research papers
Local structural studies of the cubic Cd_{1–x}Ca_{x}O system through Cd Kedge extended Xray absorption spectroscopic studies
^{a}Surface Physics Division, Saha Institute of Nuclear Physics, Kalkata 700064, India, ^{b}Condensed Matter Physics Division, Materials Science Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India, and ^{c}Photon Factory, Institute of Materials Structure Science, High Energy Accelerator Research Organization, Oho 11, Tsukuba 3050801, Japan
^{*}Correspondence email: varadu@igcar.gov.in
Cd Kedge extended Xray absorption finestructure spectroscopic studies were carried out on Cd_{1–x}Ca_{x}O (0 ≤ x ≤0.9) solid solutions and the first and second nearest neighbour (NN) distances and their mean square relative displacement σ^{2} were estimated. The first NN distance, d_{Cd–O}(x), was found to be smaller than its expected value, a(x)/2, obtained from the Xray diffraction measurements. It increases monotonically and nonlinearly with a negative curvature, comparable with that of the a(x) value variation. The variation σ^{2} of the 1NN with x is consistent with a disordered model. The 2NN distances d_{Cd–Cd}(x) and d_{Cd–Ca}(x) are found to follow the average values obtained by Xray diffraction with d_{Cd–Ca}(x) > d_{Cd–Cd}(x). From detailed analysis it is argued that the exhibits a of the 1NN distances, d_{Cd–O}(x) and d_{Ca–O}(x), and that the system belongs to a persistent type.
Keywords: EXAFS; CdO; CaO; ternary solid solution; oxide semiconductors.
1. Introduction
The effect of local atomic rearrangements on the properties of semiconductor alloys has been emphasized recently on the basis of both experimental and theoretical results (Kuzmin et al., 1993; Tsai et al., 1990; Aldrich et al., 1994; Koteski et al., 2004). Such studies received further impetus with the availability of synchrotron radiation facilities to carry out extended Xray absorption finestructure (EXAFS) (Stern, 1974; Lytle et al., 1975; Stern et al., 1975; Bunker, 2010) and atomic pair distribution function (PDF) (Egami & Billinge, 2003) studies. These studies confirm that the local atomic arrangements show substantial deviation from the average structure, though the translational symmetry prevails over much larger length scales (Kuzmin et al., 1995; Lebedev et al., 2001). The effects of such deviation include the reduced pointgroup symmetry, lattice distortions and the modification in the bonding. These in turn affect the physical, optical and electronic properties, which are of fundamental importance for the semiconducting materials. Hence, detailed local structural studies have become of importance to understand not only the average structural changes on alloying but also optical and electronic properties.
Recently we reported a wide and tunable band gap II–VI semiconducting oxide Cd_{1–x}Ca_{x}O system. Although the end members CdO and CaO crystallize in the NaCl structure with a lattice parameter mismatch of 2.5%, the lattice parameter (a) variation of their deviates from a linear variation (Vegard's law). The variation exhibits a negative curvature characterized by a bowing parameter b = 0.03088 (Srihari et al., 2011). Employing a Williamson–Hall type plot (Williamson & Hall, 1953) obtained from the profile analysis of powder Xray diffraction (XRD), the strain as a function of Ca substitution was calculated. It is found that the strain is negligibly small, a generic feature of the oxides. This implies the absence of strain as a field over the coherently diffracting volume. This clearly indicates that substitution results in local structure deviation from the average cubic symmetry, warranting a detailed structural study at the atomic level. spectroscopy is a widely used tool for such studies and is preferred over PDF studies since it selectively probes the local structure around an absorbing species. In this paper we report Cd Kedge studies on the Cd_{1–x}Ca_{x}O system. Our studies indicate that the first nearest neighbour (1NN) distance d_{Cd–O}(x) is smaller than a(x)/2 and exhibits a negative deviation with a bowing parameter same as that of a(x)/2. On the other hand, the second nearest neighbour (2NN) distance d_{Cd–Cd/Ca}(x) closely follows the variation of a(x)/2^{1/2}. It is shown that the 1NN distances d_{Cd–O}(x) and d_{Ca–O}(x) are different and the optical properties of this system would exhibit characteristics of a persistence mode system.
