Bulk Thermal Expansion Coefficient Research Articles

Optical and thermal properties of (70 − x)SiO2–xNa2O–15CaO–10Al2O3–5TiO2 (10 ≤ x ≤ 25) glasses

The optical and thermal properties are investigated for the (70 − x)SiO2–xNa2O–15CaO–10Al2O3–5TiO2 (10 ≤ x ≤ 25) glasses using different characterization techniques. Kinetic parameters such as glass transition temperature, activation energy of glass transition (Eg), fluctuation-free volume (fg) and change in bulk thermal expansion coefficient (αf) are calculated for better understanding of glass structure. The Eg shows an increasing trend with the increase of Na2O mol%. Correlation has been established between the microvoids in the glass and physical parameters like density and molar volume. Theoretical parameters like optical basicity, oxide polarizability and electro negativities have been obtained and discussed in relation to non-bridging oxygen. Along with the band gap energy, Urbach energy as well as dispersive energy has also been obtained for all the glasses.

Study of the crystalline and magnetic structures of BaFe11.4Al0.6O19 in a wide temperature range

The structural study of barium hexaferrite (BaFe12O19) whose iron ions are partly replaced by diamagnetic aluminum ions (x = 0.6) is carried out with the help of the neutron-diffraction method. Experimental data are acquired in a wide temperature range of 4–730 K via a high-resolution diffractometer, which makes it possible to obtain both precise information on changes in crystalline and magnetic structures and behavioral data on the sample microstructure. BaFe11.4Al0.6O19 retains the magnetoplumbite structure in the whole temperature range and exhibits the “invar effect,” according to which its bulk thermal-expansion coefficient is close to zero at low temperatures (<150 K). The magnetic structure is defined by the Gorter model with magnetic moments oriented along the hexagonal axis. For all nonequivalent crystallographic positions, the magnetic moment of F3+ is close to 4 μB at 4 K. The total magnetic moment per formula unit is 15.6 μB, i.e., less than the nominal value of 20 μB. This is caused by the fact that diamagnetic Al ions are included in the composition. Crystallite microstrains increase insignificantly with temperature due to increasing influence of the magnetic subsystem.

Influence of cooling rate on austenite transformation and contraction of continuously cast steels

Based on thermodynamic calculations and dilatometry experiments performed over a wide range of cooling rates with on two continuously cast steels, an empirical model was developed to describe the relationship between the critical temperatures of austenite transformation, the cooling rates, and the equilibrium temperatures of phase transformation, written as Ar(°C) = Ae−exp(B+C/Cr). The model was verified to be applicable to the calculation of Ar3 and Ar1 temperatures at various cooling rates for different steel blanks during continuous casting process. Results indicated that, the Ar3 and Ar1 temperatures decreased with increasing cooling rate; and the temperature window for ferrite formation enlarged while the cooling rate was increasing. The influence of cooling rate on the linear and bulk thermal expansion coefficients was discussed. Results showed that the peaks of thermal expansion coefficients during new phase formation apparently moved toward low temperatures as the cooling rate increased; The linear and bulk thermal expansion coefficients of single austenite phase were steady at 2.1×10−5 and 6.8×10−5°C −1 respectively. The relative contraction of steels would be larger at lower cooling rate during continuous casting.

P–V–T equation of state of molybdenite (MoS2) by a diamond anvil cell and in situ synchrotron angle-dispersive X-ray diffraction

The pressure–volume–temperature (P–V–T) equation of state (EoS) of a natural molybdenite (MoS2) has been measured at high temperature up to 700K and high pressures up to 18.26GPa, by using in situ angle-dispersive X-ray diffraction and diamond anvil cell. Analysis of room-temperature P–V data to a third-order Birch–Murnaghan EoS yields: V0=107.0±0.1Å3, K0=67±2GPa and K′0=5.0±0.3. With K′0 fixed to 4.0, we obtained: V0=106.7±0.1Å3 and K0=74.5±0.8GPa. Fitting of our P–V–T data by means of the high-temperature third order Birch–Murnaghan equations of state, gives the thermoelastic parameters: V0=107.0±0.1Å3, K0=69±2GPa, K′0=4.7±0.2, (∂K/∂T)P=−0.021±0.003GPaK−1, a=(2.2±0.7)×10−5K−1 and b=(2.9±0.8)×10−8K−2. The temperature derivative of the bulk modulus and thermal expansion coefficient of MoS2 are obtained for the first time. Present results are also compared with previously studies determined the elastic properties of MoS2 and WS2.

