Modeling non-harmonic behavior of materials from experimental inelastic neutron scattering and thermal expansion measurements

Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally- derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-harmonic thermal behaviors using perturbation theory, ab initio molecular-dynamics, or Monte-Carlo simulations. We illustrate this analysis by computing the harmonic, dilational, and anharmonic contributions to the entropy, internal energy, and free energy of elemental aluminum and the ordered compound FeSi over a wide range of temperature. Results agree well with previous data in the literature and provide an efficient approach to estimate anharmonic effects in materials.

High-resolution thermal expansion measurements under helium-gas pressure

We report on the realization of a capacitive dilatometer, designed for high-resolution measurements of length changes of a material for temperatures 1.4K ≤ T ≤ 300K and hydrostatic pressure P ≤ 250MPa. Helium ( 4He) is used as a pressure-transmitting medium, ensuring hydrostatic-pressure conditions. Special emphasis has been given to guarantee, to a good approximation, constant-pressure conditions during temperature sweeps. The performance of the dilatometer is demonstrated by measurements of the coefficient of thermal expansion at pressures P ≃ 0.1MPa (ambient pressure) and 104MPa on a single crystal of azurite, Cu 3(CO 3) 2(OH) 2, a quasi-one-dimensional spin S = 1/2 Heisenberg antiferromagnet. The results indicate a strong effect of pressure on the magnetic interactions in this system. © 2012 American Institute of Physics.

Setting time and thermal expansion of two endodontic cements

The purpose of this study was to evaluate the setting time and the thermal expansion coefficient of 2 endodontic cements, MTA-Angelus and a novel cement called CER. The setting time was determined in accordance to ANSI/ADA specifications no. 57. Three samples of 10 mm diameter and 2 mm thickness were prepared for each cement. The thermal expansion measurements were performed by strain gauge technique. Four samples of each cement were prepared using silicone rings of 5 mm diameter and 2 mm thickness. The data were analyzed statistically using the Student t test. The setting time obtained for the MTA-Angelus and CER cements was 15 (SD 1) min and 7 (SD 1) min, respectively. The linear coefficient of thermal expansion was 8.86 (SD 0.28) mu strain/degrees C for MTA-Angelus and 11.76 (SD 1.20) mu strain/degrees C for CER. The statistical analysis showed significant difference (P < .05) in the setting time and linear coefficient of thermal expansion between the 2 cements. The CER cement has a coefficient of expansion similar to dentin, which could contribute to a decrease of microleakage degree.

Multi-scale numerical simulations of thermal expansion properties of CNT-reinforced nanocomposites

In this work, the thermal expansion properties of carbon nanotube (CNT)-reinforced nanocomposites with CNT content ranging from 1 to 15 wt% were evaluated using a multi-scale numerical approach, in which the effects of two parameters, i.e., temperature and CNT content, were investigated extensively. For all CNT contents, the obtained results clearly revealed that within a wide low-temperature range (30°C ~ 62°C), thermal contraction is observed, while thermal expansion occurs in a high-temperature range (62°C ~ 120°C). It was found that at any specified CNT content, the thermal expansion properties vary with temperature - as temperature increases, the thermal expansion rate increases linearly. However, at a specified temperature, the absolute value of the thermal expansion rate decreases nonlinearly as the CNT content increases. Moreover, the results provided by the present multi-scale numerical model were in good agreement with those obtained from the corresponding theoretical analyses and experimental measurements in this work, which indicates that this multi-scale numerical approach provides a powerful tool to evaluate the thermal expansion properties of any type of CNT/polymer nanocomposites and therefore promotes the understanding on the thermal behaviors of CNT/polymer nanocomposites for their applications in temperature sensors, nanoelectronics devices, etc.

Ultrasonic velocities and thermal expansion coefficients of amorphous Se80Te20 and Se90Te10 alloys near glass transitions

Precise measurements of the ultrasonic velocities and thermal expansivities of amorphous Se80Te20 and Se90Te10 alloys are reported near the glass transition. The samples are produced by liquid quenching. The longitudinal and transverse velocities are measured at 10 MHz frequency using the McSkimin pulse superposition technique. The thermal expansivities,agr, are measured using a three-terminal capacitance bridge. Theagr-values show a sharp maximum near the glass transition temperature,T g. The ultrasonic velocities also show a large temperature derivative, dV/dT nearT g. The data are discussed in terms of existing theories of the glass transition. The continuous change inagr shows that the glass transition is not a first-order transition, as suggested by some theories. The samples are found to be deformed by small loads nearT g. The ultrasonic velocities and dV/dT have contributions arising from this deformation.