2. Experimental details
Solid solutions of the Cd_{1–x}Ca_{x}O system with x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 and 0.9 were prepared by solid state reaction described in an earlier work (Srihari et al., 2011). Cd Kedge measurements on the Cd_{1–x}Ca_{x}O system were carried out on beamline NW10A of the Photon Factory Advanced Ring (PFAR), Tsukuba, Japan (Nomura, 2001; Nomura et al., 2007). The energy was varied from 500 eV below the Cd Kabsorption edge, E_{0} (= 26711 eV), to 1100 eV above it using a Si (311) doublecrystal monochromator (d = 1.63747 Å). Measurements were carried out on finely ground powders of the Cd_{1–x}Ca_{x}O system. The optimum sample quantity for each composition was estimated such that the effective thickness of the sample corresponds to approximately one absorption length for that composition. The required quantity of a diluting medium, boron nitride powder, was thoroughly mixed with the sample and pressed under moderate pressure into pellets of diameter 10 mm for measurement. Measurements under ambient conditions were carried out in transmission mode using ionization chambers for I_{0} and I_{t}. Energy calibration was carried out using a standard Cd foil.
3. Data processing and analysis
The absorption spectra were processed using the Athena software package (Ravel & Newville, 2005) for edge alignment and preedge treatment (−500 to −150 eV before E_{0}) and background parameters were carefully chosen so that the data suffer the least from artefacts of such a processing. The postedge treatment corresponding to removal of the Kedge absorption of free Cd^{2+} ions in the range 100–1100 eV above E_{0} was carried out to obtain the signal, χ(k). The χ(k) signal was then Fourier transformed (FT) in the range 2 Å^{−1} ≤ k ≤ 14.5 Å^{−1} to obtain the real, Re[χ(R)], imaginary, Im[χ(R)] and absolute magnitude, χ(R), of χ(R). The obtained χ(R) was weighted by k^{3} and fitted to a structural model using Artemis software (Newville, 2001) to obtain local structural information; interatomic distances or the effective path length and mean square relative displacement, σ^{2}, with reference to the absorbing Cd^{2+} ion. In the analysis, singlescattering (SS) and multiplescattering (MS) paths with up to four legs within a cluster size R_{max} = 6 Å were included. In the present study, the fitting was carried out in the range 2 Å ≤ R_{eff} ≤ 6 Å with the Hanning window and dR = 1 Å; R_{eff} is the effective path length. Although our primary interest is limited to the first and second NN, paths with higher R_{eff} need to be included since they form `leakage' paths into the lowR range.
The following strategy was adopted to incorporate atom substitution, which is not a standard feature of the Artemis package. It is assumed that the substitution is random, a fair assumption for the NaCltype structure. Additional Ca^{2+} backscattering paths were included such that for every path (SS or/and MS paths) involving the Cd^{2+} ion a corresponding identical path involving the Ca^{2+} ion is also present. The degeneracy N (coordination number in the case of SS paths or multiplicity in the case of MS paths) of such paths was proportioned between Cd^{2+} and Ca^{2+} paths conforming to the nominal composition of the sample: N_{Cd} = Nx; N_{Ca} = N(1 − x). This methodology provides a scope to extract the parameters of both the 2NN paths, Cd–Cd and Cd–Ca. In the case of random alloys it is known that the distribution of NN atoms around the associated average coordination shell is nonGaussian (Crozier et al., 1988), especially so in the case of the Cd_{1–x}Ca_{x}O system, wherein the difference between Cd and Ca is large. Hence, the cumulant expansion method, which does not assume any specific form for the distribution, was adopted to fit the χ(R) signal (Bunker, 2010; Crozier et al., 1988). Accordingly, the first (C1), second (C2), third (C3) and fourth (C4) cumulants correspond to the NN distance or effective (scattering) path length R_{eff}, the mean square relative displacement (MSRD) σ^{2} of the NN atoms with reference to the absorbing atom, skewness in the distribution and its weightage, respectively. While fitting, correlated parameters were consistently floated and it was seen that the number of floating parameters is always less than the number of independent parameters N_{ind}, as given by the Nyquist criteria (Stern, 1993).
