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The electron tunneling spectroscopy is performed on PbILa 1− x Sr x CuO 4 (LSCO) junctions fabricated on high quality LSCO single crystals grown by traveling solvent floating zone (TSFZ) method. For the junctions fabricated parallel to ab -planes, periodic sharp spikes in the spectrum are observed at ∼ 6 × (2 n + 1) mV, where n is a natural number, while for the junctions fabricated on the (001) plane only gap structures corresponding to Pb and LSCO are observed. We ascribe the spike structure to subbands in the electron density of states caused by the Andreev reflections on the periodically modulated gap potential along the c -axis of LSCO.

We report on vector magnetization studies of a La{sub 1.9}Sr{sub 0.1}CuO{sub 4} single crystal, cut in the form of a disk with the anisotropy (c) axis parallel to the disk plane. We observe a sharp threshold in the angular dependences of the isothermal remanent magnetization. When the magnetic field is applied within a threshold angle to the ab plane, the remanent moment is strictly parallel to ab, and also the c-axis component of magnetization is reversible. The threshold angle scales with temperature in the same manner as the lower critical field parallel to the c axis, H{sub c1}{sup c}. These observations give direct support to the presence of a vortex lock-in transition to the CuO planes in our crystal. {copyright} {ital 1997} {ital The American Physical Society}

A strong dependence of the cerium distribution coefficient ( K Ce ) on oxygen partial pressure P [O 2 ] has been shown in direct TSFZ experiments by changing the oxygen pressure during Nd 2−x Ce x CuO 4 single crystal growth. The ratio of K 0.1 atm Ce / K 0.2 atm Ce has been found to be equal to ∼0.62. Absolute values of K Ce measured from zone compositions have been found to be about 2.42, 3.37 and 9.06 at P[O 2 ]=0.1, 0.2 and 2.0 atm, respectively. Our experiment shows good agreement between measured and calculated K Ce values. We have shown that the quite large difference in K Ce obtained in a number of investigations is explained by a strong dependence of K Ce on P [O 2 ]. We have also shown that a reason for this dependence is the variable valence of Ce. Cerium effectively incorporates in a Nd 2−x Ce x CuO 4 single crystal in the form of Ce +4 ion.

High-resolution ultrasonic measurements have been performed on single-crystalline ${\mathrm{La}}_{1.86}$${\mathrm{Sr}}_{0.14}$${\mathrm{CuO}}_{4}$ in magnetic fields H up to 14 T. We found that by reducing temperature the transverse elastic constant (${\mathit{C}}_{11}$-${\mathit{C}}_{12}$)/2 starts to soften from about 50 K and continues to soften down to ${\mathit{T}}_{\mathit{c}}$(H), even when ${\mathit{T}}_{\mathit{c}}$(H) is reduced to 14 K by magnetic field. The softening turns to rapid hardening by the emergence of superconductivity. This behavior of C${(}_{11}$-${\mathit{C}}_{12}$)/2 is a consequence of the structural instability of the orthorhombic phase and disappearance of the instability caused by emergence of the superconducting state.

Capacitance-dilatometer measurements of the anisotropic thermal expansion on a superconducting single crystal of ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$ (x\ensuremath{\sim}0.13) show large anomalies at the structural transition from the high-temperature tetragonal to the low-temperature orthorhombic phase followed by smaller anomalies of the opposite sign at the superconducting phase transition. Neutron-diffraction experiments on the same crystal indicate that at ${\mathit{T}}_{\mathit{c}}$ the tilt of the ${\mathrm{CuO}}_{6}$ octahedra related to the structural phase transition is frozen in.

It was found that NdAlO 3 has a reversible phase transition at a temperature close to its melting point. Substitution of Y for Nd in NdAlO 3 was effective in stabilizing the high temperature phase. Crystals of Nd 1-x Y x AlO 3 (0≤x≤0.25) were grown by the floating zone (FZ) method using an infrared furnace. The crystals had some cracks, subgrain boundaries and domain structure, and 'also were not uniform in Y concentration due to supercooling

Neutron scattering experiments have been performed to study the dynamic spin properties of single-crystal La 1.86 Sr 0.14 Cu 0.988 Zn 0.012 O 4 ( T C =16 K). The width of S ( Q , ω) in momentum space decreases at low ω and at low temperatures. The intensity at low energies at the incommensurate peak position (π(1-δ), π)) shows a broad maximum as a function of temperature around the superconducting transition temperature T C . This behavior is qualitatively similar to that observed by Thurston et al . in La 1.85 Sr 0.15 CuO 4 ( T C =33 K).

