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Effect of different in situ temperatures on the crystallinity and optical properties of green synthesized 8-hydroxyquinoline zinc by saffron extract

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Abstract

In this research, bis (8-hydroxyquinoline) zinc (ZnQ2) nanoparticles were synthesized by the saffron extract method in a water environment at room temperature using a simple chemical precipitation method. Based on this technique, saffron was utilized as a surfactant due to its non-toxicity and being environmentally friendly. The existence of C-H bonds in the compound of saffron makes it an appropriate material for the green synthesis of ZnQ2 nanoparticles. These kinds of bounds cause reduce the rate of agglomeration of ZnQ2 nanoparticles while of the synthesis process. In this project, the ZnQ2 nanoparticles were synthesized using saffron non-toxic surfactant in different temperatures. The temperature effects from room temperature to 200 °C were considered on the crystal structure of ZnQ2 nanoparticles and their effect on optical properties, an in-situ HT-XRD instrument has been used. The functional groups of the compound, structural, morphology, and fluorescence properties of ZnQ2 nanoparticles were examined by X-ray diffraction (XRD), scanning electron microscopy (SEM), Fourier-transform infrared spectroscopy (FTIR), photoluminescence (PL) spectroscopy, and Ultraviolet-visible spectroscopy (UV-Vis). According to the results, XRD analysis confirmed the crystalline nature of the synthesized ZnQ2 nanoparticles by the saffron extract. The same bounds were achieved at various temperatures and also with the increase in temperatures of synthesis at 200°C sizes and band gaps were altered from 3.4 nm to 2.5 nm. Therefore, the ZnQ2 nanoparticles are one of the best green materials for replacing transferred electrons materials in optical devices. In conclusion, with utilizing the green materials, Because of reduction the intensity of surface trap and absorption is reduced and the PL of ZnQ2 in the 50°C have reached to 20000. This could be an excellent perspective for using green materials in the organic light-emitting diode and other electronic-optical devices.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Nano-technology is a vital part and integral of modern life with a presence in human activities, including food production and conservation, medicine and biotechnology, telecommunications, etc. [15]. However, making nanomaterials with a chemical process pollutes the environment [69]. Due to the growing process of nanomaterials production, environmental issues related to it are becoming more and more apparent [1014]. In this regard, nanomaterial green production processes have recently attracted much attention, including environmental protection and sustainable economic development [1218]. Among the reported green production methods, plant extracts have been widely accepted as a leading green method for nanotechnology and nanomaterials production [1924]. Plants materials contain biogenic molecules capable of acting as modifiers and capping agents for the synthesis of nanomaterials [25]. Among the plants used in this regard are saffron and lemon extract, etc. [2629]. The reports show that the use of plants with different applications in the industry has been growing increasingly in the world because this method is simpler and nontoxic when compared with physicochemical methods [30]. The reason saffron extracts work so well in the synthesis of nanoparticles is that they function as reducing agents as well as capping agents [31]. Also, the presence of phenolic compounds in saffron favors its use as a more sustainable option and the phenolic and flavonoid compounds found in the plant could help in the formation of NPs. [32]

One of the most popular nanomaterials due to their excellent performance in the light emitting devices is metal chelate with hydroxyquinoline ligand [3341]. Numerous studies have been reported on the structure and unique characteristics of 8-hydroxyquinoline metals (MQ) [42,43]. As light emitters and electron transmitters, the performance of luminescence and electronic transmissions of the zinc complexes (ZnQ2) is very significant [44,45]. The excellent performance of the electronic transmission of the zinc complex is due to the better overlap of π-π* the molecular circuits of the zinc derivatives [4648]. With efficient electroluminescence and low Delta Voc, the complex can be suitable for organic solar cells [49]. Also, the zinc complex has less toxicity, high thermal stability, easy color tunability with simple synthesis, and various shape structure [5055]. In addition to light-emitting diodes, the expressed properties of the complexes such as tunability can be used in solar cells due to following the reciprocity relation between electroluminescence and proper quantum efficiency [56]. Metal complexes of 8-HQ are broadly considered to be one of the most reliable electron-transporting and emitting materials, but the zinc complex exhibits higher quantum yield and improves injection efficiency [5759].

