Mother Phase Research Articles

Solid–liquid equilibrium, crystal type, solid solubility and thermal stability studies of potassium ammonium chloride solid solution

Solid–liquid equilibria of (KCl + NH4Cl + H2O) ternary system were investigated and it was found that there were five crystalline regions in the course of crystallization (respectively pure NH4Cl, mNH4Cl·KCl solid solution, NH4Cl·nKCl solid solution, mixed mNH4Cl·KCl and NH4Cl·nKCl solid solution and pure KCl). The type of two solid solutions was determined by analysis of X-ray diffraction (XRD), Fourier transform infra-red (FTIR), lattice constant and density of solid solution crystals. It could conclude that they were limited substitutional solid solutions. Solid solubility (substitutional impurity in solvent) was measured at 25 °C and its variation was in accordance with Vergard's law. Moreover, thermal stability of two solid solutions was compared by TG-DTA. Results showed that both mNH4Cl·KCl and NH4Cl·nKCl shared the property of their mother phase and maintained its individual characteristics.

The high squareness Sm-Co magnet having Hcb=10.6 kOe at 150°C

The relationship between magnetic properties and magnetic domain structures of Sm(Fe, Cu, Zr, Co)7.5 magnet was investigated. The developed Sm-Co magnet, which is conducted homogenization heat treatment at ingot state, high temperature short time sintering and long time solid solution heat treatment showed the maximum energy product, [BH]m of 34.0 MGOe and the coercivity, Hcb of 11.3 kOe at 20°C respectively. Moreover, Hcb of 10.6 kOe at 150°C was achieved. Heat treated ingot has clear 1-7 phase in mother phase from optical microscope observation. Kerr effect microscope with magnetic field applied was used to investigate magnetic domain structure. Reverse magnetic domains were generated evenly but generation of them from inside grain were not observed. Cell structure was observed by scanning transmission electron microscope and composition analysis was conducted by energy dispersive X-ray spectroscopy. Cell size was approximately 150 ∼ 300 nm, Fe and Cu were clearly separated and concentrated to 2-17 phase and 1-5 phase respectively. Moreover, Cu concentration went up to 40 at% in 1-5 phase. That means the gap of domain wall energy between 1-5 phase and 2-17 phase was increased due to microstructure control by conducting heat treatment for compositional homogeneity.

Abnormal expansion due to pearlite-to-austenite transformation in high aluminium-added steels

Addition of alloying elements usually moves eutectoid point to left whilst aluminium enhances eutectoid carbon content. The carbon expands lattice parameters of austenite. High aluminium addition in steels led to volume expansion at pearlite-to-austenite transformation since specific volume of austenite is larger than that of mother phases, which is proposed to determine the volume expansion or contraction. It has been proven by calculations based on thermodynamics as well as accurate experimental observations of dilatometry study.

Spinel-to-Rocksalt Transition on Mg Insertion into Spinel-Oxide Cathodes in Magnesium Rechargeable Batteries

