Showing papers in "Journal of Applied Crystallography in 1974"
TL;DR: A matrix-flushing method for quantitative multicomponent analysis by X-ray diffraction is reported in this article, which is simpler and faster than, yet as reliable as, the conventional internal-standard method.
Abstract: A matrix-flushing method for quantitative multicomponent analysis by X-ray diffraction is reported. It is simpler and faster than, yet as reliable as, the conventional internal-standard method. In this new method, the calibration-curve procedure is shunted; a more fundamental `matrix-flushing' concept is introduced. The matrix-flushing theory gives an exact relationship between intensity and concentration free from matrix effect. Contrary to most theoretical methods the working equation is very simple, no complicated calculations are involved. The matrix-flushing theory and the analytical procedure are presented. Eight illustrative examples are drawn to demonstrate how this theory is applied to multicomponent analysis and amorphous-content determination. A novel `auto-flushing' phenomenon of binary systems was observed which appears to make the analysis of any binary system a simple matter.
1,112 citations
TL;DR: In this article, the matrix-flushing theory and the adiabatic principle were applied in applied X-ray diffraction analysis to obtain the quantitative composition of a mixture.
Abstract: All the information relating to the quantitative composition of a mixture is coded and stored in its X-ray diffraction pattern. It has been the goal of X-ray diffraction analysts since the discovery of X-rays to retrieve and decode this information directly from the X-ray diffraction pattern rather than resort to calibration curves or internal standards. This goal appears to be attained by the application of the `matrix-flushing theory' and the now-proposed `adiabatic principle' in applied X-ray diffraction analysis. The matrix-flushing theory offers a simple intensity-concentration equation free from matrix effects which degenerates to `auto-flushing' for binary systems. The adiabatic principle establishes that the intensity–concentration relationship between each and every pair of components in a multi component system is not perturbed by the presence or absence of other components. A key equation is derived which conducts the decoding process. Both the matrix-flushing theory and the adiabatic principle are experimentally verified.
558 citations
TL;DR: The use of neutrons in small-angle scattering has opened a wide field of applications for investigations in magnetism, polymeric science, for certain problems in biology, and in metallurgy as mentioned in this paper.
Abstract: The use of neutrons in small-angle scattering has opened a wide field of applications for investigations in magnetism, polymeric science, for certain problems in biology, and in metallurgy. In the first part, this review deals with the experimental aspects of neutron small-angle scattering. In particular, the compensation of the relatively small luminosity of neutron sources as compared to X-ray tubes will be discussed in detail. This is mainly achieved by large beam cross sections, leading to correspondingly long instruments, and by an optimization of the intensity with respect to the different contributions to the resolution width of the scattering vector κ(κ = 2πθ/λ, θ = scattering angle, λ = wavelength). Instruments which have been developed along these lines are described, especially the 40 m instrument in Julich and the 80 m instrument at the high-flux reactor in Grenoble. The Grenoble instrument covers a range of scattering vectors between 1 A−1 and 3.10−4A−1; the maximum possible resolution is about 10−4 A−1. Typical applications are reviewed and discussed, namely those dealing with (i) density and compositional fluctuations in solids (alloys, defect clusters, dislocations, grains), (ii) magnetic inhomogeneities in solids (alloys, magnetic domains), (iii) flux-line lattices in type-II superconductors (form factors, imperfections and morphology), (iv) polymers in the solid state, and (v) biological substances.
182 citations
TL;DR: In this paper, aqueous solutions of molecules with molecular weights from about one hundred to several millions have been studied at the high-flux reactor of the Institut Max von Laue-Paul Langevin at Grenoble.
Abstract: In order to get an idea of the possible neutron small-angle scattering experiments with solutions of macromolecules at the high-flux reactor of the Institut Max von Laue–Paul Langevin at Grenoble, aqueous solutions of molecules with molecular weights from about one hundred to several millions have been studied. Changing the contrast by using different H2O/D2O mixtures the basic scattering functions could be determined. Zero-angle scattering from neutron and X-ray small-angle scattering experiments are compared. In the case of ferritin the molecular-weight distribution could be determined from the dependence of zero-angle scattering on the solvent. A considerable variation of the square of the radius of gyration R at low contrast \bar \rho was observed. R2 turned out to be a linear function of 1/\bar \rho. The slope of the straight line is a measure of the homogeneity of the internal structure. Proton–deuteron exchange reactions have been studied. A time resolution of less than two seconds had been reached with myoglobin and other globular proteins.
