Dulong-Petit Research Articles

Localized Vibrations and Bound Exciton Mediated Emission in 2D Dion–Jacobson Perovskites

AbstractHerein, the emission characteristics of diammonium N,N,N′,N′‐tetramethyl‐1,4‐phenylenediammonium (TMPDA) are investigated based on lead iodide (TMPDA)PbI4 perovskite single crystals correlated with the localized lattice vibrations. Dual emission characteristics are ascribed to the existence of free exciton and bound exciton. The photoluminescence spectra as a function of excitation power and temperature show that structural distortion and exciton‐phonon coupling impact emission characteristics substantially. The coupling strength between excitons and phonons in (TMPDA)PbI4 is estimated as γac = 308.96 µeV and γLO = 62.3 meV, which is much higher than inorganic semiconductors. Further, bound exciton band recombination is significantly suppressed at lower temperatures due to increased localization of carriers. Specific heat deviation from the Dulong–Petit law indicates strong coupling in the lattice. The Debye‐Einstein model reveals multiple low‐energy localized independent vibrations, leading to phonon coupling with bound excitons. This interplay, along with Bosonic features, significantly influences emission properties. Further, it is observed that photocurrent as a function of the incident intensity follows a law ∝ I0α with α = 0.54, attributed to substantial bimolecular recombination of carriers. The findings of the study provide an in‐depth understanding of emission characteristics, lattice distortion, and interplay of electron‐phonon coupling in DJ phase 2D perovskite system.

Collective nature of phonon energies beyond harmonic oscillators

Phonon quasi-particles have been monumental in microscopically understanding thermodynamics and transport properties in condensed matter for decades. Phonons have one-to-one correspondence with harmonic eigenstates and their energies are often described by simple independent harmonic oscillator models. Higher order terms in the potential energy lead to interactions among them, resulting in finite lifetimes and frequency shifts, even in perfect crystals. However, increasing evidence including constant volume heat capacity violating the Dulong-Petit law suggests the need for re-evaluation of phonons as having independent harmonic energies. In this work, we explicitly examine inter-mode dependence of phonon energies of a prototypical crystal, silicon, through energy covariance calculations and demonstrate the concerted nature of phonon energies even at 300 K, questioning independent harmonic oscillator assumptions commonly used for phonon energy descriptions of thermodynamics and transport.

Machine-learning assistant DFT study of half-metallic full-Heusler alloy N2CaNa: Structural, electronic, mechanical, and thermodynamics properties

We studied the structural, electronic, mechanical, and thermodynamic properties of N2CaNa full Heusler alloys using density functional theory (DFT). Results for the structural analysis establish structural stability with a minimum formation energy of 29.9 eV. The compound is brittle and mechanically stable, having checked out with the Pugh criteria. The B/G ratio of bulk modulus B to shear modulus G for N2CaNa is 4.766, hence the material is ductile. N2CaNa alloy is ductile in nature. The Debye model correctly predicts the low-temperature dependence of heat capacity, which is proportional to Debye’s T3 law. Just like the Einstein model, it also recovers the Dulong–Petit law at high temperatures, suggesting the thermodynamic stability of the compounds at moderate temperatures. The results demonstrate potential N2CaNa for applications in spintronics, structural engineering, and other fields requiring materials with tailored properties.

Thermodynamic properties of the noncommutative quantum Hall effect with anomalous magnetic moment

In this paper, we study the thermodynamic properties of the noncommutative quantum Hall effect (NCQHE) with anomalous magnetic moment (AMM) for both relativistic and nonrelativistic cases at high temperatures, where the thermodynamic properties are: the Helmholtz free energy, the entropy, the mean energy, and the heat capacity. We also work with the Euler-MacLaurin formula to construct the partition function. Next, we plotted the graphs of properties as a function of temperature for different values of the magnetic field and of the NC parameters. We note that the Helmholtz free energy decreases with the temperature, increases with the NC parameters, and can decrease or increase with the magnetic field, while the entropy increases with the temperature, decreases with the NC parameters, and can decrease or increase with the magnetic field. Besides, the mean energy increases linearly with the temperature and the heat capacity satisfies the Dulong-Petit law, which also verified that the AMM does not influence the thermodynamic properties.

