I. INTRODUCTION
ABO 3 perovskite oxides, where A is either a divalent alkaline-earth or trivalent rare-earth ion and B is typically a smaller transition metal ion, exhibit many useful physical properties. These properties, which depend on the choice of the A and B cations, relate to the occurrence of such phenomena as a Jahn–Teller distortion, a variability of the valence states of the transition metal ions, ferromagnetism, ferroelectricity, piezoelectricity, colossal magnetoresistance (CMR), charge ordering, ionic conductivity, etc. A less typical property is superconductivity [a known example is the family of (Ba,X)BiO3 superconductors showing TC≤30 K (Hinks et al., Reference Hinks, Dabrowski, Jorgensen, Mitchell and Richards1988)]. Other phenomena including a metal-to-insulator transition, magnetic-field-dependent structural transition, anomalous thermal conductivity temperature dependence or the isotopic effect on the Curie temperature, TC , have also been reported for some members of this class of materials. Moreover, perovskites can also be multiferroic; i.e., some of them exhibit a coexistence of two or more “ferroic” properties: ferromagnetic order (spontaneous magnetic polarization), ferroelectricity (spontaneous electric polarization), ferroelasticity (spontaneous strain), or ferrotoroidicity (spontaneous magnetization vortices); for more details see Zeng et al. (Reference Zeng, Greenblatt and Croft1999) and Eerenstein et al. (Reference Eerenstein, Mathur and Scott2006). The properties of the given perovskite material can be tuned by composition (partial occupation of A or B sites by transition metal atoms, creation of vacancies at A, B or oxygen sites), structure (over 30 structural variants are known), temperature, pressure, electric and magnetic field, and crystallite size (down to nanometer scale).
The basic cubic perovskite unit cell (with a typical lattice parameter of ∼3.7 Å) contains one A atom, one B atom, and three oxygen atoms. The smaller B cation is coordinated to six oxygen anions to form a BO6 octahedron. Sitting within the holes between the corner sharing BO6 octahedra, the larger A cation is therefore surrounded by 12 oxygen anions. The framework structure is amenable to distortions, which may lower the symmetry of the structure. In particular, hexagonal, rhombohedral, monoclinic, tetragonal, and orthorhombic variants of the perovskite structure are well known. Moreover, the introduction of a large amount of oxygen vacancies in perovskites such as CaMnO3 leads to formation of superstructures (Reller et al., Reference Reller, Thomas, Jefferson and Uppal1984; Petrov et al., Reference Petrov, Parker and Reller1995; Fawcett et al., Reference Fawcett, Sunstrom, Greenblatt, Croft and Ramanujachary1998; Lichtenthaler, Reference Lichtenthaler2005). Importantly, studies of structural distortions, like that of Van Aken et al. (Reference Van Aken, Meetsma, Tomioka, Tokura and Palstra2002), have provided useful insights into the properties of perovskites.
Motivated by the many possible practical uses (for reviews see, e.g., Hellemans, Reference Hellemans1996 and Venkatesan et al., Reference Venkatesan, Rajeswari, Dong, Ogale and Ramesh1998) there has been extensive research into the properties of perovskites, particularly after the discovery of colossal magnetoresistance in manganese oxides (Von Helmholt et al., Reference Von Helmholt, Wecker, Holzapfel, Schultz and Samwer1993; Jin et al., Reference Jin, Tiefel, McCormack, Fastnacht, Ramesh and Chen1994). The transport and magnetic properties of perovskites create opportunities for applications in microelectronics. One potential use of AMnO3 perovskites is related to the tunability of the critical temperature, Tc, by the introduction of magnetic ions into the structure and the possibility of inducing ferromagnetic ordering at room temperature or above. Due to their spin-dependent electrical-transport properties, these materials can be used in the new field of spintronics. Applications connected with electronics include Hall probes for moderate magnetic fields and readout heads for magnetic disks (Von Helmholt et al., Reference Von Helmholt, Wecker, Holzapfel, Schultz and Samwer1993; Mahesh et al., Reference Mahesh, Mahendiran, Raychudhuri and Rao1995; Sagdeo et al., Reference Sagdeo, Anwar and Lalla2006), magnetoresistance based transducers and sensors (Ibarra et al., Reference Ibarra, Algarabel, Marquina, Blasco and García1995; Shim et al., Reference Shim, Bae, Oh and Choi1998), magnetic-field sensors (Sun et al., Reference Sun, Gallagher, Duncombe, Krusin-Elbaum, Altman, Gupta, Lu, Gong and Xiao1996), magnetoresistive microphones (Jin, Reference Jin1996) and random access memories (Dey and Zuleeg, Reference Dey and Zuleeg1990), magnetocaloric-effect based magnetic refrigerators (Pecharsky and Gschneidner, Reference Pecharsky and Gschneidner1999), microwave devices (Dominguez et al., Reference Dominguez, Bhagat, Lofland, Ramachandran, Xiong, Ju, Venkatesan and Greene1995; Tyagi et al., Reference Tyagi, Lofland, Dominguez and Bhagat1996; Wosik et al., Reference Wosik, Xie, Strikovski, Przyslupski, Kamel, Srinivasu and Long2002), bolometers (radiation energy measurement; see Goyal et al., Reference Goyal, Rajeswari, Shreekala, Lofland, Bhagat, Boettcher, Kwon, Ramesh and Venkatesan1997), and high-temperature semiconductors (Miclau et al., Reference Miclau, Hebert, Retoux and Martin2005). Moreover, a number of potential applications in chemistry have been considered, for example, manganese-based perovskites as electrodes of solid oxide fuel cells (Yamamoto, Reference Yamamoto2000) and solid electrolytes in fuel cells (Takahashi and Iwahara, Reference Takahashi and Iwahara1971), catalysts for automobile exhaust including the NO reduction (Voorhoeve et al., Reference Voorhoeve, Remeika, Trimble, Cooper, DiSalvo and Gallagher1975; Jaenicke et al., Reference Jaenicke, Chuah and Lee1991), for CO oxidation (Parravano, Reference Parravano1953), NH3 oxidation (Vrieland, Reference Vrieland1974), methane combustion (Arai et al., Reference Arai, Yamada, Eguchi and Seiyama1986), as well as ethanol (Obayashi et al., Reference Obayashi, Sakurai and Gejo1976) and oxygen sensors (Peng et al., Reference Peng, Liu and Balko2001). For CaMnO3 , a magnetocaloric effect (Bohigas et al., Reference Bohigas, Tejada, del Barco, Zhang and Sales1998) and the possibility of water splitting (Tributsch, Reference Tributsch2008) have been reported.
