbers in parentheses are e.s.d. in the last significant figure. Temp 共K兲
a 共Å兲
b 共Å兲
c 共Å兲
300 673 873 1023 1173 1273 1293 1313 1333 1353 1403
5.7516共5兲 5.7747共6兲 8.1741共12兲 5.7907共4兲 5.7993共4兲 5.8073共5兲 5.8094共5兲 5.8098共5兲 5.8127共6兲 5.8130共4兲 4.1131共1兲
5.7646共5兲 5.7831共6兲 8.1974共8兲
8.1344共9兲 8.1600共7兲 8.1797共9兲 8.2121共7兲 8.2240共7兲 8.2275共10兲 8.2279共10兲 8.2288共11兲 8.2258共9兲 8.2311共12兲
1423
4.1138共1兲
Space group Pbnm Pbnm Cmcm I4/mcm I4/mcm I4/mcm I4/mcm I4/mcm I4/mcm I4/mcm ¯m Pm3 ¯m Pm3
⫻2a orthorhombic superstructure.3 This has the a ⫹ b ⫺ b ⫺ tilt system using Glazer’s notation.10 For consistency with other studies the structure was refined in Pbnm giving the atomic coordinates listed in Table II. The refined structure is in good agreement with that described recently by Guevara and co-workers.11
FIG. 2. Part of the powder neutron-diffraction profiles ( ⫽1.500 Å) showing the temperature dependence of some of the superlattice reflections associated with the tilted octahedra. The patterns correspond to the entries in Table II. The shift of peaks to lower angle with increasing temperature is a result of lattice expansion. In each case the solid line is that calculated by the Rietveld refinement and small vertical markers show the positions of all the allowed Bragg reflections. Orthorhombic structure „Cmcm…
It was not possible to determine the space group appropriate for the structure between 673 and 1023 K by inspection of the diffraction patterns.3 However refinement of the structure at 873 K in space groups Cmcm (R p 7.68 R wp 9.33 R B 3.88) gave a significantly better fit than that obtained in Pbnm (R p 8.13 R wp 9.91 R B 5.03). At lower temperatures better fits were obtained for structures refined in Pbnm. The results of the refinement in Cmcm are listed in Table II. Tetragonal structure „I4/mcm…
FIG. 1. Temperature dependence of 共a兲 the reduced lattice parameters for SrHfO3 and 共b兲 the volume of the primitive cell for SrHfO3.
Part of the powder neutron pattern of SrHfO3 at 1023 K is illustrated in Fig. 2. It can be seen that a number of superlattice lines associated with the tilted oxygen octahedra are present at this temperature. Examination of the diffraction pattern showed splitting of the 12l type reflections indicative of tetragonal symmetry. The structure was refined in space group I4/mcm, this also being found at high temperatures in SrRuO3, 12,13 SrZrO3, 2 and CaTiO3, 3 and in SrTiO3 below 110 K.14 Refinement demonstrated this model to be appropriate, with appreciably better agreement between the observed and calculated profiles being obtained when anisotropic thermal parameters were employed. The final refined parameters and measures of fit for a representative example are given in Table II. At 1023 K the HfO6 octahedron is best described as tetragonally compressed with the axial Hf-O共1兲 bonds being about 0.01 Å shorter than the basal Hf-O共2兲 bonds 2.053 vs 2.065共3兲 Å. As the temperature is increased the in-plane HfO共2兲 bond distances decrease while the axial Hf-O共1兲 distances increase so that at 1353 K the two distances, are within the precision of the structural refinements, equal 2.057 vs 2.058共3兲 Å. This behavior is similar to that observed in SrZrO3 and SrRuO3. 2,13 A second feature of the structural refinements is the large anisotropy in the atomic
