Search NASA⌕ Search

SEARCH · Search NASA

Results for “Debye Model”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

On the validity of using the Debye model to quantitatively correlate the shear modulus with vibrational properties in cubic metals

The relationship between the shear modulus and the flexibility volume has been examined using molecular dynamics simulations in fifteen cubic metallic elements over a range of temperatures. Here we have observed a universal correlation, and identified the applicability range in which this correlation is quantitatively consistent with the prediction based on the Debye model. Deviation is observed for high modulus metals, and its origin is discussed in terms of the Debye assumptions regarding the vibrational mean squared displacement and the phonon density of states.

36 MATERIALS SCIENCE↗
NASA NTRS2021

Seawater Debye Model Function at L-Band and Its Impact on Salinity Retrieval From Aquarius Satellite Data

A model function of seawater, which specifies the dielectric constant of seawater as a function of salinity, temperature, and frequency, is important for the retrieval of sea surface salinity using satellite data. In 2017, a model function has been developed based on measurement data at 1.4134 GHz using a third-order polynomial expression in salinity ( S ) and temperature ( T ). Although the model showed improvements in salinity retrieval, it had an inconsistent behavior between partitioned salinities. To improve the stability of the model, new dielectric measurements of seawater have been made recently over a broad range of salinities and temperatures to expand the data set used for developing the model function. The structure of the model function has been changed from a polynomial expansion in S and T to a physics-based model consisting of a Debye molecular resonance term plus a conductivity term. Each unknown parameter is expressed in S and T based on the expanded measurement data set. Physical arguments have been used to limit the number of unknown coefficients in these expressions to improve the stability of the model function. The new model function has been employed in the retrieval algorithm of the Aquarius satellite mission to obtain a global salinity map. The retrieved salinity using a different model function is compared with in situ data collected by Argo floats to evaluate the impact and the performance of model functions. The results indicate that the new model function has significant improvements in salinity retrieval compared with other existing models.

Seawater↗
NASA NTRS2021

Debye Dielectric Model Function for Seawater Based on Expanded L-Band Measurement Data Set

New seawater dielectric measurements have recently been made over a broad range of salinities and temperatures at the George Washington University (GW). These measurements have been used to refine the existing dielectric model function of seawater for salinity retrieval. The mathematical structure of the new model function has been investigated to: (a) look for a physical basis for the mathematical form; and (b) to optimize the accuracy of data fitting. The Debye model has been chosen to represent the dielectric constant of seawater as a function of salinity (S), temperature (T) and frequency (f). The retrieved salinity using the Debye model has good agreement with the in-situ data collected by Argo floats. The global differences in retrieved salinity and in-situ data will be presented at the meeting.

ocean salinity↗
DOE OSTI2024

Enhancing the accuracy and generality of the Debye–Grüneisen Model: Optimizing the volume dependence for accurate predictions across varied compositions

In this work, we have introduced an optimized Debye-Grüneisen model that revolutionizes the determination of the Debye temperature and Grüneisen parameters. Unlike conventional methods, our model requires only the 0 K energy volume data for a material as input, eliminating the need to determine the bulk modulus and its pressure derivative, which often pose challenges due to numerical uncertainties. This unique feature sets our model apart from existing approaches and streamlines the process, enabling accurate predictions of thermal expansion behavior across various materials. To demonstrate its effectiveness, we showcase its excellent agreement with measured coefficients of thermal expansion (CTE) for the nickel-cobalt-chromium-aluminum-yttrium (Ni-Co-Cr-Al-Y) bond-coating system. Additionally, we apply our approach by conducting a high-throughput search for potential bond-coating materials among 90,000 compositions within the aluminum-cobalt-chromium-iron-nickel (Al-Co-Cr-Fe-Ni) system. From this extensive search, four compositions are synthesized, and the measured CTE values agree very well with theoretical predictions, hence validating our approach. In conclusion, the current optimized Debye-Grüneisen model combined with Density Functional Theory (DFT)-based thermodynamic database enables reliable and efficient high-throughput calculations of CTE of of a material without expensive phonon calculations.

