This review article represents a summary of completed, original work, embodying the results of extensive laboratory and theoretical investigations as well as new interpretations of existing problems in Materials Science. Using the examples of a number of binary Ni-base and Fe-base alloys, the TEM method has shown that the main reason for the precipitation of particles of a new phase is the chemical interactions that always exist between all atoms of an alloy, both in the solid and in the liquid state. It has been found experimentally that the sign of the chemical interaction energy in many alloys changes with a temperature change (the ‘orderingphase separation’ transition). It has been shown that the cause of the ‘ordering-phase separation’ transition is the electronic ‘ionic bond ↔ covalent bond’ transition. Such a transition takes place when delocalization of a couple of the valence electrons occurs on the A and B atoms simultaneously with the hybridization of a couple of the valence electrons on the B atoms. All these discoveries radically change the existing ideas about diffusion phase transformations in alloys.
Keywords: Phase Transitions; Chemical Interactions; Ordering; Phase separation; ‘Ordering-Phase Separation’ Transition; ‘Ionic Bond ↔ Covalent Bond’ Electronic Transition
According to existing ideas in the literature , a solid solution in metal alloys is formed in those cases when, in a system consisting of atoms of different elements, a crystal lattice common for all elements is formed on the basis of the solvent lattice. It was assumed that, in all alloys, the magnitude of solubility of an element in the lattice of the solvent depends mainly on the difference in the sizes of the atoms of the solvent and the solute. If the difference in the sizes of dissimilar atoms that form the alloy exceeds about 14- 15%, the solubility in the solid state is restricted (due to the 15% rule) and stable intermediate compounds form in the alloy . The theoretical justification for this rule was obtained by considering the energy of elastic deformation that emerges during the formation of solid solutions. The difference in the sizes of A and B atoms predetermined the appearance of elastic stresses within the crystal lattice of the alloy. The magnitude of such elastic stresses, it was considered, determined the degree of solubility of the B atoms in the crystal lattice consisting of A atoms, and was that driving force which, when the temperature and, therefore, the solubility decreased, resulted in the precipitation of ‘excess’ phases from the solid solution. It was also believed that another important factor determining the magnitude of solubility in the solid state and the stability of intermediate phases was the magnitude of the electron concentration (e/a ratio) in the alloy .
This very principle was used in the construction of equilibrium phase diagrams, in which, in the overwhelming majority of cases, regions of solid solutions were shown at high temperatures, and two-phase regions at low temperatures. All these ideas, which were formulated about 80 years ago when modern methods of investigating the crystal structure of the alloys were in their infancy, are still intact in Materials Science .
Experimental studies of the crystal structure of alloys conducted later with the help of X-ray diffraction (XRD) seemed to have fully confirmed these views. Indeed, when this method was applied to alloys quenched from high temperatures, no other phases besides the solid solution were found. Based on these data, they concluded, that at high temperatures, the microstructure of alloys was a disordered solid solution.
However, in the 1960s-1970s, when the method of transmission electron microscopy (TEM) became widely used in the study of the microstructure of alloys, many authors were surprised to find that the microstructure of many alloys, quenched from the region of solid solutions, was two-phase. It contained either particles of a new phase in the solid solution or modulations of the composition. When such a two-phase microstructure was found in as-quenched alloys, almost no one doubted that the blame for the ongoing disagreements should be laid on the experiment, not on the phase diagrams. A new version was invented, according to which the diffusion of atoms in the alloy was sharply accelerated during the process of quenching itself, since the decomposition of the alloy proceeds via the spinodal mechanism (during spinodal decomposition, the stage of critical nuclei formation is absent).
As is known , the method of X-ray diffraction is severely limited concerning the possibility of identifying highly dispersed particles of the new phase, which are usually registered by a method of local analysis – the TEM method. This is precisely why a conflict arose, when, using XRD data, they built phase diagrams containing, it was asserted, regions of solid solutions at high temperatures, but when using the TEM method, a completely different structure was discovered: a two-phase structure had been formed in these regions after quenching from these temperatures.
From an analysis of these data, it was concluded  that the regions of solid solutions in equilibrium phase diagrams were in fact two-phase regions. This conclusion agrees with the well-known axiom of thermodynamics, which states that in nature all solutions are non-ideal and have either positive or negative deviations from Raoult’s law.
Change of the sign of the ordering energy with temperature in alloys of the Fe-Cr system.
The sign of the ordering energy in alloys was usually determined by the method of measuring the partial pressure of the vapors of components at temperatures close to the melting point. Since this pressure abruptly drops with a decrease of the temperature and beginning at certain temperatures it is impossible to measure it, it was tacitly assumed that the sign of the ordering energy determined at very high temperatures remains the same at lower temperatures. This gave birth to the idea that each binary system is characterized by its own sign of ordering energy, which is constant for this system at any temperature.
