Covalent Bonding in Strongly Compressed Sodium Metal

 

A fascinating report about the conversion of sodium metal under very high pressure into an apparently nonmetallic material caught my eye recently while I was doing some literature research for another web page . This was the study , “Transparent Dense Sodium”, reported in Nature by Ma and co-workers in March , 2009 (the references are presented at the end of the text , below ; underlined blue hyperlinks can be clicked when online to retrieve the article cited . The requested document will open in a new window) . This extraordinary phenomenon naturally presented an immediate challenge to my understanding of chemical bonding in infinite atomic lattice solids . The following is a brief analysis , in simple qualitative terms , of possible covalent bonds in supercompressed elementary sodium .

Under normal circumstances – at ambient pressure – sodium is readily apparent as a metallic solid , even more so when a fresh surface of a reasonably large specimen is exposed by cutting or melting :

This picture shows a freshly cast “ingot” of sodium metal (24.6 grams) under paraffin oil . It was prepared by the electrolysis of molten sodium hydroxide by a chemistry hobbyist , “Len1”, as described in his web document , Sodium Metal – Illustrated Practical Guide . Len's remarkable home-made Castner Cell is very impressive , and was as efficient as its larger industrial cousins in producing fairly pure sodium . My thanks to Len for the use of his clear , high quality photograph of sodium on this web page .

Elementary sodium normally has the simple body centered cubic (bcc) crystal structure , in which each sodium atom is symmetrically surrounded by eight neighbouring sodiums in a square prism :

The metallic bond in the metallurgical metals is frequently described as a “sea” – sometimes called the Fermi Sea – of free , mobile electrons surrounding the atomic kernels . I prefer to picture the metallic bond as an “electron gas” swirling about in the interstitial voids between the kernels . This was the original model of the metallic bond , in physics terms called the electron theory of metals , first proposed by the German physicist Paul Drude (1863–1906) in 1900 . Drude's theory was mostly correct ; its several shortcomings were corrected in the late 1920s , taking into account the quantum (wave) nature of electrons .

Sodium and the Alkali metals in general provide good examples of this very simple sort of metallic bond . The Alkali metal elements all have a single ns1 valence electron (sodium's is 3s1) per atom . Some leakage of electron density into the np0 orbitals (3p0 in sodium) occurs , but most of the valence electrons remain in the voluminous , spherical s orbitals . These can overlap continuously throughout the lattice to form a sort of “polymerized molecular orbital”, which I have referred to throughout all my Chemexplore web pages and PDF booklets as a crystal orbital , abbreviated as XO by comparison with the native atomic orbitals , AO , and molecular orbitals , MO . The metallic bond in elementary sodium at STP is thus the 3s sigma XO . With the inclusion of the 3p “leakage reservoirs” the interatomic space in the sodium lattice containing the mobile , free valence electrons is usually referred to as the 3s,p conduction band .

In energy terms the metallic bond XO is a complicated affair . Since the Pauli Exclusion Principle permits only two electrons , having opposite spins , per MO , the XO is subdivided into a vast number of energy levels corresponding to the number of valence electrons . For example , a gram atomic weight of sodium (one mole , 22.9898 grams) contains one mole of 3s1 valence electrons ; this is an Avogadro Number (NA = 6.02214129 x 1023) of them . So there would be NA energy levels in the the metallic bond XO in one mole of sodium metal .

Most of the 3s1 electrons – in sodium , about 99% – are paired off in the lower energy levels comprising the XO , but a small population , about 1% of the valence electrons , remain in their own separate , higher energy levels as unpaired singlets . This energy distribution of the free electrons in the metallic bond is called the Fermi-Dirac distribution ; the energy level above which the singlet electrons occur is the Fermi level , EF , the surface of the Fermi sea of free electrons . The three dimensional shape of the Fermi level in a metal , the Brillouin zone – roughly speaking , the “shape” of the electron gas cloud in the interatomic space of the lattice – can be computed for a variety of metallic solids , and is usually quite complex looking .

 

Covalent Bonds in Metallurgical Metals

 

The Alkali metals are a good example – and possibly the only ones – in which there are essentially no covalent bonds present in them , at least under ambient pressure conditions , and in the solid and liquid phases (apparently diatomic Na2 molecules with covalent Na–Na bonds exist in the gas phase above the boiling point of the element , at 883 C) . The metallurgical metals and the metalloids almost certainly derive most of their internal atomic cohesion from metal–metal covalent bonds . Of course they also have “genuine” metallic bonds , similar to what was described above for sodium . As in the soft , low melting Alkali metals , these metallic bonds are very weak and contribute little to the overall bonding strength in the elements in which they occur .

The concept of covalent bonding in the metallurgical metals was introduced by Pauling in 1938 , and has been generally accepted ever since (I've seen it mentioned in High School chemistry textbooks , for example) . The electronic structures of two familiar elements , tin and iron , were presented by Pauling in that seminal paper in terms of the Valence Bond (VB) theory , of which he was the principal theorist . VB is generally considered antiquated and obsolete these days , and has been replaced by other chemical bonding theories (especially the Molecular Orbital theory) . I have found VB to be essential in the qualitative , nonmathematical analysis of the distribution of valence – and sometimes hypervalence – electrons in the covalent bonds of molecules and infinite atomic lattice solids . VB has been an indispensible tool in the study for , and writing of , many of my Chemexplore web pages .