CaMnO3 is one of more than 20 compounds reported (Balakirev and Golikov, Reference Balakirev and Golikov2006) in the Ca–Mn–O ternary compound series. It has been studied extensively since the beginning of the 1990s as a parent compound for various systems including La1−xCaxMnO3 and Sr1−xCaxMnO3. Calcium manganate has the perovskite-related GdFeO3-type orthorhombic unit cell (space group Pnma) (Poeppelmeier et al., Reference Poeppelmeier, Leonowicz, Scanlon, Longo and Yelon1982), which has cell edges (a, b, c)∼(√2,2, √2)×acubic, and thus contains 4 formula units. For higher temperatures, higher-symmetry unit cells have been reported (Taguchi et al., Reference Taguchi, Nagao, Sato and Shimada1989a). Details of the CaMnO3 structure have been determined in various laboratories using X-ray and neutron diffraction for, almost exclusively, polycrystalline samples (MacChesney et al., Reference MacChesney, Williams, Potter and Sherwood1967; Poeppelmeier et al., Reference Poeppelmeier, Leonowicz, Scanlon, Longo and Yelon1982; Taguchi et al., Reference Taguchi, Nagao, Sato and Shimada1989a; Taguchi, Reference Taguchi1996; Taguchi et al., Reference Taguchi, Sonoda and Nagao1998; Fawcett et al., Reference Fawcett, Sunstrom, Greenblatt, Croft and Ramanujachary1998; Zeng et al., Reference Zeng, Greenblatt and Croft1999; Blasco et al., Reference Blasco, Ritter, Garcia, de Teresa, Perez-Cacho and Ibarra2000; Chmaissem et al., Reference Chmaissem, Dabrowski, Kolesnik, Mais, Brown, Kruk, Prior, Pyles and Jorgensen2001; Machida et al., Reference Machida, Moritomo, Ohoyama and Nakamura2001; Melo Jorge et al., Reference Melo Jorge, Correia dos Santos and Nunes2001; Moritomo et al., Reference Moritomo, Machida, Nishibori, Takata and Sakata2001; Wiebe et al., Reference Wiebe, Greedan, Gardner, Zeng and Greenblatt2001; Rørmark et al., Reference Rørmark, Wiik, Stølen and Grande2002; Töpfer et al., Reference Töpfer, Pippardt, Voigt and Kriegel2004; Bakken et al., Reference Bakken, Boerio-Goates, Grande, Hovde, Norby, Rørmark, Stevens and Stølen2005; Gil de Muro et al., Reference Gil de Muro, Insausti, Lezama and Rojo2005; Lichtenthaler, Reference Lichtenthaler2005; Melo Jorge et al., Reference Melo Jorge, Nunes, Silva Maria and Sousa2005; Slobodin et al., Reference Slobodin, Vladimirova, Petukhov, Surat and Leonidov2005; Taguchi et al., Reference Taguchi, Hirota, Nishihara, Morimoto, Takaoka, Yoshinaka and Yamaguchi2005; Akhtar et al., Reference Akhtar, Catlow, Slater, Walker and Woodley2006; Ang et al., Reference Ang, Sun, Ma, Zhu and Song2006; Kar et al., Reference Kar, Borah and Ravi2006; Zhou and Kennedy, Reference Zhou and Kennedy2006; Nakade et al., Reference Nakade, Hirota, Kato and Taguchi2007; Søndenå et al., Reference Søndenå, Stølen, Ravindran, Grande and Allan2007; Božin et al., Reference Božin, Sartbaeva, Zheng, Wells, Mitchell, Proffen, Thorpe and Billinge2008; Moritomo, Reference Moritomo2008; Isasi et al., Reference Isasi, Lopes, Nunes and Melo Jorge2009). Of particular importance is the result obtained through a joint refinement of X-ray and neutron diffraction data by Blasco et al. (Reference Blasco, Ritter, Garcia, de Teresa, Perez-Cacho and Ibarra2000). Structural distortions in the CaMnO3 structure have also been studied by Raman spectroscopy (Abrashev et al., Reference Abrashev, Bäckström, Börjesson, Popov, Chakalov, Kolev, Meng and Iliev2002). In simulations employing density functional theory (DFT), a cubic structure of calcium manganate is usually employed, which conveniently reduces the number of variables; in one such study Freyria Fava et al. (Reference Freyria Fava, D’Arco, Orlando and Dovesi1997) investigated the electronic and magnetic properties of CaMnO3 . Due to the difficulties in detection of the minor orthorhombic distortion (deviation of axial ratios from unity), early reports on this compound also described the structure as cubic, with acubic=7.46 Å (Wollan and Koehler, Reference Wollan and Koehler1955; PDF 00-003-0830). More importantly though, considering that the accuracy of 1×10−3 Å is easily achievable with present analytical techniques for the measurement of the lattice parameters, we found that the discrepancies among the values reported by different groups for the orthorhombic-cell lattice parameters to be of the order of 2×10−2 Å, i.e., too large. We emphasize that such discrepancies should be at least one order of magnitude smaller. It is thus worth investigating whether these discrepancies are sample or analytical-technique dependent, and, if feasible, aim to select a lattice-parameter set that would serve as a reference for this material. The deviation from stoichiometry is one of the possible sources of these discrepancies. The dependence of unit-cell size on δ in a nonstoichiometric compound, CaMnO3−δ, has been experimentally investigated (Zeng et al., Reference Zeng, Greenblatt and Croft1999; Melo Jorge et al., Reference Melo Jorge, Correia dos Santos and Nunes2001; Töpfer et al., Reference Töpfer, Pippardt, Voigt and Kriegel2004; Gil de Muro et al., Reference Gil de Muro, Insausti, Lezama and Rojo2005). From these reports it can be concluded that the degree of orthorhombicity increases with a rise in δ (although the magnitudes of this effect reported by different groups are not identical).
As well as defining a reference set of lattice parameters for the perfectly stoichiometric and virtually defect-free crystal, an understanding of the effect of δ on the orthorhombic lattice parameters and structural distortions in CaMnO3−δ would be important for an analysis of physical properties of solid solutions containing CaMnO3−δ. Moreover, knowledge of the accurate lattice parameters of CaMnO3 would prove useful in analysis of materials where the lattice parameters are affected by partial substitution of other elements at the Ca or Mn sites; i.e., it could be helpful in understanding the chemical composition of doped calcium manganate samples or samples in geological or environmental studies where CaMnO3 is not necessarily pure— CaMnO3 is found in natural (Iwafuchi et al., Reference Iwafuchi, Watanabe and Otsuka1983; Fazeli and Tareen, Reference Fazeli and Tareen1991) and industrial (Bilinski et al., Reference Bilinski, Kwokal and Branica1996) deposits. The discrepancies among the reported lattice parameters of the pure compound have provided the primary motivation for the present combined experimental and computational study.
In this work, structural properties of a stoichiometric CaMnO3 sample are studied using complementary experimental techniques at ambient temperature and simulations, of both stoichiometric and nonstoichiometric compounds, using the shell model. A comparison of the crystallographic
Figure 1. (Color online) The CaMnO3 sample cut from the prepared bar. The edge length is 2 mm.
data, both the absolute values of unit-cell size and magnitude of orthorhombic distortion, obtained here and from the literature forms the basis of our discussion.
