Determination of Thermal Expansion Coefficients

The standard describes the design of dilatometer used for determination of thermal expansion coefficient. It also contains average values of coefBcients of thermal expansion coefficient of the most popular polymers and plastics. 

Concentrations of Schottky defect can be measured with experiment of thermal expansion of metals, namely the determination of thermal expansion coefficient of both the whole crystal and lattice parameters, respectively. The thermal expansion coefficient of the whole crystal includes not only the thermal expansion of crystal lattice itself, but the formation of Schottky defect. Therefore, the difference of two results can reflect both the existence and concentration of Schottky defect. For instance, at conditions near to the melting point, the concentration of Schottky vacant for alumina is about 1 x 10, and formation energy of its vacant is about 0.6eV (leV = 1.60 x 10 J) while that of NaCl is 10 -10 and formation energy is 2 eV, respectively. 

Figure 29 Determination of thermal expansion coefficients and glass transition temperatures by thermomechanical analysis of conductive adhesives (a) IP 680 silver-filled polyimide analyzed with a dilatation probe (Tg 230°C) (b) self-standing polyimide film studied with an extension probe (Tg 350°C).

Values of thermal-expansion coefficients to be used in determining total displacement strains for computing the stress range are determined from Table 10-52 as the algebraic difference between the value at design maximum temperature and that at the design minimum temperature for the thermal cycle under analysis. 

Bending beam theory calculation of elastic modulus, 361-362 calculation of glass temperature, 362 calculation of thermal expansion coefficient, 362 layer stress determination, 361 Benzophenone-3,3, 4,4 -tetracarboxydi-anhydride-oxydianiline-m-phenylenediamine (BTDA-ODA-MPDA) polyimide, properties, 115-116 Bilayer beam analysis schematic representation of apparatus, 346,348/ thermal stress, 346 Binary mixtures of polyamic acids curing, 116-124 exchange reactions, 115 Bis(benzocyclobutenes) heat evolved during polymerization vs. 

Senyshyn et al. (2005b) calculated the above-mentioned properties and determined the thermal expansion coefficient of rare earth gallates using a semi-classical approach. Ideal (X-ray) density, Griineisen parameter, isohoric heat capacity Cy, bulk and shear moduli, and thermal expansion coefficient were calculated for RGaOa (R = La-Gd) at 300 K are listed in Table 47. 

In this work the merits of the use of a natural fibrous mineral, sepiolite, as a binder to produce titania based monoliths of high mechanical strength and abrasion resistance is discussed. The monoliths of square channels were conformed with an initial 7.5 channels cm and 1 mm wall thickness. TTie textural characterization was made by mercury intrusion porosimetry (MIP), nitrogen adsorption/desorption (BET), and X-ray diffraction (XRD). The mechanical resistance, dimensional changes and weight losses al each stage of heat treatment were also determined. The thermal expansion coefficients (TEC) of the monoliths were determined between 200 and 400 C, since in practice the usual working temperature of DENOX catalysts lies between 250°-350 C. 

Figure 4. The thickness of a P(d-S-b-nBMA) film determined from x-ray reflectivity as a function of temperature. The bulk LOOT is indicated. The transition in the thin film occurs at 148 °C, lower than the bulk LCOT due to confinement effects, and is characterized by a7 A increase in the film thickness. The slopes of the lines were used to determined the thermal expansion coefficient of the film in the disordered and ordered state.

The selection of materials is usually determined by consideration of thermal expansion coefficients and mechanical properties the former are important to the maintenance of clearances and to the control of thermal stresses the latter, of course, determine the design stresses. 

A dilatometer is used to determine the thermal expansion coefficient of a specimen submitted to a thermal ramp (constant heating rate). Not only does the specimen expand but also the dilatometer (Figure C.3). Hence, differential expansion is measured and correction is necessary to include the dilatometer expansion in the experimental data. Consider for instance an alumina specimen in an alumina cylindrical support the apparent expansion would be zero because all expand the same relative length. A diagram can be constructed showing the measured and actual (and superior) expansion (Figure C.3). 

The interface region in a composite is important in determining the ultimate properties of the composite. At the interface a discontinuity occurs in one or more material parameters such as elastic moduli, thermodynamic parameters such as chemical potential, and the coefficient of thermal expansion. The importance of the interface region in composites stems from two main reasons the interface occupies a large area in composites, and in general, the reinforcement and the matrix form a system that is not in thermodynamic equiUbhum. 