180 citations
TL;DR: In this paper, the advantages of the step-scan mode over a continuous scan in X-ray data collection are discussed, and it is concluded that the continuous scan mode should be avoided in careful crystallographic studies.
Abstract: The advantages of the step-scan mode over a continuous scan in X-ray data collection are discussed. Computer analysis of the recorded profile allows corrections for effects such as non-uniform background, β-filter cut-off, thermal diffuse scattering, and counter dead time, as well as a reduction in the experimental standard deviations. It is concluded that the continuous scan mode should be avoided in careful crystallographic studies.
142 citations
TL;DR: In this article, a new iterative procedure for desmearing small-angle scattering data including the three types of resolution errors and arbitrary weighting functions is presented, where the statistical errors of the data are taken into account by a ''weighted least-squares'' approximation, i.e., the accuracy of data controls the iterative process.
Abstract: A new iterative procedure for desmearing small-angle scattering data including the three types of resolution errors and arbitrary weighting functions is presented. The statistical errors of the data are taken into account by a `weighted least-squares' approximation, i.e. the accuracy of the data controls the iterative process. The degree of smoothing is dependent on a free smoothing parameter and on the accuracy of the data. The method is not restricted to special types of scattering functions. The termination error is negligible; therefore it is possible to correct parts of scattering distributions. This is of importance for investigations in biological substances where the scattering distribution must be determined in parts with different slit widths. No artificial oscillations are generated in the solution of the integral equation. To ensure the stability of the procedure a criterion for uniform convergence of the iterative process is involved. The results of several numerical tests are shown in the figures. The Fortran program was tested for several months with very satisfactory results.
141 citations
TL;DR: In this article, high-temperature X-ray diffractometry was used to measure the interplanar spacings of 400 mesh quartz powder from 22 to 1400°C, and the maximum volume coefficient of expansion was 100±20 × 10−5deg−1 between 572 and 574°.
Abstract: The (100) and (101) interplanar spacings of 400 mesh quartz powder were measured by high-temperature X-ray diffractometry from 22 to 1400°C. Expansion through the high-low transformation was reversible and continuous, with evidence of 1–2° hysteresis; expansion from 574 to 1000° is zero, with a net decrease from 1000 to 1400°. Maximum linear coefficients of expansion at the transformation were 400±50 x 10−6 deg−1 across the (100) plane and 140±30 x 10−6 deg−1 across the (101) plane. The maximum volume coefficient of expansion was 100±20 × 10−5deg−1 between 572 and 574°. Differential thermal analyses provided ambiguous data, indicating a latent heat of transformation of 160±40 cal/mole, in apparent contradiction with thermal expansion measurements.
93 citations
TL;DR: In this article, a single-crystal diffractometer has been constructed for use with γ-radiation of wavelengths down to λ = 0.03 A. The measured rocking curves represent mosaic distribution functions well and normally no deconvolution problems are involved in the interpretation of these curves.
Abstract: A single-crystal diffractometer has been constructed for use with γ-radiation of wavelengths down to λ = 0.03 A. The relative line width at room temperature of the 412 keV line of radioactive gold is Δλ/λ = 10−6. The angular divergence of the primary beam in the scattering plane is equal to 10′′. The wavelength is so short that the Bragg scattering in imperfect single crystals with an effective thickness of 1 mm or more can be made extinction-free. Therefore the measured rocking curves represent mosaic distribution functions well and normally no deconvolution problems are involved in the interpretation of these curves. Because the absorption of the 412 keV γ-radiation is small (the mean free path for example being about 11 mm for copper), measurements with targets contained in ovens, cryostats, or high-pressure devices can be easily performed.
70 citations
TL;DR: In this article, a multiwire proportional chamber (30 × 30 cm) together with its electronic readout into a large core memory (mass core) has been used successfully as a digital area detector for protein crystallography.
Abstract: A multiwire proportional chamber (30 × 30 cm) together with its electronic readout into a large core memory (mass core) has been used successfully as a digital area detector for protein crystallography. The diffraction pattern stored in the mass core can be displayed on a TV monitor. An IBM 1800 computer has fast random access to the mass core and is used on line to estimate the integrated reflection intensities. To characterize this new area detector, the geometric linearity, the resolution and the quantum detection uniformity have been measured. Preliminary results show that with this new system one can collect intensity data from protein crystals about an order of magnitude faster than with the standard diffractometer.