II. DETAILS OF EXPERIMENTS AND SIMULATIONS
A. Sample preparation
The stoichiometric CaMnO3 sample (the same as that studied by Markovich et al., Reference Markovich, Fita, Puzniak, Rozenberg, Martin, Wisniewski, Maignan, Raveau, Yuzhelevskii and Gorodetsky2004 for its magnetic properties) was synthesized in the form of a small bar (see Figure 1) at 1300 °C in air, starting from stoichiometric ratios of CaO and Mn2O3, with intermediate crushing, forming, and heating. The CaO reaction component was prepared by heating CaCO3 (RP Normapur™, Prolabo, France, 99% min) in air at 900 °C; Mn2O3 of nominal purity 98% was supplied by Alfa Aesar). The Ca:Mn ratio (=1) was controlled using EDS analysis with accuracy of 0.02 and the δ value was zero, as verified by measurements of the electric transport and magnetic properties of the sample. The X-ray energy-dispersive analysis of the cationic composition coupled with electron diffraction confirmed the cation homogeneity in the sample. The phase purity was checked by X-ray powder diffraction.
B. Scanning and transmission electron microscopic characterization
The CaMnO3 sample was examined using scanning electron microscopy (SEM) with a JEOL JXA-50A device operating at 20-keV incident-beam energy. The surface morphology was visualized using secondary electron imaging. No effect of surface charging was observed, so there was no need to coat the crystal with a conductive layer.
The transmission electron microscopic (TEM) investigations were performed using a JEOL 2000EX microscope operating at 200-kV accelerating voltage. The specimen was prepared by crushing the material in an agate mortar and subsequently dispersed in methanol using an ultrasonic technique. A droplet of the resulting suspension was deposited on holey carbon film and then dried before being examined.
TABLE I. Characteristics of experimental setting used for data collection.
a The range 5 to 20 °2θ skipped in refinement due to absence of diffraction peaks.
b Depending mainly on the strip width (0.050 mm) and interstrip distance (0.021 mm).
C. X-ray diffraction
In the diffraction measurements, a diffractometer (Philips X’Pert MPD Pro Alpha1, Cu Kα 1 radiation) was used, the Bragg–Brentano geometry of which was modified: a Johansson Ge(111) monochromator was installed in the incident beam and a linear semiconductor strip detector was employed. A good resolution of the apparatus was achieved by combining the effect of the monochromator and the narrowness (50 μm) of the detector strips (the strip angular size is several times smaller than the typical receiving slit opening in classical diffractometers). The data were collected in the 5 to 159 °2θ range (run 1). By collecting an additional data set (run 2), a sample mixture with the commonly accepted lattice-parameter reference material (NIST SRM640c silicon powder), we were able to reduce the statistical errors in the lattice parameters by a factor of more than 1.5 and virtually remove the systematic errors. Run 2 was limited to high angles where the systematic errors are small. The experimental data-collection conditions are summarized in Table I. For a more detailed description of the applied instrument setting, see Paszkowicz (Reference Paszkowicz2005).
D. Analysis of X-ray diffraction data
Rietveld refinements were performed using the FULLPROF2K program (Rodríguez-Carvajal, Reference Rodríguez-Carvajal1993) with the pseudo-Voigt profile shape function. The structural model was based on the single-phase GdFeO3-type structure (space group Pnma) built from Ca2+, Mn4+, and O2− ions, and the refinement started from the data of Blasco et al. (Reference Blasco, Ritter, Garcia, de Teresa, Perez-Cacho and Ibarra2000). For run 1, 32 parameters were refined: the scale factor (1), background parameters (6), lattice parameters (3), atomic position parameters (7), isotropic atomic displacement parameters (4), peak-width (3) and shape (2) parameters, profile asymmetry parameters (4), sample displacement (1), and preferred orientation (1). For run 2, in addition to these parameters we refined the wavelength (justified by a marginal deviation from the expected value, due to the use of the primary-beam monochromator), the angular zero position, and, for the Si phase, the scale factor, peak profile, and preferred-orientation parameters, whereas the peaks of both components were assumed to be symmetric, and the lattice parameter of Si was fixed. The uncertainties of refined parameters were evaluated by the method of Bérar and Lelann (Reference Bérar and Lelann1991) (an option implemented within the FULLPROF2K).
E. Simulations: Methodology
The atomistic simulations, calculation of the lattice energy and physical properties, as well as the initial empirical fitting of the interatomic potentials were performed using the general utility lattice program (GULP) (Gale, Reference Gale1996; Gale and Rohl, Reference Gale and Rohl2003). Cations and anions are modeled using the rigid ion (Born and Huang, Reference Born and Huang1954) and shell (Dick and Overhauser, Reference Dick and Overhauser1958) models, respectively. The Buckingham potential, commonly used when modeling inorganic oxides,
describes the short-range interactions, where rij is the interatomic distance for each pair of ions, i and j, and Aij, ρij , and Cij are species-dependent parameters. For rij greater than 12.0 Å, contributions to the lattice energy from Eq. (1) are assumed to be negligible and therefore not calculated. The point charges placed on cations and anions yield an electrostatic-lattice-energy contribution, which is long range and is, therefore, calculated using the method of Ewald (Reference Ewald1921). The lattice energy is thus the sum of the pair-wise interactions. The calculated structural parameters for CaMnO3 are then obtained by minimizing the lattice energy using standard quasi-Newtonian procedures (Gale and Rohl, Reference Gale and Rohl2003).
Compared to the cubic phase, creation of the orthorhombic unit cell can be founded on two possible mechanisms: on Jahn–Teller distortion of MnO6 octahedra or on rotation of the regular MnO6 octahedra (with equal Mn–O bond lengths), or indeed a combination of both. As stoichiometric CaMnO3 has no Mn(III) ions, we should be able to reproduce the orthorhombic unit cell by only the latter structural change (rotation). To aid the fitting procedure and to increase the transferability of the potential parameters, we chose to use literature oxygen–oxygen Buckingham potential parameters (Sanders et al., Reference Sanders, Leslie and Catlow1984; Cherry et al., Reference Cherry, Islam and Catlow1995; Islam and Winch, Reference Islam and Winch1995; http://www.dfrl.ucl.ac.uk/Potentials), whilst initially refining the cation–oxygen potential parameters. Our final interatomic potential parameters are given in Table II.
