Welcome to visit Communications in Theoretical Physics,
Others

Exploring dielectric phenomena in sulflower-like nanostructures via Monte Carlo technique

  • N Saber 1 ,
  • Z Fadil , 1, ,
  • Hussein Sabbah 2 ,
  • A Mhirech 1 ,
  • B Kabouchi 1 ,
  • L Bahmad 1 ,
  • Chaitany Jayprakash Raorane , 3, ,
  • Siva Sankar Sana 3 ,
  • Hassan Fouad 4 ,
  • Mohamed Hashem 5
Expand
  • 1Laboratory of Condensed Matter and Interdisciplinary Sciences (LaMCScI). Research Unit Labelled CNRST, URL-CNRST-17. Faculty of Sciences. PO Box 1014, Mohammed V University in Rabat, Morocco
  • 2College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait
  • 3School of Chemical Engineering, Yeungnam University, Gyeongsan, 38541, Republic of Korea
  • 4Applied Medical Science Department, Community College, King Saud University, PO Box 11433, Riyadh Saudi Arabia
  • 5Department of Dental Health, College of Applied Medical Sciences, King Saud University, PO Box 12372, Riyadh, Saudi Arabia

Authors to whom any correspondence should be addressed.

Received date: 2023-09-25

  Revised date: 2024-02-06

  Accepted date: 2024-03-08

  Online published: 2024-04-18

Copyright

© 2024 Institute of Theoretical Physics CAS, Chinese Physical Society and IOP Publishing Printed in China

Abstract

This research focuses on the electric behavior of a mixed ferrielectric sulflower-like nanostructure. The structure includes a core with spin ${S}_{i}^{Z}-1$ atoms and a shell with spin ${\sigma }_{j}^{Z}-5/2$ atoms. The Blume–Capel model and the Monte Carlo technique (MCt) with the Metropolis algorithm are employed. Diagrams are established for absolute zero, investigating stable spin configurations correlated with various physical parameters. The MCt method explores phase transition behavior and electric hysteresis cycles under different physical parameters.

Cite this article

N Saber , Z Fadil , Hussein Sabbah , A Mhirech , B Kabouchi , L Bahmad , Chaitany Jayprakash Raorane , Siva Sankar Sana , Hassan Fouad , Mohamed Hashem . Exploring dielectric phenomena in sulflower-like nanostructures via Monte Carlo technique[J]. Communications in Theoretical Physics, 2024 , 76(4) : 045801 . DOI: 10.1088/1572-9494/ad3221