63 citations
TL;DR: In this article, the reflectivity of metal film multilayers was measured and it was shown that the reflectivities of such multilayer metal film can exceed 30% at 4'A.
Abstract: Alternating layers of two different metals such as Mn and Ge evaporated on an optical flat form a one-dimensional `crystal' which can serve as a wide wavelength band-pass neutron monochromator with a small angular divergence. Measurements of the reflectivity, which exceeds 30% at 4 A, of such metal film multilayers are presented.
56 citations
TL;DR: In this article, the Laue-case skew-symmetric two-crystal X-ray interferometer is described, and the alignment is accomplished with an auxiliary Xray beam, which is multiply reflected by both interferometers parts.
Abstract: The construction and successful operation of a Laue-case skew-symmetric two-crystal X-ray interferometer is described. The alignment is accomplished with an auxiliary X-ray beam, which is multiply reflected by both interferometer parts. As expected, the skew-symmetric two-crystal interferometer is found to be considerably less affected by vibrations than is the symmetric two-crystal interferometer. [Bonse & te Kaat (1968), Z. Phys. 214, 16–21]. The dependence of the crystal lattice moire pattern on rotations about the Δρ and Δθ axes are investigated.
TL;DR: This article showed that the mosaic structure of large single crystals is often very inhomogeneous: the mosaic distribution function has neither a Gaussian nor a Lorentzian shape and the shapes differ remarkably for different volume elements in the sample.
Abstract: Investigations of many imperfect single crystals of different materials by means of a γ-diffractometer show that the mosaic structure of large single crystals is often very inhomogeneous: the mosaic distribution function has neither a Gaussian nor a Lorentzian shape and the shapes differ remarkably for different volume elements in the sample. Current extinction theories must be considered with reservation because Darwin's intensity transport equations are solved assuming the scattering length for a given angle of incidence to be constant all over the irradiated crystal volume. This is not true for samples with inhomogeneous mosaic structure.
TL;DR: In this paper, the integrated intensity Q 0 of the G.P. zones is calculated and the boundaries of the metastable miscibility gap are estimated with more precision than previously, and the integrated intensities in the first reciprocal-space shell are discussed.
Abstract: Measurements made by small-angle X-ray scattering on Al–Ag alloys aged at various temperatures have shown that the asymptotic Porod's law was obeyed except for a constant term. This additional term represents a Laue monotonic intensity, due mainly to atomic concentration fluctuations inside G.P. zones. The integrated intensity Q0 of the G.P. zones themselves can then be calculated, and the boundaries of the metastable miscibility gap estimated with more precision than previously. Furthermore, the integrated intensities in the first reciprocal-space shell make it possible to discuss the crystallographic structure of the G.P. zones. After quenching from 550 to −80°C, the measured intensities agree with the theoretical values, which implies that small G.P. zones ∊′ are disordered. However, for aging above room temperature, there is no agreement between measured and theoretical values. When the aging temperature is increased from 140 to 190°C, an evolution towards a complex structure of G.P. zones is shown.
TL;DR: In this article, the temperature dependence of the absorption spectra of semiconducting WO3 was investigated and the effect was observed within a narrow spectral region near the fundamental absorption edge at 2.58
Abstract: Crystals of semiconducting WO3 exhibit a variation of absorption coefficient if an electric field is applied perpendicular to the direction of propagation of light. The field strengths used were extremely small. The effect is observed within a narrow spectral region near the fundamental absorption edge at 2.58 eV and the modulation frequency is less than 10 Hz. The temperature dependence of the absorption spectra is presented.
TL;DR: In this paper, the particle size and the microstrain components in the Fourier coefficients of a single diffraction profile can be separated, if the functional form of the dependence of the average micro-strain on the averaging distance is known.
Abstract: The particle size and the microstrain components in the Fourier coefficients of a single diffraction profile can be separated, if the functional form of the dependence of the average microstrain on the averaging distance is known. It is shown that if this functional form is approximated as 〈∊n2〉 = C/n, where C is a constant, acceptable separation of the two components can be obtained. In the presence of mean residual strains or peak-shifts due to faulting, the alternative approximation 〈∊n2〉 = C1 + C2/n may be used.
