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Atomic size mismatch δ and mixing enthalpy ∆Hmix of (TiZrNbCu)1−xNix and (TiZrNbNi)1−xCux alloys vs. x. The inset: ∆Hmix between the constituent elements.

Atomic size mismatch δ and mixing enthalpy ∆Hmix of (TiZrNbCu)1−xNix and (TiZrNbNi)1−xCux alloys vs. x. The inset: ∆Hmix between the constituent elements.

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The study of the transition from high-entropy alloys (HEAs) to conventional alloys (CAs) composed of the same alloying components is apparently important, both for understanding the formation of HEAs and for proper evaluation of their potential with respect to that of the corresponding CAs. However, this transition has thus far been studied in only...

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... their limitations and some erroneous predictions (such as the occurrence of an IM in the SS region and an SS in the a-HEA region, e.g., [10][11][12][13]16,23,[54][55][56]), as illustrated in Figures 2-4, these criteria are useful for a quick comparison of different HEA systems (Figure 4). The variation of thermophysical parameters with the composition within a given alloy system can, on the other hand, provide an insight into the evolution of the properties of this system (Figures 2 and 3, [24,25,52]). ...
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... their limitations and some erroneous predictions (such as the occurrence of an IM in the SS region and an SS in the a-HEA region, e.g., [10][11][12][13]16,23,[54][55][56]), as illustrated in Figures 2-4, these criteria are useful for a quick comparison of different HEA systems (Figure 4). The variation of thermophysical parameters with the composition within a given alloy system can, on the other hand, provide an insight into the evolution of the properties of this system (Figures 2 and 3, [24,25,52]). In Figures 2 and 3, we show the compositional variations of selected thermophysical parameters in characteristic quinary TE-TL [24,25] and Cantor-type alloys [45,47], respectively. ...
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... variation of thermophysical parameters with the composition within a given alloy system can, on the other hand, provide an insight into the evolution of the properties of this system (Figures 2 and 3, [24,25,52]). In Figures 2 and 3, we show the compositional variations of selected thermophysical parameters in characteristic quinary TE-TL [24,25] and Cantor-type alloys [45,47], respectively. In the calculation of these parameters, we used standard expressions (see, e.g., [12,13,24,25]), and the input parameters for ∆Hmix and δ in Figures 2 and 3 and their insets were taken from References [71] and [72], respectively. ...
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... Figures 2 and 3, we show the compositional variations of selected thermophysical parameters in characteristic quinary TE-TL [24,25] and Cantor-type alloys [45,47], respectively. In the calculation of these parameters, we used standard expressions (see, e.g., [12,13,24,25]), and the input parameters for ∆Hmix and δ in Figures 2 and 3 and their insets were taken from References [71] and [72], respectively. For simplicity, a rather wellknown variation of ∆Sconf [25], which depends only on the number of alloying components and not on their type [10][11][12][13], is not shown in these figures. ...
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... simplicity, a rather wellknown variation of ∆Sconf [25], which depends only on the number of alloying components and not on their type [10][11][12][13], is not shown in these figures. In Figure 2, showing the variations of parameters of (TiZrNbCu)1−xNix and (TiZrNbNi)1−xCux alloys with x, the concentration range of HEAs, x ≤ 0.35, is distinguished from that of Ni-or Cu-rich alloys by a different color. The range of values of ∆Hmix (from −32 to −6.6 kJmol −1 ) and of δ (from about 8% to 10%) places our alloys in a standard ∆Hmix−δ plot [12] within the region occupied with an IM (x = 0 Ni) and a-HEAs (other alloys), which is consistent with our experimental findings. ...
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... comparison of ∆Hmix and δ in Figure 2 shows that both the magnitudes and variations of δs are quite similar in the two alloy systems, whereas the corresponding variations of ∆Hmix are quite different. In (TiZrNbCu)1−xNix alloys, ∆Hmix decreases rapidly from −6.6 for x = 0 to −32 kJmol −1 at x = 0.5, whereas in (TiZrNbNi)1−xCux alloys, ∆Hmix increases nearly linearly from −28.2 to −15 kJmol −1 within the same concentration range. ...
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... (TiZrNbCu)1−xNix alloys, ∆Hmix decreases rapidly from −6.6 for x = 0 to −32 kJmol −1 at x = 0.5, whereas in (TiZrNbNi)1−xCux alloys, ∆Hmix increases nearly linearly from −28.2 to −15 kJmol −1 within the same concentration range. The inset in Figure 2 ...
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... show an ideal solution behavior [25] which results in linear variations of their properties with x such as that depicted in Figure 1. In contrast, stronger interactions of Co and Ni atoms with TE ones (inset in Figure 2) lead to more complex variations of their properties with the concentration [24,26,37,52]. ...
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... variations of ∆Hmix and δ in (CrMnFeCo)1−xNix and (CrMnCoNi)1−xFex alloys are shown in Figure 3. We selected these two alloy systems because they, as with those shown in Figure 2, exhibit very different variations of their properties with the composition [45,47]. In these alloy systems, an FCC crystalline structure forms over a broad concentration range [45][46][47]. ...
