# Dielectric and Impedance Spectroscopic Investigation of (3-Nitrophenol) -2,4,6-Triamino-1,3,5- Triazine: An Organic Crystalline Material

Authors: N. Kanagathara; S. Sankar; L. Saravanan; V. Natarajan; S. Elangovan
Journal: Advances in Condensed Matter Physics
 (2022)

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## Abstract

This article presents the investigation of dielectric and impedance spectroscopic properties of an organic product of 3-nitrophenol -2,4,6-tri amino-1,3,5- triazine (3NPTAT) single crystal, synthesized from melamine and m-nitrophenol. Comprehensive dielectric studies and charge transportation properties of the grown 3NPTAT crystal are given. The dielectric characteristics of the specimen were carried out in the frequency range of 50 Hz and 5 MHz at different temperatures, namely, 313 K, 333 K, 353 K, and 373 K. From the spectra, it was observed that the slowdown occurs at low temperatures, and the hopping mechanism takes place based on localized charge carriers. The impedance spectroscopic results indicate that there is a single relaxation process that occurs at high frequencies. The variation detected in the material properties of 3NPTAT corresponding to the temperature and frequency has been discussed in detail.


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## Body

## 1. Introduction

Single crystals with low dielectric constant, high electro-optic coefficient and ideal reaction rate, and significant thermal stability play a crucial role in producing efficient crystalline materials that might be used in optical data storage, communication, and optoelectronic systems [1–5]. Dielectric spectroscopic studies will be used to determine the electric field distribution in the formed crystal. The frequency and temperature-dependent dielectric characteristics of the produced material reveal the 3NPTAT single crystal’s applicability for a variety of applications. The dielectric characteristics of formed crystals were investigated at frequencies ranging from 50 Hz to 5 MHz.The dielectric behavior of a substance is based on its electrical properties. Materials with a high dielectric constant and low dielectric losses are said to be more suitable for electronic applications. The permittivity of nonconductive materials was previously measured using a dielectric spectroscopic approach [6–11]. Dielectric characteristics also provide useful information regarding materials and design parameters for a variety of applications. Complex impedance spectroscopic examination of frequency-dependent electrical and dielectric properties of materials provides significant information about their electrical microstructure [12–14]. The effect of solvent on material properties using impedance has been discussed by S. Khera and P. Chand in their investigation of ZnO [15]. The complex characteristics such as dielectric permittivity, electrical modulus, impedance, and admittance in the complex plane were shown to explain the whole electrical topography of material by creating a graph between real and imaginary parts in the dielectric spectrum. Dielectric spectroscopic investigations of organic single crystals with desired NLO properties have already been reported by many researchers [16–20].The dielectric and impedance behavior of 3-nitrophenol -2,4,6-tri amino-1,3,5-triazine (3NPTAT) is investigated in this study as a continuation of our research effort in organic NLO materials. We discovered that 3NPTAT has considerable optical transparency throughout the visible spectrum, implying that the dielectric susceptibility is related to precise ordering in the dielectric dipole density. To demonstrate the effect of grain and grain boundaries on the electrical properties of a produced material, we used a combined analysis of modulus and impedance spectroscopy investigation. The authors planned the study to include dielectric measurements as well as conductivity and impedance measurements on the formed crystal.


## 2. Experimental

The slow evaporation approach was used to make a single crystal of 3-nitrophenol -2,4,6-tri amino-1,3,5-triazine (3NPTAT) using an equimolar ratio of melamine and 3-nitrophenol. Melamine was dissolved in distilled water and gently heated before adding an aqueous solution of 3-nitrophenol to the hot melamine solution. The mixture was then thoroughly agitated for 6 hours at 70°C to obtain a homogeneous solution. To obtain the purity of the salt, a recrystallization process was carried out. Tiny and transparent single crystals of 3NPTAT were produced for 25–30 days [21]. The schematic of the synthesis procedure is given in the flow chart in Figure 1, and the growth mechanism of the 3NPTAT single crystal is shown in Figure 2.Figure 1
Synthesis flow chart of the 3NPTAT single crystal.Figure 2
Reaction mechanism of the grown crystal of 3NPTAT.The dielectric characterization of the synthesized compound is carried out using a suitably cut and polished pellet made of 3NPTAT crystal. Dielectric studies of 3NPTAT crystal were performed at different temperatures and frequencies in the range of 313 K–373 K and 50 Hz–5 MHz, respectively, using the HIOKI model 3532–50 LCR HITESTER impedance analyzer. The polished sides of the crystal pellet have been coated with silver paste and air-dried (for good ohmic contact) to make parallel electrodes.