Modern society strongly demands high energy-density rechargeable storage batteries. Although lithium ion batteries (LIBs) are widely used for a lot of practical applications, the growing rate of the energy densities tends to be saturated recently. If Li metal itself could be adopted as an active material of the anode, LIBs would have exhibited extremely high energy densities, but this cannot be currently realized because of the fatal problem, “dendritic growth” of Li metal on charge. Therefore, in order to further enhance the energy density of storage batteries, we have to develop new type of metal-anode battery systems. As an alternative to Li metal-anode battery, polyvalent-metal storage batteries have recently attracted much attention owing to their large capacities; for example, the capacity of Mg metal (ca. 2200 mAh/g) largely exceeds that of the current carbonaceous anode materials (ca. 370 mAh/g). What is the most important for use as an anode material is that the dendritic formation can be avoided on charging, and in terms of this Mg-metal anode is superior to Li-metal anode. Thus, the Mg rechargeable battery (MRB) field has been currently attracting much attention, but the progress rate is at present quite gradually. Namely, the MRB research is still a very challenging field and not established yet, and hence we have to make much effort to accomplish MRBs. For example, there are few cathode materials for MRBs except for Chevrel compound.[1] Therefore, unless more talented cathode materials that can accommodate polyvalent cations are sought out, MRBs comparable to LIBs in terms of the energy density would not be realized. Here, we focus Mg spinel oxides as candidates for cathode materials of MRBs. The lattice sites in the spinel structure are generally denoted as 8a, 16d (cation sites), and 32e (oxygen sites) in the Wyckoff position in the space group No. 227, while those in the rocksalt structure are denoted as 16c, 16d (cation sites) and 32e (oxygen sites) when it is assigned to the same space group. Thus, a spinel structure can be regarded as a similar rocksalt structure, whose 16c sites are vacant and instead the 8a sites are usually occupied by cations. Therefore, it is expected that Mg cations can be inserted onto 16c vacant sites in the spinel lattice, as well as the Li insertion mechanism in spinel oxide materials.[2,3] Actually, the future Mg battery is expected to be operated at moderately high temperatures in that Mg insertion and extraction can be facilitated at such temperatures. In this work, on the basis of the similarity between spinel and rocksalt structures, with several spinel oxides MgCo2O4, MgMn2O4, MgFe2O4, MgCr2O4, and Co3O4, we demonstrate that some of spinel oxides can allow the insertion of Mg cations at high potentials (about 2-3 V vs. Mg2+/Mg) via “intercalation and push-out” mechanism to form a rocksalt phase in the spinel mother phase.[4] The electrochemical-test temperature was set at 150 °C in the present study by the following two reasons: i) the melting temperature (about 120 °C) of the CsTFSA based ionic liquids[5,6] used here and ii) the enhancement of Mg diffusion in the active materials. For example, especially in MgCo2O4, by utilizing the valence change from Co(III) to Co(II) in MgCo2O4, Mg insertion occurs at a considerably high potential of about 2.9 V vs. Mg2+/Mg, and similarly it occurs around 2.3 V vs. Mg2+/Mg with the valence change from Mn(III) to Mn(II) in MgMn2O4, being comparable to the ab initio calculation. The feasibility of Mg insertion would depend on the phase stability of the counterpart rocksalt XO of MgO in Mg2X2O4 or MgX3O4 (X = Co, Fe, Mn, and Cr). This “intercalation and push-out” process would provide a safe and stable design of cathode materials for polyvalent cations.

Detailed Investigation of the Structural, Thermal, and Electronic Properties of Gold Isocyanide Complexes with Mechano-Triggered Single-Crystal-to-Single-Crystal Phase Transitions.

Mechano-induced phase transitions in organic crystalline materials, which can alter their properties, have received much attention. However, most mechano-responsive molecular crystals exhibit crystal-to-amorphous phase transitions, and the intermolecular interaction patterns in the daughter phase are difficult to characterize. We have investigated phenyl(phenylisocyanide)gold(I) (1) and phenyl(3,5-dimethylphenylisocyanide)gold(I) (2) complexes, which exhibit a mechano-triggered single-crystal-to-single-crystal phase transition. Previous reports of complexes 1 and 2 have focused on the relationships between the crystalline structures and photoluminescence properties; in this work we have focused on other aspects. The face index measurements of complexes 1 and 2 before and after the mechano-induced phase transitions have indicated that they undergo non-epitaxial phase transitions without a rigorous orientational relationship between the mother and daughter phases. Differential scanning calorimetry analyses revealed the phase transition of complex 1 to be enthalpically driven by the formation of new aurophilic interactions. In contrast, the phase transition of complex 2 was found to be entropically driven, with the closure of an empty void in the mother phase. Scanning electron microscopy observation showed that the degree of the charging effect of both complexes 1 and 2 was changed by the phase transitions, which suggests that the formation of the aurophilic interactions affords more effective conductive pathways. Moreover, flash-photolysis time-resolved microwave conductivity measurements revealed that complex 1 increased in conductivity after the phase change, whereas the conductivity of complex 2 decreased. These contrasting results were explained by the different patterns in the aurophilic interactions. Finally, an intriguing disappearing polymorphism of complex 2 has been reported, in which a polymorph form could not be obtained again after some period of time, even with repeated trials. The present studies provide us with a variety of hitherto unknown insights into mechano-responsive molecular crystals, which help us to understand the phase transition behaviors upon mechanical stimulation and establish rational design principles.

