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Superconductivity in high and medium entropy alloys based on MoReRu
Physica C: Superconductivity and its applications 566 (2019) 1353520
Contents lists available at ScienceDirect
Physica C: Superconductivity and its applications journal homepage: www.elsevier.com/locate/physc
Superconductivity in high and medium entropy alloys based on MoReRu Yea-Shine Lee , Robert J. Cava ⁎
T
Department of Chemistry, Princeton University, NJ 08544, USA
ARTICLE INFO
ABSTRACT
Keywords: High entropy alloys Medium entropy alloys Valence electron count Hexagonal close-packed structure Superconducting Transition Temperature
Hexagonal close-packed (HCP) high entropy or medium entropy alloys (HEAs or MEAs) based on alterations of the ternary superconductor Mo.33Re.33Ru.33 (valence electron count VEC = 7/atom) are tested for their potential superconductivity. Quaternary Mo.25Re.25Ru.25Rh.25 has VEC 7.5 and is superconducting at 2.5 K, implying that its electron count is too high. To decrease the VEC, Ti is added to the mixture, yielding (Mo.2375Re.2375Ru.2375Rh.2375)Ti.05 (VEC = 7.325) and (Mo.225Re.225Ru.225Rh.225)Ti.1 (VEC = 7.15), which are single phase superconducting HCP HEAs, with superconducting transition temperatures (Tc’s) of 3.6 K and 4.7 K, respectively. Materials with a significant excess of Ru over Mo.25Re.25Ru.25Rh.25 were also studied; Mo.1Re.1Ru.55Rh.1Ti.15 (VEC = 7.20) is HCP, with a Tc of 2.1 K. Decreasing the ruthenium content to Mo.105Re.105Ru.527Rh.105Ti.158 (VEC = 7.158) and Mo.118Re.118Ru.470Rh.118Ti.176 (VEC = 7.06) yields superconductivity, but with a secondary CsCl-type phase present; Tc’s are 2.2 K and 2.5 K, respectively. Upon further decrease in ruthenium content, to Mo.167Re.167Ru.25Rh.167Ti.25 (VEC = 6.674), although the Tc is relatively high at 5.5 K, three phases are present – a dominant sigma phase plus minor CsCl-type and HCP phases. These results suggest that an optimal valence electron count for this HCP based HEA/MEA alloy system is near 7.0, and that the superconducting Tc will not likely get above 10 K.
1. Introduction High entropy alloys (HEAs) are of recent interest because they can have high specific strength, excellent mechanical performance at high temperatures and pressures, simultaneous strength and ductility, and oxidation resistance [1–4]. Relevant to superconductivity, HEAs are recognized for the robustness of their superconductivity under extreme applied pressures [5]. There are several definitions available for HEAs either they are mixtures of 5 or more elements in the 5–35% range (Definition 1), or their ideal solution entropy of mixing is larger in magnitude than −1.6R (Definition 2). In this latter classification scheme, medium entropy alloys (MEAs) have entropies of mixing between −1R and −1.6R. By these definitions, the materials studied here are either high or medium entropy alloys (Table 1). Body-centered cubic (BCC) [5–8], face-centered cubic (FCC) [7,9], CsCl-type [4], and hexagonal close-packed (HCP) [10–12] HEAs have been reported. While FCC phases are more stable when the valence electron count (VEC) is greater than 8, BCC phases are stable at a lower VEC of 6.87 [8]. Between these VEC values, both BCC and FCC phases can be found [8]. Superconducting BCC HEAs reach a maximum superconducting transition temperature (Tc) at VEC = 4.7 [5]. In comparison, CsCl-type HEA superconductors have maximum Tc’s near a
⁎
VEC of 5.9 [4]. HCP HEAs, the subject of the current study, have typically been associated with a weaker solid solution strength [13]. In this work, we present single phase HCP superconducting HEAs and MEAs based on the HCP material Mo.33Re.33Ru.33 and its quaternary variant Mo.25Re.25Ru.25Rh.25. To help clarify the complex formulas, we designate the ternary basis alloy with round brackets (…), the quaternary basis alloy with square brackets […], and non-equimolar quaternary basis alloys with curly brackets {…}. We determine how changing stoichiometry affects the phases formed and the Tc’s. 2. Materials and methods All samples were synthesized by mixing stoichiometric weights of high purity commercially available constituent elements (Alfa Aesar). The materials were arc melted into a single 100 mg alloy button. Three rounds of re-arc melting were performed; between each round, the sample button was flipped. Finally, the metallic buttons were weighed to confirm a weight loss of less than 2.0%. The arc melted metallic buttons were powderized via grinding with a mortar and pestle. The powder X-ray diffraction (pXRD) data were acquired at ambient temperature on a Bruker D8 Advance Eco instrument with Cu-Kα radiation and a LynxEye-XE detector. The observed diffraction peaks were
Corresponding author. E-mail address: [email protected] (Y.-S. Lee).
https://doi.org/10.1016/j.physc.2019.1353520 Received 24 June 2019; Received in revised form 14 August 2019; Accepted 26 August 2019 Available online 26 August 2019 0921-4534/ © 2019 Elsevier B.V. All rights reserved.
