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16 pages, 457 KiB  
Article
Examples for BPS Solitons Destabilized by Quantum Effects
by Willem J. Meyer and Herbert Weigel
Symmetry 2025, 17(8), 1229; https://doi.org/10.3390/sym17081229 - 4 Aug 2025
Viewed by 41
Abstract
We investigate serval models for two scalar fields in one space dimension with topologically stable solitons that are constructed from BPS equations. The asymptotic behavior of these solitons fully determines their classical energies. A particular feature of the considered models is that there [...] Read more.
We investigate serval models for two scalar fields in one space dimension with topologically stable solitons that are constructed from BPS equations. The asymptotic behavior of these solitons fully determines their classical energies. A particular feature of the considered models is that there are several translationally invariant ground states that we call primary and secondary vacua. The former are those that are asymptotically assumed by the solitons. Solitons that occupy a secondary vacuum in finite but eventually large portions of space are classically degenerate. Thus the quantum contributions to the energies are decisive for the energetically favored soliton. While some of these solitons were constructed previously, we, for the first time, compute the leading (one-loop) quantum contribution their energies. In all cases considered we find that this contribution is not bounded from below and that it is the more negative the larger the region is in which the soliton approaches a secondary vacuum. This corroborates the conjecture, earlier inferred from the Shifman-Voloshin soliton, that the availability of secondary vacua destabilizes these solitons on the quantum level. Full article
(This article belongs to the Section Physics)
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14 pages, 1096 KiB  
Article
Short-Term Outcomes of Cementless Total Hip Arthroplasty Using a 3D-Printed Acetabular Cup Manufactured by Directed Energy Deposition: A Prospective Observational Study
by Ji Hoon Bahk, Woo-Lam Jo, Kee-Haeng Lee, Joo-Hyoun Song, Seung-Chan Kim and Young Wook Lim
J. Clin. Med. 2025, 14(13), 4527; https://doi.org/10.3390/jcm14134527 - 26 Jun 2025
Viewed by 439
Abstract
Background/Objectives: Additive manufacturing (AM) enables the production of cementless acetabular cups with porous surfaces that facilitate early osseointegration. Directed energy deposition (DED), a form of AM, allows the direct welding of porous structures onto metal substrates without requiring a vacuum environment, offering [...] Read more.
Background/Objectives: Additive manufacturing (AM) enables the production of cementless acetabular cups with porous surfaces that facilitate early osseointegration. Directed energy deposition (DED), a form of AM, allows the direct welding of porous structures onto metal substrates without requiring a vacuum environment, offering advantages over conventional powder bed fusion methods. Despite growing interest in DED, no prospective clinical studies evaluating DED-based acetabular components have been published to date. This study assessed short-term outcomes of a DED-based 3D-printed acetabular cup in total hip arthroplasty (THA). Methods: A total of 120 patients who underwent primary cementless THA using the Corentec Mirabo Z® acetabular cup were prospectively enrolled. Among them, 124 hips from 100 patients who had completed a minimum of 24 months of follow-up were included in the analysis. Clinical outcomes were assessed using the Harris hip score (HHS), WOMAC, EQ-5D-5L, and pain NRS. Radiographic evaluation included measurements of cup position, osseointegration, and detection of interfacial or polar gaps on CT and plain radiographs. Implant-related complications were also recorded. Results: At a mean follow-up of 34.6 months, the implant survival rate was 99.3%, with one revision due to suspected osseointegration failure. The HHS improved from 56.6 to 91.4 at 24 months, and the NRS decreased from 6.2 to 1.1 (both p < 0.001). Interfacial gaps were observed in 58.1% of cases on CT, though most were <1 mm and not clinically significant. Common postoperative issues included greater trochanteric pain syndrome, squeaking, and iliotibial band tightness, all of which were resolved with conservative treatment. Conclusions: DED-based 3D-printed acetabular cups demonstrated favorable short-term clinical and radiographic outcomes, with high survivorship and reliable early osseointegration in cementless THA. Full article
(This article belongs to the Section Orthopedics)
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37 pages, 596 KiB  
Article
Higher-Order Derivative Corrections to Axion Electrodynamics in 3D Topological Insulators
by R. Martínez von Dossow, A. Martín-Ruiz and Luis F. Urrutia
Symmetry 2025, 17(4), 581; https://doi.org/10.3390/sym17040581 - 10 Apr 2025
Viewed by 734
Abstract
Three-dimensional topological insulators possess surface-conducting states in the bulk energy gap, which are topologically protected and can be well described as helical 2 + 1 Dirac fermions. The electromagnetic response is given by axion electrodynamics in the bulk, leading to a Maxwell–Chern–Simons theory [...] Read more.