Among the plants used, saffron is one of the most valuable medicinal plants worldwide, and also for the first time, we have reported the biosynthesis of Zn complex using wastage of saffron extract. In this study, due to the problem of environmental protection and green synthesis of nanomaterials, the zinc complex was synthesized with a simple co-precipitation method using saffron plant extract as a surfactant in an aqueous medium. The existence of C-H bonds in the compound of saffron makes it an appropriate material for the green synthesis of nanoparticles. These kinds of bounds cause reduction the rate of agglomeration of ZnQ2 nanoparticles while of the synthesis process. Synthesized zinc complex nanostructures by saffron in terms of structurally, chemical bonds and optical properties were examined using XRD, FT-IR, SEM, Pl, and UV-Vis. In order to better understand the effect of temperature and also to change the structural phase of synthesized zinc complex nanostructures by saffron, we used HT-K XRD analysis from room temperatures to 200°C. Also, we examined the phase change of the crystal structure of zinc nanostructures on optical, chemical, and structural properties.

2. Experimental section

2.1 Materials

The zinc nitrate powder (Zn (NO3)2⋅4H2O, 99.99%), 8-hydroxyquinoline (C9H6NO (HQ), 99.99%), and deionized water were purchased from Merck and used without purification.

2.2 Synthesis of samples

Green synthesis of zinc complex with saffron extract, zinc nitrate, and 8-hydroxyquinoline was performed simply and using a co-precipitation procedure. Firstly, the saffron extract was extracted using soxhlet machinery. In this way, saffron is shed into the reservoir of the device with the desired solvent. Due to the heat, the solvent evaporates and is then shed onto the sample. This cycle continues until the soxhlet reservoir is filled and returns to the balloon through a thin glass siphon, thus completing the cycle to obtain the saffron extract.

In the following of synthesis, each of zinc nitrates and 8-hydroxyquinoline were dissolved in 100 ml of DI-water using a magnetic stirrer, separately until the transparent solution has obtained. Then, both mixtures, zinc, and 8-hydroxyquinoline solutions were added together, and the resultant suspension was stirred for 1 hour in a water bath at 50°C until uniform solution was obtained. Then, saffron extract was added to the resultant suspension drop by drop. Finally, The product autoclaved at 180°C for 15 hours. The resulting zinc complex was examined chemically, structurally, and optically at the room temperature. In the following, the zinc complex was divided into four portions to study the effects of temperature with HTK-XRD and analyzed chemically, structurally, and optically in 4 temperatures from 50 to 200°C. The green synthesized zinc complex was fabricated by a co-precipitation strategy, as illustrated in Fig. 1.

 figure: Fig. 1.

Fig. 1. Schematic diagram of synthesis and SOM images of prepared ZnQ2 Complexes with saffron extract and after of HTK process in the various temperatures

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2.4 Characterization

The synthesized zinc complex was studied using SOM, HTK-XRD, FT-IR, and TEM, PL, and UV-Vis analysis. Using an optical microscope (SOM), images of the resulting powders were taken with a magnification of 4000. The crystal structures of zinc complexes were determined by XRD using a Philips X'pert unit, armed with a PW3710 MPD diffractometer control unit, with Cu Kα radiation (λ = 1.5418 Å) and a generator setting of 40 kV and 30mA, operating in a Bragg–Brentano configuration. The samples were annealed in an HTK-XRD chamber from room temperature to the desired temperature (50, 100, 150, and 200 °C) for a period using HTK. Also, Infrared spectrums in region 200–4000 cm−1 were registered on a Perkin-Elmer, Spectrum RX FTIR, and USA instrument using KBr pellets. The scanning electron microscopy (SEM) images of the complexes were obtained on an SEM-MAG, 15KV electron source. Electronic absorption and PL spectra were measured in region 200–900 nm by using JASCO V-530 UV–Vis spectrophotometer, and with HR4000 ocean optic (under ambient conditions), respectively.