The only system that did not agree with these concepts and, therefore, gave rise to questions was the iron-chromium system. In the existing phase diagram of this system , three structural regions were observed (the temperatures indicated are for the Fe50Cr50 alloy). A solid solution exists above 830°C. The σ-phase formed because of the tendency of alloys to ordering, located in the temperature range of 830-440°C. A microstructure, which consisted of clusters of chromium atoms in the solution and formed as a result of the tendency of the alloy to phase separation, is placed below 550°C. On the basis of these data, it could already be concluded that the phase diagram, in which a microstructure of ordering is formed at one temperature but microstructure of phase separation at the other, gives grounds for talking about a boundary between them, i.e. for talking about an ‘ordering-phase separation’ transition. On the contrary, some authors, for example Turchi et al. , suggested, because positive deviations from Raoult’s law had been found in alloys of the iron-chromium system at high temperatures , suggested that the σ-phase was not a chemical compound at all. Although the σ-phase has all the attributes of a chemical compound, including a lattice of its own, distinct from that of the matrix, but they thought that the σ-phase is a phenomenon, “pertaining to surfaces (reconstruction, segregation, etc.)” and that there are no contradictions here .
The situation turned out to be even more confusing when Ustinovshikov, Shirobokova and Pushkarev  discovered a microstructure which could not be attributed either to the structure of a disordered solid solution or the structure of a σ-phase in alloys of the same system, at high (1150°C and higher) temperatures, i.e. in the solid solution region. The authors  identified it as the structure of high-temperature phase separation (Figure 1), as it was fixed after a heat treatment at the same temperatures, at which positive deviations from Raoult’s law had previously been found . In addition, a system of satellite reflections was observed in the electron diffraction pattern (Figure. 1, inset), which was obtained from these precipitates. The discovery of phase separation microstructures formed after quenching from high temperatures, i.e. from the region of solid solutions, was so unexpected that it led to the appearance of a number of critical works [9, 10].
Figure 1: Fe50Cr50 alloy. Water quenching from 1200°С. Bright-field micrographs. Inset: electron diffraction pattern taken from a coarse Cr-particle .
The first experimental study to verify the existence of hightemperature phase separation in alloys of the iron-chromium system was undertaken using the Fe-45 % Cr alloy as an example . Using the TEM method, Kosythyna et al.  found that the microstructure of this alloy after quenching from 1150-1200°С was similar to that which had been obtained in Ref. . However, they interpreted such precipitations as chromium nitrides, i.e. as a kind of ‘added’ phase formed by the chemical reaction of chromium atoms (from the alloy) with atoms of nitrogen (from the air) during a high temperature heat treatment for quenching. A second study was conducted using the Fe51Cr49 alloy with the help of Mossbauer spectroscopy . It is obvious that the choice of the method of research in Ref.  was poor, since it was hardly possible to judge a local phase separation of the alloy by the change of the partial gamma-resonance peaks of Mossbauer spectra. They were, therefore, unable to find the structure of the phase separation.
Figure 2 shows the iron-rich part of an iron-chromium phase diagram, built on the results of electron microscopic studies of the microstructure of iron alloys with 20, 30, 40 and 50 wt.% of chromium . From the diagram, it can be seen that two-phase transitions occur in the Fe-Cr system, in which, for example, the microstructure that has formed as a consequence of the tendency to ordering is dissolving and a microstructure of phase separation is forming in its place (and vice versa). This occurs within the temperature ranges of 1100-850°C and 600-550°C (Figure 2).
Figure 2:The Fe-rich portion of the Fe-Cr phase diagram. Dashed lines show the temperatures of the ‘ordering-phase separation’ transition. Designations: ο – solid solution microstructure; ■ – phase separation microstructure; ∆-σ-phase at the surface (tendency to ordering) .
The ‘Ordering-phase separation’ transition’. Based on these data, it could be concluded that at the level of microstructures, such a phase transition is bound to pass through the stage of the existence of the solid solution in the alloy. The authors  gave this phase transition the name ‘ordering-phase separation’. The transition occurs at a temperature, specific for each system, at which the sign of the chemical interaction between atoms of A and B is reversed. It is obvious that the transformation of the microstructure formed as a result of the tendency to ordering into the microstructure formed as a result of the tendency to phase separation, and vice versa, is a consequence of the ‘ordering-phase separation’ transition. The transition itself, i.e. the process of changing the sign of the chemical interaction between dissimilar atoms, occurs at the level of changes in the electronic structure of the alloy.
During the process of heating or cooling the alloy, when the temperature passes through the phase transition point, the energy of the chemical interaction between component atoms passes through zero. It therefore follows that the microstructure, which has formed in a certain temperature range near this point, is bound to be a disordered solid solution . It was believed that the transition temperature was the same for all alloys of a given system .
The discovery of the ‘ordering-phase separation’ transition in alloys has shown that the degree of the supersaturating of the solid solution by the alloying element is not the driving force of the new phase precipitation process. The factor that has a decisive influence in this process is the sign that the chemical interaction energy has at a given temperature: negative (a tendency to ordering), or positive (a tendency to phase separation). The absolute magnitude of this energy also plays a big role in whether precipitation of these phases will or will not occur . It was believed that at the temperature of the ‘ordering-phase separation’ transition, when the chemical interaction energy is close to zero, no other phases could form, except the solid solution . In a more distant neighborhood of the phase transition temperature, the absolute magnitude of the chemical interaction energy can be insufficiently high for the precipitation of a corresponding new phase to begin; this circumstance can lead to the expansion of the region in which the structure of the solid solution exists. Everything depends on the nature of the alloy.
