Thermal Lattice Vibrations Research Articles

Praseodymium doped ceria: A new sight on coupled thermo-mechanical properties and oxygen vacancy diffusion via statistical moment approach

Applications of praseodymium doped ceria (PDC) in solid oxide fuel cells require a deep insight into the thermal expansion, stresses, and ionic conduction. Nonetheless, the investigation of thermo-mechanical properties and oxygen vacancy diffusion remains incomplete. Based on free Helmholtz energy, we formulate analytical expressions to directly connect thermal expansion coefficient, elastic moduli, oxygen vacancy–dopant binding and oxygen vacancy migration energies by employing statistical moment method (SMM). The SMM calculations capture the full anharmonicity of lattice thermal vibrations. Our analyses report the significant influences of temperature and dopant content on the thermal expansion coefficient, bulk and Young’s moduli, oxygen vacancy–dopant binding and oxygen vacancy migration energies, and ionic conductivity. The role of Pr dopant on the oxygen vacancy diffusion is fully described by combining the symmetric energy profiles related to blocking effect and asymmetric energy profiles generated from trapping effect. By switching van der Waals (vdW) forces on and off in the SMM calculations, we first show that the vdW forces cause a positive effect on the mechanical properties but reduce the thermal expansion and resist the oxygen vacancy diffusion. Our findings are discussed concerning the results from other calculations and experiments in the literature. The insights on the thermo-mechanical properties and oxygen vacancy diffusion for PDC crystal can be generalized and applied to other ceramic materials that are essential for solid state batteries.

Fracture behaviors and microstructure evolution of an Al–Mg–Mn-Sc-Zr alloy at elevated and cryogenic temperature

The mechanical properties and fracture behavior of Al-5.8Mg-0.4Mn-0.25Sc-0.1Zr alloy were investigated across cryogenic temperatures (−196.15 °C ∼ −56.15 °C) and elevated temperature (room temperature ∼ 250 °C), with results indicating sensitivity of the alloy's mechanical properties to temperature. Firstly, the tensile test at elevated temperatures shows a decrease in strength and strain hardening exponent (n) due to thermal softening effects, while elongation increases and then decreases, peaking at 100 °C. Within the temperature range of −196.15 °C ∼ −56.15 °C, the yield stress (YS), ultimate tensile strength (UTS), and ductility tend to increase with the decreasing temperature gradually, which can be attributed to the decrease in lattice thermal vibration energy at low temperatures, resulting in an elevated external force requirement for dislocation motion. Meanwhile, throughout the entire high-temperature range, the alloy exhibits ductile fracture, with the number of dimples peaking at 100 °C. Differently, when the alloy is deformed at low temperatures, dislocations tend to accumulate within the grains, and with the grain boundaries acting as weak bonding areas between grains and experiencing significant stress concentration, the fracture mechanism gradually transitions from transgranular to intergranular fracture. Microstructural analysis at low temperatures shows minimal texture content changes, while at elevated temperatures, regular changes in texture components occur due to grain orientation rearrangement. Furthermore, high-resolution transmission electron microscopy was employed to investigate the evolution of precipitates at various temperatures, and the results shows that uniform and fine Al3(Sc1−x, Zrx) precipitates are distributed within the crystal, acting as effective dislocation pinning sites and leading to a uniform intragranular dislocation arrangement after tensile test at cryogenic temperature. Notably, after tensile test at higher temperatures, a few precipitates lose coherency with the matrix and started growing, which diminishing grain boundary pinning effect and promoting recrystallization.

Investigation of Debye temperature and temperature-dependent EXAFS cumulants of Zn, Zr, α-Ti, Ru and Hf metals

In this work, the anharmonic Einstein model is developed to determine the Debye temperature and investigate the temperature effects on the extended x-ray absorption fine structure (EXAFS) cumulants of hexagonal close-packed (hcp) metals. We have derived the analytical expressions of the anharmonic effective potential, the effective force constant, the Debye temperature and the first four EXAFS cumulants as a function of axial ratio e = c/a. Numerical calculations have been conducted for hcp Zn, Zr, α-Ti, Ru and Hf metals up to temperature 800 K. Our findings indicate that the anharmonicity of thermal lattice vibrations significantly influences the EXAFS cumulants, particularly at high temperatures. Ru atoms have the strongest coupling force causing a phenomenon that Ru lattice shows a smaller thermal disorder, and Zn has a greater thermal disorder. Additionally, we highlight the significant contributions of thermal disorder to the mean-square relative displacement at high temperatures due to thermal lattice vibrations. Moreover, our Debye temperatures derived from the developed model align reasonably well with those reported in previous studies.

