Systematic Design of Complex Wurtzites and Zinc Blendes
Wurtzite and zinc blende crystal structures were prominently featured in recent Chemexplore web pages about super-electrides and Drude metals , and are of continuing interest in my exploration of solid state materials . The component atoms in wurtzites and zinc blendes all have a tetrahedral coordination to one another . The M (typically metal) and X (typically nonmetal) atoms alternate in the structure , which has an MX empirical formula . The zinc blendes feature a cubic packing arrangement of their atoms, while the wurtzites have a hexagonally packed lattice , as shown in the following sketch :
The above composite sketch was prepared from separate graphics from the Wikipedia web pages , Wurtzite Crystal Structure and Cubic Crystal System . I thank the authors of these sketches , and Wikipedia , for implied permission to reproduce them on this web page .
I was both puzzled and curious as to how the MX atoms could be packed differently into the crystalline solid , yet have identical tetrahedral coordinations . I found an excellent representation of the two structures on the web page VRML Structure Type Gallery , Part 2 , AB , by Dr. Steffen Weber . 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 . Impressive models of the zinc sulfide crystal structure are presented on PDF page 17 (zinc blende , also known as sphalerite) and on PDF page 18 (wurtzite ; ZnS is one of the MX compounds that is known to have both types of structure) .
The wurtzite sketch on Dr. Weber's crystal structures web page was particularly helpful in my understanding of the difference between the zinc blende and wurtzite structures . First , using my own molecular modeling software (the now discontinued Molecules 3D) I built a model of the zinc blende structure . I presume all the readers have at least a basic knowledge of organic chemistry . The cyclohexane molecule can have two geometrical conformations , chair and boat, of which the former is more thermodynamically stable . The zinc blende structure was quickly and easily assembled from layers of MX atoms , in six-atom rings having the chair conformation :
The layers of chair-form rings are stacked neatly above each other in a nested pattern , like stacks of patio chairs . The above model can be rotated to show the cubic packing of the MX atoms :
The wurtzite model was more difficult to build , but the illustration of it on Dr. Weber's web page provided the clue necessary to solve the puzzle . Wurtzite also consists of chair-form MX rings , but now they are reversed 180º in direction from layer to layer :
Rotating this latter model clearly shows the hexagonal packing of the MX atoms in the lattice :
There apparently is only a small energy difference between the zinc blende and wurtzite forms , and a number of MX compounds can be found having both structure , under different chemical and physical conditions . Zinc sulfide , as mentioned above , is one such compound ; however , zinc oxide is uniquely wurtzite .
Chemical bonding in compounds having the zinc blende and wurtzite structures is exclusively covalent and coordinate covalent . While there is no theoretical objection for an ionic MX compound to have tetrahedrally coordinated cations and anions , in practice almost all of them (that I know of) have higher coordination numbers , mostly octahedral (CN = 6 , rocksalt) and a few square prismatic ones (CN = 8 , cesium chloride) .
Another interesting observation is that few Transition metal elements form zinc blendes or wurtzites . Copper(I) and silver(I) in the IB/11 Family do form zinc blendes and wurtzites , but arguably Cu(I) and Ag(I) are behaving more like post-Transition than Transition metal elements in these cases , with a pronounced tendency toward covalent bonding . Beryllium seems to be the only member of the s-Block (pre-Transition metal) group that forms zinc blende (BeS , BeSe , and BeTe) and wurtzite (BeO) MX compounds . Exceptionally , beryllium is noteworthy for strong covalent bonding in its compounds , which is unusual in the Alkali and Alkaline Earth families of elements , which have mostly ionic compounds :
Common features of all the zinc blendes and wurtzites from across the Periodic Table is that their MX bonds are covalent in nature , and that the s and p valence shell electrons and orbitals of the participating M and X atoms are involved in those covalent bonds . The simplest way of describing the chemical bonding in these materials is to say their native s and p orbitals form a tetrahedral sp3 hybrid orbital containing the electronically stable octet of electrons around the M and X kernels .
This is the reason why there are few if any Transition metal element wurtzites and zinc blendes . Their valence shell electrons are in d orbitals , which generally form more complicated hybrid orbitals for their chemical bonding . These complex d type orbitals typically result in coordination numbers higher than 4 (tetrahedral) , most commonly with CN = 6 (octahedral) . While the early and middle Transition elements can form tetrahedral d3s hybrid orbitals for covalent bonding , it seems that in practice they use them only for tetrahedral molecular complexes , but not for infinite atomic lattices (non-molecular crystalline solids) .