This scheme shows the experimentally determined points (1 and 2) of the ‘ordering-phase separation’ transition. The intersection points of the chemical interaction energy E curve with lines (3), (4), and (5) show energy levels, above which (in their absolute value) the formation of the second phase begins. They were determined along the temperature axis in Figure 3 as points separating the oneand two-phase regions in the phase diagram of Fe-Cr. The distances between the positive and negative thresholds on a temperature axis in the case of high-temperature and low-temperature ‘orderingphase separation’ transitions are very different (Figure 3). In the first case, this distance is approximately 300°C and about 50°C in the second.
Figure 3: Fe50Cr50 alloy. The energy of the chemical interaction (E) vs. heating temperature. Designations: 1 and 2 – points of high-temperature (1) and low-temperature (2) ‘ordering-phase separation’ transitions (E=0); 3 and 5 – energy levels above which the phase separation microstructure is formed in the alloy; 4 – energy level below which the σ-phase is formed .
Based on this, the following conclusions have been made [12, 13]:
a. The sign of the energy of the chemical interaction between dissimilar atoms is not constant for the majority of metallic systems but varies according to the change of the temperature of the alloy (sometimes more than once).
b. The precipitation of this or that phase and the formation of a solid solution depend not on the degree of solubility of the atoms of one component in the lattice of the other, but on the sign and the absolute magnitude of the energy of the chemical interaction between dissimilar atoms (Fe and Cr).
c. The microstructure of a disordered solid solution is formed over the entire bulk of the alloy only in the temperature region adjacent to the temperature of the ‘ordering-phase separation’ transition, because this is the region where the chemical interaction energy between dissimilar atoms is close to zero.
d. Every heating temperature of the alloy corresponds with a quite definite microstructure, which is formed during the exposure of the alloy at this temperature and does not depend on what the structure of the alloy was prior to the given heat treatment.
The final remark means that there is absolutely no point in quenching alloys before their tempering (aging), in order to obtain a structure of the homogeneous solid solution. What is more, in most cases the temperatures from which such quenching is usually carried out do not correspond with the regions of the solid solution.
The ‘Ordering-phase separation’ transition in Ni3Co alloy
The Ni-Co system phase diagram is characterized by great simplicity: only the solid solution for all compositions at all temperatures is shown in the diagram. No phase transformations except the allotropic α-Co → ε-Co (at 422°C), occur in the system. This may be why the literature on structural transformations in the alloys of this system is extremely scarce (there is only some structural data obtained by optical and scanning microscopy). At the same time, the presence of regions of the solid solution, which is not an equilibrium phase, indicates gaps in our knowledge rather than the actual structural state of a particular alloy at a particular temperature.
In the Ni3Со alloy, after quenching from 1200 ºC, the microstructure shown in Figure 4 is formed. At the same time, other elements of the microstructure, for example dislocations, are observed in the micrograph due to the diffraction contrast. It is obvious that the formation of these clusters occurs without any lattice changes that could lead to the appearance of the diffraction contrast. It was found with the help of TEM that the temperature of the ‘ordering-phase separation’ transition lies near 800°C 
Figure 4:Ni3Co alloy. Water quenching from 1200°C. Microstructure. Absorption contrast .
Figure 5 Round light spots with diffuse edges and dimensions of the order of 0.1-0.2 μm are observed on a dark background, apparently as an effect of the electron-microscopic absorption contrast from some clusters of atoms of the solvent component, i.e. cobalt, which has a smaller ‘mass thickness’ in comparison with the surrounding nickel-rich solid solution. Dislocations are visible due to diffraction contrast.
Figure 5:Ni3Co alloy Water quenching from 800°C. Microstructure . With a lowering of the temperature of aging to below 800°C, the number of Co clusters and their sizes in the electron microscopic images decrease, their contours become even more blurred.
Comparing the images of the microstructure in Figure 6 (a and b), it can be concluded that the process of the dissolution of clusters visually occurs in the form of the transition of their contrast from absorption to diffraction. During aging of 500°C, when particles of chemical compounds Ni3 Co begin to separate, clusters of Co atoms, visible in Figure 6 (a) due to absorption contrast, in Figure 6 (b) are observed due to diffraction contrast. This means that the concentration of cobalt in the clusters increases simultaneously with the release of dispersed Ni3 Co particles.
Figure 6: Microstructure of Ni3 Co alloys aged at 500°C for (a) 10 hours; (b) 50 hours 
Thus, in the alloys of some systems, such as the Ni-Co system, the process of the reconstruction of the microstructure formed as a result of the tendency to phase separation into the microstructure, formed as a result of the tendency to ordering occurs in a different way to that which we imagined earlier. The process does not comprise a complete dissolution of the phase-separation microstructure with a formation of a disordered solid solution and subsequent formation of the ordering microstructure in the solid solution, but instead by the simultaneous dissolution of Co-enriched clusters and formation of particles of a chemical compound.
