Low-temperature heat capacity VO2±δ and solid solutions V1-XFeXO2

The article reports the study results of the heat capacity of vanadium dioxide compounds (VO2) (within the homogeneity range) and stoichiometric solid solutions V1-xFexO2 at temperature range from 5 κ to 100 κ. Separation of various constituents of heat capacity with its additivity assumption has been conducted: crystal lattice heat capacity and defects heat capacity. It is shown that a considerable contribution to the heat capacity is produced by the crystal lattice defects (till ~ 25 κ) at low temperatures, and at higher temperatures the heat capacity is determined mainly with the crystal lattice. Using the Debye function table for the heat capacity for all compounds, the characteristic Debye temperatures θD were determined.


Problem statement
However, a number of works noted that naturally, vanadium dioxide is metastable and subject to spontaneous oxidation under the influence of atmospheric oxygen [3]. Certain phase stabilization is achieved with doping the vanadium dioxide (VO 2 ) by iron [3,4]. The study of low-temperature heat capacity (when temperature is below 20 К) [5], as well as X-ray diffraction analysis with pycnometric density measurement showed that there is a considerable number of defects both in pure vanadium dioxide and in solid solutions V 1-X Fe X O 2 [5]. Obviously, these defects influence various properties including thermophysical properties of these compounds.

Theory
The article reported the results of studies of the heat capacity at constant pressure С Р , a number of compounds VO 2±δ and solid solutions V 1-X Fe X O 2 in the temperature range from 5 К to 100 К. Heat capacity value at constant volume С V is noted to be used while discussing theoretical positions. It was shown in [6], that at low temperatures the difference between C P and C V is not large and at 100 К is no more than 3%. The heat capacity was measured by the method of a vacuum adiabatic calorimeter of the Strelkov type on an installation made in the Khabarovsk VNIIFTRI branch. Measurement of the reference materials heat capacity (in this capacity, benzoic acid and electrolytic copper of Kyshtym copper electrolytic plant were used) showed that the error in determining the heat capacity in the entire investigated temperature range does not exceed 1 %. Liquid helium and liquid hydrogen were used as refrigerants (with evacuation of vapors if necessary). The temperature was registered with a semiconductor thermometer of resistance (calibrated in Kharkov ILTPE of NASU) and a platinum resistance thermometer attested by VNIIFTRI. The initial sample VO 2 for the studies was prepared from the powdered material of vanadium pentoxide grade HSC by dissociation in vacuum at pressure 7 Pa, at temperature 1300 К. Samples VO 2-δ were obtained from VO 2 with further dissociation in vacuum 0.15 Pa at different temperatures. Samples VO 2+δ were obtained by oxidation at atmospheric pressure at temperature 620 К changing the oxidation time.
To prepare samples containing iron V 1-X Fe X O 2 , there were mixed necessary amounts of oxides V 2 O 3 and V 2 O 5 with Fe 2 O 3 : The samples were tested using a diffractometer Shimadzu Maxima Х XRD-7000, studies have shown that all samples are single-phase and belong to the structure VO 2 . The samples element composition was refined on an electronic scanning microscope JEOL JCM -5700 at voltage 15.0 kV.

Experimental results
The results of the studies are shown in Fig. 1-3 and in Tables 1-2. Having information on the heat capacity at temperatures above 50 К, characteristic Debye temperatures ϴ D for all samples in the temperature range from 50 К to 100 К are possible to be determined using Debye function tables for heat capacity. Their values are indicated in Tables 1 and 2. At temperatures Т ~ ϴ D /12, within the framework of the Debye model, the lattice heat capacity С LET is related with Debye temperature [7]: (2) where V is the volume of the unit lattice, N is the number of cells in the volume under consideration, k is Boltzmann's constant, n is the number of atoms in the cell.
Extrapolating certain values of the Debye temperatures to the low-temperature area, the heat capacity of the defects can be determined: C DEF =C P -C LET (3) Dependences of the heat capacity C P on temperatures for three samples are presented in Fig.1: VO 2 , V 0.97 Fe 0.03 O 2 and VO 1.990 . A gradual increase in the heat capacity is observed for all samples with increasing temperature. Heat capacity dependences on temperature, both the total and its components are presented in Fig. 2 and Fig. 3: the heat capacity of the crystal lattice and the heat capacity of the defects for two samples (Fig. 1 is for the sample VO 2 ; Fig. 2 is for the sample V 0.97 Fe 0.03 O 2 ). As presented, the heat capacity of crystal lattice defects first increases with increasing temperature (up to Т К ~ 14 К), and then with further increasing temperature С DEF does not depend on the temperature. It suggests that the defects in the crystal are as quantum particles, and Т К is degeneracy removal temperature.

Discussion
As the obtained results prove, at low temperatures the heat capacity of pure vanadium dioxide "VO 2 " is minimal for VO 1.990 (0.0027 J/mol К at 5 К) and it is maximum for VO 2.03 (0.0060 J/(mol К). The low-temperature heat capacity of other samples "VO 2 " varies within these limits. With temperatures close to 100 К (high temperature part of the heat capacity) for the samples "VO 2 " minimum values of heat capacity are for VO 1 In whole, alloying with iron leads to leveling heat capacity samples.

Conclusion
Thus, the article reports the results of a study of the heat capacity VO 2±δ and solid solutions V 1-X Fe X O 2. The heat capacity is established to depend strongly on the composition of the sample. Analysis of the measurement results made possible to isolate the heat capacity of the defects and its dependence on temperature. According to the nature of С DEF (Т) the quantum nature of defects is concluded.