Although we have considered 2–6 Å for obtaining structural parameters, the analysis was broken to overlapping windows in Rspace. For a given fitting, only a few paths were included such that the total number of floated parameters obeys the Nyquist criteria. In all the fitting procedures the pairs of correlated parameters, S_{0} and σ^{2} and E_{0} and ΔR, floated simultaneously. Subsequently, this window range (in R) was sifted so as to include at least one path of the previous fitting session and its parameters were fixed. The entire process was iterated so that good fitting and meaningful errors in the floated parameter were obtained.
4. Results and discussion
Fig. 1 shows the Cd Kedge absorption spectra of the Cd_{1–x}Ca_{x}O The spectra did not show perceptible changes in the XANES range (26611–26775 eV), except for a shift in the position of the first peak to higher energies with x. This shift implies changes in bond lengths and in the nature of bonding, corroborating our earlier inference deduced from the electron density distribution from the powder XRD data (Srihari et al., 2011). On the other hand, substantial and systematic changes are observed in the the k^{3}weighted signal χ(k) (Fig. 2), especially in the range 4 Å^{−1} ≤ k ≤ 12.5 Å^{−1}, indicating changes in the environment of Cd with Ca substitution. In passing, it is remarked that the absence of noise in k^{3}χ(k), even up to 16 Å^{−1}, indicates that the samples are free of pin holes. The absolute magnitude of χ(R) of the in the range 1–6 Å is shown in Fig. 3. It exhibits several peaks and substructures: a peak at ∼2.2 Å corresponding to the 1NN distance, viz. d_{Cd–O} ≃ a/2, estimated from powder XRD studies (Srihari et al., 2011). The shift in the position of this peak to higher R values with x indicates an increase of d_{Cd–O}(x) with x, conforming to the lattice dilation with Ca substitution. The second peak is centered at about ∼3.37 Å and exhibits a shoulder at R ≃ 3.05 Å; the shoulder to the second peak in CdO may be due to nonlinearity in backscattered photoelectron intensity from the Cd atom. Although the position of the second peak corresponds approximately to the 2NN distance, viz. d_{Cd–Cd/Ca} ≃ a/2^{1/2}, as will be seen below, the paths with still higher effective scattering length also contribute to this peak. Figs. 4 and 5 show a structural model fit to the real part, imaginary part and absolute magnitude of χ(R), respectively, for x = 0.3. Contributions from a few representative scattering paths up to 1–3NN are shown. It is seen from these figures that the 1NN signal is not contaminated much by higherorder paths. The contribution of the 2NN, Cd–Cd and Cd–Ca paths are not in phase [Figs. 4(a) and 4(b)] and their contributions are located at about 3.37 Å and 3.05 Å, respectively, in χ(R). The contribution of the Cd–Ca path to the second peak also falls near to the shoulder of the Cd–Cd contribution. From Fig. 5 it is observed that the Cd–Ca contribution to the second peak is at a lower R value compared with that of the Cd–Cd contribution; this may be due to the difference in the phase shift between the scattered electron wave from the Cd and Ca atoms. Also, it can be seen from Fig. 5 that contributions from the 3NN and higherorder paths strongly overlap with those of the 2NN contributions; e.g. contributions from the MS path, Cd(absorbing)–Cd(at facecentered positions)–O1(at edgecentered positions), and SS path, Cd–O2 (bodycentered position). This necessitates one to include the paths with R_{eff} = 6 Å during fitting. From the analysis of χ(R), the NN distances d_{Cd–O}(x), d_{Cd–Cd}(x) and d_{Cd–Cd}(x) were estimated and are tabulated in Table 1 along with σ^{2}, S_{0}^{2}, E_{0} and the Rfactor, a measure of the goodness of fit.