Thermal expansion mismatch between the reinforcement and the matrix is an important consideration. Thermal mismatch is something that is difficult to avoid ia any composite, however, the overall thermal expansion characteristics of a composite can be controlled by controlling the proportion of reinforcement and matrix and the distribution of the reinforcement ia the matrix. Many models have been proposed to predict the coefficients of thermal expansion of composites, determine these coefficients experimentally, and analy2e the general thermal expansion characteristics of metal-matrix composites (29-33). 

The properties of high quaUty vitreous sihca that determine its uses iaclude high chemical resistance, low coefficient of thermal expansion (5.5 X 10 /° C), high thermal shock resistance, high electrical resistivity, and high optical transmission, especially ia the ultraviolet. Bulk vitreous sihca is difficult to work because of the absence of network-modifyiag ions present ia common glass formulations. An extensive review of the properties and stmcture of vitreous sihca is available (72). 

A signihcant problem in tire combination of solid electrolytes with oxide electrodes arises from the difference in thermal expansion coefficients of the materials, leading to rupture of tire electrode/electrolyte interface when the fuel cell is, inevitably, subject to temperature cycles. Insufficient experimental data are available for most of tire elecuolytes and the perovskites as a function of temperature and oxygen partial pressure, which determines the stoichiometty of the perovskites, to make a quantitative assessment at the present time, and mostly decisions must be made from direct experiment. However, Steele (loc. cit.) observes that tire electrode Lao.eSro.rCoo.aFeo.sOs-j functions well in combination widr a ceria-gadolinia electrolyte since botlr have closely similar thermal expansion coefficients. 

A key factor in the suitabihty of cokes for graphite production is their isotropy as determined by the coefficient of thermal expansion. After the calcined coke was manufactured into graphite, the axial CTE values of the graphite test bars were determined using a capacitance bridge method over a temperature range of 25 to 100°C. The results are summarized in Table 24. Also included in the table are bulk density measurement of calcined cokes and the resistivity values of their graphites. 

The change in shape of a material when it is subjected to a change in temperature is determined by the coefficient of thermal expansion, aj- Normally for isotropic materials the value of aj will be the same in all directions. For convenience this is often taken to be the case in plastics but one always needs... 

There are standard procedures for determining aj (e.g. ASTM 696) and typical values for plastics are given in Table 1.2. It may be observed that the coefficients of thermal expansion for plastics are higher than those for metals. Thus if 50 mm lengths of polypropylene and stainless steel are each heated up by 60°C the changes in length would be... 

On the experimental side, one may expect most progress from thermodynamic measurements designed to elucidate the non-configurational aspects of solution. The determination of the change in heat capacity and the change in thermal expansion coefficient, both as a function of temperature, will aid in the distinction between changes in the harmonic and the anharmonic characteristics of the vibrations. Measurement of the variation of heat capacity and of compressibility with pressure of both pure metals and their solutions should give some information on the... 

The glass transition temperature of a dilute system, according to the free volume changes, is determined by the diluent volume fraction Vd, and changes of the thermal expansion coefficient, a, at Tg by using ... 

Network properties and microscopic structures of various epoxy resins cross-linked by phenolic novolacs were investigated by Suzuki et al.97 Positron annihilation spectroscopy (PAS) was utilized to characterize intermolecular spacing of networks and the results were compared to bulk polymer properties. The lifetimes (t3) and intensities (/3) of the active species (positronium ions) correspond to volume and number of holes which constitute the free volume in the network. Networks cured with flexible epoxies had more holes throughout the temperature range, and the space increased with temperature increases. Glass transition temperatures and thermal expansion coefficients (a) were calculated from plots of t3 versus temperature. The Tgs and thermal expansion coefficients obtained from PAS were lower titan those obtained from thermomechanical analysis. These differences were attributed to micro-Brownian motions determined by PAS versus macroscopic polymer properties determined by thermomechanical analysis. 

Both of these are equations are approximate and are useful only for giving estimates of the value of the of the polyblend or copolymer. To calculate values of more accurately requires additional information such as the coefficients of thermal expansion of both components in both their liquid and glassy states. Given the uncertainty in the numerical value of T, which as we have seen depends on the method by which has been determined, there is little point in developing such arithmetical refinements. 

Since the glass transition corresponds to a constant value of the relaxation time [15], dTjdP is just the pressure coefficient of Tg. Comparing Equations 24.10 and 24.13, we see that the scaling exponent is related to quantities—thermal pressure coefficient, thermal expansion coefficient, Tg, and its pressure coefficient—that can all be determined from PVT measurements... 

The only one that is not readily accessible by DTA is the expansion coefficient. It is determined by use of a thermal expansion apparatus, i.e.- a dilatometer. Methods and uses of thermal expansion will be described in a succeeding section. 

---