Before proceeding to examine possible covalent bonding in supercompressed sodium I thought it would be useful to take a brief look at the VB descriptions of tin and iron , so as to provide a preview – and hopefully an appreciation – of the analytical method to the reader .

The gray tin allotrope has the diamond crystal structure , and so it has a correspondingly simple tetrahedral sp3 electronic structure , as do the carbon atoms in diamond : 5s2 + 5p2x.y,z = s1a + s1b + s1c + s1d . The white tin (metal) allotrope has a more complex crystal structure , consisting of chains of tin atoms zigzagging in the x–y plane ; the layers are bonded together by longer axial Sn–Sn bonds :

The octahedral coordination of the tin atoms in this crystal structure requires a twelve-set of electrons around each of them . Since there are only four normal valence electrons in tin (4d10 + 5s2 + 5p2x.y,z ) , it's clear that two additional hypervalent electrons from the 4d orbitals are used in the twelve-set . The VB description of the covalent bonds in tin metal consists of a combination of three separate d2 , p2 , and spz hybrid orbitals (GIF image , 42 KB) , as sketched below :

At this point it would be convenient for me to copy and paste the relevant section from the Valence Bond web page , in which the tin metal electronic structure was previously discussed :

“The above sketch highlights several interesting features of the white tin electronic structure . First , it shows all seven Sn–Sn bonds per tin atom : four covalent , two coordinate covalent , and the actual metallic bond (6 s-p) XO . Second , it shows the use of two hypervalent 4d orbitals , together with their four electrons , in the covalent bonds . Note the 4d orbitals and their electrons are at approximately the same energy level as the normal valence 5 s-p orbitals in tin and so are readily accessible for use in bonding , if required . Third , it reveals the presence in white tin of not one , but two inert pairs ! The 5s2 valence electrons are located in the axial Sn–Sn bonds ; the 6s2 pair are in the metallic bond XO . Leakage of electron density from the 6s2 pair into the adjacent empty 6p orbitals opens up vacancies in the 6s sigma XO and permits it to act as the metallic bond in white tin .

While the four valence electrons in degenerate tin atoms (isolated in space , with no neighbours) are 5s2 5p2 , this VB picture predicts that in solid-state tin metal the 5p2 electrons have been promoted up to the 6 s-p energy level , as the 5p orbitals are now occupied by covalent bonds .

Hydrochloric acid can readily oxidize the 6s2 inert pair ; when that happens , the tin structure disintegrates , the 4d electrons retreat back to their native orbitals , and the remaining 5s2 inert pair surrounds the tin(II) cation , now an electrophilic sphere that is quickly coordinated by nucleophilic water ligands . In the case of gray tin , the four identical covalent bonds per tin atom are simultaneously oxidized by the HCl , leaving a residual hydrated Sn(IV) cation .

When gray tin is warmed to room temperature and higher – the actual transition temperature is 13.2 C – it's transformed into white tin . Only a small amount of environmental thermal energy is required for the hybridization of two of tin's hypervalent 4d and its normal valence 5 s-p orbitals and electrons to create the 4dx.y + 5spz + 5px.y hybrid orbital . Conversely , if that environmental energy is removed – i.e. if white tin is cooled below 0 C for a prolonged period of time – access to those hypervalent orbitals is lost , and it's slowly converted back into gray tin”.

An excellent YouTube video (MP4 , 0:29 runtime , 1080 KB) shows a time-lapse sequence of a shiny tin ingot expanding into a splintered , disintegrated mass of gray tin as it's cooled down .

Two lighter members of the IVA/14 family of elements , silicon and germanium , can also utilize their lower energy shell hypervalence electrons and orbitals to form octahedral twelve-sets like tin metal , but they can do so only under conditions of high pressure and/or high temperature . Such forcing conditions can close the wide 3s,p to 4s,p energy gap for Ge , and the even wider 2s,p to 3s,p gap for silicon :

Again copying and pasting from the Valence Bond web page :

Jamieson reported in 1963 that under high pressure the diamond crystal structure of both silicon and germanium will change into that of white tin . Subsequently , Drickamer determined that those white tin phases of silicon and germanium are excellent metallic electrical conductors . This leads us to a startling conclusion : the application of high pressure to silicon compresses its atoms to such an extent that its hypervalent 2p orbitals and electrons (from 2s2 2p6) can be combined with its normal valent 3 s-p orbitals and electrons (3s2 3p2) to create the 2(p2) + 3(sp) + 3(p2) distorted octahedral hybrid orbital , plus the 4 s-p sigma XO metallic bond in the solid :

The very large energy gap between the 2 s-p and 3 s-p energy levels normally isolates the former orbitals , preventing them from combining with the higher energy orbitals to form hybrid orbitals with more than four positive symmetry lobes . I've indicated a larger than usual energy gap between the 2 s-p and 3 s-p energy levels in the sketch above for metallic silicon . It seems that tremendous compression of the silicon atoms can squeeze and narrow that gap sufficiently to permit the hybridization of two of the hypervalent 2p orbitals and their four electrons with the normal valence 3s2 3p2 orbitals and electrons . The result is an electronic structure for highly compressed metallic silicon rather like that of tin metal .