1. Introduction

Efflorescence in science and nanotechnology have allowed for the successful synthesis of nanomaterials with diverse sizes and structures as well. In particular, carbon-sulfur compounds have gained colossal attention due to the possibility of using them in a myriad of organic electronic devices, including organic field-effect transistors, light modulators, light-emitting diodes, photovoltaic cells and hydrogen-storage devices [14]. One of the recently discovered carbon-sulfur compounds that have attracted attention is sulflower [57]. This compound has a unique molecular symmetry resulting from anti-aromaticity and orbital degeneracy, combined with its intermolecular packing due to exposed sulfur atoms, making it a promising material for organic electronics [810]. Sulflower is chemically stable [11], making it an archetypal candidate for electronic devices. Studies have shown that thin-film OFETs made with a sulflower exhibit promising characteristics, containing a gateway threshold voltage of 45 V and a hole mobility of 9.10−3 cm2 Vs−1 [12]. Additionally, researchers have investigated the potential of sulflower systems decorated with Be2+ and Mg2+ to adsorb molecular hydrogen using density-functional theory (DFT) calculations [13]. The decorated systems consist of cyclic polythiophene rings. In addition, DFT and time-dependent density functional theory (TD-DFT) computations have proclaimed by Shakerzadeh’s research [14] that the interaction among C16S8 sulflower and a lithium atoms exhibited nonlinear optical feedback, indicating the compound’s potential as a novel nonlinear optical material. However, Dong et al [15] have presented a novel method of synthesizing the first-ever fully sulfur-substituted polycyclic aromatic hydrocarbon, or ‘sulflower.’ This unique compound has a coronene core and represents an innovative carbon-sulfur hybrid with promising potential for various applications.
In recent research, investigations of the magnetic, magnetocaloric, and dielectric characteristics of diverse structures have been done via the Monte Carlo technique (MCt), including nano-islands [16], nanowires [17], Borophene Superlattices and core–shell [18, 19], graphene-like nanoribbons [20], copper fluorides [21], a nano-graphene bilayer [22], a diluted graphdiyne monolayer with defects [23], a tri-layer graphene-like structure [24], a polyhedral chain [25], the Kagome Ferromagnet [26]. Ising models have also been utilized to investigate the mixed systems, like the TbMnO3 multiferroic system [27], the Gd2O3 nanowire [28], the graphyne [29] and the core–shell Nanotube [30] systems and the Ising thin-film [31]. These models have been useful in predicting magnetic phenomena in a variety of structures, from nanoscale to bulk materials.
Moreover, according to what we know, no theoretical investigations have been conducted to analyze the dielectric properties of a sulflower-like structure with a mixed spin configuration consisting of ${S}_{i}^{Z}-1$ and ${\sigma }_{j}^{Z}-5/2.$ We employ the MCt with the Metropolis algorithm to examine the dielectric characteristics of a sulflower-like structure. It is worth noting that in our previous research, we effectively utilized the MCt to inspect the magnetic and dielectric characteristics of various types of nanostructures [3237]. Furthermore, the application of an external electric field in the study of dielectric properties is crucial for understanding the response of materials to electric fields, characterizing dielectric behavior, determining polarization, dielectric susceptibility, electric hysteresis cycles, studying phase transitions, and manipulating material properties [17, 18, 35, 36, 38, 39]. Indeed, the study of ferroelectric or ferrielectric materials can contribute to progress in the multiferroic field [27], promising diverse applications such as magnetoelectric sensors and data storage.
This article is set out as follows: in section 2, we explain the formalism and examples of how the MCt was utilized to explore the physical properties during the simulations. In section 3, we discuss the dielectric characteristics and hysteresis demeanors, and provide our findings. First, we show the major configuration of spin in the phase diagrams in subsection 3.1. Finally, we sum up our findings in section 4.

2. Model and method

Our study focuses on studying the dielectric behavior of the sulflower-like structure inside the Blume–Capel model under free frontier circumstances. For this investigation, we utilized the MCt with the Metropolis algorithm [4046]. The nanosystem contains a total of 24 atoms, including 16 atoms with values of ${S}_{i}^{Z}$ = ±1 and 0, as well as 8 atoms with values of ${\sigma }_{j}^{Z}$ = ±5/2, ±3/2, and ±1/2 (figure 1). Our results involved implementing 106 steps through Monte Carlo computations for every spin while neglecting the first 105 steps to ensure thermal stabilization.
Figure 1.  Schematic illustration of a sulflower-like structure, highlighting spins labeled as S (red balls) and σ (yellow balls), alongside different exchange linkages (depicted using blue and black).
The Hamiltonian pertaining to the sulflower-like structure takes the form:
$\begin{eqnarray}\begin{array}{c}{ \mathcal H }{\mathscr{=}}{\mathscr{-}}{J}_{{SS}}\displaystyle \sum _{\left\langle i,j\right\rangle }{S}_{i}^{Z}{S}_{j}^{Z}-{J}_{S\sigma }\displaystyle \sum _{\left\langle k,l\right\rangle }{S}_{k}^{Z}{\sigma }_{l}^{Z}\\ -2\mu {E}_{Z}\left(\displaystyle \sum _{i}{S}_{i}^{Z}+\displaystyle \sum _{j}{\sigma }_{j}^{Z}\right)-{D}_{S}\displaystyle \sum _{i}{\left({S}_{i}^{Z}\right)}^{2}-{D}_{\sigma }\displaystyle \sum _{j}{\left({\sigma }_{j}^{Z}\right)}^{2}.\end{array}\end{eqnarray}$
The terms ⟨i, j⟩ and ⟨k, l⟩ denote neighboring site pairs, specifically (i and j) and (k and l). The exchange linkages between adjacent atoms possessing spins S - S and S—σ are represented by JSS and J, respectively. The parameter μ stands for the dipole moment, and we simplify by assuming μ = 1 [38, 39]. An external longitudinal electric field is introduced as EZ. Additionally, there are crystal fields DS and Dσ influencing spins Si and σj, respectively. Our investigation is confined to cases where D is equal to DS and to Dσ.
The energy content per individual site is:
$\begin{eqnarray}E=\frac{1}{{N}_{T}}\left\langle { \mathcal H }\right\rangle ,\end{eqnarray}$
where NT = NS + Nσ = 16 + 8 = 24 defining the overall number of atoms in the studied nanosystem.
The polarizations, both partial and total, exhibited by the sulflower-like structure are as follows:
$\begin{eqnarray}{\,P}_{S}=\left\langle \frac{1}{{N}_{S}}\displaystyle \sum _{i=1}^{{N}_{S}}{S}_{i}^{Z}\right\rangle ,\,\end{eqnarray}$
$\begin{eqnarray}{P}_{\sigma }=\left\langle \frac{1}{{N}_{\sigma }}\displaystyle \sum _{j=1}^{{N}_{\sigma }}{S}_{j}^{Z}\right\rangle ,\,\end{eqnarray}$
$\begin{eqnarray}{P}_{\mathrm{tot}}=\frac{{{N}_{S}P}_{S}+{{N}_{\sigma }P}_{\sigma }}{{N}_{S}+{N}_{\sigma }}.\,\end{eqnarray}$
The dielectric susceptibilities, both partial and total, exhibited by the sulflower-like structure are as follows:
$\begin{eqnarray}{\chi }_{S}=\beta \left(\left\langle {P}_{S}^{2}\right\rangle -{\left\langle {P}_{S}\right\rangle }^{2}\right),\,\end{eqnarray}$
$\begin{eqnarray}{\chi }_{\sigma }=\beta \left(\left\langle {P}_{\sigma }^{2}\right\rangle -{\left\langle {P}_{\sigma }\right\rangle }^{2}\right),\end{eqnarray}$
$\begin{eqnarray}{\chi }_{\mathrm{tot}}=\frac{{{N}_{S}\chi }_{S}+{{N}_{\sigma }\chi }_{\sigma }}{{N}_{S}+{N}_{\sigma }},\end{eqnarray}$
where $\beta =\frac{1}{{k}_{{\rm{B}}}T},$ the Boltzmann’s constant, kB is utilized in this instance. To make calculations simpler, kB is set to 1. The absolute temperature is symbolized by T.

