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УДК 54-127; 548-51
quataron nature or the nonceassicae mechahism of crystae huceeation and growth
A. M. Askhabov
IG Komi SC of UB of RAS, Syktyvkar; xmin@geo.komisc.ru
At the end of last century the author proved the possibility of spontaneous formation and relative stable existence of special nano-size clusters in supersaturated media (solutions, vapor phase) and overcooled melts. These clusters were interpreted as prenucleation protomin-eral particles and were named clusters of «hidden» phase or quatarons. On this basis a special quataron concept of cluster self-organization of matter at nano-level was formed within which a number of debatable questions of the nucleation theory, formation of crystalline and non-crystalline materials, including hierarchically constructed amorphous (opal-like) materials was solved. In subsequent years new ideas on clusterization of substance in crystal-forming media and prenucleation clusters became extremely popular and found more and more experimental proofs. Owing to really specific character of their properties, these clusters are given special names by other authors — for example «DOLLOP». We, in turn, go further — we consider quatarons, dollops and other similar particles as the basic building units of growth of crystals. As a result a principally new concept of quataron growth of crystals, different from known concepts of microblock (Fedorov-Balarev) and atomic (Kossel-Stransky) growth of crystals was formed on this basis. The quataron concept, developed by us, allows to generalize nowadays popular ideas of nonclassical nucleation and crystal-growth, formation of nanostructured materials.
Key words: pre-nucleation clusters, nucleation end crystal growth, nanostructured materials.
КВАТАРОННАЯ ПРИРОДА НЕКЛАССИЧЕСКОГО МЕХАНИЗМА ЗАРОЖДЕНИЯ И РОСТА КРИСТАЛЛОВ
А. М. Асхабов ИГ Коми НЦ УрО РАН, Сыктывкар; xmin@geo.komisc.ru
В конце прошлого века автором была показана возможность спонтанного образования и относительно стабильного существования в пересыщенной среде (растворе, паровой фазе) и переохлажденных расплавах особые наноразмерных кластеров. Эти кластеры интерпретировались как предзародышевые протоминеральные частицы и были названы кластерами «скрытой» фазы, или кватарона-ми. На этой основе была сформулирована специальная кватаронная концепция кластерной самоорганизации вещества, в рамках которой решался ряд спорных вопросов теории зародышеобразования, формирования кристаллических и некристаллических материалов, в том числе иерархически упорядоченных аморфных (опалоподобных) материалов. В последующие годы новые идеи по кластеризации вещества в кристаллообразующих средах в предзародышевые кластеры стали чрезвычайно популярными и находятся все более и более убедительные экспериментальные доказательства. Учитывая специфические свойства этих кластеров, другие авторы также стали давать им специальные названия, например «доллопы». Мы, в свою очередь, пошли дальше и рассматриваем кватаро-ны, доллопы и другие подобные частицы как основные строительные единицы роста кристаллов. В результате была сформулирована принципиально новая кватаронная концепция роста кристаллов, отличная от известных представлений микроблочного (концепция Федорова—Баларева) и атомарного (концепция Косселя—Странского) роста кристаллов. Расматриваемая кватаронная концепция подводит общую основу под популярные в настоящее время идеи неклассического зарождения и роста кристалла и формирования наноструктурированных материалов.
Ключевые слова: предзародышевые кластеры, зарождение и рост кристаллов, наноструктурированные материалы.
Introduction
The problem of nucleation holds a central position in the crystal growth theory [1]. The concrete mechanism of the formation of crystalline nuclei is still unknown; nevertheless, due to the classical works of Gibbs, Volmer, Becker, Doering, Hirth, Pound and other scientists, the state-of-the-art level of the theoretical description of nucle-ation is believed to be quite satisfacto-
ry. However, the limitation of the classical nucleation theory describing crystal growth became evident back in the late 1940s, when it failed to explain the formation of the growth centers on growing faces at low supersaturations. The problem of working out of new ideas in the field of nucleation and existence of small particles of a new phase has become topical in connection with development and distribution of nano-tech-
nological ideas of obtaining of materials by the principle «from below-upwards». After our work [2] mechanisms of nucle-ation, alternative to classical ones, providing for preliminary structurization of matter in crystal-forming media began to be discussed widely. In the work [3] there is a great number of references to this theme.
