The aperiodic nature of incommensurately modulated structures

The discovery of aperiodic crystals is perhaps one of the most important event which has changed our vision on crystalline architectures since the discovery of diffraction 100years ago. It was the merit of a Dutch crystallographer, P.M. de Wolff, to interpret their diffraction pattern as a three dimensional projection of a higher dimensional reciprocal lattice, idea which led directly to the generalization of the concept of crystal. Aperiodic crystals are currently described as periodic objects in higher-dimensional space, i.e. the superspace and their structures can be described in terms of 3-d cuts. Incommensurate structures, composite structures and quasicrystals all belong to aperiodic structures. Many interesting properties of superspace have been discovered which are also directly applicable to crystals in the conventional sense, i.e. crystals with 3-d periodicity. In particular the concept of structure type can be extended for a better understanding of structure relations. The notion of solid solution has also benefited from superspace considerations. Moreover, superspace is a very powerful tool for a better understanding of structure-property relations in material science, e.g. luminescence properties could be directly associated to the description of structures in superspace. Recently, this concept has been used for the prediction of new structural modifications including polytypes and even polytypic modifications of a well-known pharmaceutical produc

The aperiodic nature of incommensurately modulated structures

The discovery of aperiodic crystals is perhaps one of the most important event which has changed our vision on crystalline architectures since the discovery of diffraction 100 years ago. It was the merit of a Dutch crystallographer, P.M. de Wolff, to interpret their diffraction pattern as a three dimensional projection of a higher dimensional reciprocal lattice, idea which led directly to the generalization of the concept of crystal. Aperiodic crystals are currently described as periodic objects in higher-dimensional space, i.e. the superspace and their structures can be described in terms of 3-d cuts. Incommensurate structures, composite structures and quasicrystals all belong to aperiodic structures. Many interesting properties of superspace have been discovered which are also directly applicable to crystals in the conventional sense, i.e. crystals with 3-d periodicity. In particular the concept of structure type can be extended for a better understanding of structure relations. The notion of solid solution has also benefited from superspace considerations. Moreover, superspace is a very powerful tool for a better understanding of structure–property relations in materials science, e.g. luminescence properties could be directly associated to the description of structures in superspace

Getting more out of an incommensurately modulated structure: the example of K_5Yb(MoO_4)_4

A method based on the superspace approach is presented with the aim of generating a family of modular structures from a single incommensurately modulated structure. This approach based on the variation of the modulation vector q is applied to the generation of the K5Yb(MoO4)4, potassium ytterbium tetramolybdate, family of modular structures. The $\beta$ coefficient of the modulation vector q = $\beta b*$ is a temperature-dependent variable which determines the modification. Our method gives a unified frame to describe and explain the three temperature-dependent phases of K5Yb(MoO4)4. Phase can be represented as a polytypic modification with 1/2b*\le q\le 2/3b*; phases $\gamma$ (q = 1/2b*) and \alpha (q = 1b*) are the lowest and the highest temperature members of the K5Yb(MoO4)4 family, respectively

The role of second coordination-sphere interactions in incommensurately modulated structures, using beta-K5Yb(MoO4)4 as an example.

The incommensurate palmierite-like structure of beta-K5Yb(MoO4)4, potassium ytterbium tetramolydate, has been refined in the (3 + 1)-dimensional monoclinic superspace group X2/m(0rho0)00, with X = [0 0 0 0; (1/2) (1/2) 0 0; 0 0 (1/2) (1/2); (1/2) (1/2) (1/2) (1/2)] and the unit-cell parameters a = 10.4054 (16), b = 6.1157 (12), c = 19.7751 (18) A, beta = 136.625 (10) degrees ; q = 0.6354 (30)b*. The occupations of the K and Yb atomic positions are described by crenel functions. The structure model reveals a balanced interaction between the atoms of the first and second coordination spheres. It is shown that the third coordination sphere should not be neglected in studies of modulated structures. The ordering of the K and Yb atoms appears to be the driving force for the modulation of all the other atoms

CH3NH3PbI3: precise structural consequences of water absorption at ambient conditions

The crystal structure of the pristine (I) and aged (II) crystals of CH3NH3PbI3 (hereafter MAPbI(3)) hybrid organic-inorganic lead iodide has been studied at 293 K with high-precision single-crystal X-ray diffraction using a synchrotron light source. We show that (I) and (II) are characterized by an identical tetragonal unit cell but different space groups: I422 for (I) and P4(2)2(1)2 for (II). Both space groups are subgroups of I4/ mcm, which is widely used for MAPbI(3). The main difference between (I) and (II) comes from the difference in hydrogen bonds between the MA(+) cation and the PbI3 framework which is the direct consequence of H2O insertion in the aged crystal (II)