In Fig. 6 the variation of d_{Cd–O}(x) (red circles) is compared with the corresponding distance a(x)/2 (black squares). It is seen that d_{Cd–O}(x) monotonically increases and exhibits a negative deviation from a linear behavior. The variation of d_{Cd–O}(x) was fitted to a secondorder polynomial equation (Srihari et al., 2011) (red line, `Quadratic Fit') and the bowing parameter was estimated to be d_{EXAFS} = 0.026 Å. This value compares well with the bowing parameter for the lattice parameter variation, d_{XRD} = 0.03088 Å (Srihari et al., 2011). In contrast, the 2NN distances, d_{Cd–Cd}(x) and d_{Cd–Ca}(x), increase almost linearly with x (Fig. 7) and are comparable with a(x)/2^{1/2}. It is also seen that d_{Cd–Cd}(x) is smaller than d_{Cd–Ca}(x) for all values of x, consistent with the larger ionic radius of Ca^{2+} compared with that of Cd^{2+}. Variation of , a measure of both thermal and structural disorder, is shown in Fig. 8. The 1NN of undoped CdO itself has a finite value. For x = 0.5, the value of is found to be smaller even than that for the end members. Barring this, the overall variation of exhibits a more or less symmetric variation with a positive curvature having a maximum value of ∼0.0043 Å^{2} for x ≃ 0.5 (Fig. 8). On the other hand, the disorder associated with the 2NN is comparable, ≃ ≃ 0.01 Å. This is much higher compared with that of 1NN and did not exhibit any systematic variation with Ca substitution. The third cumulant of the 1NN distribution for the CdO (x = 0) is ∼2 × 10^{−4} Å, implying a small skewness. It increases with armchair structure to ∼3 × 10^{−4} Å for x = 0.9. While the variation in the skewness in the distribution of d_{Cd–Ca}(x) was found to be negligible with no systematic variation, the variation in the skewness in the distribution of d_{Cd–Ca}(x) exhibits a bell shape: it is either zero or negligibly small for x = 0, 0.1, 0.8 and 0.9 and has a maximum value of ∼6 × 10^{−5} Å^{3} for x = 0.5. Thus, the skewness in the 2NN distribution is estimated to be one order less compared with that of 1NN.
In the past, local structural studies through PDF/EXAFS have been carried out on semiconducting alloys, which can be broadly divided into two groups. For the alloys belonging to the first group, the variation of the lattice parameter follows Vegard's law: Ga_{1–x}In_{x}As (Egami & Billinge, 2003), Hg_{1–x}Cd_{x}Te (Pong et al., 1989), Rb_{1–x}K_{x}Br (Boyce & Mikkelsen, 1985), Th_{1–x}U_{x}O_{2} and Th_{1–x}Pu_{x}O_{2} (Hubert et al., 2006). For the alloys belonging to the second group, the variation of the lattice parameter deviates from Vegard's law: Mg_{1–x}Ni_{x}O (Kuzmin et al., 1995), Mg_{1–x}Co_{x}O (Kuzmin et al., 1993) and Mg_{1–x}Fe_{x}O (Waychunas et al., 1994). In the first group of alloys the 1NN cation–anion distances (e.g. d_{Ga–As} and d_{In–As} for Ga_{1–x}In_{x}As and d_{Th–O} and d_{Pu–O} for Th_{1–x}Pu_{x}O_{2}) are either almost the same or are comparable with those of the respective endmember cation–anion distances or they vary linearly with a substantially small slope comparable with the lattice parameter variation. Among the members belonging to the second group, Kuzmin & Mironova (1998) have carried out detailed local structural