Electron Density Distribution In Crystals Research Articles

Application of the maximum entropy method to electron density determination

The principle of maximum entropy is adopted to derive a procedure for obtaining the electron density distribution in crystals from incomplete X-ray diffraction data. This method was applied to cementite and the result proved to be better than the conventional Fourier inversion in resolution as well as in the absence of ripples. The potential advantages of this method are: (1) the amount of subjective judgment imposed on unavailable data is significantly limited, and (2) the result of this method is consistent with the known information and maximally noncommittal with regard to the unknowns. It is shown that the method is especially well suited to the problem of the determination of a high-resolution electron density map from insufficient experimental data.

Electron-density distribution in crystals of lithium nitrite hydrate, LiNO2.H2O, at 120 K

Electron-density distribution in crystals of lithium nitrite hydrate, LiNO2.H2O, at 120 K

Electron-density distribution in crystals of magnetite at room temperature

Electron-density distribution in crystals of magnetite at room temperature

Electron density distribution in crystals of iron(II) potassium trifluoride

Electron density distribution in crystals of iron(II) potassium trifluoride

Electron-density distributions in crystals of KMnF3 and KNiF3

Electron-density distributions in crystals of KMnF₃ and KNiF₃

Electron-density distribution in crystals of potassium tetrachloroplatinate(II) and influence of X-ray diffuse scattering

Electron-density distribution in crystals of potassium tetrachloroplatinate(II) and influence of X-ray diffuse scattering

Electron density distribution in crystals of potassium trifluorocobaltate(II)

The electron density distribution in crystals of KCoF 3 was investigated on the basis of X-ray intensity data collected by diffractometry at 293 K. The characteristic residual electron density around the Co 2+ ion in the octahedral crystal field was observed on the difference Fourier maps when spherical scattering factors were used for the Co 2+ ion. With aspherical scattering factors for the 3d electrons of the Co 2+ ion, structure amplitudes were calculated for two electron configurations, i.e. high spin 4Tg(t2g)5(eg) 2 and low spin 2Eg(t2g)6(eg ). Refinement on the assumption of high spin decreased the R value significantly (0.0077) from that (0.0088) obtained with the spherical refinement, while assumption of low spin increased the value (0.0120). The difference density maps obtained after these refinements also showed that the high-spin (tEg)5(eg) 2 electron configuration is a good approximation of the electronic state for the Co 2+ ion in cubic KCoF 3 crystals at room temperature. [Crystal data: cubic, Pm3m, a = 4.0688 (7)A, V = 67.36 (3)/~3, Z = 1, D x = 3.821 Mg m -3, 2(MoKa) = 0.7107A, /~(Mo Ka) = 7.943 mm -~, T = 293 K; 743 reflections with IFI > 3trlFI.] crystal fields were observed in crystals of y-Co2SiO 4 (Marumo, Isobe & Akimoto, 1977) and CoA120 4 (Toriumi, Ozima, Akaogi & Saito, 1978) respectively. On the deformation density maps of y-C02SiO 4 eight positive peaks were observed around the Co 2+ ion on the lines along the (111 ) directions of the cubic lattice, and six negative peaks on the Co-O bonds. These peaks indicate that the electron density of the t2g orbitals is higher than that of the eg orbitals as a result of splitting of the d orbitals in a quasi-octahedral field. The deformation density around the Co 2÷ ion in CoA120 4 clearly shows that the density on the t2g orbitals is lower than that on the eg, giving an arrangement of negative and positive peaks reversed to that in an octahedral field. The present study was undertaken to increase knowledge on electron density distributions around the transition-metal ions in an octahedral field. In the octahedral crystal field, the ground state of a Co 2+ ion can be either high spin (t2g)5(eg) 2 or low spin (12g)6(eg) depending upon the strength of the crystal field. The refinements were performed for both configurations with aspherical scattering factors and the residual densities after these refinements were compared.

Electron-density distribution in crystals of KCuF3 with Jahn–Teller distortion: errata

Electron-density distribution in crystals of KCuF₃ with Jahn–Teller distortion: errata

Electron-density distribution in crystals of KCuF3 with Jahn–Teller distortion

Electron-density distribution in crystals of KCuF₃ with Jahn–Teller distortion

Electron-density distribution in crystals of α-K2CrO4

Electron-density distribution in crystals of α-K₂CrO₄

Electron-density distribution in crystals of CoAl2O4

Electron-density distribution in crystals of CoAl₂O₄

Electron-density distribution in crystals of γ-Ni2SiO4

Electron-density distribution in crystals of γ-Ni₂SiO₄

Survey of results in the determination of X-ray intensities and structure factors for metals, alloys and covalent compounds

The problem of the interatomic bond in molecules and crystals is first of all that of a fairly precise determination of the electron distribution. The electron density distribution in crystals can be considered as the distribution of the square of the wave function. Thus an experimental determination of structure factors is one of the most direct methods of experimental determination of wave functions. Calculations of physical and physical-chemical properties of crystals can be made by using quantum mechanical methods, making use of wave functions obtained experimentally. The question arises of the necessary limits of accuracy of experimental F2 values for solving various quantum mechanical problems as well as for comparing them with theoretical values. It should be noted that the theoretical structure factors are approximate since the exact solutions of the Schrodinger equation is possible for the hydrogen atom only. Experimental determination of F2 values on powders poses very complicated problems including the measurement of absolute X-ray scattering intensities. Results of experimental determinations of F2 values on powder of metals, alloys and compounds with covalent character, including semiconductors, are analysed. Possible reasons for deviations, including the role of extinction, particle size of the powders under investigation, possibility of preferred orientation, change of state and composition of the surface, the role of polarization of the monochromated beam and lattice dynamics, are discussed. The difference between the data of different authors, which seems to be due to the degree of the accuracy of scaling to absolute intensity values, is also discussed. Different parts of the f-curves give different information on the electron density distribution of the crystal. The amount of information which F2values contain on the outer electron distribution depends to a great extent on the type and the parameters of the crystal lattice, and on the degree of anisotropy. There are some differences mainly in absolute values between the data of different authors. Some problems of reduction of the reflexion intensities are also discussed. the results of some measurements made on powders of the elements and on the semiconducting-type compounds with covalent bonds are analysed as well. A large number of measurements were made on AIIIBV compounds. The results show the differences in F2 values due to the change of the effective charge of ions. In conclusion some experimental determinations of f-curves are quoted and the necessary accuracy and possibilities of correction of the measured intensity of Debye reflexions are evaluated.

Calculation of Electron-Density Distribution in Crystals with the Help of Convolution Operations

Calculation of Electron-Density Distribution in Crystals with the Help of Convolution Operations