The octet totally dominates the electronic structure of the zinc blende and wurtzites , as illustrated in the following simple Valence Bond sketches :
In these MX compounds the M and X valence electrons are being combined into octets in the four sigma covalent bonds surrounding the atoms , such that vM + vX = 8 , where vM = the number of M valence electrons and vX = the number of X valence electrons participating in the octets surrounding M and X . For example , in the wurtzite compound ZnO vZn = 2 (zinc's 4s2 valence electrons) , vO = 6 (oxygen's 2s2 2p4 valence electrons) , and vZn (2) + vO (6) = 8 , completing the octets around both the zinc and oxygen atoms in the ZnO lattice . Similarly in CuCl (wurtzite) , vCu (1) + vCl (7) = 8 ; in the famous electronic material gallium arsenide vGa (3) + vAs (5) = 8 ; and in silicon carbide (the industrial abrasive carborundum) vSi (4) + vC (4) = 8 .
Many binary MX wurtzites and zinc blendes are well known at this time , as shown by the examples in the above tabulation . It would be interesting to explore the possibility of designing new ternary (AMX) and quaternary (AMXZ) wurtzite and zinc blende compounds , in a rational , systematic manner . Since all the A , M , X , and Z atoms must be surrounded by an octet of valence electrons , each of them must have an average of four valence electrons from whatever source . Therefore , the ternary compounds must have a total contribution of 3 x 4 = 12 valence electrons from its three component atoms . That is , vA (av. 4) + vM (av. 4) + vX (av. 4) = 12 for the ternary compound AMX . Similarly , for the quaternary wurtzite or zinc blende AMXZ , vA (av. 4) + vM (av. 4) + vX (av. 4) + vZ (av. 4) = 16 . Let's examine the ternary AMX wurtzites and zinc blendes first .
Ternary AMX Wurtzite and Zinc Blende Compounds
The rule of thumb vA (av. 4) + vM (av. 4) + vX (av. 4) = 12 for the AMX ternary compounds resolves into (1) what numerical combinations can be devised to satisfy this relationship ; and (2) what useful , practical chemistry might represent the various combinations . We could simply insert a 4 into the binary combinations mentioned above :
1 + 7 (CuCl) + 4 = 12 and its derivative 1 + 6 + 5 ;
2 + 6 (ZnO) + 4 = 12 and its derivatives 2 + 5 + 5 and 2 + 3 + 7 ;
3 + 5 (GaAs) + 4 = 12 and its derivative 3 + 6 + 3 ;
and 4 + 4 (SiC) + 4 = 12 .
These eight numerical combinations could potentially encompass a wide range of solid state chemistry . Ignoring the oddball beryllium , the A , M , and X elements comprising the hypothetical new wurtzites and zinc blendes would be selected from the seven families (11 to 17 inclusive) shown in the tabulation above . Let's consider each of the eight combinations to see if any realistic compounds might be predicted from them .
1 + 7 + 4 :
The 1 in this group will be represented by Cu(I) , and the 7 will always be a halogen such as Cl . The 4 will have to be carbon or silicon . A reaction such as :
CuCl (m.p. 423 ºC , b.p. 1490 ºC) + Si0 (m.p. 1414 ºC) ------- [HPHT] -------> CuSiCl ,
seems impractical at first glance , as silicon is an excellent reducing agent , and copper(I) is a mild oxidizer (Cu1+ + e¯ ----> Cu0 ; E0red = 0.521 V) . The HPHT refers to the high pressurehigh temperature conditions in an anvil or belt type of press in which the reagents would be compressed and heated . If the three component elements could successfully be contained in the reaction chamber the ternary compound CuSiCl , having the wurtzite or zinc blende crystal structure , might be recovered on cooling the product to room temperature and de-pressurizing it .
The possible reaction of CuCl (1.0 eq.) with graphite (1.0 eq.) under HPHT conditions would also be interesting to investigate , possibly producing CuCCl .