Physica C: Superconductivity and its applications 566 (2019) 1353520
Y.-S. Lee and R.J. Cava
Table 1 Equivalence of different ways to write the formulas of the MEAs (medium entropy alloys) and HEAs (high entropy alloys) in this study, their Valence Electron Count per atom (VECs), the superconducting transition temperature (Tc), the superconducting phase, their ideal entropy of mixing (Σxlnx where x is the fraction of the element present) and the alloy designation as an MEA or an HEA by the atom ratio criterion (Definition 1) or the ideal mixing entropy criterion (Definition 2). Fractional Formula
“Logical” Formula
VECs
Tc
Superconducting Phase
Σxlnx
DEF 1
DEF2
Mo.33Re.33Ru.33 Mo.25Re.25Ru.25Rh.25 Mo.2375Re.2375Ru.2375Rh.2375Ti.05 Mo.225Re.225Ru.225Rh.225Ti.10 Mo.1Re.1Ru.55Rh.1Ti.15 Mo.105Re.105Ru.527Rh.105Ti.158 Mo.118Re.118Ru.470Rh.118Ti.176 Mo.167Re.167Ru.25Rh.167Ti.25
MoReRu MoReRuRh Ti.05(Mo.2375Re.2375Ru.2375Rh.2375) Ti.10(Mo.225Re.225Ru.225Rh.225) Ti.15(Mo.1Re.1Rh.1)Ru.55 Ti.15(Mo.1Re.1Rh.1)Ru.5 Ti.15(Mo.1Re.1Rh.1)Ru.4 Ti.15(Mo.1Re.1Rh.1)Ru.15
7.00 7.50 7.325 7.15 7.20 7.158 7.06 6.674
9.1 2.5 3.6 4.7 2.1 2.2 2.5 5.5
HCP HCP HCP HCP HCP HCP HCP Sigma
−1.09 −1.39 −1.52 −1.57 −1.30 −1.34 −1.42 −1.59
MEA MEA HEA HEA MEA MEA MEA HEA
MEA MEA MEA MEA MEA MEA MEA MEA
Fig. 1. pXRD spectra of the first series of materials based on alterations of MoReRu. A – (Mo.33Re.33Ru.33), B – [Mo.25Re.25Ru.25Rh.25], C – [Mo.2375Re.2375Ru.2375Rh.2375]Ti.05, and D – [Mo.225Re.225Ru.225Rh.225]Ti.10. All samples demonstrate the presence of a single homogenous HCP phase.
DynaCool equipped with a vibrating sample magnetometer (VSM) was used to perform the superconductivity tests. In order to identify the Tc of the HEA/MEA, zero-field cooled (cooled to 1.7 K) temperature-dependent magnetization measurements were implemented with an applied magnetic field of 20.0 Oe. Tc is determined as the intercept of the linear approximation of the diamagnetic state, where magnetic field is being expelled from the sample, with the normal magnetic state [4]. The mass of samples tested for magnetization analysis ranged from 29.5 mg to 56.5 mg. Therefore, a diamagnetic moment in the order of 10−3 emu signaled that the bulk sample is superconducting. A diamagnetic moment in the order of 10−4 or 10−5 emu signaled that only a partial fraction within the sample fragment is superconducting, such as an impurity phase. This distinction in the raw data was used to determine which phase is the superconducting phase in this paper.
Table 2 Series 1. Estimated lattice parameters (in Angstroms, Å) of the HCP phase in the initial series of HEA/MEA superconductors. Standard deviations are 0.003 Å for a and 0.004 Å for c. Composition
a
c
Mo.33Re.33Ru.33 Mo.25Re.25Ru.25Rh.25 Mo.2375Re.2375Ru.2375Rh.2375Ti.05 Mo.225Re.225Ru.225Rh.225Ti.10
2.76 2.74 2.74 2.752
4.44 4.39 4.40 4.40
initially modeled using the EVA software package, and unit cell refinements were performed employing the program TOPAS. A Quantum Design Physical Property Measurement Analysis 2
Physica C: Superconductivity and its applications 566 (2019) 1353520
Y.-S. Lee and R.J. Cava
Fig. 2. pXRD spectra of the second series of materials based on alterations of MoReRu. A – {Mo.1Re.1Ru.55Rh.1}Ti.15, B –{Mo.105Re.105Ru.527Rh.105}Ti.158, C – {Mo.118Re.118Ru.470Rh.118}Ti.176 and D – {Mo.167Re.167Ru.25Rh.167}Ti.25. With decreasing Ru content in B and C, the CsCl-type phase appears as a minor phase to the primary HCP structure. With further decrease in Ru content, D shows a dominant sigma phase.
giving more well-crystalized lattice structures in medium and high entropy alloys. At room temperature and pressure, pure titanium has an HCP structure; but on increasing the titanium content in the superconducting MEA alloy to [Mo.2125Re.2125Ru.2125Rh.2125]Ti.15, low intensity peaks matching a CsCl-type structure (Pm-3m) appear. This suggests a limit in the solubility of Ti in the HCP quaternary alloy superconducting phase between 0.10 and 0.15/formula unit. The factor governing the instability may be that Ti has the largest atomic radius of all the constituent elements (Ti = 147 pm; Mo = 139 pm; Re = 137 pm; Ru = 134 pm; Rh = 134 pm) [20]. This relatively large size of Ti atoms is supported by the increase in the HCP lattice parameters a and c in the HCP superconducting alloys studied here (Table 2). The effect of breaking the equimolar ratio between molybdenum, rhenium, ruthenium, and rhodium was studied as a means of subduing the CsCl-type secondary phase. Maintaining the same elements but changing the mole fractions is expected to yield results that are different from simply changing the Ti because the cocktail effect suggests that the complex interactions of the different elements present can affect the properties of the overall MEA/HEA in unpredictable ways [14]. In this vein, {Mo.1Re.1Ru.55Rh.1}Ti.15 is a single phase HCP material (Fig. 2), indicating that ruthenium can be accommodated in larger amounts in the HCP structure alloy. To explore the structural and superconducting changes to the alloy on reducing the ruthenium content as a single variable, we follow with the syntheses of {Mo.105Re.105Ru.527Rh.105}Ti.158, {Mo.118Re.118Ru.470Rh.118}Ti.176, and {Mo.167Re.167Ru.25Rh.167}Ti.25.
