Local similarity in organic crystals and the non-uniqueness of X-ray powder patterns

Two new concepts for molecular solids, 'local similarity' and 'boundary-preserving isometry', are defined mathematically and a theorem which relates these concepts is formulated. 'Locally similar' solids possess an identical short-range structure and a 'boundary-preserving isometry' is a new mathematical operation on a finite region of a solid that transforms mathematically a given solid to a locally similar one. It is shown further that the existence of such a 'boundary-preserving isometry' in a given solid has infinitely many 'locally similar' solids as a consequence. Chemical implications, referring to the similarity of X-ray powder patterns and patent registration, are discussed as well. These theoretical concepts, which are first introduced in a schematic manner, are proved to exist in nature by the elucidation of the crystal structure of some diketopyrrolopyrrole (DPP) derivatives with surprisingly similar powder patterns. Although the available powder patterns were not indexable, the underlying crystals could be elucidated by using the new technique of ab initio prediction of possible polymorphs and a subsequent Rietveld refinement. Further ab initio packing calculations on other molecules reveal that 'local crystal similarity' is not restricted to DPP derivatives and should also be exhibited by other molecules such as quinacridones. The 'boundary-preserving isometry' is presented as a predictive tool for crystal engineering purposes and attempts to detect it in crystals of the Cambridge Structural Database (CSD) are reported.

Semiempirical method for the evaluation of bond covalency in complex crystals

We report a semiempirical method for the evaluation of bond covalency in complex crystals. This method is the extension of the dielectric description theory delivered by Phillips, Van Vechten, Levine, and Tanaka (PVLT) which is mainly suitable for binary crystals. Our method offers the advantage of applicability to a broad class of complex materials. The simplicity of the approach allows a broader class of researchers to access the method easily and to calculate not only the bond covalency but also other useful. properties such as bulk modulus. For a series study, a useful trend can be illustrated and often the prediction of the properties of the-missing one(s) among the series can be possible. Finally, examples are given to show how the method is applied and the procedure is transferable to other complex crystals.

Effect of hydrogen bonds on optical nonlinearities of inorganic crystals

This work probes the role of hydrogen bonds (such as O-H ... O and N-H ... O) in some inorganic nonlinear optical (NLO) crystals, such as HIO3, NH4H2PO4 (ADP), K[B5O6(OH)(4)] . 2H(2)O (KB5) and K2La(NO3)(5) . 2H(2)O (KLN), from the chemical bond standpoint. Second order NLO behaviors of these four typical inorganic crystals have been quantitatively studied, results show hydrogen bonds play a very important role in NLO contributions to the total nonlinearity. Conclusions derived here concerning the effect of hydrogen bonds on optical nonlinearities of inorganic crystals have important implications with regard to the utilization of hydrogen bonds in the structural design of inorganic NLO crystals. (C) 1999 Elsevier Science B.V. All rights reserved.

Chemical bond analysis of the correlation between crystal structure and nonlinear optical properties of complex crystals

Second order nonlinear optical (NLO) properties of single crystals with complex structures are studied, from the chemical bond viewpoint. Contributions of each type of constituent chemical bond to the total linearity and nonlinearity are calculated from the actual crystal structure, using the chemical bond theory of complex crystals and the modified bond charge model. We have quantitatively proposed certain relationships between the crystal structure and its NLO properties. Several relations have been established from the calculation. Our method makes it possible for us to identify, predict and modify new NLO materials according to our needs. (C) 1999 Elsevier Science B.V. All rights reserved.

