Pseudocubic Unit Cell Research Articles

Transverse piezoelectric properties of epitaxial Pb(Yb 1/2Nb 1/2)O 3–PbTiO 3 (50/50) films

The transverse piezoelectric properties of (1– x)Pb(Yb 1/2Nb 1/2)O 3– xPbTiO 3 (PYbN–PT, x=0.5) epitaxial films grown on (0 0 1)SrRuO 3/(0 0 1)LaAlO 3 (indices given for the pseudocubic unit cell) were investigated by the wafer flexure technique. PYbN–PT films and SrRuO 3 bottom electrodes were deposited by pulsed laser deposition. At a deposition pressure of 400 mTorr, (0 0 1) PYbN–PT epitaxial films with high phase purity and good crystalline quality were obtained for a wide range of deposition rates (40–100 nm/min) and temperatures (620–660°C). The remanent polarization of the film was as high as 30 μC/cm 2. The e 31 coefficient and the aging rate were strongly dependent on the poling direction. The maximum e 31 coefficient was −11.0 C/m 2. The minimum aging rate of the piezoelectric coefficients for the films was 2% per decade.

Magnetic anisotropy of thin film La0.7Ca0.3MnO3 on untwinned paramagnetic NdGaO3 (001)

We describe in detail a method by which to establish the magnetic anisotropy of thin ferromagnetic films on strongly paramagnetic substrates that are slightly anisotropic. The film that we consider is composed of the much studied manganite La0.7Ca0.3MnO3 and the substrate is NdGaO3, a good lattice match. Below a Curie temperature Tc of 260 K it was found, using a vibrating sample magnetometer, that 72±3 nm La0.7Ca0.3MnO3 films grown epitaxially by pulsed laser deposition on untwinned orthorhombic NdGaO3 (001) substrates exhibit uniaxial anisotropy with K=(3.6±0.1)×105 erg cm−3. The easy direction is along [110] of the pseudocubic unit cell, i.e., diagonal to the O–Mn–O bond directions and parallel to the side of the actual unit cell which is orthorhombic. We attribute an 11±4% loss of the low temperature moment to the proximity of the paramagnetic substrate rather than to stress. It is argued that stress is minimal such that the observed anisotropy must be magnetocrystalline. Both the reduction in moment and the anisotropy must be taken into account when designing thin film experiments.