Table 3 Series 2. Estimated lattice parameters (in Angstroms, Å) of the HCP, CsCl-type, and σ-type phases in the second series of HEA/MEA superconductors. Standard deviations are 0.003 Å for a [CsCl], 0.004 Å for [HCP] and c[σ], and 0.006 Å for a[σ]. Composition
a [HCP]
c [HCP]
a [CsCl]
a [σ]
c [σ]
Mo.1Re.1Ru.55Rh.1Ti.15 Mo.105Re.105Ru.527Rh.105Ti.158 Mo.118Re.118Ru.470Rh.118Ti.176 Mo.167Re.167Ru.25Rh.167Ti.25
5.44 5.44 5.45 5.48
4.34 4.35 4.36 4.41
3.05 3.05 3.063
9.49
4.95
3. Results and discussion The (Mo.33Re.33Ru.33) ternary is an HCP structure (Fig. 1). The broad peaks in the pXRD pattern of the ternary are caused by the disorder in the lattice structure. The [Mo.25Re.25Ru.25Rh.25] alloy, derived from the (Mo.33Re.33Ru.33) HCP ternary alloy, is not considered an HEA in either classification scheme. This quaternary alloy has a single homogenous HCP structure according to the pXRD pattern (Fig. 1). The HCP pXRD pattern of the quaternary provides a starting point for analyzing the pXRD patterns of the more complex alloys. The [Mo.2375Re.2375Ru.2375Rh.2375]Ti.05 and [Mo.225Re.225Ru.225Rh.225]Ti.10 alloys are HEAs whose pXRD spectra are very similar to that of [Mo.25Re.25Ru.25Rh.25] (Fig. 1). Peaks of the quaternary and quinary are sharper than those of the ternary due to the entropy stabilization factor, 3
Physica C: Superconductivity and its applications 566 (2019) 1353520
Y.-S. Lee and R.J. Cava
for {Mo.167Re.167Ru.25Rh.167}Ti.25, more of the titanium atoms are in the CsCl-type structure. Since the criteria for sigma phase formation are yet to be understood, it is challenging to pin down the reason for the formation of the sigma phase, other than that it is stable for a wide arrange of metallic compositions [18,19]. The appearance of the sigma phase on reducing the ruthenium content of the HEA implies that ruthenium may play a role suppressing sigma phase formation. Magnetization tests for superconductivity performed on [Mo.25Re.25Ru.25Rh.25], [Mo.2375Re.2375Ru.2375Rh.2375]Ti.05, and [Mo.225Re.225Ru.225Rh.225]Ti.10 clearly indicate the Tc’s. The Tc values are well defined with Tc rising steadily from 2.5 K to 3.6 K to 4.7 K with increasing titanium content and decreasing VEC approaching VEC of 7.0, that of the ternary (Mo.33Re.33Ru.33) (Fig. 3). It seems such that with every 0.175 decrease in VEC of the 4/5-element HEAs/MEAs, the Tc increases by 1.1 K, suggesting a monotonic trend of VEC dependency on Tc for the Mo-Re-Ru-Rh-Ti HCP structure system. As a comparison, the (Mo.33Re.33Ru.33) ternary has a Tc of 9.1 K, significantly higher than the Tc’s of these three materials (Fig. 3): the transition from ternary (Mo.33Re.33Ru.33) to quaternary [Mo.25Re.25Ru.25Rh.25] appears to drive down the Tc regardless of titanium content. Moreover, the absence of rhodium in the ternary may be a factor that yields a high Tc in the ternary. Magnetization tests performed on the Ru-excess series, i.e. {Mo.1Re.1Ru.55Rh.1}Ti.15, {Mo.105Re.105Ru.527Rh.105}Ti.158, {Mo.118Re.118 Ru.470Rh.118}Ti.176, and {Mo.167Re.167Ru.25Rh.167}Ti.25 also show the presence of superconductivity. While the transition to the superconducting state occurs at similar temperatures of 2.2 K and 2.5 K for {Mo.105Re.105Ru.527Rh.105}Ti.158 and {Mo.118Re.118Ru.470Rh.118}Ti.176, respectively, the Tc for {Mo.167Re.167Ru.25Rh.167}Ti.25, at 5.5 K, is significantly higher (Fig. 3). On the other hand, {Mo.1Re.1Ru.55Rh.1}Ti.15 demonstrates a more anomalous magnetic behavior. This sample exits the normal magnetization states near 4.8 K, although the descent is very minor until 2.1 K, where the steep drop off to diamagnetic behavior begins (Fig. 3). There may be several causes to the minor descent between 4.8 K and 2.1 K. Lack of homogeneity or different atomic composition within the alloy may yield minor impurity phases during the synthesis of the alloy. It is possible that a minor impurity phase, compared to the bulk sample, has a higher Tc of 4.8 K, and begins acting diamagnetically first. In the pXRD pattern for {Mo.1Re.1Ru.55Rh.1}Ti.15, only a single HCP phase was detected. This supports that the minor drop in susceptibility at 4.8 K is truly due to a very minor impurity phase. Comparing the order of the diamagnetic moment from magnetization tests to the pXRD patterns for {Mo.105Re.105Ru.527Rh.105}Ti.158, {Mo.118Re.118Ru.470Rh.118}Ti.176, and {Mo.167Re.167Ru.25Rh.167}Ti.25, it is possible to attribute the Tc’s to the HCP, HCP, and sigma phase, respectively. The VEC dependency on Tc in these samples resembles the pattern identified from the characterizations of single phase HCP [Mo.25Re.25Ru.25Rh.25], [Mo.2375Re.2375Ru.2375Rh.2375]Ti.05, and [Mo.225Re.225Ru.225Rh.225]Ti.10. Although no longer fitting a monotonic of {Mo.105Re.105Ru.527Rh.105}Ti.158, linear trend, the Tc’s {Mo.118Re.118Ru.470Rh.118}Ti.176, and {Mo.167Re.167Ru.25Rh.167}Ti.25 rise from 2.2 K to 2.5 K to 5.5 K as their VEC falls.