## 3. Results and Discussion

### 3.1. Dielectric Analysis

Permittivityε∗, conductivity σ∗(x), and permeability μ∗(x) are inherent electrical properties of materials that are of great interest in both fundamental and application-oriented research [22]. Based on temperature variations, charge transport, the molecule, collective dipolar fluctuations, and polarisation effects at inner phase boundaries were studied. This article reports the impedance and modulus spectroscopic investigations in detail as a continuation of our prior work on the dielectric constant and dielectric loss as a function of frequency.The resistive property of the grown crystals can be obtained from dielectric studies. The measured dielectric properties are primarily related to the electro-optical properties of an optical single crystal [23]. It further gives insight into the charge transportation properties and charge storage capabilities of the dielectric material. The electronic industries require materials with a low dielectric constant that can be used as a dielectric interlayer during microelectronic device fabrication [24, 25]. Figures 3 and 4 represent the variation of dielectric constant and dielectric loss as a function of frequency, respectively, at different temperatures, namely, 313K, 333K, 353K, and 373 K. Earlier, Sangeetha et al. have previously reported a virtually consistent reduction in dielectric constant with increasing frequency, from 50 Hz to 5 MHz (2014). Figure 4 shows that the decreasing trend in dielectric loss with increasing frequency suggests that the optical quality of the formed 3NPTAT crystal is good with few imperfections, making it appropriate for photonics, laser, and electro-optic device manufacturing. The fact that the dielectric constant and dielectric loss are reduced at higher frequencies indicates that the formed crystal contains a small number of electrically active flaws, which is important in NLO applications [26].Figure 3
Dielectric constant vs log F of 3NPTAT.Figure 4
Dielectric loss vs log F of 3NPTAT.


### 3.2. Frequency Dependence of Real and Imaginary Parts of Dielectric Constant

Figures5 and 6 show the frequency-dependent real (ε′) and imaginary (ε”) parts of the dielectric constant at various temperatures, including 313 K, 333 K, 353 K, and 373 K. The ability to retain electrical energy is the real component of dielectric, whereas the ability to lose electrical energy owing to fluctuations in an applied electric field is the imaginary part. Excellent insulating properties are found in materials with a high dielectric constant and low dielectric loss (tan δ). Figure 6 shows that at low frequencies, the obtained high dielectric constant (ε r) values are due to interfacial or space charge polarisations. It can also be seen that at all temperatures, the real part of the dielectric constant (ε′) decreases with increasing frequency and reaches a maximum value at high frequencies.Figure 5
Real dielectric constant (ε) vs log F.Figure 6
Imaginary dielectric constant (ε”) vs log F.The increase in conductivity of the material at high frequencies is caused by a decreasing trend in the imaginary part of the dielectric constant, as shown in Figure7, which is similar to the earlier report [27]. At low frequencies, the grain boundary effect would be more pronounced. The effect of dielectric polarisation is caused by electrons/holes hopping between both the positive and negative surface defect centers in the grain boundary region at low frequencies. At 373 K, the imaginary dielectric constant is high, indicating that the imaginary part of the dielectric constant (ε′) grows as temperature rises, although the real dielectric constant (ε′) is high at 353 K. At high temperatures, larger grains form, lowering the energy barrier and accelerating atom diffusion to another grain in a single crystal. According to the findings, all types of polarisation (electronic, ionic, orientation, and space charge) play a significant role, but electronic polarisation is the most important [28].Figure 7
Real impedance vs log F.