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TABLE II. Representative structural parameters for the four phases of SrHfO3. Atom Sr Hf O1 O2 Sr1 Sr2 Hf O1 O2 O3 Sr Hf O1 O2 Sr Hf O
Site
x
y
z
Pbnm 300 K aⴝ5.7516„6… bⴝ5.7646„5… cⴝ8.1344„9… Å 1 0.004共3兲 0.516共1兲 4 0 0 0 1 ⫺0.063共2兲 ⫺0.014共1兲 4 0.2189共9兲 0.2789共9兲 0.0335共7兲 Cmcm 873 K aⴝ8.1741„12… bⴝ8.1974„8… cⴝ8.1797„9… Å 1 4c 0 ⫺0.062共2兲 4 1 4c 0 0.501共2兲 4 1 1 0 8d 4 4 8e 0.274共2兲 0 0 8f 0 0.241共2兲 0.041共1兲 1 8g 0.281共2兲 0.266共1兲 4 I4/mcm 1023 K aⴝbⴝ5.7907„4… cⴝ8.2121„7… Å 1 1 4b 0 2 4 4c 0 0 0 1 4a 0 0 4 8h 0.2828共6兲 0.7828共6兲 0 ¯ m 1403 K aⴝbⴝcⴝ4.1138„1… Å Pm3 1 1 1 1b 2 2 2 1a 0 0 0 1 3d 0 0 2 4c 4a 4c 8d
B 共Å2兲 1.10共6兲 0.34共4兲 1.08共14兲 0.84共8兲 2.1共3兲 1.8共2兲 0.8共1兲 3.8共2兲 2.9共3兲 0.3共2兲 2.5共1兲 0.8共1兲 3.4共2兲 2.7共1兲 3.1共1兲 1.1共1兲 4.1共1兲
The standard R factors for the four structural refinements are as follows: 300 K Pbnm R B 2.96 R p 8.60 R wp 10.42 R exp 9.58%. 873 K Cmcm R B 3.88 R p 7.68 R wp 9.33 R exp 7.95%. 1023 K I4/mcm R B 2.04 R p 7.18 R wp 8.79 R exp 8.20%. ¯ m R B 2.68 R p 7.52 R wp 9.08 R exp 8.67% 1403 K Pm3
displacement parameters of the O anions. These can be understood in terms of the vibration perpendicular to the Hf-O bonds being favored over bond compression. ¯ m… Cubic structure „Pm3
The diffraction patterns collected at or above 1400 K do not show evidence of any superlattice reflections, Fig. 2, and consequently the structure was refined in the cubic space ¯ m. Considerably better agreement between the group Pm3 observed and calculated patterns was obtained when anisotropic rather than isotropic atomic displacement parameters were included in the refinements. The oxygen atoms have their largest displacement amplitudes perpendicular to the linear Hf-O-Hf groups. This corresponds to the direction of the tilt observed in the I4/mcm structure, and as expected for a soft-mode transition to the tetragonal phase the magnitude of this displacement decreases on further heating from 1403 to 1423 K. The smaller displacement along the Hf-O bonds remains essentially constant as the temperature is raised over a similar range. The HfO6 octahedron is now regular with a Hf-O bond distance of 2.057 Å. Phase transitions
We have found that SrHfO3 undergoes a similar series of phase transitions to those observed in SrZrO3 and CaTiO3. 2,3 Owing to the difficulty in experimentally distinguishing
Pnma and Cmcm in powder diffraction studies of perovskite type oxides we have not studied the transition between these in any detail, but note that this transition is necessarily first order.6 The transitions from Cmcm to I4/mcm (a 0 a 0 c ⫺ ) and ¯ m (a 0 a 0 a 0 ) are both allowed to be from I4/mcm to Pm3 continuous in Landau theory6 and we observe a smooth variation in the cell volumes through these transitions, Fig.
FIG. 3. Temperature dependence of the rotational angle . The solid fitted line is given by ⫽A(T c ⫺T) 1/2, with A⫽0.41 and T c ⫽1385 K. The dashed line is calculated for the expression ⫽B(T c ⫺T) 1/4, with B⫽1.7.
