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 Å ; that of the sodium cation (3s0, 8-coordinate , per Shannon and Prewitt) is 1.18 Å . Sodium's 3s1 valence electron occupies a significant volume in the sodium atom . A comparison of the hydrogen atom radius (1s1, 0.37 Å ; some refs. give 0.53 Å) with that of the hydride anion (H1-, 1s2, 2.08 Å ; another ref. gives 1.40 Å) 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 CuO coordinate covalent bonds are elongated along the vertical z axis , resulting in a distorted 4+2 octahedral (tetragonal) CuO 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 CuO 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 90º 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 ºC) + 2 SiO2 (m.p. 1710 ºC) ------- [grind together , pelletize ,
heat in an inert atmosphere or under a graphite blanket] -------> Pb2+[**]Si2O4 ; or ,
PbO (m.p. 887 ºC) + ½ Si0 (m.p. 1414 ºC) + 1½ 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 PbO 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 ºC) + 2 SiS2 (m.p. 1090 ºC , sublimes) ------- [grind together , pelletize ,
heat in an inert atmosphere or under a graphite blanket] -------> Pb2+[**]Si2S4 ; or ,
PbS (m.p. 1113 ºC) + ½ Si0 (m.p. 1414 ºC) + 1½ 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 ºC , b.p. 2270 ºC) + 2 SiO2 (m.p. 1710 ºC) ------- [grind together , pelletize ,
heat in an inert atmosphere or under a graphite blanket] -------> Sn2+[**]Si2O4 ; or ,
SnO (m.p. 1080 ºC , dec.) + ½ Si0 (m.p. 1414 ºC) + 1½ SiO2 ----- [heat] -----> Sn2+[**]Si2O4 ;
or , SnO2 (m.p. 1630 ºC) + Si0 + SiO2 ------- [heat] -------> Sn2+[**]Si2O4 ;
Sn0 + 2 SiS2 (m.p. 1090 ºC , sublimes) ------- [heat ] -------> Sn2+[**]Si2S4 ; or ,
SnS (m.p. 882 ºC) + ½ Si0 + 1½ SiS2 ------- [heat] -------> Sn2+[**]Si2S4 ; or ,
SnS2 (m.p. 600 ºC , 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 ºC) + 2 PbF2 (m.p. 830 ºC) ------- [heat ] ------->
Pb0[ ]Pb2F4 = Pb2+[**]Pb2Cl4 = (Pb2+)3[**]F4 ;
Sn0 (m.p. 232 ºC) + 2 SnCl2 (m.p. 247 ºC) ------- [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 ºC , b.p. 1564 ºC) + 3 SiO2 (m.p. 1710 ºC) ------- [grind together , pelletize ,
heat in an inert atmosphere or under a graphite blanket] -------> Bi3+[**][*]Si3O6 ; or ,
½ Bi2O3 (m.p. 825 ºC) + ¾ Si0 (m.p. 1414 ºC) + 2¼ SiO2 ----- [heat] -----> Bi3+[**][*]Si3O6 ;
Bi0 + 3 SiS2 (m.p. 1090 ºC , sublimes) ------- [heat] -----> Bi3+[**][*]Si3S6 ; or ,
½ Bi2S3 (m.p. 850 ºC) + ¾ Si0 + 2¼ 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 Å , 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 Å by scaling the 1.17 Å 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 Å x 1.49 Å [CN = 12] / 1.29 Å [CN = 8] = 1.35 Å , 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 Å . The crystal ionic radii for the Al3+ , Y3+ , and Sc3+ M cations in the perovskites , CN = 6 , were r = 0.54 Å , 0.90 Å , and 0.75 Å 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 ºC , b.p. 1564 ºC) + 3 AlF3 (m.p. 1291 ºC , 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 ºC) ------- [heat] -------> Bi3+[**][*]Y3F6 ;
Bi0 + 3 ScF3 (m.p. 1515 ºC) ------- [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 ºC) ------- [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 ºC) + 3 Bi2O3 (m.p. 825 ºC) ------- [heat] ------->
Bi7O9 = Bi3+[**][*]Bi6O9 = Bi3+Bi2O3[**]Bi2O3[*]Bi2O3 .
The Bi3+Bi2O3 part of the structure is Bi3O3 , or BiO . The BiO 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 ºC) + 3 Bi2S3 (m.p. 850 ºC) ------- [heat] ------->
Bi7S9 = Bi3+[**][*]Bi6S9 = Bi3+Bi2S3[**]Bi2S3[*]Bi2S3 .
BiS bonds are even stronger than BiO 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 SnO and PbO 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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