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Grain Boundary Wetting-related Phase Transformations in Al and Cu-based Alloys Review

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Review

The Grain Boundary Wetting Phenomena in the Ti-Containing Loftier-Entropy Alloys: A Review

1

Osipyan Found of Solid State Physics of the Russian University of Sciences, Air conditioning. Osipyan Str. ii, 142432 Chernogolovka, Russia

2

Chernogolovka Scientific Center of the Russian Academy of Sciences, Lesnaja Str. 9, 142432 Chernogolovka, Russia

3

Institute of Metallurgy and Materials Scientific discipline, Smooth Academy of Sciences, Reymonta Str. 25, 30-059 Cracow, Poland

4

Constitute of Solid State Physics, Academy of Latvia, Kengaraga Str. 8, LV-1063 Riga, Latvia

five

Physics Department, Academy of the Basque State UPV/EHU, Barrio Sarriena due south/n, 48940 Leioa, Spain

6

Section of Materials Scientific discipline and Engineering, Technion—State of israel Institute of Technology, Haifa 3200003, Israel

7

Institute of Materials Science, Leibnitz University of Hannover an der Universität two, 30823 Garbsen, Germany

*

Authors to whom correspondence should be addressed.

Bookish Editor: Andriy Ostapovets

Received: 30 October 2021 / Revised: eighteen November 2021 / Accepted: eighteen Nov 2021 / Published: 22 Nov 2021

Abstract

In this review, the phenomenon of grain purlieus (GB) wetting past melt is analyzed for multicomponent alloys without principal components (too chosen high-entropy alloys or HEAs) containing titanium. GB wetting can be complete or fractional. In the former case, the liquid stage forms the continuous layers between solid grains and completely separates them. In the latter case of partial GB wetting, the melt forms the concatenation of droplets in GBs, with sure non-nothing contact angles. The GB wetting phenomenon tin can be observed in HEAs produced past all solidification-based technologies. GB leads to the appearance of novel GB necktie lines T wmin and T wmax in the multicomponent HEA stage diagrams. The then-called grain-purlieus engineering of HEAs permits the use of GB wetting to improve the HEAs' properties or, alternatively, its exclusion if the GB layers of a second phase are detrimental.

1. Introduction

According to the generally accepted definition, loftier-entropy alloys (HEAs) are materials that contain at least five unlike components, among which the main component cannot exist selected [1,two,three,4]. Therefore, they are also called alloys without principal components or multiprincipal component alloys. Loftier-entropy alloys have go extremely popular among researchers in recent years. At that place are literally thousands of articles devoted to them. For this reason, this review volition exist limited to two aspects. First, this review volition consider alloys that comprise titanium equally principal or secondary component. Secondly, nosotros will restrict ourselves to the phenomena associated with grain boundaries. Moreover, amid the grain-boundary phenomena, accent volition be placed on the phenomena associated with wetting-stage transformations.

High-entropy alloys containing titanium tin be conventionally divided into ii groups. The first group includes alloys containing zirconium and hafnium, together with titanium [5,half-dozen,7]. Ti, Zr and Hf are in the same grouping in the Mendeleev periodic table of elements. Simply like titanium, they have a trunk-centered crystal lattice at high temperatures (bcc, β-Ti, β-Zr, β-Hf), and at low temperatures, they possess a hexagonal shut-packed lattice (hcp, α-Ti, α-Zr, α Hf). Moreover, at loftier pressure, all three metals transform into the loftier-pressure ω-phase with a more complex hexagonal lattice [8,9]. In some Ti-alloys, the metastable ω-stage appears fifty-fifty after certain oestrus treatment, without application of high pressure [10,eleven,12]. In HEAs containing titanium, zirconium and hafnium, other elements with a bcc lattice are most frequently present (for case, vanadium, molybdenum, tungsten, etc.). Therefore, such a HEAs will also have a body-centered cubic lattice. The second group is composed of alloys in which titanium plays a somewhat subordinate part [13,xiv,15,xvi]. In particular, these are the alloys with a face up-centered cubic lattice (fcc) [17,18,19,20,21].