3. Results and discussion

3.1 Infrared absorption spectroscopy (FTIR)

The infrared absorption spectra of the samples ZnQ2 complex nanostructures at room temperature and after 50, 100, 150, and 200°C temperatures were measured in the wavelength range 400 to 4000 cm-1. The infrared spectrum shows the functional groups and conjugations of the samples. Figure 2 shows the analogy of the infrared spectra of ZnQ2 nanostructure and ZnQ2 nanostructure after changing temperature. The absorption spectra of all samples are almost the same and new absorption peaks are not obtained in the effect of temperature, which shows that new substances have been not formed. Also, this proves that synthesized ZnQ2 by saffron extract their conjugation is not broken in the effect of changing temperature using HT-K XRD. The absorption peaks of ZnQ2 bands at range 400–600 cm−1 can be attributed to the conjugation of metal ions with attached ligands. The vibrations at 1504 and 1464 cm−1 were attributed to the pyridyl and phenyl groups of 8 hydroxyquinolines. The peaks at 906, 820, 786, 740, and 601cm−1 were associated with in-plane ring deformations. The peak at 508 cm−1 was associated with Zn–O stretching vibration. We observed C = C vibrations (1623 cm−1), CH2 scissors vibrations (1384 cm−1), C–C (1577 cm−1) that indicating good agreement with reported data. For all the samples, the peaks at 3395 and 3044 cm−1 indicate the moisture (H2O) content in the samples [3840,60,61]. Also, the peaks at 641cm−1 were associated with CH = CH vibrations in the saffron [62]. A comparison of the intensities of the FTIR spectra of the samples shows that the broadband in the range 3044-3400 cm-1, which is attributed to the tension in the OH bond, corresponds to (ZnQ2) ⋅2H2O and at higher temperatures, the decreases of bond intensity are attributed to the presence of the structure (ZnQ2)4. The ratio of the band of 3400 cm-1 to the band in the range of 1110 cm-1 is related to the number of water molecules in metal-quinolone chelates. This ratio in the sample at room temperature is 0.8 due to the partial residual water content in the sample [44]. The peaks of 608 and 650 cm-1 become more noticeable with increasing temperature and indicate a higher ring distortion on the plate [63].

 figure: Fig. 2.

Fig. 2. FTIR spectrum analysis of prepared ZnQ2 Complexes with saffron extract and after of HTK process in the various temperatures.

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3.2 Crystallography: high temperature x-ray diffraction analysis

The high-temperature X-ray diffraction experiments were done on ZnQ2 specimens using the Philips X'pert unit, armed with a PW3710 MPD diffractometer control, with an HT-XRD chamber. The total stage was isolated from the surroundings by a vacuum chamber, which joined to a turbo molecular pump to maintain a high vacuum. During the tests, the vacuum inside the chamber was ∼10−4 bar. The sample crystal structures were determined by in situ HT-K X-ray diffraction. Data for all samples were collected at 25°C in a 2θ range of 20–75°C. Synthesized ZnQ2 nanoparticles indexed the diffraction peaks by saffron extract (JCPDS 48-2116, 39-1857). The XRD results demonstrated reflection planes at (640), (311), (112), (480), (171), (002), (731), (120), (951), (2140), (12100), (6160), (2180), (200), (201) and (004) for ZnQ2. The diffraction peaks of ZnQ2 occur at 2θ = 24.55°, 25.27°, 27.88°, 28.54°, 32.04°, 34.95°, 35.49°, 37.57°, 42.90°, 44.34°, 54.25°, 55.55°, 58.21°, 66.16°, 69.04°, and 72.60° [3840]. All of the strong peaks for the specimen can be assigned to ZnQ2, indicating good agreement with the reported data [3840,6466]. Also, the strong and sharp reflection peaks in the XRD pattern demonstrate the crystalline nature of the prepared Zn-complex nanostructure. The peaks can be indexed to be the ZnQ2.2H2O crystal form of bis (8- hydroxyquinolines) zinc [64,65]. To evaluate the effect of temperature on the structure of ZnQ2 powder, an in-situ HT-XRD has been used. For this work, ZnQ2 powder was divided into 4 samples. The first sample powder heating process was started from room temperature (25°C) then the temperature was increased to 50°C. The cooling process has been done in the same way from 50°C and returned to room temperature (25°C). Also, the X-ray diffraction pattern of ZnQ2 powder during the HT-K process was measured at each temperature (Fig3-A.). The second sample powder heating process was started from room temperature (25°C) then the temperature was increased to 50°C and then 100°C. The cooling process has been done in the same way from 100°C to 50°C and returned to room temperature (25°C). The X-ray diffraction pattern of the ZnQ2 powder during the HT-K process was measured at each temperature (Fig. 3-B). The third sample powder heating process was started from room temperature (25°C) then the temperature was increased to 50°C, 100°C, and 150°C. The cooling process has been done in the same way from 150°C to 100°C, 50°C, and returned to room temperature (25°C). The X-ray diffraction pattern of ZnQ2 powder during the HT-K process was measured at each temperature (Fig. 3(C)). The fourth sample powder heating process was started from room temperature (25°C) then the temperature was increased to 50°C, 100°C, 150°C, and 200°C. The cooling process has been done in the same way from 200°C to 150°C, 100°C, 50°C, and returned to room temperature (25°C). The X-ray diffraction pattern of ZnQ2 powder during the HT-K process was measured at each temperature (Fig. 3(D)). Changes in microstructural parameters are analyzed by in situ measurements at different temperatures for all samples both in the heating up and cooling down step, including several thermal cycles. The mean crystalline size of synthesized ZnQ2 powders by the saffron extract was measured according to FWHM of diffraction peak during heating and cooling based on Scherer’s equation for all samples. In the following, texture coefficients were computed from the XRD data using equation.1 [66,67]:

$$T{C_{hkl}} = \frac{{{\raise0.7ex\hbox{${{I_{hkl}}}$} \!\mathord{/ {\vphantom {{{I_{hkl}}} {{I_{0hkl}}}}}}\!\lower0.7ex\hbox{${{I_{0hkl}}}$}}}}{{{\raise0.7ex\hbox{$1$} \!\mathord{/ {\vphantom {1 n}}}\!\lower0.7ex\hbox{$n$}}\mathop \sum \nolimits_{i = 1}^n ({{\raise0.7ex\hbox{${{I_{hkl}}}$} \!\mathord{/ {\vphantom {{{I_{hkl}}} {{I_{0hkl}}}}}}\!\lower0.7ex\hbox{${{I_{0hkl}}}$}}} )}}$$

 figure: Fig. 3.

Fig. 3. In-situ X-ray diffraction pattern of prepared ZnQ2complexes with saffron extract during HTK process at increasing from the room temperature and decreasing to the room temperature.

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For all samples, when the temperature increased the ZnQ2 highest peak was heightened and led to appearing and disappearing a few peaks, which can be seen in Fig. 3(A) (Supplementary Table S1). During the cooling process, during temperature decreasing, the intensity of the ZnQ2 highest peak had changed and had decreased. Also decreasing temperature leads to appearing a few peaks. A little shift in the place of peaks occurred, which related to the uniform strain due to applying temperature. For fourth sample, during the cooling process, during temperature decreasing from 200°C, 150°C, 100°C, and 50°C to 25°C the intensity of the ZnQ2 highest peak had changed and drastically decreased. With the comparison of crystallite size means related to ZnQ2 during heating, it is indicated that totally the size of crystallite size increased due to the thermal treatment, then when during cooling decreased. The same thing happens with texture coefficients for the highest peak. Texture coefficients for the highest peak drastically reduced during temperature decreasing. The sample crystal structure moves to amorphous with increasing the temperature to 200°C and decreasing it to room temperature. This does not happen in the above cases of samples ZnQ2 at 50°C, 100°C, 150°C. All the results calculated from HTK-XRD show a change in the crystal phase structure of the ZnQ2 complex. Based on the HT-K XRD data, the various crystalline phases of ZnQ2 were identified. According to references, ZnQ2 will crystallize in several different forms. ZnQ2. 2H2O will form at room temperature, ZnQ2, (ZnQ2)2 and (ZnQ2)4 at temperatures of 100°C or higher. [64,65]. Differently formed crystal structures (obtained from HT-K XRD data) at different temperatures change the electron density observed in the pyridyl complex and decreasing or increasing the electron density in the ring affects HOMO and LUMO and causes luminescent changes [64,65,57].