Two mean-field approaches were employed to model the orthorhombic, nonstoichiometric CaMnO3−δ compounds. In both approaches, the occupancy of the oxygen site is reduced from 1.0 [i.e., set to (3–δ)/3 on both O(1) and O(2) sites]. This procedure gives rise to a positive charge on the unit cell, which needs to be counterbalanced; as such a model is physically unsound. Two approaches to charge neutralization were employed. In the first, a uniform neutralizing charge
TABLE II. Interatomic potential parameters. Note that we used a quadratic spring constant between each core (c)-shell (s) pair of 50 000 eV Å−4.
background (−8δ|e|) is introduced across the unit cell. Ideally, in this approach, δ should be small. In the second approach, we explicitly model reduction in manganese by decreasing the mean charge on the manganese sublattice from 4 to (4−2δ)|e|. Here we do not model a size and Jahn–Teller effect caused by the Mn(III) ion nor explicit cation ordering on the B site. These refined investigations, which are much more computationally expensive, are currently in progress and will be reported elsewhere. We will refer to the two approaches described here as the “fixed” and “variable” charge models, respectively.
III. SAMPLE MICROSTRUCTURE, MORPHOLOGY, AND STRUCTURE
A. Microstructure and surface morphology
To characterize and assess whether we have good quality materials, we have combined electron-microscopic and X-ray techniques. Electron microscopy was used to describe the grain sizes and morphology and to check for the presence of extended defects. From the SEM images (see upper panels of Figure 2 for different magnifications of our sample), we found a typical surface morphology for a sintered material, i.e., rounded edged grains that have merged together to form a continuous network. The sizes of these grains are in the range 1 to 5 μm and the network has a relatively large porosity. The morphology of a fractured polycrystal, shown in the lower panels of Figure 2, is different as the grains at the fractured surface are smaller and, moreover, have sharp edges.
High-resolution TEM images and electron diffraction patterns obtained for our finely ground sample of CaMnO3 are shown in Figure 3. The rings of the electron-powder-diffraction pattern are highlighted on the left hand side of the image (obtained for a large number of grains). The diameters of these rings relate to the interplanar distances found in the CaMnO3 structure. The widest angle TEM image shows that the finely ground material forms agglomerates built from small grains of less than 50 nm in size. Despite differing preparations, the aspect of the agglomerates is similar to that observed by Gil de Muro et al. (Reference Gil de Muro, Insausti, Lezama and Rojo2005). One typical example of a 20 gram grain is shown in the lower left panel of Figure 3. The high-resolution image of this grain, taken along the [2 0 1] direction, clearly shows atomic planes. Several tens
Figure 2. The morphology across a (100 μm)2, (25 μm)2, and (10 μ)2section of the surface for our sample (upper panels) and for the fractured surface (lower panels).
of other crystallites were inspected; typically, we found a high degree of structural perfection, i.e., an absence of extended defects.
B. Phase analysis and structure refinement
The orthorhombic distortion of CaMnO3 is small, which causes a severe peak overlap within peak clusters in diffraction patterns. Consequently, to accurately determine the lattice parameters, experimental requirements (instrument resolution, counting statistics, and angular range) are particularly high. In order to fulfill these requirements, in our X-ray diffraction experiment we used a modern instrument, a long data-collection time, and included the high-angle region.
From the phase analysis of the sample, we determined that the structure corresponded to that of CaMnO3 (space
Figure 3. The electron-powder-diffraction pattern with rings indexed according to CaMnO3 structure (upper left panel) and the following three TEM images of a small volume of CaMnO3 powder deposited on holey carbon film: a polycrystalline agglomerate (upper right); a single grain, highlighted by a dotted line (lower left panel); and the [2 0 1] zone high-resolution image (lower right panel) of the region within the white square.
Figure 4. (Color online) Rietveld-refinement results for the CaMnO3 powder used in (a) run 1 (CaMnO3). The crosses represent our experimental data and the solid lines refer to the refined data. The difference patterns are shown in the lower part. Vertical bars below the pattern show the peak positions for CaMnO3.
group Pnma). Additional diffraction peaks at 32.99 and 40.38 °2θ (d=2.713 and 2.232 Å) with relative intensities lower than 0.5% were detected. The corresponding spurious phase is different to that found by Taguchi et al. (Reference Taguchi, Kuniyoshi and Nagao1989b); the peaks represent the strongest lines of CaMn2O4 , marokite [the same secondary phase in the CaMnO3 sample as that reported by Santhosh et al. (Reference Santhosh, Goldberger, Woodward, Vogt, Lee and Epstein2000) and Bocher et al. (Reference Bocher, Aguirre, Robert, Logvinovich, Bakardjieva, Hejtmanek and Weidenkaff2009)]. The refined lattice parameters of CaMnO3 are a=5.281 59(4) Å, b=7.457 30(4) Å, and c=5.267 48(4) Å as derived from run 2. The values obtained in run 1 differ at the third decimal places: 5.283 00(7) Å, 7.459 60(7) Å, 5.268 56(6) Å. The difference, of ∼2×10−3 Å between the two runs, shows how large the uncertainty for this type of instrument could be when a small angular range and no internal standard are used. The quality of our refinement is illustrated in Figures 4–6, where our refined atomic positions are listed for comparison with the exemplary data of Blasco et al. (Reference Blasco, Ritter, Garcia, de Teresa, Perez-Cacho and Ibarra2000), which were obtained from a joint refinement of X-ray and neutron data and therefore treated here as our reference. Below, we will return to the relatively large spread in the literature lattice parameters and a comparison with our results will also be discussed.
The shortest Ca–O and Mn–O interatomic distances are shown in Table IV. The literature data for Mn–O bonds and Mn–O–Mn angles are included: they, in particular those of Blasco et al. (Reference Blasco, Ritter, Garcia, de Teresa, Perez-Cacho and Ibarra2000), are consistent with the present data.
Figure 5. (Color online) Rietveld-refinement for CaMnO3: run 1, a magnified portion of the refined pattern showing first peaks that are apparently split: 401/104 at ∼74 °2θ and 421/124 at ∼79 °2θ. The crosses represent our experimental data and the solid lines refer to the refined data. Vertical bars at the ordinate axis show the peak positions for CaMnO3). Peak splitting for CaMnO3 is not observed at lower angles.
IV. DISCUSSION: LATTICE PARAMETERS AND THE MAGNITUDE OF ORTHORHOMBIC DISTORTION
A. Absolute values of lattice parameters
1. Stoichiometric data (δ=0)
The comparison of our observed and predicted orthorhombic CaMnO3 unit-cell-size data with those in the literature demonstrates the relatively large spread of lattice parameters that has been reported by various groups for stoichiometric samples (see Table V). In fact, the range of values reported for a, b, and c lattice parameters are 5.268 to 5.283 Å, 7.435 to 7.468 Å, and 5.255 to 5.274 Å, respectively, which markedly exceed the (usually quite small) error bounds. Note that, with the exception of two papers on thermal expansion, no precise temperature is reported for the “room-temperature” X-ray studies.