Preliminary study on the charge transfer and bond ionicity of binary crystals

Charge transfer and bond ionicity of some monovalent, divalent, and trivalent binary crystals of A(N)B(8-N) type have been investigated using the self-consistent method. The method divides the binary crystal systems into two subsystems which contain only one kind of element each in physical space. The charge transfer values are obtained by adjusting the charge in a self-consistent way. Based on the obtained charge transfer values, an empirical formula for bond ionicity has been proposed. It has been shown that the present results for bond ionicity are in good agreement with the previous theoretical study delivered by Levine and Pauling. The results also indicate that a large magnitude of charge transfer (or less excess charge in the bonding region) gives rise to high bond ionicity (or low bond covalency); this agrees well with the viewpoint that the excess charge in the bonding region is the origin of the formation of bond covalency. (C) 1998 American Institute of Physics. [S0021-9606(98)00837-X].

Calculation of nonlinear optical coefficients of orthorhombic Re-2(MoO4)(3) crystals

From the chemical bond viewpoint, the second-order nonlinear optical (NLO) tensor coefficients of some Re-2(MoO4)(3) (ReMO)-type tare earth molybdates, with Re = Pr, Nd, Sm, Eu, Gd, Tb and Dy, have been calculated by using the chemical bond theory of complex crystals and the modified bond charge model. All kinds of constituent chemical bonds are considered in the calculation. The major part of the NLO properties of these ReMO crystals is found from the ReO7 groups. The NLO coefficients of these ReMO crystals decrease with Re from Pr to Dy. (C) 1998 Elsevier Science Ltd. All rights reserved.

Chemical bond properties of rare earth ions in crystals

By using the dielectric description theory of ionicity of solids, chemical bond properties of rare earth ions with various ligands are studied. Calculated results show that chemical bond properties of the same rare earth ion and the same ligand in different crystals depend on the crystal structures. In a series of compounds, chemical bond properties of crystals containing different rare earth ions are similar. The magnitude of covalency of chemical bonds of trivalent rare earth ions and various ligands has an order like F

Epitaxial crystallization of sPP on the (100) lattice plane of HDPE crystals

Crystallization behavior of syndiotactic polypropylene(sPP) on the (100) lattice plane of high-density polyethylene(HDPE) crystals was studied by means of transmission electron microscopy and electron diffraction. The results indicate that sPP crystals can grow epitaxially on the (100) PE lattice plane with their chain directions +/-37 degrees apart from the chain direction of the HDPE substrate. The contact planes are (100) lattice planes for both polymers. This kind of epitaxy is explained in terms of parallel alignment of HDPE chains along the rows formed by the {CH3, CH2,CH3} groups in the (100) lattice plane of the sPP crystals. This implies that in the epitaxial crystallization of sPP with fiber oriented HDPE substrate, not only the (110) but also the (100) HDPE lattice planes can act as the oriented nucleation sites. Furthermore, according to the poor matching between HDPE chains in the (100) lattice plane and the {CH3, CH2, CH3} group rows in the (100) lattice plane of the sPP crystals, it is concluded that the geometric matching is not the only controlling factor for the occurrence of polymer epitaxy.

High resolution electron microscopy study of single chain single crystals of gutta percha

Single chain single crystals (SCSC) of gutta percha (GP) were prepared by a dilute-solution spraying method. Electron diffraction (ED) patterns revealed that the single chain single crystal was of a new crystalline modification, the delta form. The images of SCSC of GP obtained with a high resolution electron microscope (HREM) showed a two dimensional periodic structure. Most of the images consisted of lattice fringes derived from the (001) zone. This is the first time that the single chain single crystal images of GP have been observed at a molecular level. Micrographs were image processed using optical filtering methods to improve the signal-to-noise ratio, and were compared with computer-generated simulations of the images. From the viewpoint of the defects seen in high resolution images, the crystal formation and melting processes are discussed. (C) 1998 Elsevier Science Ltd. All rights reserved.