3.3 SEM analysis: sample crystal form

The surface morphology of all samples ZnQ2 powder annealing and ZnQ2 at room temperature were analyzed using SEM. Figure 4(a)–4(e) show the scanning electron micrograph of ZnQ2 Nano-sheets after annealing. It reveals that the synthesized sample is composed of Nano-sheets with a thickness of about 100-200 nm. Based on the crystal size observed in the time dependence studies, two stages can be considered for the growth stages of ZnQ2 crystals composed of HQ species: nanoparticles and sheet-like structures. These steps appear to be similar to those of the chemical fabrication of MQX reported attributed to cavitation and an Ostwald ripening process [33,68]. In here also the mechanism for evolution of the sheet-like crystal morphologies observed in this study can be explained by Ostwald ripening; (1) the nanoparticles of ZnQ2 are formed a result of the reaction of the HQ, (2) then the precipitated particles grow to form nano-sheets due to the aggregation of the nanoparticles. The crystal form of ZnQ2 after annealing resembles an irregular sheet-like structure, as shown by the SEM image, and is stacked in layers. As the temperature rises, the nano-sheets break more and lose their sheet-like structure.

 figure: Fig. 4.

Fig. 4. The SEM surface images of prepared ZnQ2 complexes with saffron extract and after of HTK process in the various temperatures (a-e).

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3.4 Optical properties: analysis of fluorescence spectra (photoluminescence and ultraviolet–visible spectroscopy)

The photoluminescence (PL) and UV–vis absorption of samples before and after annealing ZnQ2 powder was measured. Figure 5(a) shows the UV-Vis spectra and Fig. 5(b) shows the Eg analysis of prepared ZnQ2 complexes with Saffron extract and after of HTK process in the various temperatures. The absorption spectra are shown as Fig. S3 in the supplementary file separately). According to the Fig. S3, the optical absorption peak of the sample without annealing was observed around 230 nm which corresponds to a charge transfer state of the Zinc metal ion to the 8Hq molecule [3840]. With increasing annealing from 50°C to 100°C, 150°C, and 200°C optical absorption peak of the samples after annealing was achieved to 243-245 nm. The optical absorption peak of the samples without annealing at around 314 nm are assigned to electron transition from the HOMO orbit in the phenoxide ring to the LUMO orbit in the pyridine ring due to π–π* bonding of the 8-hydroxyquinoline unit of the ZnQ2 nanoparticles [38,40] and also after annealing from 50 °C to 100 °C and 150 °C, the optical absorption peak was around 315-317, and it was almost unchanged. With increasing annealing from 150 to 200 °C, the optical absorption peak was red-shifted and broader than other samples. The absorption peak around 380 and 375nm corresponds to the transfer n -π* [38,39]. The optical absorption band of the annealing sample after 200 °C is broader than that of other samples. According to the optical absorption of samples, the optical band-gap of samples without annealing and after annealing can be estimated to be about 3.54, 3.46, 3.44, 2.84, and 2.52 eV, respectively. Due to that the HOMO of ZnQ2 is localized on the two non-bridging, terminal ligands, and the LUMO on the bridging, terminal ligands, in the effect of annealing, the inter-and intra-molecular π–π* interplays result in an extended network of overlapping phenolate and pyridyl moieties, thereby lower LUMO level energy and narrower bandgap of ZnQ2 [64]. Figure 5(e) also shows that the sample after annealing 200°C has the strongest band-tail absorption, about other samples after annealing, which originates from band tail localized states and intrinsic bandgap states resulting from the amorphous component [64].

 figure: Fig. 5.

Fig. 5. (a) UV-Vis spectra and, b) Eg analysis of prepared ZnQ2 Complexes with Saffron extract and after of HTK process in the various temperatures.

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Figure 6 shows a) Normalized PL, b) Peak-PL and c) FWHM-PL analysis of prepared ZnQ2 complexes with saffron extract before and after of HTK processing in various temperatures. Also The PL spectra are shown as Fig. S5 in the supplementary file separately. The real image of samples is shown in the inset of Fig. 6(a). According to this image the most photoluminescence is related to sample in 50 °C. From the PL spectra of samples at room temperature, after 50°C, 100°C, 150°C, and 200°C can be seen that emitting peaks from samples un-shifted. The emission peaks of ZnQ2 nanostructure complexes in an aqueous solution are 513 nm for all samples that observe the blue-green light [65]. The shoulder observed at 492 nm might be due to inhomogeneous broadening meaning that each molecule acquires a slightly different position [69]. The brightness of them strongly enhanced after annealing at 50°C then reduced after annealing at 100°C, 150°C, and brightness intensity at 200°C is the same as brightness intensity at room temperature. The annealing sample at 200 °C has the lowest brightness, which also results from band tail localized states and intrinsic band-gap states of samples attributed to high defect densities, and intense self-absorption results in a decrease in brightness [64]. The decreasing and increasing trend of brightness intensity depends on the average crystalline size and changing structure obtained from HT-K X-ray and decreasing of the -OH band as seen in FTIR [63]. The intensity of brightness increases with increasing average crystalline size at 50°C, and at other temperatures, the brightness decreases with decreasing average crystalline size (Fig. S4). The FWHM (full width at half-maximum) became narrower from the sample after annealing at 50 °C and then became wider after annealing at 100 °C, 150°C, and 200°C. Changes in FWHM and intensity PL with temperature are due to the formation of anhydrous crystalline (ZnQ2)2 and tetramer (ZnQ2)4 [70] that this restructuring from ZnQ2.2H2O to (ZnQ2)4 is well visible in the HT-K XRD and FTIR data. Not only the samples were proper for organic light-emitting diode (OLED) but also were proper for other optoelectronic applications. Also, there is a smaller peak in the photoluminescence spectrum at all temperatures (shoulder peak, an energy level that is not trapped but an energy level that can absorb electrons with energy equivalent to a wavelength of 492 nm). These types of peaks can be attributed to the rotational levels of the material.