Fig. 3. Identification of the Tc’s of the superconducting alloys. The curves are normalized by the magnetization at 1.7 K to allow a comparison of the alloys. A – the first series in which the electron count is varied by Ti content. B – the second series in which the variation of Ru content is varied to determine its effect on the Tc.
{Mo.105Re.105Ru.527Rh.105}Ti.158 and {Mo.118Re.118Ru.470Rh.118} Ti.176 show the presence of two phases: HCP and CsCl-type. The CsCltype phase peaks appear at 2θ values of 42° and 61°. The peak at 61° is very broad and of very low intensity and the peak at 42° is in close proximity with the HCP peak at a similar 2θ value (Fig. 2). This leaves a possibility that an extra peak around 42° is hidden in the higher intensity HCP peak in {Mo.1Re.1Ru.55Rh.1}Ti.15. Ti-Re [15], Ti-Ru [16], and Ti-Rh [17] are all CsCl-type binaries, and thus the eventual appearance of the CsCl-type structure in the current system is not surprising. If it is not the case, then, that excess ruthenium can quench the tendency towards CsCltype phase formation in this system, the absence of CsCl-type phase in {Mo.1Re.1Ru.55Rh.1}Ti.15, which is capable of forming the same CsCl-type titanium binary, is a phenomenon that may be due to more complex interactions between the large number of constituents present. The phase assemblage for the {Mo.167Re.167Ru.25Rh.167}Ti.25 alloy is more complex. This HEA sample gives rise to a dominant sigma phase material accommodated by some HCP and CsCl-type phases (Fig. 2). On the appearance of the sigma phase, the lattice parameter of the CsCltype structure material increases significantly (Table 3), suggesting that
4. Conclusion In this work, several single phase, homogenous HCP HEAs or MEAs were prepared. (Mo.33Re.33Ru.33), [Mo.25Re.25Ru.25Rh.25], [Mo.2375 Re.2375Ru.2375Rh.2375]Ti.05, and [Mo.225Re.225Ru.225Rh.225]Ti.10 all have an HCP structure. Furthermore, [Mo.2375Re.2375Ru.2375Rh.2375]Ti.05 and [Mo.225Re.225Ru.225Rh.225]Ti.10 were superconducting, with Tc’s of 3.6 K and 4.7 K, respectively. The mole fractions of molybdenum, rhenium, ruthenium, and rhodium were then altered to identify more single phase, homogenous HCP superconducting HEA/MEAs that are derivatives of the earlier samples. The {Mo.1Re.1Ru.55Rh.1}Ti.15 HEA appears to have an HCP structure with the bulk superconducting Tc at 2.1 K. Decreasing the 4
Physica C: Superconductivity and its applications 566 (2019) 1353520
Y.-S. Lee and R.J. Cava
ruthenium content in {Mo.105Re.105Ru.527Rh.105}Ti.158 and {Mo.118Re.118Ru.470Rh.118}Ti.176 gave rise to CsCl-type structure minor phase material accompanying the HCP structure material; they remain superconducting with Tc’s of 2.2 K and 2.5 K, respectively. Upon greater relative decrease in ruthenium content in{Mo.167Re.167Ru.25Rh.167}Ti.25, a significant structural rearrangement was observed. {Mo.167 Re.167Ru.25Rh.167}Ti.25, with Tc at 5.5 K, appeared to be mostly sigma phase with some CsCl-type and HCP phases. This study concentrated on the effect of the content of HCP Ru, which has a very low Tc, to the alloy system. Future studies may involve variation of the content of other elements to evaluate their effect on Tc. Also, future work will be of interest to determine whether increasing the Tc of this family of HCPstructure HEA alloy superconductors, through discovery of the optimal valence electron count and variation of the elemental constituents, will be successful.
