Lattice Thermal Expansion Coefficients Research Articles

Thermal properties of Cu–Pd alloy under high pressure

In this investigation, we focus on the melting of elements Cu, Pd as well as Cu x –Pd 1− x random alloys. The thermodynamic properties such as melting temperature, isobaric heat capacity and lattice thermal expansion coefficient were calculated as a function of pressure in the range of 0–100 GPa. Moreover, the temperature dependence of energy, order parameter, volume, and density were calculated in various pressures. These calculations were performed by molecular dynamics simulation technique in NPT ensemble. The results showed melting temperature increase upon increasing pressure. Furthermore, isobaric heat capacity and lattice thermal expansion decreased with increasing pressure. These variations were found to be nonlinear approximating a constant value at higher pressures. Our results are in reasonable agreement with the experimental data where they are available.

Influence of substrate metals on the crystal growth of AlN films

AlN films were deposited by reactive radio frequency (RF) sputtering on various bottom electrodes, such as Al, Ti, Mo, Au/Ti, and Pt/Ti. The effects of substrate metals on the orientation of AlN thin films were investigated. The results of X-ray diffraction, atomic force microscopy, and field emission scanning electron microscopy show that the orientation of AlN films depends on the kinds of substrate metals evidently. The differences of AlN films deposited on various metal electrodes are attributed to the differences in lattice mismatch and thermal expansion coefficient between the AlN material and substrate metals. The AlN film deposited on the Pt/Ti electrode reveals highly the c-axis orientation with well-textured columnar structure. The positive role of the Pt/Ti electrode in achieving the high-quality AlN films and high-performance film bulk acoustic resonator (FBAR) may be attributed to the smaller lattice mismatch as well as the similarity of thermal expansion coefficient between the deposited AlN material and the Pt/Ti electrode substrate.

Structural, electronic and thermo-elastic properties of Cu 6Sn 5 and Cu 5Zn 8 intermetallic compounds: First-principles investigation

The structural, elastic and thermodynamic properties of two important intermetallic compounds, Cu 6Sn 5 and Cu 5Zn 8, have been deeply investigated by performing the first-principles calculations based on density functional theory and using the quasi-harmonic approximation for the non-equilibrium Gibbs free energy. Key physical parameters, such as lattice constants, bulk modulus, heat capacity, Debye temperature and volume thermal expansion coefficients were calculated, and their dependences on temperature and pressure were also obtained. Our calculated results are in good agreement with the available experimental data. It is found that Cu 6Sn 5 is elastic anisotropy with relatively low bulk modulus, while Cu 5Zn 8 shows elastic isotropy with high bulk modulus. And the electronic origin of elastic properties was also analyzed in this paper.

First-principles calculation of elastic and thermodynamic properties of copper nitride

A first-principles full-potential linearized augmented plane wave (FP-LAPW) method based on the density functional theory is applied to the study of the static equilibrium lattice structure as well as the elastic constants of the cubic anti-ReO3 structural copper nitride(Cu3N). The quasi-harmonic Debye model, in which the phononic effects are considered, is used to investigate the thermodynamic properties of Cu3N. The pressure and temperature dependences of lattice constant, heat capacity and thermal expansion coefficient are successfully obtained . The bulk modulus and Debye temperature are also calculated at different pressures and temperatures.

Thermal property of binary tetrahedral semiconductors

Abstract In this paper we present an expression relating the lattice thermal expansion coefficient α L (10 −6 K −1 ) for the A III B V and A II B VI semiconductors with the product of ionic charges ( Z 1 Z 2 ), melting temperature ( T m ) and nearest neighbor distance d (A). The lattice thermal expansion coefficient of these compounds exhibit a linear relationship when plotted on a log–log scale against the melting temperature ( T m ), but fall on different straight lines according to the ionic charge product of the compounds. A good agreement has been found between the experimental and calculated values of the lattice thermal expansion coefficient for A III B V and A II B VI semiconductors.

