Lead , Tin , and Bismuth as the Guest Atoms in Super-electride Drude Metals

 

I've long had a particular fondness for lead and tin as metal elements . My interest in them probably began when I was around 1214 years old or so . My parents gave me a kit for making toy soldiers from lead , tin , or pewter , and I created entire armies from them , complete with cannons and airplanes . They have long since disappeared , but I still have one last remaining metal soldier , cast from pure tin , as a souvenir from that distant era :

In the past few months I've been exploring an entirely new field of inorganic chemistry , that of the Drude electron materials (as I've referred to them in previous web pages) . They are hypothesized to contain unassociated , free electrons Drude electron gas in their crystal lattices . These electrons are rather extraordinary in that they have no orbital connection to their parent atomic kernels . The Drude electrons are totally free in the lattice , and if they can move through it under an applied potential difference , they should do so in a resistance-free manner .

Drude electron materials actually exist at this very moment . Many larger hospitals (at least , in North America and in western Europe) are equipped with a Magnetic Resonance Imaging (MRI) machine , which somewhat resembles X-ray machines in being able to photograph images of the inside of the human body . This is accomplished by immersing the entire patient's body in a powerful magnetic field , which is produced by coils of a special metal surrounding the MRI chamber in which the patient lies during the scanning procedure . These metal coils are composed of a superconducting intermetallic compound made of niobium and titanium (Nb0.6Ti0.4 ; Tc = 9.8 K) , or of niobium and tin (Nb3Sn ; Tc = 18 K) , immersed in a bath of ultracold (4.2 K) liquid helium . Such superconducting coils are able to produce the intense magnetic fields required to completely saturate the human body .

The free electrons in all superconductors , while in their superconducting state , are hypothesized to be Drude electron gas , and all superconductors , in their superconducting state , are Drude electron materials . The niobium-titanium and niobium-tin MRI superconducting coils , cooled below their transition temperatures in liquid helium , are in their superconducting state and are therefore the presumed Drude electron materials . When they are warmed above their transition temperatures these metals will be in their normal electrically conducting state . Their free electrons will have been recaptured by their parent Nb , Ti , and Sn atomic kernels and will be associated with them in their respective atomic orbitals . Those valence shell orbitals can overlap continuously throughout the lattice to form the metallic bondconduction band in it . The conduction electrons in the metallic bond are regulated by Fermi-Dirac statistics , which assigns them to vast numbers of energy levels in the lattice . The free electrons are now Fermi-Dirac electron gas , which is found in all the common metals of our daily experience , and in many less common metallic solids studied by solid state scientists . These familiar (and less familiar) materials are Fermi-Dirac metals .

In several previous web pages (listed , with links , at the end of this web page below) various possible approaches to the chemical syntheses of Drude electron materials were surveyed . The general method adopted was based on the well known chemistry of the electrides (a discussion of electrides with many refs. can be found in the Electrons web page) . Electrides are formed by the solution of guest atoms in a host lattice or solvent . The guest atoms ionize into cations , which are incorporated into the host lattice or chemically bonded by the host solvent molecules . One or more valence electrons separate from the guest atom and nest in interatomic or intermolecular cavities in the host lattice . The chemical bonding strength of the guest cations with the host lattice , and how the free electron or pairs of electrons interact coulombically with the anions of the host's cation vacancies in which they reside , will be of critical importance in determining the stability of the resulting Drude electron material , and indeed whether or not it can be synthesized .

While electrons are incredibly small physical entities (the radius of an electron from classical physics calculations is re = 2.8179 x 10-15 m ; experimentally , it's probably about 10-22 m , according to this Wikipedia article) , they exert a profound influence on their atomic environments . For example , the radius of the sodium atom (3s1, in sodium metal , body-centered cubic , 8-coordinate) is 1.91 ; that of the sodium cation (3s0, 8-coordinate , per Shannon and Prewitt) is 1.18 . Sodium's 3s1 valence electron occupies a significant volume in the sodium atom . A comparison of the hydrogen atom radius (1s1, 0.37 ; some refs. give 0.53 ) with that of the hydride anion (H1-, 1s2, 2.08 ; another ref. gives 1.40 ) is even more impressive . Electrons electrostatically occupy large volumes in crystal lattices .