The existence of two different types of precipitates in one and the same image in which the signs of the chemical interaction energy are opposite indicates that the ‘ordering-phase separation’ transition in alloys of this system does not occur simultaneously at all points of the alloy. Therefore, based on the obtained experimental TEM and XPS results , in such alloys one should not evaluate the temperature, but rather the range of the temperatures. This range of temperatures in the Ni-Co system is located near 600°C. Thus, the process of rearrangement of the microstructure formed as a result of the tendency to phase separation into the microstructure formed as a result of the tendency to ordering occurs in the Ni-Co system not at all like in the iron-chromium system. It seems that at this temperature the tendency to ordering and the tendency to phase separation coexist in different microscopic volumes of the alloy.
Even more interesting is the process in alloys of the Co-V system. Quenching the alloy from the liquid state fixes the vanadium particles, the bright-field image of which is presented in Figure 7 .
Figure 7: Со3 V alloy. Water quenching from liquid state. Brightfield image of the microstructure. Particles formed in a liquid state are visible as a result of the tendency to separation. Inset: electron diffraction pattern,  zone axis .
By lowering the temperature of the alloy from 1550 to 1150°C, the absolute magnitude of the chemical interaction energy increases. This can be judged by an increase in the size or number of vanadium atom particles, formed at понижении температуры закалки от 1550 до 1150°C (Figure 8 а, b).
Figure 8: Со3 V alloy. Water quenching from 1150°C. Bright-field images of a large BCC particle of V atoms (a) and colonies of the particles (b). Inset: electron diffraction pattern,  zone axis .
At lowering the heat treatment temperature to 800°C it becomes possible to observe two different types of structures in various areas of the same foil (Figure 9 a, b). The first type formed as a result of the tendency to phase separation and another type formed as a result of the tendency to ordering. Alloys of the Ni-Co system demonstrated precisely the same picture after heat treatment at temperatures, in which the ‘ordering-phase separation’ transition took place (Figure 9). Such a transition proceeded via a simultaneous dissolution of cobalt-rich clusters and precipitation of particles of the chemical compound.
Figure 9:а. Со3 V alloy. Water quenching from 800°C. Bright-field image of the phase separation microstructure. Inset: Electron diffraction pattern,  zone axis (inset) (a) .
Figure 9:b. Со3 V alloy. Water quenching from 800°C Another microscopic site of the same foil: electron diffraction pattern,  zone axis .
The bright-field image, obtained from one of the microscopic sites of the foil after heat treatment of the Co3 V alloy at 800°C, shows a microstructure consisting of very fine grains (Figure 9 a) . It can be assumed that this microstructure is a mixture of clusters enriched and depleted in vanadium, which are fixed at the stage of the dissolution of the phase separation structure, i.e. the dissolution of particles of vanadium atoms in the lattice of cobalt. Indeed, in the electron diffraction pattern obtained from this structure, instead of satellites, one can observe diffuse scattering (Figure 9 a, inset). This may be why the dissolution stage of the phase-separation microstructure, i.e. the dissolution of particles of vanadium atoms in the cobalt lattice, is fixed in this microscopic site. Elsewhere in the microscopic sites of the foil, areas are observed where the microstructure of ordering is forming or has already formed. For example, Figure 9 b shows an electron diffraction pattern in which a system of extra-reflections, indicating a precipitation of the L12 phase, is visible. However, in the bright-field image, particles from the new phase are not detected. This indicates that precipitates producing such reflections are fully coherent with the matrix. This allows the assumption that 800°C is the temperature close to the temperature of the ‘ordering-phase separation’ transition. Unlike alloys in which the regions of ordering and phase separation are divided by the solid solution region, in the Co3 V alloy the solid solution region is absent.
It is obvious that the process of the ‘ordering-phase separation’ transition in the Со3 V alloy at 800°C occurs non-simultaneously throughout the volume. Unlike the Со3 V alloy, the regions of ordering and phase separation in many other systems are clearly demarcated, and, therefore, in these systems, quenching from the transition region, where the chemical interaction energy is close to zero, leads to the formation of the microstructure of a disordered solid solution.
Further lowering the heat treatment temperature to 500°C leads to the reflections from the L12 phase becoming clearer and more intense (Figure 10), and it becomes possible to observe particles of the L12 phase in the bright-field image. If the alloy is subjected to heat treatment at 350°C, then, according to structural data, it becomes possible to detect one more ‘ordering-phase separation’ transition taking place in the alloy at temperatures of about 450°C. Figure 11a shows a cellular structure which was found after heat treatment at 350°C. Thus, by lowering the heat treatment temperature, two phase transitions are observed in the alloy: at 800°C and at 450°C, at both of which there is an ‘orderingphase separation’ transition.