Three-dimensional topological insulators possess surface-conducting states in the bulk energy gap, which are topologically protected and can be well described as helical 2 + 1 Dirac fermions. The electromagnetic response is given by axion electrodynamics in the bulk, leading to a Maxwell–Chern–Simons theory at the boundary, which is the source of the Hall conductivity. In this paper, we extend the formulation of axion electrodynamics such that it captures higher-derivative corrections to the Hall conductivity. Using the underlying 2 + 1 quantum field theory at the boundary, we employ thermal field theory techniques to compute the vacuum polarization tensor at finite chemical potential in the zero-temperature limit. Applying the derivative expansion method, we obtain higher-order derivative corrections to the Chern–Simons term in 2 + 1 dimensions. To first order the corrections, we find that the Hall conductivity receives contributions proportional to ω2 and k2 from the higher-derivative Chern–Simons term. Finally, we discuss the electrodynamic consequences of these terms on the topological Faraday and Kerr rotations of light, as well as on the image monopole effect. Full article
(This article belongs to the Section Physics)
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16 pages, 336 KiB  
Article
Vacuum Polarization Energy of a Proca Soliton
by Damian A. Petersen and Herbert Weigel
Symmetry 2025, 17(1), 13; https://doi.org/10.3390/sym17010013 - 25 Dec 2024
Cited by 3 | Viewed by 650
Abstract
We study an extended Proca model with one scalar field and one massive vector field in one space dimension and one time dimension. We construct the soliton solution and subsequently compute the vacuum polarization energy (VPE), which is the leading quantum correction to [...] Read more.
We study an extended Proca model with one scalar field and one massive vector field in one space dimension and one time dimension. We construct the soliton solution and subsequently compute the vacuum polarization energy (VPE), which is the leading quantum correction to the classical energy of the soliton. For this calculation, we adopt the spectral methods approach, which heavily relies on the analytic properties of the Jost function. This function is extracted from the interaction of the quantum fluctuations with a background potential generated by the soliton. Particularly, we explore eventual non-analytical components that may be induced by mass gaps and the unconventional normalization for the longitudinal component of the vector field fluctuations. By numerical simulation, we verify that these obstacles do not actually arise and that the real and imaginary momentum formulations of the VPE yield equal results. The Born approximation to the The Jost function is crucial when implementing standard renormalization conditions. In this context, we solve problems arising from the Born approximation being imaginary for real momenta associated with energies in the mass gap. Full article
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19 pages, 3381 KiB  
Review
TIME REFRACTION and SPACETIME OPTICS
by José Tito Mendonça
Symmetry 2024, 16(11), 1548; https://doi.org/10.3390/sym16111548 - 19 Nov 2024
Cited by 6 | Viewed by 2030
Abstract
A review of recent advances in spacetime optics is given, with special emphasis on time refraction. This is a basic optical process, occurring at a temporal discontinuity or temporal boundary, which is able to produce various different effects, such as frequency shifts, energy [...] Read more.