Environmentally friendly Zn0.75Cd0.25S/PVA heterosystem nanocomposite: UV-stimulated emission and absorption spectra

Zn0.75Cd0.25S nanoparticles prepared at different temperatures were composited with polyvinyl alcohol for functionalization it in wide spectrum of applications such as in photocatalysis. The nanostructure of the Zn0.75Cd0.25S mother phase is confirmed by X-ray diffraction in addition to absorption and fluorescence spectra. UV/VIS. measurements show that, the transmittance coefficient of Zn0.75Cd0.25S/PVA nanocomposite is lesser than that of pure PVA by 0.33% and varies upon increasing the preparation temperature; reaching a maximum value for the sample prepared at 300 °C. It was found that the optical band gap tunes with annealing temperature which, in turns, with particle size. The refractive index of the Zn0.75Cd0.25S/PVA nanocomposite films decrease with increasing wavelength and saturates at high wavelengths. The optical conductivity increases with increasing photon energy which may be due to the excitation of electrons by photon energy. The optical conductivity of Zn0.75Cd0.25S/PVA nanocomposite is lesser than that of pure PVA and it decreases as the preparation temperature of Zn0.75Cd0.25S nanoparticles in PVA matrix increases which could be related to the decrease in the extinction coefficient and the density of localized states in the gap. Abroad peak deconvoluted, by Gaussian fitting function, into two violet and blue colors was observed in the fluorescence spectra under UV light irradiation. The two emission bands are attributed to band edge emission and neutral oxygen vacancies respectively. Analysis of fluorescence (FL) spectra reveals quenching in FL intensity and a peak shifting towards the lower wavelength side with increasing the preparation temperature of the mother phase. The results suggest that the 200 °C Zn0.75Cd0.25S/PVA nanocomposites have been regarded as a promising candidate in many technical fields, such as photocatalytic hydrogen production and/or photocatalytic degradation of organic dyes under UV irradiation due to its high optical conductivity and high FL intensity.

Electrical and optical properties of hydrogen titanate nanotube/PANI hybrid nanocomposites

Hydrogen titanate nanotube (TNT)/polyaniline (PANI) hybrid nanocomposites were made up by hydrothermal method and subsequent in situ polymerization. Various characterization techniques were employed to explore the structure, thermal, electrical, and optical properties of the investigated hybrid nanocomposites. X-ray diffraction (XRD) revealed typical characteristic of two separate peaks for pure PANI and pristine TNT up to the composition of TNT less than 20 %. The transmission electron microscopy (TEM) image shows the tubular structure of the prepared TNT with an average diameter of 8–12 nm and length range from 80 to 150 nm. Electrical measurements of TNT/PANI nanocomposites indicated that the dc conductivity decreases upon introduction of TNT. Photoluminescence (PL) properties are found to be tunable with the weight fraction of the TNT mother phase. Moreover, increasing the TNT weight content enhanced the thermal stability of TNT/PANI nanocomposite. Finally, the tunability of the chemical and physical properties of these hybrid nanocomposites offers solutions to low-cost hybrid UV irradiation photodetector.

Modeling the kinetics of consecutive phase transitions in the solid state

A theoretical approach for describing the kinetics of consecutive phase transformations ruled by nucleation and growth is reported. In the considered system, the mother phase (M) transforms to an intermediate phase (α) which, in turn, transforms to the final product (β). The classical Kolmogorov–Johnson–Mehl–Avrami theory is generalized to deal with a finite-size phase with moving boundary. To this end, the statistical method based on the differential critical region has been employed. The exact solution of the kinetics is computed in closed form for the transformation of a spherical α-nucleus growing into the mother phase. By resorting to an approximate expression for the probability function entering the differential critical region method, the consecutive transformation is studied in the case of nucleation and growth of the α-phase. The time dependence of the β/α volume fraction is found to be in very good agreement with the stretched exponential kinetics, and the dependence of Avrami’s exponent on both nucleation and growth rates of the two phases is investigated. Modeling of the non-isothermal kinetics at constant heating rate has also been performed which provides an insight into the shape of the differential scanning calorimetry curves for consecutive phase transitions.

Latent heat induced rotation limited aggregation in 2D ice nanocrystals.