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment This work was supported by the Gordon and Betty Moore Foundation grant GBMF-4412. References [1] P. Koželj, S. Vrtnik, A. Jelen, S. Jazbec, Z. Jagličić, S. Maiti, M. Feuerbacher, W. Steurer, J. Dolinšek, Discovery of a superconducting high-entropy alloy, Phys. Rev. Lett. 113 (10) (2014), https://doi.org/10.1103/PhysRevLett.113.107001. [2] J.-.W. Yeh, S.-.K. Chen, S.-.J. Lin, J.-.Y. Gan, T.-.S. Chin, T.-.T. Shun, C.-.H. Tsau, S.-.Y. Chang, Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes, Adv. Eng. Mater. 6 (5) (2004) 299–303 https://doi.org/10.1002/adem.200300567. [3] J.-.W. Yeh, Recent progress in high-entropy alloys, Ann. Chim. Sci. Matériaux 31 (6)
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Physica C: Superconductivity and its applications journal homepage: www.elsevier.com/locate/physc
Superconductivity in high and medium entropy alloys based on MoReRu Yea-Shine Lee , Robert J. Cava ⁎
T
Department of Chemistry, Princeton University, NJ 08544, USA
ARTICLE INFO
ABSTRACT
Keywords: High entropy alloys Medium entropy alloys Valence electron count Hexagonal close-packed structure Superconducting Transition Temperature
Hexagonal close-packed (HCP) high entropy or medium entropy alloys (HEAs or MEAs) based on alterations of the ternary superconductor Mo.33Re.33Ru.33 (valence electron count VEC = 7/atom) are tested for their potential superconductivity. Quaternary Mo.25Re.25Ru.25Rh.25 has VEC 7.5 and is superconducting at 2.5 K, implying that its electron count is too high. To decrease the VEC, Ti is added to the mixture, yielding (Mo.2375Re.2375Ru.2375Rh.2375)Ti.05 (VEC = 7.325) and (Mo.225Re.225Ru.225Rh.225)Ti.1 (VEC = 7.15), which are single phase superconducting HCP HEAs, with superconducting transition temperatures (Tc’s) of 3.6 K and 4.7 K, respectively. Materials with a significant excess of Ru over Mo.25Re.25Ru.25Rh.25 were also studied; Mo.1Re.1Ru.55Rh.1Ti.15 (VEC = 7.20) is HCP, with a Tc of 2.1 K. Decreasing the ruthenium content to Mo.105Re.105Ru.527Rh.105Ti.158 (VEC = 7.158) and Mo.118Re.118Ru.470Rh.118Ti.176 (VEC = 7.06) yields superconductivity, but with a secondary CsCl-type phase present; Tc’s are 2.2 K and 2.5 K, respectively. Upon further decrease in ruthenium content, to Mo.167Re.167Ru.25Rh.167Ti.25 (VEC = 6.674), although the Tc is relatively high at 5.5 K, three phases are present – a dominant sigma phase plus minor CsCl-type and HCP phases. These results suggest that an optimal valence electron count for this HCP based HEA/MEA alloy system is near 7.0, and that the superconducting Tc will not likely get above 10 K.
1. Introduction High entropy alloys (HEAs) are of recent interest because they can have high specific strength, excellent mechanical performance at high temperatures and pressures, simultaneous strength and ductility, and oxidation resistance [1–4]. Relevant to superconductivity, HEAs are recognized for the robustness of their superconductivity under extreme applied pressures [5]. There are several definitions available for HEAs either they are mixtures of 5 or more elements in the 5–35% range (Definition 1), or their ideal solution entropy of mixing is larger in magnitude than −1.6R (Definition 2). In this latter classification scheme, medium entropy alloys (MEAs) have entropies of mixing between −1R and −1.6R. By these definitions, the materials studied here are either high or medium entropy alloys (Table 1). Body-centered cubic (BCC) [5–8], face-centered cubic (FCC) [7,9], CsCl-type [4], and hexagonal close-packed (HCP) [10–12] HEAs have been reported. While FCC phases are more stable when the valence electron count (VEC) is greater than 8, BCC phases are stable at a lower VEC of 6.87 [8]. Between these VEC values, both BCC and FCC phases can be found [8]. Superconducting BCC HEAs reach a maximum superconducting transition temperature (Tc) at VEC = 4.7 [5]. In comparison, CsCl-type HEA superconductors have maximum Tc’s near a
⁎
VEC of 5.9 [4]. HCP HEAs, the subject of the current study, have typically been associated with a weaker solid solution strength [13]. In this work, we present single phase HCP superconducting HEAs and MEAs based on the HCP material Mo.33Re.33Ru.33 and its quaternary variant Mo.25Re.25Ru.25Rh.25. To help clarify the complex formulas, we designate the ternary basis alloy with round brackets (…), the quaternary basis alloy with square brackets […], and non-equimolar quaternary basis alloys with curly brackets {…}. We determine how changing stoichiometry affects the phases formed and the Tc’s. 2. Materials and methods All samples were synthesized by mixing stoichiometric weights of high purity commercially available constituent elements (Alfa Aesar). The materials were arc melted into a single 100 mg alloy button. Three rounds of re-arc melting were performed; between each round, the sample button was flipped. Finally, the metallic buttons were weighed to confirm a weight loss of less than 2.0%. The arc melted metallic buttons were powderized via grinding with a mortar and pestle. The powder X-ray diffraction (pXRD) data were acquired at ambient temperature on a Bruker D8 Advance Eco instrument with Cu-Kα radiation and a LynxEye-XE detector. The observed diffraction peaks were
Corresponding author. E-mail address: [email protected] (Y.-S. Lee).
https://doi.org/10.1016/j.physc.2019.1353520 Received 24 June 2019; Received in revised form 14 August 2019; Accepted 26 August 2019 Available online 26 August 2019 0921-4534/ © 2019 Elsevier B.V. All rights reserved.