In the superconducting state the Drude electron gas – the Cooper pairs – have escaped from the valence orbitals of their respective atomic kernels and are “hiding” from them in the relatively confining interatomic void spaces . As the crystal structure is warmed , its atoms vibrate more and more , thus increasing their “apparent” volume and decreasing the volume of the interatomic voids in which the Cooper pairs are located . As they are squeezed more and more by the atomic kernels the Drude electrons are forced back again into their original atomic orbitals , at which point they become Fermi-Dirac electrons and the material resumes being an “ordinary” metallic conductor .

Cuprates have the highest recorded transition temperatures at this time . These are copper(II) oxide derivatives in which the Cu(II) is usually partially oxidized to Cu(III) ; that is , the superconducting cuprates are Robin-Day Class II mixed-valent compounds . The extremely fast 3d electron resonance in these Cu(II)–Cu(III) mixed-valent materials undoubtedly assists in the formation of the Cooper pairs at lower temperatures .

The electronic configuration of Cu(II) in the cuprates is strongly affected by Jahn-Teller distortion . Octahedral Cu–O coordinate covalent bonds are elongated along the vertical z axis , resulting in a distorted “4+2 octahedral” (tetragonal) Cu–O coordination . The Jahn-Teller effect is caused by the 3d9 valence electron in Cu2+ being located in the spatially voluminous 3dz2 orbital , which makes the Cu2+ cation oval shaped , rather than spherical . Also , Cu(II) strongly favors a square planar coordination by oxygen linking atoms and by oxide anions , a consequence of using its dsp2 square planar hybrid orbital in the formation of the Cu–O coordinate covalent bonds . These electronic quirks result in the cuprates having a pronounced layered appearance in their crystal structures . It's interesting to speculate that the relatively high transition temperatures of the cuprate “high temperature superconductors” (HTS) might be attributed to the particularly spacious interatomic voids in their crystal structures , as illustrated by one of the best known HTS cuprates , YBCO (idealized empirical formula YBa2Cu3O7 , Tc = 93 K) :

In the above sketch the structure has been expanded to reveal the coordinations of the various component atoms . When the “normal” (front) view structure is rotated through about 90 to present the side view of YBCO the exceptionally large void spaces , both in the Y3+–O2- interlayer space and especially in between the Ba2+ cations , become readily apparent . These very large void spaces are undoubtedly the hiding places of the fugitive Cooper pairs , which are nevertheless recaptured by orbitals from their parent copper kernels when the atomic vibrations begin to squeeze them tightly at a temperature around YBCO's Tc , 93 K .

Models of YBCO and many other related HTS cuprates are presented on the web page “VRML Gallery of High Tc Superconducting Copper Oxides” , by Dr. Steffen Weber . All of these cuprate crystal structures have prominent void regions in which the Drude electron gas would have substantial space in which to reside . Dr. Weber has also published a handsome ebook on the Internet , “Crystallography Picture Book , Crystal Structures” [PDF , 2808 KB] , in which his computer-generated models of many familiar crystal structures encountered in solid state chemistry are displayed .

A new design concept for Drude electron material syntheses was introduced in the Electrons web page . The idea was to provide the free electrons with very large void spaces in the lattice in the form of empty cation vacancies , that is , positions that would normally be filled with cations . These voids are surrounded by anions , whose lone pairs of electrons will repel the Drude electrons (both singlets and pairs) into the centers of the cavities . More importantly , the anions will coulombically isolate the Drude electrons from their parent atomic kernels from which they have been separated when the guest atoms were incorporated into the host lattice . This electronic isolation will ensure that the Drude electrons remain free and can never be recaptured by their parent kernels , at any elevated temperature . If the Drude free electrons can flow through these voids in the lattice – more specifically , through channels of such voids – the material should be a high temperature superconductor with – theoretically – no upper transition temperature limit .

