Liquids and Solids

2021 ◽  
pp. 152-176
Author(s):  
Christopher O. Oriakhi
Keyword(s):  
Crystal Structure ◽  
Crystal Lattice ◽  
Vapour Pressure ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
Covalent Bonds ◽  
Chemical Structures ◽  
Structures And Properties ◽  
Ratio Rule ◽  
Unit Cell Dimensions

Liquids and Solids introduce basic physical properties of liquids and solids. An overview of the liquid state is presented, with reference to polar covalent bonds and dipole moment. The effects of temperature on the vapour pressure of a liquid are described, including the Clausius-Clapeyron equation, which can be used to calculate the vapour pressure of a liquid at various temperatures. The chapter reviews the types of solids including their chemical structures and properties. The crystal lattice system and the unit cell relationships for the seven types of crystal lattice structures and the four substructures are examined. Guidelines for determining the number of atoms in a unit cell, including calculations involving unit cell dimensions, are explained. The ionic crystal structure, radius ratio rule for the ionic compounds and determination of crystal structure by X-ray diffraction and Bragg’s equation are covered.

Synthesis and crystal structure of Na3.5Cr1.5Co0.5(PO4)3 phosphate

2006 ◽  
Vol 21 (3) ◽  
pp. 210-213 ◽  
Author(s):  
Mohamed Chakir ◽  
Abdelaziz El Jazouli ◽  
Jean-Pierre Chaminade
Keyword(s):  
Crystal Structure ◽  
Three Dimensional ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
Synthesis And Crystal Structure ◽  
Space Group ◽  
X Ray ◽  
Hexagonal Unit Cell ◽  
Cell Dimensions ◽  
Unit Cell Dimensions

A new Nasicon phosphates series [Na3+xCr2−xCox(PO4)3(0⩽x⩽1)] was synthesized by a coprecipitation method and structurally characterized by powder X-ray diffraction. The selected compound Na3.5Cr1.5Co0.5(PO4)3 (x=0.5) crystallizes in the R3c space group with the following hexagonal unit-cell dimensions: ah=8.7285(3) Å, ch=21.580(2) Å, V=1423.8(1) Å3, and Z=6. This three-dimensional framework is built of PO4 tetrahedra and Cr∕CoO6 octahedra sharing corners. Na atoms occupy totally M(1) sites and partially M(2) sites.

The diffraction pattern obtained

2010 ◽  
Author(s):  
Jenny Pickworth Glusker ◽  
Kenneth N. Trueblood
Keyword(s):  
Crystal Structure ◽  
Diffraction Pattern ◽  
Bragg Reflection ◽  
Unit Cell ◽  
X Rays ◽  
X Ray Diffraction ◽  
Primary Object ◽  
Diffraction Patterns ◽  
Unit Cell Dimensions ◽  
Electron Density Map

In this chapter we will describe those factors that control the intensities of Bragg reflections and how to express them mathematically so that we can calculate an electron-density map. The Bragg reflections have intensities that depend on the arrangement of atoms in the unit cell and how X rays scattered by these atoms interfere with each other. Therefore the diffraction pattern has a wide variety of intensities in it. Measured X-ray diffraction data consist of a list of the relative intensity I (hkl), its indices (h, k, and l), and the scattering angle 2θ, for each Bragg reflection. All the values of the intensity I (hkl) are on the same relative scale, and this entire data set describes the “diffraction pattern.” It is used as part of the input necessary to determine the crystal structure. As already indicated from a study of the diffraction patterns from slits and from various arrangements of molecules, the angular positions (2θ) at which scattered radiation is observed depend only on the dimensions of the crystal lattice and the wavelength of the radiation used, while the intensities I (hkl) of the different diffracted beams depend mainly on the nature and arrangement of the atoms within each unit cell. It is these two items, the unit-cell dimensions of the crystal and its atomic arrangement, that comprise what we mean by “the crystal structure.” Their determination is the primary object of the analysis described here. As illustrated in Figure 1.1b and the accompanying discussion, and mentioned again at the start of Chapter 3, X rays scattered by the electrons in the atoms of a crystal cannot be recombined by any known lens. Consequently, to obtain an image of the scattering matter in a crystal, the “structure” of that crystal, we need to simulate this recombination, which means that we must find a way to superimpose the scattered waves, with the proper phase relations between them, to give an image of the material that did the scattering, that is, the electrons in the atoms.