Ten of the data sets (including ours) exhibit small uncertainties: see part 1 of Table V. These recent Rietveld refined data sets have a standard deviation <0.0004 Å for each lattice parameter. Within this group, the data of Chmaissem et al. (Reference Chmaissem, Dabrowski, Kolesnik, Mais, Brown, Kruk, Prior, Pyles and Jorgensen2001), Moritomo et al. (Reference Moritomo, Machida, Nishibori, Takata and Sakata2001), and Zhou and Kennedy (Reference Zhou and Kennedy2006) are of particular value because of the following: (i) X-rays sourced from a synchrotron, which provides the best resolution as well as excellent counting statistics (both these features are desirable in the present case of strong peak overlap);
Figure 6. (Color online) Rietveld-refinement results for the mixture of CaMnO3 and Si (run 2). The crosses represent our experimental data and the solid lines refer to the refined data. The difference pattern is shown in the lower part of the panel. Vertical bars below the pattern show the peak positions for CaMnO3 (upper row) and Si (lower row).
and (ii) they report the highest accuracy. The spread of the absolute values of the lattice parameters of stoichiometric CaMnO3−δ (δ=0))is of the order of 0.02 Å. Even in part 1 of Table V, we found a difference of up to two orders of magnitude larger than the reported standard deviations.
To obtain accurate absolute values for the lattice parameters, a combination of two conditions is required: either the use of an internal standard (condition Ia) or knowledge of accurate wavelength (condition Ib), and an acquisition of very high-angle data (condition II). (Self-evident conditions of instrument alignment and good statistics are not discussed here.) When the wavelength uncertainty is due to the use of a primary-beam monochromator or to the use of a synchrotron beam, the combination of conditions Ia and II is preferred. Condition II is particularly important for CaMnO3, because of the very weak orthorhombic distortion: axial ratios close to 1 and √2 lead to the full overlap of peaks in peak clusters at low and medium angles and so only the partial peak separation observed at the highest angles (if the data-collection statistics is sufficient) may help in determination of reliable a , b, and c values. This condition is achievable at a synchrotron and in modern laboratories.
Among the nine literature data sets of part I (Table V), the highest diffraction angles of 140 and 100 °2¸ have been achieved by Blasco et al. (Reference Blasco, Ritter, Garcia, de Teresa, Perez-Cacho and Ibarra2000) and Taguchi (Reference Taguchi1996), respectively. Our procedure satisfied the combined conditions Ia and II. Moreover, to avoid the possible bias caused by the
TABLE III. Fractional atomic positions of Ca, Mn, O(1), and O(2) ions in CaMnO3. The uncertainties were calculated using the method of Bérar and Lelann (Reference Bérar and Lelann1991) with a sigma-correction factor of 3.43 in run 1.
TABLE IV. Structural data: Ca–O and Mn–O distances (Å); Mn–O–Mn angles (degrees).
a Ascription to bonds is arbitrary because these values have been defined as the shortest, medium, and longest.
influence of intense low-angle reflections that dominate the least-squares based minimization procedure, for the calculation of lattice parameters we used the data collected exclusively within the angle range of 105 to 159 °2θ. This is of particular importance for accurate refinements because only at about 2θlim=70° and above will some peak cluster display a partial resolution (using the applied Bragg–Brentano geometry). For samples producing narrow lines, the instrumental limit of 2θ can be shifted towards lower angles using high-resolution synchrotron beamlines. The above-described approach leads to particularly low uncertainties. The lattice parameters, a=5.281 59(4) Å, b=7.457 30(4) Å, c=5.267 48(4) Å, were carefully derived for our sample using this procedure and agreed very well with those derived from the data collected over a broad angular range from our laboratory diffractometers. Data collected at synchrotrons have excellent resolution so, despite the availability of a smaller angular range, they can be used to obtain very good absolute values for lattice parameters. However, as the internal standard has not been used in both synchrotron sets listed in part I of Table V, the absolute values may be affected by the possible (small) wavelength instabilities that are characteristic for synchrotron beams. One of the two synchrotron results, that of Zhou and Kennedy (Reference Zhou and Kennedy2006), is in perfect agreement with the three laboratory sets (ours and those of Blasco et al., Reference Blasco, Ritter, Garcia, de Teresa, Perez-Cacho and Ibarra2000; Božin et al., Reference Božin, Sartbaeva, Zheng, Wells, Mitchell, Proffen, Thorpe and Billinge2008), while the second has a, b, and cvalues that are slightly larger. The use of an internal standard has been explicitly reported only by Lichtenthaler (Reference Lichtenthaler2005), yielding, however, the largest a, b, and cvalues in part I of Table V. We noticed that the synthesis temperature has been quite low in the cited work, which suggests some possible influence of the preparation procedure on the unit-cell size. In general, how the preparation may influence the structural data is not clear; however, it is worth noting that the data sets collected in part I were found to originate mainly from samples prepared by solid state/ceramic reactions.
In summary, on comparison with the literature we have produced lattice parameters with the smallest uncertainties, which agreed best with the four most recent reports (Taguchi et al., Reference Taguchi, Sonoda and Nagao1998; Blasco et al., Reference Blasco, Ritter, Garcia, de Teresa, Perez-Cacho and Ibarra2000 ; Zhou and Kennedy, Reference Zhou and Kennedy2006; and Božin et al., Reference Božin, Sartbaeva, Zheng, Wells, Mitchell, Proffen, Thorpe and Billinge2008). Due to the use of an established internal standard, the present data may serve as a reference for absolute lattice-parameter values of this compound.
2. Nonstoichiometric data (δ>0)
Structural data for nonstoichiometric samples have been collected in Table VI. From studies of both stoichiometric and nonstoichiometric samples, the unit-cell volume is found to increase on average with δ. The rate of increase is not identical in the cited results; however, a rough estimation of the volume change can be obtained using
where k is approximately 5 Å3.
B. Magnitude of orthorhombic distortion
Lattice parameters of CaMnO3 can be presented in a dimensionless form, by plotting the selected axial ratios as in Figure 7, where √2c/b and c/a are the ordinate and abscissa, respectively. This pair of axial ratios is used here to describe the magnitude of orthorhombic distortion. For our sample, the distortion is (c/a, √2c/b)=(0.997 33,0.998 95). The data displayed in Figure 7 include the axial ratios for both stoichiometric (δ=0) and nonstoichiometric (δ>0)CaMnO3−δ. This approach of viewing the data has two main benefits:
(i) It virtually eliminates the systematic errors in the lattice parameters; such errors in diffraction measurements, due to inaccuracies related to sample position, X-ray absorption, uncertainties in angular scale and X-ray (neutron) wavelength, affect mainly the absolute values.