Let's examine the possibility of creating new Drude electron materials by dissolving lead , tin , and bismuth in suitable host lattices .

 

Lead and Tin as the Guest Atoms in Super-electrides

 

The two valence states of lead concerning the electrides are Pb0 (6s2 6p2) and Pb2+ (6s2 6p0) . Pb0 is only slightly reducing , and is close to being a Noble Metal :

Pb0 – 2e ---------> Pb2+ ; E0ox = 0.1262 V .

When Pb0 is dissolved in the host lattice its 6p2 valence electrons should be popped into the adjacent cation vacancy prepared for it . The Pb2+ cation with the spherical 6s2 inert pair of valence electrons will be embedded in , and then become a component part of the host lattice .

The zinc blende (and closely related wurtzite) crystal structure might provide a suitable crystal container for the Drude electron gas in its cation vacancies . The chemical trick used to design such Drude metals is to dissolve one gram-atom equivalent of the metal guest atom in two gram-formula equivalents of the host lattice compound . The first equivalent of host will accomodate the guest cation kernels , while the second equivalent of host will provide the cation vacancies for the Drude electron or electrons . This concept is illustrated for the insertion of Pb0 atoms into the silica host lattice :

Pb0 (m.p. 327 C) + 2 SiO2 (m.p. 1710 C) ------- [grind together , pelletize ,

heat in an inert atmosphere or under a graphite blanket] -------> Pb2+[**]Si2O4 ; or ,

PbO (m.p. 887 C) + Si0 (m.p. 1414 C) + 1 SiO2 ------- [heat] -------> Pb2+[**]Si2O4 .

The hypothetical lead silicate compound Pb2+[**]Si2O4 should be isostructural with the analogous chromium(II) silicon sulfide zinc blende Cr2+[**]Si2S4 , discussed in the Chromium web page :

Can all the valence electrons of the component atoms fit properly into this structure ? In particular , will the lead cations' 6p2 inert pairs be compatible with the tetrahedral coordination of the Pb2+ by the oxygen linking atoms ? To answer these questions we'll examine the covalent bonding in Pb2+[**]Si2O4 by referring to a Valence Bond sketch of the compound , as follows :

Tetrahedral bonding to the Pb(II) can be accomplished by Pb–O coordinate covalent bonds , with electron pairs provided by the coordinating oxygen linking atoms . The lead(II) 6s2 inert pairs remain unaffected , spherically surrounding the Pb(IV) kernels . An outer tetrahedral p3s hybrid orbital , instead of the more familiar inner sp3 orbital , must be used in this case . The empty 7s frontier orbital can be recruited by the lead for this task , as the 6s,p >7s,p energy level transition is relatively small and would require only a correspondingly small hybridization energy for the p3s orbital formation . All 36 system valence electrons can be precisely accounted for in this bonding scheme , which looks both feasible and practical .

As indicated in the sketch , the analogous isostructural zinc blende sulfide might similarly be prepared :

Pb0 (m.p. 327 C) + 2 SiS2 (m.p. 1090 C , sublimes) ------- [grind together , pelletize ,

heat in an inert atmosphere or under a graphite blanket] -------> Pb2+[**]Si2S4 ; or ,

PbS (m.p. 1113 C) + Si0 (m.p. 1414 C) + 1 SiS2 ------- [heat] -------> Pb2+[**]Si2S4 .

Like lead , tin is a feeble reducing agent and is close to being a Noble Metal :

Sn0 – 2e ---------> Sn2+ ; E0ox = 0.1375 V .