Generally speaking, from the very commencement of the studies of HEAs, information technology was noticed that in a certain range of compositions and temperatures, high-entropy alloys incorporate but i stage, namely a solid solution where all v or more components grade a random solid solution [1,ii,iii,4]. Recently, the involvement of researchers has shifted from such simple HEAs consisting of only one stage of a multicomponent solid solution to the alloys with certain elements of heterogeneity. These include the spatially inhomogeneous distribution of the components, the 2nd-stage precipitates in a multicomponent solid solution, various grain-boundary layers, etc. For such studies, a special term, "metastability engineering", has been coined [22,23]. In many cases, the formation of such heterogeneous structures instead of a homogeneous multicomponent solid solution tin can be discussed in terms of stage transitions at grain boundaries (GBs). Such phase transformations include the wetting of grain boundaries with a melt or a 2nd solid stage, too every bit the germination of various thin grain-purlieus layers of the second phase at the boundaries [24,25,26,27]. These phenomena depend non-trivially on the limerick, temperature and pressure in a multicomponent system. This review is devoted to these grain-boundary processes in HEAs containing titanium.

2. Grain Boundary Wetting past the Liquid Phase

In the majority of cases, multicomponent alloys are synthesized by crystallization from the melt (arc or induction melting in vacuum or argon [five,half dozen,seven,13,xiv,15,16,17,18,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43], plasma spark sintering [19], current assisted sintering [20,21], light amplification by stimulated emission of radiation or plasma cladding deposition of coatings [44,45,46,47,48,49,50,51,52,53,54,55], additive manufacturing past the laser-powder bed fusion [56,57] or laser-metallic deposition [58], self-propagating loftier-temperature synthesis (SHS) [59], and past brazing inside the brazing joints [60,61]). Figure 1 shows a schematic phase diagram for the simplest case when there are only two components in the system. Cooling routes are shown by dashed lines i to 5 in Figure 1 for alloys with different compositions. Upon cooling, after crossing the liquidus line, the alloy first enters the two-phase region, where the melt, L, is in equilibrium with the solid solution, Southward. The cook solidifies completely when the temperature drops below the solidus line. We will utilize this schematic stage diagram in further explanations of GB phenomena. In the case of HEA, the state of affairs is much more than complicated. For example, 6-component alloys are described by a stage diagram in half-dozen dimensions. In this case, between the single-phase melt, L, and the completely solidified material, S, there can be not 1 two-phase region, S + 50, only many regions in which more than ane solid and more than one liquid stage can coexist. If a polycrystalline sample is in the ii-phase region, S + L, of the stage diagram, then it contains GBs in the solid phase and interphase boundaries betwixt the solid stage and the melt. A triple junction of ii interphase boundaries and one GB is formed in the locations where the GB is in contact with the melt (see Figure i, schemes between Routes i and 2).

If the energy of the GB σGB is less than the energy of the two solid/liquid interphase boundaries, 2σSL, contacting this GB at the triple junction, then the contact angle, θ, at this triple junction is non-null (encounter Figure 1). This situation with θ > 0 is called incomplete (or partial) wetting of the GB by the cook. If the energy of the grain boundary is higher than the energy of the two solid/liquid interphase boundaries, σGB > 2σSL, then the contact bending volition exist equal to nix. In this instance, the GB must be replaced past a sufficiently thick layer of the liquid phase. This situation is called consummate wetting of the GB past the melt. In a number of systems, the bending between the GB and the melt decreases with increasing temperature [62,63,64,65]. Moreover, after reaching a certain temperature, T w, the contact angle tin can become goose egg. In other words, incomplete wetting is replaced past complete wetting of the boundary. This temperature, T w, is called the GB wetting phase-transition temperature. The wetting stage transition, similar any other stage transformation, can be of either the first or the second order [66,67,68]. In the case of a first-society phase transition, the kickoff derivative of the contact angle, with respect to temperature, exhibits a discontinuity at the temperature T w [62,66,67]. Information technology drops abruptly from a sure finite value to zero [62,66,67]. In the case of a second-order (continuous) stage transition, the start derivative of the contact angle with respect to temperature continuously decreases with increasing temperature and becomes equal to zero at the transformation temperature, T w [66,67]. The free energy of GBs depends on their misorientation angle, χ, and inclination angle, ψ [69]. It exhibits sharp cusps at certain χ and ψ values [70]. The energy spectrum of GBs tin be very wide. Patently, the college the GB energy, the smaller the contact angle, θ, at its triple junction with the melt [71]. Thus, at a stock-still temperature, a wide range of contact angles is observed in a two-stage polycrystal. Every bit the temperature rises, these contact angles, θ, too decrease at different rates. This leads to the wide scatter of the GB wetting stage-transformation temperatures for the GBs with dissimilar energies.

