Showing papers on "Debye model published in 2019"

Universal Origin of Boson Peak Vibrational Anomalies in Ordered Crystals and in Amorphous Materials

Abstract: The vibrational spectra of solids, both ordered and amorphous, in the low-energy regime, control the thermal and transport properties of materials, from heat capacity to heat conduction, electron-phonon couplings, conventional superconductivity, etc. The old Debye model of vibrational spectra at low energy gives the vibrational density of states (VDOS) as proportional to the frequency squared, but in many materials the spectrum departs from this law which results in a peak upon normalizing the VDOS by frequency squared, which is known as the ``boson peak.'' A description of the VDOS of solids (both crystals and glasses) is presented starting from first principles. Without using any assumptions whatsoever of disorder in the material, it is shown that the boson peak in the VDOS of both ordered crystals and glasses arises naturally from the competition between elastic mode propagation and diffusive damping. The theory explains the recent experimental observations of boson peak in perfectly ordered crystals, which cannot be explained based on previous theoretical frameworks. The theory also explains, for the first time, how the vibrational spectrum changes with the atomic density of the solid, and explains recent experimental observations of this effect.

Wiedemann-Franz law and Fermi liquids

Abstract: We consider in depth the applicability of the Wiedemann-Franz (WF) law, namely that the electronic thermal conductivity $(\ensuremath{\kappa})$ is proportional to the product of the absolute temperature $(T)$ and the electrical conductivity $(\ensuremath{\sigma})$ in a metal with the constant of proportionality, the so-called Lorenz number ${L}_{0}$, being a materials-independent universal constant in all systems obeying the Fermi liquid (FL) paradigm. It has been often stated that the validity (invalidity) of the WF law is the hallmark of an FL [non-Fermi liquid (NFL)]. We consider, both in two (2D) and three (3D) dimensions, a system of conduction electrons at a finite temperature $T$ coupled to a bath of acoustic phonons and quenched impurities, ignoring effects of electron-electron interactions. We find that the WF law is violated arbitrarily strongly with the effective Lorenz number vanishing at low temperatures as long as phonon scattering is stronger than impurity scattering. This happens both in 2D and in 3D for $Tl{T}_{\text{BG}}$, where ${T}_{\text{BG}}$ is the Bloch-Gr\"uneisen temperature of the system. In the absence of phonon scattering (or equivalently, when impurity scattering is much stronger than the phonon scattering), however, the WF law is restored at low temperatures even if the impurity scattering is mostly small angle forward scattering. Thus, strictly at $T=0$ the WF law is always valid in a FL in the presence of infinitesimal impurity scattering. For strong phonon scattering, the WF law is restored for $Tg{T}_{\text{BG}}$ (or the Debye temperature ${T}_{D}$, whichever is lower) as in usual metals. At very high temperatures, thermal smearing of the Fermi surface causes the effective Lorenz number to go below ${L}_{0}$, manifesting a quantitative deviation from the WF law. Our paper establishes definitively that the uncritical association of an NFL behavior with the failure of the WF law is incorrect.

Elastic properties and stability of Heusler compounds: Cubic Co2YZ compounds with L21 structure

