Role of Ionization Energies in Tri Hydride Superconductors K Subbaravamma, S Kaleemulla, G. Rao

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K Subbaravamma, S Kaleemulla, G. Rao. Role of Ionization Energies in Tri Hydride Superconductors. Mechanics, Materials Science & Engineering Journal, Magnolithe, 2017, ￿10.2412/mmse.45.73.186￿. ￿hal-01966338￿

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Role of Ionization Energies in Tri Hydride Superconductors 1 K. Subbaravamma1,a, S. Kaleemulla2, G. Venugopal Rao3

1 – Ranjani, Anupuram, Tamilnadu, India 2 – Centre for Crystal Growth, VIT University, Vellore, Tamilnadu, India 3 – Materials Physics Division, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamilnadu, India a – [email protected]

DOI 10.2412/mmse.45.73.186 provided by Seo4U.link

Keywords: superconductivity, tri hydrides, ionization energies, critical temperature, high pressure.

ABSTRACT. Hydrogen dense materials of the form AH3 (where A can be Al, Sc, Ga, S, Cr, Se, Y, La, P) are gaining interest with respect to study high temperature superconductivity at pressure with the reach of available techniques. In the present work, we have used first principle calculations to correlate the ionization energies and the superconducting critical temperatures for the metal hydrides. Using a linear regression, a straight line fit of the correlation implies a certain limit for sum of the ionization energy needed for superconductivity to occur. Alkali C60 superconductors shown similar nature with ionization energy.

Introduction. Superconductivity was first discovered in 1911 by Kamerling Onnes. In a span of 105 years greatest advances, cuprates, C60 compounds, pnictides and other systems were found. Nearly four decades ago hydrogen was suggested to be a superconductor under high pressure. However further calculations showed that highest critical temperatures possible with metallic hydrogen. Hydrogen being lightest, possess very high vibrational frequencies, a strong electron phonon interaction, hence high transition temperature Tc is expected [1]. Since then many scientists are working on metallization of hydrogen, by doping the heavier elements into hydrogen. Hydrogen rich compounds are considered to metalize at lower pressures than pure hydrogen. In this process number of hydrogen rich materials are predicted. A room temperature superconductor probably is the most needed system in science and technology. Primary role of pressure application is to modify the energies of the levels in a system, while the effect of a change in temperature is to modify the occupation of the energy levels [2]. Hence the critical temperature of a superconductor depends on both lattice and electronic properties, one expects pressure to have profound effect on transition temperatures Tc. Enhancement of Tc under pressure is experienced already in High Temperature Superconductor (HTSC) materials. Ionization potentials influence band structure, i.e., density of states. Hence ionization energies contribute to transition temperatures (Tc) of superconductors, similar studies for C60 superconductors [3] and for HTSC [4] were published. Role of ionization energies are more important in atomic level superconductors. Materials undergo structural changes on applied pressures. The pure material gallium is superconducting in four different crystal structures with transition temperature range from 1 K to 8 K. In contrast, with same lattice constant, Niobium and Tantalum have identical crystal structure (bcc), but their transition temperatures differ by a factor of two. Obviously, the structure of the material and the electron configuration are important for the understanding of superconducting phenomenon. Hydrogen, isoelectronic to alkali metal, is insulating under ambient conditions. Since it has high binding energy, high pressure is required to attain metallic phase.

1 © 2017 The Authors. Published by Magnolithe GmbH. This is an open access article under the CC BY-NC-ND license http://creativecommons.org/licenses/by-nc-nd/4.0/

MMSE Journal. Open Access www.mmse.xyz Mechanics, Materials Science & Engineering, December 2017 – ISSN 2412-5954

Emergence of high temperature superconducting phases in several pressurized hydrogen dense materials have been predicted [5]. Until now, ionization energies are correlated to C60 compound superconductors. No study has been carried out on how the superconducting critical temperature evolves with ionization energies in tri hydrides and tetra hydrides. Hence we considered the examples of AH3 series of hydrogen dense materials with preliminary calculations. In this paper, we consider set of tri hydrides under pressure and attempt to identify the role of ionization energies in effecting superconducting transition temperature. Preliminary results are presented here. Results and discussion. First we discuss, element wise pressure effects, then trihydride compounds taken from literature. The variation of critical temperature (Tc) with pressure for some of the elements is shown in figure 1.

18 S

15 Sc

La 12 P

9

6 Se Y Critical Temperature (K) 3 Al 0 0 20 40 60 80 100 120 140 160 Pressure (GPa)

Fig. 1. Pressure dependence of critical temperature for La, Sc, P, S, Se, Y and Al elements.