 figure: Fig. 6.

Fig. 6. a) Normalized-PL spectrum (samples of solution images under excitation are shown in the inset of (a) for more comparison), b) Peak-PL, and c) FWHM-PL analysis of prepared ZnQ2 complexes with saffron extract and after of HTK process in the various temperatures. (Excitation wavelength is 360 nm for PL analysis)

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4. Conclusion

The ZnQ2 particles were prepared using saffron extract as a surfactant by an easy precipitation method. The existence of C-H bonds in the compound of saffron makes it an appropriate material for the green synthesis of nanoparticles and causes reduce the rate of agglomeration of ZnQ2 nanoparticles while of the synthesis process. In the following, the ZnQ2 Nano-sheets for evaluation effect of temperature on the crystal structure, functional groups, morphology, absorption, and emissive properties were taken in situ HT-K XRD. The properties of the ZnQ2 Nano-sheets were characterized using means of HT-K XRD, FT-IR, and UV–Vis, SEM, and PL analysis. The FTIR spectra of all the ZnQ2 Nano-sheet samples were the same and new absorption peaks were not gained after annealing, which shows that new substances have not been formed. The emission peaks and absorption of ZnQ2 the Nano-sheets in aqueous solution after annealing could be transformed. The different crystal stacking in the effect of annealing leads to different X-ray diffraction spectra. The inter and intra-molecular π-π* interactions of the ZnQ2 Nano-sheet after annealing causes low LUMO level energy and narrower bandgap; as a result of will have cause increasing optical absorption and reducing emission spectrum.

Disclosures

The authors declare no conflict of interest.

Data availability

No data were generated or analyzed in the presented research.

Supplemental document

See Supplement 1 for supporting content.

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Supplementary Material (1)

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No data were generated or analyzed in the presented research.

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Figures (6)

Fig. 1.
Fig. 1. Schematic diagram of synthesis and SOM images of prepared ZnQ2 Complexes with saffron extract and after of HTK process in the various temperatures
Fig. 2.
Fig. 2. FTIR spectrum analysis of prepared ZnQ2 Complexes with saffron extract and after of HTK process in the various temperatures.
Fig. 3.
Fig. 3. In-situ X-ray diffraction pattern of prepared ZnQ2complexes with saffron extract during HTK process at increasing from the room temperature and decreasing to the room temperature.
Fig. 4.
Fig. 4. The SEM surface images of prepared ZnQ2 complexes with saffron extract and after of HTK process in the various temperatures (a-e).
Fig. 5.
Fig. 5. (a) UV-Vis spectra and, b) Eg analysis of prepared ZnQ2 Complexes with Saffron extract and after of HTK process in the various temperatures.
Fig. 6.
Fig. 6. a) Normalized-PL spectrum (samples of solution images under excitation are shown in the inset of (a) for more comparison), b) Peak-PL, and c) FWHM-PL analysis of prepared ZnQ2 complexes with saffron extract and after of HTK process in the various temperatures. (Excitation wavelength is 360 nm for PL analysis)

Equations (1)

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T C h k l = I h k l / I h k l I 0 h k l I 0 h k l 1 / 1 n n i = 1 n ( I h k l / I h k l I 0 h k l I 0 h k l )
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