Crystal structure and thermal expansion properties of new compound La 2Cu 0.8Ge 3

A new ternary compound La 2Cu 0.8Ge 3 was synthesized and studied. The crystal structure of La 2Cu 0.8Ge 3 was refined from X-ray powder diffraction data by Rietveld method. The new compound was found to have a tetragonal α-ThSi 2 structure with space group I4 1/ amd (No. 141), and a = 0.42807(2) nm, c = 1.45626(6) nm, Z = 2 and D calc = 6.931 g/cm 3. The thermal expansion properties of La 2Cu 0.8Ge 3 were investigated using high-temperature powder X-ray diffraction technique in the temperature range from 321 K to 753 K. Results show that its unit-cell parameters increase with increasing temperature. The coefficients of average lattice thermal expansion are α ¯ a m = 1.17 × 10 − 5 K − 1 , α ¯ c m = 1.09 × 10 − 5 K − 1 and α ¯ V m = 3.42 × 10 − 5 K − 1 .

Size and surface orientation effects on thermal expansion coefficient of one-dimensional silicon nanostructures

We perform classical molecular dynamics simulations based on the Tersoff interatomic potential to investigate the size and surface orientation dependence of lattice constant and thermal expansion coefficient of one-dimensional silicon nanostructures. Three different surface orientations of silicon are considered, i.e., Si(110), Si(111), and Si(100) with 2×1 reconstruction. For each surface orientation, we investigate nanostructures with thicknesses ranging from 0.3 to 5.0 nm. We compute the vibrational amplitude of surface atoms, lattice constant, and thermal expansion coefficient as a function of size and temperature, and compare them for different surface orientations. An analytical expression is developed to compute the variation of the thermal expansion coefficient with size of the nanostructure.

Thermal expansion of hydroxyapatite between − 100 °C and 50 °C

Hydroxy apatite (HAp) ceramic was synthesized using traditional sintering. Dilatometric and lattice thermal expansion properties of a HAp ceramic were evaluated at temperatures of − 100–50 °C. In that temperature range, the dilatometric thermal expansion coefficient and the lattice thermal expansion coefficient of the HAp ceramic were, respectively, 10.6 × 10 − 6 /°C and 9.9 × 10 − 6 /°C. Furthermore, thermal expansion properties of a human tooth were measured. The thermal expansion coefficient of the horizontal direction perpendicular to the growing direction of a tooth was 15.5 × 10 − 6 /°C; that of the vertical direction along with the direction of tooth growth was 18.9 × 10 − 6 /°C at the temperature range described above.

Elaboration and optical properties of GaFeO 3 thin films

GaFeO 3 thin films were prepared on MgO(001), Al 2O 3(0001) and fused quartz substrates by the pulsed laser deposition technique. The lattice match mechanisms between GaFeO 3 thin films and substrates have been analyzed. Results of optical properties analysis show that the thin films have the different band gaps and optical properties. These differences can be ascribed to the different lattice strains induced by the different lattice mismatch and thermal expansion coefficients between the GaFeO 3 thin films and the substrates.

Cracks in GaN/AlN multiple quantum well structures grown by MBE

Due to the large lattice constant mismatch and thermal expansion coefficient difference between GaN and AlN, large strain is generated inside the GaN/AlN multiple quantum wells, which causes cracks in the structure. We investigated such cracks by optical microscopy and AFM. The crack density was studied with buffer and cap layer thickness, the number of quantum well periods, and the temperature reduction rate after growth as parameters. It was found that the crack density increased exponentially, with the number of periods above 4. Besides, a very thin, 100 nm, GaN buffer layer and ~ 300 nm GaN cap layer greatly reduced the crack density.

Quantitative analysis of in situ wafer bowing measurements for III-nitride growth on sapphire

Wafer bowing measurements have been recently developed into an efficient tool for MOVPE and MBE process optimization. In combination with temperature and reflectance measurements they are applied for direct but mostly qualitative evaluation of III-nitride epitaxial growth processes. In this work, applying a quantitative analysis of wafer bowing throughout the full epitaxial process, we are able to trace the lattice constant mismatch between substrate and every single layer of the growing structures. Starting from the basic models of compressive/tensile film stress causing convex/concave wafer bowing we will describe the physical effects and models to be included for a quantitative analysis. The contributions of vertical temperature gradients, composition dependent lattice constants and thermal expansion coefficients will be separated. It is shown that for (Al,In,Ga)N growth on sapphire the lattice-mismatch induced stress can be described accurately by combining the well-known Stoney equation with the concept of a GaN–sapphire effective substrate. This enables an accurate determination of AlGaN and InGaN lattice constants already during growth.

