Showing papers on "Thermal expansion published in 2004"
TL;DR: In this paper, the thermodynamic properties of 154 mineral endmembers, 13 silicate liquid end-members and 22 aqueous fluid species are presented in a revised and updated data set.
Abstract: The thermodynamic properties of 154 mineral end-members, 13 silicate liquid end-members and 22 aqueous fluid species are presented in a revised and updated data set. The use of a temperature-dependent thermal expansion and bulk modulus, and the use of high-pressure equations of state for solids and fluids, allows calculation of mineral–fluid equilibria to 100 kbar pressure or higher. A pressure-dependent Landau model for order–disorder permits extension of disordering transitions to high pressures, and, in particular, allows the alpha–beta quartz transition to be handled more satisfactorily. Several melt end-members have been included to enable calculation of simple phase equilibria and as a first stage in developing melt mixing models in NCKFMASH. The simple aqueous species density model has been extended to enable speciation calculations and mineral solubility determination involving minerals and aqueous species at high temperatures and pressures. The data set has also been improved by incorporation of many new phase equilibrium constraints, calorimetric studies and new measurements of molar volume, thermal expansion and compressibility. This has led to a significant improvement in the level of agreement with the available experimental phase equilibria, and to greater flexibility in calculation of complex mineral equilibria. It is also shown that there is very good agreement between the data set and the most recent available calorimetric data.
4,482 citations
TL;DR: In this paper, BaZrO3 and La2Zr2O7 powders were optimized for application as powders for plasma spraying and thermal properties of these materials were determined.
Abstract: Zirconates with high melting points were investigated for
application as materials for thermal barrier coatings at operating temperatures >1300°C. SrZrO3, BaZrO3, and La2Zr2O7
powders were synthesized and sintered to compacts with
various levels of porosity. The sintering results indicated a promising low-sintering activity of the investigated materials. Thermal properties of these dense materials were determined. Thermal expansion coefficients were slightly lower than those of Y2O3-stabilized ZrO2 (YSZ); thermal conductivities of SrZrO3 and BaZrO3 were comparable or slightly higher than those of YSZ. La2Zr2O7 had a lower thermal conductivity. SrZrO3 was not suitable for application as a thermal barrier coating because of a phase transition at temperatures between 700° and 800°C. Mechanical properties (hardness, fracture toughness, and Young’s modulus) of dense BaZrO3 and La2Zr2O7 samples were determined by indentation techniques and showed lower hardness and Young’s modulus compared to YSZ. BaZrO3 and La2Zr2O7 powders were optimized for application as powders for plasma spraying. Plasma-sprayed coatings were produced and characterized. Thermal cycling with a gas burner at 1200°C showed a massive attack of the BaZrO3 coating, with loss of BaO. On the other hand, the La2Zr2O7 coating showed excellent thermal stability and thermalshock behavior.
1,074 citations
TL;DR: In this paper, an all-cellulose composite, in which both the fibers and the matrix are cellulose, was prepared by distinguishing the solubility of the matrix cellulose into the solvent from that of the fibers through pretreatment, and the structure, mechanical and thermal properties of this composite were investigated using an X-ray diffraction, a scanning electron microscope, a tensile test, and dynamic viscoelastic and thermomechanical analyses.
Abstract: An all-cellulose composite, in which both the fibers and the matrix are cellulose, was prepared by distinguishing the solubility of the matrix cellulose into the solvent from that of the fibers through pretreatment. The structure, mechanical, and thermal properties of this composite were investigated using an X-ray diffraction, a scanning electron microscope, a tensile test, and dynamic viscoelastic and thermomechanical analyses. The tensile strength of uniaxially reinforced all-cellulose composite was 480 MPa at 25 °C, and the dynamic storage modulus was as high as 20 GPa at 300 °C. These were comparable or even higher than those of conventional glass-fiber-reinforced composites. In addition, a linear thermal expansion coefficient was about 10-7 K-1. This all-cellulose composite shows substantial advantages, that is, it is composed of sustainable resources, there is less interface between the fiber and the matrix, it possesses excellent mechanical and thermal performance during use, and it is biodegradab...
691 citations
TL;DR: In this article, the thermodynamic properties of Al, Ni, NiAl, and Ni3Al were studied using the first-principles approach using the ab initio plane wave pseudopotential method within the generalized gradient approximation.