The synthesis and electronic structure of the Sn2+[**]Si2O4 and Sn2+[**]Si2S4 zinc blendes should be entirely analogous to the corresponding lead compounds :

Sn0 (m.p. 232 C , b.p. 2270 C) + 2 SiO2 (m.p. 1710 C) ------- [grind together , pelletize ,

heat in an inert atmosphere or under a graphite blanket] -------> Sn2+[**]Si2O4 ; or ,

SnO (m.p. 1080 C , dec.) + Si0 (m.p. 1414 C) + 1 SiO2 ----- [heat] -----> Sn2+[**]Si2O4 ;

or , SnO2 (m.p. 1630 C) + Si0 + SiO2 ------- [heat] -------> Sn2+[**]Si2O4 ;

Sn0 + 2 SiS2 (m.p. 1090 C , sublimes) ------- [heat ] -------> Sn2+[**]Si2S4 ; or ,

SnS (m.p. 882 C) + Si0 + 1 SiS2 ------- [heat] -------> Sn2+[**]Si2S4 ; or ,

SnS2 (m.p. 600 C , dec.) + Si0 + SiS2 ------- [heat] -------> Sn2+[**]Si2S4 .

The 5s2 inert pair in Sn(II) is quite easy to displace into higher energy levels (as in the black , electrically-conducting cubic perovskite CsSnBr3) , which suggests that Sn0, when coordinated by the nucleophilic sulfides as SnIV, could provide two pairs of Drude electrons :

Sn0 + 3 Si0 + 6 S0 ------- [grind together , press pellet , heat] -------> SnIV[**] [**]Si3S6 .

Insertion of Pb0 and Sn0 (1.0 eq.) into the YF3 host lattice (2.0 eq.) to obtain the Drude electron materials Pb2+[**]Y2F6 and Sn2+[**]Y2F6 having the cubic symmetry perovskite crystal structure was discussed in the Perovskites web page .

Lead and tin rocksalt super-electrides might be obtained by the insertion of Pb0 and Sn0 into suitable MX2 host lattices (M = Pb2+ and Sn2+ ; X = a halide anion) . The usual 1 : 2 guest atom : host lattice molar ratio should be observed in the syntheses :

Pb0 (m.p. 327 C) + 2 PbF2 (m.p. 830 C) ------- [heat ] ------->

Pb0[ ]Pb2F4 = Pb2+[**]Pb2Cl4 = (Pb2+)3[**]F4 ;

Sn0 (m.p. 232 C) + 2 SnCl2 (m.p. 247 C) ------- [heat ] -------> Sn3[**]Cl4 .

Selected physical properties of the lead(II) and tin(II) halide hosts are summarized in the following tabulations :

Based on the melting points of the lead(II) and tin(II) halides , the former seem to be more ionic than the latter . The (Pb2+)3[**]X4 compounds should be simple cubic rocksalts , but the (Sn2+)3[**]X4 products might have some structural distortion caused by the stereochemically prominent tin(II) 5s2 inert pairs .

 

Bismuth as the Guest Atom in Super-electrides

 

Unlike lead and tin , bismuth is actually a Noble Metal in the redox sense :

Bi0 – 3e ---------> Bi3+ ; E0ox = – 0.308 V (thermodynamically unfavorable) ;

or , Bi3+ + 3e ---------> Bi0 ; E0red = 0.308 V (thermodynamically favorable) .

Bismuth(0) (6s2 6p3) typically loses its 6p3 valence electrons to an oxidizer to become Bi(III) , which retains the 6s2 inert pair . Since a maximum of two spin-paired electrons can occupy a cation vacancy , two cation vacancies per formula unit of target compound must be provided for the three Bi(0) valence electrons . For example , it might be possible to synthesize a zinc blende in which one gram-atom equivalent of bismuth metal powder has been dissolved in three gram-formula equivalents of silica or silicon disulfide :

Bi0 (m.p. 271 C , b.p. 1564 C) + 3 SiO2 (m.p. 1710 C) ------- [grind together , pelletize ,

heat in an inert atmosphere or under a graphite blanket] -------> Bi3+[**][*]Si3O6 ; or ,

Bi2O3 (m.p. 825 C) + Si0 (m.p. 1414 C) + 2 SiO2 ----- [heat] -----> Bi3+[**][*]Si3O6 ;

Bi0 + 3 SiS2 (m.p. 1090 C , sublimes) ------- [heat] -----> Bi3+[**][*]Si3S6 ; or ,

Bi2S3 (m.p. 850 C) + Si0 + 2 SiS2 ----- [heat] -----> Bi3+[**][*]Si3S6 .