Planar Defects as a Way to Account for Explicit Anharmonicity in High Temperature Thermodynamic Properties of Silicon

Silicon is indispensable in semiconductor industry. Understanding its high-temperature thermodynamic properties is essential both for theory and applications. However, first-principle description of high-temperature thermodynamic properties of silicon (thermal expansion coefficient and specific heat) is still incomplete. Strong deviation of its specific heat at high temperatures from the Dulong–Petit law suggests substantial contribution of anharmonicity effects. We demonstrate, that anharmonicity is mostly due to two transverse phonon modes, propagating in (111) and (100) directions, and can be quantitatively described with formation of the certain type of nanostructured planar defects of the crystal structure. Calculation of these defects' formation energy enabled us to determine their input into the specific heat and thermal expansion coefficient. This contribution turns out to be significantly greater than the one calculated in quasi-harmonic approximation.

First-principles investigation of the electronics, optical, mechanical, thermodynamics and thermoelectric properties of Na based Quaternary Heusler alloys (QHAs) NaHfXGe (X = Co, Rh, Ir)

In this study, we explored the electronic and thermoelectric (TE) properties of the Na-based Quaternary Heusler Alloys (QHAs) NaHfXGe (X = Co, Rh, Ir) using density functional theory (DFT). We performed the spin-polarized DFT calculations at the general gradient approximation (GGA) level and confirmed the ground state non-magnetic configuration of NaHfXGe. The mechanical and thermodynamical stabilities are analyzed and discussed to validate the stability by calculating the elastic constant and phonon dispersion curve. A thorough investigation on the electronic properties are carried out by performing the GGA, GGA+U, and GGA+SOC formalism where we report the semi-conducting characteristic of NaHfCoGe and NaHfRhGe QHAs. However, NaHfIrGe is predicted to be a non-magnetic metal. From the calculated optical properties we found that the most active optical absorption occurs within the vis–UV region with 105 cm−1, therefore the studied QHAs are proposed to be a promising optoelectronic materials. The results of the thermodynamic properties have shown that NaHfXGe follows Debye’s low-temperature specific heat law and the classical thermodynamics of the Dulong-Petit law at high temperatures. The calculated TE efficiency using GGA+SOC formalism at T = 1200 K are ZT∼1.22 and 0.57 for NaHfCoGe and NaHfRhGe, suggesting that these materials are potential TE materials to operate at high temperature.

Investigating the magneto-transport and thermal properties of 2D electron systems under the influence of the Aharonov–Bohm field and Eckart potential interaction

The Eckart potential is a well-known potential model with applications cutting across chemical physics and related areas. It is often used to evaluate quantum mechanical tunneling corrections in order to obtain chemical rate constants. To this end, this study focused on extensively examining the effects of perturbations on the magnetic and thermal properties of the Eckart potential. In the presence of magnetic and Aharonov–Bohm fields with Eckart potential, the Schrödinger equation is solved using the functional analysis approach (FAA). The energy equation and wave function are obtained analytically. The energy equation is used to derive expressions for the thermo-magnetic properties of the Eckart potential. An extensive analysis of the effect of these fields and potential parameters on the wave function is presented. In several configurations of the analysis, we observe that the system exhibits a diamagnetic behavior,and the specific heat capacity agree with the Dulong–Petit law. The results of this study are valuable in areas such as molecular physics and condensed matter physics, amongst others.

Thermodynamic properties of substrate-induced graphene superlattice in homogeneous magnetic field

In this article we study the thermodynamic properties of a substrate-induced graphene superlattice in the presence of uniform magnetic field B. We derive an expression for the partition function of the system with uniform magnetic field B using the zeta function approach and find all related thermodynamic functions such as Helmholtz free energy, total energy, specific heat capacity and entropy for three cases related to the sublattice potential. We also show that the Dulong-Petit law is verified for all cases in the high-temperature limit. These results may shed light on the study of graphene superlattices in the developement of thermo-electric devices.

A Thorough Investigation of Electronic, Optical, Mechanical, and Thermodynamic Properties of Stable Glasslike Sodium Germanate under Compressive Hydrostatic Pressure: Ab Initio Study.

In this paper, we have tried to elucidate the variation of structural, electronic, and thermodynamic properties of glasslike Na2GeO3 under compressive isotropic pressure within a framework of density functional theory (DFT). The result shows stable structural (orthorhombic → tetragonal) and electronic (indirect → direct) phase transitions at P ∼ 20 GPa. The electronic band gap transition plays a key role in the enhancement of optical properties. The results of the thermodynamic properties have shown that Na2GeO3 follows Debye's low-temperature specific heat law and the classical thermodynamic of the Dulong-Petit law at high temperature. The pressure sensitivity of the electronic properties led us to compute the piezoelectric tensor (both in relaxed and clamped ions). We have observed significant electric responses in the form of a piezoelectric coefficient under applied pressure. This property suggested that Na2GeO3 could be a potential material for energy harvest in future energy-efficient devices. As expected, Na2GeO3 becomes harder and harder under compressive pressure up to the phase transition pressure (∼20 GPa) which can be read from Pugh's ratio (kH) > 1.75, however, at pressures above 20 GPa kH < 1.75, which may be due to the formation of fractures at high pressure.