The transition temperature with respect to pressure has an increasing nature except for Aluminum and Selenium. Phosphorus is having steeper increase where as Sulfur shows slow increase in transition temperature as pressure increases [6]. Many elements show superconductivity under pressure with varying critical temperature, eg., Sc, Y, Se, S and P show superconductivity under high pressure. Ga, Al, Cr and La show superconductivity at ambient pressures. Table 1 gives the data of superconducting transition temperatures, corresponding pressures and ionization energies of above mentioned elements [6]. Table 1 depicts that as the ionization energy increases, increasing trend in transition temperature is observed except for Sc and La. It is to be noted that all these elements exhibit transition temperature at different pressures.

MMSE Journal. Open Access www.mmse.xyz Mechanics, Materials Science & Engineering, December 2017 – ISSN 2412-5954

Table 1. Ionization energy (Eion), critical temperature (Tc) and pressure of some elements.

Element Eion (eV) Tc (K) Pressure(GPa) Sc 6.5613 0.34 21 Ga 5.9991 1.08 1 atm Al 5.9856 1.18 1 atm Y 6.2171 2.8 15 Cr 6.7663 3 1 atm La 5.5767 6 1 atm Se 9.7521 7 13 S 10.3597 17 160 P 10.4864 18 30

The pressure effects of trihydrides are presented here. The variation of critical temperature (Tc) with increasing pressure has been shown in Figure 2 for SH3, ScH3, CrH3, SeH3, YH3, LaH3 and PH3. The data has been collected from the references [5, 7, 8, 9]. All the tri hydrides mentioned in this figure show a decreasing trend of critical temperature with increasing pressure, except for PH3, for which an increase in critical temperature is seen with increasing pressure.

220 ScH 200 3 YH 180 3

(K)

) LaH c 160 3

T ( SeH 140 3 SH 120 3 CrH 100 3 PH 80 3 60 40 20

Critical Temperature 0 0 50 100 150 200 250 300 Pressure (GPa)

Fig. 2. Pressure dependence of critical temperature for AH3 compounds.

Now we study, nature of ionization energies to transition temperature of tri hydrides with preliminary calculations. We considered ionization energies of the isolated atoms. In molecules, calculations of ionization energies are complicated process. Table 2 (Row wise) and Table 3 (Column wise) gives the summary of different tri hydrides with their ionization energy sum (Eion), pressure and critical temperature (Tc). The data are from Ref. [7 to 14].

MMSE Journal. Open Access www.mmse.xyz Mechanics, Materials Science & Engineering, December 2017 – ISSN 2412-5954

Table 2. Row wise ionization energy sum (Eion), pressure and critical temperature (Tc) in AH3 (A = Sc, Cr, Ga, Se, Al, P and S) compounds. 4th Row 3rd Row

Material ScH3 CrH3 GaH3 SeH3 AlH3 PH3 SH3

Eion (eV) –44.1168 –54.2108 –57.2388 –61.7611 –53.2606 –60.4580 –68.4860 Pressure (GPa) 18 81 120 120 110 207 150

Tc (K) 19.3 37.1 89.78 110 24 103 203

Table 3. Column wise ionization energy sum (Eion), pressure and critical temperature (Tc) in AH3 (A = Sc, Y, La, Al, Ga, S and Se) compounds. 3rd Column 13th Column 16th Column

Material ScH3 YH3 LaH3 AlH3 GaH3 SH3 SeH3

Eion (eV) –44.1168 –38.9601 –35.8122 –53.2606 –57.2388 –68.4860 –61.7611 Pressure (GPa) 18 17.7 11.0 110 120 150 120

Tc (K) 19.3 40 22.5 24 89.78 203 110

The ionization energy sum ranging from –35.812 eV to –68.486 eV, spanning about 32.674 eV and corresponding critical temperature ranging from 19.3 K to 203 K, spanning about 183.7 K is observed from Table 2 and Table 3. From Table 2, it is worth mentioning that for the tri hydrides of Sc, Cr, Ga and Se, the transition temperature increases with decreasing ionization energies. Similar trend is observed for the tri hydrides of Al, P and S.

A decrease in transition temperature with increasing ionization energy for YH3 and LaH3, except for ScH3 is noticed from Table 3. Similar trend is observed for SH3 and SeH3, where as for AlH3 and GaH3, the transition temperature increases with decreasing ionization energy.

Figure 3 shows the sum of ionization energies Eion for different tri hydrides versus the transition temperature Tc. Using a linear regression, data fits into the range 19 K  Tc  203 K. The slope of the -3 correlation has a value of approximately –147.76×10 eV/K or –1719 KB and an ordinate intercept value of –42.05 eV.

The trend of Tc in YH3 with increasing pressure is different from that in pure Y, while the change of the d state in pure Y is the same as in fcc-YH3, indicating different origins of superconductivity in Y and YH3. In the present paper, the ordinate intercept demonstrates that there is an absolute value of ionization threshold to obtain superconductivity. Theoretical studies of YH3 and LaH3 show deviation from this threshold value. However, rest of the samples lie within this range. Experimental results may help to resolve this discrepancy.

