Single-crystal Neutron Diffraction Data Research Articles

Structure and properties of NdCuGa[formula omitted] single crystals

This manuscript reports on the structural and magnetic properties of NdCuGa3 using powder and single crystal X-ray diffraction (XRD), zero-field single crystal neutron diffraction, magnetization, and specific heat measurements. Our XRD on a single crystal specimen of NdCuGa3 confirmed that it crystallizes in the tetragonal BaNiSi3-type structure. A magnetic phase transition at TN= 3.3 K is assessed using specific heat and ac magnetic susceptibility measurements. No additional anomaly below TN down to 50 mK was detected by performing specific heat measurements. Neutron single crystal diffraction data collected at T= 300 mK confirm the antiferromagnetic phase below TN= 3.3 K with the propagation vector τ→= (0.2, 0, 0). Possible magnetic structure solutions of NdCuGa3 are discussed.

Benchmark Crystal Structure of Defect-Free Spinel ZnFe2O4.

Accurate structural models are of paramount importance for elucidating structure-property relationships in functional materials. Spinels (AB2O4) form a highly important family of materials with complex crystal structures, and subtle structural details have a critical bearing on understanding their physical properties. In some spinels, the space group symmetry is debated, and in general, point defects such as cation inversion and interstitials add complexity. Most studies of spinels concern powder materials, and this challenges deep structural characterization. In fact, most published spinel structures have dubious atomic displacement parameters (ADPs), which is a typical sign of problematic structural description in the refinement of diffraction data. Here, we use various X-ray and neutron diffraction techniques to establish a benchmark crystal structure for the essentially defect-free spinel ferrite ZnFe2O4, which is a widely studied frustrated magnet. It is shown that the appearance of Fd3̅m forbidden reflections in the ZnFe2O4 single-crystal neutron diffraction data is an artifact of multiple scattering rather than the loss of inversion symmetry. We then provide benchmark ADPs and demonstrate how strongly these parameters affect the refined cation inversion. The ADPs reported here may be used as reference data to test the soundness of refined structural models, possibly to constrain those based on suboptimal data quality, and thereby provide a more accurate fundamental understanding of the structure-property relationship in spinel-type materials.

Canted antiferromagnetic phases in the candidate layered Weyl material EuMnSb2

${\mathrm{EuMnSb}}_{2}$ is a candidate topological material which can be tuned towards a Weyl semimetal, but there are differing reports for its antiferromagnetic (AFM) phases. The coupling of bands dominated by pure Sb layers hosting topological fermions to Mn and Eu magnetic states provides a potential path to tune the topological properties. Here we present single-crystal neutron diffraction, magnetization, and heat-capacity data as well as polycrystalline $^{151}\mathrm{Eu}$ M\"ossbauer data which show that three AFM phases exist as a function of temperature, and we present a detailed analysis of the magnetic structure in each phase. The Mn magnetic sublattice orders into a C-type AFM structure below ${T}_{{\text{N}}_{\text{Mn}}}=323(1)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ with the ordered Mn magnetic moment ${\mathbf{\ensuremath{\mu}}}_{\mathbit{\text{Mn}}}$ lying perpendicular to the layers. AFM ordering of the Eu sublattice occurs below ${T}_{{\text{N}}_{\text{Eu1}}}=23(1)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ with the ordered Eu magnetic moment ${\mathbit{\ensuremath{\mu}}}_{\text{Eu}}$ canted away from the layer normal and ${\mathbf{\ensuremath{\mu}}}_{\mathbit{\text{Mn}}}$ retaining its higher temperature order. ${\mathbit{\ensuremath{\mu}}}_{\text{Eu}}$ is ferromagnetically aligned within each Eu layer but exhibits a complicated AFM layer stacking. Both of these higher-temperature phases are described by magnetic space group (MSG) $P{n}^{\ensuremath{'}}{m}^{\ensuremath{'}}{a}^{\ensuremath{'}}$ with the chemical and magnetic unit cells having the same dimensions. Cooling below ${T}_{{\text{N}}_{\text{Eu2}}}=9(1)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ reveals a third AFM phase where ${\mathbf{\ensuremath{\mu}}}_{\mathbit{\text{Mn}}}$ remains unchanged but ${\mathbit{\ensuremath{\mu}}}_{\text{Eu}}$ develops an additional substantial in-plane canting. This phase has MSG $P11\frac{{2}_{1}}{{a}^{\ensuremath{'}}}$. We also find some evidence of short-range magnetic correlations associated with the Eu between $12\phantom{\rule{4pt}{0ex}}\text{K}\ensuremath{\lesssim}T\ensuremath{\lesssim}30\phantom{\rule{4pt}{0ex}}\text{K}$. Using the determined magnetic structures, we postulate the signs of nearest-neighbor intralayer and interlayer exchange constants and the magnetic anisotropy within a general Heisenberg model. We then discuss implications of the various AFM states in ${\mathrm{EuMnSb}}_{2}$ and their potential for tuning topological properties.