Another not less important problem of the theory of crystals-forma-
Fig. 1. Variants of quataron evolution
tion concerns actually growth of crystals. As is known, in the 20th century two concepts were developed in parallel in the theory of growth of crystals. According to the first connected with the names of Kossel, Stransky, Kaishev, etc., growth units are separate atoms or ions. The second concept originating with Fedorov and more connected with the name of Balarev assumes growth of crystals by joining of ready crystal blocks. At various times there were suggestions about participation in growth of crystals of intermediate formations (molecular complexes, associates, clusters, etc.) of which existence testified the results of numerous experimental (and not only spectroscopic) researches of crystal-forming media. However on this basis it was not possible to develop the alternative concept of crystal growth first of all because of arising contradictions with the classical theory of nucle-ation. Last years in the theory of growth of crystals the new ideas of non-classical non-Kossel growth of crystals [4] began also to be discussed widely. At new level the ideas of formation of crystals by oriented aggregation of small crystallites [5], earlier stated in N. P. Yushkin's work [6], are revived.
In this connection we suggest a new approach to the analysis of processes of nucleation and growth of crystals which comes from the possibility of formation and existence in supersaturated media of special forms of the connected atoms — nano-size clusters of «hidden» phase called quatarons [7, 8]. Within this approach it is possible to describe both the processes of nucleation, and growth of crystals. Moreover, on the basis of the ideas on quatarons, we presented, genesis of the nano-structured amorphous materials can also be explained.
In the given work we generalize our ideas on quatarons, their properties, consider their role in nucleation and crystal growth, and also we indicate the possible ways of formation of amorphous nanostructured materials on the
basis of quatarons or hierarchical cluster structures formed by them.
Quatarons
in crystal-forming media
In the classical theory of nucle-ation, the energy of formation of a critical nucleus of spherical form is given by Gibbs formula:
AG = |лг2 у,
(1)
The dependence y(r) we obtained is similar to Tolmen's one. But here the parameter A = 8 is easily estimated. It is the minimum distance at which atoms of the cluster and medium can approach each other without making a bond. The minimum value of 8 is equal to the diameter of cluster-forming atoms (or other structural units). It is interesting that the value of 28/r is the portion of surface atoms in the nucleus (28/r = ns/n).
If we use formula
r=n (l - f)
at construction of the theory of nucle-ation, we will get modified formula for energy of formation of a critical nucleus:
кг 4 2 L 43 AG = 3 w Yo I 1 - —
(3)
where r — nucleus radius, Y — specific surface energy (surface tension).
Here two fundamental questions remain unclear:
1) When this nucleus becomes a crystal?
2) Whether it is necessary to consider size dependence Y from r in theory construction?
There are still questions connected with the possible presence of a charge on nuclei of a new phase, ignoring of their internal structure and dynamics in the theory, let alone the continued discussions about applicability of the classical (thermodynamic) approach to small particles as a whole.
Generally exact dependence y (r) is not established till now. There are different views: a) y does not depend from r; b) y increases with reduction of r; c) y decreases with reduction of r. We, as well as the majority of researchers, give preferences to the last point of view. Though, it is possible to agree that for crystalline particles with flat faces y (r) can be a constant irrespective of their size.
The following Tolmen formula is widely known:
7 = 7, 1--, (2)
^ r J
where Yo — superficial energy (tension) for a flat surface, A — Tolmen parameter is thickness of interphase area. But Tolmen formula is true only for lager particles (r>>A). Besides, here it is very difficult to determine a value of A.
This formula coincides with Gibbs formula only at r >> 8. It is interesting that at r < 48, AG < 0, formation of such nuclei can occur spontaneously by self-organization mechanism.
Taking into account dependence Y(r), the known Gibbs-Thomson formula also undergoes changes. In particular, for solution we obtain the following formula:
=
cn
RTr
r
(4)
where Vm — molar volume, R — gas constant, T — temperature.
From this formula there comes the essentially important consequence — even near to zero supersaturation in solution the formation of the particles which radius is equal to 5 is possible. Thus the maximum number of atoms in such particles at r = 5 makes
" = 86) '=8-
With increase of supersaturation the radius of particles increases. At r = 25, accordingly the number of atoms reaches 64. Thus, these are particles containing from several units to several tens of atoms.