Thermal expansion, lattice vibration, and isotope effect on hydrogen diffusion in BCC Fe, Cr, and W from first-principles calculations.

Fe, Cr, and W are important elements in the alloys of in-reactor materials and operate in high-temperature environments with thermal expansion. Their tritium-impeding abilities are crucial to the radiation safety of various nuclear reactors. In this study, first-principles density functional theory is combined with quasi-harmonic approximation to evaluate factors that can affect the interstitial formation energy and diffusion coefficient of hydrogen isotopes in body-centered cubic (BCC) Fe, Cr, and W, including thermal expansion, metal host lattice vibrations, phonon density-of-states (pDOS) coupling diffusing atoms, and isotope effects. Calculation results indicate that the interstitial formation energy decreases as lattice expansion increases, whereas the jump barriers remain almost constant. Thermal expansion, host lattice vibration, and pDOS coupling minimally affect the diffusion coefficients of hydrogen isotopes in Fe, Cr, and W. The diffusion coefficient ratios between hydrogen isotopes are higher than the inverse ratio of the square root of the isotope mass at low temperatures. However, they decrease to the inverse ratio of the square root of the isotope mass at temperatures exceeding 800K. This study comprehensively investigates factors that affect the diffusion coefficients of hydrogen isotopes in BCC Fe, Cr, and W, thus providing a firm theoretical foundation for predicting the diffusion coefficients of tritium at different temperatures using protium/deuterium diffusion coefficients.

Temperature dependence of phase stabilities of hexagonal hemicarbides from first principles

Transition metal hemicarbides, specifically M2C (where M = V, Nb, Ta, Mo and W), have received considerable attention in the fields of catalysis and metallurgy. However, the determination of the exact phase of each compound can still be challenging due to the close energetic proximity of its various polymorphs. This study uses first-principles calculations to carefully consider the subtle differences between different polymorphs, with temperature as a key factor. It is found that the energies of each polymorph of M2C are close, but can be distinguished when temperature effects are considered. This means that temperature plays an important role in the polymorph transformations. In addition, these phases exhibit dynamic stability at both zero and finite temperatures, in part due to the particular ordering of C atom occupancy in the metal lattice interstices. The study can provide calculations of a range of properties that help to identify stable structures and deepen the understanding of these materials in terms of chemical bonding, structural changes, lattice thermal vibrations and molecular dynamics.

Toward better understanding of anharmonic structural, thermodynamic, and elastic properties of CaSiO3 perovskite under extreme conditions via statistical moment method

CaSiO3 perovskite is thought to be the third most abundant minerals in both the Earth’s transition zone and lower mantle but its structural, thermodynamic, and elastic properties have not been well characterized. In this work, for the first time, we apply the statistical moment method (SMM) to determine analytical expressions of thermoelastic quantities such as isothermal and adiabatic elastic moduli, Grüneisen parameter, Young’s and shear moduli, compression wave and shear velocities including the full anharmonic effects of thermal lattice vibrations of perovskite crystals with cubic structure. The theoretical results are applied for numerical calculations for cubic CaSiO3 perovskite, which is a strongly anharmonic system, at temperatures and pressures up to 4000 K and 180 GPa corresponding to the extreme conditions of the Earth’s lower mantle. Our results for temperature and pressure dependences of unit cell volume, thermal expansivity, isochoric and isobaric heat capacities, Grüneisen parameter, isothermal and adiabatic elastic moduli, Young’s and shear moduli, compression wave and shear velocities are important signs of anharmonic effects under high temperatures and pressures. The SMM results are compared with experiments and other calculations. The present study provides an effective theoretical approach for finding the structural, thermodynamic, and elastic properties of strongly anharmonic materials under extreme conditions.