441 citations
TL;DR: The composite of diamond and copper have a potential for a heat spreading substrate with high performance and high reliability because not only its thermal conductivity is high but its coefficient of thermal expansion can be tailored according to a semiconductor material of electronics devices.
344 citations
TL;DR: In this article, the linear thermal expansion coefficients of single-crystal silicon have been determined in the temperature range 293 to 1000 K using a dilatometer which consists of a heterodyne laser Michelson interferometer and gold versus platinum thermocouple.
Abstract: As a part of the program to establish a thermal expansion standard, the linear thermal expansion coefficients of single-crystal silicon have been determined in the temperature range 293 to 1000 K using a dilatometer which consists of a heterodyne laser Michelson interferometer and gold versus platinum thermocouple. The relative standard deviation of the measured values from those calculated from the best least-squares fit was 0.21%. The relative expanded uncertainty in the measurement was estimated to be 1.1 to 1.5% in the temperature range, based upon an analysis of thirteen standard uncertainties. The present data are compared with the data previously obtained by similar dilatometers and the standard reference data for the thermal expansion coefficient of silicon, recommended by the Committee on Data for Science and Technology (CODATA). The present data are in good agreement with the most recently reported data but not with the earlier high-temperature data used to evaluate the standard reference data, which suggests a need for the reevaluation of the standard reference data for the thermal expansion coefficient of silicon at temperatures above 600 K.
319 citations
TL;DR: In this article, an improved thermodynamic formalism that incorporates a new physical property, the chemical expansivity, was proposed for modeling stress and strain in materials, probing defect structure, and analyzing transport and kinetic properties.
Abstract: To better understand thermal strain in electrochemical ceramics, the temperature and oxidation-state dependence of lattice volume in La0.6Sr0.4Co0.2Fe0.8O3−δ (LSCF) were measured. Large values in the apparent thermal expansion coefficient at high temperature (>50 ppm/°C) were caused by changes in oxygen content, not increases in thermal expansivity. This material can be described using an improved thermodynamic formalism that incorporates a new physical property, the chemical expansivity. Our approach opens new avenues for modeling stress and strain in materials, probing defect structure, and analyzing transport and kinetic properties.
302 citations
TL;DR: In this paper, the thermal stability of Lanthanum zirconate (LZ) was studied by long-term annealing and thermal cycling, and a preferred crystal growth direction in the coating was observed by X-ray diffraction.
Abstract: Lanthanum zirconate (La 2 Zr 2 O 7 , LZ) is a newly proposed material for thermal barrier coatings (TBCs). The thermal stability of LZ coating was studied in this work by long-term annealing and thermal cycling. After long-term annealing at 1400°C or thermal cycling, both LZ powder and plasma-sprayed coating still kept the pyrochlore structure, and a preferred crystal growth direction in the coating was observed by X-ray diffraction. A considerable amount of La 2 O 3 in the powder was evaporated in the plasma flame, resulting in a nonstoichiometric coating. Additionally, compared with the standard TBC material yttria-stabilized zirconia (YSZ), LZ coating has a lower thermal expansion coefficient, which leads to higher stress levels in a TBC system.
270 citations
TL;DR: Isotropic nearly zero thermal expansion is reported in a large temperature range for Fe[Co(CN)6], a member of the Prussian blue family with electronically active metal sublattices and a cubic framework structure built by a cyanide-bridged network of octahedral units.
Abstract: Isotropic nearly zero thermal expansion (i.e., negligible volume change) is reported in a large temperature range for Fe[Co(CN)6], a member of the Prussian blue family with electronically active metal sublattices and a cubic framework structure built by a cyanide-bridged network of octahedral units. Suitable selection of metal ions and interstitial units could allow such anomalous thermal behavior to be combined with the variety of unusual electronic, optical, and magnetic properties exhibited by Prussian blue analogues.
242 citations
TL;DR: In this paper, the authors used finite element models to predict material response in internally heated nozzle tests, and the results of the modeling suggest that HfB2 should survive the high thermal stresses generated during the nozzle test primarily because of its superior thermal conductivity.
