Lattice Parameters Of Single Crystals Research Articles

A Spectrometer for Studying Single Crystals Using the Method of Synchrotron Radiation Diffraction at Near-Backscattering Angles

A spectrometer has been developed at the beamline EXAFS-D station of the Kurchatov synchrotron-radiation source at the Kurchatov Institute National Research Center for the precision determination of relative variations in the lattice parameters of single crystals. The spectrometer allows measurements of small (up to 3 × 10−7) relative variations in the lattice parameter, which may be caused by stoichiometry violation or external actions, e.g., inverse piezoelectric effect. The method of X-ray diffraction in a geometry that is close to backscattering at angles as large as 179.5° is implemented in the spectrometer. Using a synchrotron source, it is possible to select the radiation wavelength for tuning the spectrometer to the near-backscattering diffraction geometry. The equipment of the spectrometer allows simultaneous monitoring of the lattice-parameter variation and mapping of the elemental composition over the crystal surface.

Mixed conductivity analysis of single crystals of α‴-(Cd1−x Znx)3As2 (x = 0.45)

We study the conductivity and magnetoresistance of the α‴ phase solid solution of (Cd1−xZnx)3As2 (x = 0.45). Single crystals of (Cd1−xZnx)3As2 are obtained by the modified Bridgman method. The space group and tetragonal lattice parameters of single crystals are found to be I41/amd and a = b = 8.56(5) Å, c = 24.16(6) Å. The temperature dependence of the conductivity and magnetoresistance is studied in the temperature range of 1.6–320 K and in the presence of a transverse magnetic field from 0 to 10 T. Mixed conductivity is analyzed using Hall resistivity data and standard quantitative mobility spectrum analysis. The concentration and mobility of holes are determined at different temperatures. The presence of two types of holes with different mobilities is demonstrated in the temperature range of 1.6–19 K, while with increasing temperature, just one type of charge carrier is observed in the mobility spectrum.

X-Ray diffraction on large single crystals using a powder diffractometer

Information on the lattice parameter of single crystals with known crystallographic structure allows for estimations of sample quality and composition. In many cases, it is sufficient to determine one lattice parameter or the lattice spacing along a certain, high-symmetry direction, e.g. in order to determine the composition in a substitution series by taking advantage of Vegard’s rule. Here we present a guide to accurate measurements of single crystals with dimensions ranging from 200 m up to several millimetres using a standard powder diffractometer in Bragg–Brentano geometry. The correction of the error introduced by the sample height and the optimisation of the alignment are discussed in detail. In particular for single crystals with a plate-like habit, the described procedure allows for measurement of the lattice spacings normal to the plates with high accuracy on a timescale of minutes.

Thermal expansion of thermoelectric type-I-clathrates

Thermal expansion was determined for two series of ternary compounds, Ba8MxGe46−x and Ba8MxSi46−x, with M=Cu, Zn, Pd, Ag, Cd, Pt, and Au and for several quaternary compounds for which we investigated the influence of substitution by Zn/Ni in Ba8ZnxGe46−x as well as the dependence of thermal expansion on the Si/Ge ratio in Ba8Cu5SixGe41−x. In the temperature range from 4.2 to 300 K the thermal expansion of all ternary compounds was measured with a capacitance dilatometer, whereas from 300 to 700 K for several selected samples a dynamic mechanical analyzer was employed. The low temperature data compare well with the lattice parameters of single crystals, gained from measurements at three different temperatures (100, 200, and 300 K). For a quantitative description of thermal expansion the semiclassical model of Mukherjee et al. [Phys. Rev. Lett. 76, 1876 (1996)] was used, which also provided reliable accurate values of the Debye and Einstein temperatures. Results in this respect show good agreement with the corresponding data derived from temperature dependent x-ray diffraction and specific heat measurements. Furthermore the present paper is a comprehensive collection and discussion of all thermal expansion data of intermetallic type-I-clathrate materials so far available in the literature including our results of thermal expansion measurements of the Ge- and Si-based type-I-clathrates listed above.