Crystal Structure of Lithium-Sodium (Li0.7Na0.3)-Analcime

When Na is substituted by Li in the narrow-pore zeolite analcime Na2[Al2Si4O12]⋅2H2O, the average parameter of the pseudocubic unit cell decreases from 13.67 A in the starting Na-analcime to 13.50 A in Li-analcime. Our structural data for Li-analcime [1] showed that the Li cations lie near the Na-sites in an octahedral arrangement O4(H2O)2 distorted to 4+2 or 3+3. Due to their smaller size, the Li cations are displaced toward the edge of one of the two Si,Al-tetrahedra coordination-linked to the given site, and the symmetry is reduced from Ibca to Pbca. Investigation of the Na–Li isomorphic series in analcimes showed that variation of the ratio of exchange cations leads to discontinuity in the thermal properties of the cation-substituted forms [2]. Thermal dehydration of samples with more than 30% sodium replaced by lithium led to decomposition of the solid solution into two phases, one of which (phase II) demonstrated more significant compression. According to high-temperature powder X-ray diffraction data, during dehydration, phase II undergoes a structural transformation accompanied by a change in unit cell dimensions showing that the cell has transformed from pseudocubic to pseudotrigonal and its volume has significantly decreased. This transformation is attributed to migration of the Na cations from the standard position on the twofold axis based on 4 oxygen atoms to a new position on the pseudothreefold axis based on 3 (+3) oxygen atoms. Samples with the degree of substitution 70% and higher contain phase II alone. At the first stage of our study of this structural transformation, we seek to reveal possible differences in the environment of Na and Li in the starting hydrated sample of (Li0.7Na0.3)-analcime. (Li,Na)-Analcime was obtained by ion exchange from natural analcime (Nidym River, East Siberia), whose crystal structure was refined earlier [3]. Crystals ≤0.20 mm in size were stored in a melt of LiNO3 and NaNO3 in a ratio of 0.95/0.05 at 260°C for 7 days. The ratio of the number of cations in the melt to that in the solid was 50/1. Then the sample was washed in hot distilled water to remove the salt and autoclaved in distilled water at 150°C. The Na content in the sample was determined by flame photometry. The H2O content was estimated from weight loss data obtained by sample calcination to 750°C by the thermogravimetric technique (TG-50, TA 3000, Mettler). The Li content was calculated based on the charge balance for the composition of the Li-analcime framework [1]. The formula of the resulting (Li,Na)-analcime sample is recorded as Li1.30Na0.53[Al1.83Si4.17O12]⋅2.05H2O, Z = 8; percent of Li exchange for Na is 71%. The X-ray diffraction experiment was carried out on a an Enraf-Nonius CAD-4 single crystal automatic diffractometer (MoKα radiation, 2θ = 70°, θ/2θ scan mode). The intensity data were collected twice. Collection in the full sphere of reciprocal space showed that the symmetry of the structure is not lower than orthorhombic. However, because of the wrong choice of cell dimensions in passing to the orthorhombic (pseudocubic) cell we were unable to check the deviation from I-centering of the unit cell. Therefore the intensity data were also collected in 1/8 of the sphere of reciprocal space, and the structure was solved with these data (direct methods, SHELXS-86 [4]). The full-matrix least-squares refinement was carried out anisotropically with SHELXL-93 [5] in space groups Pbca and Ibca using the complete set of F 2. Although there were 88 reflections with F0 > 3σ(F0) (five of these were “observable” reflections with F0 > 4σ), which are forbidden in a body-centered cell, structure refinement in Pbca gave unsatisfactory results. In particular, the T–O distances in the (Si,Al)O4-tetrahedra had wide variations of values in one tetrahedron (1.525-1.690 A). The correlation matrix elements were as high as 0.86. All these effects might be a consequence of understated symmetry [6]. While the Na and Li cations occupy the general positions in the given space group, their expected displacement from the center of the coordination octahedron was not observed.

Strain and Elasticity at Structural Phase Transitions in Minerals

Almost any change in the structure of a crystal, due to small atomic displacements, atomic ordering, magnetisation, etc., is usually accompanied by changes in lattice parameters. If suitable reference states are defined, such lattice parameter variations can be described quantitatively as a combination of linear and shear strains. What was originally a geometrical description then becomes a thermodynamic description if the relationships of the strains to the elastic constants are also defined. For a phase transition in which the parent and product phases are related by symmetry, only very specific combinations of strain will be consistent with the symmetry change, and the magnitudes of each strain will depend directly on the extent of transformation. In other words, such strains provide information on the evolution of the order parameter and the thermodynamic character of a phase transition. Spontaneous strains due to phase transitions in silicate minerals can be as large as a few percent, and, with modern high resolution diffractometry using neutron or X-ray sources, variations as small as ~0.1‰ can be detected routinely. This level of resolution is illustrated by the lattice parameter and strain variations through a cubic → tetragonal → orthorhombic sequence for the perovskite NaTaO3, for example (Fig. 1⇓). Figure 1. (a) Lattice parameters (expressed in terms of reduced, pseudocubic unit cell) as a function of temperature through the cubic → tetragonal → orthorhombic sequence of NaTaO3 perovskite (powder neutron diffraction data of Darlington and Knight 1999). A straight line through the data for the cubic structure gives the reference parameter a o. (b) Linear strains e 1, e 2, e 3, parallel to reference axes X, Y and Z, respectively, derived from the data in (a). Conversion from a purely geometrical description, in terms of lattice parameters, to a …

SnAl6Te10, SnGa6Te10 and PbGa6Te10: superstructures, symmetry relations and structural chemistry of filled β-manganese phases

