scholarly journals A self-consistent approach to describe unit-cell-parameter and volume variations with pressure and temperature

2021 ◽  
Vol 54 (6) ◽  
Author(s):  
Ross Angel ◽  
Mattia Mazzucchelli ◽  
Javier Gonzalez-Platas ◽  
Matteo Alvaro

A method for the self-consistent description of the large variations of unit-cell parameters of crystals with pressure and temperature is presented. It employs linearized versions of equations of state (EoSs) together with constraints to ensure internal consistency. The use of polynomial functions to describe the variation of the unit-cell angles in monoclinic and triclinic crystals is compared with the method of deriving them from linearized EoSs for d spacings. The methods have been implemented in the CrysFML Fortran subroutine library. The unit-cell parameters and the compressibility and thermal expansion tensors of crystals can be calculated from the linearized EoSs in an internally consistent manner in a new utility in the EosFit7c program, which is available as freeware at http://www.rossangel.net.

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.


2002 ◽  
Vol 17 (4) ◽  
pp. 295-300 ◽  
Author(s):  
Nichole Wonderling ◽  
Else Breval ◽  
Joseph P. Dougherty

The change in the orthorhombic structure of PbZrO3 was studied as a function of the La substitution for Pb and Ti substitution for Zr. Two types of changes can occur: (1) a change in the atom coordinates toward the positions for a perfect cubic perovskite lattice; and (2) a change of orthorhombic unit cell parameters so that ao, bo, and co exactly fit with the cubic cell parameter ac. Therefore, ao=ac√2, bo=ac.2√2, and co=ac.2, where ao, bo, and co are the orthorhombic cell parameters, and ac is the cubic cell parameter. Substitution of Pb by La in the orthorhombic PLZT leads to both a change in atom coordinates and a change in unit cell parameters toward the perfect cubic structure, especially for La≥4. Substitution of Zr by Ti in the orthorhombic PLZT leads to similar atom coordinate changes, but the unit cell parameters do not change. The composition 0/92.5/7.5 contains a major tetragonal phase and a minor orthorhombic phase. There are only small differences in the orthorhombic structure between the A and the B composition of PLZT. The A composition has a structure closer to the cubic structure than the B composition.


2020 ◽  
Vol 39 (2) ◽  
pp. 207
Author(s):  
Nikita V. Chukanov ◽  
Olga N. Kazheva ◽  
Nadezhda A. Chervonnaya ◽  
Dmitry A. Varlamov ◽  
Vera N. Ermolaeva ◽  
...  

Crystals of the natural zeolite amicite, ideally K4Na4(Al8Si8O32)·10H2O, were ion-exchanged in the reactions with 0.1 N aqueous solutions of AgNO3, RbNO3, CsNO3 and Pb(NO3)2 at 363 K for 24 h. Under these conditions, Cs+ substitutes K+ whereas the most part of Na+ remains unexchanged; Rb+ partly substitutes both Na+ and K+; Pb2+ and Ag+ completely substitute Na+ and K+. All the compounds are monoclinic. The Cs- and Rb-substituted samples have unit-cell parameters close to those of initial amicite. The exchange of Na+ and K+ for Ag+ is accompanied by a significant decrease of the unit-cell volume. The unit-cell parameter c of Pb-amicite is nearly threefold larger than the c parameter of initial amicite. Infrared spectra show that framework topology is preserved during the ion exchange. The crystal structures of initial and Cs-exchanged amicites have been solved by direct methods.


Crystals ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 812
Author(s):  
Noura Othman Alzamil ◽  
Ghareeba Mussad Al-Enzi ◽  
Aishah Hassan Alamri ◽  
Insaf Abdi ◽  
Amor BenAli

Two new nonmetal cation tetrafluoroborate phases [H3tren](BF4)3 (I) and [H3tren](BF4)3 HF (II) were synthesized by microwave-assisted solvothermal and characterized by single crystal X-ray diffraction, IR spectroscopy and thermal analysis DTA-TGA. [H3tren](BF4)3 is cubic (P213) with unit cell parameter a = 11.688(1) Å. [H3tren](BF4)3•HF is trigonal (R3c) with unit cell parameters a = 15.297(6) Å and c = 12.007(2) Å. Both (I) and (II) structures can be described from isolated tetrafluoroborate BF4- anions, triprotonated tris-(2-aminoethyl)amine (tren) [H3tren]3+. Phase (II) contains disordered BF4- tetrahedron and hydrofluoric acid.


1991 ◽  
Vol 35 (A) ◽  
pp. 431-438
Author(s):  
Hideo Toraya ◽  
William Parrish

AbstractA procedure for the accurate determination of unit-cell parameters using conventional Xray powder diffractometry is described. Two important factors in the procedure are: 1) the use of high-resolution-type diffractometer, which can suppress the axial beam divergence and thus gives nearly symmetric diffraction profiles in the low 2θ region and 2) the use of a new algorithm for systematic peak shift correction during the least-squares determination of unit-cell parameters of a sample with an internal standard [Toraya & Kitamura (1990). J. Appl. Cryst. 23 , 282-285]. The procedure has been tested by measuring successively the unit-cell parameter of W, CeO2, and Si in three mixtures, Si+W, W+CeO2, and CeO2+Si: the unit-cell parameter of W, which was first determined by using NIST SRM 640b Si powder as an internal standard reference material, was used as a standard reference value to determine the unit-cell parameter of CeO; in the next W+CeO2 mixture, and so on. The difference between the end value of observed Si unit-cell parameters and the starting value of 5.430940(35) Å were just 1 to 5 p.p.m. High accuracy is attainable in measuring the uni-cell parameters even with the conventional powder diffractometry provided with the nearly symmetric diffraction profile and the algorithm for peak shift correction used in the present study.


