If we take the ionic crystals LiF, LiCl, LiI and LiBr composed from lithium isotope (which ion is bosonic) and assume that lithium ions are subjected to periodic lattice potential due to halogen ions, then Schr?dinger equation gives the effective mass of Li-ions. Calculations show that this mass is greater then e38 me (free electron mass).
Bose ?Einstein condensation (BEC) temperature for such a heavy particles is predicted to be about e-34K. If, however, we compress the crystal to the point of substantial overlap between the wavefunctions of nearest-neighbor lithium ions, their effective mass could be reduced dramatically resulting in much higher BEC temperature. Our estimates show that in order to get BEC temperature greater than 300K it is sufficient to compress LiF, LiCl, LiI and LiBr crystals hydrostatically by 20-22%. Since exact results are presently unavailable it is difficult to estimate the errors involved due to approximations used in the calculations.
However, even if the calculated effective mass of lithium ions is increased by a factor of 25, the Bose condensation temperature of Li ions in crystals compressed by 21-23% is greater than 300K.
Practical ways to achieve such compressions in the form of specially designed layered. heterostructures are proposed, which are within the reach of current epitaxial technologies and can be used for the fabrication of high-temperature ionic superconductors. As an example, the layer of (LiCl)1-x(LiF)x on LiF substrate or thin film of (LiI)1-x(LiF)x on NaF substrate can be taken. In order to compress the LiI crystal by 22% of its initial volume the pressure applied must be in the 50-70 GPa GPa range. Since pressures of the order of 50-70 GPa are achievable in practice the experimenters have an opportunity to check if the LiI crystals are ionic superconductors at high pressure. It is, however, possible to reduce the magnitude of this pressure significantly by using epitaxially strained for example LiI/LiBr or LiBr/LiCl heterostructures and subjecting them to additional hydrostatic pressure. If on what or to the reasons Meissner effect in ionic superconductors does not become apparent, that is possible for idea?s check it is necessary to pass current through an ionic superconductor, supplied with contacts from Li6, or to carry out measurement of a capacity of ionic superconductors
with usual contacts. Current technology allows to obtain hydrostatic pressures in the range 8-100 GPa only in very small volumes (~0.01 mm3) using diamond anvils. Therefore, it is reasonable first to fabricate the LiI/LiCl heterostructure and then to subject it to hydrostatic compression with P<8 GPa.
See
http://www.v-ioffe.ruP.S. Comment 1
It has been reported in [B. Srinivasa Rao and S. P. Sanyal , Structural and elastic properties of sodium halides at high pressure, PHYSICAL REVIEW VOLUME 42, NUMBER 3 1990-11,р.1810-1816] that crystal structure for sodium halides is changed from NaCl ?type to CsCl at 35 GPa. If so, and if similar changes occur for lithium halides, than ionic superconductivity could not be obtained by direct compression for P<100GPa. The superconductivity can be fixed, hopefully, by combination of epitaxy and hydrostatic pressure.
Over the time I have had various objections to my work. Most frequently received ones are listed below with short comments.
Objection #1
is that some doubts are cast upon the possibility to make the effective mass of the ion
many orders of magnitude smaller than its gravitational mass since in metals the electron effective mass is of the order of me.
Similar doubts would probably come also to my mind before the work was started if I did not know that in several semiconductors the effective electron mass is much smaller than me (a factor of 20 in GaAs and a factor of 70 in InSb).
Objection #2
consists in that the relevance of tight-binding approximation is called in question.
In the situation when exact solution is impossible the appropriateness of any approximation could be tested only by experiment. It is known, however, that tight-binding approximation gives qualitatively correct results in the calculations of electronic band structure for both metals and semiconductors. This approximation does not lead to errors in the order of magnitude of calculated values. And the smaller the magnitude of the overlap integral is, the better (more exact) the calculated results are. In considering the ionic crystals we have exactly the case of small overlap integrals when the size of compressed lattice constant is larger than 2rm (rm is the distance between ions in a molecule).
Objection #3
For some readers it seems that in order to get the result the pressures required should provide the sufficient overlap of lithium nuclei wave functions. These pressures are orders of magnitude higher than those presented in my work.
The argument is relevant if we compress pure Li6. But for compression of ionic crystals the situation is different. In a molecule composed from lithium and halogen the wave function of lithium ion have a maximum near the surface of the sphere with radius rm. Beyond this distance the wave function is sharply diminished. Consequently, upon crystal compression the surfaces of neighboring spheres come close together and overlap integral steeply increases during compression as long as the distance between oppositely charges ions in crystal lattice is grater than corresponding distance in a molecule (rm). When the distances mentioned above become equal the spheres are in touch and further compression does not lead to substantial increase of the overlap integral. Numerical results for the lithium ion effective mass (which is inversely proportional to the overlap integral) confirm this conclusion.
Objection #4
For some people it seems that reasonable results could be obtained only if correlational interaction between lithium ions is taken into account. Their argument goes as follows. Since lithium ion is firmly sitting in the lattice site of ionic crystal and do not allow to occupy this site by other lithium ions then correlational effects must be accounted for.
Unfortunately, nor those people nor myself do know how to proceed along this route. In my opinion it is not necessary. The fact that lithium ions arrange themselves over crystal lattice sites is already accounted for by the potential used in the calculations. The potential is specifically constructed to agree with observed lattice parameter, elastic properties, dissociation energy and molecular size. The fact that ion occupy the lattice site means only the high probability to find it in that place. Unfortunately, nor those people nor myself do know how to proceed along this route. In my opinion it is not necessary. The notion of lattice site for Li6 ions in compressed crystals can become meaningless. The binding energy of Li ion at the site can be easily calculated. As long as this energy is larger than binding energy of the ion in a molecule the ions occupy lattice sites. In opposite case, which is realized already at 18-20% compression, the potential reach a minimum value not at a point but on the surface similar to spherical surface in a molecule.
I hope that someone will find more relevant objections to my work and if unable to do so will be helpful in performing the experimental test. Probably, somebody will be able to get more exact results for E(k) at least in the framework of purely ionic interactions for ions of lithium in crystalline materials subjected hydrostatic pressure?
See
http://www.v-ioffe.ru
