Kinematical and Dynamical CBED Pattern Models: Increasing the Accuracy of the Unit-Cell Parameter Measurements Based on CBED Patterns

Author(s):  
I.N. Yadhikov ◽  
S.K. Maksimov

Convergent beam electron diffraction (CBED) is widely used as a microanalysis tool. By the relative position of HOLZ-lines (Higher Order Laue Zone) in CBED-patterns one can determine the unit cell parameters with a high accuracy up to 0.1%. For this purpose, maps of HOLZ-lines are simulated with the help of a computer so that the best matching of maps with experimental CBED-pattern should be reached. In maps, HOLZ-lines are approximated, as a rule, by straight lines. The actual HOLZ-lines, however, are different from the straights. If we decrease accelerating voltage, the difference is increased and, thus, the accuracy of the unit cell parameters determination by the method becomes lower.To improve the accuracy of measurements it is necessary to give up the HOLZ-lines substitution by the straights. According to the kinematical theory a HOLZ-line is merely a fragment of ellipse arc described by the parametric equationwith arc corresponding to change of β parameter from -90° to +90°, wherevector, h - the distance between Laue zones, g - the value of the reciprocal lattice vector, g‖ - the value of the reciprocal lattice vector projection on zero Laue zone.

1987 ◽  
Vol 2 (4) ◽  
pp. 225-226
Author(s):  
Peter Bayliss ◽  
Slade St. J. Warne

AbstractMagnesium-chlorophoenicite may be differentiated from the Mn-analogue chlorophoenicite, because for magnesium-chlorophoenicite at 7Å, whereas for chlorophoenicite.In a review of the literature for the Mineral Powder Diffraction File by Bayliss et al. (1980), powder X-ray diffraction data could not be found of the mineral species magnesium-chlorophoenicite, (Mg,Mn)3Zn2(AsO4)(OH,O)6. Dunn (1981) states that the powder X-ray diffraction data of magnesium-chlorophoenicite is essentially identical to that of chlorophoenicite (Mn analogue) and confirms that the minerals are isostructural.With the crystal structure parameters determined by Moore (1968) for a Harvard University specimen from New Jersey of chlorophoenicite, a powder X-ray diffraction pattern was calculated with the programme of Langhof, Physikalische Chemie Institute, Darmstadt. The calculated pattern was used to correct and complete the indexing of the powder X-ray diffraction data of chlorophoenicite specimen ROM M15667 from Franklin, Sussex County, New Jersey, U.S.A. by the Royal Ontario Museum (PDF 25-1159). With the correctly indexed data of ROM M15667, the unitcell parameters were refined by least-squares analysis and are listed in Table 1.The most magnesium-rich magnesium-chlorophoenicite found in the literature is a description of Harvard University specimen 92803 from Franklin, Sussex County, New Jersey, U.S.A. by Dunn (1981), where Mg is slightly greater than Mn. A 114.6 mm Debye-Schemer film taken of HU92803 with Cu radiation and a Ni filter (CuKα = 1.5418Å) was obtained from Dr. P. Dunn and measured visually. The unit-cell parameters, which were refined by least-squares analysis starting from the unit-cell parameters of PDF 25-1159 in space group C2/m(#12), are listed in Table 1, and give F28 = 4.1(0.050,136) by the method of Smith & Snyder (1979).The hkl, dcalulated, dobserved and relative intensities (I/I1) of HU92803 are presented in Table 2. With the atomic positions and temperature factors of chlorophoenicite determined by Moore (1968), the Mn atomic positions occupied by 50% Mg and 50% Mn, and the unit-cell parameters of HU92803, a powder X-ray diffraction pattern was calculated and Icalculated is recorded in Table 2. A third powder X-ray diffraction pattern was calculated with the Mn atomic positions fully occupied by Mg. Because the atomic scattering factor of Mn is more than twice greater than Mg, chlorophoenicite may be differentiated from magnesium-chlorophoenicite based upon the calculated intensities of the first three reflections given in Table 3.Although the a, c and β unit-cell parameters of chlorphoenicite are similar to those of magnesium-chlorphoenicite, the b unit-cell parameter of chlorophoenicite is significantly greater than that of magnesium-chlorophoenicite (Table 1). The b unit-cell parameter represents the 0–0 distance of the Mn octahedra (Moore, 1968). Since the size of Mn is greater than that of Mg, chlorophoenicite may be differentiated from magnesium-chlorophoenicite based upon the b unit-cell parameter given in Table 1.American Museum of Natural History (New York, N.Y., U.S.A.) specimen 28942 from Sterling Hill, Ogdensburg, New Jersey is composed of willemite, haidingerite and magnesian chlorophoenicite. A spectrographic analysis of the magnesian chlorophoenicite shows As, Mg, Mn and Zn. Powder X-ray diffraction data (PDF 34-190) of the magnesian chlorophoenicite was collected by diffractometer with Cu radiation and a graphite 0002 monochromator (Kα1 = 1.5405) at a scanning speed of 0.125° 2θ per minute. The unit-cell parameters, which were refined by leastsquares analysis starting from the unit-cell parameters of PDF 25-1159, are given in Table 1. Specimen AM 28942 is called chlorophoenicite, because of its large b unit-cell parameter (Table 1), and the I/I1 of 25 for reflection 001 and of 50 for reflection 201 compared to the Icalculated in Table 3.