1 + 6 + 5 :
The 1 will once again be copper , while the 6 would be oxygen or a chalcogen such as sulfur , selenium , or tellurium . The 5 could be a pnictogen such as phosphorus , arsenic , or antimony . The simplest preparative procedure would probably be a direct combination of the three elements concerned (except for oxygen , which could be added from CuO , for example) :
Cu0 (m.p. 1085 ºC) + P0 (red , m.p. 579 ºC , sublimes 431 ºC) + S0 (m.p. 115 ºC , b.p. 445 ºC)
------- [HPHT] -------> CuPS ;
CuO (m.p. 1227 ºC) + As0 (sublimes 616 ºC) ------- [HPHT] -------> CuOAs .
2 + 6 + 4 :
Let's try 2 = zinc , 6 = a chalcogen , and 4 = silicon :
Zn0 (m.p. 420 ºC) + ½ SiS2 + ½ Si0 ------- [HPHT] -------> ZnSSi ; or ,
ZnS (m.p. 1700 ºC) + Si0 (m.p. 1414 ºC) ------- [arc furnace] -------> ZnSSi .
The latter synthesis might be best conducted in an arc furnace under an inert atmosphere of argon . Several references describing syntheses carried out in an arc furnace : T.B. Reed and E.R. Pollard , Niobium Monoxide, Inorg. Synth. 14 , A. Wold and J.K. Ruff (eds.) , McGraw-Hill , New York , 1973 ; pp. 131-134 . This was reprinted in Inorg. Synth. 30 , Nonmolecular Solids , D.W. Murphy and L.V. Interrante (eds.) , John Wiley , New York , 1995 ; pp. 108-110 . A recommended review of the arc furnace method of syntheses involving refractory materials : T.B. Reed , Arc Techniques for Materials Research, Mater. Res. Bull. 2 (3) , pp. 349-367 (1967) [DOI] . Theodore Gray describes a home-made arc furnace in Melting the Unmeltable, Popular Science , p. 134 , May , 2004 [JPEG image , 479 KB] .
2 + 5 + 5 :
Again 2 will be zinc , while 5 would be a pnictogen :
Zn0 + 2 P0 (red , m.p. 579 ºC , sublimes 431 ºC) ------- [HPHT]
-------> ZnP2 (not the conventional Zn3P2) .
2 + 3 + 7 :
Try 2 = Zn ; 3 = B , Al , Ga , In ; 7 = a halide ; for example ,
Al0 (m.p. 660 ºC) + ½ Zn0 (m.p. 420 ºC) + ½ ZnCl2 (m.p. 290 ºC , b.p. 732ºC)
------- [HPHT] -------> AlZnCl .
This reaction would probably not occur using fluoride as the halogen atom , since the fluorides of aluminum and zinc are ionic in nature . However , anhydrous AlCl3 and ZnCl2 have considerable covalent character , and this covalency could carry over into the hypothetical compound AlZnCl , which must have covalent AlCl and ZnCl bonds in its wurtzite or zinc blende structure . Note that while there would be four metalCl bonds per formula unit of AlZnCl , there would also have to be two MM covalent bonds per molecule of AlZnCl , probably AlZn but maybe AlAl and ZnZn as well . Such MM covalent bonds are a prominent feature of the well known Zintl intermetallic compounds .
3 + 5 + 4 :
Try 3 = B , Al , Ga , In ; 5 = a pnictide (P , As , Sb) ; and 4 = carbon or silicon ; for example ,
Al0 (m.p. 660 ºC) + P0 (red , m.p. 579 ºC , sublimes 431 ºC) + Si0 (m.p. 1414 ºC)
------- [HPHT] -------> AlPSi .
Silicon nitride , Si3N4 , which is readily available at a moderate cost (it has various applications as a refractory material) , could provide the 4 + 5 valence electrons in a ternary wurtzite or zinc blende . The third component must supply the 3 electrons to complete the set of 12 electrons for the three component atoms :
B0 (m.p. 2075 ºC) + ¼ Si3N4 (m.p. 1900 ºC , dec) + ¼ Si0 (m.p. 1414 ºC)
------- [fuse together in an arc furnace under an argon atmosphere] -------> BNSi ; or ,
BN (m.p. 2973 ºC , subl.) + Si0 ------- [arc furnace under Ar atmosphere] -------> BNSi .