### 3.3. Complex Impedance Spectroscopic Studies

Complex impedance spectroscopy techniques can be employed to circumvent the restrictions in frequency-dependent dielectric constant and dielectric loss [29–34]. To understand the dielectric behavior and electrical conductivity of materials, the Cole–Cole plot is commonly used in impedance spectroscopic studies to determine the variation among various parameters such as permittivity, impedance, electric modulus, and tangent loss as a function of frequency [35]. The microstructure level of the material can be determined via a complex impedance spectroscopy investigation. It aids in determining how charge transfer occurs in the material as well as how much it relaxes. The response at high frequency is attributable to grains, while the response at low frequency is due to grain boundaries, according to impedance data from the dielectric system plotted in the complex plane. Figures 7 and 8 depict the fluctuation in real and imaginary impedance as a function of frequency at various temperatures, including 313 K, 333 K, 353 K, and 373 K.Figure 8
Imaginary impedance vs log F.The complex impedance spectra of 3NPTAT at various temperatures are shown in Figure9. At all temperatures, all of the samples have a single semicircle shape, as shown in Figure 9. The linear representation of bulk resistivity is given by the semicircle on the real axis. The semicircle represents a grain boundary effect for 3NPTAT at 373 K, with the decrease in impedance value due to increased grain size or grain growth [32, 33]. Figure 10 shows how to compute the activation energy for the thermodynamic system Z. Table 1 shows the activation energy derived from different frequencies based on the imaginary impedance of single-crystal 3NPTAT. Table 1 shows that the activation energy value for a particular frequency above 1 MHz is in the range of 0.02–0.03 eV, whereas for lower frequencies below 1 MHz, the value is greater (0.04–0.07 eV). At low frequencies, charge carriers are thought to travel a great distance and are restricted to a potential well at high frequencies [27, 30].Figure 9
Real impedance vs imaginary impedance.Figure 10
ln (FZ”T) vs 1000/T (K-1).Table 1
Activation energy (Ea) obtained from impedance values.
FrequencyActivation energy (eV)Pre-exponential factor (s−1)R2 valueStandard deviation100 Hz83.338.9520.9690.4031 KHz76.044.9070.9550.45310 KHz54.414.3360.8160.707100 KHz98.978.7810.9950.1931 MHz18.6922.1520.8270.2632 MHz8.3343.7550.93290.9873 MHz28.511.5990.95470.2784 MHz34.041.96150.79211.0395 MHz36.011.91990.79815.579


### 3.4. Dielectric Modulus Studies

Sinclair and West explained that to understand the dielectric properties of a given material, both complex impedance and modulus investigations are used [31]. The grain boundary effect and the conduction mechanism were distinguished using a complex dielectric modulus analysis. The real and imaginary plots of frequency-dependent electric modulus by altering the measurement temperature are shown in Figures 11 and 12. M′ increases with frequency, reaches a peak at 0.45 rad/s, and then steadily falls at high frequencies, indicating the semiconductor property. Because of the short-range mobility of ion charges and their confinement in the potential well, the asymmetric real electric modulus shifts towards higher frequency regions [27]. Furthermore, at low frequencies, the real component of the dielectric modulus is low, implying that electrode polarisation is minimal.Figure 11
Real modulus vs log F.Figure 12
Imaginary modulus vs log F.When compared to dielectric loss, the imaginary portion of the dielectric modulus is utilized to characterize the relaxation nature of the materials. The obtained modulus plot shows that electrical relaxation occurs in the produced crystal. At room temperature, the complex moduli of the M′ and M″ series draw semicircles in the complex plane. The two depressed semicircular graphs for the 3NPTAT crystal recorded at 373 K are shown in Figure13. The linear spikes in the low-frequency band of the Nyquist plot in Figure 13 indicate a supercapacitive nature. This happens because the ions in the electrolyte intercalate and pass through the electrode [36–38].Figure 13
Real modulus vs imaginary modulus.The conductivity relaxation’s peak breadth indicates that the single relaxation time is related to the Debye process. Figure14 shows a conductivity relaxation peak in the M” vs log (f) curve, which shows a minor shift towards higher frequency with increasing 3NPTAT concentration. The shorter relaxation time (τ = 1/fmax) and greater polaronic hopping rate in the concentration of 3NPTAT are related to the rise in peak frequency. The charts plainly illustrate that the arcs' centers do not correspond to the real axis. The first semicircle is due to the grain boundary effect at lower frequencies, although this impact is not visible in the impedance plot or Nyquist plot at higher frequencies.Figure 14
Normalized curve of M’/M’‘max versus log (F/Fmax).A Bode plot is a graph that shows the amplitude and phase of a transfer function in a linear system on a logarithmic scale. Figure15 depicts the fluctuation of the Bode phase angle concerning applied angular frequency (Bode plots). In an EIS Bode plot, the crystal has nearly the same morphology across the whole frequency range and for all temperature measurements. For all the samples examined at different temperatures, a higher phase angle close to 90° was seen at low frequency (a feature of an ideal capacitor). This corresponds to the cell's capacitive functionality. The appearance of a single peak over the whole frequency range shows the presence of grain effects for the generated single-crystal 3NPTAT. The dielectric characteristics of the materials are altered by grain effects. We can adjust the dielectric characteristics by changing the grain size of dielectric materials by varying parameters such as growth temperature, stoichiometric composition, postsintering temperature, and so on.Figure 15
Phase angle vs log F.The ac conductivity is determined using the following formula:(1)σ=A2πfCd,where C is the capacitance, d is the crystal thickness, A is the crystal area of cross-section, and f is the applied field frequency. Figure 16 shows the frequency dependence of electrical conductivity at various temperatures. It signifies that as frequency rises, conductivity rises as well, following Jonscher's universal power law.(2)σac=σo+σω.Figure 16
Conductivity vs log F.σo is the frequency-independent conductivity; σω is the frequency-dependent conductivity, which is expressed as follows:(3)σω=Aωswhere0≤s≤1.Here, ω is the angular frequency of the applied ac field.(4)A=πN2e26KBT2a.Conductivity is essentially nonexistent up to 3 MHz. Beyond 3 MHz, conductivity rises and yields a slope at hopping frequency, indicating that the formed 3NPTAT crystal is thermally active [39].