Anisotropic strain on phonons in a-plane GaN layers studied by Raman scattering

The strain state of a-plane GaN layers grown on r-plane sapphire was studied by Raman spectroscopy. Some of the layers investigated have been uncoalesced stripe structures grown by epitaxial lateral overgrowth (ELOG). Apart from frequency shifts, anisotropic strain within the a-plane leads to a slight splitting of the twofold degenerate E1 and E2 phonon modes. Information about the nature of strain is obtained from plots of the frequency shift of phonons with different symmetry in selected sample regions. The ratio of the frequency shifts is independent of the absolute phonon frequency of unstrained crystals and is sensitive to the strain state, especially in the case of the A1(TO) and \( {\text{E}}^{{\text{h}}}_{2} \) phonons with lattice displacements parallel/perpendicular to the c-axis, respectively. From the Raman data it is concluded that besides biaxial strain in the a-plane due to lattice mismatch and different thermal expansion coefficients of substrate and layer additional hydrostatic components exist originating from the lattice distortion near native defects or impurities. Raman maps of the phonon frequencies and full width at half maximum of the uncoalesced ELOG structures show that the wing above the mask is relaxed and of improved crystalline quality in comparison with the window region.

Growth temperature dependence of strain in a GaN epilayer, grown on a c-plane sapphire substrate

Despite the large mismatch in the lattice constants and thermal-expansion coefficients between the epilayer and the sapphire substrate, GaN epilayer is commonly grown on a c-plane sapphire substrate due to the lack of other suitable substrates [1–3]. The GaN epilayer on a c-plane sapphire substrate is widely grown with the use of the twostep metalorganic chemical vapor deposition (MOCVD), employing an AlN [4] or a low-temperature GaN buffer layer [5]. It was reported that a biaxial strain and a hydrostatic strain could coexist in the GaN epilayer [6, 7]. In GaN, the biaxial stress is due to thermal mismatch stress and growth [6–10]. The growth stress can be caused by lattice mismatch, island coalescence, grain growth, or surface stress [8–10]. Some in-situ measurements on the growth stress have been reported during MOCVD of GaN [8–10]. The internal hydrostatic strain was shown to have been introduced by the presence of point defects, which can be compressive or expansive depending on their size [6, 7]. A study was reported on a high-resolution X-ray diffraction (HRXRD) strain–stress analysis of a GaN/sapphire heterostructure grown through molecular beam epitaxy (MBE), particularly in the deformation state, depending on the relative content of N in the Ga1-xNx buffer layer by Harutyunyan et al. [11]. In the authors previous study [12], the strain analysis of a GaN epilayer with different growth times on a c-plane sapphire substrate via a two-step growth, using low-pressure, metalorganic chemical vapor deposition was conducted on the basis of precise measurement of the lattice parameters, using HRXRD. In this continuing study, the growth temperature dependence of the residual strain in a GaN epilayer at room temperature on a c-plane sapphire was studied. The final growth temperature in a fixed two-step MOCVD was varied from 850 to 1,050 C. The cand a-lattice parameters were measured using HRXRD, followed by the out-of-plane and in-plane strains. We have extracted the levels of biaxial and hydrostatic components of strain in the GaN films on sapphire. An undoped GaN epilayer was grown on a c-plane sapphire substrate in a horizontal MOCVD reactor at a low pressure of 300 Torr, as described in the authors’ previous articles [12, 13]. We employed a two-step growth method of GaN—consisting of the deposition of the low-temperature GaN buffer layer and high-temperature GaN epitaxial growth. The growth temperature of the high-temperature GaN was varied from 850 to 1,050 C so that the temperature dependence of the strain of the GaN epilayer induced after the two-step MOCVD growth process could be studied. The V/III ratios were 2,740 and 1,370 for buffer growth and the main high-temperature growth, respectively [12]. The growth rate was fixed at 0.07 lm/min; as such, the thickness of the GaN layer that was grown for 20 min was estimated to be 1.5 lm. The c-lattice and a-lattice parameters of the GaN epilayers were measured with a x-2h scan of the wurtzite GaN epilayer through triple-axis, HRXRD, to obtain precise measurements (PANalytical X’Pert PRO MRD), as described in the authors’ previous article [12]. S. I. Cho K. Chang Department of Chemical Engineering, University of Seoul, 90 Jeonnong-dong, Dongdaemun-gu, Seoul 130-743, South Korea