In the latter reaction either the cubic boron nitride (a very hard , diamond-like material) , or hexagonal BN (a white , very soft , graphite-like solid) could be used as the BN reagent . The hexagonal form seems to be somewhat cheaper than cubic BN , and would obviously be much easier to triurate with the powdered silicon co-reagent in a mortar with a pestle when preparing the reaction mixture .
3 + 6 + 3 :
This combination suggests the reaction of two equivalents of a IIIA/13 Family element with one equivalent of oxygen or a chalcogen . For example , the hypothetical compound boron suboxide , B2O , might be a stable wurtzite or zinc blende :
4/3 B0 (m.p. 2075 ºC) + 1/3 B2O3 (m.p. 450 ºC) ------- [HPHT] -------> B2O ;
4/3 B0 + 1/3 B2S3 (m.p. 563 ºC) ------- [HPHT] -------> B2S .
Since there are twelve valence electrons per formula unit in the covalent bonds of B2O and B2S , there will be six covalent bonds per molecule of these compounds . There certainly wouldn't be any OO bonds in B2O ; given that there must be four BO bonds per molecule of B2O , the two remaining covalent bonds in its lattice must be BB . This wouldn't be a problem , since the BB covalent bonds in elementary boron are extremely strong (its m.p. is 2075 ºC ; boron is a highly refractory material) .
The BO and BB bonds might be distributed in a regular , repeating sequence in the lattice , or they might be distributed randomly , resulting in a stochastic compound . This sort of material would be both fascinating and alarming to chemists . Because of the random arrangement (stochastic : dependent on the laws of probability) of the B and O atoms in the B2O , no matter how many times the compound was synthesized , no two samples of it would ever have exactly the same atomic arrangement in the lattice . The chemical composition of the many samples might be identical , and their crystal structure wurtzite or zinc blende might be identical , but their X-ray diffraction patterns would always be slightly different . Of course , reproducibility of experimental results is of paramount importance in all scientific disciplines , so such stochastic solid state materials might be philosophically upsetting to more conventional-minded researchers .
The hypothetical compound B2S brings to mind another unusual boronsulfur compound , boron monosulfide , BS (seriously !) . It's appropriate to this present discussion because BS was prepared from equimolar quantities of B and S under HPHT conditions in a tetrahedral anvil press :
Hall's interesting review of his HPHT research can be downloaded from the Internet (PDF , 1109 KB) . I recall many years ago coming across the original reference to Hall's synthesis of BS in Chemical Abstracts , which however is no longer available to me . The diamond-like form had the zinc blende crystal structure , and was described as being metallic (I think the other form he mentioned must be hexagonal wurtzite , apparently with the excellent thermoelectric properties) .
The metallic nature of boron monosulfide originates in the odd number of valence electrons involved in the sp3 hybrid orbitals : three from boron , and six from sulfur . Sulfur would donate one electron to boron ; then both B and S could have octets . The extra ninth electrons (formally from sulfur) would be located in vacant frontier orbitals , probably sulfurs' 4s,p , as considerably less energy is required to make the 3s,p>4s,p transition in the sulfurs than the 2s,p>3s,p transition in the boron atoms . These extra , ninth electrons would be the mobile , free electrons in the conduction bandmetallic bond of zincblende BS , making the compound a metallic solid .
Hall's HPHT synthesis of BS is reminiscent of Donohue's preparation of tin(III) phosphide , SnP , which is also a covalentmetallic solid :
P.C. Donohue , The Synthesis , Structure , and Superconducting Properties of New High-Pressure Forms of Tin Phosphide, Inorg. Chem. 9 (2) , pp. 335-337 (1970) [DOI] .
When tin metal and red phosphorus are combined under ambient pressure conditions (but at elevated temperatures , eg. 200 ºC) , the compound Sn4P3 is formed ; for example ,
K.A. Kovnir et al. , A Facile High-Yield Solvothermal Route toTin Phosphide Sn4P3, J. Solid State Chem. , 179 (12) , pp. 3756-3762 (2006) [DOI] .
If equimolar quantities of Sn and P are combined under HPHT conditions (eg. 65 kbars , ~ 65,000 atm , and 800 ºC) in a tetrahedral anvil press , the covalentmetallic SnP is produced . The cubic rocksalt form of SnP is an excellent electrical conductor over a wide range of temperatures , and it is superconducting below 2.84.8 K . Donohue's preparation of SnP is the model of the sort of HPHT synthesis that would be required for all the wurtzite and zinc blende compounds proposed in this web page .
