Effect of atomic displacements in covalent solids

Solid State Communications, Vol. 18, pp. 5—8, 1976.

Pergamon Press.

Printed in Great Britain.

EFFECT OF ATOMIC DISPLACEMENTS IN COVALENT SOLIDS B. Szigeti University of Reading, England (Received 7 July 1975 by C.W. McCombie)

In covalent materials the electronic wave functions are very sensitive even to small displacements, while with displacements of increasing magnitude the stability of the covalent bond gradually decreases and eventually another type of bond becomes more favourable. This has consequences for some of the properties of covalent solids even at low temperature and produces significant changes with increasing temperature and on melting.

COVALENT SOLIDS have received considerable interest in recent years1’2 While considerations so far have been based mainly on the undisplaced configuration of the lattice, the purpose of this communication is to draw attention to some of those characteristic aspects of the behaviour of these materials which are connected with atomic displacements.

static dielectric constant, but the magnitude of this quantity bears hardly any relation to the “static charge” of the atoms, by whatever criterion the latter is defined3’5’6 Perhaps the most striking proof of this statement is provided by selenium and tellurium,7 where the infrared absorption and hence e* is quite large while, since all the atoms are of the same type, the static charge is strictly zero.

We shall use the term “covalent solid” to denote solids where each atom is bound entirely or predominantly by covalent forces to all its neighbours, i.e. the term will include materials like diamond, germanium, the IlL—V compounds, Si0 2, etc. It will however not include molecular solids, since in these the atoms in different molecules are not bound by covalent forces. 3 that in a coIt solid has been pointedcannot out elsewhere valent the atoms be looked upon as mdividual units. The electrons in a bond connecting two adjacent atoms berong to both atoms simultaneously and cannot be divided up between them. In a lattice displacement there is a complicated change in the valency electron wave functions and this electronic deformation is primarily responsible for the large vibrational absorption and the relatively large lattice contribution to the static dielectric constant exhibited by many covalent materials. One can of course define4 a vibrational effective charge e* whose value can be obtained from the infrared absorption and the

We further recall that usually only a rather narrow range of interatomic distances is favourable for the formation of a covalent bond. Moreover, taking the bonds formed by sp hybrids as an example, we expect that in materials like InSb or germanium a change in the bond type due to a change in interatomic distance will occur more readily than in materials like BN or diamond, because the substances energy of hybridization is much smaller in the latter than in the former. Changes in the bond angles will have similar effects as changes in bond lengths, although to a lesser degree. Thus it follows that in covalent solids an atomic displacement is necessarily accompanied by a significant rearrangement of the valency electrons. For small displacements this rearrangement is linear in the displacement, but even then the factor of proportionality can be expected to be large, and this is borne out by the large measured values of the vibrational effective charges. For very large displacements the 5

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EFFECT OF ATOMIC DISPLACEMENTS IN COVALENT SOLIDS

electronic rearrangement is quite fundamental and the bond usually loses its covalent character. If the conditions are not suitable for the formation of an alternative type of bond then for large changes of distance or of bond angles the bonding forces become very weak, In addition to the large effective charges,another consequence of these properties is that in pure covalent solids the number of lattice vacancies and interstitials is very small and so is the mobility of the interstitials. For data on the Ill—V compounds, see for instance Kendall.8 One of the most interesting effects of atomic motion on the covalent bond is the fact that covalency ceases on melting. This at least is the case for those covalent solids whose melting has been investigated. The reason is mainly that both the mean interatomic distance and the amplitude of the thermal motion is too large in the liquid for the covalent bond to survive. It is well established, although perhaps not widely known, that germanium, silicon and all those Ill—V compounds for which data are available, become metallic on melting. This follows from a large variety of measurements. For instance, the electrical resistance shows a sharp decrease on melting and acquires a positive temperature coefficient.9’2 X-ray measurements and other arguments13 ~16 show that on inciting the coordination number increases, usually to six, and at the same time both the density and also the mean nearest neighbour distance increase sharply, again indicating metallic behaviour in the liquid. in addition, solid-liquid phase diagrams are available for many Ill—V compounds (cf. Sirota’~)which show that while below the melting point more than a very small excess of either of the two kinds of atoms will separate as a second phase, above the inciting point the ratio of the two components can be varied within very wide limits without producing a second phase. The liquid thus behaves like a two-component metallic alloy. The case of carbon is rather interesting. Because ot the very high melting temperature of this substance

