Introduction

Compounds of the type: [M(NH3)x](ReO4)2 (x = 4, 6) are particularly interesting molecular materials because of the occurrence of different reorientational motions of the complex cations [M(NH3)x]2+, NH3 ligands, and tetrahedral ReO −4 anions. The various hexaamminenickel(II) complexes with different anions as a counter ion were intensively examined up to now. Here we will focus only on compounds containing tetrahedral anions with one negative charge. Phase polymorphism of compounds with ClO −4 and BF −4 anions and [Ni(NH3)6]2+ cation was intensively investigated over past four decades [1, 2]. At room temperature they crystallize in a cubic system, space group No. 225, Fm-3 m, with four molecules per unit cell. Two phase transitions were found in each complex: one so called large and the second so called small. In case of [Ni(NH3)6](ClO4)2, the large anomaly was found at ca. 173 K and the small and diffused at ca. 143 K. The phase transition temperatures for [Ni(NH3)6](BF4)2 equal to 140.1 K (large, sharp) and ca. 110 K (small, diffused). It is interesting to extend similar investigations also to the family of compounds containing tetrahedral perrhenate anion with one negative charge. Unfortunately, the literature concerning basic properties of the title compounds is rather limited. The decomposition of [Ni(NH3)4](ReO4)2 was investigated by Chakravorti et al. [3] by the TG method but only up to 573 K. The authors have found that complete deammination of this compounds proceeds in two stages. According to these authors, the electronic spectra indicate that [Ni(NH3)4]2+ ion is tetragonal. On the other hand, the magnetic measurements indicate that Ni2+ complex is six-coordinate [3]. We have found none TG data for [Ni(NH3)6](ReO4)2. Thus, one of the aims of this work is to fill in this gap as well as extend knowledge about their thermal properties in the wide temperature range and to make a comparison between them. The low temperature phase transition in tetraamminenickel(II) perrhenate is reported in our paper for the first time. We have also tried to get answer about final and intermediate products of decompositions using infrared spectroscopy. Most of the investigated [Ni(NH3)6]X2 compounds (X = Cl−, Br−, ClO −4 , BF −4 , and NO −3 ) is chemically stable even exposed on air. The hexaamminenickel(II) perrhenate is unstable and slowly transforms to tetraamminenickel(II) perrhenate. Change of sample color from violet to blue accompanies this process.

The second goal of this project is to compare infrared spectra and give its interpretation for both substances. The far infrared data for the [Ni(NH3)6](ReO4)2 compound were registered and discussed for the first time. The third aim of our paper is to shed a light on activation energies connected with particular steps of decomposition. To achieve this goal, we have used Kissinger–Akahira–Sunose (KAS) model-free approach [4] and Kissinger method [5, 6]. This novel approach has recently been growing in popularity and is generally used to study the kinetics of solid-state reactions. This method allows the estimation of activation energy without choosing a reaction model and reaction order. Kinetic studies on the thermal deammination reactions of hexaamminenickel(II) compounds are reported in the literature [7]. The activation energies of the deammination were calculated using isoconversional methods and indicate that this process has a multi-step nature.

Experimental

The hexaamminenickel(II) perrhenate was obtained in the manner described in [8, 9]. The nickel(II) carbonate basic hydrate (1 g, NiCO3·2Ni(OH)2·xH2O) purchased from Sigma-Aldrich Company was dissolved in perrhenic acid (5 g, 75–80 mass% in H2O, from Sigma Aldrich). The mixture was heated and filtered out in order to get rid of excess of not reacted nickel(II) carbonate. Next NH3aq was added drop wise to the filtered greenish solution. The color changed to violet. Finally, this mixture was cooled to ca. −10 °C. The precipitated needle-shaped violet crystals were filtered out and dried. The obtained [Ni(NH3)6](ReO4)2 is unstable on air and transforms to blue [Ni(NH3)4](ReO4)2 within several minutes. However, when it is kept closed (preferably under NH3 vapor) such decomposition is not observed and hexaamminenickel(II) perrhenate is stable and can be stored for a long period.

The contents of nitrogen and hydrogen in the [Ni(NH3)4](ReO4)2 were determined using elemental analysis on a EURO EA 3000 apparatus. Theoretical contents: N, 8.93 %; H, 1.93 %. Found: N, 8.90 %; H, 1.82 %. The elemental analysis of the title compound confirmed the presence of the stoichiometric number of four NH3 molecules in the complex cation.