Abstract: Elastic constants and their derived properties of various cubic Heusler compounds were calculated using the first-principles density functional theory. To begin with, Cu 2MnAl is used as a case study to explain the interpretation of the basic quantities and compare them with experiments. The main part of the work focuses on Co 2-based compounds that are Co 2Mn M with the main group elements M = Al, Ga, In, Si, Ge, Sn, Pb, Sb, Bi, and Co 2 T M with the main group elements Al or Si, and the 3 d transition metals T = Sc, Ti, V, Cr, Mn, and Fe. It is found that many properties of Heusler compounds correlate to the mass or nuclear charge Z of the main group element. Additional representation and compact simplification of the elastic data is useful to investigate and compare their influence on crystal stability and physical properties. Here, Blackman’s and Every’s diagrams are used to compare the elastic properties of the materials, whereas Pugh’s and Poisson’s ratios are used to analyze the relationship between interatomic bonding and physical properties. It is found that Pugh’s criterion on brittleness needs to be revised whereas Christensen’s criterion describes the ductile–brittle transition of Heusler compounds very well. The calculated elastic properties give hint on a metallic bonding with an intermediate brittleness for the studied Heusler compounds. The universal anisotropy of the stable compounds has values in the range of 0.57 < A U < 2.73. The compounds with higher A U values are found close to the middle of the transition metal series. In particular, Co 2ScAl with A U = 0.01 is predicted to be an isotropic material that comes closest to an ideal Cauchy solid as compared to the remaining Co 2-based compounds. Apart from the elastic constants and moduli, the sound velocities, Debye temperatures, and hardness are predicted and discussed for the studied systems. The calculated slowness surfaces for sound waves reflect the degree of anisotropy of the compounds.

Linear-in-T resistivity in dilute metals: A Fermi liquid perspective

Abstract: We consider a short-range deformation-potential scattering model of electron-acoustic phonon interaction to calculate the resistivity of an ideal metal (i.e., no other scattering mechanism except acoustic phonon scattering) as a function of temperature $(T)$ and electron density $(n)$. The resistivity calculation is based on the Boltzmann transport theory within the relaxation-time approximation in the nearly-free-electron single-band approximation. We consider both 3D metals and 2D metals and focus on the dilute limit, i.e., low effective metallic carrier density (and hence low effective Fermi wave number ${k}_{F})$ of the system. The main findings are (1) a phonon-scattering-induced linear-in-$T$ resistivity could persist to arbitrarily low temperatures in the dilute limit independent of the Debye temperature $({T}_{D})$, although, eventually, the low-$T$ resistivity turns over to the expected Bloch-Gr\"uneisen (BG) behavior with ${T}^{5}\phantom{\rule{4pt}{0ex}}({T}^{4})$ dependence, in 3D (2D), respectively, with the crossover temperature, ${T}_{\text{BG}}$, from the linear-in-$T$ to the BG behavior, being proportional to the Fermi momentum, is small in the dilute limit; (2) because of low values of $n$, the phonon-induced resistivity could be very high in the system, orders of magnitude above the corresponding room temperature resistivity of ordinary metals; and (3) the resistivity shows an intrinsic saturation effect at very high temperatures (for $Tg{T}_{D})$ and, in fact, weakly decreases with increasing $T$ above a high crossover temperature with this crossover being dependent on both ${T}_{D}$ and $n$ in a nonuniversal manner---this high-temperature crossover is not directly connected with the Mott-Ioffe-Regel limit and is a reflection of phonon phase-space restriction. We discuss the qualitative trends in the resistivity as a function of temperature, density, phonon velocity, and system dimensionality. We also provide ``high-temperature'' linear-in-$T$ resistivity results for 2D and 3D Dirac materials. Our work brings out the universal features of phonon-induced transport in dilute metals, and we comment on possible implications of our results for strange metals, emphasizing that the mere observation of a linear-in-$T$ metallic resistivity at low temperatures or a very high metallic resistivity at high temperatures is not necessarily a reason to invoke an underlying quantum critical strange-metal behavior. Dilute metals may very well have highly unusual (compared with normal metals) transport properties arising from quantitative, but not qualitatively new, underlying physics. We discuss the temperature variation of the effective transport scattering rate showing that, for reasonable parameters, the scattering rate could be below or above ${k}_{B}T$ and, in particular, purely coincidentally, the calculated scattering rate happens to be ${k}_{B}T$ in normal metals with no implications whatsoever for the so-called Planckian behavior. Our work manifestly establishes that an apparent Planckian dissipative behavior could arise from the usual electron-phonon interaction without implying any strange metallicity or a failure of the quasiparticle paradigm in contrast to recent claims.

