A technique for refining unit cell parameters of crystals belonging to arbitrary systems on modern single-crystal diffractometers is described. The technique is based on the 2D-detector position calibration. The elementary orthorhombic unit cell parameters of the α-33S single crystal have been refined. The anisotropy of change in the parameters in the range of 90–350 K has been analyzed. The relative increase in the parameter c is shown to be 6.4

An original procedure is proposed to refine unit cell parameters (UCPs) of single crystals in Bond’s scheme. The procedure involves the use of a modern laboratory diffractometer equipped with a 2D detector and a three-circle goniometer. At the first stage, preliminary UCPs, diffraction class, and crystal orientation relative to goniometer axes are determined. Then φ and ω angles are calculated to bring an appropriate (occurrence of a well-resolved doublet, intensity) reflection hkl on the equatorial plane. The measurement in Bond’s scheme is carried out at two symmetric positions of the detector ±2θD ≈ 2θhkl. The principal difference from the measurement on a single crystal spectrometer consists in refusing to plot the reflection profile I(ω) and passing to ω-scans with a width of 3-4°, which allows the measurement of the Kα1/Kα2 doublet profile. After its processing by two independent 2D functions, coordinates of the maxima are determined, and then the 4θhkl. Angle is found based on angular sizes of the detector pixel and the difference in the coordinates of X Kα1-component reflections obtained in symmetric positions. In this approach, measurement errors are related to the accuracy of placing the detector in two symmetric positions and the correctness of processing 2D reflection profiles. In the study of reference Si and Ge single crystals in the range of 2θD angles close to 100°, UCP deviations from the theoretical values are found to not exceed 0.0004 Å, and the relative measurement accuracy is 6·10–5. The refinement of UCPs of single crystals grown in the Y2O3–Eu2O3 system by the melt-solution technique indicates the formation of the (Y1–xEux)2O3 solid solution with the x value range of 0.27-0.40. A scheme is proposed to improve the measurement accuracy when the procedure is transferred to the diffractometer with synchrotron radiation.

A technique for arbitrary symmetry crystals unit cell parameters refining on modern single-crystal diffractometers is described. The technique is based on the 2D detector position calibration. The elementary orthorhombic unit cell parameters of the α-33S single crystal have been refined. The anisotropy of parameters changes in the range of 90–350 K has been studied. It is shown that the relative increase in parameter c is 6.4%. The obtained dependences are approximated by second–third degree polynomials. The absolute increase in cell volume is 138.4 A3, and the relative increase is 4.3%. The temperature dependencies of the thermal expansion tensor elements has been refined. The coefficients of α-33S thermal expansion tensor at the room temperature are: α11 = 15.35 × 10–5, α22 = 8.56 × 10–5, α33 = 9.12 × 10–5 К–1.

A fine crystalline sample of the cubic modification (space group Ia3̅ , Z = 16) of gadolinium oxide (C-Gd2O3) is grown by the solution–melt technique. The single crystal X-ray diffraction analysis performed at 150 K and 298 K reveals a relative increase in the unit cell parameter by 0.08

We propose a number of approaches for refining unit cell parameters of single crystals using serial laboratory diffractometers equipped with 2D detectors and discuss the corresponding mathematical apparatus for processing the obtained results. The approaches are demonstrated on the example of orthorhombic LiCsMo 3 O 10 crystals grown by the low-gradient Czochralski method using two different seed orientations but being identical in terms of the XRD analysis. It is shown that unit cell parameters of the crystals coincide within the estimated measurement error. The temperature dependence of unit cell parameters in the temperature range 90-450 K is studied, the view of the elements of the thermal expansion tensor is determined. The changes in the structural characteristics of LiCsMo 3 O 10 in the studied temperature range are discussed.

