Thermodynamically equilibrium point defects in the low-dimensional systems

The temperature dependencies of the electrical resistance of low-dimensional NbSe3and NbSe2-single crystals were investigated in the range of 300–540 K. Measurements of resistance were produced along the chains for quasi-one-dimensional NbSe3-single crystal and along the layer for quasi-two-dimensional NbSe2-single crystal. On the temperature dependencies the exponential deviations from linear dependencies were observed. We suppose that such deviations of resistance are connected with the contribution of selenium equilibrium vacancies.

Numerous experimental and theoretical works [1,2] are devoted to a research of properties of low-dimensional conducting systems.Due to a reduced dimensionality, such compounds have got an anisotropy of physical properties, in particular anisotropy of conductivity (ρ ⊥ /ρ // =10-20 at NbSe 3 [3]; ρ ⊥ /ρ // =30-50 at NbSe 2 [2]) and at the same time the role of thermodynamic fluctuations increase.It is known that conductivity hardly depends on concentration of defects.Magnitude of concentration of the defects is determined by the significance of the bond energy and by co-ordination of atoms in the crystal lattice.The NbSe 3 and NbSe 2 researched in the present work are typical representatives of quasi-one-dimensional and quasitwo-dimensional compounds.The compounds of NbSe 3 and NbSe 2 consist of identical atoms but they differ by space co-ordination of atoms.For this reason these compounds were selected as the objects of a comparative experimental research of vacancy formation processes.The present work is devoted to experimental study of temperature dependence of a resistance as well as the processes of formation of thermodynamically equilibrium dot defects (monovacancies) in NbSe 2 and NbSe 3 .
Crystals of NbSe 3 and NbSe 2 were prepared using gas transport reaction [4].Quasi-one-dimensional single crystals NbSe 3 [1] consist of a chain formed by trigonal prisms from Se atoms (figure 1a).At the centre of such prisms the Nb atom is located.The bond between the chain is weak.It leads to a quasi-one-dimensionality of this compound.The number of the nearest bonds for atom Se (disregarding the bonds between chains) is equal to six (4 of them are Se-Se bonds, 2 are Nb-Se bonds).The atom of Nb has 6 nearest Nb-Se bonds and 2 Nb-Nb bonds.
Quasi-two-dimensional single crystals NbSe 2 [2] consist of layers, each of which represents a sandwich from two layers of atoms Se with a layer Nb between them (figure 1a).The layers NbSe 2 interact among themselves in the crystal by weak Vander-Vaals forces.Coordination number for Se is 9 (6 bonds of Se-Se and 3 bonds of Nb-Se).At the atom Nb there are 6 Nb-Se bonds and 6 Nb-Nb bonds.As the number of bonds for atoms Se, both at NbSe 2 , and at NbSe 3 , is less than for Nb, the energy of vacancy formation of atoms Se is less than the energy of vacancy formation of atoms Nb.The ratio of the number of the nearest bonds for atoms Se in compounds NbSe 2 and NbSe 3 is 9:6.Thus, it is possible to assume that the energy of vacancy formation of atoms Se in NbSe 2 should be approximately 1.5 times higher than at NbSe 3 , the energy of vacancy formation of atoms Nb being approximately equal.
The temperature dependencies of the electroresistance of single crystals in lowdimensional systems NbSe 3 and NbSe 2 were investigated in the region of temperatures higher than 300 K.The electroresistance was measured using a four-contact DC circuit along the chains for a quasi-one-dimensional NbSe 3 -single crystal and along the layer for a quasi-two-dimensional NbSe 2 -single crystal.The transport current value was such that the electric field at the sample was lower than the threshold electric field of charge density wave sliding [1].
The temperature dependence of electroresistance of samples NbSe 3 and NbSe 2 in the temperature interval of 300-540 K is presented in figures 2a and 3a accordingly.
The obtained temperature dependencies of electroresistance for both single crystals NbSe 2 , and for NbSe 3 show the deviations from the linear dependence at T>T o .In case of well-investigated three-dimensional metals [5], the similar deviations from the linearity are stimulated by forming thermodynamically equilibrium vacancies.In our case of low-dimensional systems, the observable effects are also stimulated by forming thermodynamically equilibrium vacancies.The definition of magnitudes of activation energies is represented in figures 2b and 3b in coordinates ln(∆R/R) = f (1/T ) (∆R -residual between experimental and exponential value of resistance at the temperature T).For NbSe 3 the magnitude of energy of activation E v f has made up 0.8 eV (the same result is obtained in the experiment made in vacuum), for NbSe 2 E v f =1.2 eV.Taking into account the results obtained (E v f (NbSe 2 )≈(1,5E v f (NbSe 3 )) we consider the vacancies in NbSe 2 and NbSe 3 -single crystals to be the vacancies of Se.However in low-dimensional systems the formation vacancy may lead to breaking the lattice stability.It is a possible reason of nonrepeatability of experimental results on different samples.