The thermogravimetric analyses (TG) with simultaneous differential thermal analyses (SDTA) measurements were performed using a Mettler-Toledo 851 e apparatus. Consecutive, samples of masses equal to 26.2094 mg of [Ni(NH3)6](ReO4)2 and 28.9680 mg of [Ni(NH3)4](ReO4)2 were placed in 150 μl platinum crucibles. The measurements were made in a flow of Argon (60 cm3 min−1), within temperature range of 295–1,275 K. The TG measurements were performed at a constant heating rate of 10 K min−1. The simultaneous evolved gas analysis (EGA) was performed during the experiments by a joined on-line quadruple mass spectrometer (TG-MS) using a Thermostar-Balzers apparatus. The temperature was measured by a Pt–Pt/Rh thermocouple with an accuracy of ±0.5 K. In order to estimate the energy activation for identified decomposition steps further TG runs (with the same conditions but without MS signals) for [Ni(NH3)6](ReO4)2 were performed with the heating rates: 5, 7.5 and 15 K min−1. The following initial sample masses were used 28.3826, 20.4543, and 26.1700 mg, respectively.

The DSC measurements were performed on heating (temperature range 140–300 K) and cooling (temperature range 300–140 K) using a Mettler-Toledo 822 e calorimeter. The samples of masses equal to 22.67 mg (18.02 mg second run) for [Ni(NH3)4](ReO4)2 and 9.64 mg for [Ni(NH3)6](ReO4)2 were placed in 40 μl aluminum partially open crucibles (micro hole preserves constant pressure over the sample). Measurements were performed under constant flow of Argon (80 cm3 min−1) with the heating/cooling rate being equal to 10 K min−1. Additionally, for sample of mass equal to 18.02 mg second DSC run with scanning rate being equal to 20 K min−1 was performed.

The enthalpy change (ΔH) was calculated by numerical integration of the DSC curve under the anomaly peak after a linear background arbitrary subtraction. The entropy change (ΔS) was calculated using the formula ΔS = ΔH/T c. For sharp peaks, the values were calculated to a high accuracy (4 %), whereas for the diffuse peak they were estimated only.

Fourier transforms far and middle infrared (FT-FIR and FT-MIR) absorption measurements were performed using a Bruker Vertex 70v vacuum Fourier Transform spectrometer. The transmission spectra were collected with a resolution of 2 cm−1 and with 32 scans per each spectrum. The FT-FIR spectra (500–50 cm−1) were collected for sample suspended in Apiezon N grease and placed on polyethylene (PE) disk. The FT-MIR spectra (4,000–500 cm−1) were collected for sample in a KBr pellet.