A review of recent advances in spacetime optics is given, with special emphasis on time refraction. This is a basic optical process, occurring at a temporal discontinuity or temporal boundary, which is able to produce various different effects, such as frequency shifts, energy amplification, time reflection, and photon emission. If, instead of a single discontinuity, we have two reverse temporal boundaries, we can form a temporal beam splitter, where temporal interferences can occur. It will also be shown that, in the presence of an axis of symmetry, such as a magnetic field, the temporal beam splitter can induce a rotation of the initial polarization state, similar to a Faraday rotation. Recent work on time crystals, superluminal fronts, and superfluid light will be reviewed. Time gates based on spacetime optical effects will be discussed. We also mention recent work on optical metamaterials. Finally, the quantum properties of time refraction, which imply the emission of photon from vacuum, are considered, while similar problems in high-energy QED associated with electron–positron pairs are briefly mentioned. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry: Feature Review Papers 2024)
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5 pages, 775 KiB  
Proceeding Paper
Study of the Stability, Solubility and Geometry of the Complex of Inclusion β-CD with Nimesulide by Computer Chemistry Methods
by Ekaterina S. Barteneva, Pavel Y. Andreev, Elena V. Grekhneva and Kirill S. Efanov
Chem. Proc. 2024, 16(1), 80; https://doi.org/10.3390/ecsoc-28-20197 - 14 Nov 2024
Viewed by 300
Abstract
During this study, a molecular system was modeled: a nimesulide, β-cyclodextrin, inclusion complex. The use of the Gaussian 16W software package allowed us to optimize geometry and determine the thermochemical characteristics of molecular systems without considering a solvent. And this was also carried [...] Read more.
During this study, a molecular system was modeled: a nimesulide, β-cyclodextrin, inclusion complex. The use of the Gaussian 16W software package allowed us to optimize geometry and determine the thermochemical characteristics of molecular systems without considering a solvent. And this was also carried out in water media, accounted for by the polarized continuum model (PCM). To confirm the accuracy of the geometry of the β-cyclodextrin molecule, a structural alignment of 46 β-cyclodextrin molecules, accessible by a corresponding search query in the RCSB database, was performed. The RSMD values of carbon and oxygen atom deviations, as well as the total number of atoms aligned, were calculated. This calculation showed a complete conformational coincidence between the β-cyclodextrin structure designed by us and the RCSB database structures. This ensures the correct approach to subsequent calculations involving this structure. Quantum-mechanical modeling of the relationship was carried out in several stages with a gradual complexity of the basic set. The hybrid method of functional density B3LYP and 6-31G(d) was used. At the end of the calculation stage, on the surface of the studied complex, the potential energy of several minimal elements was detected. This means that there are several conformational forms of the molecular system with likely differences. The change in potential energies of the investigated compounds, caused by their application to optimize the in vacuum molecules of the PCM, allowed us to determine the values of the solvatization energies. The greater magnitude of these values in the complex under consideration indicates its better solubility in water compared to nimesulide. Full article
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15 pages, 3645 KiB  
Article
Comparison of Corrosion Behavior of a-C Coatings Deposited by Cathode Vacuum Arc and Filter Cathode Vacuum Arc Techniques
by Zhiqing Feng, Zhetong Zhou, Junhao Zeng, Ding Chen, Fengying Luo, Qimin Wang, Wei Dai and Ruiming Zhang
Coatings 2024, 14(8), 1053; https://doi.org/10.3390/coatings14081053 - 17 Aug 2024
Cited by 3 | Viewed by 1442
Abstract
This study explores the utilization of cathodic vacuum arc (CVA) technology to address the limitations of magnetron sputtering technology in preparing amorphous carbon (a-C) coatings, such as having a low ionization rate, low deposition rate, and insufficiently dense structure. Specifically, a-C coatings were [...] Read more.