Abstract In contrast to earlier structure determinations of SnGa6Te10 and PbGa6Te10 (space group R32), which showed disordered distributions of Sn and Pb, it could be shown for SnGa6Te10, PbGa6Te10 and the new SnAl6Te10, that weak superstructure reflections can be observed in well crystallized samples, which indicate an ordering of Sn(Pb) in all three phases. The black, air stable solids (exept the Al-compound, which is air-sensitive) crystallize trigonally in one of the two enantiomorphic space groups P3121 and P3221. Symmetry considerations based on group-subgroup relations show the relationship between β-manganese and the trigonal structures of the title compounds, which are actually nonmetallic, filled β-manganese phases. Their structures consist of a sublattice of Te atoms, closely related to the topology of the β-manganese structure, in which two of four distorted octahedral (“metaprismatic”) holes per pseudocubic unit cell are occupied by Sn(Pb). Furthermore 12 of 100 distorted tetrahedral holes are occupied by Al(Ga) atoms. It can be shown, that only the ordered Sn (Pb) distribution breaks the rhombohedral symmetry of R32 and requires P3121/P3221. The complex three-dimensional connection pattern of tetrahedra and metaprisms is discussed with respect to the crystal chemical functionality of distinct atoms and the aid of electrostatic lattice energy calculations based on the MAPLE formalism. Finally some comments concerning the probably isotypical structures of CaAl6Te10, CaGa6Te10 and PbIn6Te10 are given.

Microstructure of epitaxial potassium niobate thin films prepared by metalorganic chemical vapor deposition

The microstructure of (001)p-oriented (subscript p indicates the choice of a pseudocubic unit cell) potassium niobate (KNbO3) thin films grown by metalorganic chemical vapor deposition on (100)p lanthanum aluminate and having a large second-order nonlinear optical response is examined. Transmission electron microscopy reveals the films to be epitaxial and the film/substrate interface to be abrupt and semicoherent. The strain between the film and substrate due to the 5% lattice constant mismatch is accommodated by formation of an array of misfit dislocations as well as 60° and 120° ferroelectric microdomains. The domains are located in a 20 nm thick region adjacent to the interface. Beyond the multidomain region, the film is free of significant defects.

(Sr6N)[Ga5] and (Ba6N)[Ga5]: Compounds with Discrete (M6N) Octahedra and [Ga5] Clusters

[Ga5]7− trigonal bipyramids and (M6N)9+ octahedra are present in the crystal structures of the isotypic title compounds. The charge in these phases is balanced by two electrons in metallic states: {(M6N)9+[Ga5]7− · 2e−}. This simple model of the chemical bonding is supported by band structure calculations. A section of the hexagonal crystal structure together with a pseudo-cubic unit cell is shown on the right.

Tetraammineplatinum(II) hexachlorostannate(IV), [Pt(NH3)4][SnCl6

A crystal of the title complex is built up from square [Pt(NH 3 ) 4 ] 2+ cations and octahedral SnCl 6 2- anions. In the pseudo-cubic unit cell, the complex ions occupy the positions of the NaCl structure type. As well as coulombic forces, packing involves weak hydrogen bonds of the N-H...Cl type, which determine the orientation of the ammonia ligands

Structure of [(C2H5)2NH2]3BiCl6

In diethylammonium hexachlorobismuthate(III) the Bi atoms form a slightly distorted cubic I arrangement, i.e. they occupy the corners and the midpoint (owing to the c-glide plane) of the pseudo-cubic rhombohedral unit cell defined by the transformation a' 1 =-1/3a 1 +1/3a 2 +1/3c, a' 2 =-1/3a 1 -2/3a 2 +1/3c, a' 3 =2/3a 1 +1/3a 2 +1/3c; each Bi atom is surrounded octahedrally by six Cl atoms. The octahedron occurs in two different orientations according to the c-glide plane. The centres of the organic groups are close to the midpoints of the edges and the faces of the I-centred cubic cell. The isolated octahedra are connected to form a three-dimensional framework by hydrogen bonding via three symmetrically equivalent atoms Cl(1), which form an octahedral face