The electronic structure of compressed germanium would be similar to that of silicon , with its metallic bond located by VB in the 5 s-p sigma XO . Since the energy gap in germanium (3 s-p to 4 s-p) is narrower than the corresponding gap in silicon , we would expect that less pressure would be required to convert diamond germanium to its white tin form . In Drickamer's Fig. 7 , p. 1433 , we see that this is indeed the case , with the transition to the metallic phase occurring at about 200 kbars in silicon , but significantly lower (~ 120 kbars) in germanium .

Molten silicon (m.p. ca. 1410–1414 C) is also metallic :

“It is noteworthy that the melting of Si at ambient conditions [one atmosphere pressure] also displays a transition both from four-fold to sixfold coordination and from the semiconducting solid phase to a metallic liquid” (R.G. Hennig and co-workers [PDF , 405 KB] , p. 1) .

That silicon near its melting point changes from the diamond to the white tin structure just before liquifying is significant . This suggests that the huge amount of thermal energy applied to its lattice is sufficient to promote its inner 2p orbitals and their electrons to a higher excited state , making them accessible to the 3 s-p orbitals for creation of the 2(p2) + 3(sp) + 3(p2) hybrid orbital . The thermal conversions of silicon and gray tin to their distorted octahedral white tin structures are thus analogous , differing only in the amount of energy required for the transitions . This example of silicon shows that even the very large 2 s-p to 3 s-p energy gap can be closed , and lower energy level hypervalent orbitals and their electrons can be used in covalent bonding , provided enough heat is supplied , or pressure is applied to the material”.

Iron (Moore) has the body centered cubic crystal structure at STP , similar to that of sodium . Unlike the latter element , however , iron atoms have a profusion of valence and accessible hypervalence orbitals and electrons for forming the vast array of chemical bonds , both to themselves and to other elements , that it is so well-known for . Once again pasting from the Valence Bond web page :

“Pauling was reluctant to invoke the use of any sort of hypervalent orbitals or electrons in the creation of hybrid orbitals ........... However , in the case of bcc iron [and with white tin metal , discussed above] , we absolutely must involve hypervalent orbitals and electrons (and empty outer frontier orbitals) in the description of an electronic structure for iron which is in a reasonable agreement with its known chemical and physical properties . With this latter requirement foremost in mind , the following picture VB electronic structure for iron metal is brought forward :

Interestingly , the d5sp2 square prism hybrid orbital is one of the excited states proposed by Pauling for iron ; but while he preferred to use normal valence shell orbitals for it (and as a result didn't have enough electrons) , I've used an inner d5sp2 square prism hybrid orbital , involving two hypervalent 3p orbitals , including their four electrons , in the electronic structure . Now there are just the right number of electrons (12) for the bcc structure , with eight Fe–Fe covalent bonds per iron atom , plus two unpaired singlet electrons in the 4p native orbitals (which cause the ferromagnetism in iron) , plus the usual two electrons in the s-p metallic bond XO .

The 4px,y orbitals can overlap end-to-end between the iron atoms in the x-y plane to form p-p sigma MOs , each of which can form a one-electron bond , which can also contribute to the overall bond strength in iron . Their singlet electrons have a parallel spin orientation , and produce the strong ferromagnetism [Curie magnetism of 2.22 BM (Bohr magnetons)] in the bulk metal . The 4pz orbitals perpendicular to the planes of atoms can overlap side-to-side to form a continuous pi XO over the planes . However , since the individual 4pz orbitals have two electrons each , the XO is completely filled , and must leak some its electron density into an adjacent empty frontier orbital if it is to function as a metallic bond . This leakage likely occurs from the 4pz into the 5s orbitals , thereby producing the typical s-p metallic bond XO in iron .

The question will naturally be posed : how practical is the use of the two hypervalent 3p orbitals and their electrons in this scheme ? Are they energetically accessible ? The 3d , 4s , and 4p orbitals in iron are all at roughly the same energy level – see the sketch further up this web page showing the relative energy levels of the s , p, and d orbitals – but there is a significant energy gap separating the 3 s-p and 4 s-p levels . Considerable energy will be required to create a d5sp2 square prism hybrid orbital which includes two of the 3p native orbitals . Again , we must consider the practical chemistry of iron , and even its metallurgy , in pondering this question . The agglomeration of iron atoms into a macroscopic sample of iron metal requires a large amount of energy . Pure iron melts at 1536 C , and it's manufactured (as pig iron) in vast amounts worldwide in blast furnaces . Undoubtedly there is more than enough heat energy in a blast furnace to promote the four hypervalent 3p electrons into the d5sp2 square prism hybrid orbital ! As with the metallic silicon discussed above , the creation of hybrid orbitals should be possible even in extraordinary or unusual systems by the provision of considerable thermal energy and/or high pressure , both of which can close forbiddingly wide energy gaps between the s-p energy levels”.