TL;DR: In this paper, small-angle scattering from an Fe65Ni35 single-crystal has been measured with the magnetic field applied parallel and perpendicular to the scattering vector κ. Scattering cross sections due to longitudinal and transverse fluctuations have been calculated.
Abstract: Small-angle scattering from an Fe65Ni35 single-crystal has been measured with the magnetic field applied parallel and perpendicular to the scattering vector κ. Scattering cross sections due to longitudinal and transverse fluctuations have been calculated. The transverse cross section consists mainly of spin-wave scattering and has a long tail up to κ = 0.2 A−1. This suggests that there are spin-wave modes heavily damped by magnetic inhomogeneities. The longitudinal cross section can be described by a Guinier approximation (dσ/dΩ)0 exp (− κ2R2g/3) for the range 0.05 < κ < 0.2 A−1. The forward-scattering cross section (dσ/dΩ)0 and the radius of gyration Rg obtained from experiment are compared with values calculated from Kachi's model. In this model the magnetization is zero for every cluster of 60 atoms with a concentration of nickel below 29%. The comparison shows that the observed value for Rg (= 7.7 A) is about twice as large as the calculated one. The observed forward scattering (dσ/dΩ)0 has slightly different values for different crystal orientations and is on the average 75% of the calculated value. The agreement is remarkable with regard to the crudeness of the model.
TL;DR: In this paper, the authors present the X-ray Diffraction in Crystals, Imperfect Crystals and Amorphous Bodies (XDRB), which is a technique for the detection of imperfections in polycrystals.
Abstract: GUINIER, A. (1963). X-ray Diffraction in Crystals, Imperfect Crystals and Amorphous Bodies. San Francisco: Freeman. KAPLOW, R., STRONG, S. L. & AVERBACH, B. L. (1965). Phys. Rev. 138A, 1336-1345. LANGFORD, J. I. (1968). J. Appl. Cryst. 1, 48-52. MAAT, H. J. & MOSCOU, L. (1964). Proceedings of the International Congress on Catalysis, Amsterdam 1964, II.5, pp. 1277-1287. RYMER, T. B. (1957). Nuovo Cim. Suppl. 10, 294-299. SMn-H, W. L. (1972). J. Appl. Cryst. 5, 127-130. SPINDLER, H. & BAGINSKY, K. (1968). Chem. Tech. 9, 548555. STOKES, A. R. (1948). Proc. Phys. Soc. 61, 382-391. WARREN, B. E. (1959). Progr. Metal Phys. 8, 147-202. WARREN, B. E. & AVERBACH, B. L. (1950). J. Appl. Phys. 21,595-599. WILSON, A. J. C. (1965). Proc. Phys. Soc. 85, 807-809.
TL;DR: In this article, it is shown that the dihydrated oxalates of the magnesium series (Mg, Mn, Fe, Co, Ni, Zn) may exist either as a three-dimensional ordered phase, isostructural with humboldtine, or as a disordered phase with stacking faults parallel to (001) planes.
Abstract: The dihydrated oxalates of the magnesium series (Mg, Mn, Fe, Co, Ni, Zn) may exist either as a three-dimensional ordered phase, isostructural with humboldtine, or as a disordered phase with stacking faults parallel to (001) planes. It is possible to describe the well ordered structure as a layer succession, ABCDABCD... . Then the Stacking faults correspond to permutations between A and C on the one hand and between B and D on the other. These stacking faults give, in X-ray single-crystal photographs, a continuous diffuse intensity along the rows [hk] when h and k are odd. The analysis of this phenomena allows one to give the intensity distribution I(l) along these rows as a function of the rate of faults α. For α= 1 a new ordered structure ABABAB... is obtained which is known in the particular case of the cobalt oxalates. For α = ½ a uniform diffuse intensity is observed. For α ½ the maxima are at lo= 2n (Io is related to a double pseudo-orthorhombic cell).
TL;DR: In this article, a profile-fitting algorithm has been applied to the determination of X-ray diffraction intensities from precession photographs, where each reflection on the film has the same profile or scaled intensity distribution over a two-dimensional array of points about its center.