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... note that the concentration scale in Figure 3 extends up to x = 1 due to the very broad concentration range of a single-phase solid solution with an FCC structure in (CrMnFeCo)1−xNix [45]. Taking into account that the studied concentration range in Figure 3 is considerably broader than that in Figure 2, the variations of thermophysical parameters in Figures 2 and 3 are qualitatively similar. The variation of ∆Hmix of (CrMnFeCo)1−xNix alloys with x is qualitatively similar to that in (TiZrNbCu)1−xNix alloys, whereas that in (CrMnCoNi)1−xFex alloys is similar to the variation observed in (TiZrNbNi)1−xCux alloys. ...
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... note that the concentration scale in Figure 3 extends up to x = 1 due to the very broad concentration range of a single-phase solid solution with an FCC structure in (CrMnFeCo)1−xNix [45]. Taking into account that the studied concentration range in Figure 3 is considerably broader than that in Figure 2, the variations of thermophysical parameters in Figures 2 and 3 are qualitatively similar. The variation of ∆Hmix of (CrMnFeCo)1−xNix alloys with x is qualitatively similar to that in (TiZrNbCu)1−xNix alloys, whereas that in (CrMnCoNi)1−xFex alloys is similar to the variation observed in (TiZrNbNi)1−xCux alloys. ...
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... the qualitatively similar variations of thermophysical parameters in Figures 2 and 3, the magnitudes of these parameters are quite different. As it could be expected for alloys composed of similar, adjacent elements, the values of δ in Figure 3 are small, around 1%, thus about ten times smaller than those in Figure 2. The corresponding ∆Hmix values are larger than −7.5 kJmol −1 , thus, on average, several times larger than those in Figure 2. ...
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... the qualitatively similar variations of thermophysical parameters in Figures 2 and 3, the magnitudes of these parameters are quite different. As it could be expected for alloys composed of similar, adjacent elements, the values of δ in Figure 3 are small, around 1%, thus about ten times smaller than those in Figure 2. The corresponding ∆Hmix values are larger than −7.5 kJmol −1 , thus, on average, several times larger than those in Figure 2. ...
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... the qualitatively similar variations of thermophysical parameters in Figures 2 and 3, the magnitudes of these parameters are quite different. As it could be expected for alloys composed of similar, adjacent elements, the values of δ in Figure 3 are small, around 1%, thus about ten times smaller than those in Figure 2. The corresponding ∆Hmix values are larger than −7.5 kJmol −1 , thus, on average, several times larger than those in Figure 2. Such relatively large values of ∆Hmix in Figure 3 result from moderate interatomic interactions between the alloying components [71], as seen in the inset in Figure 3. Indeed, the smallest value of ∆Hmix among these elements is that between Mn and Ni (−11.1 kJmol −1 ). ...
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... strong interactions of Ni, Co and Cu atoms with TE atoms (inset in Figure 2) and a high melting point of Nb can all affect the distribution of constituents in our TE-TL alloys [53]. Similarly, very different strengths of interatomic interactions between different components of Cantor-type alloys (inset in Figure 3) can produce a somewhat inhomogeneous distribution of elements within these alloys [9]. ...
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... quinary TE-TL MGs studied by us [23][24][25]37,52] showed complex crystallization patterns reflected in three or more exothermic maxima spread over a broad temperature range. These consecutive crystallizations are consistent with a strong but quantitatively different bonding tendency between different TE and TL atoms inferred from their thermophysical parameters shown in the inset in Figure 2. Due to this, in Figure 6, Tx denotes the onset of the first crystallization event, and Txl denotes the temperature of the exothermic maximum corresponding to the last crystallization event appearing in the corresponding DSC trace. ...
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... rule of mixtures predicts a linear decrease in Tm from 2041 for x = 0 to 1883 K for x = 0.5, whereas the experimental values increase from 1121 to 1179 K over the same concentration range. The observed strong deviation of experimental values of Tm from those calculated by using the rule of mixtures is probably associated with a strong bonding tendency between alloying elements (inset in Figure 2) and with the local atomic arrangements around Ti and Zr atoms which are different from those in the stable phases of the corresponding pure metals [23][24][25]52,66]. By using the experimental values of Tm, we can compare the contributions to the free energy from ∆Hmix ( Figure 2) and ∆Sconf Tm. ...
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... observed strong deviation of experimental values of Tm from those calculated by using the rule of mixtures is probably associated with a strong bonding tendency between alloying elements (inset in Figure 2) and with the local atomic arrangements around Ti and Zr atoms which are different from those in the stable phases of the corresponding pure metals [23][24][25]52,66]. By using the experimental values of Tm, we can compare the contributions to the free energy from ∆Hmix ( Figure 2) and ∆Sconf Tm. As is common in TE-TL alloys [23,25,[52][53][54]66], ∆Hmix outweighs ∆Sconf Tm due to the strong interatomic bonding in all our alloys containing Ni (x ≥ 0.125). ...