We can readily understand why bcc iron , with its interlocking network of powerful covalent Fe–Fe bonds , is such a physically strong , tough , refractory metal ; combined with small amounts of carbon and other alloying elements it forms steel , the workhorse construction material indispensible to modern civilization . This is in stark contrast to bcc sodium with its feeble sigma XO metallic bond having a single resonating 3s1 valence electron per orbital : a soft , putty-like material , melting at 98 C , that can be easily cut with a knife and extruded in a hand press into a wire .

Let's now examine the Valence Bond description of the electron distribution in highly compressed sodium . We'll see how the 2s,p shell electrons can be made accessible for covalent bonding by the high pressures forcing the sodium atoms more closely together .

 

Covalent Bonds in Sodium Under High Pressure (~ 200 GPa)

 

To add some historical perspective to this narrative we should note that studies of highly compressed Alkali metals (potassium and rubidium specifically) had been carried out by H.G. Drickamer , a prominent researcher in high pressure chemistry , back in 1963 . He noted a linear increase in the electrical resistance of potassium and rubidium when they were compressed from ambient pressure up to around 500 Kbars :

My thanks to the copyright holder of the original Figs. 9 and 10 for their use on this web page .

Modern anvil type presses can greatly exceed this rather modest 500 Kbars range ; such enormous pressures were required (as demonstrated by Ma and co-workers) to observe transparency in compressed sodium . Note that less pressure was required to achieve a resistance “end-point” in rubidium (5s,p) than in potassium (4s,p) . We would expect from this trend that even greater pressure would be needed to demetallize sodium (3s,p) , and this indeed proved to be the case . On the other hand , demetallization of cesium (6s,p) might be accomplished at an applied pressure lower than 500 Kbars , should any researcher consider investigating it .

The following conversion factors for several common pressure units will be found useful in any discussion of high pressure chemistry :

1 Atmosphere = 1.01325 Bar = 1013.25 millibars = 1.03323 Kg/cm2 = 14.69595 lb/in2 (psi) ;

1 Bar = 1000 millibars = 0.986923 Atmosphere = 1.019716 Kg/cm2 = 14.5038 lb/in2 (psi) ;

The standard MKS–SI unit of pressure is the pascal (Pa) , which is 1 N/m2 . Since this is such a small unit of pressure , kilo- , mega- , and gigapascals are commonly used in actual practice :

1 kilopascal (KPa) = 9.8692 x 10-3 atmosphere = 10-2 kilobars = 0.1450377 psi ;

1 megapascal (MPa) = 9.8692 atmospheres = 10 bars = 145.0377 psi ;

1 gigapascal (GPa) = 9869.2 atmospheres = 10,000 bars = 145,037.7 psi ;

1 bar = 0.1 MPa = 10-4 GPa ; 1 Kbar = 100 MPa = 0.1 GPa ; 1 Mbar = 105 MPa = 100 GPa .

Data were obtained from the CRC Handbook of Chemistry and Physics ; from the Wikipedia web pages Conversion of units and Pascal (unit) ; and from the Pressure Conversion Factors Table .

Drickamer's experimental pressure of 500 Kbars for potassium and rubidium thus translates into 50,000 MPa or 50 GPa , which is a quarter of the pressure required to demetallize sodium .

When compressed in a diamond-anvil press sodium changes in appearance from silvery to black , then transparent and reddish , and finally to transparent and colourless :

“Na becomes optically transparent at pressures of ~ 200 GPa” [2 Mbar] Ma and co-workers , p. 182 .

The crystal structure of sodium changes from the ambient pressure bcc through several different forms at higher pressures . At 320 GPa [3.2 Mbar , 3.16 million atm] the structure was determined by X-ray diffraction to be of the double-hexagonal close-packed (dhcp) variety , the “hP4 form” :

My thanks to the copyright holder of the original Fig. 4a for its use on this web page .

In the above hexagonal close-packed structure there are alternating layers of octahedrally coordinated sodium atoms and those having a trigonal prismatic coordination with their neighbouring sodiums above and below . The crystal structures of many binary Transition metal pnictides and chalcogenides similarly have layers of hexagonally packed , octahedrally coordinated metal atoms alternating with hexagonal layers of trigonal prismatic nonmetal atoms (Wells) :

The hP4 form of sodium at 320 GPa resembles this nickel arsenide crystal structure in the same way (atomic coordinations) in which the diamond and zinc blende structures are related , for example .

This six-fold coordination of the compressed sodium atoms seems counter-intuitive at first . We would expect the eight-fold bcc coordination in STP sodium to increase , perhaps to twelve-fold (fcc/ccp or hcp) under high pressure . While there are insufficient 2s,p and 3s,p electrons to form covalent bonds with 12-coordinate Na atoms , there are enough to form Na–Na covalent bonds with 6-coordination . Apparently the formation of Na–Na covalent bonds is so energetically stabilizing in the system that the counter-intuitve 6-coordination results when the 2s,p and 3s,p electrons become available for bonding as the sodium atoms are squeezed together .