3. Results and analysis through numerical methods

The focus of this section lies in the utilization of the MCt to establish the configuration of spin in the phase diagrams in subsection 3.1. Additionally, subsection 3.2 delves into the analysis of polarizations and dielectric susceptibilities, considering their dependencies on different physical parameters.

3.1. Configuration of spin in the phase diagrams

The configuration of spin in the phase diagrams of the mixed sulflower-like structure with spins ${S}_{i}^{Z}$−1 and ${\sigma }_{j}^{Z}$−5/2 in several physical parameters (EZ, D, JSS, and J) planes are shown in this subsection. For the ground state investigation, we simulate the energy spins, we found that (2 S + 1) × (2σ+1) = 3 × 6 = 18 possible configurations using the Hamiltonian of equation (1). These diagrams provide comprehensive information about spin configurations of the system during the adjustment of different variables.
Plotting figure 2(a) in the (EZ, D) plane for the constant values of exchange coupling interactions as JSS = 1 and JσS = −0.01, it becomes evident that out of the 18 potential configurations, only 6 remained stable. Within this plane, a flawless symmetry is observable among the configurations with respect to the EZ = 0 axis. Particularly, the stable configurations corresponding to EZ > 0 are: (−1, +1/2); (−1, +3/2); and (−1, +5/2). Whereas the stable configurations obtained to E< 0 are: (+1, −1/2); (+1, −3/2) and (+1, −5/2).
Figure 2. Configuration of spins in the phase diagrams plotted for: (a) Jss set to 1 and Jsσ to −1, followed by (b) Jsσ at −1 and D at 0, (c) Jss at 1 and D at 0, (d) Jsσ at −1 and Ez at 0, (e) Jss at 1 and Ez at 0, and finally (f) D at 0 and Ez at 0.
Figure 2(b) portrays the phase diagram within the (Jss, Ez) plane in the absence of a crystal field (D = 0), while maintaining a constant exchange coupling parameter of Jsσ = −1. In this plane, only two configurations, specifically (+1, −5/2) and (−1, +5/2), remained stable, aligning with the highest spin values.
Figure 2(c) delves into the exploration of the impacts stemming from the ferrielectric parameter (Jsσ) and the external longitudinal electric field (Ez) within the (Jsσ, Ez) plane, all while refraining from applying the external longitudinal electric field (Ez = 0), and keeping the exchange coupling interaction fixed at Jss = 1. In this plane, stability is observed across four phases, namely (−1, −5/2), (+1, +5/2), (+1, −5/2), and (−1, +5/2).
Additionally, in figure 2(d), without applying the external longitudinal electric field (Ez = 0) and with a constant value set for the ferrielectric parameter J = −1, we observed that only six stable configurations exist, namely (−1, +1/2), (+1, −1/2), (+1, −3/2), (−1, +3/2), (−1, +5/2), and (+1, −5/2). The spin configurations were displayed in the (Jss, D) plane.
In order to examine how the configurations that remain stable are affected by the ferrielectric parameter J and the crystal field D, a graph was generated on the (J, D) plane with Jss = 1 and Ez = 0, as shown in figure 2(e). This graphical representation showcases six stable phases, namely: (−1, −1/2), (−1, −3/2), (−1, −5/2), (−1, +1/2), (−1, +3/2), and (−1, +5/2).
Ultimately, the impact of the ferrielectric parameter J and the exchange coupling parameter Jss was investigated. Figure 2(f) illustrates this exploration within the (Jss, J) plane, with fixed parameters Ez = 0 and D = 0. In this visual representation, merely four stable configurations are evident, namely (−1, +5/2), (+1, −5/2), (−1, −5/2), and (+1, +5/2).