Figure 10: Co3 V alloy. Water quenching from 500°C. (a) Electron diffraction pattern; (b) bright-field image of the microstructure .
(Figure11) A diffuse scattering is again observed in the electron diffraction pattern and a honeycomb structure is formed in the alloy as a consequence of the emergence of the tendency to phase separation
Figure 11: Со3 V alloy. Water quenching from 350°C. (a) Brightfield image of the phase-separation microstructure; (b) electron diffraction pattern,  zone axis .
Not all critical points found in the Co3 V alloy coincide with those indicated on the generally accepted phase diagram. Even the liquids points do not match. The Figure 12 gives a visual idea of what kind of phase diagrams the Materials Science has now.
Figure 12:The Co-V phase diagram presented by the National Physical Laboratory (USA). Dashed lines show two ‘orderingphase separation’ transitions. The real microstructures in different regions of the chart (points 1-5) are shown in italics .
Alloys of the Ni-Cr system
The variety of manifestations of the ‘ordering-phase separation’ transition in alloys of various systems can also be judged by the behavior of the Ni-Cr system: alloys of this system in which chromium predominates, at all temperatures, have a tendency to ordering, in which nickel predominates, at all temperatures, a tendency to phase separation. If the compositions of the alloys are between two compositions — Ni40Cr60 and Ni68Cr32, then in these alloys the ‘ordering – phase separation’ transition occurs not only as a result of a change in temperature, but also as a result of a change in concentration. So far, only one system of this kind is known — the Ni – Cr system [16, 17]. According to the generally accepted Ni-Cr phase diagram , with compositions close to the Ni40Cr60 alloy, a eutectic is formed in the Ni-Cr system. This could mean that in alloys of this composition there is a tendency to phase separation. However, in the entire temperature range of the study of this alloy from the liquid state to 550°С, only the structure corresponding tendency to ordering was detected experimentally by the TEM method.
Thus, the solidification process of the Ni40Cr60 alloy does not begin with the formation of a eutectic consisting of nickel and chromium grains, as follows from the diagram, but with the precipitation of the chemical compound Ni2 Cr (with the Pt2 Mo type orthorhombic lattice) from the liquid solution.
Marucco , studying the electrical resistivity of various Nimonic and Inconel alloys, tried to explain some changes in their properties by the precipitation of phases of the Pt2 Mo type, but found no diffraction evidence for this. The formation of the Pt2 Mo type superstructure was revealed by an electron diffraction method in the Ni-33.3at. % Cr alloy annealed at 500°C for 1600 hours .
Although not without reason, some researchers who are engaged in the construction of phase diagrams apparently ignore this phase. For example, the Ni-Cr phase diagram on the Computational Dynamics website only represents temperatures above 600ºС, at which the Ni2 Cr phase does not formed.
Figure 13 shows bright-field images and an electron diffraction pattern obtained from a sample quenched from a liquid, which indicate that randomly arranged large grains of an elongated shape have an orthorhombic lattice of the Pt2 Mo type inherent to the chemical compound Ni2 Cr [16, 17]. The formation of the chemical compound Ni2 Cr in a liquid solution means that the alloy Ni40Cr60 even at 1450ºС has a very strong tendency to ordering. Thus, the solidification process of the Ni40Cr60 alloy does not begin with the formation of a eutectic consisting of nickel and chromium grains, as follows from the diagram, but with the precipitation of the chemical compound Ni2 Cr with the Pt2 Mo type orthorhombic lattice from the liquid solution.
Figure 13: Ni40Cr60 alloy. Water quenching from the liquid state. Bright-field image of the microstructure. Inset: electron diffraction pattern,  zone axis .
Figure 14 presents a bright-field image obtained from a specimen of the Ni40Cr60 alloy quenched from the liquid state (1450ºC). The microstructure consists of reasonable grains of elongated shape, randomly arranged in the solid solution. An electron diffraction pattern, obtained from these grains indicates that they have an orthorhombic lattice of the Pt2 Мо type, characteristic of the Ni2 Cr chemical compound. The same chemical compound particles but more dispersive on sizes were obtained after heat treatment at lower temperatures (Figure. 14, inset).
Figure 14:Ni40Cr60 alloy. Water quenching from 1200°C. Brightfield image of the microstructure. Inset: aging at 550°C; dark-field image .
In the intervals between the Ni2 Cr phase particles (Figure 14), one more surprising fact can be observed: the formation of clusters of chromium atoms, which are observed in the bright sites between particles due to absorption contrast. To conclude that these are clusters of chromium atoms, Figure 15, which shows the same clusters in the Ni68Cr32 alloy after quenching from the liquid state and after quenching from 1000˚C (inset).