Results and discussion

Spectroscopic identification of samples and vibrational analysis

Figure 1 presents a comparison of FT-MIR (4,000–500 cm−1) and FT-FIR (500–30 cm−1) spectra registered for [Ni(NH3)6](ReO4)2 (Fig. 1a, violet curve) and [Ni(NH3)4](ReO4)2 (Fig. 1b, blue curve) with calculated spectra. The vertical line visible in Fig. 1 separates far from middle infrared region. The MIR spectra registered for both compounds are very similar to each other. Moreover, they are typical for members of the ammine complexes group [10–12]. Only one subtle difference between [Ni(NH3)6](ReO4)2 and [Ni(NH3)4](ReO4)2 can be noticed. In the latter case, a weak additional band at 1,411 cm−1 is observed which allows one to distinguish between the two title compounds. The IR data obtained for [Ni(NH3)4](ReO4)2 in the 4,000–250 cm−1 wavenumber region were presented in paper [3]. Infrared spectrum (MIR and FIR) registered by us in the 4,000–30 cm−1 wavenumber region is in good agreement with data presented by Chakravorti et al. [3]. However, our data revealed more details probably due to better resolution used. The band registered at 1,411 cm−1 is rather weak, whereas in paper [3] this band (1,400 cm−1) was denoted as very strong (vs). Moreover, we were able to register five bands in the 1,345–1,100 cm−1 region instead of only one. The splitting of ρ(NH3) at ca. 680 cm−1 is also observed in our case. Two additional bands are visible as shoulders at 645 and 580 cm−1. Since we were able to measure FIR spectrum down to 30 cm−1 five additional bands (219, 207, 150, 114, 92 cm−1) were revealed. Splitting of some bands suggests symmetry lowering of the ideal tetrahedral arrangement of anions and cations. Middle infrared spectrum obtained by us for [Ni(NH3)6](ReO4)2 is in a very good agreement with data reported by Müller et al. [13]. However, splitting of the bands at ca. 1,200 and 680 cm−1 is clearly visible. This suggests that octahedral and tetrahedral symmetry of particular cation is broken. According to Nakamoto [10] the ReO4 − has the following normal modes: fully symmetric stretching ν1(A 1 ) = 971 cm−1, double degenerated ν2(E) = 331 cm−1, triply degenerated ν3(F 2 ) = 920 cm−1 and ν4(F 2 ) = 331 cm−1. All four vibrations are Raman active, but only ν3 and ν4 are IR active. However, in the case of both discussed compounds the tetrahedral symmetry of the anion is disturbed. The distortion led to the situation that formally forbidden (by selection rules) modes are also allowed in the infrared measurements. As a result splitting of ν4 at ca. 920 cm−1 is observed. The lowering of the anion symmetry is also responsible for becoming active a fully symmetric Re–O stretching (breathing vibrations) at ca. 966 cm−1. Splitting of the bands connected with anion internal vibrations is even better visible in the far infrared region. The ν2 mode is no longer silent. Moreover, splitting of this band appears. The far infrared spectrum obtained for [Ni(NH3)6](ReO4)2 indicates that in the solid-state cations and anions are distorted. In the case of [Ni(NH3)4](ReO4)2 the situation is slightly different. The careful inspection of the FIR spectrum registered for this compound revealed additional bands at 219 (shoulder at 207), 150, 114 and 92 cm−1. Their positions agree well with bands registered for Re2O7 in Raman scattering measurements (see Table 4). The more detailed discussion concerning crystal structure and infrared spectrum of dirheniumheptaoxide can be found in [14]. Here we can conclude that FIR spectrum obtained for [Ni(NH3)4](ReO4)2 can be interpreted as evidence that in the crystal structure ReO4 units do not exist as a separate tetrahedrons but rather are joined together through complex cations to form long polymeric chain. The formation of Ni–O–Re bond is probably responsible for band at 219 cm−1.

Fig. 1
figure 1

Comparison of the experimental IR with calculated spectra for isolated molecules [Ni(NH3)6]2+, [Ni(NH3)4]2+ and ReO4 −

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In order to support interpretation of experimental data (especially in the FIR wavenumber region), the calculations of infrared frequencies and intensities were performed. Theoretical IR spectra were calculated separately for an isolated perrhenic anion and isolated complex cation using Gaussian09 package [15] installed on ZEUS supercomputer in Academic Computer Center Cyfronet AGH in Cracow. The calculation were performed using well know and widely used B3LYP functional [16, 17]. The 6-311 + G(d,p) basis were set on N, O, H atoms, whereas Lanl2DZ and Lanl2TZ basis set were used for Ni and Re, respectively [18, 19]. The tetrahedral symmetry was assumed for ReO4 −. In case of complex cation the octahedral and tetrahedral symmetry was employed for [Ni(NH3)6]2+ and [Ni(NH3)4]2+, respectively. Of course the forth coordination cation can take a square symmetry also. However, this symmetry is less popular for nickel-containing compounds. We have performed calculation also for a square symmetry of tetraaminenickel(II). One imaginary frequency was obtained in this case and the molecule (linear N–Ni–N bond) was bent after geometry optimization. We were not able to get rid of this imaginary frequency even by rotation of NH3 molecules. This suggests that square symmetry can be treated as a transition state and tetrahedral arrangement is preferred and stable. The theoretical spectra calculated for complex cations and shown in Fig. 1ab were scaled by factor 0.9688 [20]. The results obtained for ReO4 − (presented in Fig. 1 as a red line) were not scaled because they agree well with experimental ones. The following wavenumbers were obtained for anion: ν 1 = 982 cm−1, ν 2 = 332 cm−1, ν 3 = 920 cm−1, ν 4 = 332 cm−1. The obtained intensities (delta Dirac) were convoluted with Lorentzian (FWHM = 20 cm−1) line shape. The overall good match between calculated and experimental IR spectra is observed despite the simplicity of assumed model. All the bands presented in IR spectrum are predicted by calculation. Since FIR and MIR spectra were measured in two experiments, the experimental intensities in both regions were scaled independently. For better readability the intensities in FIR region (calculated and experimental) were magnified by factor 5. Bands position, relative intensities and their assignments are gathered in Table 1. Interpretation was done taking into account data presented in paper [3, 10, 13] and quantum chemical calculations (QC) described above. The analysis of normal modes was supported by visualization of particular vibrations.

