A practical measurement system for the accurate determination of linear thermal expansion coefficients

1984 ◽  
Vol 17 (8) ◽  
pp. 669-673 ◽  
Author(s):  
M Okaji ◽  
H Imai
1989 ◽  
Vol 22 (4) ◽  
pp. 380-381
Author(s):  
S. K. Pradhan ◽  
M. De

Lattice parameters for four Cu–Si alloys containing 2.2, 4.3, 6.4 and 8.7 at.% Si in the solid-solution range have been calculated in the temperature range 303–928 K. The lattice parameters increase slowly in a nonlinear manner with rise in temperature. The calculated linear thermal-expansion coefficients (α) at room temperature increase with increasing solute concentration (Si) but decrease almost linearly with increasing temperature, the rate of decrease being higher for alloys with higher solute concentration. All the alloys have almost the same average α value (α av ~ 16.0 × 10−6 K−1), which is the value of α at the temperature interval 615–625 K for all the alloy compositions.


1976 ◽  
Vol 49 (1) ◽  
pp. 34-42 ◽  
Author(s):  
A. W. Fogiel ◽  
H. K. Frensdorff ◽  
J. D. MacLachlan

Abstract The thermomechanical analyzer (TMA) is eminently suitable for the measurement of the thermal expansion coefficient of rubbers, provided the equipment is calibrated with materials of similar expansion coefficient. FKM or other thermally stable and amorphous polymers (of independently determined thermal expansion characteristics) can be used as calibration standards. The relative simplicity and precision of the TMA method for the determination of the coefficient of isotropic linear expansion, and hence, of volumetric expansion of rubbers, makes this important thermodynamic parameter easily accessible experimentally. Because of the frequently observed anisotropy of molded elastomeric compounds, measurements in all three dimensions are required to define linear, isotropic expansion and shrinkage which, to an excellent approximation, are represented by arithmetic averages of the three unidirectional values. Good agreement has been found between the average (isotropic) shrinkage determined experimentally and that calculated from the average (isotropic) coefficient of linear thermal expansion, α. The effect of fillers, such as carbon black, on α is additive. This makes it possible to predict α and shrinkage of all filled compounds from a single value of α of the unfilled rubber. The linear thermal expansion coefficients of the tested rubbers (FKM, NBR, EPDM) increase linearly with temperature, the increase being generally stronger for FKM than for the other elastomers. The appreciably higher mold shrinkage of FKM relative to NBR is directly due to the higher α of FKM for comparable levels of fillers. This must be kept in mind when expedience dictates the use of the same molds for FKM and NBR compounds.


2000 ◽  
Author(s):  
Chi Hsiang Pan

Abstract This work presents a simple method for determination of linear thermal expansion coefficients (LTEC) of thin films with a compact microstructure. The microstructure comprises of a pair of cantilever beams with different lengths connected by a short tip. By heating the microstructure, the thermal strain causes two beams to deflect each other, thereby magnifying the deflection, which is measured by the tip directly under an optical microscope with the specimen placed in a heating stage. An analytical model is derived to relate the measured displacement to thermal strain, therefore, LTEC of thin films can be calculated. The analytical model is free from any correction factor. Furthermore, the accuracy of LTEC measurement is significantly enhanced because the measured displacement is independent of some physical values, namely the Young’s modulus, Poisson’s ratios and thickness of the substrate and the thin film, and the LTEC of the substrate. Finite element model is also used to support the analytical model and to perform nonlinear analysis. Experimental results with SiO2 films as well as undoped LPCVD polysilicon films are used herein to demonstrate the effectiveness of the proposed method.


2017 ◽  
Vol 32 (S2) ◽  
pp. S38-S42
Author(s):  
Matthew R. Rowles ◽  
Cheng-Cheng Wang ◽  
Kongfa Chen ◽  
Na Li ◽  
Shuai He ◽  
...  

The crystal structure and thermal expansion of the perovskite samarium cobalt oxide (SmCoO3) have been determined over the temperature range 295–1245 K by Rietveld analysis of X-ray powder diffraction data. Polycrystalline samples were prepared by a sol–gel synthesis route followed by high-temperature calcination in air. SmCoO3 is orthorhombic (Pnma) at all temperatures and is isostructural with GdFeO3. The structure was refined as a distortion mode of a parent $ Pm{\bar 3}m $ structure. The thermal expansion was found to be non-linear and anisotropic, with maximum average linear thermal expansion coefficients of 34.0(3) × 10−6, 24.05(17) × 10−6, and 24.10(18) × 10−6 K−1 along the a-, b-, and c-axes, respectively, between 814 and 875 K.


1999 ◽  
Vol 14 (1) ◽  
pp. 2-4 ◽  
Author(s):  
Rui-sheng Liang ◽  
Feng-chao Liu

A new method is used in measuring the linear thermal expansion coefficients in composite consisting of a substrate Gd3Ga2Ga3O12 (GGG) and its epitaxial layer Y3Fe2Fe3O12 (YIG) within the temperature range 13.88 °C–32.50 °C. The results show that the thermal expansion coefficient of GGG in composite is larger than that of the GGG in single crystal; the thermal expansion coefficient of thick film YIG is also larger than that of thin film. The results also show that the thermal expansion coefficient of a composite consisting of film and its substrate can be measured by using a new method.


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