Accurate crystal structure of ice VI from X-ray diffraction with Hirshfeld atom refinement.

Water is an essential chemical compound for living organisms, and twenty of its different crystal solid forms (ices) are known. Still, there are many fundamental problems with these structures such as establishing the correct positions and thermal motions of hydrogen atoms. The list of ice structures is not yet complete as DFT calculations have suggested the existence of additional and - to date - unknown phases. In many ice structures, neither neutron diffraction nor DFT calculations nor X-ray diffraction methods can easily solve the problem of hydrogen atom disorder or accurately determine their anisotropic displacement parameters (ADPs). Here, accurate crystal structures of H2O, D2O and mixed (50%H2O/50%D2O) ice VI obtained by Hirshfeld atom refinement (HAR) of high-pressure single-crystal synchrotron and laboratory X-ray diffraction data are presented. It was possible to obtain O-H/D bond lengths and ADPs for disordered hydrogen atoms which are in good agreement with the corresponding single-crystal neutron diffraction data. These results show that HAR combined with X-ray diffraction can compete with neutron diffraction in detailed studies of polymorphic forms of ice and crystals of other hydrogen-rich compounds. As neutron diffraction is relatively expensive, requires larger crystals which can be difficult to obtain and access to neutron facilities is restricted, cheaper and more accessible X-ray measurements combined with HAR can facilitate the verification of the existing ice polymorphs and the quest for new ones.

The spontaneous self-assembly of a molecular water pipe in 3D space.

The self-assembly and self-organization of water molecules are relevant in many fields of research. When water spontaneously reacts with 2,2,6,6-tetra-methyl-piperidine (TMP) to form colourless and crystalline discrete needles, only in the exact ratio of 2:1, it is important to understand the phenomenon. Single-crystal X-ray and neutron diffraction data have unveiled that TMP self-assembles around columns of water molecules, and as such, the resulting adduct may be described as a series of molecular water pipes.

Use of a miniature diamond-anvil cell in a joint X-ray and neutron high-pressure study on copper sulfate pentahydrate.

Single-crystal X-ray and neutron diffraction data are usually collected using separate samples. This is a disadvantage when the sample is studied at high pressure because it is very difficult to achieve exactly the same pressure in two separate experiments, especially if the neutron data are collected using Laue methods where precise absolute values of the unit-cell dimensions cannot be measured to check how close the pressures are. In this study, diffraction data have been collected under the same conditions on the same sample of copper(II) sulfate pentahydrate, using a conventional laboratory diffractometer and source for the X-ray measurements and the Koala single-crystal Laue diffractometer at the ANSTO facility for the neutron measurements. The sample, of dimensions 0.40 × 0.22 × 0.20 mm3 and held at a pressure of 0.71 GPa, was contained in a miniature Merrill-Bassett diamond-anvil cell. The highly penetrating diffracted neutron beams passing through the metal body of the miniature cell as well as through the diamonds yielded data suitable for structure refinement, and compensated for the low completeness of the X-ray measurements, which was only 24% on account of the triclinic symmetry of the sample and the shading of reciprocal space by the cell. The two data-sets were combined in a single 'XN' structure refinement in which all atoms, including H atoms, were refined with anisotropic displacement parameters. The precision of the structural parameters was improved by a factor of up to 50% in the XN refinement compared with refinements using the X-ray or neutron data separately.

Insights into Host–Guest Binding in Hydroquinone Clathrates: Single-Crystal X-ray and Neutron Diffraction, and Complementary Computational Studies on the Hydroquinone-CO2 Clathrate

High-resolution 100 K X-ray and neutron single-crystal diffraction data of the non-stoichiometric hydroquinone-CO2 (HQ-CO2) clathrate are combined, with the aim of providing further insight into ho...