Abstract: The thermal conductivity, thermal expansion, Young's Modulus, flexural strength, and brittle-plastic deformation transition temperature were determined for HfB2, HfC0.98, HfC0.67, and HfN0.92 ceramics. The mechanical behavior of αHf(N) solid solutions was also studied. The thermal conductivity of modified HfB2 exceeded that of the other materials by a factor of 5 at room temperature and by a factor of 2.5 at 820°C. The transition temperature of HfC exhibited a strong stoichiometry dependence, decreasing from 2200°C for HfC0.98 to 1100°C for HfC0.67 ceramics. The transition temperature of HfB2 was 1100°C. Pure HfB2 was found to have a strength of 340 MPa in 4 point bending, that was constant from room temperature to 1600°C, while a HfB2 + 10% HfCx had a higher room temperature bend strength of 440 MPa, but that dropped to 200 MPa at 1600°C. The data generated by this effort was inputted into finite element models to predict material response in internally heated nozzle tests. The theoretical model required accurate material properties, realistic thermal boundary conditions, transient heat transfer analysis, and a good understanding of the displacement constraints. The results of the modeling suggest that HfB2 should survive the high thermal stresses generated during the nozzle test primarily because of its superior thermal conductivity. The comparison the theoretical failure calculations to the observed response in actual test conditions show quite good agreement implying that the behavior of the design is well understood.
233 citations
TL;DR: The ZrW2O8 family of materials has been shown to exhibit the unusual property of negative thermal expansion over a wide temperature range α-ZrW 2O8 itself shows positive thermal expansion from 2 K to 1443 K with a coefficient of thermal expansion α 1 of -91×10-6 K-1 between 2 and 300 K as mentioned in this paper.
Abstract: The ZrW2O8 family of materials has been shown to exhibit the unusual property of negative thermal expansion over a wide temperature range α-ZrW2O8 itself shows negative thermal expansion from 2 K to 1443 K with a coefficient of thermal expansion α1 of -91×10-6 K-1 between 2 and 300 K This behaviour can be related to the unusual structure of these materials, which possess a family of low energy phonon modes with negative Gruneisen parameters α-ZrW2O8 also shows a phase transition at 448 K to β-ZrW2O8 in which oxygen atoms are dynamically disordered These phenomena have been investigated by a number of techniques Results of powder neutron diffraction at 260 different temperatures are presented
TL;DR: A series of microcapsules containing n-octadecane with a urea-melamine-formaldehyde copolymer shell were synthesized by in-situ polymerization.
Abstract: A series of microcapsules containing n-octadecane with a urea-melamine-formaldehyde copolymer shell were synthesized by in-situ polymerization. The surface morphology, diameter, melting and crystallization properties, and thermal stability of the microcapsules were investigated by using FTIR, SEM, DSC, TGA and DTA. The diameters of the microcapsules are in the range of 0.2–5.6 μm. The n-octadecane contents in the microcapsules are in the range of 65–78wt%. The mole ratio of urea-melamine has been found to have no effect on the melting temperature of the microcapsules. Two crystallization peaks on the DSC cooling curve have been observed. The thermal damage mechanisms are the liquefied n-octadecane leaking from the microcapsule and breakage of the shell due to the mismatch of thermal expansion of the core and shell materials at high temperatures. The thermal stability of materials can be enhanced up to 10 °C by the copolymerization of urea, melamine and formaldehyde in a mole ratio 0.2:0.8:3. The thermal stability of 160 °C heat-treated microcapsules containing 8.8% cyclohexane can be further enhanced up to approximately 37 °C.
TL;DR: In this article, the cementite phase of Fe3C was studied by high-resolution neutron powder diffraction at 4.2 and 20 K intervals between 20 and 600 K. The average volumetric coefficient of thermal expansion above Tc was found to be 4.1
Abstract: The cementite phase of Fe3C has been studied by high-resolution neutron powder diffraction at 4.2 K and at 20 K intervals between 20 and 600 K. The crystal structure remains orthorhombic (Pnma) throughout, with the fractional coordinates of all atoms varying only slightly (the magnetic structure of the ferromagnetic phase could not be determined). The ferromagnetic phase transition, with Tc ≃ 480 K, greatly affects the thermal expansion coefficient of the material. The average volumetric coefficient of thermal expansion above Tc was found to be 4.1 (1) × 10−5 K−1; below Tc it is considerably lower (< 1.8 × 10−5 K−1) and varies greatly with temperature. The behaviour of the volume over the full temperature range of the experiment may be modelled by a third-order Gruneisen approximation to the zero-pressure equation of state, combined with a magnetostrictive correction based on mean-field theory.