Investigation of temperature-dependent optical properties of TiO2 using diffuse reflectance spectroscopy

Abstract: Temperature-dependent diffuse reflectance spectroscopy (DRS) measurements have been carried out on the polycrystalline sample TiO2. Important values from optical parameters such as band gap (Eg), Urbach energy (EU), and Urbach focus (E0) have been estimated in the range of 300–450 K. In order to understand the experimental value of band gap (Eg) of TiO2, i.e., obtained from DRS, a first-principle calculation has been performed. The dependency of EU and the slope of exponential tails (β1, β2) of the density of states has also been studied which determines the distribution of exponential tails near the valence and conduction bands in semiconducting oxides. The behavior of optical band gap and EU has also been investigated with the influence of temperature using Cody model. From the temperature dependence of band gap measurements, the value of thermodynamical parameter such as Debye temperature (θD) has also been estimated. Thus it appears that the temperature-dependent optical absorption spectroscopy is very powerful and economical tool to probe the electronic structure near band edge and also to estimate the important thermodynamical parameter.

Origin of Intrinsically Low Thermal Conductivity in Talnakhite Cu17.6Fe17.6S32 Thermoelectric Material: Correlations between Lattice Dynamics and Thermal Transport.

Abstract: Understanding the nature of phonon transport in solids and the underlying mechanism linking lattice dynamics and thermal conductivity is important in many fields, including the development of efficient thermoelectric materials where a low lattice thermal conductivity is required. Herein, we choose the pair of synthetic chalcopyrite CuFeS2 and talnakhite Cu17.6Fe17.6S32 compounds, which possess the same elements and very similar crystal structures but very different phonon transport, as contrasting examples to study the influence of lattice dynamics and chemical bonding on the thermal transport properties. Chemically, talnakhite derives from chalcopyrite by inserting extra Cu and Fe atoms in the chalcopyrite lattice. The CuFeS2 compound has a lattice thermal conductivity of 2.37 W m-1 K-1 at 625 K, while Cu17.6Fe17.6S32 features Cu/Fe disorder and possesses an extremely low lattice thermal conductivity of merely 0.6 W m-1 K-1 at 625 K, approaching the amorphous limit κmin. Low-temperature heat capacity measurements and phonon calculations point to a large anharmonicity and low Debye temperature in Cu17.6Fe17.6S32, originating from weaker chemical bonds. Moreover, Mossbauer spectroscopy suggests that the state of Fe atoms in Cu17.6Fe17.6S32 is partially disordered, which induces the enhanced alloy scattering. All of the above peculiar features, absent in CuFeS2, contribute to the extremely low lattice thermal conductivity of the Cu17.6Fe17.6S32 compound.

Optical evidence of the type-II Weyl semimetals MoTe 2 and WTe 2

Abstract: The carrier dynamics and electronic structures of type-II Weyl semimetal candidates ${\mathrm{MoTe}}_{2}$ and ${\mathrm{WTe}}_{2}$ have been investigated by using temperature-dependent optical conductivity $[\ensuremath{\sigma}(\ensuremath{\omega})]$ spectra. Two kinds of Drude peaks (narrow and broad) have been separately observed. The width of the broad Drude peak increases with elevating temperature above the Debye temperature of about 130 K in the same way as those of normal metals, on the other hand, the narrow Drude peak becomes visible below 80 K and the width is rapidly suppressed with decreasing temperature. Because the temperature dependence of the narrow Drude peak is similar to that of a type-I Weyl semimetal TaAs, it was concluded to originate from Dirac carriers of Weyl bands. The result suggests that the conductance has the contribution of two kinds of carriers, normal semimetallic and Dirac carriers, and this observation is evidence of the type-II Weyl semimetals ${\mathrm{MoTe}}_{2}$ and ${\mathrm{WTe}}_{2}$. The obtained carrier mass of the semimetallic bands and the interband transition spectra suggest the weak electron correlation effect in both materials.

Universal non-mean-field scaling in the density of states of amorphous solids.