The positive muon (μ+) spin relaxation method under zero external field is applied to probe magnetic ordering in the superconducting phase of a high quality single crystal of La2−xSrxCuO4 (0.10

By using a monodomain single crystal La2CuO4 grown by the travelling solvent floating zone method, the strength and direction of the local hyperfine field vector at positive muon sites were determined. Combining with the μ+ location determined separately, we found the importance of the local hyperfine field contributions with dipolar symmetry as well as the distant dipolar field from surrounding point dipoles of Cu atomic moments.

Measurements are reported of the static, instantaneous, and dynamic spin correlations in single crystals of ${\mathrm{Nd}}_{1.85}$${\mathrm{Ce}}_{0.15}$${\mathrm{CuO}}_{4+\mathrm{\ensuremath{\delta}}}$. The as-grown crystals show antiferromagnetic long-range order. However, the N\'eel temperatures and spin-stiffness constants are greatly reduced from their respective values in ${\mathrm{Nd}}_{2}$${\mathrm{CuO}}_{4+\mathrm{\ensuremath{\delta}}}$. After reduction and annealing, the crystals superconduct with ${\mathit{T}}_{\mathit{c}}$=23 K, but inclusions of the antiferromagnetic phase, albeit with reduced N\'eel temperatures, are always present. Based on these data, we suggest that the disorder due to excess oxygen in as-grown samples stabilizes the magnetic correlations. This leads to a speculative model for the effects of deoxygenation in which the removal of the excess oxygen causes the magnetic correlations to diminish and hence superconductivity to become possible.

We have measured the magnetic susceptibility and the anisotropy for a (La1-xSrx)2CuO4 (x=0.075) single crystal in the fluctuation regime for fields between 0 and 5 T. The fluctuation contribution close to Tc is smaller than the one expected from standard 3D or 2D Ginzburg-Landau theory. Our data could be rescaled according to the model proposed by Ullah and Dorsey, using 2D exponents. The anisotropy data shows a deviation from linearity in the vicinity of Tc, for fields close to the plane direction, which we attribute to the onset of bulk superconductivity.

Magnetization curves of large single crystals of (La1-xSrx)2CuO4 (x=0.065 and 0.07) were measured at temperatures from 4.2 to 30K under magnetic fields of up to 9T. The crystals utilized had long dimensions in either the c-axis or the a-axis direction along which the magnetic field was applied, in order to minimize the demagnetization effect. The analysis of the hysteresis data revealed strong anisotropy in flux pinning and critical current density, Jcab(H//c), Jcab (H//ab) and Jcc (H//ab). It was found that the field and temperature dependence was most pronounced for Jcab(H//c) and discussion will be made for this particular case in terms of the conventional scaling law.

Flux jumps have been observed in a large (138 mg) single crystal of La 1.86 Sr 0.14 CuO 4 . Both complete and incomplete flux jumps are observed with the energy dissipated by complete flux jumps consistent with temperature rises to nearly T c . The systematics of these flux jumps with respect to field history, temperature and the time duration of the hysteresis measurements are reported. The field at which flux jumps first occur and their subsequent spacing are not consistent with a simple adiabatic theory of flux jumps for our experimental conditions. Instead, the crystal is observed to be stabilized against flux jumps by flux creep which occurs during the time interval over which field steps are accomplished as well as during imposed time intervals between field steps.