A quenching of the Ni68Cr32 alloy from the liquid state (1450ºC) results in the formation of the structure shown in Figure 15. Round dark spots with diffuse edges are observed in the image. The author  considered them as clusters of chromium atoms in the nickel lattice. A similar structure of chromium atom clusters was also observed in electron microscope images after quenching the alloy from 1200°C, 1000°C (Figure 15, inset) and below. At the same time, the Ni2 Cr phase in this alloy was not found at any temperature
Figure 15:Ni68Cr32 alloy. Water quenching from a liquid state. Bright-field image of the microstructure. Inset: after water quenching from 1000°C. Absorption contrast 
Thus, experimental results have been obtained  that indicate that the signs of the chemical interaction between component atoms in the Ni40Cr60 and Ni68Cr32 alloys are constant over the entire temperature range of their heating; in the Ni40Cr60 alloy, this sign is negative and in the Ni68Cr32 alloy, it is positive. This means that the boundary between the areas of ordering and phase separation in the Ni-Cr phase diagram should be located between these two compositions and should largely depend on the change in concentration rather than the change in temperature. In order to determine the transition line, a project was undertaken to melt three intermediate compositions-Ni46Cr54 (3), Ni56Cr44 (4) and Ni62Cr38 (5) and carry out a TEM study on them. Figure 16
Figure 16: Ni56Cr44 alloy (№4). Quenching from the liquid state (1450°С). Bright-field image of the microstructure. Cr-clusters in the form of the long curved stripes (absorption contrast). Dislocation structure is in the rest matrix.
The results were compared with the data obtained previously for the Ni40Cr60 and Ni68Cr32 alloys. It was found that in the Ni62Cr38 alloy, for example, the tendencies to ordering or phase separation are already manifested but not in the whole temperature range of its heating. If, after quenching from the liquid state, clusters of chromium atoms are observed in the structure of the alloy (Figure 17), then, upon lowering the temperature of the heat treatment to 1000°C, a microstructure characteristic of the tendency to ordering (Figure 18) can be observed, and after aging at 550°C – again a structure of phase separation.(Figure 19).
Figure 17: Ni62Cr38 alloy. Water quenching from a liquid state. Bright-field image of the microstructure. Absorption contrast . Cr-clusters in the form of the dark longed strips.
Figure 18: Ni56Cr44 alloy. Water quenching from 1000̊ C. Bright-field image of the microstructure. Inset: electron diffraction pattern . The Ni2 Cr phase particles are visible.
Figure 19: Ni62Cr38 alloy (№5). Bright-field images of the microstructure after aging at 550°С. Cr-clusters.
A dashed line in Figure 20 is considered to separate the points in the phase diagram in which ordering structures and structures of phase separation had formed. This dashed line can be regarded as the line of the ‘ordering-phase separation’ transition. As can be seen, its position in the diagram depends on the concentration of the alloy to a greater degree than the heat-treatment temperature.
Figure 20:Accepted Ni-Cr phase diagram with our experimental data [16, 17]. Compositions of the alloys are pointed out in the diagram by the vertical lines. Symbols: ●- microstructure of ordering; ▲- microstructure of phase separation [16, 17].
Changes in the electronic structure of alloys at the ‘orderingphase separation’ transition.
It is obvious that the observed changes in the microstructure of the alloys at the ‘ordering-phase separation’ transition do not occur by themselves, but are due to definite changes in the electronic structure of the alloys at quite specific temperatures for each system. For example, Figure 21 shows specific formations which were previously found in alloys of the Fe-Cr system and named as ‘electron domains’ [11, 12]. Such domains appearing at high-temperature (Figure 21a) and low-temperature (Figure 21b) ‘ordering-phase separation’ transitions are best observed when defocusing the electron microscopic images. The domains were later discovered in Fe-Cr-Ni-Mo duplex alloy .
Figure 21: Fe50Cr50 alloy. Electron domains formed at (a) a high-temperature ‘ordering-phase separation’ transition (heat treatment: water-quenched from 1200°C for 1 hour and then from 700°C for 4 hours) and (b) at a low-temperature transition (heat treatment: water-quenched from 700°C for 1 hour and then from 550°C for 4 hours) .
Electron domains are considered as microscopic areas, inside which the sign of the chemical interaction energy has already changed to the opposite of the other surrounding microscopic areas, in which the sign remains as before. An electron beam passing through the foil, in which electron domains have formed, deviates in opposite directions on both sides of the domain boundary, and leads to a deficiency (bright lines) or an excess (dark lines) of electrons when defocusing the electron-microscopic image . It should be noted here, that similar domains are observed in electron micrographs of the alloys at their transitions both in a ferromagnetic state (when the domains differ in the magnetization vector orientation) and in a ferroelectric state (when the difference is in the direction of spontaneous polarization). This means that the nature of the contrast from all the above-mentioned domains is the same and that the contrast is formed due to the difference in the electronic structure of the neighboring domains.
Previously, the formation of chemical domains was considered as a temporary, unstable state of the alloy (the state of transition from the tendency to phase separation to the tendency to ordering) . However, it was later found that domains in the alloys of the FeCr system might testify that a certain metastable state of the alloy is characteristic for the given temperature . The existence of such a metastable state (an incomplete ‘ordering-phase separation’ transition) in the bulk of the alloy prevents the formation of the σ-phase in the entire volume of the alloy. The σ-phase forms only in a thin surface layer, where, apparently, the surface plays some form of catalytic role for the process of the transition from ordering to phase separation .