Table 1 Comparison of experimental and calculated spectra (DFT, B3LYP6-311 + G(d,p), Lanl2DZ, Lanl2TZ) for [Ni(NH3)6]2+, [Ni(NH3)4]2+ and ReO −4
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Thermal decomposition

Figure 2 shows comparison of thermal decomposition for both compounds. The violet and blue colors were used for [Ni(NH3)6](ReO4)2 and [Ni(NH3)4](ReO4)2, respectively. The TG, DTG, MS and SDTA curves were recorded at a constant heating rate of 10 K min−1 in the temperature range of 300–1,275 K. During the TG experiment, the following, selected MS line were registered m/e: 14, 16, 17, 18, 28, 30, 32, 44, 46 but only lines representing NH3 showed some signal, and thus only m/e = 17 is shown. Decomposition process can be divided into two main stages. In the first stage both compounds lost all NH3 ligands up to ca. 600 K. In case of [Ni(NH3)6](ReO4)2 all the ammonia ligands are released in three sub-steps (2NH3 + 2NH3 + 2NH3), whereas two sub-steps (2NH3 + 2NH3) are observed for [Ni(NH3)4](ReO4)2. This behaviour suggests firstly that some kind of non-equivalency of NH3 groups exists and secondly that two out of six ligands in [Ni(NH3)6](ReO4)2 are considerably weaker bounded to central atom and are released in temperatures just above room temperature. Next, formed Ni(ReO4)2 or NiO⋅Re2O7 is stable to ca. 890 K. On further heating a drastic change of mass on TG curve is observed. This can be explained assuming that Re2O7 is evaporated. According to Material Safety Data Sheet [21] the pure rhenium(VII) oxide melts at 220 °C and boils at 360 °C. It is commonly known that Re2O7 sublimes [22]. The most probable mechanism of decomposition is given in section “Analysis of thermal decomposition products”. The temperatures, percentage mass of losses and the products of the decomposition of [Ni(NH3)4](ReO4)2 and [Ni(NH3)6](ReO4)2 at particular stages are presented in Tables 2 and 3, respectively. Decomposition of [Ni(NH3)4](ReO4)2 was also a subject of investigations performed by Chakravortiet al. [3]. The measurements were performed up to 573 K. The authors have found that complete deammination takes place in two steps, which is in a good agreement with our results. The intermediate product [Ni(NH3)2](ReO4)2 was characterized using infrared spectroscopy, electronic spectra and magnetic susceptibility measurements [3]. The authors claim that electronic spectra suggest tetragonal symmetry. However, magnetic susceptibility data are characteristic for six coordinated.

Fig. 2
figure 2

TG, DTG, SDTA and MS curves for [Ni(NH3)4](ReO4)2 and [Ni(NH3)6](ReO4)2 in the temperature range of 295–1,275 K, at a constant heating rate of 10 K min−1

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Table 2 Parameters of [Ni(NH3)4](ReO4)2 thermal analysis
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Table 3 Parameters of [Ni(NH3)6](ReO4)2 thermal analysis
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We compared our results with those available in the literature for thermal decomposition of the other hexaamminemetal(II) complexes. The first step observed in the following samples: [Ca(NH3)6](ClO4)2, [Ba(NH3)4](ClO4)2 and [Ni(NH3)6]X2 (where X = Cl, Br) involving deammination is similar to our results [7, 23, 24]. At the higher temperatures the perchlorates explodes and CaCl2 and BaCl2 are formed as a final product of decomposition. The data presented in [7] suggest that both [Ni(NH3)6]Cl2 and [Ni(NH3)6]Br2 decompose to Ni as a final product.