Structural, elastic, electronic, and thermodynamic properties of intermetallic Zr2Cu: A first-principles study

Three competing structures (C11b, C16 and E93) of intermetallic Zr2Cu have been systematically investigated by first-principles calculations and quasi-harmonic Debye model. Both the calculated equation of states (EOS) and pressure–enthalpy results indicate a structural phase transition from C11b to C16 phase at around 11–14 GPa. The calculated equilibrium crystal parameters and elastic constants are in consistence with available experimental or theoretical data. All three phases are mechanically stable according to the elastic stability criteria, and ductile according to Pugh's ratio, while the ambient-stable C11b phase shows a higher elastic anisotropy. Furthermore, differences in the nature of bonding between three competing structures are uncovered by electron density topological analysis. C11b Zr2Cu possesses an intriguing pseudo BaFe2As2-type structure with the charge density maxima at Zr tetrahedral interstices serving as Fe-position pseudoatoms; C16 Zr2Cu contains Zr-pair configurations bonded through bifurcated Zr–Zr bonding paths; while the E93 phase has only conventional straight bonding. Additionally, through quasi-harmonic Debye model, the pressure and temperature dependences of the bulk modulus, specific heat, Debye temperature, Grüneisen parameter and thermal expansion coefficient for three phases are obtained and discussed.

Effect of graphene nanoplatelets on coefficient of thermal expansion of polyetherimide composite

Thermal expansion is one of the major concerns for polymer composites. In this research, graphene nanoplatelets (GNPs) were added to polyetherimide (PEId) thermoplastic polymer in order to reduce the coefficient of thermal expansion (CTE) of the injection molded composite. First, the coefficient of linear thermal expansion (LTE) was measured in three directions in the anisotropic coupon: 0°, 90° and the out of plane Z direction. It is found that the GNP particles are very effective in terms of reducing the LTE in 0° direction due to high degree of alignment. After annealing above glass transition temperature, significant increase of 0° LTE and decrease of Z° LTE were observed. The bulk CTE was calculated by adding up the LTEs in all three directions and is found to be independent of annealing. Second, several models were applied to predict both CTE and LTE. It is found that Schapery's lower limit model fits the experimental CTE very well. Chow's model was applied for LTEs in three directions. The behavior of GNP-5/PEId composites is explained by the combination of Chow's model and morphology obtained by scanning electron microscope (SEM).

First-principles study of thermal transport inFeSb2

We study the thermal transport properties of FeSb${}_{2}$, a promising thermoelectric material for cooling applications at cryogenic temperatures. A first-principles formalism based on density functional theory and ab initio lattice dynamics is applied. We calculate the electronic structure, the phonon dispersion relation, the bulk thermal expansion coefficient, and the thermal conductivity of FeSb${}_{2}$ and compare them with other calculations and experiments. Our calculation is found insufficient to fully explain the temperature dependence of the lattice thermal conductivity of FeSb${}_{2}$, suggesting new scattering mechanisms in this strongly correlated system. The mean free path distribution of different phonon modes is also calculated, which may provide valuable guidance in designing nanostructures for reducing the thermal conductivity of FeSb${}_{2}$ and improving the thermoelectric figure of merit zT.

(Pb,Cd)–O covalency in PbTiO3–CdTiO3 with enhanced negative thermal expansion

Recently experiments have found that negative thermal expansion is a common phenomenon in PbTiO3-based materials, and their negative thermal expansion is affected by various substitutions. Interestingly, Cd substitution in PbTiO3 has a unique effect in enhancing negative thermal expansion compared with any other A-site substitutions. Therefore, studying Cd substitution in PbTiO3, the role of which still remains unclear, would bring us deeper understanding on the nature of the negative thermal expansion of PbTiO3-based materials. Structure calculations, density of states, Bader analysis and the minimum electron density of Pb1-xCdxTiO3 supercells have been reported on the chemical bond through first-principles calculations here. We found that the hybridization between (Pb,Cd)-O orbitals exists in tetragonal phase. Furthermore, the hybridization between Cd-O orbitals is stronger than that between Pb-O orbitals, and Cd-O covalency promotes the average A-site hybridization. Simultaneously, the average bulk coefficient of thermal expansion is negative and inversely proportional to the Cd substitution amount. So, (Pb,Cd)-O covalency in the tetragonal Pb1-xCdxTiO3 is responsible for the nature of enhanced negative thermal expansion in accordance with our previous experimental investigations.

