porosity—open and closed, linear defects, various phase and chemical composition
of particular grains in polycrystalline material and the resulting phenomena and
processes of mass transport on grain boundaries, etc.). Both groups of problems
require completely different approaches, and while the problem of complexity at the
structural level is currently in many cases taken into account in theoretical modeling
in an approximate way, often allowing to obtain also quantitatively accurate results,
the complexity at the microstructural level is still a huge challenge and apart from
few cases of attempts to model these effects using ab inito methods (obviously with
very simplified models) requires the use of coarse classical methods that give at best
the acceptable quality results and is still waiting for the development of better
models and theories, as well as more efficient algorithms and significantly faster and
more powerful computers. Therefore, in the following paragraphs, only selected
problems related to structural complexity will be discussed and some most common
practical ways of solving them effectively will be presented.
1.3.1 The Size and Complexity of the System
The development of computer technologies, their increasing availability, and
growing computing power with simultaneous development of theoretical methods
and the increase in the efficiency of computational algorithms have caused significant increase in applications of theoretical calculations in scientific research. In
turn, this resulted in increasing importance of calculations, both in the first, early
stages of research, to reduce the number of compounds and compositions requiring
experimental study, by screening possible materials and narrowing potential candidates to those with the most promising properties, as well as later, during the
synthesis and experimental research, to modify and improve the physicochemical
properties of the materials of interest.
All this increases the interest in the application of theoretical methods and in
silico experiments in the study of materials with a very wide range of applications,
huge diversity, and structural complexity.
Unfortunately, despite the extremely rapid progress observed, still many materials are beyond the scope of modeling possibilities using the available tools. This is
mainly due to the fact that in general the ab inito calculations refer to ideal systems
(e.g., ideal crystals of infinite sizes, isolated molecules or clusters) at the absolute
zero temperature. However, real systems are much more complex–neutral or
charged particles and clusters are not isolated, but they interact (in the gas phase,
liquid or molecular crystals) with a various strength; solids are always—to a different extent—defective, and these defects can exhibit various types of structural
disorder or local ordering and clustering. Moreover, ab initio computational
methods for solids are, by definition—due to Bloch theorem—dedicated to periodic
systems exhibiting translational symmetry, which makes them unable to handle
amorphous solids. The mentioned factors cause that in practically every case when
structural complexity appears; it is necessary to use various types of simplifications,
32
A. Koleżyński
of particular grains in polycrystalline material and the resulting phenomena and
processes of mass transport on grain boundaries, etc.). Both groups of problems
require completely different approaches, and while the problem of complexity at the
structural level is currently in many cases taken into account in theoretical modeling
in an approximate way, often allowing to obtain also quantitatively accurate results,
the complexity at the microstructural level is still a huge challenge and apart from
few cases of attempts to model these effects using ab inito methods (obviously with
very simplified models) requires the use of coarse classical methods that give at best
the acceptable quality results and is still waiting for the development of better
models and theories, as well as more efficient algorithms and significantly faster and
more powerful computers. Therefore, in the following paragraphs, only selected
problems related to structural complexity will be discussed and some most common
practical ways of solving them effectively will be presented.
1.3.1 The Size and Complexity of the System
The development of computer technologies, their increasing availability, and
growing computing power with simultaneous development of theoretical methods
and the increase in the efficiency of computational algorithms have caused significant increase in applications of theoretical calculations in scientific research. In
turn, this resulted in increasing importance of calculations, both in the first, early
stages of research, to reduce the number of compounds and compositions requiring
experimental study, by screening possible materials and narrowing potential candidates to those with the most promising properties, as well as later, during the
synthesis and experimental research, to modify and improve the physicochemical
properties of the materials of interest.
All this increases the interest in the application of theoretical methods and in
silico experiments in the study of materials with a very wide range of applications,
huge diversity, and structural complexity.
Unfortunately, despite the extremely rapid progress observed, still many materials are beyond the scope of modeling possibilities using the available tools. This is
mainly due to the fact that in general the ab inito calculations refer to ideal systems
(e.g., ideal crystals of infinite sizes, isolated molecules or clusters) at the absolute
zero temperature. However, real systems are much more complex–neutral or
charged particles and clusters are not isolated, but they interact (in the gas phase,
liquid or molecular crystals) with a various strength; solids are always—to a different extent—defective, and these defects can exhibit various types of structural
disorder or local ordering and clustering. Moreover, ab initio computational
methods for solids are, by definition—due to Bloch theorem—dedicated to periodic
systems exhibiting translational symmetry, which makes them unable to handle
amorphous solids. The mentioned factors cause that in practically every case when
structural complexity appears; it is necessary to use various types of simplifications,
32
A. Koleżyński