Silicide Clusters, Be nSi n, Be 2n Si n (n = 1 – 4) and

possible MgB 2-like Superconductivity in some of them

O. P. Isikaku-Ironkwe 1, 2 1The Center for Superconductivity Technologies (TCST) Department of Physics, Michael Okpara University of Agriculture, Umudike (MOUAU), Umuahia, Abia State, Nigeria and 2RTS Technologies, San Diego, CA 92122

Abstract

The symmetry of the Periodic Table makes it possible to predict certain properties of similar elements and compounds using one of them as a template. Magnesium diboride, MgB 2, presents a useful template in the search for similar materials. Starting from , valence electron and atomic number equivalency, we identify many potential similar materials. One of them is the beryllium silicide, Be 2nSi n cluster system. We establish that though not yet produced in bulk, Be 2Si exists. We show from symmetry principles that beryllium silicide and some of its clusters will be MgB 2-like superconductors with Tcs close to or higher than 39K.

Introduction The discovery of superconductivity in MgB 2 in 2001 [1] came as a surprise to many researchers in superconductivity. A bigger surprise also came when application of electronic structure principles [2 - 5] and crystal symmetry concepts [6 – 13] failed to produce MgB 2-like superconductors with Tcs close to the 39K of MgB 2. In searching for MgB 2-like superconductors and other superconductors, we decided to look for materials specific correlations, often ignored by standard theories of superconductivity. Some of the chemical correlations with superconductivity are electronegativity, valence electron count, atomic number and formula weight. Our studies [14 - 18] indicate that they play a very significant role in the search for superconductivity. In this paper, we first review studies [19 – 24] on the existence, properties and preparation of beryllium silicide clusters. We then use the material specific characterization system (MSCD), symmetry rules [15], and the Tc equation to compare the material specific characteristics of Be2n Si n clusters which have same valence electron count and atomic number as MgB 2 and to estimate the Tc of Be 2Si, based on this symmetry.

Beryllium Silicide Studies Group IIA-IV alkaline-earth silicides have been studied by the ab initio pseudopotential method [19] and the full-potential linearized augmented plane wave method [20], within the local density approximation (LDA). This family is found to have an anti-fluorite structure and semiconducting. Beryllium silicide, Be 2Si, a member of this family was however computed to be a metallic [19], antifluorite, with Si atoms in face-centered cubic structure and the Be atoms arranged around them in tetrahedral structure. In addition, the Be-Si bonding has been studied [21, 22] by density functional theory (DFT) Monte Carlo simulated annealing (DFT- MCSA) methods and cluster geometries discovered. In particular, the structures and energetics of Be nSi n and Be 2n Si n (n = 1 – 4) clusters [21, 22] strongly suggest that they could be explored for superconductivity like the -60 fullerene [23]. Hite et al [24] have explored the possible formation of Beryllium silicide. Using scanning tunneling microscopy (STM) and photoelectron spectroscopy, they studied the nucleation, growth and structure of beryllium on Si(111)-(7x7)surface at temperatures ranging from 120K to 1175K. They produced amorphous ring nanocluster structure with Be-Si bond length less than 2.5 A of Beryllium silicide. Further studies by Saranin et al. [25] confirmed the cluster structure and discovered four types of nanostructure arrays formed by Be interaction with Si(111)-(7x7) surface in a not fully understood “self assembly” process.

MSCD of Be 2Si, Symmetry Rules and Tc Estimation In [15, 16] we showed that a material may be characterized in terms of averages of electronegativity, ,,,, valence electron count, Ne, atomic number, Z, and formula weight, Fw, in a method described as material specific characterization dataset (MSCD). MSCD makes it possible to quickly compare two or more materials. Table 1 gives the MSCD of MgB 2, LiBSi and Be 2nSi n clusters. We also showed in [15 ] that the maximum transition temperature, Tc, of a superconductor can be estimated in material specific properties of electronegativity, , valence electrons, Ne, atomic number, Z, and a parameter, Ko by the equation: T = KKKooo (1) c where KKKooo is a parameter that determines the value of Tc. Ko = n(Fw/Z) and n is dependent on the family of superconductors. Fw represents formula weight of the superconductor. For

MgB 2, with Tc of 39K and Fw/Z of 6.26, Ko = 22.85, making n = 3.65. Note that the MSCDs of

LiBSi and Be 2Si are identical. One of the symmetry rules [15] states that two materials with exactly identical MSCDs will have the same Tc. Following this symmetry rule and the MSCD displayed in Table 1, we estimate that the Tc of Be2Si will be the same as that of LiBSi [17], which is 36K.

Discussion Even though bulk Be 2Si has yet to be produced and fully characterized, recent computations

[19, 21, 22] and experiments [24, 25] strongly suggest that beryllium silicide exists. Be 2Si is an image of LiBSi, formed by replacing LiB with 2 atoms of Be. Thus Be 2Si and LiBSi have the same electronegativity, valence electrons and atomic number. Be 2Si also has the same valence electron count and atomic number as MgB 2 making it an MgB 2-like material. From the symmetry rules for searching for superconductors [15], materials with the same valence electron count and same atomic number will have Tcs proportional to their . The challenge of producing bulk Be 2Si is akin to that of producing bulk C 60 fullerene [23, 26]. We note too that well-ordered binary cluster Cs 3C60 attained a Tc of 38K

[27]. It will be interesting if well-ordered Be 2Si could achieve a higher Tc than the 38K of

Cs 3C60 . The verification (or otherwise) of superconductivity in Be 2Si and some of its clusters will be a strong test of the symmetry rules [15, 18] for searching for superconductors.

Conclusion We have studied the hypothetical cluster compound beryllium silicide. Using symmetry rules for searching for equivalent superconductors and MgB 2 as a template, we find that Be 2Si,

Be 4Si 2, Be 8Si 4 are copies of MgB 2 but with reduced electronegativity. Be 2Si too is very similar to LiBSi, which we had earlier shown [17] should be superconducting. We conclude that Be 2Si will be found to be superconducting with a Tc of about 36.2K. The clusters: Be 4Si 2, Be 6Si 3,

Be 8Si 4 may have Tcs higher than MgB 2 since they have higher Fw/Z ratio [15].

Acknowledgements The author acknowledges financial support for this research from M.J. Schaffer, then at General Atomics, enlightening discussions with M.B. Maple at UC San Diego and literature support from J.R. O’Brien at Quantum Design, San Diego .

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TABLE

Table 1: MSCDs of MgB2, LiBSi and Beryllium Silicide Clusters Be 2n Si n (n = 1 – 4) computed from equations in ref. [15] and equation (1) in this paper. Note that LiBSi and Be2Si have exactly the same electronegativity, , valence electron count, Ne, atomic number Z and almost the same formula weight Fw. Symmetry rule given in [15] predicts that their Tcs will be about the same.

Material Ne Z Ne / Fw Fw/Z Tc(K) Ko

1 MgB 2 1.7333 2.6667 7.3333 0.9847 45.93 6.263 39 22.85

2 LiBSi 1.6 2.6667 7.3333 0.9847 45.84 6.251 35.95 22.85

3 Be 2Si 1.6 2.6667 7.3333 0.9847 46.11 6.288 36.2 22.85

4 Be 4S2 1.6 2.6667 7.3333 0.9847 92.22 12.58 >39? 22.85?

5 Be 6S3 1.6 2.6667 7.3333 0.9847 138.33 18.86 >39? 22.85?

6 Be 8S4 1.6 2.6667 7.3333 0.9847 184.44 25.15 >39? 22.85?