The Solution X-Ray Diffraction Method

The solution X-ray diffraction method has been widely used for the structural analysis of liquids, solvated ions, and complexes in solution, 

The reduced intensities i(s) are calculated with respect to a given stoichiometric volume of the solution according to 

The structure parameters rpq, 6pq, and npq in Eq. (9) are finally refined by the least-squares method to minimize the error square sum U, 

X-Ray diffraction experiments have been carried out for four saturated and supersaturated aqueous solutions of simple salts (26), in order to compare the results obtained by the MD simulations (21) with the experimental results. The aqueous solutions examined were 6.18 mol (kg H20) 1 NaCl (H20/salt molar ratio, 8.98), 4.56 mol (kg H20)-1 KC1 (molar ratio, 12.18), 16.15 mol (kg f O) 1 KF (molar ratio, 3.44), and 31.96 mol (kg H20) 1 CsF (molar ratio, 1.74) (26). The saturation concentrations of these salts at 298 K were 6.15 mol (kg H20) 1 for NaCl, 4.81 mol (kg H20) 1 for KC1, 17.50 mol (kg H20) 1 for KF, and 24.13 mol (kg H20) 1 for CsF. The supersaturated solutions were stable for several weeks without formation of crystals. 

---

In aqueous solutions of low concentration, when theories of ionic conductivities are applicable, no ion pairs will be formed in the case of the lithium and sodium halides at room temperature. Even in 13.9 mol (kg H20)"1 LiCl aqueous solution where the molar ratio of LiCl to H20 is 1 4, essentially no ion pairs between Li+ and Cl- ions are formed around 25°C, according to an MD simulation (28). Formation of the 1 1 ion pair between Li+ and Cl in aqueous solution is, however, concluded in 18.5 mol (kg H20) 1 aqueous solution where the nLiCI h2o molar ratio is 1 3, which is close to the saturation concentration of LiCl in water (29). Formation of the 1 1 Li+ Cl" ion pair has been suggested by a neutron diffraction method (30), but the data derived from such measurements were not in good agreement with the simulation results. No evidence has been found for ion-pair formation between Li+ and I ions at 20 and 50°C in 2.78 and 6.05 mol (kg H20) 1 aqueous lithium iodide using the solution X-ray diffraction method (31). 

However, the usual skepticism concerning the solution X-ray diffraction method applied to weak interactions should be exercised, in particular in the malonate case where the temperature factors for all interactions involving thallium(I) were found to be very large. With increasing water content, and thus coming closer to what we normally mean by aqueous solution, the polynuclear units decompose. From the measured physicochemical properties, such as density, refractive index, specific... 

The local structure of aluminate in aqueous solution has been found by Radnai et al. to be a fourfold coordination structure, [Al(OH)4], using a solution X-ray diffraction method [5]. We have spectroscopically examined the dynamic change in the structural transition from aluminate to Al(OH)3 [6], which happens with the polymerization of aluminate due to the reduction of pH [7], using the in situ soft X-ray absorption spectroscopy we have developed [8,9]. The X-ray... 

The many possible oxidation states of the actinides up to americium make the chemistry of their compounds rather extensive and complicated. Taking plutonium as an example, it exhibits oxidation states of -E 3, -E 4, +5 and -E 6, four being the most stable oxidation state. These states are all known in solution, for example Pu" as Pu ", and Pu as PuOj. PuOl" is analogous to UO , which is the stable uranium ion in solution. Each oxidation state is characterised by a different colour, for example PuOj is pink, but change of oxidation state and disproportionation can occur very readily between the various states. The chemistry in solution is also complicated by the ease of complex formation. However, plutonium can also form compounds such as oxides, carbides, nitrides and anhydrous halides which do not involve reactions in solution. Hence for example, it forms a violet fluoride, PuFj. and a brown fluoride. Pup4 a monoxide, PuO (probably an interstitial compound), and a stable dioxide, PUO2. The dioxide was the first compound of an artificial element to be separated in a weighable amount and the first to be identified by X-ray diffraction methods. 

The formation of such materials may be monitored by several techniques. One of the most useful methods is and C-nmr spectroscopy where stable complexes in solution may give rise to characteristic shifts of signals relative to the uncomplexed species (43). Solution nmr spectroscopy has also been used to detect the presence of soHd inclusion compound (after dissolution) and to determine composition (host guest ratio) of the material. Infrared spectroscopy (126) and combustion analysis are further methods to study inclusion formation. For general screening purposes of soHd inclusion stmctures, the x-ray powder diffraction method is suitable (123). However, if detailed stmctures are requited, the single crystal x-ray diffraction method (127) has to be used. 

As has been shown by the X-ray diffraction method the parent metals (i.e. Pd or Ni), the a-phase, and /3-phase all have the same type of crystal lattice, namely face centered cubic of the NaCl type. However, the /9-phase exhibits a significant expansion of the lattice in comparison with the metal itself. Extensive X-ray structural studies of the Pd-H system have been carried out by Owen and Williams (14), and on the Ni-H system by Janko (8), Majchrzak (15), and Janko and Pielaszek (16). The relevant details arc to be found in the references cited. It should be emphasized here, however, that at moderate temperatures palladium and nickel hydrides have lattices of the NaCl type with parameters respectively 3.6% and 6% larger than those of the parent metals. Within the limits of the solid solution the metal lattice expands also with increased hydrogen concentration, but the lattice parameter does not depart significantly from that of the pure metal (for palladium at least up to about 100°C). 