Refinement of the Crystal Structure of Synthetic Chervetite, Pb2V2O7

1973 ◽  
Vol 51 (1) ◽  
pp. 70-76 ◽  
Author(s):  
Robert D. Shannon ◽  
Crispin Calvo
Keyword(s):  
Crystal Structure ◽  
Least Squares ◽  
Unit Cell ◽  
Type Structure ◽  
Covalent Bonds ◽  
Full Matrix ◽  
Space Group ◽  
Cell Dimensions ◽  
Unit Cell Dimensions

The structure of synthetic chervetite has been refined by full matrix least-squares to a ωR = 0.029 using 1105 reflections. Unit cell dimensions are a = 13.3689(7), b = 7.1607(4), c = 7.1027(4) Å, β = 105935(5)°, and the space group is P21/a. The structure, originally solved by Kawahara, is a dichromate-type structure with a V2O74− group eclipsed to within 11 ± 5°. The Pb2+ ions are irregularly coordinated to 8 or 9 oxygens with distances from 2.40 to 3.20 Å. The distortion of the Pb–O distances is considerably greater than the corresponding distortions of the Sr–O distances in the similar β-Sr2V2O7 structure and is related to the tendency of Pb2+ to form directional covalent bonds. The V–O distances range from 1,665 to 1.720 Å for terminal oxygens and are 1.812 and 1.821 Å for the bridging oxygens. The V–O distances are consistent with the strengths of the Pb—O bonds.

Outline of a crystal structure determination

2010 ◽  
Author(s):  
Jenny Pickworth Glusker ◽  
Kenneth N. Trueblood
Keyword(s):  
Crystal Structure ◽  
Diffraction Pattern ◽  
Structure Determination ◽  
Reciprocal Lattice ◽  
Crystal Structure Analysis ◽  
Unit Cell ◽  
Main Question ◽  
X Ray Diffraction ◽  
Heavy Atoms ◽  
Unit Cell Dimensions

The stages in a crystal structure analysis by diffraction methods are summarized in Figure 14.1 for a substance with fewer than about 1000 atoms. The principal steps are: (1) First it is necessary to obtain or grow suitable single crystals; this is sometimes a tedious and difficult process. The ideal crystal for X-ray diffraction studies is 0.2–0.3mm in diameter. Somewhat larger specimens are generally needed for neutron diffraction work. Various solvents, and perhaps several different derivatives of the compound under study, may have to be tried before suitable specimens are obtained. (2) Next it is necessary to check the crystal quality. This is usually done by finding out if the crystal diffracts X rays (or neutrons) and how well it does this. (3) If the crystal is considered suitable for investigation, its unitcell dimensions are determined. This can usually be done in 20 minutes, barring complications. The unit-cell dimensions are obtained by measurements of the locations of the diffracted beams (the reciprocal lattice) on the detecting device, these spacings being reciprocally related to the dimensions of the crystal lattice. The space group is deduced from the symmetry of, and the systematic absences in, the diffraction pattern. (4) The density of the crystal may be measured if the crystals are not sensitive to air, moisture, or temperature and can survive the process. Otherwise an estimated value (about 1.3g cm−3 if no heavy atoms are present) can be used. This will give the formula weight of the contents of the unit cell. From this it can be determined if the crystal contains the compound chosen for study, and how much solvent of crystallization is present. (5) At this point it is necessary to decide whether or not to proceed with a complete structure determination. The main question is, of course, whether the unit-cell contents are those expected. One must try to weigh properly the relevant factors, among which are: (i) Quite obviously, the intrinsic interest of the structure. (ii) Whether the diffraction pattern gives evidence of twinning, disorder, or other difficulties that will make the analysis, even if possible, at best of limited value.