Analysis of thermal decomposition products

First, the final product of decomposition was identified. The mass lost registered in TG measurements clearly suggests that the nickel oxide may be the final decomposition product. The remaining substance after heating the [Ni(NH3)6](ReO4)2 to the ca. 1,275 K was examined after cooling to the room temperature by means of middle (4,000–350 cm−1) and far (600–30 cm−1) infrared spectroscopy. Two separate measurements with appropriate settings of the Bruker VERTEX 70v spectrometer were made for particular IR region. The obtained spectra are shown in Fig. 3a. The MIR and FIR data overlap in the 600–350 wavenumber region. Spectra were normalized (overlapping region was used) to the same intensity and shifted vertically for better visibility. We have compared our results with data available in the literature for nickel oxide. A great similarity between data registered by us and found in Ref. [25–28] can be noticed. Broad and diffused band at ca. 3,410 cm−1, shoulder at 3,219 cm−1 and very weak at ca. 1,628 cm−1 can be assigned to water O–H stretching vibrations and H–O–H bending vibration, respectively [10]. The presence of these bands is caused by absorption of water from the air during preparing sample pellet in KBr. The traces of Re2O7 remained in the sample are probably responsible for the band at 910 cm−1. In case of samples containing ReO4 − anion, this band is very intensive in IR measurements. The most intense and broad band with maximum at 406 cm−1 can be assigned to Ni–O vibrations. One should notice an excellent agreement between MIR and FIR spectra in the overlapping region. However, the FT-FIR measurements reveal more detail. Three, well-separated components at 571 (shoulder), 492, and 406 cm−1 are readily visible, whereas in the FT-MIR spectrum rather one broad maximum with shoulders is present. This is probably due to different detectors used. Below 400 cm−1 none bands appear. A question has arisen what product remains after complete deammination but before the last step of decomposition? One can assume that the [Ni(NH3)6]2+ simply loses NH3 ligands, and the Ni(ReO4)2 is formed in which Ni2+ and ReO −4 ions exists separately in the crystal structure. The crystal structure of Ni(ReO4)2 was reported by Butz et al. [29]. The Ni atom is surrounded by six oxygen atoms. The formed octahedron is fairly regular. Three of the oxygen atoms belonging to each ReO −4 anion are engaged in formation of the bonds (so called bridge bond) to Ni, whereas one oxygen (so called terminate) atom is bound only to Re. Each ReO4 unit links three cation octahedra. The Ni–O distance is equal to 1.976 Å and is slightly shorter than observed in pure NiO (2.096 Å). Anion is distorted. One Re–O bond is longer (1.976 Å) in comparison with the three remaining (1.789 Å). The structure is built from layers consisting of octahedra linked by anion tetrahedra. In order to check the intermediate product, the second thermogravimetric measurement was run. A [Ni(NH3)6](ReO4)2 sample of mass equal to 31.7,521 mg was heated from 298 to 748 K and next cooled to room temperature. The final mass lost registered on TG curve was equal to 14.6 % which well corresponds to theoretical value for six ligands lost. The remaining, so called intermediate product was examined using FT-FIR and FT-MIR spectroscopy. Figure 3b presents obtained spectra. In the MIR region, five main bands are clearly visible. The strong, broad band at ca. 3,388 cm−1 and shoulder at 3,226 cm−1 can be assigned to both NH3 and H2O stretching vibrations. The former possibility should be rather excluded from our consideration for the following reasons. Firstly, TG measurements clearly showed that NH3 ligands were almost completely removed from the sample. Even if we assume that deammination was not complete and some small amount remained in the investigated sample, the resulting spectrum should show much less intense band than it is observed experimentally. Secondly, the position of these bands corresponds well with those visible in Fig. 3a. The shape and its broadening also recalls bands observed in the compounds containing O–H stretching vibrations. Moreover, these bands are shifted toward lower wavenumbers (by ca. 30 cm−1) with respect to NH3 stretching vibrations bands registered for [Ni(NH3)6](ReO4)2 and [Ni(NH3)4](ReO4)2. Thirdly, when the dry sample was prepared for IR transparent measurements (KBr was also dried for 4 days at 470 °C), we have noticed that it becomes sticky. The last indicates that intermediate product of decomposition is very hygroscopic. The H–O–H bending vibration is responsible for a band visible at 1,624 cm−1. Next strong band at 908 cm−1 is associated with ν3 antisymmetric ReO −4 vibration [10]. Two weak and broad bands at 639 and 457 cm−1 are connected with rocking H2O vibrations.

