Thermodynamic Study of Formamidinium Lead Iodide (CH5N2PbI3) from 5 to 357 K

In the present study, the molar heat capacity of solid formamidinium lead iodide (CH5N2PbI3) was measured over the temperature range from 5 to 357 K using a precise automated adiabatic calorimeter. In the above temperature interval, three distinct phase transitions were found in ranges from 49 to 56 K, from 110 to 178 K, and from 264 to 277 K. The standard thermodynamic functions of the studied perovskite, namely the heat capacity C°p(T), enthalpy [H0(T) − H0(0)], entropy S0(T), and [G°(T) − H°(0)]/T, were calculated for the temperature range from 0 to 345 K based on the experimental data. Herein, the results are discussed and compared with those available in the literature as measured by nonclassical methods.


Introduction
Since their first appearance in 2009, perovskite solar cells have attracted a great deal of attention, owing to their relatively simple technology and good performance. Nowadays, they constitute the photovoltaic technology with the fastest-growing conversion efficiency [1,2]. The first compound of the hybrid perovskite family to be extensively studied for photovoltaic devices was methylammonium lead iodide, CH 3 NH 3 PbI 3 [3][4][5]. Its intriguing photophysical properties, such as its direct band gap, with a value very near optimal one for photovoltaic conversion of solar radiation, and its defect tolerance, were thoroughly studied following the discovery of its exceptional photovoltaic performance [6][7][8]. However, the limited chemical and thermal stability of CH 3 NH 3 PbI 3 immediately emerged as a very serious problem. In spite of their impressive performances in photovoltaic devices, perovskite solar cells seem quite far from commercial debut.
In order to assess the stability under various operating conditions, a full thermodynamic characterization of the material and of its possible decomposition pathways is mandatory. To date, enthalpy and free-energy data have been published for CH 3 NH 3 PbI 3 [17][18][19][20][21][22] and, to a lesser extent, for CsPbI 3 [23][24][25][26]. Recently, data on the thermodynamic stability of CH 5 N 2 PbI 3 were published by our group [27].
In this connection, the measurement of heat capacities from low temperature up to decomposition temperatures is of utmost importance to derive absolute entropy values and to calculate the values of thermodynamic quantities at temperatures different from those explored in the experiments. Furthermore, the study of heat capacities is of great help to investigate the low-temperature phase transitions that occur in the material, the dynamics of molecular motions, and the nature of the molecule-cage interaction [28], which is important to clarify the role of the organic cations in the photovoltaic performance. To the best of our knowledge, heat-capacity values measured by adiabatic calorimetry are available in literature only for CH 3 NH 3 PbI 3 [5,29]. In regard to CH 5 N 2 PbI 3 , few papers are available wherein the heat capacity was reported [28,30,31]. In particular, Fabini and colleagues measured the heat capacities of powder samples in temperature ranges across the phase transitions by the pulse-relaxation method [28] and by differential scanning calorimetry [30], whereas Kawachi and colleagues [31] reported measurements of single crystal samples by the relaxation technique. The aim of the present paper is to present the first experimental determination of the heat capacities of CH 5 N 2 PbI 3 in the temperature range from 5 to 357 K by classic adiabatic calorimetry and to provide the thermodynamic functions derived therefrom.

Materials and Methods
Synthesis and structural characterization of either methylammonium lead iodide (MAPI) or FAPI were carried out according to procedures reported in detail in previous studies [18,27].
The heat capacity of MAPI and FAPI was measured over the range of T = (5-357) K using an automatic BCT-3 low-temperature adiabatic calorimeter. The calorimeter was manufactured at "Termis" joint-stock company at the All-Russian Metrology Research Institute, Moscow, Russia. Its design and operation procedure are described in [32]. The iron and rhodium thermometer (resistance at T = 273.1 K is~51 Ω) was calibrated on the basis of ITS-90 [33]. Liquid helium and nitrogen were used as cooling agents.
The ampoule with the fine crystalline substance was filled with dry helium as a heatexchange gas to a pressure of 4 kPa at room temperature. The reliability of the calorimeter was checked by measuring C • p,m of standard samples of high-purity copper [34], standard synthetic corundum, n-heptane (chromatographically pure) [35], and K-3 benzoic acid [36,37] prepared at the Institute of Metrology of the State Standard Committee of the Russian Federation.
The test of the calorimeter revealed that average deviations of the experimental data from the precision literature data were 2% at T = (5-15) K, 0.5% at T = (15-40) K, and 0.2% at T = (40-357) K. The phase-transition temperatures were measured within a standard uncertainty of about u(T) = 0.01 K. The mass of the sample loaded in a 1.5 cm 3 thin-walled cylindrical titanium ampoule of the BCT-3 device was 1.5551 g. The C • p,m measurements were carried out in the range of T = (5-357) K.
The experimental C • p,m values (Table 1) were obtained in six runs. The heat capacity of the sample varied from 54 to 92% of the total heat capacity of the (calorimetric ampoule + substance) in the range of T = (5-357) K.
The experimental C • p,m points were smoothed in all the temperature regions for which any transformations were absent, according to the following polynomials (Equations (1)-(3)): where A j represents the fitting polynomial coefficients, and n is the number of coefficients. The standard atomic masses recommended by the IUPAC Commission in 2013 [38] were used in the calculation of all molar quantities.