Thermal expansion of skutterudites

The current paper gives an overview of the newly obtained thermal expansion coefficients of skutterudites as well as those so far available in literature. Thermal expansion was determined for CoSb3, Pt4Sn4.4Sb7.6, for As- and Ge-based skutterudites as well as for various high-ZT skutterudites (micro- and nanostructured) with didymium (DD) and mischmetal (Mm) as filler atoms in frameworks of (Fe1−xCox)4Sb12 and (Fe1−xNix)4Sb12, and for double and triple-filled skutterudites such as Ca0.07Ba0.23Co3.95Ni0.05Sb12 and Sr0.025Ba0.075Yb0.1Co4Sb12. For low temperatures, a capacitance dilatometer was used (4–300 K), whereas for temperatures 300<T<750 K, a dynamic mechanical analyzer was employed. For a set of Ge-, P-, and Sb-based skutterudites, lattice parameters of single crystals, measured at three different temperatures, were used to derive the thermal expansion coefficient. The semiclassical model of Mukherjee [Phys. Rev. Lett. 76, 1876 (1996)] has been successfully used to quantitatively describe the thermal expansion coefficient in terms of Einstein and Debye temperatures, which compare well with the corresponding results from specific heat, electrical resistivity, or temperature dependent x-ray measurements.

Dielectric tunability of coherently strained LaAlO3/SrTiO3 superlattices

Dielectric LaAlO3 and SrTiO3 thin films and LaAlO3/SrTiO3 multilayers were grown epitaxially by pulsed laser deposition on (001) oriented (LaAlO3)0.3(Sr2AlTaO6)0.7 substrates. Their structural characterization was carried out by x-ray diffraction and cross section transmission electron microscopy, which allowed us to determine the degree of strain in the dielectric material. For a film thickness of 200 nm we observed significant structural relaxation of the LaAlO3 and SrTiO3 single layers toward their single crystal lattice parameters in contrast to LaAlO3/SrTiO3 multilayer structures, where the dielectric material remained coherently strained. The influence of strain on the dielectric properties was studied by impedance spectroscopy in the frequency range of 40 Hz–10 MHz at room temperature. The measurements were performed on parallel plate capacitors, using epitaxial La0.4Sr0.6CoO3 films as bottom and top electrodes. The dielectric constant ε of partially relaxed and coherently strained material was nearly the same. However, the dielectric tunability, i.e., the influence of a direct current bias voltage on ε, was found to be significantly larger for coherently strained dielectrics. For [LaAlO3(30 Å)/SrTiO3(60 Å)]20 multilayers we observed a tunability of nearly 20% at room temperature for a bias voltage of only 1 V, corresponding to an electric field strength of 50 kV/cm. The total dielectric loss of the multilayer capacitors is below 1% for frequencies above 1 MHz and depends only slightly on the bias voltage.

Thermal expansion of RNi 2B 2C single crystals

Structure data and variation of lattice parameters of single crystals of RNi 2B 2C (R=Y, Tb, Dy, Ho, Er, Lu) have been investigated as a function of temperature. Eight quaternary and pseudo-quaternary compounds, respectively, were investigated between 90 and 360 K. Lattice parameters a and unit cell volumes V UC increased for all compounds with increasing temperature, while the axial ratios c/ a of the unit cell parameters decreased. The most notable observation is a minimum in the temperature dependence of the lattice parameter c, which shifts towards lower temperatures with increasing atomic number Z R of the rare earth element. Coefficients of linear thermal expansion for YNi 2B 2C, for example, vary between α a=4.71×10 −6 K −1 (100 K)–13.0×10 −6 K −1 (300 K) and α c=−9.93×10 −6 K −1 (100 K)–8.24×10 −6 K −1 (300 K). Bulk expansion β varies between β=0.73×10 −5 K −1 (100 K) and 2.78×10 −5 K −1 (300 K).

The preparation and characterization of monomeric lanthanide tetraphenylporphyrin crystals, [Ln(tpp)acac · 3TCB · 8H 2O] (Ln = Gd, Sm)

Crystals of tetraphenylporphyrinato lanthanoid(III) complexes, [Ln(tpp)acac·3TCB·8H 2O] (Ln = Gd, Sm), were prepared and isolated by direct crystallization of the reaction mixture from solution of toluene:TCB (10:1). Its monomeric composition was characterized on the basis of UV-vis, magnetic circular dichroism (MCD), IR, Raman, 1H NMR spectra and elemental analysis. Single-crystal lattice parameters were obtained by X-ray crystallography of triclinic [Gd(tpp)acac·8H 2O·3TCB], a = 19.72 A ̊ , b = 21.62 A ̊ , c = 23.15 A ̊ , α = 69.64°, β = 81.52°, γ = 83.06°, and V = 9048 A ̊ 3 .