High-pressure high-temperature EXAFS and Debye–Waller factor of platinum

The temperature and pressure effects on the mean-square relative displacement (MSRD) corresponding to the extended X-ray absorption fine structure (EXAFS) Debye–Waller factor of platinum have been studied based on the statistical moment method in quantum statistical mechanics. We implement numerical calculations for platinum up to pressure of 400 GPa. Examining the temperature effects on the EXAFS Debye–Waller factor at ambient pressure we show that theoretical MSRD curve is in good agreement with the previous measurement and calculations up to nearly 800 K. When pressure increases, our pressure-dependent MSRD curve follows very well with the prediction based on the numerical integration along the Hugoniot. Using the theoretical EXAFS Debye–Waller factor, we obtain the Hugoniot temperatures which are highly consistent with recent experimental results. This research advances the correlated Einstein model on the calculation of MSRDs of materials at high temperature and high pressure, specifically, it includes the zero-point vibrations at low temperature and contains the anharmonicity contributions caused by thermal lattice vibrations at high temperature.

Performance of a deep convolutional neural network to classify crystal structures using selected area electron beam diffraction patterns containing lattice defect information.

A deep convolutional neural network (DCNN) architecture ResNet has been tested to verify its ability to handle selected area electron diffraction pattern (SADP) datasets carrying information on lattice defects including strains, thermal lattice vibrations, point defects, dislocations, and twin boundaries. The disordered states of the crystal lattices in the presence of these defects were predicted by ab initio molecular dynamics simulations, first principles geometry optimizations, and lattice manipulation operations in an effort to establish a possible dataset augmentation strategy for the improvement of classification performance of the ResNet. Using the disordered lattice information originating from the defects, test dataset SADPs were generated by simulating electron diffraction in transmission electron microscopy. The ResNet, pre-trained using SADPs from defect-free materials, showed decreasing but acceptable classification accuracies with increasing degrees of lattice disorder regarding the lattice vibrations and point defects. When tested using the diffraction patterns for strained lattices, the ResNet responded to the changing lattice symmetry when strain levels are relatively high suggesting that it has capability to discern different symmetries induced by large strains. However, the ResNet failed to recognize lattice structure when dislocations and twin boundaries were considered. It is suggested that DCNN architectures be trained over various scenarios including changes in the image feature characteristics in the diffraction patterns related to defects in future developments for improved general classification performances.

Unleashing multi-scale mechanical enhancement in NiTi shape memory alloy via annular intra-laser deposition with homogenized Ti2Ni nanoprecipitates

Additive manufacturing (AM) of composition-sensitive NiTi shape memory alloys (SMAs) is hindered by uncontrollable non-equilibrium microstructures, leading to functional performance degradation and limitations in high-throughput net-shaping applications. To address these challenges, we propose a novel approach combining annular intra-laser directed energy deposition (AIL-DED) with a tailored gradient post-treatment process. This enables the fabrication of nanocomposite microstructures in NiTi SMAs with precise control over the homogenization of Ti2Ni nanoprecipitates. In-situ monitoring and characterization of thermal history, microstrain, and constitutional phases, were utilized to uncover the relationship between multi-scale structural features and mechanical responses. The interplay between laser reflectivity, energy input, and lattice thermal vibrations affects forming quality in AIL-DED. Dynamic temperature variations were studied before reaching thermal equilibrium, revealing insights into thermal and mechanical interactions during the process. These findings contribute to understanding challenges in fabricating high-quality NiTi SMAs. Examining phase transformation behavior and its correlation with processing parameters deepens understanding of microstructural evolution and provides insights for tailoring material properties. The stress relaxation and dislocation evacuation at elevated temperatures caused the expansion of lattice and interplanar spacing in the age-treated SMA's B2 matrix phase, exhibiting a stable two-step phase transformation behavior (B19′↔R↔B2). AIL-DED combined with two-stage heat treatment strategy demonstrated enhanced homogeneity of non-equilibrium microstructures, resulting in the formation of high-density, well-dispersed Ti2Ni nanoprecipitates, with a semi-coherent interface to B2 matrix. The combination of load-bearing strengthening through well-dispersed Ti2Ni nanoprecipitates and Orowan strengthening at the semi-coherent interface yielded simultaneous enhancements in nanohardness, ultimate compressive strength, compressive fracture strain, and deformation recovery, following the AIL-DED combined with two-stage heat treatment process. The fracture mechanism transitioned from a mixture of brittle-ductile behavior to predominantly ductile characteristics. This study provides valuable insights that advance additive manufacturing and enhance the functional performance of SMAs in critical applications.