Abstract: Amorphous solids have excess soft modes in addition to the phonon modes described by the Debye theory. Recent numerical results show that if the phonon modes are carefully removed, the density of state of the excess soft modes exhibit universal quartic scaling, independent of the interaction potential, preparation protocol, and spatial dimensions. We hereby provide a theoretical framework to describe this universal scaling behavior. For this purpose, we extend the mean-field theory to include the effects of finite-dimensional fluctuation. Based on a semiphenomenological argument, we show that mean-field quadratic scaling is replaced by the quartic scaling in finite dimensions. Furthermore, we apply our formalism to explain the pressure and protocol dependence of the excess soft modes.

A lower bound to the thermal diffusivity of insulators.

Abstract: It has been known for decades that thermal conductivity of insulating crystals becomes proportional to the inverse of temperature when the latter is comparable to, or higher than, the Debye temperature. This behavior has been understood as resulting from Umklapp scattering among phonons. We put under scrutiny the magnitude of the thermal diffusion constant in this regime and find that it does not fall below a threshold set by the square of sound velocity times the Planckian time ([Formula: see text]). The conclusion, based on scrutinizing the ratio in cubic crystals with high thermal resistivity, appears to hold even in glasses where Umklapp events are not conceivable. Explaining this boundary, reminiscent of a recently-noticed limit for charge transport in metals, is a challenge to theory.

Pump-probe spectroscopy study of ultrafast temperature dynamics in nanoporous gold

Abstract: We explore the influence of the nanoporous structure on the thermal relaxation of electrons and holes excited by ultrashort laser pulses ($\ensuremath{\sim}7\phantom{\rule{0.16em}{0ex}}\mathrm{fs}$) in thin gold films. Plasmon decay into hot electron-hole pairs results in the generation of a Fermi-Dirac distribution thermalized at a temperature ${T}_{\mathrm{e}}$ higher than the lattice temperature ${T}_{\mathrm{l}}$. The relaxation times of the energy exchange between electrons and lattice, here measured by pump-probe spectroscopy, is slowed down by the nanoporous structure, resulting in much higher peak ${T}_{\mathrm{e}}$ than for bulk gold films. The electron-phonon coupling constant and the Debye temperature are found to scale with the metal filling factor $f$ and a two-temperature model reproduces the data. The results open the way for electron temperature control in metals by engineering of the nanoporous geometry.

Synthesis and deciphering the effects of sintering temperature on structural, elastic, dielectric, electric and magnetic properties of magnetic Ni0.25Cu0.13Zn0.62Fe2O4 ceramics

Abstract: In this study, Ni0.25Cu0.13Zn0.62Fe2O4 polycrystalline ferrites were synthesized through a solid-state reaction route. The standard techniques such as XRD, FTIR, FESEM, EDX, and VSM were employed to analyze and understand the crystallized single-phase, crystallite size, functional groups, morphology and magnetic properties. FTIR and XRD analyses revealed the different band modes in structure, formation and the compositions of the cubic spinel structure. FESEM revealed that the grain size increases as the sintering temperature increases and the presence of the required elements as per the stoichiometric ratio were ascertained by EDX. The longitudinal wave velocity ( $$V_{l}$$ ), transverse wave velocity ( $$V_{t}$$ ), mean elastic wave velocity ( $$V_{m}$$ ), bulk modulus ( $$B$$ ), rigidity modulus ( $$n$$ ), Young’s modulus ( $$Y$$ ), Poisson ratio ( $$\sigma$$ ) and Debye temperature (ΘD) were evaluated. The elastic moduli were corrected to zero porosity through Hasselman and Fulrath model and Ledbetter and Datta model. The dielectric constant increases with sintering temperature which is accounted for the partial reduction of Fe3+ to Fe2+ and exhibited dispersive behavior as a result of Maxwell–Wagner-type interfacial polarization. The small polaron hopping phenomenon is responsible for the electrical conduction process. The initial permeability was found to increase with sintering temperature as a result of the increased densities and grain sizes. The Q-factor decreases and the cut-off frequency shifts toward the lower frequency side with sintering temperature. The magnetic parameters drastically deteriorate with sintering temperature which may be ascribed to the sample inhomogeneity and presence of intragranular porosity.