Study on Leaky Fault Mechanism and Influential Factors of Hydraulic System of Artillery

Hydraulic technique is more and more applied in weapon equipments; hydraulic system is becoming one of the important subsystems of modern artillery. In this paper, considering effects of operating pressure, temperature and mixed air rate of hydraulic system, the mathematical model of hydraulic fluid internal leakage rate of artillery is built to analyze leaky fault form and leaky reason. The conclusion shows that the internal leakage rate of the hydraulic system of artillery is depend on temperature, pressure, dynamic viscosity, and bulk modulus and thermal expansion coefficient of hydraulic system. The variation rule of hydraulic fluid internal leakage rate is gotten according to operating parameters. Special reference will be given to leakage detection and location of the hydraulic system of artillery.

Crystal structure, Raman and FTIR spectroscopy, and equations of state of OH-bearing MgSiO3 akimotoite

MgSiO3 akimotoite is stable relative to majorite-garnet under low-temperature geotherms within steeply or rapidly subducting slabs. Two compositions of Mg–akimotoite were synthesized under similar conditions: Z674 (containing about 550 ppm wt H2O) was synthesized at 22 GPa and 1,500 °C and SH1101 (nominally anhydrous) was synthesized at 22 GPa and 1,250 °C. Crystal structures of both samples differ significantly from previous studies to give slightly smaller Si sites and larger Mg sites. The bulk thermal expansion coefficients of Z674 are (153–839 K) of a 1 = 20(3) × 10−9 K−2 and a 0 = 17(2) × 10−6 K−1, with an average of α 0 = 27.1(6) × 10−6 K−1. Compressibility at ambient temperature of Z674 was measured up to 34.6 GPa at Sector 13 (GSECARS) at Advanced Photon Source Argonne National Laboratory. The second-order Birch–Murnaghan equation of state (BM2 EoS) fitting yields: V 0 = 263.7(2) A3, K T0 = 217(3) GPa (K′ fixed at 4). The anisotropies of axial thermal expansivities and compressibilities are similar: α a = 8.2(3) and α c = 10.68(9) (10−6 K−1); β a = 11.4(3) and β c = 15.9(3) (10−4 GPa). Hydration increases both the bulk thermal expansivity and compressibility, but decreases the anisotropy of structural expansion and compression. Complementary Raman and Fourier transform infrared (FTIR) spectroscopy shows multiple structural hydration sites. Low-temperature and high-pressure FTIR spectroscopy (15–300 K and 0–28 GPa) confirms that the multiple sites are structurally unique, with zero-pressure intrinsic anharmonic mode parameters between −1.02 × 10−5 and +1.7 × 10−5 K−1, indicating both weak hydrogen bonds (O–H···O) and strong OH bonding due to long O···O distances.

Phase transition character and thermodynamic modeling of the [formula omitted] and [formula omitted] hexagonal Si–N system supplemented by first-principles calculations

The phase boundaries of the β→P6¯′→δ transitions are investigated using first-principles calculations within the quasi-harmonic approximation. The agreement between the calculated properties of β-Si3N4 (benchmark system) and other results has proven the validity of our calculation. The lattice parameters, elastic constants and bulk moduli of P6¯′-, P6¯- and δ-Si3N4 are also analysed. At 300K, the transition pressures of the β→P6¯′→δ transitions are 40.0 and 53.1GPa, respectively. The predicted β→P6¯′→δ phase boundaries have positive slopes, hence, at higher temperatures it require higher pressures to synthesize P6¯′- and δ-Si3N4. It turns out that the bulk modulus and thermal expansion coefficient of the P6¯′ phase are greater than those of the P6¯ phase. The bulk moduli are high and only weakly temperature dependent. Moreover, the heat capacity, entropy, thermal expansion coefficient and Debye temperature are also analysed. The different temperature dependences of entropy between P6¯′-Si3N4 and P6¯-Si3N4 can be ascribed to the fact that large channels in P6¯-Si3N4 which allow for more vigorous thermal motion than in P6¯′-Si3N4.

BAND STRUCTURE, HARDNESS, THERMODYNAMIC AND OPTICAL PROPERTIES OF SUPERCONDUCTING Nb2AsC, Nb2InC AND Mo2GaC

First-principles investigation of the geometry, electronic band structure, Vickers hardness, thermodynamic and optical properties of three superconducting MAX compounds Nb 2 AsC , Nb 2 InC and Mo 2 GaC have been carried out by the plane-wave pseudopotential method based on density functional theory (DFT) implemented in the CASTEP code. The theoretical Vickers hardness has been studied by means of Mulliken bond population analysis and electronic densities of states. The thermodynamic properties such as the temperature and pressure dependent bulk modulus, Debye temperature, specific heats and thermal expansion coefficient of the three 211 MAX phases are derived from the quasi-harmonic Debye model with phononic effect for the first time. Furthermore, all the optical properties are determined and analyzed for the first time for two different polarization directions. The theoretical findings are compared with relevant experiments (where available) and the various implications are discussed in details.