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1共b兲. The variable oxygen position parameter also shows no measurable discontinuities at the high temperature transition ¯ m indicating that it is continuous. We from I4/mcm to Pm3 believe the small discontinuity in the lattice c parameter, observed near 1300 K, is a consequence of the weakness of the tetragonal reflections alluded to above. In the single tilt tetragonal phase the angle of rotation of the oxygen octahedron 兵 ⫽tan⫺1 4u, where u⫽x(O2)⫺ 41 其 can be taken as the order parameter. The tilt angle decreases steadily as the temperature approaches the phase transition 共Fig. 3兲, the variation with temperature being well described by ⬀(T c ⫺T) 1/2, where T c is the transition temperature. This behavior is consistent with a second order transition. In both SrZrO3 and CaTiO3 the oxygen tilt angle below the tetragonal-cubic transition was described by expression of the type ⬀(T c ⫺T) 1/4 which is typical of a tricritical phase transition.15 As illustrated in Fig. 3 this is clearly inappropriate for SrHfO3. ¯ m transitions in the three group III The I4/mcm˜ Pm3 oxides SrM O3, M ⫽Ti, Zr, and Hf, have now been studied in some detail.2,14 The transition temperature is essentially a
*On leave from Australian Nuclear Science and Technology Organization, PMB 1, Menai, NSW 2234, Australia. 1 P. M. Woodward, Acta Crystallogr., Sect. B: Struct. Sci. B53, 44 共1997兲. 2 B. J. Kennedy, C. J. Howard, and B. C. Chakoumakos, Phys. Rev. B 59, 4023 共1999兲. 3 B. J. Kennedy, C. J. Howard, and B. C. Chakoumakos, J. Phys.: Condens. Matter 11, 1479 共1999兲. 4 M. Ahtee, A. M. Glazer, and A. W. Hewat, Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. B34, 752 共1978兲. 5 S. A. T. Redfern, J. Phys.: Condens. Matter 8, 8267 共1996兲. 6 C. J. Howard and H. T. Stokes, Acta Crystallogr., Sect. B: Struct. Sci. B54, 782 共1998兲. 7 A. E. Ringwood, S. E. Kesson, K. D. Reeve, D. M. Levins, and E. J. Ramm, in Radioactive Waste Forms for the Future, edited by W. Lutze and R. C. Ewing 共Elsevier, Amsterdam, 1988兲, p. 233. 8 B. C. Chakoumakos, Physica B 241, 361 共1997兲.
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product of the relative size of the Sr2⫹ and M 4⫹ cations, the smaller the M 4⫹ ion the lower the transition temperature. For Zr4⫹ and Hf4⫹ the temperatures for the series of transi¯ m are very similar in tions Pnma˜Cmcm˜I4/mcm˜Pm3 keeping with the similar ionic radii of these ions. The major difference between SrZrO3 and SrHfO3 is the nature, second ¯ m transition. The order vs. tricritical, of the I4/mcm˜ Pm3 atomic displacements clearly implicate a soft mode of the anion in the transition and this has been characterized in considerable detail in SrTiO3. 14 The atomic weight of Hf is approximately twice that of Zr, 178.5 vs 91.2 amu, and this difference may be significant in the detail of the transition. ACKNOWLEDGMENTS
Support from the Access to Major Facilities Program to carry out the work is gratefully acknowledged. Oak Ridge National Laboratory is managed by Lockheed Martin Energy Research Corporation for the U.S. Department of Energy under Contract No. DE-AC05-96OR22464.
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R. J. Hill and C. J. Howard, Australian Atomic Energy Commission Research Establishment, Report No. AAEC/M112, 1986 共unpublished兲. 10 A. M. Glazer, Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. B28, 3384 共1972兲; A. M. Glazer, Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. A31, 756 共1975兲. 11 J. A. Guevara, S. L. Cuffini, Y. P. Mascarenhas, R. E. Carbonio, J. A. Alonso, M. T. Fernandez, P. de la Presa, A. Ayala, and A. Lopez Garcia, Mater. Sci. Forum 278-281, 720 共1998兲. 12 B. C. Chakoumakos, S. E. Nagler, S. T. Misture, and H. M. Christen, Physica B 241, 358 共1997兲. 13 B. J. Kennedy and B. A. Hunter, Phys. Rev. B 58, 653 共1998兲. 14 G. Shirane and Y. Yamada, Phys. Rev. 177, 858 共1969兲. 15 E. K. H. Salje, Phase Transitions in Ferroelastic and Co-elastic Crystals 共Cambridge University Press, Cambridge, England, 1990兲.