TABLE V. Lattice parameters of CaMnO3 (space group Pnma) at room temperature and ambient pressure. Axial ratios, unit-cell volume and the volume per formula unit, Vfu, temperature, and measurement/calculation details are also given. Part 1—Rietveld refined data with the highest precision reported. Part 2—remaining data. Part 3—simulation data. Data in each section are ordered by date of publication. The referencesFootnote a are identified below.
a [R1] Zeng et al. (Reference Zeng, Greenblatt and Croft1999); [R5] Fawcett et al. (Reference Fawcett, Sunstrom, Greenblatt, Croft and Ramanujachary1998); [R6] Lichtenthaler (Reference Lichtenthaler2005); [R14] Poeppelmeier et al. (Reference Poeppelmeier, Leonowicz, Scanlon, Longo and Yelon1982); [R17] Taguchi (Reference Taguchi1996); [R18] Taguchi et al. (Reference Taguchi, Sonoda and Nagao1998); [R19] Blasco et al. (Reference Blasco, Ritter, Garcia, de Teresa, Perez-Cacho and Ibarra2000); [R20] Chmaissem et al. (Reference Chmaissem, Dabrowski, Kolesnik, Mais, Brown, Kruk, Prior, Pyles and Jorgensen2001); [R21] Machida et al. (Reference Machida, Moritomo, Ohoyama and Nakamura2001); [R22] Melo Jorge et al. (Reference Melo Jorge, Correia dos Santos and Nunes2001); [R23] Moritomo et al. (Reference Moritomo, Machida, Nishibori, Takata and Sakata2001); [R25] Rørmark et al. (Reference Rørmark, Wiik, Stølen and Grande2002); [R28] Gil de Muro et al. (Reference Gil de Muro, Insausti, Lezama and Rojo2005); [R29] Melo Jorge et al. (Reference Melo Jorge, Nunes, Silva Maria and Sousa2005); [R30] Slobodin et al. (Reference Slobodin, Vladimirova, Petukhov, Surat and Leonidov2005); [R32] Ang et al. (Reference Ang, Sun, Ma, Zhu and Song2006); [R33] Akhtar et al. (Reference Akhtar, Catlow, Slater, Walker and Woodley2006); [R34] Božin et al. (Reference Božin, Sartbaeva, Zheng, Wells, Mitchell, Proffen, Thorpe and Billinge2008); [R35] Kar et al. (Reference Kar, Borah and Ravi2006); [R36] Zhou and Kennedy (Reference Zhou and Kennedy2006); [R38] Søndenå et al. (Reference Søndenå, Stølen, Ravindran, Grande and Allan2007); [R39] Moritomo (Reference Moritomo2008); [R40] Isasi et al. (Reference Isasi, Lopes, Nunes and Melo Jorge2009).
b Notations: LXRD—laboratory X-ray diffraction. SXRD—synchrotron X-ray diffraction. “Monocrystal” indicates the use of a single crystal, rather than a polycrystalline sample. ND refers to neutron diffraction; NDT—neutron diffraction time-of-flight method. Abbreviation “Riet” indicates data obtained through Rietveld refinement of powder diffraction data. LSQ—least-squares refinement; RNR—refinement method not reported. RT indicates room temperature; NQ—temperature not quoted. We also include record ID numbers from the PDF and ICSD databases. The r[2θmax] symbol refers to the maximum diffraction angle used in refinements; rQ refers to time-of-flight data ranging to Q=12.4. The s:Si symbol indicates the internal standard reference material (if used). (and): δ value between 0 and 0.02.
c Excess oxygen suggested by the refinements.
d Excess oxygen suggested by neutron powder diffraction; the unit-cell dimensions read from a graph.
(ii) It provides a useful platform for analysis of orthorhombic distortion of any orthorhombic perovskite cell. The figure highlights the distortions: they are the normalized (dimensionless) axial ratios of the orthorhombic cell (with α=β=γ=90°)), x=c/a, y=(c/b) √2. In this representation, the point (x,y)=(1,1) represents the cubic perovskite cell (as we have chosen to use a unit-cell size that contains four octahedra and an orientation such that there are more atomic layers in the b direction, at (1,1) we have a/ √2=b/2=c/ √2=a cubic)); the lines x=1, y=x, and y=1 (gray lines in Figure 7) represent the possible tetragonal distortions when a/ √2=c/ √2, a/ √2=b/2, and b/2=c/ √2, respectively; and every other point represents a true orthorhombic distortion. Naturally, the gray lines cross at (1,1). If we define our origin to be at (1,1) and use polar coordinates (r, ϕ), then the distance, r, measures the magnitude of the distortion, whereas the angle ϕ, measured from the nearest solid gray line, measures the deviation of the orthorhombic distortion from the tetragonal one. The highest deviation is observed for Δϕ=22.5°. The broken line in Figure 7 marks one example of a maximum in orthorhombicity; in this example |b/2−a/ √2|=|b/2−c/ √2|(and b=a/ √2+c/ √2).
Assuming that the required high resolution in X-ray or neutron diffraction is achieved in a given experiment, the distortion at ambient conditions is expected to be influenced only by the chemical composition and sample preparation method. Therefore, the location of each point in this graph is mainly dependent upon δ, the presence of impurities (the Ca:Mn ratio is assumed to be unity), and conditions during measurements. To estimate the effect of different temperatures at which the data have been collected by the different authors, we used the data of Moritomo et al. (Reference Moritomo, Machida, Nishibori, Takata and Sakata2001) and Zhou and Kennedy (Reference Zhou and Kennedy2006). The effect of a temperature scatter of ±10 K (near room temperature) is smaller than the size of the symbols plotted in Figure 7. Therefore, we can disregard temperature during measurements as the cause for the discrepancies between data displayed in Figure 7.
The data shown in the graph have some interesting features:
(i) The spread of c/a and √2c/b values for stoichiometric (δ=0) samples is relatively large, 0.3 and 0.2%, respectively. The reasons for the scatter exceeding the error bounds may be different and stem from the sample composition and preparation, as well as from diffraction data collection and refinement. [As for the latter, we note that for data from different runs in our experiments, there are only slight differences in the refined lattice parameters. The resulting difference in orthorhombic distortion is of the order of 0.0001 only: c/a=0.997 33, √2c/b=0.998 95 (run 2) and c/a=0.997 27, √2c/b=0.998 82 (run 1).] Ten data sets of the best accuracy (see part I of Table V) are contained within the narrow ranges 0.9969<c/a<0.9977 and 0.9988<√2(c/b)<0.9993. These points, representing the data of recently studied stoichiometric samples of highest reported accuracy, are grouped together around the point (0.9973, 0.9990). In our discussion of the distortion magnitude, we will make use of the straight “reference line,”
which connects these points and the (1,1) point that represents the ideal (undistorted) structure. It is interesting to observe that this line differs only slightly (Δϕ=∼19° instead of 22.5°) with the broken line representing the above-defined maximum orthorhombicity (see Figure 7). In fact, data points above the broken line indicate that |b/2−a/ √2|>|b/2−c/ √2| (i.e., b/2 is less than the average value of a/ √2 and c/ √2), which is true for all stoichiometric samples of highest reported accuracy.