The ion equation of state of plasmas in the warm dense matter regime

The existing “quotidian equation of state (QEOS)” model [More et al., Phys. Fluids 31, 3059 (1988)] has been revised, and an alternative set of formulas is provided for the Helmholtz free energy, internal energy, heat capacity, and pressure. A novel scheme for constructing the ion equation-of-state is proposed based on the additive of solid and fluid components that act throughout the temperature range, in contrast to the QEOS that matches the thermodynamic parameters at selected interfaces. These components are continuous along with their first and second derivatives and obey limiting cases and thermodynamics laws (Lindemann melting, Dulong–Petit law, Grüneisen pressure law, and ideal gas law). Thus, the new scheme eliminates discontinuities in thermodynamics parameters across interfaces and ensures that the thermodynamics parameters are consistent with each other. The Helmholtz free energy, internal energy, heat capacity, and pressure have been approximated with computationally efficient formulas that can be used as parts of other models, e.g., hydro-simulations.

Weyl conjecture and thermal radiation of finite systems

In this work, corrections for the Weyl law and Weyl conjecture in d dimensions are obtained and effects related to the polarization and area term are analyzed. The derived formalism is applied on the quasithermodynamics of the electromagnetic field in a finite d-dimensional box within a semi-classical treatment. In this context, corrections to the Stefan–Boltzmann law are obtained. Special attention is given to the two-dimensional scenario, since it can be used in the characterization of experimental setups. Another application concerns acoustic perturbations in a quasithermodynamic generalization of Debye model for a finite solid in d dimensions. Extensions and corrections for known results and usual formulas, such as the Debye frequency and Dulong–Petit law, are calculated.

Proportional correlation between heat capacity and thermal expansion of atomic, molecular crystals and carbon nanostructures

Correlation between thermal expansions β(T) and heat capacity C(T) of atomic and molecular crystals, amorphous materials with a structural disorder, carbon nanomaterials (fullerite C60, bundles SWCNTs of single-walled carbon nanotubes) was analyzed. The influence of the contribution to the coefficient of linear thermal expansion αXe(T) of Xe atoms adsorbed on the SWCNTs bundles is considered. The proportional correlation was found between the contribution to the coefficient of linear thermal expansion αXe(T) and the normalized to the gas constant heat capacity C Xe(T)/R of Xe atoms adsorbed on the SWCNTs bundles. The proportional correlation (β/β*) ∼ (CV/R) with the parameter β* for the bulk thermal expansion coefficient for cryocrystals is proposed. In the case of atomic crystals such as Xe and Ar, the proportional correlation (β/β*) ∼ (CV/R) is observed in the temperature range from the lowest experimental to temperatures where CV/R ≈ 2.3. The correlation is not observed in the temperatures where 2.3 &lt; C V/R &lt; 3 (classical Dulong-Petit law). It was found that the universal proportional correlation is also observed for molecular crystals with linear symmetry, such as CO2, CO, and N2O if the normalized heat capacity below the values CV/R ≈ 3 ÷ 3.5. It indicates that the proportional correlation between thermal expansions (β/β*) and heat capacity (CV/R) is related not only to the translational, but also to the rotational degrees of freedom of the molecule in the crystal. In the case of the C0, molecular crystal with translational and rotational degrees of freedom and intramolecular vibrations, the discussed above correlation occurs below the values of normalized heat capacity CV/R ≈ 7.5. In strongly anisotropic systems, such as systems of compacted bundles of single-walled carbon nanotubes and SWCNTs bundles with adsorbed Xe atoms, this universal dependence appears in a limited temperature range that does not include the lowest temperatures. A qualitative explanation of the observed correlation is proposed.