Heat Capacity
A preliminary set of heat-capacity measurements under the identical operative conditions used for the tested compound were carried out on MAPI in order to check the internal consistency of either adiabatic measurements. The data of three experimental runs for MAPI are compared with the available literature data in Figure S1 [5]. A good agreement was found with relative deviations that do not exceed 0.9% up to-250 K and 3% in the range of 250-357 K, thus confirming that a reliable C • p,m may also be expected for FAPI.
The experimental values of the molar heat capacity of FAPI in the range of 5-357 K and the smoothing plot, C • p,m = f (T), are illustrated in Table 1  The C°p,m values were smoothed according to Equations (1)-(3) using a polynom regression least-square method, while the corresponding fitting coefficients are liste Table 2. The C • p,m values were smoothed according to Equations (1)-(3) using a polynomialregression least-square method, while the corresponding fitting coefficients are listed in Table 2. The relative deviation of the experimental data from the fitting values related to the studied compound is illustrated in Figure 2. The C°p,m values were smoothed according to Equations (1)-(3) using a p regression least-square method, while the corresponding fitting coefficients a Table 2. The relative deviation of the experimental data from the fitting values rel studied compound is illustrated in Figure 2.  Three distinct phase transitions were found in the ranges of 49-56 K, 110-178 K, and 264-277 K. The characteristics of these transitions are summarized in Table 3. By means of thermal-expansion measurements, the hexagonal δ-FAPI phase was reported to undergo two phase transitions at 54.5 K and 173.0 K [39], in agreement with our findings. A transition at around 50 K was also reported in [28] (heat-capacity measurements of a powder sample by the pulse-relaxation technique) in the form of two closely-spaced peaks and assigned to the glassy freezing of molecular motions. The total entropy change reported in [28], ranging from 1.7 to 2.2 JK −1 mol −1 , is similar to our result (see Table 3). However, this transition was not reported in [31], wherein a crystal sample was used. The anomaly at around 275 K could corresponds to the previously reported λ-shaped continuous tetragonal-to-cubic (β to α) phase transition [31] due to the formation of small amounts of tetragonal phase in our sample.

Standard Thermodynamic Functions
The standard thermodynamic functions of FAPI reported in Table 4 were calculated from the C • p,m values in the temperature range of 0-345 K. To calculate the standard thermodynamic functions of FAPI, its C • p,m values were extrapolated from 5 to 0 K according to the Debye law and the multifractal theory of heat capacity in the extremely low-temperature limit [40][41][42]: where n is the number of degrees of freedom, D is the Debye function, and Θ D refers to the Debye characteristic temperature. The parameters selected for this study are n = 6 and Θ D = 60.5 K. They were selected so that the errors associated with the heat capacity in the region below 20 K did not exceed the experimental error of its determination.
where all details related to the procedure adopted are available in [43].   As mentioned in the Introduction, the occurrence of gas-releasing decomposition reactions is one of the most severe obstacles on the road to the practical application of hybrid perovskites in photovoltaic technology. The absolute entropy of CH 5 N 2 PbI 3 measured in this work, S • (298 K) = 385.5 J·K −1 ·mol −1 , enables the calculation of the entropy change of the possible decomposition reactions undergone by the compound under real-use conditions.

Conclusions
This study reports original results regarding the calorimetric study on formamidinium lead iodide (FAPI). In particular, the heat capacity of FAPI was measured in the experimental