Magnetic relaxation and hysteresis studies have been performed for a c-axis-oriented single crystal of ${\mathrm{La}}_{1.86}$${\mathrm{Sr}}_{0.14}$${\mathrm{CuO}}_{4}$. We demonstrate that the effective activation energy for flux creep, ${\mathit{U}}_{\mathrm{eff}}$, is a strongly nonlinear function of the current density J (as given by the irreversible magnetization). For fixed fields of 0.5, 1.0, 2.0, and 3.0 T and temperatures between 4 and 15 K (as consistent with full field penetration of the sample), ${\mathit{U}}_{\mathrm{eff}}$(J) is seen to vary approximately logarithmically with J. A scaling relationship, ${\mathit{U}}_{\mathrm{eff}}$(J)=[-${\mathit{U}}_{1}$g(T)/${\mathit{H}}^{\mathit{n}}$]ln(J/${\mathit{J}}_{\mathit{c}}$), is shown to be obeyed for this crystal with n\ensuremath{\simeq}0.9 (H in T), ${\mathit{U}}_{1}$\ensuremath{\simeq}180${\mathit{k}}_{\mathit{B}}$, and ${\mathit{J}}_{\mathit{c}}$(1 T)\ensuremath{\simeq}3.2\ifmmode\times\else\texttimes\fi{}${10}^{5}$ A/${\mathrm{cm}}^{2}$. Several functional forms of g(T) have been explored and shown to give reasonable fits if monotonically decreasing in temperature over the range where flux creep is observed. We also explore the ramifications of this functional dependence in explaining an observed exponential temperature dependence of the hysterically determined critical current density. Finally, we show that comparison of the temperature dependence of logarithmic relaxation rate A=dM/d ln(t) and the derivative of the magnetization with respect to ln(T) at fixed time, ${\mathit{dM}}_{0}$/d ln(T), can be used to set a scale of the attempt frequency for flux motion consistent with the other measurements.

The torque signal near T c was studied on a (La 1− x Sr x ) 2 CuO 4 ( x =0.075) single crystal. For fields applied close to the plane direction, the reversible torque signal could be fitted with the anisotropic London theory using an anisotropy ratio γ( T )=10 to 20, (d(1/λ 2 )/d T ) T c ≈2.7 μm -2 K -1 and (d(η H c2· )/d T ) T c ≈2T K -1 . The signal exhibits irreversibility associated with the trapping of flux lines between the superconducting planes. The magnitude of the effect decays exponentially with temperature and field.

The positive muon spin relaxation method is applied to probe magnetic ordering in the superconducting phase of a high quality single crystal of La2−xSrxCuO4−σ (0.11≤x≤0.14). The well characterized crystal ofx=0.11 (T c=34.5 K) with nearly complete flux exclusion exhibits spin freezing at 8K(T f) with significant spin fluctuation up to 20 K. The onset of spin fluctuation andT f decrease against increasingx towardsx=0.15, suggesting an existence of a magnetic phase boundary aroundx whereT c becomes maximum.

The anisotropic lower critical fields ${\mathit{H}}_{\mathit{c}1}$ are determined from a novel procedure based on the Bean's critical-state model to pick up the onset of flux penetration in broad zero-field-cooled magnetization curves in (${\mathrm{La}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${)}_{2}$${\mathrm{CuO}}_{4}$ (x\ensuremath{\approxeq}0.07) single crystals. The values of ${\mathit{H}}_{\mathit{c}1}$ at T=0 K are estimated to be 70 G for H\ensuremath{\parallel} layer and 300 G for H\ensuremath{\perp} layer. The temperature dependence of ${\mathit{H}}_{\mathit{c}1}$ is such that it tends to saturate towards the lowest temperature measured (2 K) in contrast to the other recent results which report the abnormal upturn of the ${\mathit{H}}_{\mathit{c}1}$-T curve at low temperatures. Instead the results indicate that the critical current density in plane has a strong temperature dependence even in the temperature range well below ${\mathit{T}}_{\mathit{c}}$ and becomes \ensuremath{\sim}${10}^{6}$ A/${\mathrm{cm}}^{2}$ at 2 K.

We have measured two phonon-dispersion curves above 50 meV in a superconducting (T c = 33 K) single crystal of La 1.85 Sr 0.15 CuO 4 . In the normal phase (T = 45 K), we show that the Λ 1 mode compatible with the Raman A 1g (425 cm -1 ) mode is weakly dispersive, falling from 53.7 meV at the zone center to about 51 meV at the zone boundary along the tetragonal (0,0,ξ) direction. For the Λ 1 mode compatible with the infra-red A 2u (480 cm -1 ) mode, we observe a significant dispersion of the phonon energy which drops monotonically from 60 to 56 meV. The global features of these dispersion curves are similar to those previously reported in studies of both pure and 10% Sr doped La 2 CuO 4 . However significant differences in the shape of the dispersion of the highest Λ 1 branch is shown, as well as a significant softening with increasing carrier concentration.