3.2. Monte Carlo technique (MCt)

Within this segment, the dielectric attributes of the Sulflower-like structure are scrutinized using the MCt with the Metropolis algorithm.
The temperature-evolving tendencies of polarizations (PS, Pσ, and Ptot) are presented in figure 3(a), with Jss = 1, Jsσ = −0.01, Ez = 0.1, and D = 0. At exceedingly low temperatures, partial polarizations PS = 1 and Pσ = 5/2 yield ${P}_{\mathrm{tot}}=\frac{16\times {P}_{s}+8\times {P}_{{\sigma }}}{16+8}=1.5.$ The intricate relationship between spin polarization and dielectric reliability holds substantial importance, given that dielectric reliability serves as the precise indicator of the transition point where spin polarization undergoes a shift from order to disorder. This critical juncture is identified as the ‘blocking temperature,’ and it signifies a transformative phase within the system. During this phase, the system experiences a notable transition from a state of orderliness to a state of disorder, marking a significant change in its overall behavior and characteristics. As the temperature nears the transition temperature (Ttr), polarizations decrease. Interestingly, polarizations decrease as the system transitions into the superparaelectric phase around the transition temperature. For accurate determination of the transition temperature, we scrutinize the partial and total dielectric susceptibilities against temperature, employing the same parameter values featured in figures 3(a) and (b). The dielectric susceptibility peaks related to polarization transition temperatures for σ and S spins were approximately Ttr(σ) ≈ 2.83 and Ttr(S) ≈ 4.5, respectively. The total susceptibility also showed a peak, which occurs at Ttr(tot) ≈ 4.
Figure 3. (a) The total of polarization, and (b) the total dielectric susceptibility relative to temperature. The depicted figures were generated using constant parameters: JSS = 1, J = −0.01, Ez = 0.5, and D = 0.
Results obtained for the JSS interaction on the total polarization and the dielectric susceptibility were summarized in figures 4(a)–(c). The results were presented for: D = 0, Jss = 1, J = −0.01 and Ez = 0.5. As indicated in figure 4(a), an augmentation of the JSS parameter leads to the noticeable shifting of the transition temperature towards high temperatures. Similarly, for the purpose of identifying the precise transition temperature that distinguishes between the ferrielectric and superparaelectric phases, figure 4(b) was generated alongside the total dielectric susceptibility, with varying Jss values and using the same set of fixed parameter values as presented in figure 4(a). The outcome showcases that the displacement of the peaks in total dielectric susceptibility gravitates towards higher temperature values as Jss values increase, confirming the behavior observed in the total polarization. The determined transition temperatures for Jss values of 1, 2, 3, and 4 are approximately Ttr ≈ 2.3, 2.7, 3.4 and 4, respectively. Drawing upon figures 4(a) and (b), we created figure 4(c) to enhance our comprehension of how the transition temperature relates to the JSS parameter. This visual representation reaffirms the nearly linear increase in the transition temperature when increasing JSS.
Figure 4. Total polarization (a), total dielectric susceptibility (b), in relation to temperature, and (c) transition temperature with respect to the JSS parameter. These figures were plotted while adhering to consistent parameters D = 0, J = −0.01 and Ez = 0.5.
To delve into the impact of the ferrielectric parameter J on the thermal total polarization and total dielectric susceptibility, we illustrate the behavior of this parameter in figures 5(a)—(c). These visualizations were derived across varying ferrielectric parameter values: J = −1, −2, −3, and −4, all while adhering to fixed parameters: D = 0, Jss = 1, Ez = 0.5. From the insight provided by figure 5(a), it’s evident that with an increase in the absolute value of the ferrielectric parameter |J|, there is a corresponding decrease in the total polarization Ptot. Furthermore, it’s observable that the curve of the total polarization closely resembles the pattern of the total polarization Ptot (figure 4(a)). To accurately determine the transition temperature values, we mapped out the total dielectric susceptibility as illustrated in figure 5(b). The shift of the peaks of the total dielectric susceptibility towards lower temperature values becomes pronounced with an increase in the ferrielectric parameter |J|. The transition temperatures identified for the ferrielectric parameters |J | = 1, 2, 3, and 4 are approximately Ttr ≈ 4.2, 4.6, 5, and 5.2, respectively. To emphasize the outcomes of figures 5(a) and (b), we delineate the trend of the transition temperature with respect to the parameter J in figure 5(c). This graphical representation clearly demonstrates that the transition temperature rises almost linearly as the ferrielectric parameter |J| increases.