## 3.1. Dielectric Analysis

Permittivityε∗, conductivity σ∗(x), and permeability μ∗(x) are inherent electrical properties of materials that are of great interest in both fundamental and application-oriented research [22]. Based on temperature variations, charge transport, the molecule, collective dipolar fluctuations, and polarisation effects at inner phase boundaries were studied. This article reports the impedance and modulus spectroscopic investigations in detail as a continuation of our prior work on the dielectric constant and dielectric loss as a function of frequency.The resistive property of the grown crystals can be obtained from dielectric studies. The measured dielectric properties are primarily related to the electro-optical properties of an optical single crystal [23]. It further gives insight into the charge transportation properties and charge storage capabilities of the dielectric material. The electronic industries require materials with a low dielectric constant that can be used as a dielectric interlayer during microelectronic device fabrication [24, 25]. Figures 3 and 4 represent the variation of dielectric constant and dielectric loss as a function of frequency, respectively, at different temperatures, namely, 313K, 333K, 353K, and 373 K. Earlier, Sangeetha et al. have previously reported a virtually consistent reduction in dielectric constant with increasing frequency, from 50 Hz to 5 MHz (2014). Figure 4 shows that the decreasing trend in dielectric loss with increasing frequency suggests that the optical quality of the formed 3NPTAT crystal is good with few imperfections, making it appropriate for photonics, laser, and electro-optic device manufacturing. The fact that the dielectric constant and dielectric loss are reduced at higher frequencies indicates that the formed crystal contains a small number of electrically active flaws, which is important in NLO applications [26].Figure 3
Dielectric constant vs log F of 3NPTAT.Figure 4
Dielectric loss vs log F of 3NPTAT.


## 3.2. Frequency Dependence of Real and Imaginary Parts of Dielectric Constant

Figures5 and 6 show the frequency-dependent real (ε′) and imaginary (ε”) parts of the dielectric constant at various temperatures, including 313 K, 333 K, 353 K, and 373 K. The ability to retain electrical energy is the real component of dielectric, whereas the ability to lose electrical energy owing to fluctuations in an applied electric field is the imaginary part. Excellent insulating properties are found in materials with a high dielectric constant and low dielectric loss (tan δ). Figure 6 shows that at low frequencies, the obtained high dielectric constant (ε r) values are due to interfacial or space charge polarisations. It can also be seen that at all temperatures, the real part of the dielectric constant (ε′) decreases with increasing frequency and reaches a maximum value at high frequencies.Figure 5
Real dielectric constant (ε) vs log F.Figure 6
Imaginary dielectric constant (ε”) vs log F.The increase in conductivity of the material at high frequencies is caused by a decreasing trend in the imaginary part of the dielectric constant, as shown in Figure7, which is similar to the earlier report [27]. At low frequencies, the grain boundary effect would be more pronounced. The effect of dielectric polarisation is caused by electrons/holes hopping between both the positive and negative surface defect centers in the grain boundary region at low frequencies. At 373 K, the imaginary dielectric constant is high, indicating that the imaginary part of the dielectric constant (ε′) grows as temperature rises, although the real dielectric constant (ε′) is high at 353 K. At high temperatures, larger grains form, lowering the energy barrier and accelerating atom diffusion to another grain in a single crystal. According to the findings, all types of polarisation (electronic, ionic, orientation, and space charge) play a significant role, but electronic polarisation is the most important [28].Figure 7
Real impedance vs log F.