(ii) The data for the stoichiometric samples from various laboratories tend to be grouped in close vicinity of the reference line. With the exception of one, all stoichiometric data sets are contained within the hashed area, whereas the majority of the data for oxygen-deficient samples are further afield. It is noteworthy that the distortion derived from our experiment is close to the average obtained from data collected in part I of Table V (filled black squares).
The conditions necessary for the calculation of reliable values of lattice parameters (discussed in Sec. IV A1) are illustrated through the splitting of (401)/(104) and (421)/(124) peak pairs (Figure 5); such splitting is not observed at lower angles. Clearly for the combination of our sample and apparatus, it is impossible to obtain accurate lattice parameters using data collected at low angles only. One can achieve reliable values if the barrier of 70 °2θ is overcome, but even then the weak intensities of split peaks necessitate measurements with excellent statistics. Here the advantage of strategies that avoid the dominance of the low-angle region in refinements is evident. The influence of selection of various angular ranges on the value of refined distortion was tested for the present data: the cases of upper limit fixed at 80 and 60 °2θ are illustrated in Figure 7.
Grouping of the stoichiometric samples in a region of Δϕ=∼19° is probably connected with the ratio of ionic radii of the calcium manganate components; location of this region near the maximum orthorhombicity may require further studies. However, why the data lie along the line described by Eq. (3) is not fully understood. Most probably this location expresses minor differences between properties of these samples, among which the oxygen nonstoichiometry is most plausible, but the influence of other factors such as grain size, presence of impurities, residual strain, and thermal history of the given sample should not be excluded.
C. Effect of nonstoichiometry on lattice parameters and orthorhombic distortion
Literature data for nonstoichiometric samples are collected in Table VI. In Figure 7, the arrows highlight the trends found within the results from several laboratories that studied the correlation between lattice parameters and ϔ . Each arrow indicates the direction for an increase in nonstoichiometry. These arrows show (despite a different inclination that is not very far from the diagonal) that an increase in δ leads to an increase in the distortion for all reported samples (Zeng et al., Reference Zeng, Greenblatt and Croft1999; Melo Jorge et al., Reference Melo Jorge, Correia dos Santos and Nunes2001; Töpfer et al., Reference Töpfer, Pippardt, Voigt and Kriegel2004; Gil de Muro et al., Reference Gil de Muro, Insausti, Lezama and Rojo2005).
To rationalize the observed phenomena, we have performed a series of computer simulations using two different
TABLE VI. Lattice parameters for nonstoichiometric CaMnO3−δ (space group Pnma), where data are ordered by δ. Part I—experimental data. Part II—theoretical data. Data from simulations (F qm and V qmindicate fixed and variable charge models employed) are given in italics. The referencesFootnote a are identified below.Footnote b
a [R1] Zeng et al. (Reference Zeng, Greenblatt and Croft1999); [R15] Taguchi et al. (Reference Taguchi, Nagao, Sato and Shimada1989a); [R16] MacChesney et al. (Reference MacChesney, Williams, Potter and Sherwood1967); [R22] Melo Jorge et al. (Reference Melo Jorge, Correia dos Santos and Nunes2001); [R24] Wiebe et al. (Reference Wiebe, Greedan, Gardner, Zeng and Greenblatt2001); [R26] Töpfer et al. (Reference Töpfer, Pippardt, Voigt and Kriegel2004); [R27] Bakken et al. (Reference Bakken, Boerio-Goates, Grande, Hovde, Norby, Rørmark, Stevens and Stølen2005); [R28] Gil de Muro et al. (Reference Gil de Muro, Insausti, Lezama and Rojo2005); [R31] Taguchi et al. (Reference Taguchi, Hirota, Nishihara, Morimoto, Takaoka, Yoshinaka and Yamaguchi2005); [R37] Nakade et al. (Reference Nakade, Hirota, Kato and Taguchi2007).
b Notations: PCR—polymerized complex route; HSIR—lattice parameters calculated from high-angle reflections using Si standard structure from Rietveld refinement. See also notations used in Table V.
Figure 7. (Color online) Orthorhombic distortion for CaMnO3−δ shown through correlation between the √2c/b and c/a axial ratios. The axial-ratio values were derived from unit-cell-size data of different samples. The ten solid squares (which include the present data) correspond to the data sets with the highest reported accuracy (standard deviations 0.0004 Å or better for all three lattice parameters) for stoichiometric compound. The least-squares fit straight line to these squares is constrained to pass through the point (1,1). The open squares represent the remaining data for stoichiometric samples, whereas the triangles refer to samples with oxygen vacancies (solid for Rietveld refined data and open for others). Unlabelled stars refer to tests of refinement for limited angular ranges (up to 80 °2θ, upper star, and up to 60 °2θ, lower star). For most of the refined data, uncertainties of the axial ratios are smaller than the symbol size. Data from our simulations using the fixed and variable charge models are shown as gray triangles and squares (colored green online), where the color intensity increases with δ (the increment used was 0.03)—the large open circle marks the stoichiometric case. The three solid lines (green online) correspond to the possible tetragonally distorted phases (which cross at the point representing the cubic phase). Any other point represents a further distortion to the orthorhombic cell; the dashed line corresponds to the most orthorhombically distorted one when b√2=a+c (see the beginning of Sec. IV B). The dashed area covers all but one (the K point) of the stoichiometric samples; it includes only one nonstoichiometric sample (the G2 point). Arrows indicate how the distortion changes (as reported in Zeng et al., Reference Zeng, Greenblatt and Croft1999; Melo Jorge et al., Reference Melo Jorge, Correia dos Santos and Nunes2001; Töpfer et al., Reference Töpfer, Pippardt, Voigt and Kriegel2004; Gil de Muro et al., Reference Gil de Muro, Insausti, Lezama and Rojo2005) with the number of oxygen vacancies; the corresponding δ value is presented as a percentage as part of the sample label. Labels (from left to right in the graph, the references are identified below): W6 [R24], K [R35], T2 (δ=0.02) [R15], M [R23], A [R32]; ZE, ZE6 (δ=0.06), ZE11 (δ=0.11) [R1], T [R18], Z [R36], P [R14]; G2 (δ=0.02), GA (sample prepared in air), GO (sample prepared in oxygen) [R28]; L [R6], B [R34], TW—this work, MA [R21], S [R30], F [R5], BL [R19], C [R20], M5 (δ=0.05) [R22], MN [R29]; N3 [R37], BA8 (δ=0.08) [R27], IS [R40], MJ [R22], MC2 (δ=0.02) [R16]; TR5, TR7, TR9 [δ=0.05 (three samples), 0.07, 0.09] [R26], T3 [R17] (references are defined in legends of Tables V and VI). The data of Melo Jorge et al. (Reference Melo Jorge, Correia dos Santos and Nunes2001) differ less than the reported uncertainties; however, they were included because these data represent the same trend as those for other sets. Due to large uncertainties, the point of Rørmark et al. (Reference Rørmark, Wiik, Stølen and Grande2002) is not shown.
approaches to model the vacancies, as described in Sec. II E. We first note that our model for the stoichiometric compound produces an average Mn–O bond distance of 1.897 Å and the deviations of Mn–O–Mn bond angles from 180°, which provide a measure of the rotation of the MnO6 octahedra from the idealized cubic phase, are 20.4 and 21.7°. The predicted change in the lattice parameters, with respect to δ in the range 0 to 0.30, is shown in the upper panels of Figure 8, while the axial ratios are in the lower panels. Remarkably, the two models produce contradicting results for the change in the lattice parameters with δ.
