A Parameter-Free First-Principles-Based Debye Model to Predict Thermodynamic Properties of Complex Alloy Systems
For presentation at CALPHAD 50, Cambridge, MA, June 25-30, 2023
Wang, Yi↗
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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↗
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↗
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↗
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↗
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↗
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↗
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↗
EXAFS investigation of the local structure in URu 2-x Fe x Si 2 : Evidence for distortions below 100 K
X-ray absorption measurements at the U L III , Ru K , and Fe K edges are reported for the hidden order (HO) material URu 2 - x Fe x Si 2 ( x = 0 , 0.05, 0.08, 0.10, 0.12, 0.15, and 0.20) as a function of x and temperature T . Furthermore, when Fe is substituted for Ru, the local structure about Fe shrinks slightly and the first neighbor Fe-Si bond length decreases by ≈ 0.05 Å . More importantly excess disorder is observed below 80–100 K (the coherence temperature T * ) in plots of the Debye-Waller factor σ 2 ( σ is the width of the pair distribution function); at low T the data deviate from the usual Einstein or correlated-Debye model plots. This excess disorder is most prominent for the Ru-Si bond, and σ 2 actually increases below 80 K. These results suggest a local orthorhombic distortion with B 1 g -like symmetry that develops below 80–100 K. A model that describes these local distortions is presented, and discussed in terms of other measurements that indicate a breaking of fourfold symmetry at low T . In addition, the square root of the difference between σ 2 ( T ) for the Ru-Si pair and a Debye fit to these data serves as an order parameter for this orthorhombic distortion, in the temperature range below 100 K. This quantity is a length related to a - b , the difference between the a and b lattice constants in the orthorhombic phase, and provides a connection between this distortion and T * . X-ray absorption near edge structure (XANES) measurements also show that there are no changes in the edge positions down to 0.1 eV for any edge as a function of x , for T in the HO regime.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
High Throughput Computational Framework of Materials Properties for Extreme Environments
This project aims to establish a framework capable of efficiently predicting the properties of structural materials for service in harsh environments over a wide range of temperatures and over long periods of time. The approach is to develop and integrate high throughput first-principles calculations in combination with machine learning (ML) methods, perform high throughput CALPHAD (calculations of phase diagrams) modeling, and carry out finite element method (FEM) simulations. Relevant to high temperature service in fossil power system, nickel-based superalloys such as Inconel 740 and Haynes 282 as well as the associated (Ni-Cr-Co)-Al-C-Fe-Mn-Mo-Nb-Si-Ti system, were investigated. The present framework was built on the concept of phase-based property data, in which properties of individual phases are modeled as a function of internal and external independent variables. This project established an open-source infrastructure with the following capabilities: (1) High throughput implementation of first-principles calculations at finite temperatures and variable compositions using both accurate phonon calculations and the efficient Debye model for thermodynamic properties, elastic constants, diffusion coefficients, vacancy formation, stacking and twin faults, and dislocation mobility; i.e., using the developed code DFTTK; (2) Machine learning capabilities to predict the above properties so that the number of first-principles calculations can be significantly reduced; e.g., using the developed code SIPFENN; (3) High throughput CALPHAD modeling of the above properties as a function of temperature and composition using our unique capability based on ESPEI and PyCalphad; (4) New capabilities to predict the stress-strain behavior of individual phases; and (5) New models for tensile strength prediction in common FEM software with the crystal plasticity finite element simulations (CPFEM).
, Ni-based superalloys↗
P-V-T equation of state of boron carbide
We report the P-V-T equation of state measurements of B 4 C to 50 GPa and approximately 2500 K in laser-heated diamond anvil cells. We obtain an ambient temperature, third-order Birch–Murnaghan fit to the P-V data that yields a bulk modulus K 0 of 221(2) GPa and derivative, (dK/dP) 0 of 3.3(1). These were used in fits with both a Mie–Grüneisen–Debye model and a temperature-dependent, Birch–Murnaghan equation of state that includes thermal pressure estimated by thermal expansion (α) and a temperature-dependent bulk modulus (dK 0 /dT). The ambient pressure thermal expansion coefficient (α 0 + α 1 T), Grüneisen γ(V) = γ 0 (V/V 0 ) q and volume-dependent Debye temperature, were used as input parameters for these fits and found to be sufficient to describe the data in the whole P-T range of this study.