Figure 5. Total polarization (a), total dielectric susceptibility (b), in relation to temperature, and (c) transition temperature with respect to the J parameter. These figures were plotted while adhering to consistent parameters D = 0, JSS = 1 and Ez = 0.5.
Pursuing a similar rationale, we investigated the influence of the electric field parameter Ez on the thermal tendencies of total polarizations and total dielectric susceptibility across various Ez values (Ez = 0.5, 1, 1.5, and 2). The outcomes are presented in figures 6(a) and (b), assuming D = 0, Jss = 1, and J = −0.01. As depicted in figure 6(a), we observed that the total polarization diminishes towards an earlier transition temperature Ttr for lower external longitudinal electric field values compared to higher ones. This effect arises due to the interplay between the promoting influence of the external longitudinal electric field on order within the system and the temperature’s role in promoting disorder. Additionally, figure 6(b) showcases the thermal total dielectric susceptibility. The transition temperature values align with the peaks of the total dielectric susceptibility, with Ttr values approximately ≈ 4, 4.5, 5.5, and 6.5 for Ez values of 0.5, 1, 1.5, and 2 respectively. To synthesize the findings from figures 6(a) and (b), we present a graphical representation in figure 6(c), illustrating the correlation between the transition temperature and the Ez parameter. In order to consolidate the results depicted in figures 6(a) and (b), we have included a graphical representation in figure 6(c) that illustrates the correlation between the transition temperature and the parameter Ez. The figure effectively demonstrates that there was an almost linear increase in the transition temperature as the ferrielectric parameter Ez is progressively elevated.
Figure 6. Total polarization (a), total dielectric susceptibility (b), in relation to temperature, and (c) transition temperature with respect to the Ez parameter. These figures were plotted while adhering to consistent parameters D = 0, JSS = 1 and J = −0.01.
To complete the study, our focus is on scrutinizing the effect of temperature (T) on hysteresis loops, visualized in figure 7 with fixed parameters D = 0, Jss = 1, and J = 0.01. As the temperature rises, the hysteresis loop maintains its singular nature, though its area contracts. Upon reaching a threshold temperature of 2, the loop vanishes, denoting the system’s transition from the ferrielectric to the paraelectric phases. This occurrence underscores the gradual evolution of the system into a paraelectric state with increasing temperature.
Figure 7. Hysteresis cycles of the sulflower-like structure, for different values of T for: Jss = 1, J = 0.01 and D = 0.
Furthermore, figure 8 portrays the influence of the exchange coupling parameter JSS on the hysteresis loop, with constants J = −0.01, T = 0.1, and D = 0. The system retains a singular loop structure. Yet, in contrast to the effect of JSS, the loops change in area, coercivity, and saturation field as JSS values rise. This transformation arises due to the enhanced exchange coupling, imparting greater stability to the system.
Figure 8. Hysteresis cycles of the sulflower-like structure, for different values of JSS for: J = −0.01, T = 0.1 and D = 0.
In figure 9, we also examined the effect of the ferrielectric parameter J on the hysteresis cycles, plotted with D = 0, Jss = 1 and T = 0.1 and by decreasing the parameter J, the hysteresis cycles show multiple loops. The saturation also increases when decreasing the parameter J.
Figure 9. Hysteresis cycles of the sulflower-like structure, for different values of J when Jss = 1, T = 0.1 and D = 0.
To wrap up, we analyze the effect of the crystal field D on hysteresis loops, illustrated in figure 10 while maintaining constants Jss = 1, J = −0.01, and T = 0.1. A reduction in the D parameter correlates with a reduction in the hysteresis loop’s size. Upon reaching a crystal field value of −7, the loop’s presence vanishes. This shift signifies the transition of the system from the ferrielectric to the paraelectric phases.
Figure 10. Hysteresis cycles of the sulflower-like structure, for different values of D for: Jss = 1, J = −0.01 and T = 0.1.