Surface of La2CuO4 single crystals were oxidized by KMnO4 aqueous solutions. The oxidation conditions such as KMnO4 concentration, soaking time and solution temperature of KMnO4, were systematically controlled. The magnetic properties of the crystals were drastically dependent on the oxidation conditions. The superconducting transition properties under the optimum condition, 48 h, 150°C and 5 wt%, were T c = 28 K and ∆T c = 2K. The chemical oxidation was limited only to the surface region of the crystals. Therefore, chemical oxidation may be useful for the preparation of superconducting single-crystalline films.

Precision lattice parameter in La1.85Sr0.15CuO4 single crystal superconductor has been measured in a wide temperature range between 4.2 K and room temperature by the X-ray Bond’s method. An anomalous lattice contraction associated with the appearance of the superconductivity was found in c-plane. Along c-direction, on the contrary, an anomalous expansion of the lattice was observed. The relative spontaneous change in the lattice parameter in c-plane was 2.3xl0­-5 and that of c-axis was 1.5×l0-5 at 4.2 K. The temperature dependence of the spontaneous lattice change was compared with currently existing theories for high Tc superconductivity.

We studied the superconducting properties of an electron irradiated La1.85Sr0.15CuO4 single crystal. Point-like defects are introduced into the crystal with the irradiation. The irradiation decreases the correlation between CuO2 layers. However, both before and after the irradiation, the flux creep activation energy Ueff (J,T,H) can be expressed the same formula as Ueff (J,T,H) = const.*In(J)*(1-T/Tc)n/H, where n is a constant determined from the irreversibility line.

Bulks of YBCO superconductor were prepared by melt process with seeding single grains of YBCO and SmBCO superconductors and single crystals of SrTiO3 and MgO. The seedeing of YBCO single grain and MgO single crystal was effective for the growth of single-grained bulk of YBCO superconductor. The maximum size of the single-grained YBCO bulk was 45 mm in diameter and 15 mm in thickness.

Magnetization curves of (La1−xSrx)2CuO4 (x=0.065−0.07) single crystals were measured at temperatures from 4.2 to 35K under magnetic field of up to 9T. The field was applied along the a- or the c-axis of the two types of the crystals having different macroscopic geometry. The analysis of the hysteresis data revealed strong anisotropy in flux pinning and critical current density. At 4.2 K and 5 T, for example, Jc//ab-plane(H//c-axis), Jcc(H//ab) were determined to be 2.1×105, and 3.0×104 A/cm2, respectively and Jcab(H//ab) was estimated to be 4.2×105 A/cm2. It was also found that the field and temperature dependence was quite appreciable in Jc//ab(H//c), as expected from the generally observed behavior in cuprate-based HTSC oxides.

Using a transverse vibrating sample magnetometer, we have made vector magnetisation measurements on a disk-shaped single crystal La1.9Sr0.1CuO4. Reversible behaviour of the c-axis component of magnetisation, and the angular dependences of the remanent moment are evidence of the vortex lock-in state. The lock-in angle dependence on temperature and applied magnetic field are in agreement with theory.

We present high-resolution dilatometry measurements of a La 1.87 Sr 0.13 CuO 4 -single crystal parallel and perpendicular to the CuO 2 -planes in magnetic fields up to 14 Tesla. We find a strong suppression of the thermal expansion anomalies for magnetic fields parallel to the c-axis. In contrast, a magnetic field perpendicular to the c-axis affects the anomalies only weakly.

An increase of the sound velocity reflecting the elastic constant of the flux line lattice and its pinning are observed in the mixed states of a La1.85Sr0.15CuO4 single crystal. Each anisotropic activation energy which is necessary to depin the flux line lattice is evaluated independently from measurements under various settings of the wave vector k , the polarization vector u and magnetic fields H using the analysis based on the thermally assisted flux flow model. It is found that the activation energy in the case of H ⊥ c -axis and u | c -axis is extremely higher than others. This result suggests the importance of the intrinsic pinning mechanism due to the layer structure.