Ultrasonic velocities and thermal expansion coefficients of amorphous Se80Te20 and Se90Te10 alloys near glass transitions

Precise measurements of the ultrasonic velocities and thermal expansivities of amorphous Se80Te20 and Se90Te10 alloys are reported near the glass transition. The samples are produced by liquid quenching. The longitudinal and transverse velocities are measured at 10 MHz frequency using the McSkimin pulse superposition technique. The thermal expansivities,agr, are measured using a three-terminal capacitance bridge. Theagr-values show a sharp maximum near the glass transition temperature,T g. The ultrasonic velocities also show a large temperature derivative, dV/dT nearT g. The data are discussed in terms of existing theories of the glass transition. The continuous change inagr shows that the glass transition is not a first-order transition, as suggested by some theories. The samples are found to be deformed by small loads nearT g. The ultrasonic velocities and dV/dT have contributions arising from this deformation.

Thermal expansion and a new phase transition in pyroelectric LiKSO4

Single crystal macroscopic thermal expansion coefficient measurements have been made on uniaxial lithium potassium sulphate crystal both along and normal to the six fold axis, employing Fizeau’s interferometer method. Measurements were made in the range of −120°C to 500°C. The results show that lithium potassium sulphate exhibits two major anomalies in its expansion coefficients around −95°C and 422°C respectively, the one at −95°C has been observed for the first time. The nature of dimensional changes of the crystal at the upper and lower transition points are opposite in nature. The crystal shows considerable lattice anisotropy. Megaw’s tilt concept has been invoked to explain the relative magnitudes of expansion coefficients alonga andc directions. Structural features responsible for the absence of ferroelectricity in this crystal have been pointed out.

Synthesis and thermal expansion hysteresis of Ca1-xSrxZr4P6O24

The low thermal expansion ceramic system, Ca1-xSrxZr4P6O24, for the compositions with x = 0, 0.25, 0.50, 0.75 and 1 was synthesized by solid-state reaction. The sintering characteristics were ascertained by bulk density measurements. The fracture surface microstructure examined by scanning electron microscopy showed the average grain size of 2.47 mum for all the compositions. The thermal expansion data for these ceramic systems over the temperature range 25-800degreesC is reported. The sinterability of various solid solutions and the hysteresis in dilatometric behaviour are shown to be related to the crystallographic thermal expansion anisotropy. A steady increase in the amount of porosity and critical grain size with increase in x is suggested to explain the observed decrease in the hysteresis.

Investigation of the Young's modulus and thermal expansion of amorphous titania-doped tantala films

The current generation of advanced gravitational wave detectors utilize titania-doped tantala/silica multilayer stacks for their mirror coatings. The properties of the low-refractive-index silica are well known; however, in the absence of detailed direct measurements, the material parameters of Young's modulus and coefficient of thermal expansion (CTE) of the high refractive index material, titania-doped tantala, have been assumed to be equal to values measured for pure tantala coatings. In order to ascertain the true values necessary for thermal noise calculations, we have undertaken measurements of Young's modulus and CTE through the use of nanoindentation and thermal-bending measurements. The measurements were designed to assess the effects of titania doping concentration and post-deposition heat-treatment on the measured values in order to evaluate the possibility of optimizing material parameters to further improve thermal noise in the detector. Young's modulus measurements on pure tantala and 25% and 55% titania-doped tantala show a wide range of values, from 132 to 177 GPa, dependent on both titania concentration and heat-treatment. Measurements of CTE give values of (3.9 +/- 0.1) x 10^-6 K^-1 and (4.9 +/- 0.3) x 10^-6 K^-1 for 25% and 55% titania-doped tantala, respectively, without dependence on post-deposition heat-treatment.

Relationship between phonons and thermal expansion in Zn(CN)2 and Ni(CN)2 from inelastic neutron scattering and ab initio calculations

Zn(CN)2 and Ni(CN)2 are known for exhibiting anomalous thermal expansion over a wide temperature range. The volume thermal expansion coefficient for the cubic, three dimensionally connected material, Zn(CN)2, is negative (alpha(V) = −51  10(-6) K-1) while for Ni(CN)2, a tetragonal material, the thermal expansion coefficient is negative in the two dimensionally connected sheets (alpha(a) = −7  10(-6) K-1), but the overall thermal expansion coefficient is positive (alpha(V) = 48  10(-6) K-1). We have measured the temperature dependence of phonon spectra in these compounds and analyzed them using ab initio calculations. The spectra of the two compounds show large differences that cannot be explained by simple mass renormalization of the modes involving Zn (65.38 amu) and Ni (58.69 amu) atoms. This reflects the fact that the structure and bonding are quite different in the two compounds. The calculated pressure dependence of the phonon modes and of the thermal expansion coefficient, alpha(V), are used to understand the anomalous behavior in these compounds. Our ab initio calculations indicate that phonon modes of energy approx. 2 meV are major contributors to negative thermal expansion (NTE) in both the compounds. The low-energy modes of approx.8 and 13 meV in Zn(CN)2 also contribute significantly to the NTE in Zn(CN)2 and Ni(CN)2, respectively. The measured temperature dependence of the phonon spectra has been used to estimate the total anharmonicity of both compounds. For Zn(CN)2, the temperature-dependent measurements (total anharmonicity), along with our previously reported pressure dependence of the phonon spectra (quasiharmonic), is used to separate the explicit temperature effect at constant volume (intrinsic anharmonicity).