Physica C: Superconductivity and its applications 566 (2019) 1353520
Y.-S. Lee and R.J. Cava
Table 1 Equivalence of different ways to write the formulas of the MEAs (medium entropy alloys) and HEAs (high entropy alloys) in this study, their Valence Electron Count per atom (VECs), the superconducting transition temperature (Tc), the superconducting phase, their ideal entropy of mixing (Σxlnx where x is the fraction of the element present) and the alloy designation as an MEA or an HEA by the atom ratio criterion (Definition 1) or the ideal mixing entropy criterion (Definition 2). Fractional Formula
“Logical” Formula
VECs
Tc
Superconducting Phase
Σxlnx
DEF 1
DEF2
Mo.33Re.33Ru.33 Mo.25Re.25Ru.25Rh.25 Mo.2375Re.2375Ru.2375Rh.2375Ti.05 Mo.225Re.225Ru.225Rh.225Ti.10 Mo.1Re.1Ru.55Rh.1Ti.15 Mo.105Re.105Ru.527Rh.105Ti.158 Mo.118Re.118Ru.470Rh.118Ti.176 Mo.167Re.167Ru.25Rh.167Ti.25
MoReRu MoReRuRh Ti.05(Mo.2375Re.2375Ru.2375Rh.2375) Ti.10(Mo.225Re.225Ru.225Rh.225) Ti.15(Mo.1Re.1Rh.1)Ru.55 Ti.15(Mo.1Re.1Rh.1)Ru.5 Ti.15(Mo.1Re.1Rh.1)Ru.4 Ti.15(Mo.1Re.1Rh.1)Ru.15
7.00 7.50 7.325 7.15 7.20 7.158 7.06 6.674
9.1 2.5 3.6 4.7 2.1 2.2 2.5 5.5
HCP HCP HCP HCP HCP HCP HCP Sigma
−1.09 −1.39 −1.52 −1.57 −1.30 −1.34 −1.42 −1.59
MEA MEA HEA HEA MEA MEA MEA HEA
MEA MEA MEA MEA MEA MEA MEA MEA
Fig. 1. pXRD spectra of the first series of materials based on alterations of MoReRu. A – (Mo.33Re.33Ru.33), B – [Mo.25Re.25Ru.25Rh.25], C – [Mo.2375Re.2375Ru.2375Rh.2375]Ti.05, and D – [Mo.225Re.225Ru.225Rh.225]Ti.10. All samples demonstrate the presence of a single homogenous HCP phase.
DynaCool equipped with a vibrating sample magnetometer (VSM) was used to perform the superconductivity tests. In order to identify the Tc of the HEA/MEA, zero-field cooled (cooled to 1.7 K) temperature-dependent magnetization measurements were implemented with an applied magnetic field of 20.0 Oe. Tc is determined as the intercept of the linear approximation of the diamagnetic state, where magnetic field is being expelled from the sample, with the normal magnetic state [4]. The mass of samples tested for magnetization analysis ranged from 29.5 mg to 56.5 mg. Therefore, a diamagnetic moment in the order of 10−3 emu signaled that the bulk sample is superconducting. A diamagnetic moment in the order of 10−4 or 10−5 emu signaled that only a partial fraction within the sample fragment is superconducting, such as an impurity phase. This distinction in the raw data was used to determine which phase is the superconducting phase in this paper.
Table 2 Series 1. Estimated lattice parameters (in Angstroms, Å) of the HCP phase in the initial series of HEA/MEA superconductors. Standard deviations are 0.003 Å for a and 0.004 Å for c. Composition
a
c
Mo.33Re.33Ru.33 Mo.25Re.25Ru.25Rh.25 Mo.2375Re.2375Ru.2375Rh.2375Ti.05 Mo.225Re.225Ru.225Rh.225Ti.10
2.76 2.74 2.74 2.752
4.44 4.39 4.40 4.40
initially modeled using the EVA software package, and unit cell refinements were performed employing the program TOPAS. A Quantum Design Physical Property Measurement Analysis 2
Physica C: Superconductivity and its applications 566 (2019) 1353520
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Fig. 2. pXRD spectra of the second series of materials based on alterations of MoReRu. A – {Mo.1Re.1Ru.55Rh.1}Ti.15, B –{Mo.105Re.105Ru.527Rh.105}Ti.158, C – {Mo.118Re.118Ru.470Rh.118}Ti.176 and D – {Mo.167Re.167Ru.25Rh.167}Ti.25. With decreasing Ru content in B and C, the CsCl-type phase appears as a minor phase to the primary HCP structure. With further decrease in Ru content, D shows a dominant sigma phase.