We compared superconducting properties of a La1.85Sr0.15CuO4 single crystal between before and after electron irradiation. About 100 ppm point-like defects are introduced into the crystal with the irradiation. Both irreversibility lines and hysteries measurements indicate that the irradiation decreases the superconducting currents flowing between CuO2 layers. The flux creep activation energy UeffJ) is proportional to g(T)1n(J), where g ( T )=(1- T / Tc ) n .

Ultrasonic and specific-heat measurements have been performed across the superconducting transition on a single crystal of La1.86Sr0.14CuO4. A pronounced jump of the elastic constant ΔC33(Tc) = -0.15 GPa is observed at Tc = 34 K as well as a specific-heat jump Δcp/Tc = 9.6 mJ/K2mol, whereas a jump in C11 is less obvious. The results allow quantitative estimation of the strain dependence of Tc and the condensation energy along the a and c axes.

Temperature dependence of the sound velocity V s in a La 1.85 Sr 0.15 CuO 4 single crystal has been measured in the ( c 11 − c 12 )/2 mode and in the c 33 mode under high magnetic fields up to 23T. In the field above 6T, V s in the ( c 11 − c 12 )/2 mode anomalously decreases with decreasing temperature, followed by the increase below about 10K. In the c 33 mode, similar behavior of V s can be observed above 20T. Such a temperature dependence of V s may suggest the existence of a strain sensitive narrow band near the Fermi level or a phase transition related to the flux line lattice.

Lattice parameter measurements have been made in a La1.85Sr0.15CuO4 single crystal superconductor between 4.2 K and room temperature by the X-ray Bond method. A structural distortion near the superconducting transition temperature of 33 K has been observed. The lattice spacing in the c-direction increases below the superconducting transition temperature with decreasing temperature. The change in the lattice parameter, Δc/c0, between 4.2 K and 33 K, is 2×10−5. Along a direction perpendicular to the c-axis, on other hand, the lattice spacing decreases more rapidly than expected from normal thermal contraction. The possible importance of these results for existing theories of high temperature superconductivity is noted.

Magnetic susceptibility of single-crystal La 2−x Sr x CuO 4 with various x was measured with a SQUID magnetometer. The susceptibility with magnetic field ( H ) perpendicular to the CuO 2 plane is 1.5≈ 3 times as large as that with H parallel to the CuO 2 plane, whereas they have similar temperature dependence. The field-dependent susceptibility in the vicinity of T c was also studied. From these data, T c ( H ), i.e., the field dependence of T c for H normal to the CuO 2 plane, was determined by a new method. The coherence length at 0 K in the CuO 2 plane estimated from T c ( H ) is about 30 A for the samples of x = 0.12, 0.14 and 0.19

We present results of single crystal neutron diffraction experiments on La 2− x Sr x CuO 4− δ . The analysis of the temperature dependence of the LaO bond lengths shows that almost the entire thermal contraction of La 2 CuO 4 between 540 K an 50 K is due to the decrease of the LaO 9 polyhedron, the CuO bond distances remain almost constant. Doping of La 2 CuO 4 with Sr (or additional O) decreases both CuO bond lengths. The large thermal parameters especially of the apical O indicate the instability of all examined crystals against a second phase transition.

Temperature dependence of the ultrasonic attenuation α and the sound velocity V s have been measured in a La 1.85 Sr 0.15 CuO 4 single crystal under the magnetic field. A jump and a kink in V s have been observed at the superconducting transition temperature T c in the C 33 and the C 11 mode, respectively. A peak in α has been also observed at T c in the C 33 mode. Furthermore, an anomalous stiffening in V s and an attenuation peak have been observed below 10K. Magnetic field effects on these elastic anomalies and a possibility of a new phase transition below 10K are presented.

High-angle double-crystal X-ray diffractometry (HADOX) has been applied to examine the quality of La2- x Sr x CuO4 single crystals grown by the travelling-solvent floating-zone method. The two-dimensional intensity distribution in reciprocal space is measured at room temperature for 0014 with CoKα1 radiation. Measurements are made over a range of 7 mm along the axis of growth at intervals of 1 mm. It is found that the crystal contains small part of different orientation with slightly different chemical composition Δx

Using high-quality single crystal samples, the structural phase transition in La1.86Sr0.14CuO4 was investigated by the low-temperature X-ray diffraction method in the range from ambient temperature down to 10 K. The transition temperature from tetragonal to orthorhombic lattice was determined to be 182.5±2.5 K, and neither the monoclinic nor the new tetragonal phase was detected. Since no noticeable change was found in the peak width of (004)t during the phase transition, the shear was estimated to be confined in the direction normal to [001]t. The tilt angle between adjacent domains, determined by (220)t reflection, was of a very small value as 0.013±0.002° at 10 K. This may be related to the observed fourfold symmetry of the upper critical field (H C2 ) in the plane of (001)t.