This study explores the utilization of cathodic vacuum arc (CVA) technology to address the limitations of magnetron sputtering technology in preparing amorphous carbon (a-C) coatings, such as having a low ionization rate, low deposition rate, and insufficiently dense structure. Specifically, a-C coatings were prepared by the cathodic vacuum arc (CVA)and the filtered cathodic vacuum arc (FCVA) technology,, one with embedded carbon particles and one without, both having closely related carbon structures. Research is currently underway on bipolar plate coatings for fuel cells. The corrosion behavior of the prepared a-C coatings was examined through Tafel polarization analysis under simulated fuel cell operating conditions as well as potentiostatic analysis at 0.6 V under normal conditions and 1.6 V under start–stop conditions for 7200 s. The coatings before and after corrosion are characterized using scanning electron microscopy, energy-dispersive X-ray spectroscopy, Raman spectroscopy, and infrared spectroscopy. The results reveal that the incorporation of conductive graphite-like particles in the coatings reduces their contact resistance. However, the gaps between these particles and the coatings act as pathways for corrosive solution, exacerbating the corrosion of the coatings. After corrosion at 0.6 V, both sets of coatings with sp2-hybridized carbon structures are contaminated by elements such as hydrogen and oxygen, leading to an increase in their contact resistance. Under high potential conditions (1.6 V), large corrosion pits and defects appear at the locations of graphite-like carbon particles. Furthermore, both sets of samples exhibit more severe oxygen contamination and a transformation of broken carbon bonds from sp3- to sp2-hybridized forms, irrespective of whether embedded graphite particles are present. Full article
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11 pages, 318 KiB  
Article
Thermodynamics of Magnetic Black Holes with Nonlinear Electrodynamics in Extended Phase Space
by Sergey Il’ich Kruglov
Universe 2024, 10(7), 295; https://doi.org/10.3390/universe10070295 - 13 Jul 2024
Cited by 1 | Viewed by 990
Abstract
We study Einstein’s gravity in AdS space coupled to nonlinear electrodynamics. Thermodynamics in extended phase space of magnetically charged black holes is investigated. We compute the metric and mass functions and their asymptotics, showing that black holes may have one or two horizons. [...] Read more.
We study Einstein’s gravity in AdS space coupled to nonlinear electrodynamics. Thermodynamics in extended phase space of magnetically charged black holes is investigated. We compute the metric and mass functions and their asymptotics, showing that black holes may have one or two horizons. The metric function is regular, f(0)=1, and corrections to the Reissner–Nordström solution are in the order of O(r3) when the Schwarzschild mass is zero. We prove that the first law of black hole thermodynamics and the generalized Smarr relation hold. The magnetic potential and vacuum polarization conjugated to coupling are computed and depicted. We calculate the Gibbs free energy and the heat capacity showing that first-order and second-order phase transitions take place. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2024 – Compact Objects)
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14 pages, 16731 KiB  
Article
Corrosion Behavior of FeCrMnxAlCu High-Entropy Alloys in NaOH Solutions
by Yang Yang, Junpeng Cui, Zhipeng Wang and Li Feng
Metals 2024, 14(4), 468; https://doi.org/10.3390/met14040468 - 17 Apr 2024
Cited by 4 | Viewed by 1474
Abstract
FeCrMnxAlCu (x = 2.0, 1.5, 1.0, 0.5, and 0.0) high-entropy alloys (HEAs) were prepared using vacuum arc melting. The phase structure, microstructure, and element distribution of FeCrMnxAlCu (x = 2.0, 1.5, 1.0, 0.5, and 0.0) HEAs were analyzed using [...] Read more.