A DFT Characterization of Structural, Mechanical, and Thermodynamic Properties of Ag9In4 Binary Intermetallic Compound

The intermetallic compounds (IMCs) at the interface between the solder joint and metal bond pad/under bump metallization (UBM) exert a significant impact on the thermal–mechanical behavior of microelectronic packages because of their unique physical properties. In this study, a theoretical investigation of the physical properties, namely structural, mechanical, and thermodynamic properties, of the Ag9In4 IMC was conducted using ab initio density functional theory (DFT) calculations. The calculated equilibrium lattice constants were in good agreement with the literature experimental data. Furthermore, with the calculated elastic constants, we can derive the ductility and brittleness nature, elastic anisotropy, and direction-dependent elastic properties of Ag9In4 through several elastic indices, three-dimensional surface representation, and two-dimensional projections of elastic properties. The calculations inferred that the cubic Ag9In4 IMC confers structural and mechanical stability, ductility, relative low stiffness and hardness, and elastic anisotropy. Finally, the thermodynamic properties, i.e., Debye temperature, heat capacity, and minimum thermal conductivity, were also investigated. Evidently, the low-temperature heat capacity conforms to the Debye heat capacity theory and the high-temperature one complies with the classical Dulong–Petit law.

Crystalline-liquid duality of specific heat in halide perovskite semiconductor

Crystalline-liquid duality in specific heat is observed in lead-free bismuth halide perovskite A3Bi2×9 [A= FA, MA, Cs, and X = I, Br, Cl] semiconductor. All crystals exhibit unusual liquid-like behavior and show substantial deviation from the classical Dulong-Petit law at room temperature. This unusual liquid-like behavior of specific heat is attributed to the dynamic disorder and strong anharmonicity in the soft crystal lattice. The low-temperature specific heat was modeled using the combined Debye-Einstein model and obtained Einstein modes demonstrate strong anharmonic coupling of the low-energy optical modes with acoustic modes resulting in ultrasoft frequency dampening of acoustic phonons. The combination of strong acoustic−optical phonon coupling, soft elastic layered structure, and abundance of low-energy optical phonons results in anomalous thermodynamic specific heat duality in these bismuth-based phonon glass electron crystals. Our study is of fundamental interest in thermodynamics and will help to design novel thermoelectric materials.

DFT based Investigation of Structural, Thermodynamic, Mechanical and Electronic Properties of RuVZ (Z: As, Bi, Sb) Half-Heusler Semiconductors

Half-Heusler (hH) alloys are an intriguing class of materials with significant potential for applications in spintronics, thermoelectrics, optoelectronics, and magnetoelectronics due to their unique adjustable properties. In this work, we have investigated the structural, thermodynamic, mechanical, and electronic properties of RuVZ (Z: As, Bi, Sb) half-Heusler materials using the density functional theory (DFT) as implemented in the quantum espresso computational suite. The structural, thermodynamic, and mechanical properties were also predicted using the linear response density functional perturbation theory. We observed that the hH alloys are non-magnetic semiconductors and have an indirect narrow band gap. The band gap values and lattice constants for RuVSb and RuVAs cubic crystals are consistent with published reports. RuVBi has a lattice constant of 6.18 and a band gap of 0.16 eV. The elastic parameter results obtained satisfy Born's stability requirements, suggesting mechanical stability of the hH materials. All three alloys are found to be ductile. The RuVZ alloys obey the Dulong-Petit law at heat capacity of 74.7, 74.5, and 74.3 J mol-1K-1 and temperatures of 556, 754, and 775 K, respectively. The Debye temperature of 353.75K suggests that the RuVAs alloy is the hardest, with a significant Debye sound velocity (2997.12 m/s) and will have high thermal conductivity.&#x0D;

Magneto-transport and Thermal properties of TiH diatomic molecule under the influence of magnetic and Aharonov-Bohm (AB) fields

In this study, the effects of Aharonov-Bohm (AB) and magnetic fields on the thermodynamic and magneto-transport properties of TiH diatomic molecule using the Deng-Fan potential as a model are investigated. The functional analysis approach (FAA) is used to solve the Schrodinger equation in the presence of magnetic and AB fields with Deng-Fan potential. The energy equation, as well as the wave function, have been derived. The analytic expressions for the thermo-magnetic and transport properties of the Deng-Fan potential are derived using the energy equation and the partition function. These properties obtained are thoroughly analysed utilising graphical representations. Our analysis shows that the magnetic susceptibility of the TiH exhibits a diamagnetic behaviour, and the specific heat capacity behaviour agrees with the famous Dulong-Petit law when the system is subjected to AB field variations and a fixed magnetic field. Albeit, a slight anomaly is observed in the behaviour of the specific heat capacity. Our findings will be valuable in various fields of physics, including chemical and molecular physics and condensed matter physics, where the derived models could be applied to study other diatomic molecules and quantum dots, respectively.