investigations on Mg_{1–x}Ni_{x}O (space group ) employing Mg and Niedge Although the lattice parameter of this system exhibits a negative deviation from Vegard's law, with b_{XRD} ≃ 0.01 Å (Kuzmin & Mironova, 1998), both the 1NN distances d_{Mg–O}(x) and d_{Ni–O}(x) are reported to vary linearly. These authors have used the decrease of 2NN distances d_{Mg–Mg}(x) and d_{Ni–Ni}(x) to explain the lattice parameter variation. This is to be contrasted with the Cd_{1–x}Ca_{x}O system under investigation. For the Cd_{1–x}Ca_{x}O system the 1NN distance d_{Cd–O}(x) exhibits a negative deviation with a bowing parameter comparable with that of the lattice parameter variation. Considering that d_{Cd–O}(x) is always smaller than a(x)/2, Cd_{1–x}Ca_{x}O mimics the behavior of the former group of alloys with the exception that both the lattice parameter and the d_{Cd–O}(x) variation deviates from Vegard's law. Compared with semiconducting alloys with wurzite or chalcopyrate structure, the difference between a(x)/2 and d_{Cd–O}(x) for the Cd_{1–x}Ca_{x}O system is smaller, as has been observed for purely ionic systems like K_{1–x}Rb_{x}Br (Boyce & Mikkelsen, 1985). Since the wurzite structure allows larger changes in the bond angles rather than in the bond lengths, to minimize the strain, the endmembers' 1NN distances are more or less preserved, leading to a larger difference between a(x)/2 and 1NN distances. On the other hand, the NaCltype structure with the to which the Cd_{1–x}Ca_{x}O system belongs, does not allow for large bond angle variations and results in larger changes in the bond lengths. This leads to a smaller difference between a(x)/2 and d_{Cd–O}(x) compared with that of the systems belonging to the wurzite structure. Additionally, for systems where the lattice parameter variation obeys Vegard's law, the Phillips ionicity (Phillips, 1970, 1973) of the end members are closely matched (e.g. 0.31 for GaAs and 0.357 for InAs) and changes in the nature of the chemical bonding are not expected. The Phillips ionicity of CdO and CaO are widely different: 0.785 for CdO and 0.913 for CaO. Alloying of such end members brings out change in the nature of the chemical bonding; from more covalentlike for smaller values of Ca substitution to ionic bonding for higher Ca substitution (Srihari et al., 2011). This, coupled with the rather rigid cubic symmetry, is possibly responsible for the observed bowing in the variation of d_{Cd–O}(x) and hence in a(x).
To quantitatively explain the variation of d_{Cd–O}(x), it is necessary to consider the neighborhood of Ca. Owing to the proximity of the Cd L_{I}edge (4018 eV) to the Ca Kedge (4038.5 eV), Ca Ledge could not be carried out and d_{Ca–O}(x) could not be estimated. However, the local structure averaged over a much larger length scale should conform to the as obtained from the diffraction studies. In other words, the sum of the compositional weighted 1NN distances of Cd and Ca should give the lattice parameter as (Azoulay et al., 1982)
In the above equation, the fitted values of a(x) and d_{Cd–O}(x) were used to estimate d_{Cd–O}(x), and its variation is plotted as the solid blue line (`expected d_{Cd–O}') in Fig. 6. Thus the studies indicate a for 1NN distances.