1983 ◽  
Vol 47 (343) ◽  
pp. 221-227 ◽  
Author(s):  
R. J. Gilkes ◽  
B. Palmer

AbstractUnit-cell parameters of synthesized members of the crandallite (a = 7.007 Å, c = 16.216 Å)-goyazite (a = 7.013 Å, c = 16.650 Å) series vary linearly with composition between end-members. Most members of the series consist of 0.1 μm platy crystals, but crandallite also contains some larger (1–5 µm) tapered crystals elongated along the c axis.With increasing Sr substitution the dehydroxylation temperature decreases from c. 475 °C for crandallite to 420 °C at 20 mole % Sr, and then increases to 440 °C for goyazite. Partial dehydroxylation of crandallite is accompanied by contraction of the c unit cell parameter and expansion of a, thereby retaining an unaltered unit cell volume. The much greater sensitivity of c to both Sr substitution and dehydroxylation may be due to the rigidity of continuous sheets of Al(OH)4O2 octahedra which are parallel to the (001) plane in these minerals.


2019 ◽  
Vol 83 (03) ◽  
pp. 339-347 ◽  
Author(s):  
Gabriele Zaffiro ◽  
Ross J. Angel ◽  
Matteo Alvaro

AbstractWe present an assessment of the thermo-elastic behaviour of rutile based on X-ray diffraction data and direct elastic measurements available in the literature. The data confirms that the quasi-harmonic approximation is not valid for rutile because rutile exhibits substantial anisotropic thermal pressure, meaning that the unit-cell parameters change significantly along isochors. Simultaneous fitting of both the diffraction and elasticity data yields parameters of KTR0= 205.14(15) GPa, KSR0= 207.30(14) GPa, $K_{TR0}^{\prime} $= 6.9(4) in a 3rd-order Birch-Murnaghan Equation of State for compression, αV0= 2.526(16) × 10–5 K–1, Einstein temperature θE = 328(12) K, Anderson-Grüneisen parameter δT = 7.6(6), with a fixed thermal Grüneisen parameter γ = 1.4 to describe the thermal expansion and variation of bulk modulus with temperature at room pressure. This Equation of State fits all of the available data up to 7.3 GPa at room temperature, and up to 1100 K at room pressure within its uncertainties. We also present a series of formulations and a simple protocol to obtain thermodynamically consistent Equations of State for the volume and the unit-cell parameters for stiff materials, such as rutile. In combination with published data for garnets, the Equation of State for rutile indicates that rutile inclusions trapped inside garnets in metamorphic rocks should exhibit negative residual pressures when measured at room conditions.


2012 ◽  
Vol 7 (2) ◽  
pp. 93-97
Author(s):  
Anton Panchenko ◽  
Alexey Alekseev ◽  
Sergey Gromilov

A quick test has been proposed for the refinement of the unit cell parameters of polycrystalline samples including massive those with a large absorption coefficient. The Debye – Scherrer scheme used as the basis was realized on a Bruker X8APEX diffractometer (MoK radiation, the plate two-coordinate CCD detector position 2  90, the resolution 1 024 × 1 024, accumulation time 15 min). External standards were -Al2O3 and Au. A polished section of the Ir0.85Re0.15 metal tablet was studied. The measurement precision of the unit cell parameter, afcc = 3.8470(4) A, was confirmed by studying the sample in the Bragg-Brentano geometry


2016 ◽  
Vol 80 (7) ◽  
pp. 1195-1203 ◽  
Author(s):  
Stuart J. Mills ◽  
Andrew G. Christy ◽  
Mike S. Rumsey ◽  
John Spratt

AbstractA crystallographic and chemical study of two 'elsmoreite' samples (previously described as 'ferritungstite') from the Hemerdon mine (now known as the Drakelands mine), Devon, United Kingdom has shown them to be two different polytypes of hydrokenoelsmoreite. Hydrokenoelsmoreite-3C(HKE-3C) crystallizes in space group , with the unit-cell parameter a = 10.3065(3) Å. Hydrokenoelsmoreite-6R (HKE-6R) crystallizes in space group , with the unit-cell parameters a = 7.2882(2) Å and c = 35.7056(14)Å. Chemical analyses showed that both polytypes have Na and Fe/Al substitution giving the formulae: (Na0.28Ca0.04K0.02(H2O)0.20⁏1.46)∑2.00(W1.47Fe3+0.32Al0.21As5+0.01)∑2.00[O4.79(OH)1.21]∑6.00·(H2O)(3C) and (Na0.24Ca0.04K0.03(H2O)0.63⁏1.06)∑2.00(W1.42Fe3+0.49Al0.08As5+0.01)∑2.00[O4.65(OH)1.35]∑6.00·(H2O)(6R). The doubling of the unit cell in the 6R phase is due to ordering of Na and ( ,H2O) in the A site; no long-range ordering is observed between W and Fe/Al in the B site.


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.


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