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... is common in TE-TL alloys [23,25,[52][53][54]66], ∆Hmix outweighs ∆Sconf Tm due to the strong interatomic bonding in all our alloys containing Ni (x ≥ 0.125). Since our as-cast alloy TiZrNbCu, in which ∆Sconf Tm (12.84 kJ/mole) considerably outweighs ∆Hmix (6.6 kJ/mole, Figure 2), ∆Sconf Tm /∆Hmix = 1.95, was multiphase (IM) [23], it seems that in our alloys, configurational entropy has limited influence on the formation of either an SS or an amorphous phase. ...
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... discussed in some detail elsewhere [52], there are several reasons which support BCC-like local atomic arrangements in the studied glassy alloys composed of Ti, Zr, Nb, Cu and Ni or Co and probably all other a-HEAs composed of TE and TL atoms (e.g., [51,54,56]). We note that the large difference between the sizes of TE and TL atoms [72] and the corresponding atomic size mismatch, δ, ( Figure 2) also make the formation of a BCC-like local atomic arrangement in TE-TL alloys more likely than the FCC one [12,53,54,56]. Indeed, in all ∆Hmix vs. δ diagrams, the single-phase BCC alloys are situated at larger values of δ than those with an FCC crystalline structure [10- 13]. ...
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... variation is probably the best evidence for the ideal solution behavior which marks all properties of this alloy system from the parameters associated with the atomic structure [25] to the magnetic and mechanical parameters, which will be addressed later in the next section. The ideal solution behavior in these chemically complex MGs is likely, as in binary TE-Cu MGs [66,95], caused by the moderate bonding tendency between the TE and Cu atoms (Figure 2) and the nonmagnetic nature of Cu. . Sommerfeld coefficient γ of (TiZrNbNi)1−xCux MGs vs. x. ...
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... between the dendritic (rich in Mn) and interdendritic (some excess of Fe and Co) regions in (a) disappears upon annealing in (b). Figure S2: SEM-BSE image of a surface of a (CrMnFeCo)0.92Ni0.08 alloy and corresponding elemental mappings for (a) as-cast and (b) sample annealed at 1373 K for 6 h. ...

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... Usually, conventional alloys are based on one and rarely two principal elements [2] such as silver in sterling silver, iron in steel, and nickel in superalloys, with only smaller amounts of other elements. But this traditional strategy has become less successful due to the limited number of base elements in the periodic table [3]. Fortunately, a novel class of alloys based on multi-principal elements was independently introduced in 2004 by Yeh and his collaborators to reinforce the development of new materials. ...
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... However, as noted in our previous reports, 8,25-28 a combination of experimental photoemission spectroscopy (PES) and low temperature specific heat (LTSH) studies, with the theoretical studies is required to obtain a reliable insight into the ES of the studied alloy. Indeed, a detailed insight into the ES and superconducting and other properties of binary TE-TL glassy alloys, such as Zr-TL alloys (TL=Fe, Co, Ni, Cu, Rh and Pd) has been obtained through a comparison of the calculated VB structure with the experimental one, obtained from PES. 8,29 Unfortunately, there is a very limited number of PES studies performed on HEAs and CCAs,8,[25][26][27][28]30,31 with no comparison with the theoretical electronic density of states (DOS) in these studies. ...
... In order to get some insight into the effects of Al-doping on the properties of conventional TE-TL glassy alloys we also prepared and studied three Cu-Zr based alloys, Cu45Zr55, Cu45Zr45Al10, and Cu51Zr42Al7 amorphous ribbons. For the sake of completeness these results will be compared with literature data for a similar CCAs 8,26,28,31,35 and conventional alloys. 42,43 The experimental details were described in our previous reports. ...
... 42,43 The experimental details were described in our previous reports. 8,[25][26][27][28][29]31 The valence-band structure of the as-cast Al0.5TiZrPdCuNi sample was studied by XPS. The experiments were performed at the 21-ID beamline of the NSLS II synchrotron, with 350 eV photons. ...
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... However, the basic understanding of CCAs is still quite limited, which is detrimental to their design and their application. We note that in addition to the intrinsic complexity of CCAs, the deficiencies in their current understanding also result from shortcomings in the previous research, as already noted in previously published papers [7][8][9]11,[15][16][17][18][19][22][23][24][25][26][27][28][29]. Some examples of these caveats include the highly uneven distribution of research on CCAs regarding their composition [7], the frequently unjustified use of the rule of mixtures (ROM) for the calculation of their properties [22][23][24][25][26][27][28][29][30], the excessive use of mixing entropy to explain their formation and properties [11,[15][16][17][18][19][22][23][24][25][26][27][28][29][30][31] and highly insufficient experimental studies of their electronic structure (ES) [11,22,23,28]. ...
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... (Very recently, the validity of the approximate proportionality between E and H V has been established for Ti-Zr-Nb-Cu-Ni MGs.) 88 For this type of MGs, one can also estimate the yield stress from H V 84 and, providing that one knows Poisson's ratio, calculate the values of G and B from that of E. Since the vibrational properties, in particular, the Debye temperatures, of MGs (e.g., Refs. 17, 24, and 27) are also related to the strength of interatomic bonding, the observed increase in the Debye temperature in our alloys, going from x = 0.2 to 0.43, 51 also supports the increase in the strength of interatomic bonding with increasing Co content. ...
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