The Na–Na interatomic distances decrease from 3.72 (sketch near the top of the web page) at ambient pressure to 1.89 at 300 GPa (Ma and co-workers , p. 184) . That is , at that elevated pressure the metallic radius of the sodiums is 1.89/2 = 0.945 . The crystal ionic radius of sodium cations , 6-coordinate , per Shannon-Prewitt , is 1.02 . Sodium cations have the neon electronic configuration , 1s2 2s2 2p6. The implication is that the 2s,p and 3s,p electron shells are physically overlapping in the compressed sodium . The hypervalent 2s,p orbitals and their eight electrons then become available for hybridization with the 3s,p valence shell orbitals and the 3s1 valence electron . Each sodium atom now has a variety of s,p orbitals it can hybridize , with nine valence and hypervalence electrons , to form the six-coordinate Na–Na covalent bonds per sodium in the observed hP4 crystal structure .

A simple , nonmathematical Valence Bond picture of the electron distribution in compressed sodium is outlined in the following sketch :

The Valence Bond orbitals indicated in the sketch are composite hybrid orbitals , comprised of simpler linear (sp) , bent (p2) , and trigonal planar (sp2) orbitals . The use of such composite orbitals was discussed at length in the Valence Bond web page , to which the interested reader is referred .

Ma and co-workers suggested that localization of the metallic bond electrons in compressed sodium was accomplished via the hybridization of its 3p and 3d orbitals :

“Our calculations reveal that an insulating electronic state emerges because compression causes the 3d bands to rapidly drop in energy relative to the 3p bands and increasingly hybridize with them . This hybridization is the key to strong electron localization : a marked charge accumulation occurs only in the open interstitial regions (Fig. 4c)” (p. 184) .

With the greatest respect to Professor Ma and his co-researchers , I consider the use of the 3d orbitals in any covalent bonding scheme in sodium , under any conditions , as highly doubtful . Yes , d orbitals can certainly be combined with p orbitals to form many useful hybrid orbitals for chemical bonding (GIF image , 42 KB) . The hybrid orbitals are usually formed by the combination of native orbitals from the valence shells of the various elements . The Transition metals are d-block elements with d electrons and orbitals in their valence shells , so we would expect native d orbitals to form hybrid orbitals predominately in covalent compounds of the Transition metals .

For example , the tetrahedral sp3 hybrid orbital is used for covalent bonding by pre-Transition and post-Transtion metal elements . Its Transition metal equivalent is the d3s tetrahedral orbital . The sp5 octahedral orbital is similarly used by p-block elements , while the d5s octahedral orbital is used by the earlier Transition metal elements . The later ones tend to use the d2sp3 (inner) and sp3d2 (outer) hybrid orbitals , as those elements approach the p-block families . That is , more and more p character appears in the hybrids as the Transition metal moves toward the p-block and its d orbitals fill up with electrons .

Consider the following points :

* Sodium is a pre-Transition s-block element , and has no access whatsoever to d orbitals . Covalent sodium compounds are rare , and have very simple coordinations , illustrating the isolation of the 3s,p energy levels from the 2s,p and 4s,p levels (hence no higher coordinations are normally possible) . For example , in the compound phenylsodium the highly polar NaC covalent bond may be formed by combining sodium's spx linear hybrid orbital (from 3s + 3px) with the carbon s orbital on the phenyl ring .

* In order to form covalent bonds with a coordination number of 6 each sodium atom will require a twelve-set . The lower energy level 2s2 2p6 orbitals with their eight electrons must be used in the octahedral and trigonal prismatic hybrid orbitals to form the 6-coordinate covalent bonds with their twelve-sets on the sodium atoms . Since the 2s2 electrons will be used in the covalent bonds , the container 2s orbital will also be used in the 6-coordinate hybrid orbitals , as will the 3s orbital . Fortunately , suitable 6-coordinate composite orbitals can be formed from s and p native orbitals (sp5 octahedral and s2p4 trigonal prism) , as shown in the VB sketch above .

* Hypervalent orbitals , both empty outer frontier orbitals and filled inner shell orbitals , can be used for hybrid orbital formation under extraordinary circumstances of high pressure , high temperature , or both . Pauling pointed out that hybrid orbitals are excited states of the atoms , and require energy for their creation from the degenerate ground state native orbitals . Thus , high temperature reactions can provide the necessary energy to create the hybrid orbitals and so make both the lower filled , and higher empty frontier orbitals available for combination with the valence shell orbitals and electrons . The energy in such reactions can thermally promote electrons from the lower energy levels up into the frontier orbitals for the creation of higher coordination number covalent bonds (eg. as in highly exothermic fluorination reactions to produce sulfur hexafluoride and other hexafluoro molecules) .

On the other hand , high pressure makes the lower , filled orbitals available for hybridization with the valence shell orbitals by physically overlapping with them as the atoms are compressed together [as in silicon at 200 Kbars (20 GPa) , which transformed from tetrahedral (octets) to distorted octahedral (white tin , twelve-sets)] . Very hot silicon near its melting point also transforms into the white tin structure , but this time via thermal promotion of its 2 s,p level electrons into the 3 s,p levels (sketch above) . Ma and co-workers didn't mention the temperature at which they carried out their high pressure experiments with sodium ; I assume they were done at room temperature . If so , there wouldn't have been any thermal promotion of the 2s2 2p6 electrons required for the covalent bonds . They and their orbitals would have been hybridized in situ with the 3s1 3p0 orbitals to form the sp5 and s2p4 hybrid orbitals , as mentioned above .