In the above examples the first equivalent of host substrate (SiO2 or SiS2) absorbs the Bi3+ ; the second equivalent provides a cation vacancy for two of the valence electrons ; and the third equivalent of SiO2 or SiS2 provides another one for the third electron : Bi3+[**][*]Si3O6 = Bi3+SiO2–[**]SiO2–[*]SiO2 . The Bi3+SiO2 part of the compound sets its overall crystal structure ; in this case it should be that of the zinc blende , with all of the atomic components tetrahedrally coordinated to one another . The valence electron distribution in Bi3+[**][*]Si3O6 should be similar to that shown above in the sketch for Pb2+[**]Si2O4 , but with the addition of a second cation void for the third Bi0 6p valence electron .

Bismuth might be dissolved in a suitable MX3 host lattice (M = a redox inert trivalent metal cation , and X = fluoride or chloride) , in a 1 Bi0 : 3 MX3 molar ratio , to obtain a perovskite structure with A cation vacancies for the [*] and [**] Drude electrons .

The crystal ionic radius for Bi3+ is r = 1.17 , CN = 8 , per Shannon and Bierstedt . It apparently hasn't been reported for CN = 12 (as in the A cation for AMX3 perovskites) , so I calculated this value as r = 1.35 by scaling the 1.17 value up in the same proportion as the known values for Pb2+, which is quite similar to Bi3+ with a 6s2 inert pair : 1.17 x 1.49 [CN = 12] / 1.29 [CN = 8] = 1.35 , CN = 12 , for Bi3+. The crystal ionic radius of the fluoride anion , for a linear coordination in the perovskites , CN = 2 , was similarly calculated as r = 1.15 . The crystal ionic radii for the Al3+ , Y3+ , and Sc3+ M cations in the perovskites , CN = 6 , were r = 0.54 , 0.90 , and 0.75 respectively . The Goldschmidt equation was used to calculate the tolerance factors for the resulting AMX3 perovskites .

The tolerance factor for Bi3+AlF3 was calculated as t = 1.05 , which suggests that the bismuth perovskite might be hexagonally distorted from a cubic symmetry . That for Bi3+YF3 was calculated as t = 0.86 , which again implies a slight distortion from cubic symmetry (maybe orthorhombic or rhombohedral) . The tolerance factor for Bi3+ScF3 is t = 0.93 , which is excellent for a cubic symmetry for the bismuth(III) scandium fluoride perovskite :

Bi0 (m.p. 271 C , b.p. 1564 C) + 3 AlF3 (m.p. 1291 C , sublimes) -------

------- [grind together , pelletize , heat in an inert atmosphere or under a graphite blanket]

-------> Bi3+[**][*]Al3F6 = Bi3+AlF3–[**]AlF3–[*]AlF3 ;

Bi0 + 3 YF3 (m.p. 1367 C) ------- [heat] -------> Bi3+[**][*]Y3F6 ;

Bi0 + 3 ScF3 (m.p. 1515 C) ------- [heat] -------> Bi3+[**][*]Sc3F6 .

Unfortunately scandium is a very rare element , and Sc and its compounds are all very costly . The bismuth(III) aluminum fluoride perovskite would be the most economically attractive one of these materials , if it could be successfully synthesized and proved to be a Drude electron material .

The insertion of Bi0 into BiX3 in a 1 : 3 molar ratio might produce a corundum-like product :

Bi0 + 3 BiF3 (m.p. 727 C) ------- [heat] -------> Bi3+[**][*]Bi3F9 = Bi3+BiF3–[**]BiF3–[*]BiF3 .