Abstract: A profile-fitting algorithm has been applied to the determination of X-ray diffraction intensities from precession photographs. It is assumed that each reflection on the film has the same profile or scaled intensity distribution, over a two-dimensional array of points about its center. The integrated intensity of a reflection is that scale factor which gives the best fit between a scaled model profile and the optical density measurements of the reflection. The systematic error in the calculated intensity was evaluated from the discrepancy between the model and observed profiles and was about 2% for strong reflections (about 1.5 OD units). Profile fitting reduced the likely random error in the intensity, produced by errors in optical density measurements, to half the value given by conventional integration. This gain is especially significant for weak reflections which form the bulk of protein data sets. A comparison between film data processed by this method and diffractometer data for the protein lactate dehydrogenase, (34000 Dalton in asymmetric unit), showed that film data agreed with diffractometer data as well as diffractometer data sets agreed among themselves. Film data for glyceraldehyde-3-phosphate dehydrogenase (144000 Dalton in asymmetric unit) had a reliability index of 6% and significant Bijvoet differences were measured for mercury derivatives of the protein. Methods for the correction for non-linear effects in film data are evaluated for model data. It is shown that these corrections give significant improvement only when the data satisfy two conditions: they extend over a wide range of optical densities (at least 20D units) and they are reliable (better than 4% reliability index). Under these conditions an extended version of the Hamilton, Rollett and Sparks scaling algorithm performs better than the other methods considered.
TL;DR: In this paper, a phase diagram around the composition of CuPt3 has been determined based on selected-area electron diffraction and dark-field electron microscopy using thin foils prepared from bulk specimens.
Abstract: The ordered structures of Cu–Pt alloys containing 65–78 at. % Pt have been investigated by a combined technique of selected-area electron diffraction and dark-field electron microscopy using thin foils prepared from bulk specimens, and three different types of ordered structure have been observed. Below the order–disorder transformation temperatures, alloys containing less than about 70 at. % Pt have the rhombohedral superlattice of the Cu3Pt5 type and those with more than 70 at. % Pt, the CuPt3-type superlattice with cubic symmetry. At lower temperatures, however, the orthorhombic superlattice is stable in the composition range from about 68 to 75 at. % Pt. On the basis of the present observations, a partial phase diagram around the composition CuPt3 has been determined.
TL;DR: In this paper, a computer program is described which simulates section topographs of dislocations and it is shown that the contrast of the image is greatly modified when the direction, magnitude and sign of the Burgers vector of a given dislocation are varied.
Abstract: A computer program is described which simulates section topographs of dislocations It is shown that the contrast of the image is greatly modified when the direction, magnitude and sign of the Burgers vector of a given dislocation are varied and that it is now possible, by comparison of the simulation with the experiment, to determine quantitatively the Burgers vector of any straight dislocation in any crystal
TL;DR: In this article, two methods of calculation of indicatrices of diffuse X-ray scattering by globular proteins in a medium with a non-zero electron density are described, which are used in calculation of curves of scattering by sperm whale native myoglobin in different solvents.
Abstract: Two methods of calculation of indicatrices of diffuse X-ray scattering by globular proteins in a medium with a non-zero electron density are described. The methods are used in calculation of curves of scattering by sperm whale native myoglobin in different solvents. The indicatrices obtained are close to the experimental. The nature of the so-called `10 A, maximum', which is observed on the scattering curves of globular proteins in dense solvents as well as in concentrated protein solutions and protein gels, is discussed.
TL;DR: In this paper, the authors measured the thermal expansion and contraction of single-crystal quartz, 400 mesh quartz powder, and chert with a highly sensitive dilatometer apparatus and interpreted the results in terms of a Dauphine twinning mechanism.
Abstract: Thermal expansion and contraction of single-crystal quartz, 400 mesh quartz powder, and chert were measured with a highly sensitive dilatometer apparatus. Below 560°C expansion characteristics were identical and in agreement with X-ray diffractometer measurements. Between 571 and 573°C single-crystal quartz expanded with a volume coefficient of 250 × 10−5 deg−1 and exhibited 2.5°C hysteresis. Between 571 and 576°C 400 mesh quartz expanded with a volume coefficient of 150 x 10−5 deg−1 and exhibited 1°C hysteresis. Chert expanded more gradually between 560 and 650°C, with a maximum volume coefficient of 31 × 10−5 deg−1 and exhibited no hysteresis. The results are interpreted in terms of a Dauphine twinning mechanism and related to observations from the literature, particularly those relating to light-scattering phenomena and strength measurements.