The typical microstructures of such 2-stage polycrystals are shown in Figure 1 for the binary Al–Mg alloys. Two tie lines for the transition from partial to complete wetting appear in the stage diagram. The first line at T wmin corresponds to the GBs with the highest energy, σGB. Beneath this temperature, at that place are no completely wetted GBs in a polycrystal. It exhibits only partially wetted GBs with a nonzero contact bending, θ. Above the minimum wetting phase-transition temperature, T wmin, the completely wetted GBs announced in the polycrystal. With a farther increase in temperature, the fraction of such completely wetted boundaries in the sample increases until it reaches unity at T wmax. This temperature, T wmax, is indicated on the phase diagram by another horizontal necktie line. Above this line, all grain boundaries are completely wetted (encounter diagram), and each grain is fully embedded in the melt without touching the other solid grains since the formation of "dry" GBs is thermodynamically unfavorable. Thus, in this region of the phase diagram, all solid crystallites are separated from each other past interlayers of the liquid stage. Consequently, in the phase diagram in the South + L two-stage region, where the solid and liquid phases are in equilibrium, the new necktie lines appear. They are associated with GB wetting phase transformations. These lines are absent-minded in traditional stage diagrams, which do not take into account the presence of grain boundaries in the sample. Accordingly, the microstructure of the polycrystal subsequently solidification will exist dissimilar for different solidification routes (see dotted lines i to 5). It will depend on the path along which the sample crosses the two-phase region during solidification. Such principally dissimilar situations for solidification are schematically shown in Effigy 1 by vertical dotted lines 1 to 5.

The commencement dotted line, 1, on the right-manus side of Figure i does not intersect the grain boundary lines, T wmin and T wmax, in the phase diagram. When the cook is cooled, Road 1 crosses merely the lines of majority liquidus and the line of eutectic transformation. When such a sample solidifies, grain boundaries inside are formed immediately since they are not separated from each other by the liquid phase. The last pockets of the cook (the richest in the second component) are pushed into the triple junctions between the boundaries upon cooling and solidify there. This is the classical dendrite structure. Thus, after the solidification of such a cook, we tin observe a relatively small difference in concentration betwixt the centers of grains and the edge regions, while the highest concentration of the 2d component is observed at the triple junctions of the GBs. Equally a consequence, the relatively homogeneous solid solution crystallizes, in which the enriched areas are well-visible. This scheme likewise works for multicomponent loftier-entropy alloys. Classical samples of single-phase loftier-entropy alloys, nearly likely, are simply formed according to the scheme corresponding to the rightmost dotted line, 1. A typical sample of such a microstructure is shown in Effigy two from Ref. [5]. When the melt is cooled, the 2nd dashed line (Route 2) on the correct-manus side of Figure 1 intersects not only the lines of the bulk liquidus and eutectic transformation but likewise the GB line at T wmin. This means that the solid grains are separated from each other by liquid layers between the bulk liquidus and the grain-boundary necktie line. Below the T wmin tie line, these GB interlayers, enriched with the second component, solidify. Thus, enriched interlayers remain in the solid sample along these first GBs. Upon farther cooling, the melt solidifies without the formation of grain-purlieus-enriched interlayers. As dashed line 2 moves from right to left to Route iii, the sample will contain more than and more GBs enriched with the second component afterward solidification. If the vertical dashed line (Route 3) also intersects the upper grain boundary necktie line, T wmax, then at the beginning stages of solidification, a continuous network of enriched interlayers is formed in the polycrystal betwixt the solid grains (come across the respective micrograph). Information technology is later clearly visible on the microstructure of the solidified alloy. At high concentrations of the 2nd component, such a network has characteristic discontinuities (run into, for example, the microstructure shown in Figure three). The fourth vertical dashed line (Route 4) crosses only the bulk liquidus and tie line at T wmax, and so the bulk solidus. In this example, thick enriched layers are visible at many GBs in the solidified sample. If the alloy does not cross the GB lines during cooling (the fifth dotted line, Route 5), and then the melt interlayers rich in the second component have no chance of redistributing in the solid state at all. They remain in the solidified sample in the form of a continuous network surrounding the grains poor in the 2nd component (see, for example, the microstructure in Figure 4).