As seen from Fig. 7, the variation of the 2NN distance d_{Cd–Cd/Ca}(x) closely follows that of the average 2NN distance a(x)/2, in contrast to the 1NN distance d_{Cd–O}(x) variation. Such a behavior has been reported for both purely covalent and ionic systems like the Ga_{1–x}In_{x}As (Mikkelsen & Boyce, 1983) and K_{1–x}Rb_{x}Br (Boyce & Mikkelsen, 1985) systems, respectively. This is explained by Boyce & Mikkelsen (1985) by invoking a radial force model, wherein bondstretching radial forces alone are considered while weak bondbending forces are omitted (Shih et al., 1985). Alternatively, one should also take into account (x) to explain this (Frenkel et al., 1993). Upon lattice dilation, d_{Cd–Cd/Ca}(x), as expected, increases by 0.06 Å, from 3.3292 Å (x = 0) to 3.3892 Å (x = 0.9). However, no appreciable changes in (x) are observed indicating that the `packing' around 2NN Cd/Ca is preserved over the entire composition range, as has been reported for the K_{1–x}Rb_{x}Br system (Frenkel et al., 1993). Hence, an increase in d_{Cd–Cd/Ca}(x) is interpreted as an increase in the size of the ionic species with x. With this in the background, variations in (x) clearly indicate that `packing' around 1NN O is rather loose and it undergoes substantial local structural deviation to accommodate the substitution of the larger Ca^{2+} for the smaller Cd^{2+}.
5. Conclusions
Cd Kedge measurements at room temperature were carried out on Cd_{1–x}Ca_{x}O (0 ≤ x ≤ 0.9). Employing the cumulant expansion method, the first [d_{Cd–O}(x)] and second nearest neighbour distances [d_{Cd–Cd}(x) and d_{Cd–Ca}(x)] and mean square relative displacement, σ^{2}, were estimated. It was found that the d_{Cd–O}(x) variation exhibits a negative deviation from linearity with a curvature quite close to that of the lattice parameter variation a(x) and is smaller than a(x)/2. By analyzing the variation of d_{Cd–O}(x) and a(x), it is inferred that the 1NN distance for Ca, d_{Ca–O}(x), is larger than d_{Cd–O}(x), implying a for the nearest neighbour distances. From this, it is expected that the optical properties of the Cd_{1–x}Ca_{x}O system should conform to a persistent type system. From the linear increase in 2NN distances d_{Cd–Cd}(x) and d_{Cd–Ca}(x), with the associated σ^{2} being almost constant, it is reasoned that the ionic sizes of the species are concentrationdependent.
Acknowledgements
The authors would like to acknowledge the NW10A beam staff and PF staff for their support in carrying out the
measurement. This work was undertaken by financial support from the Department of Science and Technology, India, under the project `Utilization of International Synchrotron Radiation and Neutron Scattering Facilities'. V. Srihari would like to acknowledge financial support from the Department of Atomic Energy.References
Aldrich, D. B., Nemanich, R. J. & Sayers, D. E. (1994). Phys. Rev. B, 50, 15026–15033. CrossRef CAS Web of Science Google Scholar
Azoulay, J., Stern, E. A., Shaltiel, D. & Grayevski, A. (1982). Phys. Rev. 25, 5627–5630. CrossRef CAS Google Scholar
Boyce, J. B. & Mikkelsen, J. C. Jr (1985). Phys. Rev. B, 31, 6903–6905. CrossRef CAS Web of Science Google Scholar
Bunker, G. (2010). Introduction to XAFS: A Practical Guide to Xray Absorption Fine Structure Spectroscopy. Cambridge University Press. Google Scholar