The [(Pt(NH 3 ) 4 ) x (Pd(NH 3 ) 4 ) 1– x ]CrO 4 single-phase solid solution ( x = 0.5-0.6) is prepared by the cocrystallization of [Pt(NH 3 ) 4 ](NO 3 ) 2 and [Pd(NH 3 ) 4 ](NO 3 ) 2 aqueous solutions with ammoniac (NH 4 ) 2 CrO 4 . The structure and parameters of the tetragonal ( I 4 1 / amd , Z = 4) unit cell ( a = 7.3091(1) Å, c = 15.2720(6) Å) of this compound and the molar fraction of Pt ( x = 0.568(7)) are determined using the single-crystal X-ray diffraction method. The unit cell parameters of the studied crystal are additionally refined by an original method ( a = 7.3207(9) Å, c = 15.2527(19) Å, V = 817.4(3) Å 3 ) and are further utilized to refine also the molar fraction of Pt using Zen′s law ( x = 0.57(1)). A single crystal of [(Pt(NH 3 ) 4 ) 0.57 (Pd(NH 3 ) 4 ) 0.43 ]CrO 4 and two samples of the synthesized product selected from the total mass are thermally decomposed in hydrogen. A study of thermolysis products by XRD, scanning and transmission electron microscopy methods demonstrates the formation of a Pt 0.49 Pd 0.38 Cr 0.13 nanoalloy included in the Cr 2 O 3 matrix in the form of blocks (~1 µm) and smaller (>2 nm) spherical formations.

New techniques for the calibration of single-crystal diffractometers equipped with a 2D detector are proposed to improve the accuracy of measuring the unit cell parameters. According to these methods, reflection profiles are processed using the original SearchXY-2θ program, and the detector position is refined by recording an external reference. Details of the calibration of diffractometers equipped with a three- or four-circle goniometer are discussed. The use of reflections with 2θ ≈ 100° when refining the unit cell parameters of a test InSb single crystal allowed measuring parameter a of the cubic unit cell with a relative error of 7·10 –5 . The possibilities of the techniques are also demonstrated on the measurements of the a ( T ) dependence for InSb in the range of 90-490 K.

Министерство науки и высшего образования Российской Федерации Российская академия наук Научный совет по неорганической химии РАН Научный совет по аналитической химии РАН Научный совет по химической технологии РАН Российское химическое общество имени Д.И

The procedure of using the internal standard in refining unit cell parameters of single crystals is described. The study is carried out on single crystal Bruker diffractometers equipped with three- and four-circle goniometers. The procedure is based on gluing the reference crystal to the studied one and the further determination of the orientation of each of them relative to goniometer axes. It is followed by the calculation of angles to bring certain reflections to the equatorial plane and the record of their profiles by ω-scanning. It is shown that when the reflections with 2θ ≈ 80° are used, the collection and processing of experimental frames allows the measurement of interplanar distances with a relative error Δd/d ≈ 1·10–4.

By the single crystal X-ray diffraction (XRD) analysis it is shown that on slow co-crystallization of [Pd(NH 3 ) 4 ]MoO 4 and [Pd(NH 3 ) 4 ]CrO 4 salts, [Pd(NH 3 ) 4 ](MoO 4 ) x (CrO 4 ) 1– x solid solutions with x ranging from 0.05 to 0.80 are formed. To construct the V ( x ) dependence an original procedure of refining unit cell parameters is used. It is revealed that in the thermal decomposition of the [Pd(NH 3 ) 4 ](MoO 4 ) 0.18 (CrO 4 ) 0.82 single crystal (composition is determined by the single crystal XRD analysis) a mixture of phases based on the fcc lattice of Pd (Pd 0.88 Cr 0.10 Mo 0.01 ) and on Cr 2 O 3 is formed.

A calibration procedure for the three-circle goniometer/2D detector system is described. It is based on the construction of calibration graphs Δ2θ(2θ) from the results of processing Kα1 and Kα2 components of external reference reflections successively brought to the equatorial circumference. A Si single crystal is used as the reference. Random errors are estimated. Results of the refinement of unit cell parameters of [Pt(NH3)4]MO4 (М = Cr, Mo, W) are compared by several procedures, including the obtained calibration. The relative error of the performed measurements does not exceed 2·10–4.