The scheme in Effigy 1 is fatigued for the uncomplicated binary systems. The real HEAs per definitio contain at least five components. This ways that the corresponding HEAs' phase diagrams demand five, six or more dimensions to be fatigued. Moreover, according to the thermodynamic rule of phases, the multiphase areas containing different amounts of several solid and liquid phases should exist in the equilibrium phase diagrams for HEAs. This simple fact makes the description of GB wetting phenomena in HEAs much more complicated in comparison to binary systems. This review is a first endeavour to discuss GB wetting in HEAs, to give the corresponding examples and draw the attending of readers to the open questions. We also promise to shed some light on possible causes of the formation of inhomogeneities in (traditionally homogeneous) HEAs.

iii. GB Wetting in HEAs Obtained by the Arc or Consecration Melting

The scheme shown in Figure i describes the nigh important scenarios of solidification in the presence of GB wetting phase transitions. Nevertheless, in reality, the positions of T wmax and T wmin necktie lines in relation to the melting temperature, T thousand, and eutectic temperature, T e, can be unlike. Let the states consider some examples of HEA solidification. First, we discuss the crystallization from the melt during arc or induction melting in vacuum or argon [five,six,7,13,14,15,16,17,18,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37]. If the two-phase S + L surface area of the phase diagram does not contain any tie lines, T wmax or T wmin, of the GB wetting transition, then the one-phase solid solution polycrystal with typical dendritic structure forms after solidification of the melt. This is the case of the equiatomic HfNbTaTiZr high-entropy blend with bcc structure prepared past plasma arc melting (Figure 2a) [5]. After homogenization at 1473 Thou, this dendritic structure disappears and the bcc solid solution becomes homogenous (Effigy 2b).

Quite a unlike microstructure forms if the HEA solidifies following Route 3 or 4. In Figure 3, the SEM images of as-bandage AlCoCuFeNiC (Figure 3a) and AlCoCuFeNiCrTi (Figure 3b) HEAs prepared past arc melting are shown [37]. The primary grains of the bcc phase were surrounded past the cook solidified every bit fcc phase. The majority of GBs were completely wetted by the melt. We describe the GB in a micrograph every bit completely wetted in the case when the melted layer is continuous from one GB triple junction (TJ) to another. If the melt layer between two TJs is broken and the portions of dry out GB remain in between, we draw the GB every bit partially (incompletely) wetted. In this case, ane tin measure the non-zero contact angles in the contact points between the liquid phase and GB. Nonetheless, some partially wetted GBs are also visible in micrographs in Figure 3. A similar microstructure was observed in the equally-cast Al0.fiveCoCuNiTi alloy prepared by arc melting [xiv]. In the as-cast state, the Al0.5CoCuNiTi alloy is composed of the fcc matrix grains separated past the 1–four µm thick layers of the bcc phase. It is also well visible from the micrographs in Ref. [xiv] that not all GBs were completely wetted by the liquid phase. Some of the GBs remained incompletely wetted with a not-zippo contact angle.

The change in HEA composition tin modify the position of GB wetting T wmax and T wmin tie lines and, therefore, also the solidification route. Thus, in Ref. [28], two equiatomic AlCrCuFeTi and AlCrCuFeV HEAs were prepared by arc melting in a titanium-getter argon atmosphere. After solidification, the HEA consist of a bcc matrix with pronounced GB layers from other phase(s) (Figure 4 in [28]). These GB phases formed afterward solidification of the final (intergranular) fractions of the melt. They are Cu-rich and are fcc in AlCrCuFeV blend and bcc-2, with L1two Heussler and hexagonal Laves phases in the AlCrCuFeTi alloy. It is visible in Figure 4 in [28] that in the V-containing HEA, the fraction of completely wetted GBs is much higher (though fifty-fifty not 100%) than in the Ti-containing HEA (where information technology is 10–20%). This ways that AlCrCuFeTi HEA solidified following Route 2 and AlCrCuFeV alloy solidified following Road three or 4 (see scheme in Figure 1).

A skillful example of consummate GB wetting can be seen in the Ti3VtwoNbNi0.five blend produced by the vacuum arc melting with multiple remelting passes (Figure 4) [13]. XRD, TEM and SAED data prove that the matrix grains accept disordered bcc structure, while the GB precipitates take cubic MgCuii-type (C15) construction (so-called Laves phase). Here, the bcc solid crystallites were completely surrounded by the melt. Further, the final fractions of the melt eutectically decomposed into a bcc+ C15 mixture of solid phases.