As a result we come to a conclusion about the possibility of existence in crystal-forming medium of nucleus particles which are not considered by the classical theory of nucleation. They were called clusters of «hidden» phase or, on their characteristic quasispherical form controlled by peculiarities of surface energy, quatarons. In terms of the classical theory they could be named pre-nucleation clusters.
Classical theory Critical nucleus
Critical cluster "hidden" phase (quataron), r>45
Fig. 2. Alternative way of nucleation through quataron
Here we will just give some characteristic properties of clusters of «hidden» phase — quatarons which in fact represent the special form of the atomic-molecular organization of matter in the nanoworld [7, 8].
— Quatarons are formed and exist only in nonequilibrium conditions. These are nonequilibrium living clusters.
— Quatarons are amorphous pre-nucleation clusters with dynamic structure and oscillating bonds between atoms forming them.
— During each moment of time quatarons can have unpredictable enough geometrical configuration. In any case their form is close to spherical one, and in polyhedral interpretation these are usually icosahedral or similar to them structures which are approximated by sphere.
— They differ from usual molecular complexes by increased energies. A part of energy which could be discharged at their formation, remains in them in the reserved kind. Thanks to that quatarons are objects of the increased reactionary ability and structural mobility.
— In the field of small sizes quatar-ons have mainly hollow structure. Filling of internal space occurs in process of approach of their radius r to 48.
In Fig. 1 all possible variants of quatarons evolution are represented.
— At full realization of valency, in particular, at covalent interactions between atoms forming them, quatarons can turn into large molecules. At that, hollow quatarons are transformed into fullerenes.
— At minimization of energy and optimization of their geometry on the basis of quatarons all other types of nano-particles, including the so-called dense packed magic clusters, are formed.
— At establishing of a three-dimensional order (arrangement of atoms under lattice laws) quatarons transform into crystalline nano-particles.
Unfortunately, our ideas on topology and dynamics of quatarons structure were formed, mainly, on the basis of the theoretical analysis. To get rid of that, the development of new experimental research techniques to study the nucleation processes and properties of quatarons, time evolution of their internal structure and external morphology is necessary. On the other side, we have already many experimental data testifying to pre-crystallization structurization (clusterization) of substance in solutions, in melts, in vapor phase. The re-
view of the problem of pre-nucleation clusters formation in solutions see in [3]. By the way, in this work it was proposed to name pre-nucleation clusters as DOLLOPS (Dinamically Ordered Liquid-Like Oxyonion Polymers).
Crystallization of quatarons — the new mechanism of nucleation
Until now we have not made any assumptions on their nature. They were considered only as a group of the connected atoms or molecules, as clusters. These clusters, obviously, are not yet true crystalline nuclei, and represent the original intermediate state [8].
If we interpret quatarons in terms of Delone system, we understand when they become crystalline nuclei [9].
Indeed, if we can regard quatarons as finite pieces (R, r) of systems, we get R ~ 8. And according to the local theorem [10], local order in a sphere of the radius, equal to 4R in, is necessary for crystallization. Since the parameter 8 is equal to R, then the geometrical sense of value 48 becomes perfectly clear. It defines the region where local order must be achieved. Consequently, the r = 48 value defines the region of the minimal assembly of atoms required for crystallization to start. Thus, 48 is the value that indicates the geometrical boundary between a crystal and a non-crystal.
Transformation of quataron into crystalline nucleus demands fulfillment of some not very strict conditions [7]:
— Quataron radius must be equal to 48.
— Internal space of quataron must be filled.
— Structural reconstructions in quataron must be possible.
— Quataron must not be fractal cluster.
— Diameter of the fundamental region of the crystal's space group must not be more than 5. The last condition results from Krivovichev theorem [11].
Thus, despite necessity of fulfillment of some conditions (fullness of internal spaces, non-fractality, symmetry peculiarities etc.) the probability of crystallization of quataron with radius 45 is great enough. The structure of quataron sooner or later gets in symmetry «trap» of a crystal.
As a result a new scheme of formation of a crystal looks as follows: first quatarons are formed in the crystal-forming medium which at achieving of certain sizes can be transformed in crystalline nuclei (Fig. 2). This scheme of nucleation of crystals essentially differs from the classical mechanism of formation of critical nucleus. Such scheme of two-step nucleation of crystals has also been independently suggested by P. Vekilov [12]. Last years the considered mechanisms of non-classical nucleation get the increasing popularity.