For the fixed charged model, as δ increases: the rate of decrease in the lattice parameters increases; there is no significant change in the difference between a and b/ √2; but they both approach the value of c , the smaller of the lattice parameters, so that the orthorhombic distortion is predicted to weaken (smaller rotation of the MnO6 octahedra; 19.8 and 18.5° for δ=0.15) with an increasing concentration of oxygen vacancies. By employing a partial occupancy for the oxygen site (0.95 for δ=0.15, for example), it appears that the average size of the oxygen atom decreases with δ as our model of the nonstoichiometric compound generates a small size reduction of the MnO6 octahedra (average Mn–O bond length is 1.887 Å for δ=0.15).
For the variable charge model, the lattice parameters increase with δ and the behavior is approximately linear. Although there is a small variation in the b/a ratio (a minimum at δ≈0.09), the behavior is similar to that seen for the previous model in that there is a greater change in the c/a ratio, although the ratios now diverge with δ . The fall in the c/a ratio corresponds to a greater rotation of the MnO6 octahedra (29.6 and 28.5° for δ=0.15) and the structure becomes tetragonal for δ=0.30, where we have the higher concentration of oxygen vacancies. In the variable charge model the charge on the manganese sites reduces with δ; e.g., for δ=0.15 the average oxidation state of manganese cation is 3.7, so the Coulomb attraction between the manganese and oxygen ions will also decrease. Although there is still a partial occupancy of the oxygen sites, the MnO6 octahedra increase in size (average Mn–O bond length is 1.960 Å for δ=0.15).
The trends found for the variable charge model are in better agreement with experiment, i.e., a volume increase
Figure 8. (Color online) Lattice parameters dependence on δ (upper panels) and resulting axial ratios (lower panels) for the variable (left panels) and fixed (right panels) charge models.
with δ , even though the rate of increase being an order of magnitude greater. Although we can expect a lower average charge on the manganese site for nonstoichiometric compounds, even when Jahn–Teller effects are ignored, our simulations suggest that the charge on the manganese site is one of the important factors that determine the atomic structure. To facilitate a comparison to the experimental data shown in Figure 7, we have also plotted our data for both models in Figure 7 (gray triangles and squares, where the intensity increases with δ). For the fixed charge model, as the concentration of oxygen vacancies increases the data points (filled triangles) approach closer to (1,1), a point representing the cubic phase. This trend represents correctly the high-temperature behavior of electrons in the conduction bands, even though it is a simple model of the uniform electron gas. The data on the correlation graph are more sensitive to δ when the variable charge model is employed and, compared to the results obtained using the fixed charged mode, the reverse is found. Now we represent the localization of electrons on the Mn-cationic sublattice as determined by the chemical nature of the lowest conduction band of this material at low or room temperatures. Compared to experiments, the latter set of results still overestimates the absolute values of the distortion, but the distortions [change in c/a of 0.0009 and √2(c/b) of 0.0012 when δ rises from 0 to 0.01] are similar. In fact the calculated gradient with δ is close to that observed (blue arrows in Figure 7).
The bond distances and angles obtained from our simulations can be compared with the experimental data. The rotation of the modeled MnO6 octahedra is similar to that observed, i.e., Mn–O–Mn bond angles reduced from 180° by just over 20°, although our relaxed structure corresponds to the local minimum that has Mn–O(1) as the longest Mn–O bond length.
V. CONCLUDING REMARKS
In this paper, structural properties of CaMnO3−δ are studied experimentally and computationally. In the experimental part, a stoichiometric polycrystalline CaMnO3 (δ=0) sample is characterized using the X-ray diffraction and scanning and transmission electron microscopy. The crystal structure is refined using the Rietveld method. The unit-cell dimensions and orthorhombic distortion of CaMnO3 are determined and discussed on the basis of a comparison with literature data. The lattice parameters a=5.281 59(4) Å, b=7.457 30(4) Å, and c=5.267 48(4) Å are in good agreement with the data from several recent works but (i) show markedly better uncertainties and (ii) are considered to adopt reliable absolute values as they were derived using a well recognized internal standard. The orthorhombic distortion for the studied sample is (c/a, √2c/b)=(0.997 33, 0.998 95). Using graphs such as that in Figure 7 may be useful in the analysis of distortions of other (mainly perovskite-type) oxides.
The magnitude of the orthorhombic distortion, derived from the literature data for both stoichiometric and nonstoichiometric CaMnO3−δ samples, has a non-negligible scatter. However, several data sets, which have a high accuracy in lattice-parameter values and have been reported in the last decade, are consistently close. We believe that this is a good indication of reliability (i.e., the data within this subset of results can be treated as the most reliable). The most accurate experimental data obtained for stoichiometric (δ=0) samples are grouped around the point (0.9973, 0.9990) in agreement with our data. The samples, where the magnitude of the distortion is significantly different, represent nonstoichiometric crystals with oxygen vacancies at the level of several percent. The differences and similarities in the correlations between the orthorhombic distortion and the concentration of the oxygen vacancies (nonstoichiometry) found here and in the literature were discussed. As reported elsewhere, an increase in oxygen vacancies leads to an increase in the orthorhombic distortion. Similar trends are observed in our simulations when the additional electrons are localized on the manganese: the calculated distortion values are markedly larger, but the character of changes is reproduced correctly. However, further experimental studies and simulations, where the cation (and vacancy) ordering and the Jahn–Teller effect are explicitly modeled, are still required.
Our discussions, based on available experimental data and our simulations, provide insight on the relatively large discrepancies between lattice parameters reported for calcium manganate. Good quality structural data for calcium manganate are important in studies of physical properties (particularly magnetic) of this material and composite materials including CaMnO3 as a component.
ACKNOWLEDGMENTS
The authors are grateful to Dr. Alexey A. Sokol (UCL) and Dr. Vladimir Markovich (Ben-Gurion University of the Negev) for valuable comments. Professor Yutaka Moritomo (Nagoya University) is acknowledged for providing the unpublished data. This work was supported in part by Ministry of Science and Higher Education under Research Project No. 1 P03B 12330.