Ab Initio Investigation of Nitride in Comparison with Carbide Phase of Superconducting InX (X = C, N)

The structural, elastic, electronic, thermal, and optical properties of superconducting nanolaminates Ti2InX (X = C, N) are investigated by density functional theory (DFT). The results obtained from the least studied nitride phase are discussed in comparison with those of carbide phase having value half as that of the former. The carbide phase is found to be brittle in nature, while the nitride phase is less brittle. Elastic anisotropy demonstrates that the c-axis is stiffer in Ti2InN than in Ti2InC. The band structure and density of states show that these phases are conductors, with contribution predominantly from the Ti 3d states. The bulk modulus, Debye temperature, specific heats, and thermal expansion coefficient are obtained as a function of temperature and pressure for the first time through the quasiharmonic Debye model with phononic effects. The estimated values of electron-phonon coupling constants imply that Ti2InC and Ti2InN are moderately coupled superconductors. The calculated thermal expansion coefficient is in fair agreement with the only available measured value for Ti2InC. Further the first time calculated optical functions reveal that the reflectivity is high in the IR-visible-UV region up to ~10 eV and 12.8 eV for Ti2InC and Ti2InN, respectively, showing these to be promising coating materials.

The effect of microstructure on thermal expansion coefficients in powder-processed Al2Mo3O12

Orthorhombic Al2Mo3O12 was investigated as a model anisotropic phase to understand the influence of powder preparation routes and bulk microstructure (mean grain size) on the bulk coefficient of thermal expansion (CTE) and to compare it to the intrinsic CTE of powder samples. A co-precipitation route was used for the synthesis of pure single-phase nanopowders, while a polyvinyl alcohol-assisted sol–gel method was utilized for the synthesis of micron-sized powders. Sintered samples prepared from both powders exhibited different microstructures in terms of mean crystal sizes and porosity. Bulk samples obtained from nanopowders were highly porous and contained crystals of approximately 100-nm diameter, while the bulk pieces produced from the micron-sized powders were denser, contained crystals larger than 5 μm, and showed occasional intergranular and transgranular microcracks. Such different microstructures hugely impact the bulk CTE: the nanometric sample possesses a bulk CTE (0.9 × 10−6 °C−1, from 200 to 700 °C) closer to the instrinsic CTE (2.4 × 10−6 °C−1) than for the micrometric sample, which showed a negative CTE (−2.2 × 10−6 °C−1) from 200 to 620 °C, and an even more negative CTE above 620 °C (−35 × 10−6 °C−1). A finite element analysis showed that the local maximum thermal tensile stresses could be as high as 220 MPa when simulating a temperature drop of 700 °C as an example of thermal treatment following sintering. This tensile stress is expected to exceed the tensile strength of Al2Mo3O12, explaining the origin of microcracks in bulk samples prepared from the micron-sized powders. The thermal behavior of the microcracks leads to differences between the intrinsic and bulk thermal expansion; we show experimentally that such differences can be reduced by nanostructuring.

Self‐Healing Behavior of Barium–Lanthanum–Borosilicate Glass and Its Reactivity with Different Electrolytes for SOFC Applications

The diffusion couples of lanthanum‐based barium borosilicate glass with high‐ and low‐temperature electrolytes have been heat‐treated at 850°C and 800°C, respectively, for 5, 100 and 750 h. These prepared diffusion couples have been characterized using various techniques like X‐ray diffraction (XRD), scanning electron microscopy (SEM), X‐ray dot mapping, and electron probe microanalysis (EPMA). The thermodynamic parameters like frequency factor, crystallization constants, free volume, and bulk thermal expansion coefficients have been calculated to understand the behavior of glass. Interestingly, glass revealed self‐healing tendency with heat treatment duration.