TL;DR: In this paper, a method for least-squares refinement of lattice parameters from powder diffraction measurements is described. But this method is not suitable for measurements obtained from Guinier cameras.
Abstract: A method is described for least-squares refinement of lattice parameters from powder diffraction measurements. Unusual features are: (1) an individual standard error can be assigned to each line, (2) variances and covariances for all parameters are calculated from those errors, (3) the three parameters of a second-degree correction curve are added to the unknowns, and (4) the method uses both the measurements of internal standard lines – if any – and the lines of the substance under investigation for the simultaneous refinement of all unknowns. Because of the last-mentioned feature, the method is especially suitable for measurements obtained from Guinier cameras. The description of a computer program based on this method is added.
TL;DR: An extensive computer program has been developed to check the internal consistency of published, numeric, crystallographic data prior to storage in the data files of the Cambridge Crystallographic Data Centre as mentioned in this paper.
Abstract: An extensive computer program has been developed to check the internal consistency of published, numeric, crystallographic data prior to storage in the data files of the Cambridge Crystallographic Data Centre. The coding is in Fortran IV for an IBM 3701165 with 1 megabyte store. The atomic coordinates, constitution and connectivity of the unique bonded residue(s) are determined from the published asymmetric unit coordinates. Bond lengths are calculated and compared with published values, and any discrepancies are flagged. Checks are made to ensure that the valency requirements of certain elemental types are not violated. The connectivity of the system is expressed in a compact notation. Axial projection plots may optionally be produced on the line printer. The program is likely to be generally useful to individual crystallographers at various stages of an analysis as well as for checking of published data.
TL;DR: In this paper, Schmidt et al. developed a method for correcting small-angle X-ray scattering curves for the effects of the length of the collimating slits, where the scattering data are assumed to be measured at integral multiples of an angular increment Δ.
Abstract: Two improvements have been made in a method which was previously developed [Schmidt, P. W. (1965). Acta Cryst. 19, 938–942] for correcting small-angle X-ray scattering curves for the effects of the length of the collimating slits. In both the original and modified correction methods, the scattering data are assumed to be measured at integral multiples of an angular increment Δ. With the earlier procedure, if the smallest measured intensity was recorded at an angle j0Δ, where j0 is an integer, the smallest angle at which corrected intensities could be computed was (j0 + 2)Δ. The correction method has been modified to permit evaluation of corrected intensities beginning with the angle j0Δ, thus avoiding the loss of the information contained in the intensities measured at the two smallest angles. In addition, a technique has been developed for estimating the uncertainty in the corrected intensity when all measured intensities are recorded for equal counting times and the uncertainty in the measured intensity is assumed to be proportional to the square root of the number of counts recorded.
TL;DR: In this article, the authors measured absolute reflectivities, width of rocking curves and effective absorption coefficients for pyrolytic graphite crystals at different wavelengths at different frequencies. But the results can be described within a few percent by the formulae for the ideal mosaic crystal with absorption.
Abstract: Absolute reflectivities, width of rocking curves and effective absorption coefficients for many pyrolytic graphite crystals at different wavelengths were measured. The results can be described within a few percent by the formulae for the ideal mosaic crystal with absorption. Effective absorption is caused by unavoidable parasitic reflections. The measured effective absorption coefficient is the same for different specimens; it does not depend on the mosaic width. By means of this effective absorption, the peak reflectivity decreases with increasing mosaic width.
TL;DR: The structure of the interstitially ordered lattice formed in zirconium-oxygen alloys has been studied with use of single-crystal data obtained by X-ray and neutron diffraction methods.
Abstract: The structure of the interstitially ordered lattice formed in zirconium–oxygen alloys has been studied with use of single-crystal data obtained by X-ray and neutron diffraction methods The structure belongs to space group P312 and the lattice parameters a and c are related to a0 and c0 of the host hexagonal metal lattice by a = √3a0 and c = c0 The ordered arrangement of interstitial oxygen atoms is described as a regular stacking of layers parallel to the (001) plane with the sequence (AC)B(AC)B⋯ which is of the same type as that of nitrogen atoms in ∊-Fe2N The occupancy probability of oxygen atoms is high for interstitial sites of the A and B types while it is low for sites of the C type The host metal lattice is distorted in such a way that spacings of successive (002) planes are not the same and a hexagonal network of atoms in these planes is periodically deformed