Carbonization Study of Different Silicon Orientations

3C-SiC/Si heteroepitaxy is hampered by large mismatches in lattice parameters (19.7%) and thermal expansion coefficient (8%) leading to 3C-SiC films containing high defects density. To reduce the presence of defects, a multi-step growth process in a CVD reactor is used. The aim of the work is to study the effect of carbonization on differently oriented Si surfaces, experiencing a 200°C-wide temperature range in a CVD reactor, to improve the crystalline quality. TEM analysis are carried out to evaluate thickness, crystal orientations and defects of carbonized layers with respect to the time-dependence of the process and to the different orientations of the Si substrate. It will be shown that process-related defects are strictly correlated to the substrate orientation either for size, density, occupied area, shape or thickness. Uniform, flat and crystalline thin SiC films are obtained with a low defect density.

Characterization of Mn–Zn Ferrite Prepared by a Hydrothermal Process From Used Dry Batteries and Waste Steel Pickling Liquor

In this study, we propose a process to prepare Mn–Zn ferrite powder, using oxides of manganese and zinc extracted from used dry batteries, and ferrous chloride solution from waste steel pickling liquor. The hydrothermal process was used to convert the starting raw materials into Mn–Zn ferrite powder. This powder revealed the formation of cubic ferrite with a saturation magnetization (Ms) of 58.8 emu/g and an intrinsic coercive force (Hc) of 3.8 Oe. The average lattice thermal expansion coefficient αa (200°–500°C) of this Mn–Zn ferrite powder was 14.14 × 10−6 K−1. The toroidal specimen sintered at 1300°C in a controlled oxygen atmosphere presented a flat profile of initial permeability (μi) of 2150–2200, in the frequency range 0.1–20 kHz, which allows its use in magnetic applications. This useful technology, combined with environment and materials engineering, can promote the recycling of dry batteries and contribute to the preservation of the earth. Moreover, this technology can also decrease the cost of disposal of the used dried batteries and waste steel pickling liquor.

Phase transition of O-orthorhombic LaMn0.95O3.02 at high-temperature

Abstract The high-temperature behavior of O -orthorhombic LaMn 0.95 O 3.02 in air was studied by using high-temperature XRD combined with TG/DSC analysis. A phase transition from O -orthorhombic to rhombohedral was found between 573 and 773 K. TG/DSC curves showed a weight gain and no DSC peaks within the temperature range of the phase transition. The phase transition is attributed to the change of oxygen content in LaMn 0.95 O 3.02 . The lattice thermal expansion coefficients of rhombohedral LaMn 0.95 O 3.02 were calculated using lattice parameters.

Crystal structure, thermal expansion and magnetic properties of new compound Dy 1.2Fe 4Si 9.8