Bond coating materials↗
DOE OSTI2019

An analytic expression approximating the Debye heat capacity function

It is important to have analytic expressions for critical functions in the equations of state of materials. The Debye model has been very successful in approximating the thermal energy properties of a variety of solids, but is nonanalytic. Existing approximations suffer from various shortcomings, the most common being lack of applicability over some temperature range. A new analytic and integrable functional form that closely approximates the Debye model for the heat capacity is presented. This form, based on the mean of two Einstein heat capacity functions with a low temperature correction, exhibits deviations from the Debye model smaller than typical experimental scatter in heat capacity data.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Vibrational Properties of Pd Nanocubes

The atomic disorder and the vibrational properties of Pd nanocubes have been studied through a combined use of X-ray diffraction and molecular dynamics simulations. The latter show that the trend of the mean square relative displacement as a function of the radius of the coordination shells is characteristic of the nanoparticle shape and can be described by a combined model: A correlated Debye model for the thermal displacement and a parametric expression for the static disorder. This combined model, supplemented by results of line profile analysis of the diffraction patterns collected at different temperatures (100, 200, and 300 K) can explain the observed increase in the Debye–Waller coefficient, and shed light on the effect of the finite domain size and of the atomic disorder on the vibrational properties of metal nanocrystals.

36 MATERIALS SCIENCE↗
DOE OSTI2022

LiMo 8 O 10 : Polar Crystal Structure with Infinite Edge-Sharing Molybdenum Octahedra

Here, polycrystalline LiMo 8 O 10 was prepared in a sealed Mo crucible at 1380 °C for 48 h using the conventional high-temperature solid-state method. The polar tetragonal crystal structure (space group I4 1 md) is confirmed based on the Rietveld refinement of powder neutron diffraction and 7 Li/ 6 Li solid-state NMR. The crystal structure features infinite chains of Mo 4 O 5 (i.e., Mo 2 Mo 4/2 O 6/2 O 6/3 ) as a repeat unit containing edge-sharing Mo 6 octahedra with strong Mo–Mo metal bonding along the chain. X-ray absorption near-edge spectroscopy of the Mo-L 3 edge is consistent with the formal Mo valence/configuration. Magnetic measurements reveal that LiMo 8 O 10 is paramagnetic down to 1.8 K. Temperature-dependent resistivity [ρ(T)] measurement indicates a semiconducting behavior that can be fitted with Mott’s variable range hopping conduction mechanism in the temperature range of 215 and 45 K. The ρ(T) curve exhibits an exponential increase below 5 K with a large ratio of ρ 1.8 /ρ 300 = 435. LiMo 8 O 10 shows a negative field-dependent magnetoresistance between 2 and 25 K. Heat capacity measurement fitted with the modified Debye model yields the Debye temperature of 365 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Theoretical Study of Structural, Magnetic, Elastic, Phonon, and Thermodynamic Properties of Heusler Alloys Fe{sub 2}CrX (X = Al, Ga)

First-principle calculations based on generalized gradient approximation and quasi-harmonic Debye model were executed to analyze the structural, magnetic, elastic, phonon, and thermodynamic properties of Fe{sub 2}CrX (X = Al, Ga) Heusler alloys. The computed lattice parameters concurred well with available experimental and theoretical data. The calculated elastic constants reveal that the Fe{sub 2}CrAl is brittle and Fe{sub 2}CrGa is ductile. The phonon dispersion relation of Fe{sub 2}CrX (X = Al, Ga) are calculated using finite displacement method with a cutoff radius of 5 Å. We likewise explored the thermodynamic properties by utilizing quasi-harmonic Debye model in which bulk modulus, heat capacity, Debye temperature, Grüneisen parameter, and thermal expansion coefficient are resolved at 0–30 Gpa pressure and 0–900 K temperature from the non-equilibrium Gibbs functions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2017

Influence of Plasma Environment on K-Line Emission in Highly Ionized Iron Atoms Evaluated Using a Debye-Huckel Model

The influence of plasma environment on the atomic parameters associated with the K-vacancy states has been investigated theoretically for several iron ions. To do this, a time-averaged Debye-Huckel potential for both the electron-nucleus and electron-electron interactions has been considered in the framework of relativistic multiconfiguration Dirac-Fock computations. More particularly, the plasma screening effects on ionization potentials, K-thresholds, transition energies, and radiative rates have been estimated in the astrophysical context of accretion disks around black holes. In the present paper, we describe the behavior of those atomic parameters for Ne-, Na-, Ar-, and K-like iron ions.

