Nonisothermal Kinetic Study: IV. Comparative Methods To Evaluate E_a for Thermal Decomposition of KZn₂(PO₄)(HPO₄) Synthesized by a Simple Route

Abstract

The single-phase KZn2(PO4)(HPO4) was synthesized via solid-state reaction at 80 °C using K3PO4·3H2O, K2HPO4·3H2O, and ZnSO4·7H2O as raw materials. The thermal decomposition of KZn2(PO4)(HPO4) experienced one step, which was the intramolecular dehydration of the protonated phosphate groups to form Zn2P2O7. The apparent activation energy E a was estimated with six comparative isoconversional procedures. The average value of the apparent activation energy E a associated with the thermal decomposition of KZn2(PO4)(HPO4) was determined to be 411.49 ± 14.37 kJ mol–1, which demonstrates that the thermal decomposition of KZn2(PO4)(HPO4) is a single-step kinetic process and can be described by a unique kinetic triplet [E a, A, g(α)]. A new modified method for multiple rate isotemperature was used to define the most probable reaction mechanism g(α), and reliability of the used method for the determination of the kinetic mechanism was tested by the comparison between experimental plots and modeled results for every heating rate. The results show that the mechanism function is reliable. The value of pre-exponential factor A was obtained on the basis of E a and g(α). Some thermodynamic functions (ΔS ⧧, ΔH ⧧, and ΔG ⧧) of the transition state complex were also calculated.

Solid State Reaction Mechanisms of the LiMnPO4 Formation Using Special Function and Thermodynamic Studies

“…Isoconversional procedure, − the thermal decomposition kinetic investigation of the single crystalline compounds, is a solid-state reaction of the type: A (solid) → B (solid) + C (gas) − as well as the solid-state reaction of two or more solids can be described as the type of ∑ A i (solid) → ∑ B j (solid) + ∑ C k (gas). ,, The nonisothermal (isoconversional) kinetic model is a model-free method, which involves measuring temperatures ( T ) corresponding to the fixed value of extent of conversion (α) at different heating rates (β, β = (d T /d t )/°C min –1 , t is time/min). The α-values from thermogravimetric analysis may be defined as the ratio of actual mass loss to the total mass loss corresponding to the investigated process: where m t is the mass of the sample at time t , and m 0 and m f are the masses of the sample at beginning and end of the mass loss in the TG curve reaction results, respectively.…”

Synthesis of a new phosphor (LaPO4:Ce, Li, Mn) and kinetics study for thermal process of its precursor

“…It is noticeable that, among many synthetic methods of metal co-doped phosphate, the low-heating temperature solid state reaction process [25][26][27] has many advantages such as relatively low reaction temperature, simplicity, high purity, good homogeneity and so on. Therefore, in this paper, the hydrate precursor of La 0.9 Ce 0.05 Li 0.05 Mn 0.05 PO 4 was prepared via this way.…”

Nonisothermal Kinetics Study with Isoconversional Procedure and DAEM: LiCoPO4 Synthesized from Thermal Decomposition of the Precursor

“…A major practical application is the prediction of process rates and material lifetimes. Hence, different methods such as isoconversional procedure − and distributed activation energy model (DAEM) − have been employed to study the kinetics of the thermal decomposition process of substances. For this reason, kinetic analysis is very essential and useful for the preparation and application of various materials.…”

“…Kinetic data were collected using simultaneous TG/DTG technique. Nonisothermal kinetics of the decomposition process was analyzed using isoconversional procedure − and DAEM. − The values of E α were obtained from both isoconversional procedure and DAEM. The pre-exponential factor A and distributions of activation energy f ( E α ) were calculated using DAEM.…”