36 MATERIALS SCIENCE↗
Magneto-Electronic, Thermodynamic, and Thermoelectric Properties of 5f-Electron System BaBkO{sub 3}
In the present work, the structural, electronic, magnetic, mechanical, thermodynamic, and thermoelectric properties of cubic perovskite BaBkO{sub 3} were investigated within the framework of density functional theory using generalized gradient approximation, onsite Coulomb interaction, and modified Becke-Johnson methods. BaBkO{sub 3} is stable in the ferromagnetic phase with a magnetic moment of 7 μ{sub B}. The spin-polarized electronic band structure reveals 100% spin polarization of the material with metallic character in spin-up state and semiconducting in spin-down state. Pugh and Cauchy relation displays that the material is highly ductile. The quasi-harmonic Debye model was used to determine the thermodynamic properties of BaBkO{sub 3} under high pressure and temperature. BaBkO{sub 3} presents high value of Seebeck coefficient and power factor at room temperature with a value of 135 μVK{sup − 1} and 1.5 × 10{sup 12}μWcm{sup − 1} K{sup − 2} s{sup − 1}, respectively. The possession of half metallicity and high Seebeck coefficient makes BaBkO{sub 3} suitable for spintronic and thermoelectric device applications.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Effect of High Pressure and Temperature on Magneto-Electronic, Thermodynamic, and Transport Properties of Antiferromagnetic HoPdX (X = As, Ge) Alloys
We present electronic, magnetic, thermoelectric, and thermodynamic properties of half-Heusler HoPdAs and HoPdGe materials in stable α-phase. They crystallize in cubic MgAgAs-type structure. The stable phase is found to be antiferromagnetic in comparison to the other magnetic and nonmagnetic states. The electronic structure calculations display the metallic behavior in both spin states. The effect of pressure and temperature on unit cell volume, thermal expansion coefficient, heat capacity, and Grüneisen parameter have also been analyzed using the quasi-harmonic Debye model. The alloys present a high absolute Seebeck coefficient with a value of 203.26 μV/K for HoPdAs and 53.19 μV/K for HoPdGe at room temperature.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Theoretical predictive screening of noble-metal-containing M 3 AuC 2 (M = Ti, V, and Cr) MAX phases
Using first-principles density functional theory (DFT), the ground state physical properties of the newly synthesized noble-metal-containing Ti 3 AuC 2 MAX phase have been investigated. The effect of transition-element Ti replacement (V and Cr) on physical properties, including structural, elastic, electronic, thermal, and optical are presented. The optimized lattice parameters of Ti 3 AuC 2 MAX phase are in good agreement with the experimental values and decrease when we replace Ti with V and then Cr. The magnetic properties of M 3 AuC 2 are predicted by using generalized gradient approximation (GGA) incorporating onsite electron correlation parameter (Hubbard U parameter) within DFT. Out of three studied MAX phases, V 3 AuC 2 and Cr 3 AuC 2 phases exhibit magnetism. The thermodynamical stability of M 3 AuC 2 (M = Ti, V, and Cr) phases is discussed by the formation enthalpy with respect to their most competing phases. The electronic structure reveals that these phases have metallic nature and are electrically anisotropic. The M-element replacement has an effect on the bonding properties of M 3 AuC 2 . The bonding between M-C is in the order of Cr 3 AuC 2 > V 3 AuC 2 > Ti 3 AuC 2 according to their peak positions and heights of density of states in the occupied site, which is also confirmed from the charge density distribution. The elastic properties indicate that M 3 AuC 2 phases are ductile, machinable, less stiff, and better resistant to thermal shock and are elastically anisotropic. To understand the properties of M 3 AuC 2 for the extreme environment, we employed a quasi-harmonic Debye model at the pressure and temperature range of 0–50 GPa and 0–1600 K, respectively. Additionally, we evaluated thermal conductivity and melting temperature to further understand the potential of these MAX phases in coating applications at elevated temperature. In relation to optical properties, these MAX phases have a reasonable absorption coefficient in the visible as well as in the ultra-violet regions. The reflectivity of M 3 AuC 2 phases is polarization dependent and of 45 % against the visible region, which reveals its potential as coating material to minimize solar heating.