High pressure and low temperature X-ray crystallography: the crystal structure of the molecular charge transfer salt α'- (bis(ethylenedithio)-tetrathiafulvalene) 2 AuBr 2

An X-ray diffraction technique is described that allows determination of crystal structure and the variation of lattice parameters of single crystals as a function of hydrostatic pressure up to 14 kbar and of temperature from 300 K to 12 K. As an example of the technique results are presented on the molecular charge transfer salt α'-(BEDT TTF )2 AuBr 2 (BEDT-TTF = bis(ethylenedithio)-tetrathiafulvalene) to elucidate the nature of a structural phase transition which occurs at 250 K at ambient pressure and 7 kbar at 300 K. The transition, of second order, is characterized by the appearance of ½b* superlattice reflections at high pressure or low temperature but without any drastic change in the basic crystal structure. The isobaric thermal expansions and the isothermal compressibilities are anisotropic, being larger along a than along b and c , though of different magnitudes and directional properties, i. e. the effect of applying pressure at ambient temperature is not equivalent to lowering the temperature at ambient pressure. Transfer integral calculations show that marked dimerization along the stacking axis, already present at 300 K, is related to electronic localization.

The geometry of twinning in HoCu2

The twinning relationship in the intermetallic compound HoCu 2 was determined by single-crystal X-ray diffraction techniques. A 60 o rotation about the b axis between the two components of the twins was found. The twin plane is (103). The measured single-crystal lattice parameters deviate from those obtained from powder data by 0.03 A for a and 0.10 A for c. These deviations may be due to strain in the structure caused by the twinning. The same twinning geometry is believed to hold true for the other rare-earth-metal (REM 2 ) intermetallic compounds with the KHg 2 -type structure that exhibit massive twinning

Lattice-parameter measurements of PbHPO4 single crystals by the ratio method

Temperature dependences of PbHPO4 single-crystal lattice parameters were measured by the ratio method in the range 158–421 K. Below the ferroelectric phase transition (T c = 310 K) lattice parameter b increases non-linearly with decreasing temperature while all others decrease linearly. The ratio method was generalized to the monoclinic crystal system for this purpose.

Charge transfer and transition-metal cluster: Boron bonding in the bct superconductingY(Rh1−xRux)4B4system

An analysis of the bonding and charge transfer as a function of transition-metal concentration is presented for the bct superconducting system Y(Rh/sub 1-x/Ru/sub x/)/sub 4/B/sub 4/. A sharp drop in the superconducting critical temperature T/sub c/ from 9.5 K to below 1.0 K near a critical concentration is not reflected in the smooth, linear variation of the single-crystal lattice parameters and B-B interatomic distances. Analysis of the boron KVV Auger data indicates the boron p-like states near the Fermi energy are increasingly populated in a continuous manner with increasing x. We find no evidence of any abrupt changes in the electronic structure near x/sub cr/.

Transport and optical properties ofTi1+xS2

We report measurements of the electrical resistivity, Hall coefficient, magnetoresistance, thermoelectric power, infrared reflectivity, and $c$-axis lattice parameter of single crystals of titanium disulfide ${\mathrm{Ti}}_{1+x}{\mathrm{S}}_{2}$ with varying degrees of nonstoichiometry. The strong correlations we find between different measurements made on the same sample allow us to conclude that titanium disulfide is a semiconductor rather than a semimetal. Even though this fact is established, our most stoichiometric samples continue to exhibit metallic behavior, and the source of these conduction electrons is unknown. In addition, none of the scattering mechanisms examined here is capable of explaining the unusual temperature dependence of the electrical resistivity which varies as ${T}^{3}$ at low $T$ and as ${T}^{y}$ above 100 K where $y$ ranges from 1.85 for the least stoichiometric samples to 2.2 for the most stoichiometric.

Czochralski growth of solid solutions of strontium hexagallate with magnesium and zirconium as dopants

Strontium hexagallate in which the gallium ions were partly substituted by coupled substitution of magnesium and zirconium has been grown from the SrO-Ga 2O 3-MgO/ZrO 2 melt system using the Czochralski technique. Single crystals of 30 mm in diameter and 70 mm in length were obtained. They are colorless and optically transparent. Wafers cut from the best crystals have dislocation and inclusion densities below 20 cm -2. The lattice parameters of single crystals corresponding to a composition of Sr 1.03Ga 10.81Mg 0.58Zr 0.58O 18.99 are a 0 = 0.5822±1 x10 -4 nm and c 0 = 2.3061∓2 x10 -4 nm.