Spin Coherence and Spin Relaxation in Hybrid Organic-Inorganic Lead and Mixed Lead-Tin Perovskites.

Metal halide perovskites make up a promising class of materials for semiconductor spintronics. Here we report a systematic investigation of coherent spin precession, spin dephasing and spin relaxation of electrons and holes in two hybrid organic-inorganic perovskites MA0.3FA0.7PbI3 and MA0.3FA0.7Pb0.5Sn0.5I3 using time-resolved Faraday rotation spectroscopy. With applied in-plane magnetic fields, we observe robust Larmor spin precession of electrons and holes that persists for hundreds of picoseconds. The spin dephasing and relaxation processes are likely to be sensitive to the defect levels. Temperature-dependent measurements give further insights into the spin relaxation channels. The extracted electron Landé g-factors (3.75 and 4.36) are the biggest among the reported values in inorganic or hybrid perovskites. Both the electron and hole g-factors shift dramatically with temperature, which we propose to originate from thermal lattice vibration effects on the band structure. These results lay the foundation for further design and use of lead- and tin-based perovskites for spintronic applications.

Probabilistic-Bits Based on Ferroelectric Field-Effect Transistors for Probabilistic Computing

A probabilistic bit (p-bit) is the fundamental building block in the circuit of probabilistic computing (PC), and it produces a random binary bitstream with tunable probability. Utilizing the randomness induced by thermal noise-induced lattice vibration in the ferroelectric (FE) material, we propose the p-bits based on stochastic ferroelectric FET (FeFET). The domain dynamic is revealed to play crucial roles in FE p-bits’ stochasticity, as the domain coupling suppresses the dipole fluctuation. The proposed FE p-bits possess the advantages of both extremely low hardware cost and scalability for p-bit circuitry, rendering it a promising candidate for PC.

Temperature effects on thermodynamic and mechanical properties of the InP, InAs and InSb compounds

The thermodynamic and mechanical properties of the zinc-blende indium pnictides InP, InAs and InSb compounds have been investigated thanks to the statistical moment method in statistical mechanics. We have derived the analytical expressions of thermal induced atomic displacement, lattice constant, elastic moduli (Young’s modulus, bulk modulus and shear modulus) and elastic constants of the zinc-blende compounds. The difference of temperature effects on mechanical properties of InSb comparing to InP and InAs compounds has been pointed out. We show that InSb is less affected by temperature while InP changes its mechanical properties from hardness to softness quickly when the temperature increases. The advancement of this method is that it has included the anharmonic effects of thermal lattice vibrations by taking into account the higher-order atomic displacement terms.

Thermal transport properties and lattice vibration modes in crystalline and amorphous LaMgAl11O19

Thermal energy transport plays a crucial role in determining the performance of LaMgAl11O19-based applications. Herein, we report the inherent thermal transport in crystalline (c-LMA) and amorphous LMA (a-LMA) using atomistic simulations. It is found that c-LMA have a low κ comparable to the classical 7YSZ at 300–1500 K, while the κ of a-LMA is 8–68% lower than that of c-LMA. The mode decomposition shows that the phonon modes in c-LMA consist of local, normal and diffuse modes, while those in a-LMA consist of local and diffuse modes. The dual-channel model reveals that the thermal conduction in c-LMA is dominated by the normal modes at low temperatures (<420 K) while by the diffusive modes at high temperatures, but that in a-LMA results entirely from diffusive modes. This new insight into the thermal transport properties in c-LMA and a-LMA provides a foundation for designing LH-based thermal management applications.