Another case of concentration dependence of solidification route in the presence of GB wetting necktie lines tin be found in the Ti-free CoCrFeNi-Ta 10 HEAs with different concentration of Ta (10 = 0.1, 0.25, 0.75, 1) [29]. HEAs were prepared by arc melting under argon atmosphere. The kickoff two HEAs are hypoeutectic, and last ii are hypereutectic (see phase diagram in Figure 5). In first two HEAs, the matrix has fcc structure, and GB layers incorporate the Laves phase formed after solidification. Figure 6a,b demonstrate that CoCrFeNi-Ta0.one HEA solidifies according to Route 2 (few completely wetted GBs), and the CoCrFeNi-Ta0.25 HEA solidifies post-obit Road 4 (nearly all GBs are wetted). In hypereutectic CoCrFeNi-Ta0.75 and CoCrFeNi-Ta1.00 HEAs, the situation is more complicated, but the GB wetting phenomena are, nevertheless, obvious (Figure 6c,d).

iv. GB Wetting in HEAs Obtained by Electrical-Current-Assisted Sintering

In HEAs produced by methods other than arc melting, one can also detect the indications of GB wetting transitions. In Ref. [20], CoCrFeNi, CoCrFeNi Ti0.5Al0.5 and CoCrFeNiAl0.v high-entropy alloys were produced using electric-electric current-assisted sintering (ECAS). Afterwards the production of HEAs, they were light amplification by stimulated emission of radiation remelted (LR). The CoCrFeNi alloy contained simply one fcc phase and was completely uniform later LR (Figure 7a). Its solidification corresponds, therefore, to Route one (Effigy ane). In the CoCrFeNiAl0.5 and CoCrFeNi Ti0.5Al0.five HEAs, however, the GBs of the bcc grains were completely wetted by the melt (Route 1 or 2). After solidification, the GB layers contained the second bcc stage rich in Cr (Figure 7b,c). This result besides demonstrates that slight modification of the composition one tin can strongly change the morphology of phases by shifting the position of GB wetting tie lines, T wmax and T wmin, or (alternatively) the position of the solidification route when the temperatures, T wmax and T wmin, are stock-still.

v. GB Wetting in HEAs Obtained by Laser Cladding and Additive Manufacturing

In Ref. [45], MgMoNbFeTitwoYx (x = 0, 0.4%, 0.viii%, 1.ii%) HEA coatings were synthesized past light amplification by stimulated emission of radiation cladding. After crystallization, they contain the matrix grains of the bcc-stage rich in Mo and Ni surrounded by the layers of Mg, Ti-rich phase (Effigy viii). Near all bcc grains are separated from each other by the Mg, Ti-rich 200–300 nm thick layers. Only a few GBs were partially wetted by the cook. This corresponds to solidification Routes 5 or four (Figure i).

In Ref. [46], Al10Mo0.vNbFeTiMn (x = 1, i.v, 2) HEA coatings were synthesized past laser cladding. Their microstructure consists of an Mo,Ni-rich bcc-phase (matrix grains) surrounded past the layers of Mg,Ti-rich phase (Figure 9), similar to the alloys studied in Ref. [45]. Information technology is interesting that the amount of onetime liquid phase (crystallized then as Mg,Ti-rich phase) increases with increasing concentration of aluminum (Figure 9a–c). It is important to underline that in Figure 9a,b some GBs are visible that are incompletely wetted by the cook (with non-zero contact angle). In Figure 9c, even so, all GBs are completely wetted, and thick layers of the Mg,Ti-rich stage separate all grains of the Mo,Ni-rich bcc-phase from one another. The reason for that could be the then-called apparently complete GB wetting [72]. In case of patently consummate GB wetting, also GBs with a depression but non-zero contact angle can also become completely replaced by the melt just because the wedges of the liquid stage from neighboring GB triple junctions run across each other and thus separate the solid grains.