Solid state properties of crystalline ionenes

The solid state properties of poly[(dialkylimino)alkylene] salts (‘ionenes’) −[−( CH 2) N− N( R) 2−] nq.n.X where m = 6 or 10, R = CH 3 or Ch 2CH 3 and X = monovalent ( q = 1) or bivalent ( q = 0.5) counterions, are discussed with respect to their thermal behaviour and crystal structure. The melting of ionenes strongly depends on the type of counterion X and with the same counterion decreases with increasing m and size of R. The melting enthalpies are surprisingly low, despite the relatively high melting transitions. Thus, the entropy of melting must be small, which indicates a relatively high disorder in the crystals. Due to an extraordinary crystallization behaviour, macroscopic polymer single crystals have been obtained from ionenes, the crystal structure of which has been analysed. In general, highly symmetrical lattice geometries have been found, with the type of unit cell depending on m and the type of X: (1) ionenes with spacer length m = 6 in combination with monovalent spherical anions X give rise to hexagonal unit cells; (2) ionenes with spacer length m = 6 in combination with divalent spherical anions X give rise to pseudocubic tetragonal unit cells; (3) ionenes with spacer length m = 10 give rise to hexagonal unit cells if combined with spherical monovalent anions X. The details of the crystal structures turned out to be very unusual. The ionic sites (X −, N +R 2) form a regular lattice of high symmetry. The arrangement of chains connecting the ammonium groups can at present best be interpreted as ‘random walk’.

Preparation and characterization of Ca1 −x La x Ti1 −x Co x O3 (0·00<x⩽0·50) system

The possibility of the formation of solid solution in the system Ca1 −x La x Ti1 −x Co x O3 forx⩽0·5 has been investigated. X-ray diffraction studies show that compositions withx=0·05, 0·1, 0·2, 0·3 and 0·5 prepared by the ceramic method are single-phase materials. All the compositions have a structure similar to CaTiO3 with a pseudo-cubic unit cell. Preliminary studies show that interfacial polarization contributes significantly to their dielectric constant.

Lattice Vibrations of Ba(Zn1/3Ta2/3)O3 Crystal with Ordered Perovskite Structure

Ba(Zn1/3Ta2/3)O3 dielectric ceramics are known to be useful materials for microwave dielectric resonators. The lattice vibrations of Ba(ZnTa)O3, a crystal which has a pseudocubic unit cell with a hexagonal superstructure because Zn and Ta ions are in an ordered configuration, are investigated in this paper. Also, the symmetry properties of Ba(ZnTa)O3 and its ion displacements are examined. The far-infrared reflection spectra and Raman spectra of the ceramics are also presented and discussed in relation to the dielectric losses.

Electron Microscopic Studies on Domain Structure of PbZrO3

The domain structure of a typical antiferroelectric substance, lead zirconate, is examined in detail fori the first time by electron diffraction and electron microscopy. The 90° and 60° domain configurations can be consistently understood on the basis of the pseudo-cubic unit cell. 180° domains, which are characteristic of the antiferroelectric phase, are observed. The displacement vectors between the domains are determined as ¼[21n], ¼[21̄n] and ¼[02n] (n=0 or 2) by the α-fringe theory for off-Bragg settings. Crystal structure images of the domains reveal how the unit cells connect across the domain boundary. 90° and 180° domains are found in the intermediate phase between the antiferroelectric and the paraelectric phases. The fact that 180° domains are observed is important evidence indicating that the phase is ferroelectric.

New phases with fluorite-derived structure in CaF 2(Y, Ln)F 3 systems

Crystallographic characteristics of six new phases of idealized composition Ca 8R 5F 31 which are formed in the CaF 2RF 3 (R = Y, HoLu) systems are reported. All the phases have a similar structure derived from CaF 2 with slight distortion and pseudocubic unit cell parameters a ord = 13 a dis (where a dis is the parameter of the fluorite subcell). The degree of ordering increases in the lanthanide series with decrease of ionic radius and, in every system given, with an increase in the RF 3 content of the solid solution. Significant influence of temperature and time of annealing on the degree of ordering was not detected.