## 3.3. Complex Impedance Spectroscopic Studies

Complex impedance spectroscopy techniques can be employed to circumvent the restrictions in frequency-dependent dielectric constant and dielectric loss [29–34]. To understand the dielectric behavior and electrical conductivity of materials, the Cole–Cole plot is commonly used in impedance spectroscopic studies to determine the variation among various parameters such as permittivity, impedance, electric modulus, and tangent loss as a function of frequency [35]. The microstructure level of the material can be determined via a complex impedance spectroscopy investigation. It aids in determining how charge transfer occurs in the material as well as how much it relaxes. The response at high frequency is attributable to grains, while the response at low frequency is due to grain boundaries, according to impedance data from the dielectric system plotted in the complex plane. Figures 7 and 8 depict the fluctuation in real and imaginary impedance as a function of frequency at various temperatures, including 313 K, 333 K, 353 K, and 373 K.Figure 8
Imaginary impedance vs log F.The complex impedance spectra of 3NPTAT at various temperatures are shown in Figure9. At all temperatures, all of the samples have a single semicircle shape, as shown in Figure 9. The linear representation of bulk resistivity is given by the semicircle on the real axis. The semicircle represents a grain boundary effect for 3NPTAT at 373 K, with the decrease in impedance value due to increased grain size or grain growth [32, 33]. Figure 10 shows how to compute the activation energy for the thermodynamic system Z. Table 1 shows the activation energy derived from different frequencies based on the imaginary impedance of single-crystal 3NPTAT. Table 1 shows that the activation energy value for a particular frequency above 1 MHz is in the range of 0.02–0.03 eV, whereas for lower frequencies below 1 MHz, the value is greater (0.04–0.07 eV). At low frequencies, charge carriers are thought to travel a great distance and are restricted to a potential well at high frequencies [27, 30].Figure 9
Real impedance vs imaginary impedance.Figure 10
ln (FZ”T) vs 1000/T (K-1).Table 1
Activation energy (Ea) obtained from impedance values.
FrequencyActivation energy (eV)Pre-exponential factor (s−1)R2 valueStandard deviation100 Hz83.338.9520.9690.4031 KHz76.044.9070.9550.45310 KHz54.414.3360.8160.707100 KHz98.978.7810.9950.1931 MHz18.6922.1520.8270.2632 MHz8.3343.7550.93290.9873 MHz28.511.5990.95470.2784 MHz34.041.96150.79211.0395 MHz36.011.91990.79815.579


