Calculation Of Thermal Expansion Coefficient Research Articles

Reedmergnerite and stillwellite-(Ce) from the Dara-i-Pioz alkaline massif: insights into high-temperature behavior of borosilicates

Research subject. Reedmergnerite and stillwellite-(Ce) were obtained from the rocks of the Dara-i-Pioz alkaline massif located on the southern slope of the Alai Range in Tajikistan, which is characterized by the presence of rare mineral species including borosilicates and lithium minerals. Aim. To investigate the thermal behavior of reedmergnerite and stillwellite-(Ce) using high-temperature X-ray diffraction, including the determination of phase transition temperatures and expansion/compression of the unit cell parameters, as well as the calculation of thermal expansion coefficients. Materials and methods. Chemical analysis was performed using a TESCAN MIRA 3 microscope (EDS mode) and a JEOL JXA-8230 electron probe microanalyzer (WDS mode). High-temperature powder X-ray diffraction data were collected using a D8 ADVANCE Bruker diffractometer with an HTK16 heating chamber, covering temperatures from 30°C to 750°C in ambient air. Results. The thermal expansion coefficients of reedmergnerite and stillwellite-(Ce) were determined. Heating reedmergnerite resulted in slight changes in the unit cell parameters, with the parameter c experiencing the smallest change and the parameter a showing the greatest increase. The unit cell volume increased by 1.8% when heated to 750°C and returned to its initial value upon cooling. When stillwellite-(Ce) is heated in the temperature range of 400–450°C, a phase transition occurs, which is confirmed by previously recorded temperature values. The conducted heating and subsequent cooling experiments revealed that the volume and unit cell parameters of stillwellite-(Ce) did not fully revert to their original values. Conclusions. The coefficients of thermal expansion tensor (αij) of rhodmerdgnertite and stillwellite-(Ce) were investigated as a function of temperature using high-temperature in-situ experiments. The phases exhibited relatively low values of thermal expansion parameters compared to the general data for feldspars and borosilicates obtained from literature. These findings contribute to the understanding of the thermoelastic behavior of this group of minerals and their potential applications in various fields.

High-temperature behavior of the UV-luminescent sodalite-type natural compound Na8(Al6Si6O24)(HS)2: Comparative study by in situ single-crystal X-ray diffraction and Raman spectroscopy

The in situ single-crystal X-ray diffraction and Raman spectroscopy were performed for a sapozhnikovite Na8(Al6Si6O24)(HS)2, a rare mineral with sodalite-type crystal structure. The crystal chemical analysis and calculation of thermal expansion coefficients based on the refinement of Na8(Al6Si6O24)(HS)2 crystal structures in the temperature range of 300–1273 K show that this sodalite-type compound undergoes: (1) reversible phase transition P4‾ 3n ↔ Pm3‾n at 1223 K, (2) drastic increase of linear expansion coefficient at 1173 K, (3) non-elastic behavior of sapozhnikovite framework after cooling. The temperature dependencies of the unit-cell parameters were divided into two parts and described by quadratic a = 8.911(12) – 0.000018(33)T + 0.000000138(22)T2 (from 300 to 1173 K) and linear a = 7.765(13) + 0.001130(11)T (from 1173 to 1273 K) polynomial functions. Raman spectroscopy data reveal the partial transformations of the extra-framework HS− anion by follows reactions: 6HS–→ S3•– + 3H2S (gas) and 2HS– – 2e → S22− + 2H+. These transformations may cause the observed discontinuity in the thermal expansion curve for sapozhnikovite at 1173 K with drastic increase of linear expansion coefficient and not fully elastic behavior of framework after removal of temperature exposure. After the heat treatment experiments (300–1273 K) the HS− anion restores in the β-cage of sapozhnikovite crystal structure. In the synthetic analogue of sapozhnikovite the heat treatment leads to the irreversible transformation according to the reactions: 2HS– + 2.5O2 (gas) → SO42− + 0.25S4 + H2O (gas) and 2HS– + 3.5O2 (gas) → SO42− + SO2 (gas) + H2O (gas). The orange luminescence of Na8(Al6Si6O24)(HS)2 is stable up to the 1073 K.

Calculation of Thermal Expansion Coefficient of Rare Earth Zirconate System at High Temperature by First Principles

Compounds of rare earth zirconates with pyrochlore structure are candidates for the application of thermal barrier coatings of next generation. In order to modify the mechanic properties and maintain the low thermal conductivity, other trivalent rare-earth element substitution is commonly used. Presently, investigation on the evaluation of the property of thermal expansion is attracting more attention. In this paper, a feature parameter of thermal expansion coefficient at high temperature (α∞) was proposed by combining Grüneisen’s equation and the Debye heat capacity model. Using α∞ model, the thermal expansion property of different compounds can be easily figured out by first principles. Firstly, α∞ of ZrO2, HfO2, were calculated, and results are in good agreement with the experimental data from the literature. Moreover, α∞ of La2Zr2O7, Pr2Zr2O7, Gd2Zr2O7, and Dy2Zr2O7 were calculated, and results demonstrated that the model of α∞ is a useful tool to predict the thermal expansion coefficient at high temperature. Finally, Gd2Zr2O7 with 4 different Yb dopant concentrations (Gd1-xYbx)2Zr2O7 (x = 0, 0.125, 0.3125, 0.5) were calculated. Comparing with the experimental data from the literature, the calculation results showed the same tendency with the increasing of Yb concentration.