giving more well-crystalized lattice structures in medium and high entropy alloys. At room temperature and pressure, pure titanium has an HCP structure; but on increasing the titanium content in the superconducting MEA alloy to [Mo.2125Re.2125Ru.2125Rh.2125]Ti.15, low intensity peaks matching a CsCl-type structure (Pm-3m) appear. This suggests a limit in the solubility of Ti in the HCP quaternary alloy superconducting phase between 0.10 and 0.15/formula unit. The factor governing the instability may be that Ti has the largest atomic radius of all the constituent elements (Ti = 147 pm; Mo = 139 pm; Re = 137 pm; Ru = 134 pm; Rh = 134 pm) [20]. This relatively large size of Ti atoms is supported by the increase in the HCP lattice parameters a and c in the HCP superconducting alloys studied here (Table 2). The effect of breaking the equimolar ratio between molybdenum, rhenium, ruthenium, and rhodium was studied as a means of subduing the CsCl-type secondary phase. Maintaining the same elements but changing the mole fractions is expected to yield results that are different from simply changing the Ti because the cocktail effect suggests that the complex interactions of the different elements present can affect the properties of the overall MEA/HEA in unpredictable ways [14]. In this vein, {Mo.1Re.1Ru.55Rh.1}Ti.15 is a single phase HCP material (Fig. 2), indicating that ruthenium can be accommodated in larger amounts in the HCP structure alloy. To explore the structural and superconducting changes to the alloy on reducing the ruthenium content as a single variable, we follow with the syntheses of {Mo.105Re.105Ru.527Rh.105}Ti.158, {Mo.118Re.118Ru.470Rh.118}Ti.176, and {Mo.167Re.167Ru.25Rh.167}Ti.25.
Table 3 Series 2. Estimated lattice parameters (in Angstroms, Å) of the HCP, CsCl-type, and σ-type phases in the second series of HEA/MEA superconductors. Standard deviations are 0.003 Å for a [CsCl], 0.004 Å for [HCP] and c[σ], and 0.006 Å for a[σ]. Composition
a [HCP]
c [HCP]
a [CsCl]
a [σ]
c [σ]
Mo.1Re.1Ru.55Rh.1Ti.15 Mo.105Re.105Ru.527Rh.105Ti.158 Mo.118Re.118Ru.470Rh.118Ti.176 Mo.167Re.167Ru.25Rh.167Ti.25
5.44 5.44 5.45 5.48
4.34 4.35 4.36 4.41
3.05 3.05 3.063
9.49
4.95
3. Results and discussion The (Mo.33Re.33Ru.33) ternary is an HCP structure (Fig. 1). The broad peaks in the pXRD pattern of the ternary are caused by the disorder in the lattice structure. The [Mo.25Re.25Ru.25Rh.25] alloy, derived from the (Mo.33Re.33Ru.33) HCP ternary alloy, is not considered an HEA in either classification scheme. This quaternary alloy has a single homogenous HCP structure according to the pXRD pattern (Fig. 1). The HCP pXRD pattern of the quaternary provides a starting point for analyzing the pXRD patterns of the more complex alloys. The [Mo.2375Re.2375Ru.2375Rh.2375]Ti.05 and [Mo.225Re.225Ru.225Rh.225]Ti.10 alloys are HEAs whose pXRD spectra are very similar to that of [Mo.25Re.25Ru.25Rh.25] (Fig. 1). Peaks of the quaternary and quinary are sharper than those of the ternary due to the entropy stabilization factor, 3
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for {Mo.167Re.167Ru.25Rh.167}Ti.25, more of the titanium atoms are in the CsCl-type structure. Since the criteria for sigma phase formation are yet to be understood, it is challenging to pin down the reason for the formation of the sigma phase, other than that it is stable for a wide arrange of metallic compositions [18,19]. The appearance of the sigma phase on reducing the ruthenium content of the HEA implies that ruthenium may play a role suppressing sigma phase formation. Magnetization tests for superconductivity performed on [Mo.25Re.25Ru.25Rh.25], [Mo.2375Re.2375Ru.2375Rh.2375]Ti.05, and [Mo.225Re.225Ru.225Rh.225]Ti.10 clearly indicate the Tc’s. The Tc values are well defined with Tc rising steadily from 2.5 K to 3.6 K to 4.7 K with increasing titanium content and decreasing VEC approaching VEC of 7.0, that of the ternary (Mo.33Re.33Ru.33) (Fig. 3). It seems such that with every 0.175 decrease in VEC of the 4/5-element HEAs/MEAs, the Tc increases by 1.1 K, suggesting a monotonic trend of VEC dependency on Tc for the Mo-Re-Ru-Rh-Ti HCP structure system. As a comparison, the (Mo.33Re.33Ru.33) ternary has a Tc of 9.1 K, significantly higher than the Tc’s of these three materials (Fig. 3): the transition from ternary (Mo.33Re.33Ru.33) to quaternary [Mo.25Re.25Ru.25Rh.25] appears to drive down the Tc regardless of titanium content. Moreover, the absence of rhodium in the ternary may be a factor that yields a high Tc in the ternary. Magnetization tests performed on the Ru-excess series, i.e. {Mo.1Re.1Ru.55Rh.1}Ti.15, {Mo.105Re.105Ru.527Rh.105}Ti.158, {Mo.118Re.118 Ru.470Rh.118}Ti.176, and {Mo.167Re.167Ru.25Rh.167}Ti.25 also show the presence of superconductivity. While the transition to the superconducting state occurs at similar temperatures of 2.2 K and 2.5 K for {Mo.105Re.105Ru.527Rh.105}Ti.158 and {Mo.118Re.118Ru.470Rh.118}Ti.176, respectively, the Tc for {Mo.167Re.167Ru.25Rh.167}Ti.25, at 5.5 K, is significantly higher (Fig. 3). On the