Crystal chemistry of borates: the classification and algebraic description by topological type of fundamental building blocks

Abstract

The structural characteristics of all the borates available were analyzed using the Inorganic Crystal Structure Database. The fundamental building blocks (FBBs) in 841 borates were systematically classified into 6 types in terms of their topological structures. By including the polymerization of the FBBs in the borate structure, a novel systematic classification and an algebraic description of borates have been proposed. The current systematic borate classification, in which all the identical FBBs can be classified into the same type, is more reasonable and provides new insight into the structural differences between various borates. The current, simpler, algebraic description is more extensive and can reflect more of the structural information of borates. This thus provides an impetus for elucidating the topological features of borates. Our work also provides much useful information on the design and search for novel borates, which is also helpful to classify newly synthesized borates and to strengthen the understanding of the overall scope of borate structures.

Borates—Crystal Structures of Prospective Nonlinear Optical Materials: High Anisotropy of the Thermal Expansion Caused by Anharmonic Atomic Vibrations

“…It was shown that the frequency of occurrence for borate anions in 460 anhydrous borates [35] is the following: isolated triangles and tetrahedra-52%, layers-15%, frameworks-12%, finite B-O groups-12%, infinite chains-9%. The distribution of boron-oxygen [35] and 841 hydrous and anhydrous borates, respectively [30]. It was shown that the frequency of occurrence for borate anions in 460 anhydrous borates [35] is the following: isolated triangles and tetrahedra-52%, layers-15%, frameworks-12%, finite B-O groups-12%, infinite chains-9%.…”

“…Becker in 2001 as well as Guan and Xue in 2007 examined how often B-O polyanions of different dimensionality (the degree of polymerization-0D, 1D, 2D, 3D) do occur in 460 anhydrous [35] and 841 hydrous and anhydrous borates, respectively [30]. It was shown that the frequency of occurrence for borate anions in 460 anhydrous borates [35] is the following: isolated triangles and tetrahedra-52%, layers-15%, frameworks-12%, finite B-O groups-12%, infinite chains-9%.…”

“…It was shown that the frequency of occurrence for borate anions in 460 anhydrous borates [35] is the following: isolated triangles and tetrahedra-52%, layers-15%, frameworks-12%, finite B-O groups-12%, infinite chains-9%. The distribution of boron-oxygen groups in 841 borates [30] is as follows: isolated anions-55%, chains-12%, layers-11%, frameworks-22.6%. The frequency of occurrence of different FBBs was also represented in [30] with differentiation between non-centrosymmetric and centrosymmetric hydrated and anhydrous borates.…”

“…The distribution of boron-oxygen groups in 841 borates [30] is as follows: isolated anions-55%, chains-12%, layers-11%, frameworks-22.6%. The frequency of occurrence of different FBBs was also represented in [30] with differentiation between non-centrosymmetric and centrosymmetric hydrated and anhydrous borates.…”

“…According to the notation after Touboul, Penin, and Nowogrocki [29], these triborate, tetraborate and pentaborate groups are symbolized as 3:[3:(2∆ + T)], 4:[4:(2∆ + 2T)] and 5:[(3∆ + 2T)], respectively. On the basis of both of these approaches, modified descriptors for the description of rigid groups were worked out by Guan and Xue [30]. Modified descriptors after Burns, Grice and Hawthorne [28,31] are used in this review.…”