The hypothetical compounds B2O and B2S are not unreasonable , as boron compounds have exclusively covalent bonding . Al2O , on the other hand , is probably not stable at STP as a zinc blende or wurtzite under any conditions , because the aluminumoxygen system is strongly ionic (Al3+O2-) and not covalent in nature .
Several unsuccessful attempts to synthesize subvalent aluminum oxides and sulfides (Al2O , AlO , Al2S , and AlS) have been reported in the chemical literature : M. Hoch and H.L. Johnston , Formation , Stability and Crystal Structure of the Solid Aluminum Suboxides : Al2O and AlO, J. Amer. Chem. Soc. 76 (9) , pp. 2560-2561 (1954) [DOI] ; C.N. Cochran , Aluminum Suboxide Formed in Reaction of Aluminum with Alumina, J. Amer. Chem. Soc. 77 (8) , pp. 2190-2191 (1955) [DOI] . See also T. Forland et al. , Measurements of Phase Equilibria in the Aluminum Aluminum Sulfide System, Acta. Chem. Scand. , Series A28 (2) , pp. 226-228 (1974) [PDF , 375 KB ; DJVU , 109 KB ; a suitable DjVu reader for your computer can be downloaded for free from djvu.org . The WinDjView reader v. 1.0.3 for older FAT 32 Windows OS can be downloaded for free from FileHorse] . The compound AlS has a narrow window of stability between 1010 ºC and its m.p. of 1060 ºC .
Forland and co-workers mention that ....... the compound Al2S only exists in the gas phase. The aluminumsulfur system is more covalent than the ionic Al3+O2- compounds , so there remains some hope that Al2S might be isolated as a stable phase at STP provided that it is synthesized under HPHT conditions in an anvil or belt type of press :
2 Al0 (m.p. 660 ºC) + S0 (m.p. 115 ºC , b.p. 445 ºC) ------- [HPHT] -------> Al2S ; or ,
4/3 Al0 + 1/3 Al2S3 (m.p. 1100 ºC) ------- [HPHT] -------> Al2S .
The HPHT conditions employed in this latter reaction might at least initially be similar to those Donohue used in his preparation of the cubic rocksalt SnP . Hall's synthesis of the unusual boron monosulfide under HPHT conditions in his tetrahedral anvil press , and indeed the extraordinary achievements of high pressure chemistry in general , provide some encouragement that stable , isolable , wurtzite or zinc blende Al2S might some day be accessible by this route .
The chemical bonding in Al2S should resemble that in the hypothetical B2O discussed above . There would be four AlS bonds per molecule of Al2S , plus two additional AlAl bonds per formula unit of the compound . Aluminumheteroatom covalent bonds are well known both in inorganic compounds such as anhydrous AlCl3 , and in organometallic chemistry , where they are strongly polarized (Al+H- and Al+C-) . The AlAl bonds required in Al2S might not be very strong , and could detract from the overall stability of any crystalline Al2S prepared by a HPHT procedure .
Gallium and indium have a few reasonably stable low-valent compounds with some covalent bonding character , so there is a good chance they can particpate in the formation of 3 + 3 + 6 M2O and M2S ternary wurtzites or zinc blendes . Gallium is also known to form GaGa covalent bonds in certain of its compounds (such as in GaS , GIF image , 47 KB) . This ability would be advantageous in the synthesis of Ga2O and Ga2S wurtzites or zinc blendes in which such GaGa bonds would be present together with GaO and GaS .
4 + 4 + 4 :
With only two useful elements , carbon and silicon , in the 4 group (IVA/14 Family of elements) [tin(IV) has been used in certain wurtzites such as Cu2ZnSnS4 , discussed below] , the possibilities for the design and synthesis of ternary wurtzites and zinc blendes with 4 atoms will be limited . One interesting investigation that comes to mind is a study of carbonsilicon compounds with variable mole ratios of C and Si , eg. C + C + Si , C + Si + Si , and so on .