Decoherent phonon effects in fast atom-surface scattering

The study of the influence of phonon-mediated processes on grazing-incidence fast atom diffraction (GIFAD) patterns is relevant for the use of GIFAD as a surface analysis technique. In this work, we apply the Phonon-Surface Initial Value Representation (P-SIVR) approximation to investigate lattice vibration effects on GIFAD patterns for the He/LiF(001) system at room temperature. The main features introduced by thermal lattice vibrations in the angular distributions of the scattered helium atoms are analyzed by keeping a fixed impact energy and varying the incidence angle to consider normal energies in the 0.1–3 eV range. In all the cases, thermal fluctuations introduce a wide polar spread that transforms the interference maxima into elongated strips. We found that the log-normal polar widths of the specular and outermost maxima do not depend on the normal energy, as it was experimentally observed. In addition, when the normal energy increases, not only the relative intensities of interference peaks are affected by the crystal vibrations, but also the visibility of the interference structures, which disappear completely for normal energies approximately equal to 3 eV. These findings qualitatively agree with recent experimental data, but the simulated polar widths underestimate the experimentally-derived limit, suggesting that there are other mechanisms, such as inelastic processes involving the net exchange of phonons, that contribute to the polar dispersion of the GIFAD patterns.

High-precision measurements and first-principles explanation of the temperature-dependent C13 and N14 hyperfine interactions of single NV− centers in diamond at room temperature

Revealing the properties of single spin defects in solids is essential for quantum applications based on solid-state systems. However, it is intractable to investigate the temperature-dependent properties of single defects, due to the low precision for single-defect measurements in contrast to defect ensembles. Here we report that the temperature dependence of the Hamiltonian parameters for single negatively charged nitrogen-vacancy centers in diamond at room temperature is precisely measured and the results are in reasonable agreement with first-principles calculations. In particular, the hyperfine interactions with randomly distributed $^{13}\mathrm{C}$ nuclear spins are clearly observed to vary with temperature and the relevant coefficients are measured with hertz-level precision. The temperature-dependent behaviors are attributed to both thermal expansion and lattice vibrations by first-principles calculations. Our results pave the way for taking nuclear spins as more stable thermometers at nanoscale. The methods developed here for high-precision measurements and first-principles calculations can be further extended to other solid-state spin defects.

Localized Unipolar Shear Deformation Autowaves in a Nonequilibrium Paramagnet

It is shown that a nanosecond unipolar soliton-like pulse of the type of a localized shear deformation autowave propagating perpendicular to the magnetic field can be formed in a cubic paramagnetic crystal subjected to longitudinal static deformation in the direction of external magnetic field. The influx of the energy stored in paramagnetic ions into the pulse due to the nonequilibrium initial population of their stationary quantum states is compensated by irreversible losses caused by pulse damping due to its interaction with thermal lattice vibrations, defects, and microinhomogeneities.

Coherent charge carrier dynamics in the presence of thermal lattice vibrations

We develop the coherent state representation of lattice vibrations to describe their interactions with charge carriers. In direct analogy to quantum optics, the coherent state representation leads from quantized lattice vibrations (phonons) naturally to a quasiclassical field limit, i.e., the deformation potential. To an electron, the deformation field is a sea of hills and valleys, as ``real'' as any external field, morphing and propagating at the sound speed, and growing in magnitude with temperature. In this disordered potential landscape, the charge carrier dynamics is treated nonperturbatively, preserving its coherence beyond single collision events. We show the coherent state picture agrees exactly with the conventional Fock state picture in perturbation theory. Furthermore, it goes beyond by revealing aspects that the conventional theory could not explain: transient localization even at high temperatures by charge carrier coherence effects, and band tails in the density of states due to the self-generated disorder (deformation) potential in a pure crystal. The coherent state paradigm of lattice vibrations supplies tools for probing important questions in condensed matter physics as in quantum optics.

Effects of temperature on the electrical properties of samaria-doped ceria predicted with the statistical moment method

Samaria-doped ceria (SDC) is an important candidate electrolyte for use in solid oxide fuel cells, but the effect of lattice thermal vibrations on its electrical properties are unclear. In this study, the statistical moment method was employed to predict the temperature dependences of vacancy–dopant association, migration and activation energies, and ionic conductivity in four theoretical regimes comprising static, harmonic, semi-classical anharmonic, and quantum anharmonic regimes. The lattice thermal vibrations weakened vacancy–dopant associations and significantly inhibited vacancy hopping, and these effects were more pronounced as the temperature increased. The strongest vacancy–dopant associations and less convenient movement of oxygen vacancies could occur in the crystal lattice including anharmonic vibrations. Considerable enhancement of the ionic conductivity and a shift in the optimal dopant concentration toward higher values were found in the harmonic regime. Increasing the temperature also led to similar changes in the ionic conductivity. The maximum ion conductivity was governed by trapping and blocking effects, but also by lattice thermal vibrations. The results indicated the trivial influence of quantum effects in the anharmonic vibrations on the electrical properties. These findings provide a deeper understanding of the underlying atomistic mechanisms that determine the effects of temperature and lattice thermal vibrations on the electrical properties, and they may be beneficial for optimizing the ionic conductivity of SDC electrolytes.