Noncollinear magnetic structure and magnetoelectric coupling in buckled honeycomb Co4Nb2O9 : A single-crystal neutron diffraction study

Through analysis of single crystal neutron diffraction data, we present the magnetic structures of magnetoelectric Co4Nb2O9 under various magnetic fields. In zero-field, neutron diffraction experiments below TN=27 K reveal that the Co2+ moments order primarily along the a* direction without any spin canting along the c axis, manifested by the magnetic symmetry C2/c'. The moments of nearest neighbor Co atoms order ferromagnetically with a small cant away from the next nearest neighbor Co moments along the c axis. In the applied magnetic field H//a, three magnetic domains were aligned with their major magnetic moments perpendicular to the magnetic field with no indication of magnetic phase transitions. The influences of magnetic fields on the magnetic structures associated with the observed magnetoelectric coupling are discussed.

Magnetic properties and magnetic structure of the frustrated quasi-one-dimensional antiferromagnet SrCuTe2O6

Magnetization measurements on single-crystal cubic SrCuTe$_2$O$_6$ with an applied magnetic field of along three inequivalent high symmetry directions $[100]$, $[110]$, and $[111]$ reveal weak magnetic anisotropy. The fits of the magnetic susceptibility to the result from a quantum Monte Carlo simulation on the Heisenberg spin-chain model, where the chain is formed via the dominant third-nearest-neighbor exchange interaction $J_3$, yield the intra-chain interaction $(J_3/k_B)$ between 50.12(7) K for the applied field along $[110]$ and 52.5(2) K along $[100]$ with about the same $g$-factor of 2.2. Single-crystal neutron diffraction unveils the transition to the magnetic ordered state as evidenced by the onset of the magnetic Bragg intensity at $T_\textrm{N1}=5.25(9)$ K with no anomaly of the second transition at $T_\textrm{N2}$ reported previously. Based on irreducible representation theory and magnetic space group analysis of powder and single-crystal neutron diffraction data, the magnetic structure in the Shubnikov space group $P4_132$, where the Cu$^{2+}$~$S=1/2$ spins antiferromagnetically align in the direction perpendicular to the spin chain, is proposed. The measured ordered moment of $0.52(6)~\mu_B$, which represents 48% reduction from the expected value of $1~\mu_B$, suggests the remaining influence of frustration resulting from the $J_1$ and $J_2$ bonds.

Understanding the Correlation between Oxide Ion Mobility and Site Distributions in Ba3NbWO8.5.

A correlation between oxygen site distributions and ionic conductivity has been established in the recently discovered family of oxide-ion conductors Ba3M2O8.5±δ (M = Nb, V, Mo, W). We rationalize this observation on the basis of structural insights gained from the first single-crystal neutron diffraction data collected for a member of this family, Ba3NbWO8.5, and theoretical considerations of bonding and O site energies.

Magnetic properties of ferrimagnetic Mn3Si2Se6

The physical properties of Mn3Si2Se6 have been investigated using single crystals grown by iodine-assisted vapor transport. The material possesses a ferrimagnetic ground state and the properties are similar to those in the isostructural compound Mn3Si2Te6. In these trigonal materials, the dominant magnetic exchanges are antiferromagnetic and intrinsically frustrated, leading to a variety of competing ground states. In Mn3Si2Se6, the Curie temperature is TC = 67(1)K, which is slightly lower than that of Mn3Si2Te6 where TC = 78K. The anisotropy field is also smaller in the selenide relative to the telluride. In both materials, short-range correlations likely exist well-above TC. Neutron single crystal diffraction data on Mn3Si2Se6 suggest a collinear ferrimagnetic structure with the moments tilting out of the ab-plane in zero-field. Finally, the magnetization of vapor grown Mn3Si2Te6 is shown for comparison; these vapor grown crystals do not show a sharp onset of magnetic anisotropy above 300K as was previously observed for melt grown Mn3Si2Te6 crystals.