Fig. 3
figure 3

FT-MIR and FT-FIR spectra of a final and b intermediate decomposition products

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The FIR region is rich in bands. The first band at 457 cm−1 covers the same region as MIR. Next at 409 cm−1 comes from the Ni–O (compare Fig. 3a). Three bands located at 368, 347, 324 cm−1) are associated with vibrations in ReO −4 . As was stated in the section “Spectroscopic identification of samples,” the regular ReO −4 has the following vibrations: v 1(A1) ≈ 971 cm−1, v 2(E) ≈ 331 cm−1, v 3(T2) ≈ 920 cm−1, and v 4(T2) ≈ 331 cm−1 but only T2 are IR active. However, when the symmetry is disturbed the selection rules are broken and splitting and shifting of the particular bands can occur. It is interesting to notice that the remaining frequencies (at 213, 178, 120, 85, 46 cm−1) agree well with those reported in the literature for solid state of Re2O7 and acquired by Raman spectroscopy [30–32]. The comparison of frequencies obtained in this work and in Ref [30–32] is given in Table 4. The Re2O7 compound consists of ReO4 tetrahedral and distorted ReO6 octahedral units which are connected through corners to form polymeric chain [14]. The evidence of Ni–O bond formation is also clearly visible. The similar behaviour was found in Ni(ClO4)2 [10, 33]. Strong interaction between Ni2+ and ClO −4 exists and as a result bridging tridentate bonds are formed. Pascal et al. suggests the octahedral environment around the metal atom, and a polymeric structure [33, 34].

Table 4 Comparison of Re2O7 wavenumbers obtained by different authors in the 500–30 cm−1 with data registered for Ni(ReO4)2 and [Ni(NH3)4](ReO4)2
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Phase transition

Figure 4 shows the temperature dependencies of the heat flow (DSC curves) obtained on heating (lower, red curves) and on cooling (upper, blue curves) of the [Ni(NH3)4](ReO4)2 (denoted as 1) and of the [Ni(NH3)6](ReO4)2 (denoted as 2) samples with scanning rate 10 K min−1. In the same figure additional curves in a limited temperature range registered on heating for [Ni(NH3)4](ReO4)2 are also presented. These curves were obtained in the second run of DSC measurements (scanning rate = 10, 20 K min−1). One can see in Fig. 4 that in the temperature range 140–300 K [Ni(NH3)4](ReO4)2 possesses phase transition in solid state. One very small, diffused anomaly on each of appropriate DSC curves was registered at \( T_{\text{Cpeak}}^{\text{h}} \) = 187.8 K (on heating) and at \( T_{\text{Cpeak}}^{\text{c}} \) = 185.3 K (on cooling). Small hysteresis and the λ shape of this phase transition suggest the second-order type phase transition. The thermodynamic parameters of the detected phase transition obtained during heating are presented in Table 5. On cooling at different rates this anomaly becomes very broad and diffused and hence determination of phase transition parameters is impossible. In contradiction to [Ni(NH3)4](ReO4)2 the [Ni(NH3)6](ReO4)2 does not have any phase transition in the temperature range of 300–140 K. This is rather unusual behaviour because hexaamminenickel(II) complexes with different anions (Cl−, Br−, ClO −4 , BF −4 NO −3 ) exhibit rich polymorphism. Moreover, these compounds are rather stable even in air. The phase transitions temperatures detected for compounds containing simple anions are the lowest in the series [2 and papers cited therein]. As one could expected exchanging simple anion to the tetrahedral one cause that phase transition are observed at higher temperatures [1, 2]. We expected that in the case of hexaamminenickel(II) perrhenate the situation will be analogical i.e. one or two phase transitions will be found at even higher temperatures.

Fig. 4
figure 4

DSC curves registered on heating and cooling of [Ni(NH3)4](ReO4)2 and [Ni(NH3)6](ReO4)2 samples in the temperature range of 140–300 K at a rate of 10 K min−1

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Table 5 Thermodynamic parameters of the phase transitions of [Ni(NH3)4](ReO4)2
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Calculation of the activation energy by isoconversional methods

In this work we have used KAS model-free approach and Kissinger method for determination of activation energy for the decomposition steps. The model-free methods employed in this work are based on dynamic TG/DTG analysis and they are recommended by ICTAC Kinetics Committee. Moreover, the KAS method provides more accurate results for solid-state reactions [35]. The theoretical background of non-isothermal kinetics of condensed phase reactions can be found in the most papers [36–39].