Single crystals of barium tetratitanate (BaTi 4 O 9 ) were grown by the floating zone method using an infrared heating furnace. The grown crystals were about 5 mm in diameter by 50 mm in length, colorless and transparent. BaTi 4 O 9 melts incongruently, so that in addition to BaTi 4 O 9 , also TiO 2 and BaTi 2 O 5 precipitated at the intial and final stages of growth. However, the middle section from which both ends of the grown crystals were eliminated was a single crystal, had a stoichiometric composition of BaTi 4 O 9 and was homogenous in composition.

Using neutron-scattering techniques, we have studied the temperature dependence of the magnetic excitations at varied energies in a high-quality single crystal of ${\mathrm{La}}_{1.85}$${\mathrm{Sr}}_{0.15}$${\mathrm{CuO}}_{4}$. This crystal exhibits a sharp superconducting transition at 33 K with nearly 100% flux exclusion. For magnetic excitation energies of 9 meV and lower, the intensity drops dramatically with decreasing temperature for temperatures below \ensuremath{\sim}150 K. However, at 12 MeV the intensity is independent of temperature between 300 and 5 K.

The broadening of the resistive transition under magnetic fields up to 5 T was measured on a (La0.93Sr0.07)2CuO4 high-quality single crystal. The extent of the broadening did not depend on the current direction, but only depended on the relative orientation of the magnetic field and the crystal axis. Hence the phenomenon is attributed to the enhanced fluctuation of superconductivity rather than to the flux motion induced by the Lorentz force. In the entire transition region, the resistivity-H-T relationship can be described by the scaling law ΔT 3 2 ∝H at any given ϱ, differing from the linear GL scaling law. Therefore, the whole range of the broadening is discussed in terms of the extremely broadened fluctuation region in the presence of a magnetic field.

The barium tetratitanate (BaTi4O9) single crystals grown in a nitrogen gas by the floating zone method was characterized by dielectric property in the frequency range 1 kHz to 1 MHz. The as-grown crystals had an electric behaviour such as shown by a semiconductor. When the crystals were annealed at 1300° C for 5 h in air, the dielectric constant was independent of the frequencies and was anisotropic, and theQ-value became higher than that of the grown crystals. Further, from electron spin resonance measurements it was found that the as-grown crystals contained the Ti3+ ion. This seems to suggest that the electrical conductivity of the as-grown crystals is due to the Ti3+-Ti4+ hopping mechanism.

A universal scaling (ΔT∼H 2/3 ) is observed in the resistive transition of an LSCO single crystal under magnetic fields. It holds for the whole temperature range of the transition and for any configuration of the magnetic field and the current. We propose a “giant fluctuation” model to explain the experimental results.

The resistive transitions near the superconducting critical temperature were measured under magnetic field up to 5 T on a FZ-grown high-quality single crystal (La0.93Sr0.07)2CuO4 (T c=37.5 K) The crystal was sufficiently large along the c-axis that the dc four-probe method could be applied along this axis as well as along the usual a-b plane. It was found that the width of the temperature region over which the resistive transition is broadened depends only on the relative orientation between the magnetic field and the crystalline c-axis, but not on that between the field and the current. It indicates that the mechanisms based on the fluxoid motion, such as the flux creep model, the Kosterlitz-Thouless transition model and the superconducting glassy state model, are unlikely to explain the broadening of the resistive transition under magnetic fields in (La1-x Sr x )2CuO4.

Superconducting thin films of the Y-Ba-Cu-O system were prepared on single crystal MgO(100) substrates by a new technique, the mist microwave plasma decomposition method. The onset and zero resistance temperatures occurred at 85 K and 78 K, respectively, for the as-grown film. The lattice constant c 0 estimated from Bragg angles of (00n) planes was 11.69 Å.