The Crystal Structure of Vanillosmopsis-Derived (-) α-Bisabolol p-Phenylazophenylurethane

1989 ◽  
Vol 42 (11) ◽  
pp. 2041 ◽  
Author(s):  
RM Carman ◽  
WT Robinson ◽  
MD Sutherland
Keyword(s):  
Crystal Structure ◽  
Melting Point ◽  
Diffraction Pattern ◽  
Optical Rotation ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
X Ray ◽  
Cell Dimensions ◽  
Unit Cell Dimensions

The p-phenylazophenylurethane of Vanillosmopsis-derived (-)-α-bisabolol has unit cell dimensions and an X-ray diffraction pattern identical with those reported for the p-phenylazophenylurethane of Matricaria-derived (-)-α-bisabolol, despite having a higher melting point and different optical rotation.

X-Ray Crystal Structure of [Rh(OH2)6](ClO4)3.3H2O

1989 ◽  
Vol 42 (11) ◽  
pp. 2051 ◽  
Author(s):  
GD Fallon ◽  
L Spiccia
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
Space Group ◽  
X Ray ◽  
Octahedral Sites ◽  
Cell Dimensions ◽  
Unit Cell Dimensions

The crystal structure of [Rh(OH2)6](ClO4)3.3H2O has been determined by single-crystal X-ray diffraction and found to be isomorphous with that of M(ClO4)2.6H2O (M= Fe, Zn, Mn, Co, Ni) and LiClO4.3H2O. Crystal: are hexagonal, space group P63mc with unit cell dimensions a 7.817(2) and c 5.208(1) �. The lattice consists of a uniform arrangement of H2O and ClO4- groups with the RhIII centre occupying 1/3 of the octahedral sites formed by the H2O groups. The RhIII is not situated at the centre of the octahedron. However, the two Rh-O distances [2.128(6) and 2.136(6) �] may be considered identical, i.e. within the errors.

scholarly journals Crystal Structure Refinements of Four Monazite Samples from Different Localities

Minerals ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 1028 ◽  
Author(s):  
M. Mashrur Zaman ◽  
Sytle M. Antao
Keyword(s):  
Crystal Structure ◽  
Electron Probe ◽  
Unit Cell Volume ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
Unit Cell Parameters ◽  
X Ray ◽  
Cell Parameters ◽  
Large Unit Cell ◽  
A Site

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.

The crystal chemistry of the uranyl carbonate mineral grimselite, (K, Na)3Na[(UO2)(CO3)3](H2O), from Jáchymov, Czech Republic

2012 ◽  
Vol 76 (3) ◽  
pp. 443-453 ◽  
Author(s):  
J. Plášil ◽  
K. Fejfarová ◽  
R. Skála ◽  
R. Škoda ◽  
N. Meisser ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Czech Republic ◽  
Structure Refinement ◽  
Unit Cell ◽  
Carbonate Mineral ◽  
X Ray Diffraction ◽  
The Czech Republic ◽  
Cell Parameters ◽  
Uranyl Carbonate ◽  
Diffraction Peaks

AbstractTwo crystals of the uranyl carbonate mineral grimselite, ideally K3Na[(UO2)(CO3)3](H2O), from Jáchymov in the Czech Republic were studied by single-crystal X-ray diffraction and electron-probe microanalysis. One crystal has considerably more Na than the ideal chemical composition due to substitution of Na into KO8 polyhedra; the composition of the other crystal is nearer to ideal, and similar to synthetic grimselite. The presence of Na atoms in KO8 polyhedra, which are located in channels in the crystal structure, reduces their volume, and as a result the unit-cell volume also decreases. Structure refinement shows that the formula for the sample with the anomalously high Na content is (K2.43Na0.57)Σ3.00Na[(UO2)(CO3)3](H2O). The unit-cell parameters, refined in space group P2c, are a = 9.2507(1), c = 8.1788(1) Å, V = 606.14(3) Å3 and Z = 2. The crystal structure was refined to R1 = 0.0082 and wR1 = 0.0185 with a GOF = 1.33, based on 626 observed diffraction peaks [Iobs>3σ(I)].