The KAS model-free method that can be obtained by applying the following approximation [4, 5]:

$$ { \ln }\left( {\frac{\beta }{{{T}_{\alpha }^{ 2} }}} \right)_{\text{i}} = { \ln }\left( {\frac{{{R} \cdot {A}}}{{{E}_{{\text{a}},\alpha } \cdot {g}\left( \alpha \right)}}} \right) - \frac{{{E}_{{{\text{a,}}\alpha }} }}{R} \cdot \frac{ 1}{{{T}_{\alpha ,{\text{i}}} }} $$
(1)

where: i is the number of experiment, β is the linear heating rate, E a,α is the activation energy corresponding to conversion α, and R is the gas constant, A is the Arrhenius frequency factor, g(α) is the mechanism function, T α,i is the temperature at a given conversion α for the experiment i.

The method is based on measurements of temperatures for each conversion degree α and different heating rates β. The plots of \( { \ln }\left( {\frac{\beta }{{{T}_{\alpha }^{ 2} }}} \right) \) versus 1/T α at constant α will give straight line and from the slope \( - \frac{{{E}_{\text{a}} }}{R} \), activation energies are determined.

Kissinger equation [5] which yields a single value of activation energy was also used to determine the activation energy.

$$ { \ln }\left( {\frac{\beta }{{{T}_{\hbox{max} }^{ 2} }}} \right)_{i} = {\text{Const}} .- \frac{{{E}_{\text{a}} }}{R} \cdot \frac{ 1}{{{T}_{\text{max,i}} }} $$
(2)

where: T max is the temperature of peak maximum from the DTG graph.

A plot of \( { \ln }\left( {\frac{\beta }{{{{T}}_{\alpha }^{ 2} }}} \right) \) against 1/T max gives the Arrhenius plot from the slope of which activation energy can be determined.

The kinetic parameters obtained by KAS method for all decomposition steps were calculated according to Eq. (1) for a given value of conversion α. In the present study, three different heating rates were used (5, 7.5 and 15 K min−1). The calculation procedures of Kissinger equation were applied according to Eq. 2.

The corresponding lines of KAS method obtained at different conversion degrees (α from 0.15 to 0.9) and different heating rates β for first step of deammination process of [Ni(NH3)6](ReO4)2 are shown in Fig. 5, where the analogous lines of the remaining stages were obtained with the same methodology (see Figs. 6–8).

Fig. 5
figure 5

Application of KAS kinetic method and isoconversional activation energy for first step of deammination process of [Ni(NH3)6](ReO4)2 at each extent of conversion (α from 0.15 to 0.9)

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Fig. 6
figure 6

Application of KAS kinetic method and isoconversional activation energy for second step of deammination process of [Ni(NH3)6](ReO4)2 at each extent of conversion (α from 0.15 to 0.9)

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Fig. 7
figure 7

Application of KAS kinetic method and isoconversional activation energy for third step of deammination process of [Ni(NH3)6](ReO4)2 at each extent of conversion (α from 0.15 to 0.9)

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Fig. 8
figure 8

Application of KAS kinetic method and isoconversional activation energy for decomposition process of [Ni(NH3)6](ReO4)2 at each extent of conversion (α from 0.15 to 0.9)

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The apparent activation energies of [Ni(NH3)6](ReO4)2 for all stages of decomposition were calculated using KAS and Kissinger methods and are shown in Figs. 5–8. In Table 6, the R 2 parameters of the fit and activation energy values E by KAS method for all the steps of decomposition.

Table 6 The activation energy values E at β = 5, 7.5, and 15 K min−1 by KAS method
Full size table

From the dependence of activation energy on the extent of conversion, we can predict the nature of solid-state reactions. If E a values are independent of α, the decomposition process is dominated by a single step reaction [40, 41]; on the contrary, a significant variation of E a with α should be interpreted in terms of multi-step mechanism [42, 43]. As we can see in Fig. 5 for the first step of deammination of [Ni(NH3)6](ReO4)2, the activation energy calculated by KAS method slightly decreases with conversion (α from 0.15 to 0.9). This behaviour indicates that probably only one mechanism is involved for the first step of deammination. The mean value for the activation energy obtained from the KAS method is E a(KAS)  = 76.66 ± 3.07 kJ mol−1 and from the Kissinger method is E a(KIS) = 78.21 ± 18.60 kJ mol−1.