2019 ◽  
Vol 484 (2) ◽  
pp. 181-183
Author(s):  
A. V. Khoroshilov ◽  
A. A. Ashmarin ◽  
V. N. Guskov ◽  
E. G. Sazonov ◽  
K. S. Gavrichev ◽  
...  

The isobaric heat capacities of two monoclinic (M' and M) modifications of yttrium orthotantalate at temperatures 5–1300 K have been measured by the adiabatic and differential scanning calorimetry methods. It has been demonstrated that the difference in structure between the crystal lattices of M' and M has small effect in the heat capacity, and the difference between the heat capacities of these phases Cp(M)-Cp(M') is small, always positive, and increases in the range of the lowest temperatures. The unit cell parameters of M-YTaO4 have been determined as a function of temperature in the range 300–1173 K.


2012 ◽  
Vol 7 (2) ◽  
pp. 98-102
Author(s):  
Polina Vanina ◽  
Sergey Gromilov

The main purpose of the work is the improving of accuracy of the unit cell parameters the measurements by diffraction data at small angles. The basis of this approach is creating of new laboratory standard, which is the mixture of the etalon silicon SRM-640 and chelate compound of the copper (II) 4-phenatsetiliden-2,2,5,5-tetramethyl-3-imidazoline-1- oxyl (CuL2). The feature of the preparing of this standard is a crystallizing of CuL2 directly on a sample holder. That causes almost ideal orienting of the needle tetragonal crystals on a cuvette and there are diffraction reflections on the diffractogram only of hk0 type. Their depositions allow to make a calibration of the goniometer starting with 4 2


2012 ◽  
Vol 27 (1) ◽  
pp. 8-11 ◽  
Author(s):  
A. Dominic Fortes ◽  
Ian G. Wood

A new hydrate of magnesium chromate is synthesized by quenching aqueous solutions of MgCrO4 in liquid nitrogen. MgCrO4·11H2O is isostructural with the rare mineral meridianiite (MgSO4·11H2O) being triclinic, $P{\bar 1}$, Z = 2, with unit-cell parameters a = 6.811 33(8) Å, b = 6.958 39(9) Å, c = 17.3850(2) Å, α = 87.920(1)°, β = 89.480(1)°, γ = 62.772(1)°, and V = 732.17(1) Å3 at −15 °C. The difference in unit-cell parameters between SO4- and CrO4-bearing species is only partially accounted for by the difference in S–O and Cr–O bond lengths; the remainder of the difference (over 90% in the cell volume) is attributed to weakening of the interpolyhedral hydrogen-bond network.


