A new method for quantitative estimation of the degree of similarity of coordination polyhedra

March 29, 2018, Lobachevsky University
The triangles denote the CPs corresponding to trigonal bipyramid and the open and gray squares denote tetragonal pyramid with the central atom in the base and at the center of mass, respectively. Credit: Lobachevsky University

The problem of the relationship between the structure of materials and their physical properties is one of the global problems of the present day. For many years, researchers of the Lobachevsky University's Faculty of Physics have been working to solve it. In particular, systematic experimental and theoretical studies of the atomic structures of crystals of various materials are conducted at the UNN Department of Crystallography and Experimental Physics.

The traditional approach to describe the atomic structure of a crystal is to use the polyhedral method based on the description of the model of a crystal by means of coordination polyhedra (polyhedra built on atoms as their vertices). An important contribution to the development of this method was made by Academician N.V. Belov, the originator of the crystallographic research at the UNN Faculty of Physics. The polyhedral method greatly simplifies the crystallochemical analysis of complex atomic structures. Crystal structure as a whole is represented in the form of a spatially ordered system of coordination polyhedra, thus, a transition is performed from an atom to a larger structural unit, the coordination polyhedron. On the other hand, the analysis of individual coordination polyhedra makes it possible to determine the symmetry of a particular atom's environment, its energy and chemical state.

In real crystals, coordination polyhedra often have a distorted shape, that is, they differ from ideal polyhedra. The presence of distortion of the coordination polyhedron and its magnitude are due to a variety of factors, including the energy state of the central atom, the chemical and physical features of the environment of the central atom, the mechanical stresses arising in the atomic framework of the crystal, and many more. Some types of coordination polyhedra distortion significantly affect the physical properties of materials. For example, distortion of the coordination polyhedron of an activator ion in a laser crystal can lead to a Stark splitting of electron terms, which often results in emission spectra broadening. Thus, the problem arises of giving a quantitative estimate of the distortion in a real coordination polyhedron.

Associate Professor Nikolai Somov and Assistant Professor Pavel Andreev from the Department of Crystallography and Experimental Physics at the Lobachevsky State University of Nizhny Novgorod have proposed a new approach to estimate the degree of similarity of a coordination polyhedron to a certain reference polyhedron. The degree of similarity of a coordination polyhedron is a scalar value strictly equal to unity if the coordination polyhedron is similar to the reference ; in other cases it takes values from zero to one. The proposed method is implemented in the form of a computer program that is freely available (http://phys.unn.ru/ps/).

The method for quantitative estimation of the degree of similarity of polyhedra was tested on more than 400 crystalline structures of organometallic compounds of pentavalent antimony and bismuth. It was shown that the proposed approach is consistent with one of the main theorems of structural crystal chemistry, and the advantages of the new approach were demonstrated using concrete examples.

Explore further: New 3-D structure shows optimal way to divide space

More information: N. V. Somov et al, On Quantitative Estimation of the Degree of Similarity of Coordination Polyhedra, Crystallography Reports (2018). DOI: 10.1134/S1063774518010170

Related Stories

New 3-D structure shows optimal way to divide space

November 25, 2016

(Phys.org)—Researchers have discovered a new 3D structure that divides space into 24 regions, and have shown that it is the best solution yet to a modified version of a geometrical space-partitioning problem that has challenged ...

A new way of making glass

November 9, 2012

(Phys.org)—A new way to make glass has been discovered by a collaboration of researchers at the Universities of Düsseldorf and Bristol using a method that controls how the atoms within a substance are arranged around each ...

A baby crystal is born

January 17, 2012

Lead sulfide (PbS) forms when an equal number of lead and sulfur atoms exchange electrons and bond together in cubic crystals. Now scientists have determined that a structure comprising 32 lead-sulfur pairs is the smallest ...

Chemists create molecular polyhedron

July 21, 2011

Chemists have created a molecular polyhedron, a ground-breaking assembly that has the potential to impact a range of industrial and consumer products, including magnetic and optical materials.

Recommended for you

Coffee-based colloids for direct solar absorption

March 22, 2019

Solar energy is one of the most promising resources to help reduce fossil fuel consumption and mitigate greenhouse gas emissions to power a sustainable future. Devices presently in use to convert solar energy into thermal ...

EPA adviser is promoting harmful ideas, scientists say

March 22, 2019

The Trump administration's reliance on industry-funded environmental specialists is again coming under fire, this time by researchers who say that Louis Anthony "Tony" Cox Jr., who leads a key Environmental Protection Agency ...


Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.