Three members of this SiC family are of course very well known : diamond , 100 mole % carbon ; silicon carbide , SiC , 50 mole % carbon , 50 mole % silicon ; and silicon , 100 mole % Si . Very pure , undoped diamond and chemically pure silicon carbide (the latter usually referred to by its mineral name of moissanite) are both colorless , transparent , highly refractive , hard , refractory solids . Silicon is an opaque , brittle , crystalline solid with a bluish gray color and metallic luster :
The controlled doping of graphite with increasing mole ratios of silicon could be of possible industrial significance . The sp2 (trigonal planar) carbon atoms from the graphite might recrystallize into the sp3 tetrahedral carbon in the diamond structure , using the doped silicon atoms (always sp3) as the seed, or template tetrahedral atoms . It might thus be possible to synthesize inexpensive industrial diamonds in relatively large batches , containing only very low mole ratios of silicon dopant atoms :
x Si0 (m.p. 1414 ºC) + (1x) C0 (graphite , m.p. 3825 ºC , sublimes)
------- [arc furnace , argon atmosphere] -------> SixC1-x .
The proposed arc furnace synthesis would somewhat resemble the principal industrial method for the manufacture of carborundum , the Acheson Process . In the above equation x = a mole ratio taken experimentally from 0 to 1 by the researcher . In the case of the industrial diamonds , x might be fairly low , perhaps only 0.1 , ie. 10 mole % silicon in the compound Si0.1C0.9 (I'm just guessing this value) . Synthetic diamonds of pure carbon are of course well known , such as the Apollo diamond , made by a chemical vapor deposition (CVD) process :
My thanks again to Wikipedia for implied permission to reproduce this photograph here . It was copied from the web page Diamond , and was size-reduced to fit comfortably on this web page) .
Diamonds doped with heteroatoms often have interesting optical and electronic properties . Both natural and synthetic diamonds may be obtained in a wide spectrum of colors . Apparently the most common of the natural colored stones are the yellow diamonds :
This photograph was copied from the web page Yellow Diamonds , by Roy W. Macdonald . My thanks to Mr. Macdonald (presumably the copyright holder of this picture) .
The yellow color is caused by the replacement of a very small mole percent of the carbon atoms by nitrogen atoms in the tetrahedral lattice . Since nitrogen is a 5 in the wurtzitezinc blende scheme , its excess fifth valence electron must be relocated in the interatomic void space . These free , singlet electrons can absorb radiant energy in the blue-green end of the visible light spectrum passing through the transparent crystal . The emergent light , having lost some of its blue-green wavelengths to the free electrons , now looks yellow . Such yellow diamonds might be synthesized by doping the graphitesilicon reaction mixture in the above equation with a very small mole ratio of silicon nitride , mentioned earlier in connection with the 3 + 5 + 4 wurtzitezinc blendes .
Diamonds can be colored blue by the replacement of very small numbers of their carbon atoms by boron atoms . The Hope Diamond is a famous (some might say notorious) blue diamond :
My thanks again to Wikipedia for implied permission to reproduce this photograph here . It was copied from the web page Hope Diamond , and was trimmed slightly and size-reduced to fit comfortably on this web page .
Since boron is a 3 with respect to its valence shell electrons , inclusion of very small mole ratios of boron in the diamond's tetrahedral lattice will result in one-electron BC bonds (one of the four BC covalent bonds per B atom) . These one-electron bonds can resonate throughout the lattice with their neighbouring two-electron BC bonds , especially when they are photoexcited by the absorption of radiant energy (visible light wavelengths) passing through the structure . In this case the red , yellow , and orange wavelengths are absorbed by the singlet electrons in the one-electron bonds , with blue light emerging from the crystal . Blue diamonds might be synthesized in this present context by the inclusion of very small mole ratios of elementary boron in the graphitesilicon reaction mixture , in the equation shown above .
The solid state physics lecture , Zincblende vs Wurtzite Structures [web document from Simon Fraser University , Burnaby , British Columbia , Canada , PDF , 164 KB] discusses wurtzite and zinc blende semiconductor compounds on pp. 16-19 . The author mentions Family IVA/14 binary compounds he refers to them as alloys such as SixC1-x on p. 18 , and more complex ternary and quaternary compounds on p. 19 .