The basic science responsible for the fascinating shapes of ice crystals and snowflakes is still not understood. Insufficient knowledge of the interaction potentials and the lack of relevant experimental access to the growth process are to blame for this failure. Here, we study the growth of fractal nanostructures in a two-dimensional (2D) system, intercalated between mica and graphene. Based on our scanning tunneling spectroscopy data, we provide compelling evidence that these fractals are 2D ice. They grow while they are in material contact with the atmosphere at 20 °C and without significant thermal contact to the ambient. The growth is studied in situ, in real time and space at the nanoscale. We find that the growing 2D ice nanocrystals assume a fractal shape, which is conventionally attributed to Diffusion Limited Aggregation (DLA). However, DLA requires a low mass density mother phase, in contrast to the actual currently present high mass density mother phase. Latent heat effects and consequent transport of heat and molecules are found to be key ingredients for understanding the evolution of the snow (ice) flakes. We conclude that not the local availability of water molecules (DLA), but rather them having the locally required orientation is the key factor for incorporation into the 2D ice nanocrystal. In combination with the transport of latent heat, we attribute the evolution of fractal 2D ice nanocrystals to local temperature dependent rotation limited aggregation. The ice growth occurs under extreme supersaturation, i.e., the conditions closely resemble the natural ones for the growth of complex 2D snow (ice) flakes and we consider our findings crucial for solving the "perennial" snow (ice) flake enigma.

Opening up a philosophical space in early literacy with <i>Little Beauty</i> by Anthony Browne and the movie <i>King Kong</i>

The article begins with setting the South African educational context for a postgraduate early literacy research project in the foundation phase (ages 4–9). The research examines how philosophy with children (P4C) might be part of a solution to current problems in reading comprehension. The second author reports on her P4C action research with her own children as well as her observations of a Grade 2 classroom in a school near Johannesburg. The research shows how the picturebook Little Beauty by Anthony Browne opens up a philosophical space within which children are allowed to draw on their own life experiences and prior knowledge. The project reveals the depth of their thinking when making intra-textual connections between Little Beauty and the movie King Kong. The facilitated philosophical space also makes it possible for the children to make complex philosophical links between the emotion anger, destructive behaviour and the ethico-political dimensions of punishment. Central to this article are the second author’s critical reflections on how her literacy practices as a mother and foundation phase teacher have fundamentally changed as a result of this project. The article concludes with some implications for the teaching of early literacy in South Africa.

Experimental Establishment of Mother–Daughter Orientation Relationships and Twinning Effects in Phase Transitions: A Great Legacy from Jack Gougoutas and Peggy Etter

A simple procedure, with an available program, may readily be used to establish the three-dimensional relationships between a mother and daughter phase, where mother and daughter are either two different phases of a material or a reactant and product in a solid-state transformation. The only requirements are that (i) the process involves a crystal-to-crystal transformation, and (ii) the experiment must be carried out without changing the alignment of the mother crystal. Application of the method supports the inferred alignment of mother and daughter phases in the published structures of two polymorphs of 4-cyanopyridinium perchlorate monohydrate 1. A new low-temperature, monoclinic polymorph of ferrocenium tetrafluoroborate 2 is produced when the known orthorhombic polymorph is cooled from 173 to 120 K. The major features of the transformation include “conservative twinning” and a modulation of the structure along the crystallographic b direction upon cooling. Redetermination of the structure of the low-temperature polymorph of ferrocenium hexafluorophosphate 3 reveals that the phase change is accompanied by reproducible four-component twinning, providing a proper explanation for the previously reported, very high R-factor of 12.4%. Included tutorial information on the process will assist the reader in obtaining topotactic relationships, as well as in preparing figures and animations describing phase transitions or reactions.

Intercalation and Push-Out Process with Spinel-to-Rocksalt Transition on Mg Insertion into Spinel Oxides in Magnesium Batteries.

On the basis of the similarity between spinel and rocksalt structures, it is shown that some spinel oxides (e.g., MgCo2O4, etc) can be cathode materials for Mg rechargeable batteries around 150 °C. The Mg insertion into spinel lattices occurs via “intercalation and push‐out” process to form a rocksalt phase in the spinel mother phase. For example, by utilizing the valence change from Co(III) to Co(II) in MgCo2O4, Mg insertion occurs at a considerably high potential of about 2.9 V vs. Mg2+/Mg, and similarly it occurs around 2.3 V vs. Mg2+/Mg with the valence change from Mn(III) to Mn(II) in MgMn2O4, being comparable to the ab initio calculation. The feasibility of Mg insertion would depend on the phase stability of the counterpart rocksalt XO of MgO in Mg2X2O4 or MgX3O4 (X = Co, Fe, Mn, and Cr). In addition, the normal spinel MgMn2O4 and MgCr2O4 can be demagnesiated to some extent owing to the robust host structure of Mg1−xX2O4, where the Mg extraction/insertion potentials for MgMn2O4 and MgCr2O4 are both about 3.4 V vs. Mg2+/Mg. Especially, the former “intercalation and push‐out” process would provide a safe and stable design of cathode materials for polyvalent cations.