* As shown in the Energy Levels sketch above , the 3d orbitals are very high in energy (in the 4s,p level) , and without any thermal promotion none of the 2s2 2p6 electrons will reach them . Also , d orbitals are known to be physically small , diffuse , and close to the nucleus . This is why they are considered as unlikely components (highly doubtful) of molecular orbitals in compounds of the p-block elements .

The Valence Bond picture presented above represents the colourless , transparent sodium under the maximum compression experimentally used by the researchers . A transfer of a valence electron from one Na to its neighbour as shown in the sketch will result in a completely diamagnetic lattice , devoid of any unpaired electrons . This represents the formation of “sodium sodide”, Na1+ Na1, both components of which are diamagnetic . As with the common diamagnetic Na1+ Cl1, such a material is expected to be colourless and possibly also transparent . Note that in the Valence Bond scheme above the Aufbau Principle of the filling of successively higher energy orbitals with electrons is observed .

The presence of two different types of atoms in highly compressed sodium has been theoretically computed by Ma and co-workers :

My thanks to the copyright holder of the original Fig. 4c for its use on this web page .

Gatti , Tokatly , and Rubio (2010) have also theorized that highly compressed , transparent sodium forms a sort of charge transfer compound that they describe as a new , uncoventional inorganic electride. Actually , I think the black , lower pressure form of sodium is more like an electride than the colourless , transparent phase is . As is well known , a dilute solution of sodium metal in pure , anhydrous liquid ammonia has an inky , blue-black colour (more concentrated solutions of Na0 in NH3 have a golden colour and a strong metallic luster) . In black , compressed sodium there are undoubtedly free , unpaired 3s1 valence electrons resonating in the interatomic voids between the sodiums , as the valence electrons do in sodiumammonia electride solutions .

The intermediate coloured , but transparent phase of compressed sodium may , on the other hand , resemble the F-centers (colour centers) that can form in the Alkali metal halides . For example , when a colourless , transparent crystal of sodium chloride is irradiated with a narrow beam of high energy X-rays , a circular , intensely reddish-orange patch will form in the irradiated section . The X-rays have knocked electrons off some of the chloride anions ; they become chlorine atoms which can migrate and diffuse out of the crystal lattice . The displaced electrons can resonate over the surrounding sodium cations in the empty cavities vacated by the chlorine atoms . In effect , the F-centers represent a sort of mixed-valent Na0–Na1+ compound , with the free electrons resonating over the base of sodium cations surrounding the cavities .

The irradiation of a crystal of potassium chloride by high energy X-rays can produce an F-center in it having a pretty violet colour . This suggests that if potassium was supercompressed in a similar sort of apparatus used by Ma and co-workers , it might first appear black (electride-like) , then transparent and violet-coloured (F-centers) , and finally transparent and colourless (diamagnetic potassium potasside , K1+ K1) .

The electronic behaviour of supercompressed sodium is an educational study from the amazing and endlessly fascinating realm of high pressure chemistry . It's not at all surprising that high pressure conditions can demetallize metallic solids , and conversely can metallize materials that are insulators (eg. hydrogen and iodine) at ambient pressure . Other extraordinary transformations , like the synthesis of crystalline nitrogen and polymeric carbon dioxide (carbonia glass) have been accomplished only under extremely high pressure conditions . I hope that in future decades high pressure chemistry can be expanded and adapted to the synthesis of remarkable new materials that are stable and isolable under ambient conditions .

 

References and Notes

 

Some interesting high pressure chemistry is discussed in an earlier Chemexplore booklet , “High Pressure Solid State Structures of Simple Molecules” [PDF , 231 KB] . The following review article is also recommended to interested readers : A. Jayaraman , “The Diamond Anvil Cell and High Pressure Research”, J. de Physique 45 (11) , Coll. C8 , pp. C8-355C8-363 (1984) [PDF , 1384 KB] . Note : this PDF file can be opened only with Adobe Acrobat Reader v. 6 or later . If desired , a suitable version of this application can be downloaded for free from Oldversion.com .

Ma and co-workers : Y. Ma et al. , Transparent Dense Sodium, Nature 458 (7235) , pp. 182-185 (2009) [PDF , 701 KB] ; Supplementary Information [PDF , 1414 KB] .

crystal orbital : I use the term crystal orbital to mean a polymerized molecular orbital, spanning the entire crystal dimensions . Thus , crystal orbital is synonymous with the terms metallic bond (chemistry) and conduction band (physics) . I abbreviate crystal orbital as XO , since Xal is sometimes used as an abbreviation for crystal (and I don't want to use CO , the formula of carbon monoxide !) . Crystal orbitals are discussed in two excellent solid state chemistry textbooks : P.A. Cox , The Electronic Structure and Chemistry of Solids , Oxford University Press , Oxford (UK) , 1987 ; Ch. 4 , pp. 79-133 ; R. Hoffmann , Solids and Surfaces , A Chemist’s View of Bonding in Extended Structures , VCH Publishers , New York , 1988 ; pp. 43-55 .

about 99% : A.B. Ellis et al. , Teaching General Chemistry , A Materials Science Companion , American Chemical Society , Washington , D.C. , 1993 ; pp. 191-192 (example of sodium metal) .