FeCrMnxAlCu (x = 2.0, 1.5, 1.0, 0.5, and 0.0) high-entropy alloys (HEAs) were prepared using vacuum arc melting. The phase structure, microstructure, and element distribution of FeCrMnxAlCu (x = 2.0, 1.5, 1.0, 0.5, and 0.0) HEAs were analyzed using X-ray diffraction, scanning electron microscopy, and energy-dispersive spectroscopy. The corrosion resistance of the alloy in a NaOH solution was evaluated using a potentiodynamic polarization curve, electrochemical impedance spectroscopy, an immersion test, WLI, and X-ray photoelectron spectroscopy. The results showed that FeCrMnxAlCu HEAs are an FCC+BCC bi-phase mixed structure with typical dendrite and interdendrite structures. The corrosion test demonstrated that the HEAs presented a breakthrough characteristic of activation–passivation–passivation. With an increase in Mn content, the corrosion potential shifted first positively and then negatively, and the corrosion current first decreased and then increased. Among HEAs, the FeCrMn0.5AlCu HEA had the best electrochemical corrosion resistance. After corrosion, both oxide and hydroxide corrosion product films were formed on the surface, which reduced the ion diffusion rate, slowed down the corrosion process, and improved the corrosion resistance. Full article
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29 pages, 3696 KiB  
Review
The Modeling of Pulsar Magnetosphere and Radiation
by Gang Cao, Xiongbang Yang and Li Zhang
Universe 2024, 10(3), 130; https://doi.org/10.3390/universe10030130 - 7 Mar 2024
Cited by 1 | Viewed by 2237
Abstract
We review the recent advances in the pulsar high-energy γ-ray observation and the electrodynamics of the pulsar magnetospheres from the early vacuum model to the recent plasma-filled models by numerical simulations. The numerical simulations have made significant progress toward the self-consistent modeling [...] Read more.
We review the recent advances in the pulsar high-energy γ-ray observation and the electrodynamics of the pulsar magnetospheres from the early vacuum model to the recent plasma-filled models by numerical simulations. The numerical simulations have made significant progress toward the self-consistent modeling of the plasma-filled magnetosphere by including the particle acceleration and radiation. The current numerical simulations confirm a near force-free magnetosphere with the particle acceleration in the separatrix near the light cylinder and the current sheet outside the light cylinder, which can provide a good match to the recent high-energy γ-ray observations. The modeling of the combined multi-wavelength light curves, spectra, and polarization are expected to provide a stronger constrain on the geometry of the magnetic field lines, the location of the particle acceleration and the emission region, and the emission mechanism in the pulsar magnetospheres. Full article
(This article belongs to the Special Issue Pulsar Astronomy)
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20 pages, 3230 KiB  
Article
Modeling of Integrated Hollow-Fiber Solar-Powered VMD Modules for Desalination for a Better Understanding and Management of Heat Flows
by Gina Alfonso, Stéphanie Laborie and Corinne Cabassud
Membranes 2024, 14(2), 50; https://doi.org/10.3390/membranes14020050 - 11 Feb 2024
Viewed by 2057
Abstract
The direct integration of membrane distillation and solar energy collection in a single module is a promising technology for autonomous seawater desalination in remote regions; however, the modeling and design of such modules are challenging because of the coupling of the radial and [...] Read more.
The direct integration of membrane distillation and solar energy collection in a single module is a promising technology for autonomous seawater desalination in remote regions; however, the modeling and design of such modules are challenging because of the coupling of the radial and longitudinal heat and mass transfers. In a previous study, we provided as a first modeling approach a hollow fiber solar collector vacuum membrane distillation (VMD) module, considering a constant temperature at the shell side and a pure water feed. Here, a full model is developed to describe the coupled effects of the solar collector and a hollow fiber VMD module operating in an outside/in mode with saline water. The model considers all the main phenomena (membrane distillation, temperature and concentration polarization, absorption of solar radiation and energy balances over the solar collector, radial and longitudinal heat and mass transfer, seawater properties, and more than 30 variables). Applied to simulate the behavior of a semi-industrial-scale module, it allows the influence of solar radiation on the performance/limits of the integrated module to be discussed based on the radial and longitudinal profiles and heat flows. The model can be used to identify key points in the module design to better utilize solar radiation and manage heat flows. Full article
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23 pages, 6480 KiB  
Article
Vacuum Effects Induced by a Plate in de Sitter Spacetime in the Presence of a Cosmic String
by Wagner Oliveira dos Santos and Eugenio R. Bezerra de Mello
Universe 2024, 10(1), 20; https://doi.org/10.3390/universe10010020 - 29 Dec 2023
Cited by 2 | Viewed by 1652
Abstract
In this paper, we investigate the vacuum expectation values of the field squared and the energy–momentum tensor associated to a charged massive scalar quantum field in a (1+D)-dimensional de Sitter spacetime induced by a plate (flat boundary) and [...] Read more.