All four bismuth(III) halides are commercially available at a moderate cost , and could be examined in the above reaction :

Bismuth(III) fluoride is essentially ionic in nature , while there is substantial covalent bonding in the chloride , bromide , and iodide . BiCl3 has a molecular structure (GIF image , 34 KB) , while the infinite atomic lattice structure (GIF image , 53 KB) of BiI3 has much interchain open space . The corundum structure is of particular interest with respect to the possible superconducting properties of the materials , since there would be many cation vacancies in the Bi3+ layers . In the normal corundum crystal structure every third position in the cation layer is vacant (GIF image , 55 KB ; GIF image , 26 KB) ; in the Bi4F9 (Bi3+[**][*]Bi3F9) structure two more cation vacancies would be added to the Bi3+ layers for the [*] and [**] electrons . All these cation vacancies should provide spacious channels for the flow of the Drude electron gas through the lattice .

The formation of a bismuth electride in the bismuth(III) oxide host lattice could also provide a potential Drude electron material :

Bi0 (m.p. 271 C) + 3 Bi2O3 (m.p. 825 C) ------- [heat] ------->

Bi7O9 = Bi3+[**][*]Bi6O9 = Bi3+Bi2O3–[**]Bi2O3–[*]Bi2O3 .

The Bi3+Bi2O3 part of the structure is Bi3O3 , or BiO . The Bi–O chemical bonding in Bi7O9 would be entirely covalent in nature , and the Bi(III) would have a stereochemically prominent axial lone pair of electrons (its 6s2 inert pair , now in a hybrid orbital) . Bi7O9 is predicted to have the litharge crystal structure , in common with the chemically related lead(II) oxide , PbO , and tin(II) oxide , SnO :

The anticipated valence electron distribution in Bi7O9 is shown in the following sketch :

All 89 system electrons per formula unit can be precisely accounted for in the above analysis .

Litharge has voluminous interlayer spaces into which the stereochemically bulky , axial 6s2 inert pairs protrude (the inert pairs aren't directly observable in X-ray diffraction spectra , but their presence in the interlayer spaces is inferred) . These interlayer spaces in the litharge crystal structure , combined with the cation voids for the Drude electrons , should provide excellent channels for the flow of the free electrons through the lattice of Bi7O9 .

The sulfide analogue of Bi7O9 might be synthesized as follows :

Bi0 (m.p. 271 C) + 3 Bi2S3 (m.p. 850 C) ------- [heat] ------->

Bi7S9 = Bi3+[**][*]Bi6S9 = Bi3+Bi2S3–[**]Bi2S3–[*]Bi2S3 .

Bi–S bonds are even stronger than Bi–O bonds , so the molten Bi0 should soak into and readily combine with the Bi2S3 host lattice . The product , Bi7[**][*]S9 , is predicted to be a stable compound and a possible Drude electron material .

Finally , tin and lead might be dissolved in Bi2O3 and Bi2S3 in a 1 : 2 molar ratio to produce the corresponding tin and lead super-electrides in those host structures . The tin(II) and lead(II) parent kernels should form a litharge superstructure with the Bi2O3 host , having covalent Sn–O and Pb–O bonds , as they do in SnO and PbO . However , Sn(II) and Pb(II) have more ionic bonding in SnS (distorted rocksalt structure , GIF image , 56 KB) and in PbS (rocksalt structure) . The Sn(II) and Pb(II) components of Sn2+[**]Bi4S6 and Pb2+[**]Bi4S6 , respectively , might result in these latter products having some sort of hybrid crystal lattice , possibly a heterostructure with layers of cubic SnS and PbS alternating with tetragonal layers of “BiS”.

 

Related web pages in this series about Drude electron materials :

A New Picture of Superconductivity : Lightning Bolt Electrons in a Crystal” ;

Perovskites Designed as Drude Metals and Ambient Superconductors” ;

Rocksalts Designed as Super-electrides , Drude Metals , and as Possible High Temperature Superconductors” ;

Chromium as the Guest Atom in Super-electride Drude Metals” ;

* Betaines and Electrides : From Sugar Beets and Baby Shampoo to Superconductors ; and ,

* Drude Electron Materials Having Rutile and Layered Structures” .

 

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