Oxide single crystals with high lithium-ion conductivity as solid electrolytes for all-solid-state lithium secondary battery applications

Li6.5La3Zr1.5Nb0.5O12 and Li6.5La3Zr1.5Ta0.5O12 single-crystal rods were grown by floating zone melting. A typical single-crystal rod is 8 mm in diameter and 70 mm in length. Crystallized Li6.5La3Zr1.5Nb0.5O12 and Li6.5La3Zr1.5Ta0.5O12 have cubic structures in the I21d space group. The crystal structures of Li6.5La3Zr1.5Nb0.5O12 and Li6.5La3Zr1.5Ta0.5O12 belong to the cubic I213 space group, while the final structure refinements were performed based on an approximate space group Ia3d. The lattice parameter (a) of Li6.5La3Zr1.5Nb0.5O12 was 12.9130(8) Å (1 Å = 0.1 nm), while that of Li6.5La3Zr1.5Ta0.5O12 was 12.9455(6) Å. The crystallographic reliability factors (R-values) of the Li6.5La3Zr1.5Nb0.5O12 and Li6.5La3Zr1.5Ta0.5O12 crystal structures were 7.09% (wR = 7.94%) and 8.82% (wR = 7.45%), respectively, based on the single-crystal neutron diffraction data. Li ions in the crystal structures occupied both distorted tetrahedral 96h sites and distorted octahedral 96h sites. From the results of alternating current impedance measurements, we estimated the total Li-ion conductivity of Li6.5La3Zr1.5Nb0.5O12 and Li6.5La3Zr1.5Ta0.5O12 at 298 K to be 1.39 × 10−3 and 1.27 × 10−3 S cm−1, respectively. These are the highest conductivities reported to date for Li6.5La3Zr1.5Ta0.5O12 members. The bulk properties of garnet-type electrolyte single crystals were advantageous for bulk conductivity and lacked the grain boundaries characteristic of sintered polycrystalline bodies. These solid electrolytes represent a game-changing technology for realizing advanced battery systems with strong safety features.

A multi-methodological study of kurnakovite: A potential B-rich aggregate

AbstractThe crystal structure and crystal chemistry of kurnakovite from Kramer Deposit (Kern County, California), ideally MgB3O3(OH)5·5H2O, were investigated by single-crystal neutron diffraction (data collected at 293 and 20 K) and by a series of analytical techniques aimed to determine its chemical composition. The concentration of more than 50 elements was measured. The empirical formula of the sample used in this study is Mg0.99(Si0.01B3.00)Σ3.01O3.00(OH)5·4.98H2O. The fraction of rare earth elements (REE) and other minor elements are, overall, insignificant. Even the content of fluorine, as a potential OH-group substituent, is insignificant (i.e., ~0.008 wt%). The neutron structure model obtained in this study, based on intensity data collected at 293 and 20 K, shows that the structure of kurnakovite contains: [BO2(OH)]-groups in planar-triangular coordination (with the B-ions in sp2 electronic configuration), [BO2(OH)2]-groups in tetrahedral coordination (with the B-ions in sp3 electronic configuration), and Mg(OH)2(H2O)4-octahedra, connected into (neutral) Mg(H2O)4B3O3(OH)5 units forming infinite chains running along [001]. Chains are mutually connected to give the tri-dimensional structure only via hydrogen bonding, and extra-chains “zeolitic” H2O molecules are also involved as “bridging molecules.” All the oxygen sites in the structure of kurnakovite are involved in hydrogen bonding, as donors or as acceptors.The principal implications of these results are: (1) kurnakovite does not act as a geochemical trap of industrially relevant elements (e.g., Li, Be, or REE), (2) the almost ideal composition makes kurnakovite a potentially good B-rich aggregate in concretes (for example, used for the production of radiation-shielding materials for the elevated ability of 10B to absorb thermal neutrons), which avoids the risk to release undesirable elements, for example sodium, that could promote deleterious reactions for the durability of cements.