quite complex looking : A.R. Mackintosh , “The Fermi Surface of Metals”, Scientific American 209 (1) , pp. 110-120 (July , 1963) . The electron theory of metals is reviewed by W.J. Moore , Seven Solid States , An Introduction to the Chemistry and Physics of Solids , W.A. Benjamin , New York , 1967 ; Ch. 2 , “Gold”, pp. 41-72 ; see Fig. 2.4 , p. 49 for a graph of a typical Fermi-Dirac distribution curve . The Brillouin zone of gold is sketched in Fig. 2.9 , p. 62 , and the Fermi surface of gold is illustrated in Fig. 2.11 , p. 66 .

exist in the gas phase : G.R. Harrison and J.C. Slater , “Line Breadths and Absorption Probabilities in Sodium Vapor”, Phys. Rev. 26 (8) , pp. 176-188 (1925) . “It is suggested that this high pressure broadening is due to the presence of a large proportion of diatomic sodium molecules in varying states of stability which disturb the absorbing atoms far more than an inert gas would .....” [from the article abstract] . Na2 molecules may actually be quite common , at least in urban areas whose streets are lit with sodium vapour lamps , emitting that rather lurid pinkish-orange light .

Pauling in 1938 : L. Pauling , “The Nature of the Interatomic Forces in Metals”, Phys. Rev. 54 (11) , pp. 899-904 (1938) .

Jamieson : J.C. Jamieson , “Crystal Structures at High Pressures of Metallic Modifications of Silicon and Germanium”, Science 139 (3556) , pp. 762-764 (1963) .

Drickamer : H.G. Drickamer , Pressure and Electronic Structure, Science 142 (3598) , pp. 1429-1435 (1963) .

Moore : W.J. Moore , Seven Solid States (quite complex looking) , Ch. 4 , Steel, pp. 100-132 .

one-electron bond : L. Pauling , The Nature of the Chemical Bond and the Structure of Molecules and Crystals , 3rd ed. , Cornell University Press , Ithaca (NY) , 1960 , p. 340 ; A. Holden , The Nature of Solids , Dover Publications , New York , 1992 [reprint of the Columbia University Press textbook , 1965] ; p. 91 .

Curie magnetism of 2.22 BM : W.J. Moore , Seven Solid States (quite complex looking) , p. 104 .

electrical resistance of potassium and rubidium : see Drickamer above , pp. 1435 , and Figs. 9 and 10 on p. 1434 .

demetallization of cesium : Drickamer mentions Bridgman's study of compressed (2241 Kbars) cesium , in which ...... “There is a further large-volume discontinuity at 41 kilobars , accompanied by a very definite cusp in the electrical resistance (p. 1435) .

Wells : A.F. Wells , Structural Inorganic Chemistry , 3rd ed. , Clarendon Press , Oxford (UK) , 1962 . The sulfides , selenides , and tellurides of iron , cobalt , and nickel mostly have the nickel arsenide structure (Fig. 168 , p. 514) .

highly doubtful : The hybridization of native d orbitals in the molecular orbitals of the post-Transition metal elements has been extensively debated in the chemical literature , centering about various bonding schemes for sulfur hexafluoride , SF6 , in which the sulfur atom clearly uses some sort of hypervalent orbitals for its twelve-set :

R.G.A.R. Maclagan , “Symmetry , Ionic Structures and d Orbitals in SF6”, J. Chem. Educ. 57 (6) , pp. 428-429 (1980) ; A.E. Reed and F. Weinhold , “On the Role of d Orbitals in SF6”, J. Amer. Chem. Soc. 108 (13) , pp. 3586-3593 (1986) . These latter authors rather bluntly state :

“Models of SF6 requiring sp3d2 hybridization should be discarded” (p. 3586) .

See also E. Magnusson , “Hypercoordinate Molecules of Second-Row Elements : d Functions or d Orbitals ? ”, J. Amer. Chem. Soc. 112 (22) , pp. 7940-7951 (1990) ; P.G. Nelson , “Modified Lewis Theory , Part 1 . Polar Covalent Bonds and Hypervalency”, Chemistry Education : Research and Practice in Europe 2 (2) , pp. 67-72 (2001) [PDF , 161 KB] ; SF6 is discussed on pp. 70-71 .

In other Chemexplore web pages I have from time to time indicated the possible use of hypervalent d orbitals in post-Transition element hybrid orbitals , combined with their normal valent s and p orbitals , where their chemistry might reasonably permit such a hypothetical hybrid orbital . For example , the 4d orbitals and electrons in tin (4d10) seem to be quite accessible – tin readily forms hexahalostannate anions , and tin is octahedrally coordinated in perovskites such as BaSnO3 – so I was confident of using hypervalent 4d10 electrons in the Valence Bond electronic structure of white tin metal , which is sketched above . But the use of d orbitals for compressed sodium's 6-coordinate hybrid orbitals remains highly dubious to me !

Pauling pointed out : L. Pauling , The Nature of the Chemical Bond (one-electron bond) , pp. 118-120 .