In this paper, we investigate the vacuum expectation values of the field squared and the energy–momentum tensor associated to a charged massive scalar quantum field in a (1+D)-dimensional de Sitter spacetime induced by a plate (flat boundary) and a carrying-magnetic-flux cosmic string. In our analysis, we admit that the flat boundary is perpendicular to the string, and the scalar field obeys the Robin boundary condition on the plate. In order to develop this analysis, we obtain the complete set of normalized positive-energy solutions of the Klein–Gordon equation compatible with the model setup. Having obtained these bosonic modes, we construct the corresponding Wightman function. The latter is given by the sum of two terms: one associated with the boundary-free spacetime, and the other induced by the flat boundary. Although we have imposed the Robin boundary condition on the field, we apply our formalism considering specifically the Dirichlet and Neumann boundary conditions. The corresponding parts have opposite signs. Because the analysis of bosonic vacuum polarization in boundary-free de Sitter space and in the presence of a cosmic string, in some sense, has been developed in the literature, here we are mainly interested in the calculations of the effects induced by the boundary. In this way, closed expressions for the corresponding expectation values are provided, as well as their asymptotic behavior in different limiting regions. We show that the conical topology due to the cosmic string enhances the boundary-induced vacuum polarization effects for both field squared and the energy–momentum tensor, compared to the case of a boundary in pure de Sitter spacetime. Moreover, the presence of a cosmic string and boundary induces non-zero stress along the direction normal to the boundary. The corresponding vacuum force acting on the boundary is also investigated. Full article
(This article belongs to the Section Field Theory)
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15 pages, 319 KiB  
Article
A Variational Approach to Excited Fermions on Kinks
by Herbert Weigel and Danial Saadatmand
Universe 2024, 10(1), 13; https://doi.org/10.3390/universe10010013 - 27 Dec 2023
Cited by 5 | Viewed by 1489
Abstract
We study the back-reaction of fermion fields on the kink solution in one space and one time dimension. We employ a variational procedure to determine an upper limit for the minimum of the total energy. This energy has three contributions: the classical kink [...] Read more.
We study the back-reaction of fermion fields on the kink solution in one space and one time dimension. We employ a variational procedure to determine an upper limit for the minimum of the total energy. This energy has three contributions: the classical kink energy, the energy of valence fermions and the fermion vacuum polarization energy. The latter arises from the interaction of the kink with the Dirac sea and is required for consistency of the semi-classical expansion for the fermions. Earlier studies only considered the valence part and observed a substantial back-reaction. This was reflected by a sizable distortion of the kink profile. We find that this distortion is strongly mitigated when the Dirac sea is properly accounted for. As a result, the back-reaction merely produces a slight squeeze or stretch of the kink profile. Full article
(This article belongs to the Section Field Theory)
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17 pages, 3304 KiB  
Review
Aging of Plasma-Activated Polyethylene and Hydrophobic Recovery of Polyethylene Polymers
by Miran Mozetič
Polymers 2023, 15(24), 4668; https://doi.org/10.3390/polym15244668 - 11 Dec 2023
Cited by 8 | Viewed by 2240
Abstract
Available literature on the aging of plasma-activated polyethylene due to hydrophobic recovery has been reviewed and critically assessed. A common method for the evaluation of hydrophobic recovery is the determination of the static water contact angle, while the surface free energy does not [...] Read more.
