The previously described algorithm for constructing isobaric–isothermal subsolidus sections of four-component systems comprising stoichiometric compounds is used as the base for developing an approach to the enumeration of melting diagrams of such the systems. The underlying idea of the approach is the placement of different types of invariant points over the tetrahedration elements of the phase diagram. Next, adjacent invariant points are connected by lines on which arrows are placed to indicate the decreasing temperature direction. This procedure is carried out within the limits imposed by the properties of the phase diagrams. Exemplary schematic melting diagrams constructed with the use of the described approach are provided. The results of the work can be used to design an optimization algorithm for an experimental study of phase diagrams, as well as to develop databases for such the diagrams.

The topology of phase diagrams of five-component systems with stoichiometric compounds in the subsolidus region was studied using graph theory. A set of four classification features for such diagrams was proposed. This set served as the basis for developing a classification of this type of phase diagram; an algorithm for their construction and enumeration is presented. A set of four-dimensional homogeneous polytopes was formed, comprising polytopes having seven through 10 vertices, in order to construct all isobaric–isothermal subsolidus sections of five-component systems. Exemplary classification and construction are given, as well as an enumeration table, for the phase diagrams of systems containing up to three compounds of different types. The results of the work can appear helpful to optimize experimental studies of phase diagrams of five-component systems, as well as to develop databases on phase diagrams.

Temperature dependence of methane hydrate nucleation rate in 50 wt% water in oil emulsion was studied within the temperature range from +2 to -6 degrees C (supercooling values: 13-21 degrees C). It turned out that the temperature dependence of nucleation rate in this temperature interval cannot be described by the equations of the classical nucleation theory. This point is discussed with use of available literature data. An approach to the analysis of isothermal survival curves is suggested. Using the approach allows us to establish the amount of nucleation centers in the system and their relative activity. A probable number of nucleation centers and the effect of temperature on the manifestation activity of these centers were determined for the obtained experimental data. (C) 2020 Elsevier B.V. All rights reserved.

An algorithm and programs are developed for optimizing the experimental study of isobaric–isothermal phase diagrams of quaternary systems with constant-composition phases or phases with narrow homogeneity range. These include (a) a program for enumerating phase diagrams with phases of specified composition and (b) an algorithm and a program software for the iterative analysis of phase diagrams. At each iteration, the researcher enters experimental data into the program to obtain a list of compositions for further study. Data are presented from modeling the plotting of phase diagrams with one binary, three ternary, and one quaternary compounds. It is found that among ten given examples, the number of iterations sufficient for charting the diagram is 1 (one example), 2 (four examples), 3 (two examples), 4 (one example), and 5 (two examples).

Examples of phase diagrams with two binary compounds or with one binary compound and one ternary compound are considered. Basic structural features of the relevant class of phase diagrams are enumerated. It is shown that the phase diagrams of quinary systems without solid solutions at constant pressure and constant temperature are regular simplexes in 4D space that are separated into elementary simplexes (pentatopes). The vertices of the simplexes are marked with symbols representing components and compounds. The elements of a diagram are edges, triangular faces, tetrahedral hyperfaces, and pentatopes. It is noted that the projection of the phase diagram onto a plane is the vertex adjacency graph, and the topology of the partition of the initial simplex is described by the pentatope adjacency graph. The two graphs characterize the structure of the phase diagram, i.e., allow enumeration of all elements of the phase diagram and determination of their relative positions in 4D space.

A model developed for the description of experimental data on heterogeneous nucleation in disperse systems with metastable dispersed phases is applied to the case of ice nucleation in a water emulsion in decane under methane pressure . Activity spectra are obtained for ice-forming particles in the water–decane–methane system. The frequency of ice nucleation on these particles is calculated. Activities of ice- and clathrate-forming particles in this system are compared. It is shown that small amounts of active particles incorporated into the system from an environment can have a significant effect on ice nucleation.

In this work the model which allowes to receive information about characteristics (number, content and relative activity) of heterogeneous nucleation centers in dispersed systems with metastable dispersed phase was used to treat the experimental results on the nucleation of methane hydrate and ice in the water-in-crude oil emulsions. More than ten types of nucleation centers differing from each other in activity was detected in the experiments. Hydrate and ice nucleation occured in the temperature intervals 264-269K and 261-265K, respectively.

Heterogeneous nucleation in disperse systems with metastable disperse phases plays an important role in the mechanisms of environmental and technological processes. The effect the concentration and activity of particles that initiate the formation of a new phase have on nucleation processes in such systems is considered. An approach is proposed that allows construction of a spectrum of particle activity characterizing the features of nucleation in a sample, based on the fraction of crystallized droplets depending on the level of supercooling and the use of Weibull’s distribution. The proposed method is used to describe experimental data on the heterogeneous nucleation of methane hydrate in an emulsion in a water–decane-methane system.

Гетерогенная нуклеация в дисперсных системах с метастабильной дисперсной фазой играет сущест­венную роль в механизмах природных и технологических процессов. В работе рассмотрено влияние концентрации и степени активности частиц, стимулирующих образование новой фазы, на процессы нуклеации в таких системах. Предложен подход, позволяющий на основе данных по зависимости доли закристаллизовавшихся капель от величины переохлаждения с использованием распределения Вейбулла построить спектр активности частиц, характеризующий особенности нуклеации в образце. Предложенный метод использован для описания экспериментральных данных по гетерогенной нук­леации гидрата метана в эмульсии в системе вода-декан-метан.

A problem of constructing subsolidus isobaric–isothermal sections of phase diagrams of quaternary reciprocal systems with constant-composition compounds and limited solid solutions was considered. Relations between the topological characteristics of such sections were derived. Their topological classification was proposed. An algorithm for constructing sections using the theory of finite graphs was developed. A problem of enumerating sections for diagrams with a given set of classification characteristics was solved.

A problem of constructing subsolidus isobaric-isothermal sections of phase diagrams with constant-composition compounds and limited solid solutions was considered. Relations between the topological characteristics of such sections were derived. Their topological classification was proposed. An algorithm for constructing sections using the theory of finite graphs was developed. A problem of enumerating sections for diagrams with a given set of classification characteristics was solved.

The topological properties were studied for isobaric-isothermal subsolidus sections of the phase diagrams of ternary reciprocal systems with phases of constant compositions or limited solid solutions. Systems with the triangulation schemes of diagonal and adiagonal types were analyzed. Relations between the topological parameters of graphs corresponding to such schemes were found. Algorithms for solving the problems of generation and enumeration of these triangulation schemes were presented. A wide diversity of types of triangulations was demonstrated. Their classification was proposed.