## 3.4. Dielectric Modulus Studies

Sinclair and West explained that to understand the dielectric properties of a given material, both complex impedance and modulus investigations are used [31]. The grain boundary effect and the conduction mechanism were distinguished using a complex dielectric modulus analysis. The real and imaginary plots of frequency-dependent electric modulus by altering the measurement temperature are shown in Figures 11 and 12. M′ increases with frequency, reaches a peak at 0.45 rad/s, and then steadily falls at high frequencies, indicating the semiconductor property. Because of the short-range mobility of ion charges and their confinement in the potential well, the asymmetric real electric modulus shifts towards higher frequency regions [27]. Furthermore, at low frequencies, the real component of the dielectric modulus is low, implying that electrode polarisation is minimal.Figure 11
Real modulus vs log F.Figure 12
Imaginary modulus vs log F.When compared to dielectric loss, the imaginary portion of the dielectric modulus is utilized to characterize the relaxation nature of the materials. The obtained modulus plot shows that electrical relaxation occurs in the produced crystal. At room temperature, the complex moduli of the M′ and M″ series draw semicircles in the complex plane. The two depressed semicircular graphs for the 3NPTAT crystal recorded at 373 K are shown in Figure13. The linear spikes in the low-frequency band of the Nyquist plot in Figure 13 indicate a supercapacitive nature. This happens because the ions in the electrolyte intercalate and pass through the electrode [36–38].Figure 13
Real modulus vs imaginary modulus.The conductivity relaxation’s peak breadth indicates that the single relaxation time is related to the Debye process. Figure14 shows a conductivity relaxation peak in the M” vs log (f) curve, which shows a minor shift towards higher frequency with increasing 3NPTAT concentration. The shorter relaxation time (τ = 1/fmax) and greater polaronic hopping rate in the concentration of 3NPTAT are related to the rise in peak frequency. The charts plainly illustrate that the arcs' centers do not correspond to the real axis. The first semicircle is due to the grain boundary effect at lower frequencies, although this impact is not visible in the impedance plot or Nyquist plot at higher frequencies.Figure 14
Normalized curve of M’/M’‘max versus log (F/Fmax).A Bode plot is a graph that shows the amplitude and phase of a transfer function in a linear system on a logarithmic scale. Figure15 depicts the fluctuation of the Bode phase angle concerning applied angular frequency (Bode plots). In an EIS Bode plot, the crystal has nearly the same morphology across the whole frequency range and for all temperature measurements. For all the samples examined at different temperatures, a higher phase angle close to 90° was seen at low frequency (a feature of an ideal capacitor). This corresponds to the cell's capacitive functionality. The appearance of a single peak over the whole frequency range shows the presence of grain effects for the generated single-crystal 3NPTAT. The dielectric characteristics of the materials are altered by grain effects. We can adjust the dielectric characteristics by changing the grain size of dielectric materials by varying parameters such as growth temperature, stoichiometric composition, postsintering temperature, and so on.Figure 15
Phase angle vs log F.The ac conductivity is determined using the following formula:(1)σ=A2πfCd,where C is the capacitance, d is the crystal thickness, A is the crystal area of cross-section, and f is the applied field frequency. Figure 16 shows the frequency dependence of electrical conductivity at various temperatures. It signifies that as frequency rises, conductivity rises as well, following Jonscher's universal power law.(2)σac=σo+σω.Figure 16
Conductivity vs log F.σo is the frequency-independent conductivity; σω is the frequency-dependent conductivity, which is expressed as follows:(3)σω=Aωswhere0≤s≤1.Here, ω is the angular frequency of the applied ac field.(4)A=πN2e26KBT2a.Conductivity is essentially nonexistent up to 3 MHz. Beyond 3 MHz, conductivity rises and yields a slope at hopping frequency, indicating that the formed 3NPTAT crystal is thermally active [39].


## 4. Conclusion

In the frequency range of 50 Hz to 5 MHz, the dielectric and charge transport properties of the synthesized nonlinear optical material 3NPTAT single crystal were investigated at four different temperatures 313 K, 333 K, 353 K, and 373 K. The determined dielectric constant ′ and dielectric loss ′′ showed decreasing trends with frequency elsewhere. The influence of the electric field on the dipoles explained the drop inε′. At low frequencies, these dipole moments easily follow the direction of the alternating applied field, resulting in significant polarisation values, as shown by high values of ε′. However, at high frequencies, dipoles have difficulties following the field’s direction, polarisation weakens, and constant dielectric ε′ values fall. After analyzing the data, it was shown that charge transportation relaxation and hopping mechanisms occur at low temperatures with concentrated charge carriers. The results also show that the grain boundary effect causes a single relaxation process at a high frequency. The increase in modulus with frequency attains the maximum value again, and a decrease in modulus shows the semiconducting character. This trend also shows that the relaxation mechanism is dominated by dipole orientation relaxation under the influence of the electric field. The combination of impedance spectroscopy and modulus yields a lot of information on the electrical relaxation process in the microstructure of materials. At higher frequencies, the activation energy is determined to be 8–36 eV, which explains relaxation in the lower region, where charge carriers are stable and can travel long distances. 3NPTAT is activated at high temperatures according to the frequency-dependent electrical conductivity measurements, and the material exhibits a low dielectric loss and a high dielectric constant. As a result, possible dielectric relaxations, conduction mechanisms, and the electrical field effect were examined in the context of this formalism. According to the findings, the produced 3NPTAT single crystal acts as a perfect insulator and a superior dielectric material for high-frequency device applications.



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