Further studies on the nickel–aluminium system. I. β-NiAl and δ-Ni2Al3phase fields

New lattice parameter and density results have been obtained for alloys in the β-NiAl and 6-Ni2Al3 phase fields of the nickel–aluminium system. The lattice parameter of the β-NiAl phase (CsCl-type) falls linearly from 2.8870 A at 50 at.% Ni to 2.8618 A at 66. at.% Ni, with 2.00 atoms per unit cell. On the other hand, the lattice parameter on the Al-rich side of NiAl falls linearly from 2.8870 A to 2.8652 A, while the number of atoms per unit cell falls from 2.00 to 1.817 by the creation of vacancies in normally nickel sites. The trigonal 6-Ni2Al3 phase-structure, which is essentially an extension of cubic β-NiAl, but with every third plane of nickel atoms perpendicular to the trigonal axis missing, shows a minimum in the a and c spacings at stoichiometric Ni2Al3. Density measurements indicate that the vacancies formed by the missing planes are progressively filled as nickel is added to Ni2Al3, but that a substitutional solid solution is formed on the aluminium-rich side of stoichiometric Ni2Al3 with aluminium replacing nickel atom by atom. In the NiAl phase, the number of valence electrons increases from 2.28 per unit cell at 61.9 at.% Ni to 3.00 at stoichiometric NiAl, and remains constant at 3.00 as the vacancies form until Ni2Al3 is reached, at which stage the number of vacancies will have reached a maximum when there are only 1.67 atoms per pseudo-cubic cell. The number of electrons per pseudo-cubic unit cell then begins to rise and reaches the phase boundary value of 3.12 at 37.6 at.% Ni.

Neutron Diffraction Data for Ta2D and the Probable Arrangement of the Deuteriums in Two of Its Polymorphic Varieties

Neutron diffraction data are presented for Ta2D at 4°K, 78°K, room temperature, and 53°C. The patterns are indexed assuming a pseudocubic unit cell, the cell edge being 6.74 A at the three lowest temperatures and 3.37 A at 53°C. The enlarged unit cell in the low temperature (β1) form is attributed to ordering of the deuteriums in the tetrahedral interstices. Attempts are made to establish the arrangement of the deuteriums (D's) in the β1 and β2 forms. For the latter, the stable form at 53°C, the intensities can be accounted for in three ways—by random distribution over ⅔ (L group), over ⅓ (S group) or over all of the tetrahedral interstices. From general considerations the first of these is thought to represent the actual situation in β2—Ta2D. In this the D's are distributed over the sites at ½ ¼ 0, ½ ¾ 0, ¼ ½ 0, ¾ ½ 0+000 and +½ ½ ½. Analysis of the β1 pattern shows that despite the fact that this form has a vanishing residual entropy there is no unique configuration of the deuteriums. Instead, to account for the observed intensities one must accept a structure in which each deuterium is statistically occupying more than one site. Assuming each D to be distributed over two sites three satisfactory structures are obtained. These, designated A, B, and C, belong to space groups I4, I4̄, and I41, respectively. Structure A seems the most reasonable of the three and hence is accepted as the one which is probably correct. In it the 8 D's are statistically occupying the 16 tetrahedral sites at ⅛ ¼ 0, ¼ ⅞ 0, ⅞ ¾ 0, ¾ ⅛ 0, ⅝ 0 ¼, ⅜ 0 ¼, 0 ⅜ ¼, 0 ⅝ ¼+000, and +½ ½ ½. There is an apparent conflict between conclusions based on thermodynamic work and those developed from analysis of the diffraction data for the β2 form as well as for the β1 form. The observed configurational entropies of both forms are much less than those expected for the accepted structures. The discrepancies are thought to be due to local order.

Structure of Cu32Al19

POWDER photographs show that the deformed gamma structure Cu32Al19 has 51 atoms in each of the pseudo-cubic unit cells; it is closely related to the cubic structure of Cu9Al4 with 52 atoms per unit cell1. Whereas the latter is found with 21/13 or 22/13 electrons per atom, the deformed structure takes up to 89 electrons to 51 atoms. The complex quantities may be approximately simplified to the ratios 5/3 and 7/4 respectively; these improper fractions correspond to the monotonic sequence2 (2n−1)/n. (Cu is monovalent, Al trivalent.)