Quatarons as the basic growth
units. The new mechanism
of crystals growth
Evidently, if considerable part of substance in the crystal-forming medium is in cluster form described here, then they will evidently participate in
Fig. 3. Quataron concept of crystal formation
growth of crystals. Moreover, quatarons, thanks to their unique properties, are ideal units for crystals growth [13]. Their joining to a crystal is facilitated by that they topologically are close to structural modules of a crystal. These modules are already potentially contained in quatarons. Complete adaptation of quataron structure to a crystal structure occurs on a growing face. As a result the «two-di-mensional» nucleus is formed on the face and by that the problem of formation of a source of steps at level-by-level growth of a crystal is solved. Thus, fundamental importance of the idea of qua-tarons for development of the theory of crystals growth consists in that it allows solve debatable questions on the source of steps of growth, on the nature and sizes of crystal-forming particles.
On the whole, the following variants of crystals growth with participation of quatarons are possible (Fig. 3):
— Transformation of quatarons into two-dimensional nuclei on a growing face layer-by-layer growth of crystals (2D mechanism of crystal growth).
— Decay of quatarons on a growing face into separate atoms (atomic Kossel growth of crystals).
— Crystallization of quatarons in medium space and their transport to a growing face (3D growth of crystals).
These three variants make the essence of the quataron concept of crystals growth. Except these variants the following cases are also possible:
— Formation of crystals from crystallites grown in medium (block growth of crystals).
Inhibition of growth of crystals by stabilized cluster structures, fullerenes, etc!
The limiting case of the block mechanism is the oriented aggregation (agglomeration) of crystalline particles. The good review of such growth was recently been published by V. K. Ivanov et al. [5].
Thus, the new quataron concept of crystals growth asserts that clusters of «hidden» phase (quatarons) are the basic building units. This concept differs not only from Kossel concept where building units are separate atoms, molecules, but also from Balarev concept where a crystal is formed from separate blocks [14]. Rather universal position of the quataron concept is seen in the scheme presented in Fig. 3.
It is specially noted that only the quataron concept operates with non-equilibrium structural units at description of crystals growth, the process, in turn, is possible only in nonequilibri-um conditions, this being one of the
advantages of the quataron concept. At the same time, giving preference to the quataron mechanism of crystals growth, we cannot exclude multiroute character of this process. In the growth of crystals both separate atoms (ions), and molecular complexes, and substructural cluster units, and three-dimensional nuclei, and crystal blocks can take part.
The quataron nature
of amorphous materials
Quatarons and formed on their basis relatively rigid cluster nano-parti-cles play rather an important role in the formation of ultra-disperse solid materials. Structural-textural peculiarities of such materials depend on the nature, sizes, properties, ways of conjugation and degree of relaxation of condensed nano-particles. The formation of a wide class of amorphous materials is thus possible — from usual glasses to more or less ordered materials of the type of noble opal. The theory of formation of spherical structural units of opal-like materials is stated by us in [15]. Often ultradisperse materials retain some features inherited from properties of quatarons generating them, first of all it is revealed in their certain metastability.
Quite often quatarons, fullerenes or other cluster particles in the condensed state are disposed under the laws of lattice, and then we have the objects possessing properties of supra-molecular crystals. For example, ful-lerites are crystals consisting of clusters of carbon (fullerenes). It is also interesting that amorphous objects at certain packing of particles forming them are capable to form outwardly symmetric final objects of non-crystallograph-ic form. Such an example was first described in [16].
In conclusion we should say that quatarons and the quataron form of the organization of nano-matter have fundamental importance for mineral science. First of all, quatarons are pre-crystallization clusters, protominer-al particles, «embryos» of minerals, latent «mineral phase», mineral-forming building units. These are primary particles that define peculiarities of the structural and morphological organization of non-crystalline mineral objects (miner-aloides).
Conclusion
1. Special nano-size clusters — clusters of «hidden» phase or quatarons
can be formed and exist in non-equilibrium conditions in crystal-forming medium (in solution, melt, vapor phase).
2. Nucleation and growth of crystals goes through quatarons.
3. Quatarons and cluster structures on their basis are primary particles at formation of hierarchical nano-structured amorphous materials.
Acknowledgements
This work is supported by RFBR (14-05-00592а), Grant of the President of the Russian Federation for support of Leading Science School (SC-4795.2014.5) and the Program of Basic Researches of the Ural Branch of RAS (15-18-5-45).
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