MMSE Journal. Open Access www.mmse.xyz Mechanics, Materials Science & Engineering, December 2017 – ISSN 2412-5954

Temperature (K) 0 40 80 120 160 200 0

 147.76 x 10-3 eV/K . T  42.05 eV ion c -20 -18  1719 . K T  6.74 x 10 J ion B c

-40

(eV)

ion -60

E



-80

-100

Fig. 3. Relationship between ionization energy sum and critical temperature. Data points are from Table 2. The slope is calculated for all data points.

Summary. An effort is made for correlation between ionization energies and the superconducting critical temperature of metal hydrides, using preliminary calculations. Fitting the data of Eion versus Tc for tri hydrides using linear regression, gives an ordinate intercept value of –42.05 eV, which demonstrates that to obtain superconductivity for the hydrides studied, there is an absolute value of ionization threshold. We continue to do systematic further study. This work may provide piece of advice for future understanding of the superconductivity under pressure with respect to ionization energies, in particular atomic level superconductors. References [1] N.W. Ashcroft (1968), Metallic Hydrogen: A High-Temperature Superconductor? Phys. Rev. Lett. 21, 1748. [2] H.G. Drickamer (1961), Optical studies at high pressure, in F.P. Bundy, W.R. Hibbard Jr., H. M. Strong Eds., Progress in very high pressure research, pp. 16, John Wiley & Sons, Inc., New York. [3] Florian Hetfleisch, Marco Stepper, Hans-Peter Roeser, Artur Bohr, Juan Santiago Lopez, Mojtaba Mashmool and Susanne Roth, Physica C 513 (2015) 1. [4] H.P. Roeser, D.T. Haslam, J.S. Lopaz, M. Stepper, M.F. von Schoenermark, F.M. Huber, A.S. Nikoghosyan (2011), Electronic Energy Levels in High-Temperature Superconductors, J. Supercond. Nov. Magn., 24(5), 1443-1451, DOI 10.1007/s10948-010-0850-5 [5] D.Y. Kim, R.H. Scheicher, H. Mao, T.W. Kang, R. Ahuja (2010), General trend for pressurized superconducting hydrogen-dense materials, Proc. Natl. Acad. Sci., 107 (7), 2793-2796, DOI 10.1073/pnas.0914462107 [6] Cristina Buzea and Kevin Robbie, Supercond. Sci. Technol. 18 (2005) R1-R8. [7] A. Drozdov, M.I. Eremets, I.A. Troyan, arXiv:1508.06224 (2015), Superconductivity above 100 K in PH3 at high pressures. [8] S. Zhang, Y. Wang, J. Zhang, H. Liu, X. Zhong, H. Song, G. Yang, L. Zhang, Y. Ma (2015), Phase Diagram and High-Temperature Superconductivity of Compressed Selenium Hydrides, Scientific Reports 5, 15433, DOI 10.1038/srep15433

MMSE Journal. Open Access www.mmse.xyz Mechanics, Materials Science & Engineering, December 2017 – ISSN 2412-5954

[9] S. Yu, X. Jia, G. Frapper, D. Li, A.R. Oganov, Q. Zeng, L. Zhang (2015), Pressure-driven formation and stabilization of superconductive chromium hydrides, Scientific Reports 5. 17764, DOI 10.1038/srep17764 [10] A.P. Durajski, R. Szczesniak, Superconducting state above the boiling point of liquid nitrogen in the GaH3 compound, Supercond. Sci. Technol. 27 (2014) 11501, DOI 10.1088/0953- 2048/27/1/015003. [11] A. Drozdov, M.I. Eremets, I.A. Troyan, V. Ksenofontov, S.I. Shylin (2015), Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system, Nature, 525 73-76, DOI 10.1038/nature14964 [12] D.Y. Kim, R.H. Scheicher, R. Ahuja (2009), Predicted high-temperature superconducting state in the hydrogen-dense transition-metal hydride YH3 at 40 K and 17.7 GPa, Phys. Rev. Lett. 103 (7) 077002, DOI 10.1103/PhysRevLett.103.077002 [13] I. Goncharenko, M.I. Eremets, M. Hanfland, J.S. Tse, M. Amboage, Y. Yao, I.A. Trojan (2008), Pressure-induced hydrogen-dominant metallic state in aluminum hydride, Phys. Rev. Lett. 100 (4), 045504, DOI 10.1103/PhysRevLett.100.045504 [14] A.P. Durajski, R. Szczesniak, Superconducting state above the boiling point of liquid nitrogen in the GaH3, compound, Supercond. Sci. Technol. 27, (2014) 015003, DOI 10.1088/09532048/27/1/015003

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