TL;DR: In this paper, the glass forming regions in the two systems have been determined and the dilatometric properties of the melted glasses (coefficient of thermal expansion, glass transition temperature and softening temperature) have been measured to identify the glasses that best fulfill the cell requirements, such as a thermal expansion coefficient in the range (8.5 −12) −10 −6 K −1.
Abstract: Glass-ceramics in the systems RO–BaO–SiO 2 (R = Mg, Zn) have good thermal properties for sealing materials on planar-type solid oxide fuel cells (SOFC) at high and intermediate temperatures. In this work, the glass forming regions in the two systems have been determined. Composition lines with different BaO/RO ratios have been defined varying the silica content. The dilatometric properties of the melted glasses (coefficient of thermal expansion, glass transition temperature and softening temperature) have been measured to identify the glasses that best fulfill the cell requirements, such as a thermal expansion coefficient in the range (8.5–12) × 10 −6 K −1 . Since the sealing process is carried out employing paste technology during the heating and working schedule of the cell, it is important to study the interaction between sintering and crystallization to make dense materials with an adequate microstructure. The sintering and crystallization kinetics have been characterized for some selected glass compositions by using hot-stage microscopy (HSM) and differential thermal analysis (DTA). A new parameter S C = T X − T MS which takes into account the onset crystallization temperature ( T X ), temperature of maximum shrinkage ( T MS ) is proposed as an empirical method to evaluate the ability of glass sintering of the studied compositions and indicate good materials for glass-ceramic SOFC products.
TL;DR: In this article, five different carbon/carbon composites (C/C) have been prepared and their thermophysical properties studied and the results show that the X -Y direction thermal expansion coefficient (CTE) is negative in the range 0 -100 °C with values ranging from −0.29 to −0.85 −10 −6 /K. The microstructure of the PyC has no obvious effect on the CTE for composites with the same preform architecture.
TL;DR: In this article, the authors present a theoretical analysis and the results of measurements of thermorefractive noise in microcavities, which may be considered direct observations of fundamental fluctuations of temperature in solid media.
Abstract: We present a theoretical analysis and the results of measurements of thermorefractive noise in microcavities. These measurements may be considered direct observations of fundamental fluctuations of temperature in solid media. Our experimentally measured noise spectra are in agreement with our theoretical model.
TL;DR: In this paper, the authors derived the fabric and the stiffness tensor in average over those pairs of interacting particles with contact within the averaging volume, starting from a linear expansion of the interaction potential around static equilibrium.
TL;DR: The report of a systematic increase of the superconducting transition temperature T(c) with a biaxial tensile strain in MgB2 films to well beyond the bulk value suggests that the E(2g) phonon softening is a possible avenue to achieve even higher T( c) in M gB2-related material systems.
Abstract: We report a systematic increase of the superconducting transition temperature T(c) with a biaxial tensile strain in MgB2 films to well beyond the bulk value. The tensile strain increases with the MgB2 film thickness, caused primarily by the coalescence of initially nucleated discrete islands (the Volmer-Weber growth mode.) The T(c) increase was observed in epitaxial films on SiC and sapphire substrates, although the T(c) values were different for the two substrates due to different lattice parameters and thermal expansion coefficients. We identified, by first-principles calculations, the underlying mechanism for the T(c) increase to be the softening of the bond-stretching E(2g) phonon mode, and we confirmed this conclusion by Raman scattering measurements. The result suggests that the E(2g) phonon softening is a possible avenue to achieve even higher T(c) in MgB2-related material systems.
TL;DR: In this article, the thermal conductivities of 40 pyrochlores with the composition A2B2O7 (A = La, Pr, Nd, Sm, Eu, Gd, Y, Er or Lu; B = Ti, Mo, Sn, Zr or Pb) are predicted by molecular dynamics simulations.
Abstract: The thermal conductivities of 40 pyrochlores with the composition A2B2O7 (A = La, Pr, Nd, Sm, Eu, Gd, Y, Er or Lu; B = Ti, Mo, Sn, Zr or Pb) are predicted by molecular dynamics simulations. The trends in the behaviour can be fully understood in terms of the differences in the density and the speed of sound in the materials. Increased structural disorder, arising from O diffusion in most of the Pb-containing systems, leads to a further reduction in the thermal conductivity. We suggest strategies for lowering the thermal conductivity even further.
TL;DR: In this paper, the thermal expansion of cast MCrAlY (M = Ni and/or Co) alloys and cast aluminides (NiAl, (Ni,Pt)Al and Ni3Al) was measured at temperatures up to 1300°C and compared to that of a single-crystal Ni-base superalloy.