Zirconocene dichloride 121 derived from (l-phenylethyl)cyclopentadienyl ligand is formed as a mixture of diastereomers from which the racemic form can be isolated by fractional crystallization. This complex was studied by X-ray diffraction methods and revealed a virtually chiral C2-symmetrical conformation in which the chiral ring-substituents are arranged in a synclinal position relative to the five-membered ring. It was proposed that this conformation is preserved in solution. Using 121 as catalyst the influence of double stereodifferentiation during isospecific polymerization of propylene (Eq. 32) was demonstrated for the first time [142],... 

As a result of compelling three-dimensional models and remarkably high levels of precision, it is often assumed that structural elucidation by single crystal X-ray diffraction is the ultimate structural proof. Spatial information in the form of several thousands of X-ray reflection intensities are used to solve the position of a few dozen atoms so that the solution of a structure by X-ray diffraction methods is highly overdetermined, with a statistically significant precision up to a few picometers. With precise atomic positions, structural parameters in the form of bond distances, bond... 

As an example for the specific case of vanadium alloys with palladium, the trend of the average atomic volume of the alloys is shown in Fig. 4.20 and compared with the phase diagram. These data were obtained by Ellner (2004) who studied the solid solutions of several metals (Ti, V, Cr, Mn, Fe, Co and Ni) in palladium. The alloys were heat treated at 800°C and water-quenched. From the unit cell parameters measured by X-ray diffraction methods, the average atomic volume was obtained Vat = c 14 (see Table 4.3). These data together with those of the literature were reported in a graph, and the partial molar (atomic) value of the vanadium volume in Pd solid solution (Fv)... 

Synthesis of sulfo-selenide Chevrel phases Phases ofM Mo x xSex composition (M = Cr, Mn) were prepared by the reaction of stoichiometric mixtures of MoS2 and MoSe2 binary powders with Mo and Cr, or Mn, metallic powders (Mantjour-Billah and Chevrel 2004). The mixtures were pressed into pellets and then (inside an alumina crucible) sealed in evacuated silica tubes. After heating to 800°C and then to 1000°C for 24 hours, two further grinding and annealing (at 1000°C) treatments were performed. Powder X-ray diffraction methods were used to study the solid solutions, the trend of the lattice parameters, etc. 

Okazaki and co-workers <93JA8855, 94PS(95-96)2l> succeeded in generating all four sterically crowded metallothiones (344) by desulfurization of 1,2,3,4,5-tetrathiametallolanes (343) (M = Si, Ge, Sn, Pb) the first two compounds are quite stable crystalline substances which were studied by x-ray diffraction methods while the latter were identified only in solution. 

The chemical properties of berkehum are rare earth-like character because of its half-filled 5/ subsheU and should be simdar to cerium. The element readily oxidizes to berkelium dioxide, Bk02 when heated to elevated temperatures (500°C). In aqueous solutions, the most common oxidation state is -i-3 which may undergo further oxidation to +4 state. A few compounds have been synthesized, the structures of which have been determined by x-ray diffraction methods. These include the dioxide, Bk02 sesquioxide, Bk203 fluoride,... 

The ju--propylidene(2) complex [ -C(CH3)2]( -CO)[(t)5-C5H5)-Ru(CO)]2 has been established by X-ray diffraction methods to exist as a cis isomer in the crystalline state. However, both cis and trans isomers were detected in solution by NMR techniques. The interconversion of these two compounds is concluded to involve bridge-terminal carbene... 

A clean and dry 20-gallon reactor was charged with 17.4 gallons of deionized water and 4.44 L of concentrated hydrochloric acid, to give a 0.77 M solution. To the solution was added 4.44 kg of the anhydrous 5-(2-(4-(l,2-benzisothiazol-yl)-l-piperazinyl)-ethyl)-6-chloro-l,3-dihydro-2H-indol-2-one free base. The slurry was warmed to 65°C and held for 18 hours. The slurry was cooled to room temperature. The product was filtered and washed with 2x5-gallon portions of deionized water, and then air dried at 50°C for 30 hours. The dried product contained 4.4% water and the x-ray diffraction method confirmed that the desired product was obtained. 

Polynuclear complexes, which contain several metal atoms, have structures, which cannot usually be derived from solution X-ray diffraction data alone. However, since the intramolecular metal-metal distances in these complexes are well defined and limited in number, they give distinct contributions to the diffraction data and can often be precisely analyzed in terms of distances, frequencies, and rms variations. When compositions and concentrations of the complexes are known from other measurements, this information can be sufficient for a derivation of the structures. The method has been applied to several hydroxo and oxo complexes and to some halogeno complexes of primarily heavy metal ions. 

Molecular orientations of grafted celluloses can be changed to a small extent. Interactions of monomer solutions with cellulosic fibers to decrease crystallinities and to change lattice type of the products from those of unmodified fibers have been reported. X-ray diffraction methods are used to determine the changes (24). 

---