Available literature on the aging of plasma-activated polyethylene due to hydrophobic recovery has been reviewed and critically assessed. A common method for the evaluation of hydrophobic recovery is the determination of the static water contact angle, while the surface free energy does not reveal significant correlations. Surface-sensitive methods for the characterization of chemical composition and structure have limited applicability in studying the aging phenomenon. Aging is driven by thermodynamics, so it is observed even upon storage in a vacuum, and hydrophobic recovery increases with increasing temperature. Storage of plasma-activated polyethylene in the air at ambient conditions follows almost logarithmic behavior during the period studied by most authors; i.e., up to one month. The influence of the storage medium is somehow controversial because some authors reported aging suppression by storing in polar liquids, but others reported the loss of hydrophilicity even after a brief immersion into distilled water. Methods for suppressing aging by hydrophobic recovery include plasma treatment at elevated temperature followed by brief treatment at room temperature and application of energetic ions and photons in the vacuum ultraviolet range. Storing at low temperatures is a trivial alternative, but not very practical. The aging of plasma-activated polyethylene suppresses the adhesion of many coatings, but the correlation between the surface free energy and the adhesion force has yet to be addressed adequately. Full article
(This article belongs to the Special Issue Characterizations for the Polymer Aging)
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20 pages, 1209 KiB  
Article
Phase Transition and Point Defects in the Ferroelectric Molecular Perovskite (MDABCO)(NH4)I3
by Francesco Cordero, Floriana Craciun, Patrizia Imperatori, Venanzio Raglione, Gloria Zanotti, Antoniu Moldovan and Maria Dinescu
Materials 2023, 16(23), 7323; https://doi.org/10.3390/ma16237323 - 24 Nov 2023
Cited by 3 | Viewed by 1281
Abstract
We measured the anelastic, dielectric and structural properties of the metal-free molecular perovskite (ABX3) (MDABCO)(NH4)I3, which has already been demonstrated to become ferroelectric below TC= 448 K. Both the dielectric permittivity measured in air on [...] Read more.
We measured the anelastic, dielectric and structural properties of the metal-free molecular perovskite (ABX3) (MDABCO)(NH4)I3, which has already been demonstrated to become ferroelectric below TC= 448 K. Both the dielectric permittivity measured in air on discs pressed from powder and the complex Young’s modulus measured on resonating bars in a vacuum show that the material starts to deteriorate with a loss of mass just above TC, introducing defects and markedly lowering TC. The elastic modulus softens by 50% when heating through the initial TC, contrary to usual ferroelectrics, which are stiffer in the paraelectric phase. This is indicative of improper ferroelectricity, in which the primary order parameter of the transition is not the electric polarization, but the orientational order of the MDABCO molecules. The degraded material presents thermally activated relaxation peaks in the elastic energy loss, whose intensities increase together with the decrease in TC. The peaks are much broader than pure Debye due to the general loss of crystallinity. This is also apparent from X-ray diffraction, but their relaxation times have parameters typical of point defects. It is argued that the major defects should be of the Schottky type, mainly due to the loss of (MDABCO)2+ and I, leaving charge neutrality, and possibly (NH4)+ vacancies. The focus is on an anelastic relaxation process peaked around 200 K at ∼1 kHz, whose relaxation time follows the Arrhenius law with τ01013 s and E0.4 eV. This peak is attributed to I vacancies (VX) hopping around MDABCO vacancies (VA), and its intensity presents a peculiar dependence on the temperature and content of defects. The phenomenology is thoroughly discussed in terms of lattice disorder introduced by defects and partition of VX among sites that are far from and close to the cation vacancies. A method is proposed for calculating the relative concentrations of VX, that are untrapped, paired with VA or forming VX–VA–VX complexes. Full article
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