4. Conclusion

In this study, we utilized the MCt to explore the dielectric characteristics of a sulflower-like structure. The structure considered in our investigation consists of mixed spins (1, 5/2). One of the main objectives was to determine and analyze the configuration of spin in the phase diagrams. Moreover, we examined dielectric characteristics of the system considering their dependencies on different physical parameters. Specifically, we investigated the impact of temperature, as well as external longitudinal electric on polarization, dielectric susceptibility, and hysteresis cycles. In summary, the findings demonstrate a linear decrease in transition temperature as JSS increases, a corresponding increase in transition temperature with |J|, and a clear linear rise in transition temperature with increasing Ez. As temperature rises, the solitary hysteresis loop contracts and vanishes at 2, signifying the transition from ferrielectric to paraelectric phases. Maintaining a uniform loop structure, the system exhibits altered traits as JSS values increase, influenced by enhanced exchange coupling. Besides, decreasing J yields multiple loops and elevated saturation. Moreover, lowering D further contracts hysteresis loops, and a crystal field of −7 erases the loop, marking the ferrielectric to paraelectric transformation.

Acknowledgments

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2020R1I1A3052258). This work is funded by Researcher Supporting Project number (RSP2024R117), King Saud University, Riyadh, Saudi Arabia.

Conflicts of interest or competing interests

The authors confirm that there are no known conflicts of interest associated with this publication.

Author contributions

Not Applicable

Data and code availability

This investigation was made using Monte Carlo simulations under the Metropolis algorithm by a Fortran code.
1
Torroba T, García-Valverde M 2006 Rigid annulated carbon-sulfur structures Angew. Chem. Int. Ed. 45 8092

DOI

2
Mas-Torrent M, Durkut M, Hadley P, Ribas X, Rovira C 2004 High mobility of dithiophene-tetrathiafulvalene single-crystal organic field effect transistors J. Am. Chem. Soc. 126 984

DOI

3
Yamada K, Okamoto T, Kudoh K, Wakamiya A, Yamaguchi S, Takeya J 2007 Single-crystal field-effect transistors of benzoannulated fused oligothiophenes and oligoselenophenes Appl. Phys. Lett. 90 072102

4
Datta A, Pati S K 2007 Computational design of high hydrogen adsorption efficiency in molecular ‘sulflower’ J. Phys. Chem. C 111 4487 4490

DOI

5
Chernichenko K Y, Sumerin V V, Shpanchenko R V, Balenkova E S, Nenajdenko V G 2006 Angew, cover picture: ‘Sulflower’: a new form of carbon sulfide (Angew. Chem. Int. Ed. 44/2006) Chem. Int. Ed. 45 7367

DOI

6
Chernichenko K Y, Balenkova E S, Nenajdenko V G 2008 From thiophene to sulflower Mendeleev Commun. 18 171

DOI

7
Bukalov S S 2008 Two modifications formed by ‘Sulflower’ C16S8 molecules, their study by XRD and optical spectroscopy (Raman, IR, UV–vis) methods J. Phys. Chem. A 112 10949

DOI

8
Friederich P, Fediai A, Kaiser S, Konrad M, Jung N, Wenzel W 2019 Toward design of novel materials for organic electronics J. Adv. Mater. 31 1808256