Quaternary AMXZ Wurtzite and Zinc Blende Compounds
For the quaternary AMXZ compounds vA (av. 4) + vM (av. 4) + vX (av. 4) + vZ (av. 4) = 16 , as mentioned earlier . Many permutations and combinations of the different valence electron contributions from the four participating elements are possible . For example , we could consider various couples of the binary wurtzites and zinc blendes discussed above :
(1 + 7) + (2 + 6) ; (1 + 7) + (3 + 5) ; and (1 + 7) + (4 + 4) ;
(2 + 6) + (3 + 5) and (2 + 6) + (4 + 4) ;
and (3 + 5) + (4 + 4) .
Most of these formulations probably would be neither feasible nor useful in actual practice , though .
The thermochromic ionic conductor Cu2Hg[ ]I4 was introduced in the Electrons web page . It's a double wurtzite (GIF image , 52 KB . Note : this graphic actually represents a cubic zincblende structure . My apologies !) , with alternating layers of CuI and Hg[ ]I2 , where [ ] is a cation void space . This system has 32 valence electrons per formula unit : 2 x 1(Cu) + 1 x 2 (Hg) + 4 x 7 (I) . The number of atoms per formula unit is 7 , plus the cation void . Each atom , including [ ] , thus has an average of 4 valence electrons . There are 28 MI covalent bonds per formula unit , plus 4 additional iodide lone pairs surrounding the cation vacancy .
The valence electron distribution in Cu2Hg[ ]I4 breaks down as follows : 1 + 7 (CuI) , 1 + 7 (CuI) , 2 + 7 (HgI) , and 0 + 7 ([ ] I) . This analysis suggests another design concept for a series of quaternary compounds modelled on Cu2Hg[ ]I4 :
1 + 7..............1 + 7..............2 + 7..............0 + 7 ; eg. Cu2Zn[ ]Cl4 and CdLi2[ ]Br4 .
2 + 6..............2 + 6..............3 + 6..............1 + 6 ; eg. AlCuZn2S4 and LiMg2BSe4 .
3 + 5..............3 + 5..............4 + 5..............2 + 5 ; eg. Al2SiZnP4 and Ga2GeCdAs4 .
The quaternary wurtzite Cu2ZnSnS4 is currently receiving considerable attention as an electronic component of solar cells (eg. PDF , 764 KB ; this DOI ; and this DOI . Download this PDF , 417 KB , for an article about its selenium analogue , Cu2ZnSnSe4) . Both Cu2ZnSnS4 and Cu2ZnSnSe4 have eight atoms per formula unit , with 32 system electrons , or an average of four valence electrons per atom . The valence electron breakdown in Cu2ZnSnS4 is : 1 + 6......1 + 6......2 + 6......4 + 6 . Formulation of tin(IV) in the compound permits the use of a chalcogen (sulfur , 6) as the nonmetal element , instead of a halogen , like the iodine in Cu2Hg[ ]I4 . Note that tin(IV) is usually octahedrally coordinated by nonmetal ligands in non-molecular solids , such as in tin(IV) sulfide , SnS2 (GIF image , 24 KB) .
Zn2LiGaO4 is another quaternary wurtzite being studied as a semiconductor (DOI) . It also has 32 system electrons and eight atoms per formula unit . Its nonmetal atom component is surprisingly oxygen . Generally , greater electronic activity is observed in compounds having heavier nonmetal atoms such as sulfur and selenium , for example . This is because the s , p, and d energy levels are spaced more closely in the heavier than in the lighter elements (GIF image , 16 KB) . The more closely together the energy levels are spaced , the less energy is required to promote valence shell electrons from one level to another , or to vacant , higher energy level frontier orbitals . In essence , as the element becomes heavier and heavier , its valence electrons and their orbitals become fuzzier and fuzzier and blend together into broad , diffuse bands . Those heavier atoms and their compounds are easier to stimulate with various forms of energy , making them electronically active and thus of considerable interest to investigators . The lighter elements and their compounds , with valence shell electrons and orbitals at the 2s,p and 3s,p levels , by comparison tend to be more electronically inactive , if not inert , than the heavier atoms with 4s,p , 5s,p , and 6s,p valence shell electrons .
The vast number of possible combinations of the four tetrahedral AMXZ atoms in quaternary wurtzites and zincblendes provides solid state researchers with a wide scope for designing many new compounds in this important class of materials . Most such formulations would probably be created with an electronic end-use in mind , such as in the solar photovoltaics field , for example . In any event I hope the design concepts outlined above will be useful in the future study and development of ternary and quaternary wurtzites and zincblendes .
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