Structural disorder and magnetic correlations driven by oxygen doping in Nd2NiO4+δ ( δ∼0.11 )

We investigated the influence of oxygen over-stoichiometry on apical oxygen disorder and magnetic correlations in Nd2NiO4+d (d~0.11) in the temperature range of 2-300 K by means of synchrotron x-ray powder diffraction, neutron single crystal and powder diffraction studies, combined with macroscopic magnetic measurements. In the investigated temperature range, the compound crystalizes in a tetragonal commensurate structure with the P42/ncm space group with excess oxygen atoms occupy the 4b (3/4 1/4 1/4) interstitial sites, coordinated by four apical oxygen atoms. Large and anisotropic thermal displacement parameters are found for equatorial and apical oxygen atoms, which are strongly reduced on an absolute scale compared to the Nd2NiO4.23 phase. Maximum Entropy analysis of the neutron single crystal diffraction data uncovered anharmonic contributions to the displacement parameters of the apical oxygen atoms, toward the nearest vacant 4b interstitial site, related to the phonon assisted oxygen diffusion mechanism. Macroscopic magnetization measurements and neutron powder diffraction studies reveal long-range antiferromagnetic ordering of the Ni-sublattice at TN ~ 53 K with a weak ferromagnetic component along the c-axis, while the long-range magnetic ordering of the Nd-sublattice occurs below 10 K. Temperature dependent neutron diffraction patterns show the appearance of a commensurate magnetic order at TN with the propagation vector k = (100) and the emergence of an additional incommensurate phase below 30 K, while both phases coexist at 2 K. The commensurate magnetic structure is best described by the P42/nc`m` Shubnikov space group. Refined magnetic moments of the Ni and Nd-sites at 2 K are 1.144(76) muB and 1.632(52) muB respectively. A possible origin of the incommensurate phase is discussed and a tentative magnetic phase diagram is proposed.

Measurement of Electric Fields Experienced by Urea Guest Molecules in the 18-Crown-6/Urea (1:5) Host-Guest Complex: An Experimental Reference Point for Electric-Field-Assisted Catalysis.

High-resolution synchrotron and neutron single-crystal diffraction data of 18-crown-6/(pentakis)urea measured at 30 K are combined, with the aim of better appreciating the electrostatics associated with intermolecular interactions in condensed matter. With two 18-crown-6 molecules and five different urea molecules in the crystal, this represents the most ambitious combined X-ray/synchrotron and neutron experimental charge density analysis to date on a cocrystal or host-guest system incorporating such a large number of unique molecules. The dipole moments of the five urea guest molecules in the crystal are enhanced considerably compared to values determined for isolated molecules, and 2D maps of the electrostatic potential and electric field show clearly how the urea molecules are oriented with dipole moments aligned along the electric field exerted by their molecular neighbors. Experimental electric fields in the range of 10-19 GV m-1, obtained for the five different urea environments, corroborate independent measurements of electric fields in the active sites of enzymes and provide an important experimental reference point for recent discussions focused on electric-field-assisted catalysis.

A single-crystal neutron diffraction study of wardite, NaAl3(PO4)2(OH)4·2H2O

The crystal structure and crystal chemistry of wardite, ideally NaAl3(PO4)2(OH)4·2H2O, was investigated by single-crystal neutron diffraction (data collected at 20 K) and electron microprobe analysis in wavelength-dispersive mode. The empirical formula of the sample used in this study is: (Na0.91Ca0.01)Σ = 0.92(Al2.97Fe3+0.05Ti0.01)Σ = 3.03(P2.10O8)(OH)4·1.74H2O. The neutron diffraction data confirm that the crystal structure of wardite can be described with a tetragonal symmetry (space group P41212, a = b = 7.0577(5) and c = 19.0559(5) A at 20 K) and consists of sheets made of edge-sharing Na-polyhedra and Al-octahedra along with vertex-sharing Al-octahedra, parallel to (001), connected by P-tetrahedra and H bonds to form a (001) layer-type structure, which well explains the pronounced {001} cleavage of the wardite crystals. The present data show that four crystallographically independent H sites occur in the structure of wardite, two belonging to a H2O molecule (i.e., H1–O6–H2) and two forming hydroxyl groups (i.e., O5–H3 and O7–H4). The location of the hydrogen atoms allows us to define the extensive network of H bonds: the H atoms belonging to the H2O molecule form strong H bonds, whereas both the H atoms belonging to the two independent hydroxyl groups form weak interactions with bifurcated bonding schemes. As shown by the root-mean-square components of the displacement ellipsoids, oxygen and hydrogen atoms have slightly larger anisotropic displacement parameters compared to the other sites (populated by P, Al and Na). The maximum ratio of the max and min root-mean-square components of the displacement ellipsoids is observed for the protons of the hydroxyl groups, which experience bifurcated H-bonding schemes. A comparative analysis of the crystal structure of wardite and fluorowardite is also provided.