Author(s):  
J. Gjønnes ◽  
N. Bøe ◽  
K. Gjønnes

Structure information of high precision can be extracted from intentsity details in convergent beam patterns like the one reproduced in Fig 1. From low order reflections for small unit cell crystals,bonding charges, ionicities and atomic parameters can be derived, (Zuo, Spence and O’Keefe, 1988; Zuo, Spence and Høier 1989; Gjønnes, Matsuhata and Taftø, 1989) , but extension to larger unit cell ma seem difficult. The disks must then be reduced in order to avoid overlap calculations will become more complex and intensity features often less distinct Several avenues may be then explored: increased computational effort in order to handle the necessary many-parameter dynamical calculations; use of zone axis intensities at symmetry positions within the CBED disks, as in Figure 2 measurement of integrated intensity across K-line segments. In the last case measurable quantities which are well defined also from a theoretical viewpoint can be related to a two-beam like expression for the intensity profile:With as an effective Fourier potential equated to a gap at the dispersion surface, this intensity can be integrated across the line, with kinematical and dynamical limits proportional to and at low and high thickness respctively (Blackman, 1939).


Author(s):  
Gunnel Karlsson ◽  
Jan-Olov Bovin ◽  
Michael Bosma

RuBisCO (D-ribulose-l,5-biphosphate carboxylase/oxygenase) is the most aboundant enzyme in the plant cell and it catalyses the key carboxylation reaction of photosynthetic carbon fixation, but also the competing oxygenase reaction of photorespiation. In vitro crystallized RuBisCO has been studied earlier but this investigation concerns in vivo existance of RuBisCO crystals in anthers and leaves ofsugarbeets. For the identification of in vivo protein crystals it is important to be able to determinethe unit cell of cytochemically identified crystals in the same image. In order to obtain the best combination of optimal contrast and resolution we have studied different staining and electron accelerating voltages. It is known that embedding and sectioning can cause deformation and obscure the unit cell parameters.


Author(s):  
H. S. Kim ◽  
S. S. Sheinin

The importance of image simulation in interpreting experimental lattice images is well established. Normally, in carrying out the required theoretical calculations, only zero order Laue zone reflections are taken into account. In this paper we assess the conditions for which this procedure is valid and indicate circumstances in which higher order Laue zone reflections may be important. Our work is based on an analysis of the requirements for obtaining structure images i.e. images directly related to the projected potential. In the considerations to follow, the Bloch wave formulation of the dynamical theory has been used.The intensity in a lattice image can be obtained from the total wave function at the image plane is given by: where ϕg(z) is the diffracted beam amplitide given by In these equations,the z direction is perpendicular to the entrance surface, g is a reciprocal lattice vector, the Cg(i) are Fourier coefficients in the expression for a Bloch wave, b(i), X(i) is the Bloch wave excitation coefficient, ϒ(i)=k(i)-K, k(i) is a Bloch wave vector, K is the electron wave vector after correction for the mean inner potential of the crystal, T(q) and D(q) are the transfer function and damping function respectively, q is a scattering vector and the summation is over i=l,N where N is the number of beams taken into account.


2021 ◽  
Vol 62 (5) ◽  
Author(s):  
П.C. Серебренникова ◽  
В.Ю. Комаров ◽  
А.С. Сухих ◽  
С.А. Громилов

Minerals ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 1028 ◽  
Author(s):  
M. Mashrur Zaman ◽  
Sytle M. Antao

This study investigates the crystal chemistry of monazite (APO4, where A = Lanthanides = Ln, as well as Y, Th, U, Ca, and Pb) based on four samples from different localities using single-crystal X-ray diffraction and electron-probe microanalysis. The crystal structure of all four samples are well refined, as indicated by their refinement statistics. Relatively large unit-cell parameters (a = 6.7640(5), b = 6.9850(4), c = 6.4500(3) Å, β = 103.584(2)°, and V = 296.22(3) Å3) are obtained for a detrital monazite-Ce from Cox’s Bazar, Bangladesh. Sm-rich monazite from Gunnison County, Colorado, USA, has smaller unit-cell parameters (a = 6.7010(4), b = 6.9080(4), c = 6.4300(4) Å, β = 103.817(3)°, and V = 289.04(3) Å3). The a, b, and c unit-cell parameters vary linearly with the unit-cell volume, V. The change in the a parameter is large (0.2 Å) and is related to the type of cations occupying the A site. The average <A-O> distances vary linearly with V, whereas the average <P-O> distances are nearly constant because the PO4 group is a rigid tetrahedron.


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