Calculation of thermal expansion coefficient of glasses based on topological constraint theory

In this work, the thermal expansion behavior and the structure configuration evolution of glasses were studied. Degree of freedom based on the topological constraint theory is correlated with configuration evolution; considering the chemical composition and the configuration change, the analytical equation for calculating the thermal expansion coefficient of glasses from degree of freedom was derived. The thermal expansion of typical silicate and chalcogenide glasses was examined by calculating their thermal expansion coefficients (TEC) using the approach stated above. The results showed that this approach was energetically favorable for glass materials and revealed the corresponding underlying essence from viewpoint of configuration entropy. This work establishes a configuration-based methodology to calculate the thermal expansion coefficient of glasses that, lack periodic order.

First principles calculation of thermal expansion coefficients of pure and Cr doped α-alumina crystals

We have performed theoretical analysis of thermal expansion behavior of alumina crystals under finite temperature based on first principles phonon state calculations. Liner thermal expansion coefficients of a pure α-alumina crystal have been evaluated based on quasi-harmonic approximation including crystalline anisotropy. The Cr doping effect on the alumina crystal has also been examined and found that the doping can cause a noticeable change on the thermal expansion coefficient. The present results demonstrate that the first principles theoretical approach can be helpful for reproducing or predicting thermal expansion behaviors including dopant effects, which may pave a way for possible control of thermal expansion of materials by doping or alloying.

Analysis of rail cooling strategies through numerical simulation with instant calculation of thermal expansion coefficient

En este articulo se describe una nueva metodologia para simular el proceso de enfriamiento de un rail asimetrico Ri60, disenado para tranvias, de una forma mucho mas realista que lo realizado hasta ahora para perfiles largos de acero. La propuesta considera los efectos de la transformacion de fases del acero y el enfriamiento por conveccion forzada. El proceso es simulado como un proceso termo-mecanico desacoplado. Primero, las curvas de enfriamiento del rail son obtenidas a partir de un modelo basado en dinamica de fluidos computacional y posteriormente introducidas en el modelo de elementos finitos para calcular las tensiones y desplazamientos. En esta segunda fase se calcula, para cada elemento finito y en cada iteracion, el coeficiente de dilatacion termica lineal segun el diagrama de curvas de enfriamiento continuo. Estos resultados permiten determinar las tensiones residuales al final del proceso con muy buena fidelidad respecto a los datos experimentales obtenidos en la planta industrial. La metodologia permite estudiar con precision dos tipos de estrategias de enfriamiento del Ri60 y seleccionar la mas conveniente.

Molecular dynamics calculation of thermal expansion coefficient of a series of rare-earth zirconates

To develop more reliable and stable thermal barrier coatings, low thermal conductivity materials with higher thermal expansion coefficients (TECs), like rare-earth zirconates (A(2)Zr(2)O(7), A = La, Nd, Sm, Eu, Gd, Er, Yb and Lu), have been the focus of a great deal of attention in recent years. But the mechanisms underlying the values of TECs are still poorly understood. In this paper, the TECs of a series of rare-earth zirconates are calculated using molecular dynamics. Two typical crystal structures, pyrochlore and fluorite, are considered. By investigating the potential functions and the equilibrium-location deviations between the atoms, it is found that the Zr-O bond is the most important factor that determines the overall TECs, and the A-O bond plays a secondary role. However, O-O has little effect on the TECs. In addition, the fluorite structure has a relatively higher TEC due to a weaker Zr-O bond. Calculated values are consistent with the experimental observations. Using the method presented in this study, two doped zirconates (Gd(0.4)Sm(0.5)Yb(0.1))(2)Zr(2)O(7) and Sm(2)(Ce(0.3)Zr(0.7))(2)O(7) are designed and compared. As expected, both of them have higher TECs than undoped Sm(2)Zr(2)O(7), and doping at the A-site is more efficient than doping at the Zr-site. (C) 2009 Elsevier B.V. All rights reserved.

Calculation of thermal expansion coefficients of pure elements and their alloys

A simple algorithm for computing the coefficient of thermal expansion of pure elements and their alloys, based on features of the binding energy curve, is introduced. The BFS method for alloys is used to determine the binding energy curves of intermetallic alloys and Ni-base superalloys.

The glass transition zone in high solids pectin and gellan preparations

Dynamic oscillatory data on deacylated gellan and high methoxy pectin, in the presence of sucrose and glucose syrup, and presented over a wide temperature range. High levels of the co-solute induce a transition from rubberlike to glasslike consistency in the two biopolymers. The time-temperature superposition method is employed to construct composite curves, around the glass transition region, covering a nine-decade frequency range. The shift factors thus derived are fitted against the experimental temperatures using the Williams, Landel and Ferry equation. These observations are interpreted on the basis of the free volume theory which allows calculation of thermal expansion coefficient and fractional free volume parameters, at the glass transition temperatures of the high solids gellan and pectin systems. Values are in excellent agreement with those for synthetic polymers, a result which emphasizes the universal utility of the above approach (experiment and theory) in studying glasses of synthetic or biological origin.

A differential scheme for multiphase composites: II. Thermal expansion coefficients and conductivities

Click to increase image sizeClick to decrease image size Abstract The differential scheme developed in Part I of this work is applied to the calculation of thermal expansion coefficients and conductivities of isotropic and transversely isotropic multiphase composites. The results obtained herein are compared with the existing experimental results as well as those by other schemes. The effect of the inclusion shape on the overall property of the composites is investigated. The inclusions of disk shape produce the most pronounced effect, followed by inclusions of needle shape and spherical shape.

Calculation of thermal expansion coefficient of glasses

Thermal expansion of oxide glasses has been theoretically studied to derive an equation for the calculation of the thermal expansion coefficient of glass from chemical composition. Grüneisen's constant may be correlated with packing density and a ratio of cation-to-anion radius and, considering the packing density and dissociation energy per unit volume, a semi emprical equation was derived. The agreement between observed and calculated values was satisfactory over 150 glasses of the binary, ternary and quarternary systems.