The discovery of such formations as electron domains in the microstructure of alloys of the Fe-Cr system  and stainless Ni-Cr steel  indicates that the ‘ordering-phase separation’ transition begins at the level of changes in the electronic structure of these alloys. Therefore, it would be interesting to find out exactly what changes occur in the electronic structure that may lead to a change in the sign of chemical bonds between dissimilar atoms.
X-ray photoelectron spectroscopy (XPS)
Another method that indicates that the ordering-separation phase transition begins with changes in the electronic structure of the alloy is the X-ray photoelectron spectroscopy (XPS). This method was first used to determine the temperature at which the sign of the chemical interaction energy is changed . The shape of the valence bands, obtained at the temperatures, above and below this transition, allowed the determination of the temperature of the phase transition. In this case, if the shape of the valence band of the alloy is similar to the shape of the valence band of the pure А solvent, then it means that in the immediate environment of A atoms there are A atoms. It can suppose that A-A and B-B bonds form in the alloy (there is a tendency to phase separation). If the distribution of the density of 3d-states in the alloy is similar to the distribution of the electron density in the valence band of the dissolved component, then it can suppose that in the alloy, at this temperature, there are no А-А bonds between the atoms of the solvent. It means that each atom of the A solvent is involved in a bond with atoms of the dissolved B component, i.e. there is a tendency to ordering and AmBn chemical compounds precipitate in the solid solution.
For example, X-ray photoelectron spectra of the valence band were presented, for the Fe3 Ni alloy, at Figure 22. Experimental spectra obtained at 200 (c), 500 (d), 800 (e) and 1100°С (f) . At temperatures of 200 and 500°C, the valence band spectra of the alloy have a double band structure due to a small overlap of the d-bands of the Co and Ni atoms. At temperatures of 800 and 1100°C, the spectra of the valence bands have the form of a superposition of the valence bands, where the form of the valence band of the solvent atoms, i.e. Co, is predominant. The reference spectra of pure Co and Ni were obtained at room temperature. This allowed the authors  to say that at temperatures 200 and 500 a tendency to phase separation is displayed, at 800 and 1100°C – a tendency to ordering. Therefore, in the temperature range between 500 and 800°C, an ‘ordering-phase separation’ transition takes place in the alloy, during which the sign of the chemical interaction energy is reversed.
Figure 22:Fe3 Ni alloy. Photoelectron spectra of the valence band. Reference spectra: (a) Ni, (b) Fe.
It is known that fundamental properties of solids are determined by the nature of the chemical bond between the nearest neighbors. The chemical bond is usually understood as a combination of all forces acting on each atom in the solid holding it in the state of equilibrium. Three main types of strong chemical bonds exist between metallic atoms: metallic, ionic and covalent. It is believed that the metallic bond occurs in metals and metallic alloys, when the valence electrons are collectivized and form an electron gas .
For metallic alloys, these understandings are not entirely consistent with what we observe experimentally. There is no doubt that in metallic alloys, as well as in pure metals, there is a metallic bond. However, in contrast to pure metals, where this bond is the only one possible, in metal alloys there must also be other types of bonds alongside this. Otherwise, it would be impossible to explain the presence of second phase particles in the microstructure of alloy.
The ‘ordering-phase separation’ transition occurs at a temperature, which is quite definite for each binary system. With the help of the method of X-ray photoelectron spectroscopy, it has been shown that this transition occurs at the level of changes in the electronic structure of alloys (the shape of the valence band changes at such a transition [14, 21, 23]. From the results obtained by the method of transmission electron microscopy, it has been concluded that the change of the type of the alloy microstructure occurs at approximately the same temperature at which the shape of the alloy valence band changes.
If we compare the understandings of the nature of chemical bonds in metallic alloys that exist today in Physics and Chemistry with the results of the microstructure study considered in this review, there arises a feeling that the subject of the discussion in both cases is the same phenomenon, merely they are described with the help of different terminology. Indeed, the ionic component of the bond that takes place in an A (B) alloy between atoms of the solute component B and their nearest neighbors (atoms of the solvent A) manifests itself when, according to current ideas in Materials Science, a tendency to ordering in the alloy and the chemical compound АmВn is formed .
The covalent component of the chemical bond manifests itself if two atoms of the solute component B, diffusing in the alloy, at some time, happen to be nearest neighbors. As a result of this momentary neighborhood, a hybridization of two valence orbitals occurs, and these two atoms B become a cluster. The cluster consists first from two B atoms and then from a greater number of pairs of B atoms. Such a process of clustering is considered as occurring in alloys due to the tendency to phase separation.