Deprince, J.↗
DOE OSTI2019

Theoretical Study of Mechanical Stability and Physical Properties of Co{sub 2}V{sub 1−x}Zr{sub x}Ga

The mechanical stability and physical properties of Co{sub 2}V{sub 1−x}Zr{sub x}Ga (x = 0, 0.25, 0.50, 0.75, 1) have been predicted by using ab initio calculations based on density functional theory. The exchange-correlation potentials are treated within the generalized gradient approximation-Perdew-Burke and Ernzerhhof (GGA-PBE) and Hubbard coefficient (GGA+U). The investigated minimum lattice parameter of Co{sub 2}VGa is 5.8030 Å, which is in excellent agreement with available experimental and theoretical data and for Co{sub 2}V{sub 1−x}Zr{sub x}Ga (x = 0.25, 0.50, 0.75, 1) are 5.9026, 5.9625, 6.0060 and 6.0021 Å, respectively, which are predicted for the very first time. The total magnetic moments decrease with increasing concentration of x in Co{sub 2}V{sub 1−x}Zr{sub x}Ga, in agreement with the Slater-Pauling rule. Band structure and density of states calculations show that the minority spin channel exhibits band gaps of 0.43, 0.46, 0.52, 0.54 and 1.01 eV for GGA+U scheme around the Fermi level confirming that all the studied composites are half-metallic in nature. In this study, we also studied the elastic constant and it is established that all the materials are mechanically stable and ductile in nature. The Co{sub 2}VGa is stiffer than other materials and all the studied composites have anisotropic behaviour. Moreover, by using a quasi-harmonic Debye model and calculated elastic constant, the Debye temperature and temperature-dependent constant volume heat capacity have been investigated.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Simulating dielectric spectra: A demonstration of the direct electric field method and a new model for the nonlinear dielectric response

Here we demonstrate a method to compute the dielectric spectra of fluids in molecular dynamics (MD) by directly applying electric fields to the simulation. We obtain spectra from MD simulations with low magnitude electric fields (≈0.01 V/Å) in agreement with spectra from the fluctuation–dissipation method for water and acetonitrile. We examine this method’s trade-off between noise at low field magnitudes and the nonlinearity of the response at higher field magnitudes. We then apply the Booth equation to describe the nonlinear response of both fluids at low frequency (0.1 GHz) and high field magnitude (up to 0.5 V/Å). We develop a model of the frequency-dependent nonlinear response by combining the Booth description of the static nonlinear dielectric response of fluids with the frequency-dependent linear dielectric response of the Debye model. We find good agreement between our model and the MD simulations of the nonlinear dielectric response for both acetonitrile and water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Analysis of Experimental Results by the Havriliak–Negami Model in Dielectric Spectroscopy

The problem of identifying experimental results on studying frequency dependences of the real and imaginary parts of dielectric permittivity concerning the correspondence to one of accepted frequency dispersion models: Debye, Cole–Cole, Davidson–Cole, and Havriliak–Negami models is considered. Based on expressions for components of complex dielectric permittivity with the use of mathematical analysis, a sequence of steps for the determination of the following characteristic parameters of the generalized Havriliak–Negami model is developed: static ε{sub S} and high-frequency ε{sub ∞} dielectric permittivity, frequency dispersion indices α and β, and relaxation time τ. As an example, the parameters ε{sub S}, ε{sub ∞}, α, β, and τ are calculated for a sample of a frozen disperse medium based on fine-grained quartz powder at a humidity of 13% in a temperature range from –140 to 0°C.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Heat Capacity and Mössbauer Study of Self-Flux Grown FeTe Single Crystal

We report mainly the heat capacity and Mössbauer study of self-flux grown FeTe single crystal, which is a ground state compound of the Fe chalcogenides superconducting series i.e. FeTe{sub 1−x}(Se/S){sub x} The as grown FeTe single crystal is large enough to the tune of a few centimetres and the same crystallizes in tetragonal structure having space group of P4/nmm. FeTe shows the structural/magnetic phase transition at 70 K in both magnetic and resistivity measurements. Heat capacity measurement also confirms the coupled structural/magnetic transition at the same temperature. The Debye model fitting of low temperature (below 70 K) heat capacity exhibited Debye temperature (𝜃{sub D}) to be 324 K. Mössbauer spectra are performed at 300 and 5 K. The 300-K spectra showed two paramagnetic doublets and the 5-K spectra exhibited hyperfine magnetic sextet with an average hyperfine field of 10.6 Tesla matching with the results of Yoshikazu Mizuguchi et al.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

First-Principles Investigation of Ferromagnetic, Thermodynamic, Elastic, and Half-Metallic Behavior of ReCrTe and RuCrTe Half-Heusler Alloys