Crozier, E. D., Rehr, J. J. & Ingalls, R. (1988). Xray Absorption, edited by D. C. Koningsberger and R. Prins, pp. 373–442. New York: John Wiley and Sons. Google Scholar
Egami, T. & Billinge, S. J. L. (2003). Underneath the Bragg Peaks: Structural Analysis of Complex Materials. Oxford: Pergamon. Google Scholar
Frenkel, A., Stren, E. A., Voronel, A., Qian, M. & Newville, M. (1993). Phys. Rev. Lett. 72, 3485–3488. CrossRef Web of Science Google Scholar
Hubert, S., Purans, J., Heisbourg, G., Moisy, P. & Dacheux, N. (2006). Inorg. Chem. 45, 3887–3894. Web of Science CrossRef PubMed CAS Google Scholar
Koteski, V., Haas, H., HolubKrappe, E., Ivanovic, N. & Mahnke, H.E. (2004). J. Alloys Compd. 371, 138–141. Web of Science CrossRef CAS Google Scholar
Kuzmin, A. & Mironova, N. (1998). J. Phys. Condens. Matter, 10, 7937–7944. Web of Science CrossRef CAS Google Scholar
Kuzmin, A., Mironova, N., Purans, J. & Rodionov, A. (1995). J. Phys. Condens. Matter, 7, 9357–9368. CrossRef CAS Web of Science Google Scholar
Kuzmin, A., Mironova, N., Purans, J. & Sazonov, A. (1993). Phys. Status Solidi A, 135, 133–141. CrossRef CAS Web of Science Google Scholar
Lebedev, A., Sluchinskaya, I. & Munro, I. (2001). J. Synchrotron Rad. 8, 800–802. Web of Science CrossRef CAS IUCr Journals Google Scholar
Lytle, F. W., Sayers, D. E. & Stern, E. A. (1975). Phys. Rev. B, 11, 4825–4835. CrossRef CAS Web of Science Google Scholar
Mikkelsen Jr, J. C. & Boyce, J. B. (1983). Phys. Rev. B, 28, 7130–7140. Google Scholar
Newville, M. (2001). J. Synchrotron Rad. 8, 96–100. Web of Science CrossRef CAS IUCr Journals Google Scholar
Nomura, M. (2001). Handbook of EXAFS Experimental Stations. KEK Internal 2001–5, KEK, Japan. Google Scholar
Nomura, M., Yuichiro, K., Masato, S., Atsushi, K., Yasuhiro, I. & Kiyotaka, A. (2007). AIP Conf. Proc. 882, 896–898. CrossRef CAS Google Scholar
Phillips, J. C. (1970). Rev. Mod. Phys. 42, 317–356. CrossRef CAS Google Scholar
Phillips, J. C. (1973). Bonds and Bands in Semiconductors. New York: Academic Press. Google Scholar
Pong, W. F., Mayanovic, R. A. & Bunker, B. A. (1989). Physica B, 158, 617–618. CrossRef CAS Web of Science Google Scholar
Ravel, B. & Newville, M. (2005). J. Synchrotron Rad. 12, 537–541. Web of Science CrossRef CAS IUCr Journals Google Scholar
Shih, C. K., Spicer, W. E., Harrison, W. A. & Sher, A. (1985). Phys. Rev. B, 31, 1139–1140. CrossRef CAS Web of Science Google Scholar
Srihari, V., Sridharan, V., Chandra, S., Sastry, V. S., Sahu, H. K. & Sundar, C. S. (2011). J. Appl. Phys. 109, 013510. Web of Science CrossRef Google Scholar
Stern, E. A. (1974). Phys. Rev. B, 10, 3027–3037. CrossRef CAS Web of Science Google Scholar
Stern, E. A. (1993). Phys. Rev. B, 48, 9825–9827. CrossRef CAS Web of Science Google Scholar
Stern, E. A., Sayers, D. E. & Lytle, F. W. (1975). Phys. Rev. B, 11, 4836–4846. CrossRef CAS Web of Science Google Scholar
Tsai, M.H., Dow, J. D. & Newman, K. E. (1990). Phys. Rev. B, 41, 7744–7748. CrossRef CAS Web of Science Google Scholar
Waychunas, G. A., Dollase, W. A. & Ross, C. R. II (1994). Am. Miner. 79, 274. Google Scholar
Williamson, G. K. & Hall, W. H. (1953). Acta Metall. 1, 22–31. CrossRef CAS Web of Science Google Scholar
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