Crystal structure and crystal growth of the polar ferrimagnet CaBaFe4O7

Magnetic materials are a cornerstone for developing spintronic devices for the transport of information via magnetic excitations. To date, relatively few materials have been investigated for the purpose of spin transport, mostly due to the paucity of suitable candidates as these materials are often chemically complex and difficult to synthesize. We present the crystal growth and a structure solution on the high-temperature crystal structure of the layered, polar ferrimagnet ${\mathrm{CaBaFe}}_{4}{\mathrm{O}}_{7}$, which is a possible new contender for spintronics research. The space group is identified as $P3$ by refinement of single crystal and powder neutron diffraction data. At 400 K, the trigonal lattice parameters are $a=11.0114(11)\phantom{\rule{4pt}{0ex}}\AA{}$ and $c=10.330(3)\phantom{\rule{4pt}{0ex}}\AA{}$. The structure is similar to the low-temperature phase with alternating layers of triangular and Kagome-arranged Fe-O tetrahedra. We also present details of the crystal growth by traveling solvent method.

Polarized single crystal neutron diffraction study of the zero-magnetization ferromagnetSm1−xGdxAl2 (x=0.024)

We have determined the temperature evolution of the spin and orbital moments in the zero magnetization ferromagnet Sm$_{1-x}$Gd$_x$Al$_2$ (x = 0.024) by combining polarized and unpolarized single crystal neutron diffraction data. The sensitivity of the polarized neutron technique has allowed the moment values to be determined with a precision of $\approx 0.1$~\mub. Our results clearly demonstrate that, when magnetised by a field of 8T, the spin and orbital moments in Sm$_{1-x}$Gd$_x$Al$_2$ are oppositely directed so that the net magnetization is very small. Below 60 K the contributions from spin and orbital motions are both about 2\mub\ with that due to orbital motion being slightly larger than that due to spin. Between 60 and 65 K the contributions of each to the magnetization fall rapidly and change sign at \Tcomp\ $\approx 67$K above which the aligned moments recover but with the orbital magnetization still slightly higher than the spin one. These results imply that above \Tcomp\ the small resultant magnetization of the \smion\ ion is oppositely directed to the magnetizing field. It is suggested that this anomaly is due to polarization of conduction electron spin associated with the doping Gd$^{3+}$ ions.

Crystal chemistry and temperature behavior of the natural hydrous borate colemanite, a mineral commodity of boron

Colemanite, CaB3O4(OH)3⋅H2O, is the most common hydrous Ca-borate, as well as a major mineral commodity of boron. In this study, we report a thorough chemical analysis and the low-temperature behavior of a natural sample of colemanite by means of a multi-methodological approach. From the chemical point of view, the investigated sample resulted to be relatively pure, its composition being very close to the ideal one, with only a minor substitution of Sr2+ for Ca2+. At about 270.5 K, a displacive phase transition from the centrosymmetric P21/a to the acentric P21 space group occurs. On the basis of in situ single-crystal synchrotron X-ray (down to 104 K) and neutron diffraction (at 20 K) data, the hydrogen-bonding configuration of both the polymorphs and the structural modifications at the atomic scale at varying temperatures are described. The asymmetric distribution of ionic charges along the [010] axis, allowed by the loss of the inversion center, is likely responsible for the reported ferroelectric behavior of colemanite below the phase transition temperature.

The origin of the polar symmetry in huebnerite-type multiferroics

The magnetic structure of the multiferroic phase AF2 of huebnerite (MnWO4) has been re-investigated based on the polar space group P2, instead of P2/c widely accepted in literature. The site character between two independent sites for Mn2+, Mna and Mnb, fairly differs from each other in terms of bond valence sums. This hidden intrinsic dipole moment is the true origin of the chiral magnetic order in AF2 in the polar superspace group P2.1′ (α, 1/2, γ)0s. From structure refinements using single crystal neutron diffraction data at 10 K the ellipticity of the spin helix could be determined to be 0.92 and 0.77 at Mna and Mnb, respectively. The different contributions of two chiral spin-textures to electric polarisation microscopically measurable in the b axis (Pb) could be estimated with Pb (Mna) = 22.8 μCm−2 and Pb (Mnb) = 12.2 μCm−2.