Precise measurement of lattice parameters of single crystals in conjunction with a hot stage

When a hot stage is used with a two-circle diffractometer the range of 2θ angles available is often restricted to the positive side of the main beam. The d spacings of single crystals have to be calculated from the separation of two reflections. The best choice of reflections for maximum precision is discussed. Residual errors due to speciment tilt can be eliminated by comparing values obtained at room temperature with and without the hot stage.

A Strategy Foe Rapid Aid Accurate (p.p.m.) Measurement of Lattice Parameters of Single Crystals by Bond's Method

All published accounts of the use of Bond's method for lattice parameter measurements have used step-scanning (at equal angle increments) of the diffraction peaks, followed by graphical or computer analysis of the data to locate the peak positions. It has been found that the peaks angles can be determined with little loss in accuracy or precision by manually setting the crystal angle to give a counting rate (observed on a rate-meter) equal to l/2 the peak rate and defining- the peak angle as the average of the angles on the two sides of the peak. Because of the asymmetry of the spectral line, defining the peak in this manner results in a shift of the peak angle from that determined by the mid-chord peak method. This shift can be compensated by determining an effective value of the wavelength based on a silicon standard. Using the method described, a lattice parameter measurement, including mounting and orienting the sample, taking the data and computing the result using a time-sharing computer terminal, can be made in less than 20 mins.

Crystal growth and neutron studies of large single crystals of the alloy series SnTe-GeTe

Abstract A simple method is described for growing massive single crystals of the alloy series SnTe-GeTe, suitable for inelastic neutron studies. A table of the time-temperature cycle is provided. The conventional techniques to establish the single crystal character of opaque solids were found to be useless. A new technique (neutron photograph of a Bragg reflection) is described, which gives reliable data about the single crystal character of the solids formed. Single crystal lattice parameters were obtained by neutron diffraction and are in good agreement with the values obtained from X-ray powder diffraction studies.

Hydrothermal preparation, single-crystal lattice parameters, and decomposition data for some lathanide dihydroxy chlorides and the related hydroxy chloride, Yb3O(OH)5Cl2

Hydrothermal preparation, single-crystal lattice parameters, and decomposition data for some lathanide dihydroxy chlorides and the related hydroxy chloride, Yb3O(OH)5Cl2

A survey of precision lattice parameter measurements as a tool for the characterization of single-crystal materials

Bond's method of measuring the lattice parameter of single crystals has been improved and the Bragg angle can be readily measured with a probable error of 0.5 arc secs. Ignoring the wavelength uncertainty, this gives the lattice parameter (averaged over the diffracting volume) for many materials to a probable error of 0.5 ppm. The diffracting volume can be as small as 0.5×0.02×0.005 mm. Results of measurements on Si, GaAs whiskers, K(Ta xNb 1−x)O 3 and KTaO 3 are shown as examples of the use of lattice parameter measurements for the characterization of materials.

Lattice Parameter of Alpha Iron by Divergent Beam Diffraction

The divergent beam diffraction technique has been used to determine the lattice parameter of single crystals of alpha iron made by vapor deposition techniques. An electron beam focused to approximately 10 μ was used to produce a source of K series characteristic radiation within the samples. All unique Kossel conics which emerged from the specimens were recorded on flat photographic films. The back-reflection geometry was employed. Three different crystal orientations were investigated: a fourfold symmetry axis normal to the film plane, a threefold symmetry axis normal to the film plane, and mirror—mirror symmetry of the crystal normal to the plane of the film. Data obtained from the latter photographs have been used to demonstrate the application of the method of ratios. These analytical techniques were applied to Kossel conics that were continuous and interrupted. The lattice parameter was established by five different series of calculations. The most accurate value of the lattice parameter obtained in this investigation was 2860.6±0.1 xu. Stereographic projections have been made for three different orientations of bcc crystals. The value of the dimensionless parameter (λ/a) is 0.675 in these representations. All Kossel conic intersections required by symmetry considerations are indicated.