It becomes clear that the tendency to ordering occurs because in a metallic alloy, along with the metallic component, there exists an ionic component of the chemical bond between A and B atoms and the covalent component between atoms B only and A only. It should be noted that the ionic and the covalent components can only simultaneously co-exist during the ‘ordering-phase separation’ transition, i.e. the ‘the ionic component of the bond ↔ the covalent component of the bond’ transition. Thus, the ‘orderingphase separation’ transition includes two elementary acts: the delocalization of the valence electrons on A and B atoms, and the hybridization of the valence electrons on B atoms. The ‘orderingphase separation’ transition includes the de-hybridization of the valence electrons on B atoms and the localization of the valence electrons on A and B atoms. The existence of such an electronic transition may indicate that, with a change in temperature or concentration, the ionic component of the chemical bond between the atoms is replaced by the covalent component in the alloy, and vice versa .
In addition to the above links, confirming the conclusions made by the author of the review, the following is a list of original articles describing other systems. These articles were not included in the review, but similar results were obtained in all these articles Ni-Mo ; Ni-Al ; Ni-V ; Fe-Mo ; Fe-W ; Fe-Ti ; Co-Mo , etc.
Concluding Remark and Future Perspective
The discovery of the “ordering – phase separation” transition opens new perspectives for Materials Science in the study of alloys and sets new problems.
1. Our understanding of this or that physical phenomenon always changes with time and usually corresponds to the level of experimental technique at the given period. However, there are exceptions. Recall the once fashionable classical theory of “nucleation & growth” of a new phase, the theory of “in-situ” nucleation of special carbides in alloyed steels, and so on. Where are they now? They are being gradually forgotten because their description of processes occurring in nature differs from reality. However, at the same time, there are other theories and ideas, which have come to us from the past century, but have so deeply rooted into our minds, that even now, when the experiment does not verify them, we believe that they are the unquestionable truth. For example, we cannot imagine equilibrium phase diagrams without regions of solid solutions at high temperatures, although the latter, from the point of view of thermodynamics, are not an equilibrium phase at any temperature. We cannot imagine the probability of decomposition of a quenched solid solution without its “supersaturation” in the alloying component, which occurs at a decrease of the solution temperature. We cannot imagine a heat treatment, carried out to obtain a highly dispersed two-phase structure, which would not include a preliminary high-temperature quenching from the solid solution region. The discovery of the phase transition ordering –phase separation in alloys puts an end to these ideas.
2. In nature, as we know, any solutions consisting of different type atoms of A and B, are not ideal, and therefore, they decompose at temperatures, when the component atoms are able to diffuse over relatively long distance. This axiom of thermodynamics has long been known, and it applies to all solid solutions in metallic alloys. At the same time, the majority of equilibrium phase diagrams constructed to date for A-B metallic systems, contain solid solution regions, especially at high temperatures, when the diffusion mobility of A and B atoms and their energy of the chemical interaction are sufficient for their decomposition. Thus, in the existing equilibrium phase diagrams, regions are presented, in which the phase (solid solution) is not an equilibrium one.
3. The discovery of the ‘ordering-phase separation’ transition in alloys puts an end to these ideas. It becomes clear that the ideas about the nature of alloys that we acquired in our universities turn out to be largely outdated, as they are based on experimental data obtained as far back as the mid-twentieth century and without the use of the method of TEM. From the above discussion, it follows that introduction of such a concept as the ‘ordering-phase separation’ transition into common use changes our previous understanding of the driving forces of the process of new phase formation. In addition, it becomes apparent that in order to change this situation a great number of experimental studies is to be carried out to upgrade existing phase diagrams. The ‘ordering-phase separation’ transition, regarded as a consequence of changes in the chemical interaction sign, is such a transition, in the process of which the ionic component of the chemical bond between the atoms, due to the electron-phonon interaction, is replaced by the covalent component, or vice versa.
4. All processes occurring in alloys during heat treatment and leading to a change in their properties are currently considered from the point of view that the disordered solid solution is the initial phase in these processes, and the elastic forces arising between dissimilar atoms are the driving force. The experimental results presented in this viewer article debunk this point of view and show that it is necessary to take the liquid state of the alloy as the initial phase, and interatomic chemical interactions should be considered as the driving force of all diffusion processes occurring in the condensed state of an alloy.
The results discussed in this review show that there are still a lot of unclear points, and sometimes just erroneous judgments, exist in the Materials Science. The author of this review has been working alone for a long time, without assistants and like-minded people, so it is natural that he conducted research only on a small group of alloys. But even these few studies show how much more work remains to be done to get rid of the empirical approach in Materials Science when creating alloys. Therefore, the author would like to present here some points to which you should pay attention in the first place.
It is necessary to rebuild almost all binary phase diagrams that currently exist, using the TEM method. If you count how many binary systems exist, you can imagine how many years such a job can last.
It is necessary to exclude the use in production and in science of such heat treatments as quenching (to obtain the microstructure of a “solid solution”) and isochronous tempering, as useless.
Ideas about the conditions for the existence of a homogeneous solid solution will have to be reconsidered.
It should be realized that chemical interatomic interactions always exist in alloys, at all temperatures of the condensed state.
There is a lot of experimental work to be done using the TEM method in order to determine the ‘ordering-phase separation’ transition temperature for each system (and, if necessary, an individual alloy).
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