Analysis of oxidation decomposition reaction scheme and its kinetics of delafossite-type oxide CuLaO2 by thermogravimetry and high-temperature X-ray diffraction

The oxidation decomposition reaction and its reaction kinetics of delafossite-type oxide CuLaO2, which is a mother phase of new luminescent material, at various temperatures were investigated by thermogravimetry and high-temperature X-ray diffraction. It was clarified that CuLaO2 is not thermodynamically stable in air and reacts with O2, which is represented as the chemical reaction formula, 4CuLaO2 + O2 → 2CuLa2O4 + 2CuO, above 500 °C. It was also revealed that CuLaO2 transforms to a metastable CuLaO2.66 phase with a copper valence of 2.32+ and some phases with lower crystallinity below 500 °C. At 800 °C, a metastable defect perovskite Cu2La2O5 phase was generated at initial period of the decomposition, resulting in variation to mixture of CuLa2O4 and CuO as reaction proceeded. It was found that a first-order reaction model can be applied to the reaction kinetics of the oxidation decomposition reaction. The activation energy for the reaction was estimated to be 65 kJ mol−1 under air flow. It was concluded that CuLaO2 has lower kinetic stability than the other delafossite-type oxides such as CuAlO2 and CuGaO2.

Formation of new polymorphs without any nucleation step. Desolvation of the rimonabant monohydrate: directional crystallisation concomitant to smooth dehydration.

Rimonabant monohydrate can be dehydrated at 100 °C or above with complete loss of structural information; in this case the amorphous material can lead to nucleation and crystal growth. The water molecules can also be removed by a smooth process below Tg (78 °C) of the anhydrous phase. In that latter process there is a structural filiation between the mother phase and the daughter phase. The solvent molecules escape from the mother structure by using a network of specific channels; the new non-solvated material undergoes a relaxation process similar to a directional crystallization. By this soft mode of desolvation inside a material which has a very limited mobility, the nucleation of a non-solvated material can be avoided. The structural information contained in the mother phase is not used as a template for crystal growth but it is more a progressive rearrangement of the new desolvated material towards the nearest well in energy. Thus, a metastable new polymorph of a non-solvated component can be obtained by: (i) the crystallization of the component as a solvate and (ii) a smooth desolvation at T < Tg. Other parameters liable to interfere with that transmission of structural information are discussed.

Urea homogeneous nucleation mechanism is solvent dependent.

The composition of the mother phase plays a primary role in crystallization processes, affecting both crystal nucleation and growth. In this work, the influence of solvents on urea nucleation has been investigated by means of enhanced sampling molecular dynamics simulations. We find that, depending on the solvent, the nucleation process can either follow a single-step or a two-step mechanism. While in methanol and ethanol a single-step nucleation process is favored, in acetonitrile a two-step process emerges as the most likely nucleation pathway. We also find that solvents have a minor impact on polymorphic transitions in the early stages of urea nucleation. The impact of finite size effects on the free energy surfaces is systematically considered and discussed in relation to the simulation setup.

Shape and area fluctuation effects on nucleation theory

In standard nucleation theory, the nucleation process is characterized by computing ΔΩ(V), the reversible work required to form a cluster of volume V of the stable phase inside the metastable mother phase. However, other quantities besides the volume could play a role in the free energy of cluster formation, and this will in turn affect the nucleation barrier and the shape of the nucleus. Here we exploit our recently introduced mesoscopic theory of nucleation to compute the free energy cost of a nearly spherical cluster of volume V and a fluctuating surface area A, whereby the maximum of ΔΩ(V) is replaced by a saddle point in ΔΩ(V, A). Compared to the simpler theory based on volume only, the barrier height of ΔΩ(V, A) at the transition state is systematically larger by a few kBT. More importantly, we show that, depending on the physical situation, the most probable shape of the nucleus may be highly non-spherical, even when the surface tension and stiffness of the model are isotropic. Interestingly, these shape fluctuations do not influence or modify the standard Classical Nucleation Theory manner of extracting the interface tension from the logarithm of the nucleation rate near coexistence.