Computation of stability, elasticity and thermodynamics in equiatomic AlCrFeNi medium-entropy alloys

Abstract: We investigated the phase stability, elastic and thermodynamic properties of equimolar medium-entropy alloys (MEAs) AlCrFeNi by performing first-principles calculations in combination with quasi-harmonic Debye–Gruneisen model. Both body-centered cubic (BCC) and face-centered cubic structures in ferromagnetic (FM) and non-magnetic states are described using the special quasirandom structures technique. All the considered MEAs can form single-phase solid solutions and are dynamically stable, and FM BCC AlCrFeNi is the most stable. The elastic moduli including bulk modulus B, shear modulus G and Young’s modulus E of AlCrFeNi are calculated by first-principles and estimated by using the rule of mixtures (ROM) from their pure components. The lattice constants a of first-principles calculations are well reproduced by ROM. The obtained B and G of the two methods are close to equality lines with a minor scatter. The relevant free energies’ contributions including structural, configurational, vibrational and electronic excitations are taken into account to calculate the equilibrium lattice constants a, volumetric thermal expansion coefficient α, Debye temperature ΘD, constant volume heat capacity Cv, vibrational entropy Svib, electronic entropy Selec, vibrational Helmholtz free energies Fvib and electronic Helmholtz free energies Felec of AlCrFeNi MEAs at finite temperature. The thermodynamic properties strongly depend on crystal structures and magnetic states, and FM BCC AlCrFeNi shows the largest Svib and α, and the lowest Fvib among the considered MEAs. Finally, electronic density of states is analyzed to clarify the physical origin of AlCrFeNi MEAs with different crystal structures and magnetic states.

Temperature dependent optical and dielectric properties of liquid water studied by terahertz time-domain spectroscopy

Abstract: Terahertz waves have found wide applications in the biological and medical areas. Since water is one of the most important ingredients in the biological systems, it is necessary to investigate its optical and dielectric properties in the terahertz range. These fundamental physical parameters play an important role in many applications, such as biological imaging and hyperthermia applications, and are temperature dependent. In order to shed more light on the property of temperature dependence, we performed a systematic investigation by changing the temperature of the water sample and using a terahertz time-domain spectrometer. The experimental results show that when the temperature increases from 275 K to 340 K, the refractive index and the complex dielectric constant of water increase noticeable, with the absorption coefficient increased observably. A good agreement is found between experimental data and the double Debye model.

Optical and electrical properties of MoO2 and MoO3 thin films prepared from the chemically driven isothermal close space vapor transport technique.

Abstract: Chemically-driven isothermal close space vapour transport was used to prepare pure MoO2 thin films which were eventually converted to MoO3 by annealing in air. According to temperature-dependent Raman measurements, the MoO2/MoO3 phase transformation was found to occur in the 225 °C-350 °C range while no other phases were detected during the transition. A clear change in composition as well as noticeable modifications of the band gap and the absorption coefficient confirmed the conversion from MoO2 to MoO3. An extensive characterization of these two pure phases was carried out. In particular, a procedure was developed to determine the dispersion relation of the refractive index of MoO2 from the shift of the interference fringes of the used SiO2/Si substrate. The obtained data of the refractive index was corrected taking into account the porosity of the samples calculated from elastic backscattering spectrometry. The Debye temperature and the residual resistivity were extracted from the electrical resistivity temperature dependence using the Bloch-Gruneisen equation. MoO3 converted samples presented a very high resistivity and a typical semiconducting behavior. They also showed intense and broad luminescence spectra composed by several contributions whose temperature behavior was examined. Furthermore, surface photovoltage spectra were taken and their relation with the photoluminescence is discussed.