The role of Li-O bonds in calculations of nonlinear optical coefficients of LiXO3-type complex crystals

The second-order nonlinear optical (NLO) tenser coefficients of LiXO3 (X = I; Nb or Ta) type complex crystals have been calculated using the chemical bond theory of complex crystals. Contributions of each type of bond to the total second-order NLO coefficient d(ij) and the linear susceptibility X are quantitatively determined. All tensor values thus calculated are in good agreement with experimental data. The Li-O bonds are found to be an important group in the contributions to the total NLO tenser coefficient, especially for those in LiNbO3 and LiTaO3. The importance of Li-O bonds depends on the environment of Li atom in these crystals.

Calculations of nonlinear optical responses of isomorphous crystals NaClO3 And NaBrO3 with natural optical activity

This work considers the isomorphous optically active crystals NaClO3 and NaBrO3. The connection between their second-order nonlinear optical (NLO) responses and chemical bond structures is established, starting from the experimental optical activities. The calculation reproduces the well-known experimental fact that crystals of NaClO3 and NaBrO3 with similar structures have different signs of optical rotation and of second harmonic generation (SHG). Unlike previous bond charge models, the method may include more than one type of bond in the calculation, and therefore may be used to study the optical activity and nonlinear optical properties of more general crystals. (C) 1998 Elsevier Science B.V. All rights reserved.

Studies on the energy band structures and chemical bond properties of LaX(X=N, P, As, Sb) crystals

The energy band structures of LaX(X=N, P, As, Sb) crystals have been studied by using LMTO-ASA method. The calculated energy gaps of these crystals are 2. 30 eV for LaN, 2. 05 eV for LaP, 1. 66 eV for LaAs and 1. 34 eV for LaSb. The results are in good agreement with experimental data, At the same time, using these calculated results of energy band structures of these crystals, the chemical bond properties have been analyzed and calculated, The covalency values of these crystals are 26.15% for LaN, 32.54% for LaP, 33.30% for LaAs and 36.49% for LaSb, which agree satisfactorily with the calculated ones by using PV (Phillips-Vechten) theory.

Structure-property relationships in Li1-xHxIO3 type complex crystals

Chemical bond parameters and the linear and nonlinear optical (NLO) properties of all constituent chemical bonds in Li1-xHxIOx [x (the amount of hydrogen) = 0.0, 0.28, and 0.34] (LHIO) type complex crystals have been investigated from the chemical bond viewpoint, At the same time, the relationship between the crystal structure and its optical properties has been obtained, based on the calculated results of LiIO3, Li0.72H0.28IO3, and Li0.66H0.34IO3. The nonlinear optical properties of LHIO single crystals are found to be particularly sensitive to the H+ impurity concentration. (C) 1998 Academic Press.

Bond-charge calculation of nonlinear optical susceptibilities of LiXO3 type complex crystals

Second order nonlinear optical (NLO) tensor coefficients of LiXO3 (X = I, Nb, Ta) type crystals have been evaluated on the basis of the dielectric theory of complex crystals and the modified bond charge model. The current method is capable of calculating single bond contributions to the total second order NLO susceptibility. The tenser values thus calculated agree well with experimental data. By introducing the subformula equation and the concept of the effective charge of one valence electron, we are able to successfully treat such complex crystals as LiXO3 type compounds. In addition, the bond charge expression is modified to a more reasonable form for complex crystals. (C) 1998 Elsevier Science B.V.

Morphology and structure of poly(aryl ether ketone ketone) containing isophthaloyl moieties crystallized from dilute solution

Spherulites and lamellar single crystals of poly(aryl ether ketone ketone) containing isophthaloyl moieties (PEKK(I)) were obtained from dilute alpha-chloronaphthalene solution. The morphology and structure of the spherulites and single crystals were studied by electron microscopy and electron diffraction. The spherulites were found to consist of elongated lamellar branches that grow with the b crystallographic axis in the radial direction. Single crystals possess a similar habit, with b parallel to the long axis, a transverse, and c perpendicular to the lamellae plane. High-resolution images of the PEKK(I) crystals which show the perfection of and defects in the crystals, were obtained, and many defects or dislocations a,ere observed. (C) 1997 Elsevier Science Ltd.