Heterogeneous nucleation in multi-component vapor on a partially wettable charged conducting particle. I. Formulation of general equations: Electrical surface and line excess quantities

Thermodynamics is applied to formulate general equations for internal energies and grand potential for a system consisting of a dielectric liquid nucleus of a new phase on a charged insoluble conducting sphere within a uniform macroscopic one- or multicomponent mother phase. The currently available model for ion-induced nucleation assumes complete spherical symmetry of the system, implying that the seed ion is immediately surrounded by the condensing liquid from all sides. We take a step further and treat more realistic geometries, where a cap-shaped liquid cluster forms on the surface of the seed particle. To take into account spontaneous polarization of surface layer molecules we introduce the electrical surface and line excess quantities.

Heterogeneous nucleation in multi-component vapor on a partially wettable charged conducting particle. II. The generalized Laplace, Gibbs-Kelvin, and Young equations and application to nucleation

Based on the results of a previous paper [M. Noppel, H. Vehkamäki, P. M. Winkler, M. Kulmala, and P. E. Wagner, J. Chem. Phys. 139, 134107 (2013)], we derive a thermodynamically consistent expression for reversible or minimal work needed to form a dielectric liquid nucleus of a new phase on a charged insoluble conducting sphere within a uniform macroscopic one- or multicomponent mother phase. The currently available model for ion-induced nucleation assumes complete spherical symmetry of the system, implying that the seed ion is immediately surrounded by the condensing liquid from all sides. We take a step further and treat more realistic geometries, where a cap-shaped liquid cluster forms on the surface of the seed particle. We derive the equilibrium conditions for such a cluster. The equalities of chemical potentials of each species between the nucleus and the vapor represent the conditions of chemical equilibrium. The generalized Young equation that relates contact angle with surface tensions, surface excess polarizations, and line tension, also containing the electrical contribution from triple line excess polarization, expresses the condition of thermodynamic equilibrium at three-phase contact line. The generalized Laplace equation gives the condition of mechanical equilibrium at vapor-liquid dividing surface: it relates generalized pressures in neighboring bulk phases at an interface with surface tension, excess surface polarization, and dielectric displacements in neighboring phases with two principal radii of surface curvature and curvatures of equipotential surfaces in neighboring phases at that point. We also re-express the generalized Laplace equation as a partial differential equation, which, along with electrostatic Laplace equations for bulk phases, determines the shape of a nucleus. We derive expressions that are suitable for calculations of the size and composition of a critical nucleus (generalized version of the classical Kelvin-Thomson equation).

Comments on the thermodynamic analysis of nucleation in confined space

The effect of depletion of the ambient phase in confined systems on the parameters of the critical clusters in nucleation-growth processes is analyzed by employing the generalized Gibbs' approach. Depletion effects result, in addition to variations of the parameters of the critical clusters (corresponding to a maximum or, in general, saddle point of the thermodynamic potential surface), in the existence of a minimum of the appropriate thermodynamic potential corresponding to a stable state of a cluster in the ambient phase. It is shown that – due to depletion effects – with decreasing volume of the mother phase, the work of formation of both the critical cluster and the stable cluster increases. The results of the analysis of nucleation in confined systems are shown further to allow one to develop a general scenario of first-order phase transitions and to derive, as a particular result, relatively simple equations for the description of the kinetics of competitive growth of the clusters (coarsening or Ostwald ripening) including, in addition to the asymptotic, the initial stages of this process and, as a particularly important special case, the possibility to account for the effect of elastic stresses on coarsening. Experimental examples, where such effects modify the kinetics of coarsening qualitatively, are given here as well as their theoretical interpretation based on thermodynamic considerations as outlined in the present paper.

Eutectic and Peritectic Lines for Diagrams of Quasi Equilibria of Binary Systems with Partially Soluble Components

Topologies of the nucleation rate surfaces over phase equilibria diagrams with eutectic and peritectic points are constructed schematically. Theoretical methods to obtain the topology of these surfaces are not yet available. Individual eutectic and peritectic points, empirically observed previously in non-equilibrium conditions, are following as particular cases of the common results of the present paper. It is shown that there are lines of eutectic and peritectic compositions in general, depending on the mother phase invasion depth into the region of the coupled phase equilibria