Abstract: The thermal expansion mismatch between a metallic substrate and its external oxide scale generates a strain on cooling that is a primary cause of spallation of protective oxide scales. This study compares thermal expansion behavior and cyclic oxidation performance of the two major composition classes of high-temperature commercial coatings for protection of single-crystal superalloys. The thermal expansion of cast MCrAlY (M = Ni and/or Co) alloys and cast aluminides (NiAl, (Ni,Pt)Al and Ni3Al) was measured at temperatures up to 1300°C and compared to that of a single-crystal Ni-base superalloy. The tendency for scale spallation from each alloy was evaluated by cyclic oxidation testing at 1150°C. The coefficients of thermal expansion for the aluminides were lower than those of the MCrAlY-based alloys at all temperatures and scale adherence to the Hf-doped aluminides was generally superior. Scale adherence to the various compositions of MCrAlY-type alloys did not directly correlate to their thermal ...
TL;DR: In this paper, the thermophysical properties of all stainless steels for temperatures between 300 and 1800 K (austenitic 3 series, ferritic-4 series and precipitation-hardened 6 series alloys) were derived.
Abstract: Equations have been derived to calculate values of the thermophysical properties of all stainless steels for temperatures between 300 and 1800 K (austenitic 3 series, ferritic-4 series and precipitation-hardened 6-series alloys). Values of the following properties are given in both figures and tables: density (ρ), thermal expansion coefficient (α), heat capacity (Cp), enthalpy (HT−H298), thermal conductivity (λ) and thermal diffusivity (a), electrical resistivity (R), viscosity (η) and surface tension (γ).
TL;DR: The average linear thermal expansion coefficients of strontium series perovskite type oxides are 1.13×10−5 K−1 for SrHfO3 in the temperature range between 423 and 1073 K as discussed by the authors.
TL;DR: In this paper, the phase transition path was described as the Si atoms sliding between 2b and 2d Wyckoff positions on the (11(2) over bar 0) plane.
Abstract: The Nanolaminate Ti3SiC2 ceramic exhibited unique mechanical properties, such as high modulus, low anisotropic hardness to modulus ratio and microscale ductility etc. The planar close-packed Si atoms were expected to play a dominant role in deducing these properties. By performing first-principles total energy calculations, we demonstrated that a reversible polymorphic phase transition occurred when shear strain energy was large enough to close an energy barrier. The phase transition path was described as the Si atoms sliding between 2b and 2d Wyckoff positions on the (11(2) over bar 0) plane. The electronic band structure, lattice dynamics, and structure stability were discussed for the two polymorphs, respectively. We demonstrated that the alpha-Ti3SiC2 was more stable than beta-Ti3SiC2 by comparing the ground-state total energy and ab initio Gibbs free energy. Raman and infrared active phonon modes were illustrated for feasibly identifying the two phases in experimental spectra. The results were used to assign peaks in the experimental Raman spectrum with distinct vibrational modes, and to clarify the origin of the uncertain peak. The calculated heat capacity and volume thermal expansion coefficient agreed with experimental values well. The elastic mechanical parameters of the polymorphs were presented and compared with respect to various strain modes. Based on electronic band structure discussions, we clarified the mechanism of anisotropic hardness of Ti3SiC2, which attributed to different covalent bonding strengths involved in kink migration.
TL;DR: In this article, temperature-dependent changes of their crystal lattices have been evaluated from the second-rank thermal expansion tensors, showing that γ- and ∊-hexanitrohexaazaisowurtzitane (γ-HNIW, space group P21/n for both crystals) undergo anisotropic thermal expansion.
Abstract: Crystals of γ- and ∊-hexanitrohexaazaisowurtzitane (γ- and ∊-HNIW, space group P21/n for both crystals) have been investigated in the 100–298 K temperature range using single-crystal X-ray diffraction techniques. Temperature-dependent changes of their crystal lattices have been evaluated from the second-rank thermal expansion tensors. Both lattices undergo anisotropic thermal expansion, that of γ-HNIW being more anisotropic than that of the ∊ phase. Comparison with previously reported predictions from molecular dynamics calculations indicates significant differences. Although there are many short (less than van der Waals) intermolecular interactions in both polymorphs, there is no obvious relationship between the short distances and the difference in thermal expansion behavior. Non-linear temperature dependence of the atomic displacement parameters is indicative of anharmonicity of the crystal mean field potential.