Microstructural Analysis of Interfaces between Lanthanum Contained Glass and Two Different Electrolytes for SOFC Applications

AbstractThe diffusion couples of lanthanum based strontium borosilicate glass with two different (high and low temperature) electrolytes have been heat‐treated at 850 and 800 °C, respectively, for 5, 100, and 750 h to understand the mechanism of interface formation and growth. These prepared diffusion couples have been characterized using various techniques like X‐ray diffraction (XRD), scanning electron microscope (SEM), X‐ray dot mapping, and electron probe microanalysis (EPMA). XRD revealed no detrimental phase formation. Other thermodynamic parameters like frequency factor, crystallization constants, free volume, and bulk thermal expansion coefficients have been calculated to understand the behavior of glass under the influence of temperature. These theoretical parameters will enable to understand the interfacial growth observed in heat‐treated couple for its end application in SOFC. The observed results indicate that lanthanum containing glass exhibit stable and smooth interface with yttria‐stabilized zirconia (high‐temperature electrolyte) as compared to doped bismuth vanadate (low temperature electrolyte).

Effect of Doping on the Thermal Expansion of β‐Eucryptite Prepared by Sol–Gel Methods

The thermal expansion behavior of pure β‐eucryptite and Zn‐doped β‐eucryptite (substituting Zn for Li), prepared using sol–gel methods and hot pressing, were investigated. β‐eucryptite exhibits an anisotropic negative coefficient of thermal expansion (CTE), which leads to microcrack formation in sintered polycrystalline samples. This is manifested by the presence of a hysteresis in the thermal expansion curves. The hysteresis disappears when a small amount of Zn (0.5–3 mol% Zn) is present. Furthermore, the bulk CTE increases significantly in magnitude (from −4 × 10−6/°C for pure β‐eucryptite to 1 × 10−6/°C to 2 × 10−6/°C), and is slightly positive in the range from 25°C to 1000°C. No difference in grain size was observed between the pure and doped samples, and all the ceramics exhibited high relative densities. It is likely that Zn substitutes for Li in the β‐eucryptite structure and reduces the c‐axis thermal expansion, thereby lowering the CTE anisotropy and lowering the tendency for microcracking.

Effective stiffness and thermal expansion coefficients of unidirectional composites with fibers surrounded by cylindrically orthotropic matrix layers

An approach to predict the effective thermoelastic properties of unidirectional composites consisting of cylindrically orthotropic fibers surrounded by layers of cylindrically orthotropic matrix is developed and applied to carbon/carbon composites. Micromechanical modeling is based on elastic solutions for basic loadcases including prescribed axial tension, transverse hydrostatic loading, axial and in-plane shear, and unconstrained thermal expansion. The composite cylinder assemblage model (Hashin, 1990) is utilized to predict axial elastic properties, transverse bulk modulus and thermal expansion coefficients of the overall composite. The effective transverse shear modulus is evaluated using a self-consistent method. The approach is illustrated by considering a representative carbon/carbon material system containing pyrolytic carbon matrix of two different texture levels.

Thermodynamic Stability of Yttrium Alkaline Earth Borosilicate Glasses and Their Compatibility with Crofer for SOFC

Crystallization kinetics and stability are very important and essential parameters for glasses and glass ceramics. These parameters are highly dependent on initial composition as well as processing conditions. Thus, the role of modifier cation on thermal parameters have been studied for AO-SiO2-B2O3-Y2O3 (A = Ca, Sr, Ba) glasses. Various kinetic parameters such as fluctuation free volume (fg), change in bulk thermal expansion coefficient (αf) and frequency factors (ky(Tp), kb(Tp), kf(Tp)) have been calculated for better understanding of crystallization mechanics of present glasses. According to these parameters, CaO- SiO2-B2O3-Y2O3 glass shows good thermodynamic and kinetic stability than other two glasses. The morphology of Crofer22APU/glass–ceramics diffusion couples (heat-treated at 850°C for 50 h) were analyzed by SEM and EPMA. The kinetic parameters and microstructural studies of glasses showed an excellent correlation with each other. CaY/Crofer22APU couple showed good interfacial adhesion along with minimum diffusion of ions on either side of the interface.

High-pressure effect on the ferroelectric-paraelectric transition in PbTiO3

The crystal structure of lead titanate PbTiO3 was investigated by energy dispersive X-ray diffraction at high pressures up to 4 GPa in a temperature range of 300–950 K. At the ambient conditions, the PbTiO3 structure is tetragonal with the space group P4mm (ferroelectric phase). A structural phase transition into the cubic phase with a space group $$Pm\bar 3m$$ is observed at T = 747 K. It was found that the phase transition temperature decreases upon applying the high pressure with the coefficient dT C /dP = -65 K/GPa. Dependences of parameters and volume of the unit cell on the pressure and temperature was found, and the bulk modulus and thermal expansion coefficients for the tetragonal and cubic phases of lead titanate have been calculated.