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there is not much information on the liquid phase. but there can be little doubt that carbon also ceases to be covalent on melting. The melting temperature of graphite at various pressures has been measured by 17 who found that above 60 Kbar the liquid is Bundy, denser than the solid, while at low pressures the liquid is much less dense. The electrical conductivity substantially increases on melting at all pressures. Using Bundy’s thermodynamic data, Korsiinskaya

ci al. 18 calculated that at zero pressure, at the melting temperature the liquid is at least 40% less dense than solid graphite, hence about twice less dense than diamond. These authors suggest that liquid carbon is a mixture of a high-pressure or metallic form and of a low pressure form which consists of neutral atoms, and that the proportion of the “metallic form” increases with pressure. Independently of whether oi not this model is correct, from the large change of density on melting at both high and low pressures we can safely conclude that the liquid is not covalent. However, in that case the s and p electrons are no longer hybridized and the valency bonds are then only partially filled, and the liquid may be expected to have metallic properties even at low pressures. Professor H. Bilz points out to me that about thirty years ago J.C. Slater showed that for similar reasons solid carbon would he matallic if the interatomic distance were either substantially larger or substantially smaller than its actual value. In solid tellurium, and also in the most stable form of solid selenium, the atoms are arranged in helix-shaped molecules. The intramolecular forces are of course predominantly covalent, while the forces between atoms of adjacent molecules are partly of the Van der Waals type, partly dipolar and also partly covalent. The dipolar forces arise because as a result of the low symmetry each atom has a permanent dipole moment while the covalent forces are due to those valency electrons which are not involved in the intramolecular binding. It follows from structural details and also from other properties (cf. for instance Grigorovici19) that the covalent contribution to the inter-molecular forces is substantially weaker in selenium than in tellurium. It is thus thought that sdenium is essentially a molecular solid and it is known that on melting it forms a molecular liquid. Whether the inter-molecular covalency in the solid is strong or weak, we expect that it disappears or at any rate

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becomes very much weaker on melting, although on this point there is no direct experimental information, It is significant that not only are the intermolecular covalent forces stronger in solid tellurium than in solid selenium, but at the same time the two substances also behave rather differently on melting. As Tourand etaL20 have shown, when tellurium melts the molecular helixes disappear and the coordination number of the atoms increases. Contrary to earlier view, these authors also conclude that liquid tellurium is metallic. Enderby2’ also concludes that liquid tellurium “is a semi-metal, i.e. essentially metallic in character”. It thus appears that all those covalent materials for which there is sufficient information cease to be covalent when they melt. In connection with the melting of silicon, germanium and the Ill—V cornpounds a rather similar view as expressed here has been taken by several chemists some years ago (e.g. Krebs eta!.’6), who considered that these substances become metallic on melting because the covalent structure is too rigid for the liquid state. This opinion was however largely ignored in the literature; as the wave functions of these materials exhibit a certain amount of “metallicity” even in the solid state (i.e. the shared electrons are not concentrated in the bonds as strongly as for instance in diamond), and as they exhibit strongly increasing semiconduction with in-

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and the stability of the covalent bond. With rising temperature the increasing vibrational amplitude makes the covalent bond gradually less stable and thus semiconductivity grows with temperature more strongly than for non-covalent semiconductors, and on melting the strong increase of the thermal motion which accompanies melting makes covalent binding impossible in the liquid. We may expect that the bonds, or a fraction of them, still retain some covalent character even above melting and that this gradually decreases with further increase of temperature. Concerning the electronic rearrangement at low temperature which is linear in the displacements, the large values of the vibrational effective charge of course only provide direct verification for the dipolar component being large. But we must conclude that this rearrangement is generally rather large, not only its dipolar component, and that it is large also for those covalent materials for which a first order dipole moment is excluded by symmetry. This must have a pronounced effect on the force constants, the photoelastic constants and various other properties. Finally, we remark that the covalent substances which have been specifically mentioned here are those on whose melting we could find experimental information. All these materials become metallic on melting, but we note that in the solid state most of them ex-

creasing temperature, it was not thought surprising

hibit some “metalicity” and at the same time either

that they become metallic when they melt,

very little ionicity or none at all. Diamond, whose metalicity is negligibly small, has no ionicity either. On the basis of the arguments presented here we may expect that materials which are partly covalent and partly ionic without appreciable metalilcity also lose their covalency on melting, but such materials should form ionic liquids.

According to the arguments presented here, the large effective charges of covalent materials at ordinary temperatures, the exceptionally strong increase of semiconduction with temperature and the disappearance of covalency on melting are all caused by the effects of the atomic displacements on the nature

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