DOI

9
Gahungu G, Zhang J P 2008 Shedding light on octathio [8] circulene and some of its plate-like derivatives Phys. Chem. Chem. Phys. 10 1743

DOI

10
Gahungu G, Zhang J P, Barancira T 2009 Charge transport parameters and structural and electronic properties of octathio [8] circulene and its plate-like derivatives J. Phys. Chem. A 113 255

DOI

11
Fujimoto T, Suizu R, Yoshikawa H, Awaga K 2008 Molecular, crystal, and thin-film structures of octathio [8] circulene: release of antiaromatic molecular distortion and lamellar structure of self-assembling thin films Chem. Eur. J. 14 6053

DOI

12
Dadvand A 2008 Heterocirculenes as a new class of organic semiconductors Chem. Commun. 42 5354

DOI

13
Banerjee S, Ash T, Debnath T, Das A K 2021 Be2+ and Mg2+ decorated sulflower: potential systems for molecular hydrogen storage Int. J. Hydrog. Energy. 46 17839

DOI

14
Shakerzadeh E 2018 Tailoring C24S12 and C16S8 sulflowers with lithium atom for the remarkable first hyperpolarizability Chem. Phys. Lett. 709 33

DOI

15
Dong R 2017 Persulfurated coronene: a new generation of ‘sulflower’ J. Am. Chem. Soc. 139 2168

DOI

16
Chen L, Cai J, Zhang W 2022 Magnetic and thermodynamic behaviors of an L10 structure nanoisland: a Monte Carlo study J. Magn. Magn. Mater. 562 169757

DOI

17
Masrour R 2023 Study of magnetic properties of Ising nanowires with core–shell structure Eur. Phys. J. B 96 100

DOI

18
Masrour R, Sahdane T, Jabar A 2022 Monte carlo study of dielectric properties of borophene superlattices J. Inorg. Organomet. Polym. Mater. 32 1868

DOI

19
Gao Z Y, Wang W, Sun L, Yang L M, Ma B Y, Li P S 2022 Dynamic magnetic properties of borophene nanoribbons with core–shell structure: Monte Carlo study J. Magn. Magn. Mater. 548 168967

DOI

20
Boughazi B, Kerouad M, Kotri A 2022 Theoretical study of the magnetic properties of a ferrimagnetic graphene-like nanoribbon: Monte Carlo treatment J. Solid State Sci. Technol. 11 051005

DOI

21
Obeidat A, Alqaiem S, Al-Qawasmeh A, Badarneh M, Qaseer M K 2023 Magnetic properties of copper fluorides (Cu2F5 inverse spinel-like structure): A Monte Carlo study Phys. B: Condens. 654 414698

DOI

22
Sun L, Wang W, Liu C, Xu B H, Lv D, Gao Z Y 2021 The magnetic behaviors and magnetocaloric effect of a nano-graphene bilayer: a Monte Carlo study Superlattices Microstruct. 149 106775

DOI

23
Liu Z Y, Lv D, Zhang F, Wang S Y 2022 Thermodynamic characteristics and magnetocaloric effect of a diluted graphdiyne monolayer with defects: a Monte Carlo study Micro Nano Lett. 168 207299

DOI

24
Fadil Z, Maaouni N, Mhirech A, Kabouchi B, Bahmad L, Benomar W O 2021 Magnetic properties and compensation temperature in tri-layer graphyne-like structure: Monte Carlo simulations Int. J. Thermophys. 42 1

DOI

25
Yang M, Wang F, Lv J Q, Li B C, Wang W 2022 Thermodynamic properties and magnetocaloric effect of a polyhedral chain: a Monte Carlo study, Condens Matter. Physica B 638 413954

DOI

26
Magar A, Somesh K, Singh V, Abraham J J, Senyk Y, Alfonsov A, Nath R 2022 Large magnetocaloric effect in the kagome ferromagnet Li9 Cr3 (P2O7)3 (PO4)2 Phys. Rev. Appl. 18 054076

DOI

27
Kassimi F Z, Zaari H, Benyoussef A, Rachadi A, Balli M, El Kenz A 2022 A theoretical study of the electronic, magnetic and magnetocaloric properties of the TbMnO3 multiferroic J. Magn. Magn. Mater. 543 168397

DOI

28
Bandyopadhyay A, Sharma S, Nath M, Karmakar A, Kumari K, Sutradhar S 2021 Dielectric study and magnetic property analysis of Gd2O3 nanorods/nanowire in combination with Monte Carlo simulation J. Alloys Compd. 882 160720