TL;DR: This paper measured changes in thermal expansion coefficient and excess free volume content during in situ heating-cooling cycles of metallic glasses in the as-quenched state and after indentation were measured in the temperature range between 350 and 670 K by real-time diffraction.
Patent•
30 Mar 2004TL;DR: In this article, various composition materials may be selected according to their thermal expansion coefficient and used to form resonator components on a substrate, when exposed to temperature variations, the relative expansion of these composition materials creates a compensating stiffness, or a compressive/tensile strain.
Abstract: Thermally induced frequency variations in a micromechanical resonator are actively or passively mitigated by application of a compensating stiffness, or a compressive/tensile strain. Various composition materials may be selected according to their thermal expansion coefficient and used to form resonator components on a substrate. When exposed to temperature variations, the relative expansion of these composition materials creates a compensating stiffness, or a compressive/tensile strain.
TL;DR: LiInS2 is a chalcogenide biaxial material transparent from 0.4 to 12 μm that has been successfully grown in large sizes and with good optical quality as mentioned in this paper.
Abstract: Lithium thioindate (LiInS2) is a new nonlinear chalcogenide biaxial material transparent from 0.4 to 12 μm that has been successfully grown in large sizes and with good optical quality. We report on new physical properties that are relevant for laser and nonlinear optics applications. With respect to AgGaS(e)2 ternary chalcopyrite materials, LiInS2 displays a nearly isotropic thermal expansion behavior, a 5-times-larger thermal conductivity associated with high optical damage thresholds, and an extremely low-intensity-dependent absorption, allowing direct high-power downconversion from the near-IR to the deep mid-IR. Continuous-wave difference-frequency generation (5–11 μm) of Ti:sapphire laser sources is reported for the first time to our knowledge.
TL;DR: In this paper, the authors measured the extended x-ray-absorption fine-structure (EXAFS) of copper from 4 to 500 K and analyzed by the cumulant method, to check the effectiveness of EXAFS as a probe of local dynamics and thermal expansion.
Abstract: Extended x-ray-absorption fine-structure (EXAFS) of copper has been measured from 4 to 500 K and analyzed by the cumulant method, to check the effectiveness of EXAFS as a probe of local dynamics and thermal expansion. The comparison between parallel mean square relative displacements (MSRD) of the first four coordination shells has allowed detecting a significant deviation from a pure Debye behavior. The first-shell EXAFS thermal expansion is larger than the crystallographic one: the difference has allowed evaluating the perpendicular MSRD, whose Debye temperature is slightly larger than the one of the parallel MSRD, due to anisotropy effects. High-order first-shell cumulants are in good agreement with quantum perturbative models. The anharmonic contribution to the first-shell parallel MSRD amounts to less than 1.5 percent. The third cumulant cannot be neglected in the analysis, if accurate values of the first cumulant are sought; it cannot however be used to directly estimate the thermal expansion. The shape of the effective pair potential is independent of temperature; a rigid shift, partially due to the relative motion perpendicular to the bond direction, is however observed.
TL;DR: In this paper, the properties of the strontium perovskite type oxide, SrHfO 3 have been measured and the thermal and mechanical properties have been evaluated by an X-ray diffraction method.
TL;DR: The thermal expansion behavior of polystyrene (PS) thin films was investigated using x-ray reflectivity, focusing on ultrathin films below 10 nm, and it was found that the thermal expansivity decreases with thickness in the glassy state as well as in the molten state while the reduction is smaller in the lava state.
Abstract: The thermal expansion behavior of polystyrene (PS) thin films was investigated using x-ray reflectivity, focusing on ultrathin films below 10 nm. It was found that the glass transition temperature T(g) decreases with thickness as reported by many researchers while it is almost independent of thickness and constant at 354 K for films below approximately 10 nm. The thickness dependence of T(g) was well reproduced by a two-layer model consisting of a mobile surface layer with T(g) of 354.5 K and a bulklike layer with T(g) of 373 K ( =bulk T(g) ), suggesting that the so-called immobile dead layer near the substrate is negligible or very thin in this system. This surface T(g) of 354 K was confirmed by the relaxation of surface roughness of as-deposited films at about 354 K. It was also found that the thermal expansivity decreases with thickness in the glassy state as well as in the molten state while the reduction is smaller in the molten state.