312 MAX phases↗
Structural and thermodynamic effects of hydration in Na-zeolite A (LTA) from low-temperature heat capacity
Zeolite A (Linde Type A; LTA) is an industrially important porous mineral that has recently been shown to exhibit framework flexibility upon changes in hydration level. Here, to investigate the flexibility transition from a thermodynamic perspective, we have performed heat capacity measurements on sodium zeolite A at seven incremental hydration levels ranging from zero to equilibrium with ambient air. Excess low-frequency vibrations beyond the predictions of the Debye model are found in all samples, and the frequency of these vibrations increases as a function of hydration level. This suggests that an increase in hydration causes a decrease in at least one type of framework flexibility for sodium zeolite A. In addition, a subtle excess heat capacity contribution from 150 to 280 K is observed only for low and intermediate hydration levels, which may arise from a transformation tied to framework flexibility previously observed in zeolite A via gas absorption calorimetry. Values of the standard thermodynamic functions C p,m °, Δ 0 T S m °, Δ 0 T H m °, and Φ m ° are also reported.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Structural, Electronic, and Thermal Properties of CdSnAs 2
Structural, electrical, and thermal properties of CdSnAs 2 , with analyses from temperature-dependent transport properties over a large temperature range, are reported. Phase-pure microcrystalline powders were synthesized that were subsequently densified to a high-density homogeneous polycrystalline specimen for this study. Temperature-dependent transport indicates n-type semiconducting behavior with a very high and nearly temperature independent mobility over the entire measured temperature range, attributed to the very small electron effective mass of this material. The Debye model was successfully applied to model the thermal conductivity and specific heat. Furthermore, this work contributes to the fundamental understanding of this material, providing further insight and allowing for investigations into altering this and related physical properties of these materials for technological applications.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
In Situ EXAFS-Based Nanothermometry of Heterodimer Nanocrystals under Induction Heating
The ability to heat nanocrystalline materials through magnetic induction has been used in the fields of catalysis, biomedical sciences, and polymer degradation. However, the working temperature to which the inductively coupled material rises is still poorly understood. Herein, we use extended X-ray absorption fine structure spectroscopy in conjunction with thermal imaging to improve the understanding of heating in inductively coupled systems. After extraction of the Debye–Waller factor from the spectroscopy, we obtain the temperature of inductively heated nanocrystals from the correlated Debye model. We combine carbon-supported iron oxide nanocrystals as induction heating agents with platinum nanocrystals as thermal probes. By testing these nanocrystal species as both unattached nanocrystals and heterodimers, we report that nanostructured systems show a significant temperature difference of up to 73.60 °C when compared to their local support environment. Furthermore, this result has implications for inductively heated catalysis, magnetic hyperthermia for targeted cell death, and polymer synthesis.
09 BIOMASS FUELS↗
Phase Transitions and Thermal Equation of State of Fe‐9wt.%Si Applied to the Moon and Mercury
Abstract Accurate knowledge of the phase transitions and thermoelastic properties of candidate iron alloys, such as Fe‐Si alloys, is essential for understanding the nature and dynamics of planetary cores. The phase diagrams of some Fe‐Si alloys between 1 atm and 16 GPa have been back‐extrapolated from higher pressures, but the resulting phase diagram of Fe 83.6 Si 16.4 (9 wt.% Si) is inconsistent with temperature‐induced changes in its electrical resistivity between 6 and 8 GPa. This study reports in situ synchrotron X‐ray diffraction (XRD) measurements on pre‐melted and powder Fe 83.6 Si 16.4 samples from ambient conditions to 60 GPa and 900 K using an externally heated diamond‐anvil cell. Upon compression at 300 K, the bcc phase persisted up to ∼38 GPa. The hcp phase appeared near 8 GPa in the pre‐melted sample, and near 17 GPa in the powder sample. The appearance of the hcp phase in the pre‐melted sample reconciles the reported changes in electrical resistivity of a similar sample, thus resolving the low‐pressure region of the phase diagram. The resulting high‐temperature Birch‐Murnaghan equation of state (EoS) and thermal EoS based on the Mie‐Gruneisen‐Debye model of the bcc and hcp structures are consistent with, and complement the literature data at higher pressures. The calculated densities based on the thermal EoS of Fe‐9wt.%Si indicate that both bcc and hcp phases agree with the reported core density estimates for the Moon and Mercury.
Berrada, Meryem↗