Synthesis, crystal structure and molecular conformation of (±)-1-oxoferruginol and (±)-shonanol

2004 ◽  
Vol 219 (10) ◽  
Author(s):  
Swastik Mondal ◽  
Monika Mukherjee ◽  
Arnab Roy ◽  
Debabrata Mukherjee
Keyword(s):  
Crystal Structure ◽  
Hydrogen Bonds ◽  
Diffraction Data ◽  
Molecular Conformation ◽  
Membered Ring ◽  
Methyl Groups ◽  
Single Bond ◽  
X Ray Diffraction ◽  
X Ray ◽  
Chemical Structures

Abstract(±)-1-oxoferruginol and (±)-shonanol, two potential intermediates in the synthesis of tricyclic diterpenoid ferruginol, have been prepared and crystal structures of the compounds have been investigated using single-crystal X-ray diffraction data. The methyl groups of the isopropyl moiety in (±)-shonanol are disordered over two positions with occupation factors 0.65(1) and 0.35(1), respectively. Although the chemical structures of two compounds are very similar, a C—C single bond in the terminal six-membered ring of (±)-1-oxoferruginol is replaced by a C=C bond in (±)-shonanol, the quantitative isostructurality index calculations indicate that the structures are not isostructural. Intermolecular O—H…O hydrogen bonds between pairs of molecules in the compounds related by center of inversion lead to characteristic dimers forming R

scholarly journals Magnetically Oriented Powder Crystal to Indexing and Structure Determination

2014 ◽  
Vol 70 (a1) ◽  
pp. C1560-C1560
Author(s):  
Fumiko Kimura ◽  
Wataru Oshima ◽  
Hiroko Matsumoto ◽  
Hidehiro Uekusa ◽  
Kazuaki Aburaya ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Crystal Lattice ◽  
Powder Diffraction ◽  
Diffraction Method ◽  
Lattice Parameters ◽  
X Ray Diffraction ◽  
X Ray ◽  
Crystal Lattice Parameters

In pharmaceutical sciences, the crystal structure is of primary importance because it influences drug efficacy. Due to difficulties of growing a large single crystal suitable for the single crystal X-ray diffraction analysis, powder diffraction method is widely used. In powder method, two-dimensional diffraction information is projected onto one dimension, which impairs the accuracy of the resulting crystal structure. To overcome this problem, we recently proposed a novel method of fabricating a magnetically oriented microcrystal array (MOMA), a composite in which microcrystals are aligned three-dimensionally in a polymer matrix. The X-ray diffraction of the MOMA is equivalent to that of the corresponding large single crystal, enabling the determination of the crystal lattice parameters and crystal structure of the embedded microcrytals.[1-3] Because we make use of the diamagnetic anisotropy of crystal, those crystals that exhibit small magnetic anisotropy do not take sufficient three-dimensional alignment. However, even for these crystals that only align uniaxially, the determination of the crystal lattice parameters can be easily made compared with the determination by powder diffraction pattern. Once these parameters are determined, crystal structure can be determined by X-ray powder diffraction method. In this paper, we demonstrate possibility of the MOMA method to assist the structure analysis through X-ray powder and single crystal diffraction methods. We applied the MOMA method to various microcrystalline powders including L-alanine, 1,3,5-triphenyl benzene, and cellobiose. The obtained MOMAs exhibited well-resolved diffraction spots, and we succeeded in determination of the crystal lattice parameters and crystal structure analysis.

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