Non-Relativistic Treatment of the 2D Electron System Interacting via Varshni–Shukla Potential Using the Asymptotic Iteration Method

The nonrelativistic treatment of the Varshni–Shukla potential (V–SP) in the presence of magnetic and Aharanov–Bohm fields is carried out using the asymptotic iteration method (AIM). The energy equation and wave function are derived analytically. The energy levels are summed to obtain the partition function, which is employed to derive the expressions for the thermomagnetic properties of the V–SP. These properties are analyzed extensively using graphical representations. It is observed that in the various settings of the analysis, the system shows a diamagnetic characteristic, and the specific heat capacity behavior agrees with the recognized Dulong–Petit law, although some slight anomaly is observed. This irregular behavior could be attributed to a Schottky anomaly. Our findings will be valuable in a variety of fields of physics, including chemical, molecular and condensed matter physics, where our derived models could be applied to study other diatomic molecules and quantum dots, respectively.

DFT study of structural, electronic, magnetic, elastic, vibrational, thermodynamic and thermoelectric properties of XCrP (X= Ni, Pd and Pt)

This study of physical properties of the half-Heuslers compounds of XCrP (X = Ni, Pd, Pt) is performed in the framework of density functional theory (DFT). The results show that all compounds are stable in the ferromagnetic state. The DOSs reveal that NiCrP is half-metallic, whereas, PdCrP and PtCrP are nearly half-metallic. The elastic properties indicate that these compounds are ductile and anisotropic. The phonons dispersions show that NiCrP is dynamically stable, while the two others are unstable. The variation of specific heat at constant volume Cv with temperature obeys the Debye's law at low-temperature, and it obeys the classical Dulong–Petit's law at high temperature for NiCrP, while Cv of PdCrP and PtCrP don't follow the Debye law due to the negative phonons frequencies. The thermoelectric properties (TE) indicate that these compounds are n-type materials and suitable for TE applications.

Stability of X-IV-IV half Heusler semiconductor alloys: a DFT study

We present reports for the structural, electronic, mechanical (elastic), and thermodynamic properties of NiHfX (X = Si, Sn, Ge) half Heusler compounds. We performed the calculation based on the density functional theory as implemented in the quantum espresso computational suite. We also predict the structural stability of the alloys, and the mechanical and thermodynamic properties using the linear response density functional perturbation theory. The compounds are non-magnetic semiconductors with narrow bandgaps. Results for the equilibrium lattice parameter for NiHfSn is in reasonable agreement with reports in the existing literature. The elastic parameters obey Born’s stability criteria, and there are no negative phonon dispersions, hence, establishing the compounds’ mechanical stability. NiHfGe is a brittle and hard material with directional covalent bonding, while NiHfSi and NiHfSn alloys are ductile and malleable. The alloys obey the Dulong-Petit law at a heat capacity of 72 and 74 J/Kmol and temperatures of 720 K and 800 K. The phonon frequencies shows that the wavelength of the materials is the far-infrared region. NiHfSi has the highest of 411.68 K at zero pressure and will have the highest thermal conductivity implying less viability as a thermoelectric material than NiHfSn with a of 340.19 K.

Lattice Dynamics and thermodynamic Responses of XNbSn Half-Heusler Semiconductors: A First-Principles Approach

In this work, we have evaluated how CoNbSn, IrNbSn, and RhNbSn half Heusler alloys respond to temperature change and the accompanying lattice vibrations as a cubic crystal. There are reports in the literature for CoNbSn with which we compared our result; there are, however, no reports for the other two alloys except for their Debye temperature obtained via machine learning, and our results compare well. Considering that results in the literature for IrNbSn and RhNbSn are scanty, we first computed the alloys' structural and electronic properties to establish their structural stability using the density functional theory and generalised gradient approximation as implemented in the quantum espresso computational suite. We confirmed the equilibrium lattice structure by exploring the three possibilities for a half Heusler alloy and fitting the results to the state's Murnaghan equation. The negative formation energies obtained supports experimental simulation of the alloys. Results from the lattice dynamics and thermodynamic evaluation show that the alloys favour ionic bonding and are ductile. The Debye temperature positions IrNbSn to be the most promising material for thermoelectric application because it has the least Debye temperature; hence it is supposed to have the lowest thermal conductivity. The Dulong-Petit law is obeyed at high temperature as expected. The phonon dispersion and density of states show that the d orbitals of Co and Nb are the significant contributors to the dispersions at both the acoustic and optical modes of the alloys.