A. V. Markin

Standard thermodynamic functions of CaNi0.5Zr1.5(PO4)3 crystalline phosphate in the range of T → 0 to 640 K

The temperature dependence of the heat capacity Cp○ = f(T) of CaNi0.5Zr1.5(PO4)3 crystalline phosphate is studied by precision adiabatic vacuum and differential scanning calorimetry over the temperature range of 7–640 K. Its standard thermodynamic functions Cp○ (T), H○(T)-H○(0), S○(T), and G○(T)-H○(0) for the region T → 0 to 640 K and the standard entropy of formation at T = 298.15 K are calculated from the obtained experimental data. Using data on the low-temperature (30–50 K) heat capacity, the D fractal dimension of phosphate is determined and conclusions about the character of the topology of its structure have been made. The final results are compared to data from thermodynamic investigations of the structurally related crystalline phosphates Zr3(PO4)4, Ni0.5Zr2(PO4)3, and Ca0.5Zr2(PO4)3.

Thermodynamic properties of LiZr2(PO4)3 crystal phosphate

The temperature dependence of the heat capacity of LiZr2(PO4)3 crystal phosphate is studied in an adiabatic vacuum calorimeter in the temperature range of 6 to 358 K. A phase transition caused by the transition of a low-temperature (triclinic) modification to a high-temperature (rhombohedral) modification is observed in the temperature range of 290–338 K and its standard thermodynamic characteristics are estimated and analyzed. Standard thermodynamic functions are calculated from experimental data: heat capacity, enthalpy, entropy, and Gibbs function in the range of T → 0 to 358 K. Fractal dimensionality D is calculated from the data on low-temperature (20 K ≤ T ≤ 50 K) heat capacity and the topology of the phosphate’s structure is estimated.

The heat capacity and standard thermodynamic functions of Ni0.5Zr2(PO4)3 phosphate over the temperature range from T → 0 to 664 K

The temperature dependence of the heat capacity of crystalline nickel zirconium phosphate C°p = f(T) was measured over the temperature range 6–664 K. The experimental data obtained were used to calculate the standard thermodynamic functions of Ni0.5Zr2(PO4)3 from T → 0 to 664 K. The standard entropy of phosphate formation from simple substances at 298.15 K was calculated from the absolute entropy of the compound. The data on the low-temperature heat capacity were used to determine the fractal dimension of Ni0.5Zr2(PO4)3 over the temperature range 30–50 K. Conclusions concerning the heterodynamic characteristics of the structure of Ni0.5Zr2(PO4)3 were drawn.

The heat capacity and thermodynamic functions of Ca0.5Zr2(PO4)3 crystalline phosphate from T → 0 to 650 K

The temperature dependence of the heat capacity Cpo = f(T) of crystalline calcium-zirconium phosphate was studied over the temperature range 7–650 K by precision adiabatic vacuum and dynamic scanning calorimetry. The experimental data were used to calculate the standard thermodynamic functions Cpo(T), Ho(T) − Ho(0), So(T), and Go(T) − Ho(0) at temperatures from T → 0 to 650 K and the standard entropy of formation of Ca0.5Zr2(PO4)3 at T = 298.15 K. The data on low-temperature (30 K ≤ T ≤ 50 K) heat capacity were used to calculate fractal dimension D. Conclusions about the character of the topology of the structure of the phosphate were drawn.

The thermodynamic properties of crystalline Sr0.5Zr2(PO4)3 phosphate from T → 0 to 665 K

The temperature dependence of the heat capacity of crystalline Sr0.5Zr2(PO4)3 phosphate was studied by precision adiabatic vacuum and dynamic scanning calorimetry over the temperature range 7–665 K. The low-temperature dependence of the heat capacity was analyzed using the Debye theory of the heat capacity of solids and its multifractal generalization, which allowed conclusions to be drawn about the heterodynamic characteristics of the structure. The experimental data obtained were used to calculate the standard thermodynamic functions of Sr0.5Zr2(PO4)3 from T → 0 to 665 K. The standard absolute entropy of Sr0.5Zr2(PO4)3 was in turn used to calculate the standard entropy of its formation from simple substances at 298.15 K.

Thermodynamic properties of NaZr2(AsO4)3

The heat capacity Cp0 of crystalline NaZr2(AsO4)3 has been measured in the range 7–650 K using precision adiabatic calorimetry and differential scanning calorimetry. The experimental data have been used to calculate the standard thermodynamic functions of the arsenate: Cp0, enthalpy H0(T) − H0(0), entropy S0(T), and Gibbs function G0(T) − H0(0) from T → 0 to 650 K. The standard entropy of its formation from elements is ΔfS0(NaZr2(AsO4)3, cr, 298.15 K) = −1087 ± 1 J/(mol K).

Standard Thermodynamic Functions of Crystalline Arsenate Mg0.5Zr2(AsO4)3 in the Range from T → 0 to 670 K

The temperature dependence of heat capacity C°p= f(T) of crystalline arsenate Mg0.5Zr2(AsO4)3 was studied by precision adiabatic vacuum and differential scanning calorimetry in the temperature range 8−670 K. The standard thermodynamic functions C°p(T), H°(T)–H°(0), S°(T), and G°(T)–H°(0) of the arsenate for the range from Т → 0 to 670 K and the standard formation entropy at Т = 298.15 K were calculated from the obtained experimental data. Based on the low-temperature capacity data (30–50 K) the fractal dimension D of the arsenate was determined, and the topology of its structure was characterized. The results were compared with the thermodynamic data for the structurally related crystalline phosphates M0.5Zr2(PO4)3 (M = Mg, Ca, Sr, Ba, Ni) and arsenate NaZr2(AsO4)3.

The thermodynamic properties of crystalline pentasodium hafnium tris(phosphate)

The temperature dependence of the heat capacity of crystalline pentasodium hafnium tris(phosphate) was studied over the temperature range 6–650 K. The experimental data were used to calculate the thermodynamic functions of Na5Hf(PO4)3 from 0 to 650 K and the fractal dimension at 20–50 K. The standard entropy of formation from simple substances at 298.15 K was calculated from the absolute entropy value. The thermodynamic properties of Na5M(PO4)3 (M = Ti, Zr, and Hf) phosphates were compared.