Probing the Mott physics in kappa-(BEDT-TTF)(2)X salts via thermal expansion

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Phonon anharmonicity and negative thermal expansion in SnSe

The anharmonic phonon properties of SnSe in the Pnma phase were investigated with a combination of experiments and first-principles simulations. Using inelastic neutron scattering (INS) and nuclear resonant inelastic X-ray scattering (NRIXS), we have measured the phonon dispersions and density of states (DOS) and their temperature dependence, which revealed a strong, inhomogeneous shift and broadening of the spectrum on warming. First-principles simulations were performed to rationalize these measurements, and to explain the previously reported anisotropic thermal expansion, in particular the negative thermal expansion within the Sn-Se bilayers. Including the anisotropic strain dependence of the phonon free energy, in addition to the electronic ground state energy, is essential to reproduce the negative thermal expansion. From the phonon DOS obtained with INS and additional calorimetry measurements, we quantify the harmonic, dilational, and anharmonic components of the phonon entropy, heat capacity, and free energy. The origin of the anharmonic phonon thermodynamics is linked to the electronic structure.

Effect of Coulomb blockade, gold resistance, and thermal expansion on the electrical resistance of ultrathin gold films

Controlling the electrical resistance of granular thin films is of great importance for many applications, yet a full understanding of electron transport in such films remains a major challenge. We have studied experimentally and by model calculations the temperature dependence of the electrical resistance of ultrathin gold films at temperatures between 2 K and 300 K. Using sputter deposition, the film morphology was varied from a discontinuous film of weakly coupled meandering islands to a continuous film of strongly coupled coalesced islands. In the weak-coupling regime, we compare the regular island array model, the cotunneling model, and the conduction percolation model with our experimental data. We show that the tunnel barriers and the Coulomb blockade energies are important at low temperatures and that the thermal expansion of the substrate and the island resistance affect the resistance at high temperatures. At low temperatures our experimental data show evidence for a transition from electron cotunneling to sequential tunneling but the data can also be interpreted in terms of conduction percolation. The resistivity and temperature coefficient of resistance of the meandering gold islands are found to resemble those of gold nanowires. We derive a simple expression for the temperature at which the resistance changes from non-metal-like behavior into metal-like behavior. In the case of strong island coupling, the total resistance is solely determined by the Ohmic island resistance.

Prediction of thermal expansion properties of carbon nanotubes using molecular dynamics simulations

The axial coefficients of thermal expansion (CTE) of various carbon nanotubes (CNTs), i.e., single-wall carbon nanotubes (SWCNTs), and some multi-wall carbon nanotubes (MWCNTs), were predicted using molecular dynamics (MDs) simulations. The effects of two parameters, i.e., temperature and the CNT diameter, on CTE were investigated extensively. For all SWCNTs and MWCNTs, the obtained results clearly revealed that within a wide low temperature range, their axial CTEs are negative. As the diameter of CNTs decreases, this temperature range for negative axial CTEs becomes narrow, and positive axial CTEs appear in high temperature range. It was found that the axial CTEs vary nonlinearly with the temperature, however, they decrease linearly as the CNT diameter increases. Moreover, within a wide temperature range, a set of empirical formulations was proposed for evaluating the axial CTEs of armchair and zigzag SWCNTs using the above two parameters. Finally, it was found that the absolute value of the negative axial CTE of any MWCNT is much smaller than those of its constituent SWCNTs, and the average value of the CTEs of its constituent SWCNTs. The present fundamental study is very important for understanding the thermal behaviors of CNTs in such as nanocomposite temperature sensors, or nanoelectronics devices using CNTs.

Anomalous dynamical charges, phonons, and the origin of negative thermal expansion in Y2W3O12

We use a combination of classical model and first-principles density functional theory calculations to study lattice dynamics of Y2W3O12 and identify phonons responsible for its negative thermal expansion (NTE). Born dynamical charges of various atoms are found to deviate anomalously from their nominal values. We find that the phonons with energy from 4 to 10 meV are the primary contributors to its NTE. These phonons involve rotations of the YO6 octahedra and WO4 tetrahedra in mutually opposite sense and collective translational atomic displacements, reflecting a strong mixing between acoustic and optic modes.