DOI

29
Fadil Z, Mhirech A, Kabouchi B, Bahmad L, Benomar W O 2019 Dielectric properties of a monolayer nano-graphyne structure: Monte Carlo simulations Superlattice Microstruct. 135 106285

DOI

30
Tarnaoui M, Zaim N, Zaim A, Kerouad M 2023 Investigation of the thermal and ferroelectric properties of a Spin-1 Ising thin film: Insight from path integral Monte Carlo J. Mater. Sci. Eng. B 288 116204

DOI

31
Saadi H, Jalal E M, Elgaraoui O, El antari A, Madani M, El bouziani M 2023 Magnetic properties of a mixed spin-1/2 and spin-7/2 hexagonal core–shell nanotube Romanian, J. Phys. 68 619

32
Saber N, Fadil Z, Mhirech A, Kabouchi B, Bahmad L, Benomar W O 2023 Magnetic properties and compensation temperature behaviors in the hexacene-like nanostructure: a Monte Carlo study J. Low Temp. Phys. 210 310

DOI

33
Fadil Z, Saber N, Mhirech A, Kabouchi B, Bahmad L 2022 Magnetic properties and compensation temperature of a mixed monolayer coronene-like nanostructure: Monte Carlo study SPIN 12 2250020

DOI

34
Saber N, Fadil Z, Mhirech A, Kabouchi B, Bahmad L, Benomar W O 2022 Magnetic behaviors of the kesterite and the stannite nanostructures: Monte Carlo study SPIN 12 2250008

DOI

35
Fadil Z, Qajjour M, Eraki H, Mhirech A, Kabouchi B, Bahmad L, Benomar W O 2022 Dielectric properties of carbon-like nanotube structure: Monte Carlo study SPIN 12 2250007

DOI

36
Fadil Z, Saber N, Mhirech A, Kabouchi B, Bahmad L 2022 Dielectric properties of ovalene-like nanostructure with RKKY interactions: Monte Carlo study SPIN 12 2250031

DOI

37
Saber N, Fadil Z, Mhirech A, Kabouchi B, Bahmad L 2023 Magnetic properties and thermal behavior of the monolayer Rubrene-like nano-island: Monte Carlo simulations Solid State Commun. 362 115084

DOI

38
Benhouria Y, Essaoudi I, Ainane A, Ahuja R, Dujardin F 2018 Hysteresis loops and dielectric properties of a mixed spin Blume–Capel Ising ferroelectric nanowire Physica A, Stat. Mech. Appl. 506 499

DOI

39
Benhouria Y, Essaoudi I, Ainane A, Ahuja R, Dujardin F 2014 Spin-12 Ising double walled ferrielectric nanotubes: A Monte Carlo study Superlattices Microstruct. 75 761

DOI

40
Ren J, Zhang C, Li J, Guo Z, Xiao H, Zhong J 2016 Strain engineering of magnetic state in vacancy-doped phosphorene Phys. Lett. A 380 3270

DOI

41
Chen P, Li N, Chen X, Ong W J, Zhao X 2017 The rising star of 2D black phosphorus beyond graphene: synthesis, properties and electronic applications 2D Mater. 5 014002

DOI

42
Shaabani A, Afshari R 2018 Magnetic Ugi-functionalized graphene oxide complexed with copper nanoparticles: Efficient catalyst toward Ullman coupling reaction in deep eutectic solvents J. Colloid Interf. Sci. 510 384

DOI

43
Xu Q, Cai W, Li W, Sreeprasad T S, He Z, Ong W J, Li N 2018 Two-dimensional quantum dots: fundamentals, photoluminescence mechanism and their energy and environmental applications Mater. Today Energy 10 222

DOI

44
Tang T, Li S, Sun J, Wang Z, Guan J 2022 Advances and challenges in two-dimensional materials for oxygen evolution Nano Res. 15 8714

DOI

45
Chai L, Cui X J, Qi Y Q, Teng N, Hou X L, Deng T S 2021 A new strategy for the efficient exfoliation of graphite into graphene New Carbon Mater. 36 1179

DOI

46
Metropolis N, Rosenbluth A W, Rosenbluth M N, Teller A H, Teller E 1953 equation of state calculations by fast computing machines J. Chem. Phys. 21 1087

DOI

Outlines

/