本研究以實驗觀察，配合理論計算，探討超導高熵合金的Tc, Jc與Hc，以及ξ, λL與κ等超導臨界與特徵參數。試片以單一BCC為主的四元NbTaTiZr為基礎，分別添加Hf, V, Mo, Fe，透過真空電弧熔煉，得到幾種四元到七元的等莫耳高熵鑄造態合金。鑄造態合金以石英封管，經過24小時的1100 oC持溫後，水淬成為「均質化態」合金。最後，對試片進行300 K的XRD, SEM-BEI與EDS之分析、以及4.2 K至300 K的電阻率、2 K至300 K的磁化率、2 K, 5 K與300 K的磁滯曲線、與300 K的霍爾效應等之量測與分析。
鑄造態與均質化態的四元至六元合金: NbTaTiZr, NbTaTiZrHf與NbTaTiZrHfV，主要由單一的擬一元BCC「固溶體」構成。五元的NbTaTiZrMo，除了擬一元BCC相之外，還會產生HCP相。七元的NbTaTiZrHfVMo，會出現兩個BCC相，均質化後則會產生HCP相。五元的NbTaTiZrFe，除了含有擬一元BCC相之外，因小原子Fe和大原子Nb, Ta, Ti, Zr的結合焓較負，而容易形成強鍵結的Laves相。
本研究設計的大部分高熵合金，經過電阻對溫度的量測，具有超導電性；越多元，臨界溫度越低；超導轉換發生在一個溫度區間ΔTc範圍內，ΔTc < 1 K。殘餘電阻率比值(RRR)分布在1.06至1.15之間；亦即，合金的「晶格缺陷」對導電的效應，較「溫度」的效應為大。
在100 Oe外加磁場下，變換溫度，量測的鑄造態合金磁化率，除了五元含Mo合金外，皆呈現反磁性；超導臨界溫度在3.49 K至7.97 K之間。除五元與七元含Mo合金外，均質化處理後合金的Tc，均較相對應的鑄造態合金的Tc為低。影響Tc大小的因素，按重要性依次為(1)與超導相中的Nb + Ta含量、(2) e/a比值、(3)晶格扭曲大小、(4)電子態密度D(εF)、以及(5) Debye溫度θD的大小有關。本研究合金在正常態時，磁化率不隨溫度改變，且300 K磁滯曲線呈現順磁性，所以本研究正常態高熵合金為庖立順磁性(Pauli paramagnetism)。
從2 K與5 K的磁滯曲線看，鑄造態與均質化態合金，皆屬於第二類超導體。上臨界磁場Hc2在0.50 T至2.01 T之間；越多元，Hc2越高；均質化處理後，Hc2下降。臨界電流密度Jc分布在0.6 x 104 A/cm2至1.5 x 105 A/cm2之間；Jc最大者為鑄造態的NbTaTiZrHfVMo；均質化處理後，Jc下降。
300 K的霍爾效應量測顯示，鑄造態合金的載子都為「類電洞」，濃度約1022 cm-3，與過往研究之「非超導」高熵合金相似。利用載子濃度可計算λL, ξ與κ值；從κ值在2.3至12.5之間的數值看，也驗證：「超導高熵合金為第二類超導體。」

This study aims to explore superconducting HEAs and to find their critical parameters, Tc, Jc, & Hc, and characteristic parameters, ξ, λL, & κ, by experimental analyses and accompanied theoretical calculations, respectively. The materials selected were alloys that were added by Hf, V, Mo, or Fe to pseudo-unitary BCC quaternary NbTaTiZr-based HEAs, and were arc-melted in as-cast equi-molar specimens containing numbers of alloying elements from four to seven. Samples were homogenized at 1100oC for 24 h in a quartz tube filled with argon gas and then quenched in water. Both as-cast and homogenized samples were characterized by XRD, SEM-BEI, EDS, four-point probe resistivity (4.2 K ~ 300 K), magnetization vs. temperature curve (2 K ~ 300 K), magnetic hysteresis loop (2 K, 5 K and 300 K) and Hall (300 K) measurements.
NbTaTiZr, NbTaTiZrHf, & NbTaTiZrHfV are single-pseudo-unitary BCC solid solutions in both their as-cast and homogenized states. As-cast and homogenized NbTaTiZrMo alloys are composed of one BCC and one HCP. As-cast NbTaTiZrHfVMo has two BCCs, while the HCP phase will appear after homogenization. One Laves phase, which is composed of small Fe atoms and large Nb, Ta, Ti, and Zr atoms, as well as one BCC phase, occurs in NbTaTiZrFe, because the negative mixing enthalpy of Fe with Nb, Ta, Ti, and Zr are large.
Most HEAs in this study show superconductivity in resistivity vs. temperature measurements. Tc falls as number of alloying elements in alloys increases. Superconducting transitions are in temperature intervals, ΔTc, and ΔTc < 1 K. Values of residual resistivity ratio (RRR) range from 1.06 to 1.15, that is to say, the effect of “lattice defects” to electrical conducting is larger than does that of “temperature” in HEAs.
For as-cast HEAs, except NbTaTiZrMo, magnetization at 100 Oe vs. temperature curves show diamagnetism. Values of critical temperatures, Tc, range from 3.49 K to 7.97 K. Except that in NbTaTiZrMo and NbTaTiZrHfVMo, Tc of as-cast state in other alloys is higher than their corresponding Tc of homogenization.
Some factors that affect the values of Tc in superconducting HEAs are demonstrated. According to their contribution order, they are, successively, (1) Nb + Ta contents in superconducting phase, (2) e/a ratio, (3) lattice distortion, (4) electron density of state, D(εF), and (5) Debye temperature, θD. Because susceptibility of the as-cast superconducting HEAs does not change with temperature, and their magnetic hysteresis loops at 300 K show paramagnetism, accordingly, these HEAs are Pauli paramagnetism at their normal state.
From the results of magnetic hysteresis loops at 2 K and 5 K, both as-cast and homogenized alloys are type II superconductors. Values of upper critical fields, Hc2, range from 0.50 T to 2.01 T. For as-cast alloys, Hc2 increases as number of alloying elements increases. Hc2 decreases after homogenization. Values of critical current densities, Jc, range from 0.6 x 104 A/cm2 to 1.5 x 105 A/cm2. As-cast NbTaTiZrHfVMo has the largest Jc, and Jc for alloys decreases after homogenization.
The results of Hall measurement at 300 K show carriers of as-cast alloys are “hole-like”. Carrier concentrations are in order of magnitude of 1022 cm-3, which are similar to that of non-superconductig HEAs ever investigated. In this study, characteristic parameters, ξ, λL, & κ, are calculated from the above-mentioned carrier concentrations by relevant theories. Values of κ range from 2.3 to 12.5, which also show that the superconducting HEAs are type II superconductors.

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