other hand, {Mo.1Re.1Ru.55Rh.1}Ti.15 demonstrates a more anomalous magnetic behavior. This sample exits the normal magnetization states near 4.8 K, although the descent is very minor until 2.1 K, where the steep drop off to diamagnetic behavior begins (Fig. 3). There may be several causes to the minor descent between 4.8 K and 2.1 K. Lack of homogeneity or different atomic composition within the alloy may yield minor impurity phases during the synthesis of the alloy. It is possible that a minor impurity phase, compared to the bulk sample, has a higher Tc of 4.8 K, and begins acting diamagnetically first. In the pXRD pattern for {Mo.1Re.1Ru.55Rh.1}Ti.15, only a single HCP phase was detected. This supports that the minor drop in susceptibility at 4.8 K is truly due to a very minor impurity phase. Comparing the order of the diamagnetic moment from magnetization tests to the pXRD patterns for {Mo.105Re.105Ru.527Rh.105}Ti.158, {Mo.118Re.118Ru.470Rh.118}Ti.176, and {Mo.167Re.167Ru.25Rh.167}Ti.25, it is possible to attribute the Tc’s to the HCP, HCP, and sigma phase, respectively. The VEC dependency on Tc in these samples resembles the pattern identified from the characterizations of single phase HCP [Mo.25Re.25Ru.25Rh.25], [Mo.2375Re.2375Ru.2375Rh.2375]Ti.05, and [Mo.225Re.225Ru.225Rh.225]Ti.10. Although no longer fitting a monotonic of {Mo.105Re.105Ru.527Rh.105}Ti.158, linear trend, the Tc’s {Mo.118Re.118Ru.470Rh.118}Ti.176, and {Mo.167Re.167Ru.25Rh.167}Ti.25 rise from 2.2 K to 2.5 K to 5.5 K as their VEC falls.
Fig. 3. Identification of the Tc’s of the superconducting alloys. The curves are normalized by the magnetization at 1.7 K to allow a comparison of the alloys. A – the first series in which the electron count is varied by Ti content. B – the second series in which the variation of Ru content is varied to determine its effect on the Tc.
{Mo.105Re.105Ru.527Rh.105}Ti.158 and {Mo.118Re.118Ru.470Rh.118} Ti.176 show the presence of two phases: HCP and CsCl-type. The CsCltype phase peaks appear at 2θ values of 42° and 61°. The peak at 61° is very broad and of very low intensity and the peak at 42° is in close proximity with the HCP peak at a similar 2θ value (Fig. 2). This leaves a possibility that an extra peak around 42° is hidden in the higher intensity HCP peak in {Mo.1Re.1Ru.55Rh.1}Ti.15. Ti-Re [15], Ti-Ru [16], and Ti-Rh [17] are all CsCl-type binaries, and thus the eventual appearance of the CsCl-type structure in the current system is not surprising. If it is not the case, then, that excess ruthenium can quench the tendency towards CsCltype phase formation in this system, the absence of CsCl-type phase in {Mo.1Re.1Ru.55Rh.1}Ti.15, which is capable of forming the same CsCl-type titanium binary, is a phenomenon that may be due to more complex interactions between the large number of constituents present. The phase assemblage for the {Mo.167Re.167Ru.25Rh.167}Ti.25 alloy is more complex. This HEA sample gives rise to a dominant sigma phase material accommodated by some HCP and CsCl-type phases (Fig. 2). On the appearance of the sigma phase, the lattice parameter of the CsCltype structure material increases significantly (Table 3), suggesting that
4. Conclusion In this work, several single phase, homogenous HCP HEAs or MEAs were prepared. (Mo.33Re.33Ru.33), [Mo.25Re.25Ru.25Rh.25], [Mo.2375 Re.2375Ru.2375Rh.2375]Ti.05, and [Mo.225Re.225Ru.225Rh.225]Ti.10 all have an HCP structure. Furthermore, [Mo.2375Re.2375Ru.2375Rh.2375]Ti.05 and [Mo.225Re.225Ru.225Rh.225]Ti.10 were superconducting, with Tc’s of 3.6 K and 4.7 K, respectively. The mole fractions of molybdenum, rhenium, ruthenium, and rhodium were then altered to identify more single phase, homogenous HCP superconducting HEA/MEAs that are derivatives of the earlier samples. The {Mo.1Re.1Ru.55Rh.1}Ti.15 HEA appears to have an HCP structure with the bulk superconducting Tc at 2.1 K. Decreasing the 4
Physica C: Superconductivity and its applications 566 (2019) 1353520
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ruthenium content in {Mo.105Re.105Ru.527Rh.105}Ti.158 and {Mo.118Re.118Ru.470Rh.118}Ti.176 gave rise to CsCl-type structure minor phase material accompanying the HCP structure material; they remain superconducting with Tc’s of 2.2 K and 2.5 K, respectively. Upon greater relative decrease in ruthenium content in{Mo.167Re.167Ru.25Rh.167}Ti.25, a significant structural rearrangement was observed. {Mo.167 Re.167Ru.25Rh.167}Ti.25, with Tc at 5.5 K, appeared to be mostly sigma phase with some CsCl-type and HCP phases. This study concentrated on the effect of the content of HCP Ru, which has a very low Tc, to the alloy system. Future studies may involve variation of the content of other elements to evaluate their effect on Tc. Also, future work will be of interest to determine whether increasing the Tc of this family of HCPstructure HEA alloy superconductors, through discovery of the optimal valence electron count and variation of the elemental constituents, will be successful.
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