Gatti , Tokatly , and Rubio : M. Gatti , I.V. Tokatly , and A. Rubio , “Sodium : A Charge-Transfer Insulator at High Pressures”, Phys. Rev.Lett. 104 , 216404 (2010) [PDF from ArXiv.org , 637 KB] .

inky , blue-black colour : J.L. Dye , “The Solvated Electron”, Scientific American 216 (2) , pp. 76-83 (February , 1967) [nice photos] ; J.L. Dye , “Electrides , Negatively Charged Metal Ions , and Related Phenomena”, Prog. Inorg. Chem. 32 , pp. 327-441 , S.J. Lippard (ed.) , John Wiley , New York , 1984 ; J.L. Dye , “Electrides : Ionic Salts with Electrons as the Anions”, Science 247 (4943) , pp. 663-668 (1990) ; M.J. Wagner and J.L. Dye , “Alkalides , Electrides , and Expanded Metals”, Ann. Rev. Mater. Sci. 23 , pp. 223-253 , R.A. Huggins et al. (eds.) , Annual Reviews , Palo Alto , CA , 1993 ; P.P. Edwards , “The Electronic Properties of Metal Solutions in Liquid Ammonia and Related Solvents”, Adv. Inorg. Chem. Radiochem. 25 , pp. 135-185 , H.J. Emelus and H.G. Sharpe (eds.) , Academic Press , New York , 1982 ; W.L. Jolly , “Metal-Ammonia Solutions”, Prog. Inorg. Chem. 1 , pp. 235-281 , F.A. Cotton (ed.) , Interscience , New York , 1959 ; M.C.R. Symons , “Nature of Metal Solutions”, Quart. Rev. 13 (2) , pp. 99-115 (1959) ; and , M.C.R. Symons , “Solutions of Metals : Solvated Electrons”, Chem. Soc. Rev. 5 (4) , pp. 337-358 (1976) .

F-centers : There is a nice color photo of such irradiated salt crystals in Van Nostrand’s Scientific Encyclopedia , fourth edition , 1968 , p. 374 . The F-centers are described as follows : “Certain crystals , such as the alkali halides , can be colored by the introduction of excess alkali metal into the lattice , or by irradiation with X-rays , energetic electrons , etc. Thus sodium chloride acquires a yellow color and potassium chloride a blue-violet color” (p. 384) . F-centers are also discussed by Moore , Seven Solid States (quite complex looking) , pp. 37-39 .

hydrogen : S.T. Weir , A.C. Mitchell , and W.J. Nellis , “Metallization of Fluid Molecular Hydrogen at 140 GPa (1.4 Mbar)”, Phys. Rev. Lett. 76 (11) , pp. 1860-1863 (1996) ; P.M. Celliers et al. , “Shock-Induced Transformation of Liquid Deuterium into a Metallic Fluid”, Phys. Rev. Lett. 84 (24) , pp. 5564-5567 (2000) ; W.J. Nellis , “Jumpin' Jupiter ! Metallic Hydrogen”, web page .

I wondered if a more stable type of metallic hydrogen might be synthesized by the inclusion with the hydrogen , under supercompression , of a quantity of lithium hydride , LiH . The resulting material would be LixH2-x , with mixed-valent hydrogen ( a hydrogen synthetic metal , Robin-Day Class IIIB) . The subscript “x” is a mole ratio taken experimentally between 0 and 1 , but would in practice probably be very small , maybe ~ 0.1 . The hydrogen's 1s sigma XO metallic bond would have an enhanced population of mobile , free electrons , the added electrons coming of course from the hydride anions' 1s2 orbitals . This mixed-valent lithium “superhydride” might be stabilized to a certain extent by the metallic bond electron resonance in its lattice . Similarly lithium superdeuteride , LixD2-x , might be synthesized . If it was stable at STP it could be examined as a potential fuel for nuclear fusion reactors .

iodine : see Drickamer , pp. 1432-1434 ; he and his co-workers did the pioneering work in the metallization of iodine .

crystalline nitrogen : M.I. Eremets et al. , “Single-Bonded Cubic Form of Nitrogen”, Nature Materials 3 , pp. 558-563 (August , 2004) ; Y. Ma et al. , “Novel High Pressure Structures of Polymeric Nitrogen”, Phys. Rev. Lett. 102 , 065501 , 4 pp. (2009) [PDF , 778 KB] ; X. Wang et al. , Diamondoid Structure of Polymeric Nitrogen at High Pressures”, June 25 , 2012 , ArXiv.org [PDF , 2780 KB] ; A. Goho , Nitrogen Power : New Crystal Packs a Lot of Punch”, Science News Online web page ; S.K. Ritter , “Polymeric Nitrogen”, Chemical & Engineering News , July 27 , 2004 web page ; “Polymeric Nitrogen : A Potential Compound to Store Energy”, ScienceMadness [PDF , 674 KB] ; J.M. Crow , “Nitrogen Does Diamond”, Chemistry World , October 31, 2012 web page ; “Cubic Nitrogen with Single N–N Bonds”, WebElements Nexus web page .

carbonia glass : M. Santoro et al. , “Amorphous Silica-like Carbon Dioxide”, Nature 441 (7095) , pp. 857-860 (2006) ; “Dry Ice Creates Toughened Glass”, BBC web page ; “Carbon Dioxide Glass Created in the Lab”, New Scientist Tech , June 15 , 2006 web page ; “Amorphous Carbonia”, Wikipedia web page .

 

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