The activation energy of the second and third steps of deammination process of [Ni(NH3)6](ReO4)2] is almost constant for α between 0.3 and 0.9 (see Figs. 6, 7). This behaviour suggests that this process is simple and can be described by a single reaction. The mean values of the activation energy corresponding to the second and third stages of deammination are: E a(KAS) = 100.62 ± 1.24 kJ mol−1 and E a(KIS) = 98.52 ± 11.72 kJ mol−1 (the second stage) and E a(KAS) = 137.99 ± 3.62 kJ mol−1 and E a(KIS) = 141.09 ± 12.30 kJ mol−1 (the third stage). The data show that energy of activation was found to be independent of conversion degrees (α from 0.3 to 0.9). The values of activation energy obtained from the Kissinger method are consistent with the range of values obtained by the KAS method and are very near to their average values.

Chakravorti et al. [3] investigated deammination of the [Ni(NH3)4](ReO4)2 compound. They were able to determine activation energy but only for the last step, i.e., [Ni(NH3)2](ReO4)2 → Ni(ReO4)2. The Ea value obtained by these authors equals to 97 kJ mol−1 and is lower than obtained by us. We have used three independent TG measurements (according to ICTAC Kinetics Committee recommendation) in order to estimate the Ea instead of only one. Moreover, one can see that linear fit obtained in Ref [3] is not very good and hence the estimated value of Ea is associated with larger error.

For the last decomposition stage (Fig. 8), the activation energy fluctuates with α increasing (degree of conversion α from 0.15 to 0.5). This means that the reaction mechanism is not the same as in the decomposition process and that activation energy is dependent on conversion degrees (α from 0.15 to 0.5). On conversion degrees α from 0.5 to 0.9, the activation energy remains practically constant, with the average values of E a(KAS) = 369.66 ± 9.78 kJ mol−1 calculated using the KAS method. Activation energy calculated by Kissinger method equal to 365.86 ± 48.22 kJ mol−1. As one could expect the energy activation for the first step of deammination is the lowest. This fully confirms that 2 of 6 NH3 ligands in [Ni(NH3)6](ReO4)2 are weaker bonded.

Conclusions

  1. 1.

    One phase transition at ca. T hc  = 188 K (on heating) and T cc  = 185 K (on cooling) in [Ni(NH3)4](ReO4)2 was detected by means of differential scanning calorimetry in the temperature range 300–140 K. The λ shape of the anomaly suggests the second-order phase transition. The [Ni(NH3)6](ReO4)2 does not exhibit any phase transition in this region.

  2. 2.

    Decomposition of both compounds can be divided into two main steps. The first step connected with the deammination can be further divided into three or two sub-steps for [Ni(NH3)6](ReO4)2 and [Ni(NH3)4](ReO4)2, respectively. It is completed up to ca. 600 K. In the second step, the Re2O7 is released above ca. 900 K and NiO is formed as a final product.

  3. 3.

    The FT-MIR spectra of both compounds are very similar, however, in case of [Ni(NH3)4](ReO4)2 a weak band at ca. 1,411 cm−1 appears. Infrared spectra calculated by the DFT method (Gaussian09 B3LYP, 6-311 + G(d,p), Lanl2DZ, Lanl3TZ) for isolated [Ni(NH3)4]2+, [Ni(NH3)6]2+ cations, and ReO −4 anion are in a good agreement with respective experimental data.

  4. 4.

    The FT-FIR data revealed that ReO −4 anions situation is different in both discussed compounds. In the [Ni(NH3)6](ReO4)2, these anions have disturbed tetrahedral symmetry. In the case of [Ni(NH3)4](ReO4)2, some additional bands can be interpreted as an evidence of forming polymeric chains by ReO4 units.

  5. 5.

    The activation energy for particular steps was determined for [Ni(NH3)6](ReO4)2 using Kissinger–Akahira–Sunose model-free approach and Kissinger method. The lowest value was obtained for the first step of deammination. The activation energies calculated for the deammination steps of [Ni(NH3)6](ReO4)2 by this two methods were found to be consistent and indicate that only one mechanism is involved for the decomposition.