The new ternary compound Dy 1.2Fe 4Si 9.8 have been prepared and studied by means of X-ray powder diffraction technique and vibrating sample magnetometer. The ternary compound Dy 1.2Fe 4Si 9.8 crystallizes in the hexagonal Er 1.2Fe 4Si 9.8-type structure, space group P6 3/ mmc (no. 194) with lattice parameters a = 0.39415(1) nm and c = 1.52771(3) nm. The crystal structural refinement of the compound Dy 1.2Fe 4Si 9.8 has been performed by using Rietveld method. Lattice thermal expansion studies on the compound were carried out in the temperature range from 298 to 1013 K. The variation of the unit cell parameters shows that the unit cell parameters increase with the increase in temperature. The coefficients of average lattice thermal expansion along various axes in the temperature range from 298 to 1013 K are α ¯ a = 1.42 × 10 − 5 K − 1 , α ¯ b = 9.17 × 10 − 6 K − 1 and α ¯ V = 3.78 × 10 − 5 K − 1 . The temperature dependence of the magnetization for the compound was also investigated in the range from 90 to 300 K. The experimentally determined magnetic effective paramagnetic moment is μ eff = 11.3 μ B per formula unit (10.3 μ B per Dy atom).

Sublimation growth of aluminum nitride on silicon carbide substrate with aluminum nitride–silicon carbide alloy transition layer

The advantages of depositing AlN–SiC alloy transition layers on SiC substrates before the seeded growth of bulk AlN crystals were examined. The presence of AlN–SiC alloy layers helped to suppress the SiC decomposition by providing vapor sources of silicon and carbon. In addition, cracks in the final AlN crystals decreased from ∼5 × 106/mm2 for those grown directly on SiC substrates to less than 1 × 106/mm2 for those grown on AlN–SiC alloy layers because of the intermediate lattice constants and thermal expansion coefficient of AlN–SiC. X-ray diffraction confirmed the formation of pure single-crystalline AlN upon both AlN–SiC alloys and SiC substrates. X-ray topography (XRT) demonstrated that strains present in the AlN crystals decreased as the AlN grew thicker. However, the XRT for AlN crystals grown directly on SiC substrates was significantly distorted with a high overall defect density compared to those grown on AlN–SiC alloys.

Sub-solidus phase relations in CeO 2–YSZ and ThO 2–YSZ systems: XRD, high temperature-XRD and EPMA studies

In the present manuscript, synthesis, XRD, high temperature-XRD as well as electron probe for microanalysis (EPMA) studies on CeO 2–YSZ and ThO 2–YSZ are being reported. It is found that CeO 2–YSZ system shows formation of a cubic solid solution throughout the homogeneity range. The lattice parameter of this cubic solid solution in CeO 2–YSZ system decreases linearly on going from CeO 2 to YSZ side. On the other hand ThO 2–YSZ system was bi-phasic throughout the range. XRD results indicate that YSZ has no solubility in ThO 2, however, EPMA studies revealed that a very small amount of YSZ is soluble in ThO 2. High Temperature XRD studies were performed on few representative compositions in CeO 2–YSZ system and the lattice thermal expansion coefficients (20–1200 °C) of the compositions YSZ, Ce 0.2(YSZ) 0.8O 1.90, Ce 0.4(YSZ) 0.6O 1.925 and Ce 0.6(YSZ) 0.4O 1.950 were observed as 11.32 × 10 −6, 11.38 × 10 −6, 11.43 × 10 −6 and 11.48 × 10 −6 °C −1, respectively.

Effect of inclusions on heterogeneous crack nucleation in nanocomposites

A two-dimensional theoretical model is proposed for the heterogeneous nucleation of a grain-boundary nanocrack in a nanocomposite consisting of a nanocrystalline matrix and nanoinclusions whose elastic moduli are identical to those of the matrix. The inclusions have the form of rods with a rectangular cross section and undergo dilatation eigenstrain induced by the differences in the lattice parameters and thermal expansion coefficients of the matrix and inclusions. In terms of the model, a mode-I–II nanocrack nucleates at the negative disclination of a biaxial dipole consisting of wedge grain-boundary (or junction) disclinations; then, the nanocrack opens along a grain boundary and reaches an inclusion boundary. Depending on the relative positions and orientations of the initial segment of the nanocrack and the inclusion, the nanocrack can either penetrate into the inclusion or bypass it along the matrix-inclusion interface. The nanocrack nucleation probability increases near an inclusion with negative (compressive) dilatation eigenstrain. A decrease in the inclusion size decreases (increases) the probability of a crack opening along the interface if the dilatation eigenstrain is negative (positive).