In Ref. [58], AlCoCrFeNiTi0.5 HEA was prepared by the additive manufacturing method, namely laser metallic degradation (LMD). The resulting microstructure consists of Al-, Ni-, Ti- and Co-rich grains (with fully ordered bcc structure B2), which are completely surrounded during solidification by the melt (encounter Effigy 10). The cook later crystallized in the Cr- and Fe-rich solid stage with disordered bcc construction A2. It has been observed that changing the LMD regimes 1 tin switch from a structure with equiaxial B2 grains surrounded by thick A2 layers (Figure 10) to a conventional dendrite structure similar to that shown in Figure 2a.

In this review, we presented several examples of complete and partial GB wetting in solidified HEAs. These examples practice not exhaust the cases of GB wetting in HEAs. They are just typical cases from recent publications. Indeed, similar microstructures tin can exist frequently seen in publications devoted to HEAs.

As we can see, modern HEAs frequently incorporate more than only 1 random solid solution phase. Moreover, the morphology of small phase(s), especially their distribution between the grains of major phases, tin can be governed by the GB wetting phenomena. These phenomena are well studied for the binary metallic alloys [73,74,75,76,77,78], and the respective knowledge can be successfully applied to multicomponent HEAs. In detail, in the two-phase S + 50 expanse(s) of a multicomponent stage diagram, the additional necktie lines of the GB wetting stage transition can appear (at minimum T wmin and maximum T wmax temperatures). As a effect, the modest melt stage (which later crystallizes) can class rather thick (at to the lowest degree few μm) layers separating the grains of major phases. The influence of such layers on HEA properties can be both favorable or detrimental. Knowledge of GB wetting transformations in HEAs tin be used for tailoring their backdrop, as well every bit for the further development of these advanced materials.

6. Conclusions

The thick (at least few μm) grain-boundary layers of the second phase(s) tin appear in HEAs during crystallization of the melt in all synthesis technologies (such as arc or induction melting, plasma-spark or electric-current-assisted sintering, deposition of coatings by laser or plasma cladding, additive manufacturing, self-heating synthesis or fifty-fifty in brazing applications). These thick GB layers are liquid during cooling in the Due south+50 expanse of the HEA phase diagram so crystallize equally a second solid stage or decompose in eutectic or peritectic reactions. The germination of such thick GB layers is due to the phenomenon of complete or partial GB wetting. Thus, the equilibrium liquid layers between solid grains appear if the GB energy is higher than the free energy of two solid-liquid interfaces. The presence of GB layers of a second phase(due south) can take either a positive or a negative effect on the properties of HEAs. In any instance, one can use the GB wetting phenomena to tailor the microstructure and properties of HEAs. For such so-called grain-boundary engineering of HEAs, knowledge of the position of GB wetting tie lines in the S + 50 areas of HEA stage diagrams is required.

Author Contributions

Conceptualization, B.B.Due south., A.B.Due south., A.S.Thou. and A.K. (Anna Korneva); methodology, A.K. (Anna Korneva), A.One thousand. (Alexei Kuzmin), G.A.L. and Eastward.R.; formal analysis, A.K. (Anna Korneva), A.Chiliad. (Alexei Kuzmin), One thousand.A.50. and Eastward.R.; writing—original draft preparation, A.Yard. (Anna Korneva), A.K. (Alexei Kuzmin), Yard.A.L., A.B.South. and E.R.; writing—review and editing, B.B.S. and A.Southward.G.; supervision, B.B.S., G.Grand. and A.M. (Anna Korneva); project administration, B.B.Due south., G.G. and A.K. (Anna Korneva); funding acquisition, B.B.South. and A.M. (Anna Korneva). All authors accept read and agreed to the published version of the manuscript.

Funding

This research was funded by the Russian Ministry building of Science and Higher Education (contract no. 075-15-2021-945 grant no. xiii.2251.21.0013). Support from the University of the Basque Country nether the GIU19/019 project is also best-selling.

Institutional Review Board Statement

Not applicable.

Informed Consent Argument

Non applicable.

Information Availability Argument

Information are independent within the article.

Acknowledgments

This review is written during the preparation of 1000-era.Net full proposal "Grain boundaries in multicomponent alloys without primary component" (A.K., A.K., G.A.Fifty. and E.R., awarding No. 9345). The Institute of Solid State Physics, University of Latvia, every bit a center of excellence, has received funding from the European Union's Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement no. 739508, project CAMART2.

Conflicts of Interest

The authors declare no disharmonize of interest. The funders had no role in the pattern of the study; in the collection, analyses or estimation of data; in the writing of the manuscript or in the conclusion to publish the results.

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