Calculations are realized within the full-potential linearized augmented plane wave (FP-LAPW) computational approach with the generalized gradient approximation (GGA) for the exchange-correlation potential. In this work, we present investigation of structural, electronic, ferromagnetic, elastic, and thermodynamic properties and half-metallic behavior of ReCrTe and RuCrTe compounds. Analysis of band structures and densities of states show the half-metallic ferromagnetic behavior of these compounds. The values of total magnetic moments µ{sub tot} are 1 µ{sub B} per unit cell for ReCrTe and 3 µ{sub B} per unit cell for RuCrTe. The contribution of Cr is the most important. The calculated values of a total magnetic moment nicely follow the rule µ{sub tot} = Z{sub t}− 18. The study of the impacts of strains on the magnetic moment reveals that the two compounds are stable ferromagnetic compounds. RuCrTe compound preserves the half-metallic behavior when the unit cell volume is changed in the range of [ − 4%, 4%], whereas, weak strain destroys the half metallic nature for ReCrTe compound. Using the quasi-harmonic Debye model, the effects of pressure P and temperature T on thermal expansion coefficient, Debye temperature, heat capacity and Grüneisen parameter for these two compounds are investigated for the first time. The study of the elastic constants shows that ReCrTe and RuCrTe are mechanically stable. RuCrTe is stiffer than ReCrTe compounds. The obtained values of Pugh’s ratio B/G and Cauchy pressure (C{sub 12} − C{sub 44}) reveal that ReCrTe and RuCrTe are brittle. The study of the electron charge density and Poisson’s ratio proves that the ionic character dominates the atomic bonding for the two compounds.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Complete Equations of State for Cyclotetramethylene Tetranitramine

Complete equations of state for the volumetric deformation of the β-polymorph of cyclotetramethylene tetranitramine (β-HMX) have been derived from its Helmholtz free energy. Dispersion-corrected density functional theory calculations were used to compute the dependence of the frequencies of the vibrational normal modes on specific volume. Here, the normal mode frequencies were used directly to generate both a tabular equation of state and an approximate model where the sum over normal mode frequencies is replaced by a set of five Debye models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Effect of Temperature and Pressure on Structural and Magnetic Properties of Strontium-Filled Skutterudites SrT{sub 4}Sb{sub 12}: LDA and LSDA Calculations

The structural, elastic, thermodynamic, magnetic, and electronic properties of strontium-filled skutterudite component SrFe{sub 4}Sb{sub 12} using the full potential-linear muffin-tin orbital (FP-LMTO) calculation were studied. The local density approximation (LDA) and local spin density approximation (LSDA) for predicting the physical properties were used. The internal parameters used to calculate the ground state properties such as lattice constant, bulk modulus, and its derivative pressure were optimized. Then, we have deduced the elastic constants, shear modulus G, Young modulus E, Poisson’s ratio ν, anisotropic parameter A, ratio B/G, and the Debye temperature (𝜃{sub D}). The quasi-harmonic Debye model as implemented in the Gibbs program is applied to determine the thermal properties such as the Debye temperature (𝜃{sub D}), heat capacity C{sub v} and C{sub p}, thermal expansion coefficient α Helmholtz free energy (A), Gibbs free energy (G), entropy (S) and internal energy (U) at different pressures and temperatures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1995

Thermal Line Shift and Broadening of Ho(3+) in Y3AI5O12 and Lu3AIO12

The interaction between the active ion and the host lattice manifests itself in two distinct ways: the static interaction with the crystal field that causes the splitting of the free ion energy levels and the active interaction through the surrounding phonon system that produces temperature dependent characteristics in the optical spectrum of the ion (e.g. line broadening and line shift). The strength of the splitting depends heavily on the electronic configuration of the atom. The model give by McCumber and Sturge describes the thermal effects on line width and position above 77 K with Raman scattering of Debye model phonons. These processes predict a Lorentzian line shape. However, below 77 K the principal contributions are from crystal inhomogeneities that result in a Gaussian line shape. We have investigated the experimental Stark levels as well as the thermal effects on the line width and the position of trivalent holmium ions in both yttrium aluminum garnet, Y3Al5O12 (YAG) and lutetium aluminum garnet, Lu3Al5O12 (LuAG) crystals. We have compared the Stark levels of the (5)I(6) state, and the thermal line shift and broadening of an isolated transition (Z2 to X13) between the (5)I(8) and (5)I(6) stark levels in these crystals. This transition occurs in the near infrared region at approximately 1117 nm.

Snoke, Elizabeth R.↗