Thermal radiation resonating with longitudinal optical phonon from surface micro-stripe structures on metal-gallium nitride and sapphire

Thermal emissions from metal/dielectric-material stripe structures on the surface of dielectric materials are observed. These emissions are attributed to electric-dipole emissions induced by coherent thermal lattice vibrations in the surface structures of a few micrometers. Thermal emission based on coherent lattice vibrations has been reported via surface phonon polariton (SPhP), where metal ingredients have been excluded, whereas the present emission is independent of SPhP. The structures on undoped GaAs shows the emission close to the longitudinal optical (LO) phonon energy, while the peak energy of the emission from the structures on GaN is located in between the LO and transverse optical (TO) mode energies. The present studies on several vibration modes of α-Al2O3 and the dependence of the emission peak energy on geometrical conditions of surface structures reveal that modification of electric permittivity by the local depolarization field induces additional zero points of the real part of the permittivity, which yields additional local LO-like modes and the shift of the main emission peak energy from the original LO mode. This shift is significant for materials with a large energy difference between the LO and TO modes, such as 270 cm−1 for a mode of α-Al2O3 and 170 cm−1 for GaN. This is contrasted with the case of GaAs with 30 cm−1 difference.

Low temperature-promoted surface plasmon resonance effect and ultrasensitive surface-enhanced Raman scattering detection of creatinine

Creatinine is a key biomarker for diagnosing and monitoring kidney disease, so rapid and sensitive testing is very important. Raman spectroscopy is particularly suitable for quantitatively detecting the creatinine in the human environment because it is sensitive to subtle changes in the concentration of the analyte. In this work an effective strategy is provided to promote the activity of surface-enhanced Raman scattering spectroscopy by enhancing the photon-induced charge transfer efficiency at low temperature. The nano-gold icosahedron (Au&lt;sub&gt;20&lt;/sub&gt;) is obtained by the seed-growing method, which is used as an active substrate for SERS. The ultra-low temperature (98 K) SERS detection technology is used to realize the rapid and sensitive detection of the dye molecule crystal violet (CV) and creatinine in normal saline. The experimental results show that at room temperature of 296 K, the detection limit of Au&lt;sub&gt;20&lt;/sub&gt; substrate for CV molecules is as low as 10&lt;sup&gt;–12&lt;/sup&gt; mol/L, and the signals are uniform; at a low temperature of 98 K, the detection limit of CV molecules can reach 10&lt;sup&gt;–14&lt;/sup&gt; mol/L, which is two orders of magnitude lower than that at 296 K. As a result, the adopted cryogenic temperature can effectively weaken the lattice thermal vibration and reduce the release of phonons, then suppress phonon-assisted non-radiative recombination. So, it will increase the number of photo-induced electrons to participate in the photo-induced charge transfer efficiency. Finally, we perform the label-free detection of creatinine in saline by using an Au&lt;sub&gt;20&lt;/sub&gt; substrate. The results show that the detection limit of the SERS substrate for creatinine is 10&lt;sup&gt;–6&lt;/sup&gt; mol/L at 296 K, and the linear correlation coefficient of the 1619 cm&lt;sup&gt;–1&lt;/sup&gt; peak is 0.9839. At a low temperature of 98 K, the detection limit of creatinine concentration is as low as 10&lt;sup&gt;–8&lt;/sup&gt; mol/L, and the linear correlation coefficient of the 1619 cm&lt;sup&gt;–1&lt;/sup&gt; peak becomes 0.9973. It can be seen that low temperature may further improve the detection limit of creatinine concentration and the linearity of characteristic peak. In summary, the current work provides a new idea for accurately detecting the creatinine concentration in the field of biomedicine.