Linear Expansion Coefficient Measurement

Figure 2.23 Apparatus for linear expansion coefficient measurement using a differential transducer (reproduced by permission of Ulvac Sinku Riko)...

The measurement of the linear expansion coefficient can be carried out by several methods (see Chapter 13), for example, by means of an interferometric dilatometer [77], a capacitance dilatometer [78] or a SQUID dilatometer [74]. The latter can achieve resolutions as small as 2 x l(T14m. 

Several methods of measurement of the thermal expansion have been developed as a function of the material, dimension and shape of the sample, temperature range and requested accuracy. The measurement of the linear expansion coefficient a = 1/L (AL/A7) of a sample is done by recording the length change AL (in a definite direction) due to a temperature variation AT. 

Several methods have been used to measure the linear expansion coefficient for T< 300K [1,2], These different techniques are ... 

For materials that are isotropic, that is, have the same properties in all directions, it can be shown that ay = 3ai. A material that has different properties in different directions is said to be anisotropic. Thus, a linear expansion coefficient, if no direction of measurement is explicitly stated, implies an isotropic material. Conversely, a volume thermal expansion coefficient implies an anisotropic material, and one should exercise caution when deriving linear thermal expansion coefficients from volume-based measurements. 

TMA measures the mechanical responses of a polymer as a function of temperature. Typical measurements include (1) expansion properties, i.e., the expansion of a material leading to the calculation of the linear expansion coefficient (2) tension properties, i.e., the shrinkage and expansion of a material under tensile stress e.g., elastic modulus (3) dilatometric properties, i.e., the volumetric expansion within a confining medium e.g., specific volume ... 

A nitrogen blanket was used whenever measurements were made at temperatures above 50°C to prevent oxidation of the samples. Specimen dimensions were corrected for temperature expansion using a linear expansion coefficient of 0.0002 (°C)"1. This is the coefficient for an SBR of about the same composition. 

The densities (d), refractive indices at sodium D-line (nD) and linear expansion coefficients (a) are also given in Table 1, for information. One should remark the higher refractive indices measured for glasses containing highly polarizable elements such as Pb or Cl. 

The linear expansion coefficient values shown in Table 3.1 and Figure 3.2 illustrate that filler addition results in composite systems with clearly decreased linear expansion coefficient values in the xy-plane. It also introduces, however, anisotropy in such a composite system i.e. an equal or even higher linear expansion coefficient value is measured in the z-direction. 

The coefficient of thermal expansion can be determined in two different ways. The first, and most direct, is simply to take a single crystal of ice and measure its dimensions as a function of temperature. From the symmetry of the crystal the results can be expressed in terms of two linear expansion coefficients a = l dljdT) in directions parallel to the r-axis and to an a-axis respectively. Alternatively X-ray diffraction methods can be used to measure the c and a dimensions of the unit cell as a function of temperature. These two methods do not, in fact, measure exactly the same thing, since in a real crystal there will be an equilibrium concentration of vacancies and interstitial molecules, and these concentrations will change with temperature. As we shall see, however, the experimental results for ice are not sufficiently accurate to enable a meaningful distinction to be drawn. 

It is evident from Fig. 5 that the ratios /uly for the aluminum and the nitrogen ions increased with rising temperature. Measurements of the linear expansion coefficient (a) by the x-ray diffraction method showed that this coefficient was also anisotropic. In the temperature range 298-670°K, the linear expansion coefficient along the c axis ) was (3.0 0.2) XO d , and in the basal plane it was a y = (3.8 0.2) 10 d ". The ellipsoid of the square of the linear expansion coefficient was elongated in the basal plane (Fig. 4). 

Kimmel and Andrews [195] have summarized measurements of the PAN Tg, up to the year 1965. The values fall into two ranges. For static measurements, distinct changes in the temperature dependence of the measured property are observed around 85 95°C. Higher values of Tg, 105 140°C, are obtained using dynamic mechanical and dielectric measurements, Tg values of 85 and 87°C, based on the linear expansion coefficient, were reported by Bohn et al. [120] and Howard [196]. Howard determined the Tg for a series of (AN-VA) copolymers by measuring the linear expansion coefficient of copolymer discs. The Tg for the PAN homopolymer was determined to be 87°C. Upon incorporation of VA, the value of Tg... 

Finally, dilatometric measurements performed between room temperature and 1300°C showed that the linear expansion coefficient remains constant over this temperature range. For both materials, its value ranges between 4.7x1 O and 4.9x10 °C. This observation and these... 

Thermomechanical analysis (TMA) is the measurement of the deformation of the phenolic material imder a constant strain as a function of temperature or time. TM A invesfigalion of crosslinked, modified phenolics gives the linear expansion coefficient and the glass tiansifion temperature of this material [33]. The linear expansion coefficient ( ) is measured by thermal expansion in one dimension. It is defined by equation 62 where dL/dT is the slope of the jdot of the longest sample dimension versus sample temperature and L is the original length of the crosslinked phenolic sample. 

A similar effect has been observed in the measurement of the linear expansion coefficient S in TmV04 (Kazey and Sokolov 1986). The contribution to the value of 5 from the CITE does not vanish at T TJy, but continues up to T 3T . Kazey and Sokolov (1986) have connected such a behaviour of d T) with the presence of significant distortions in the tetragonal crystal lattice of TmV04 at T> Tjt-... 

The precise value of the linear expansion coefficient can be measured using the apparatus shown in Figure 2.23 from -17 to 1000 °C, with a sample size of 8-10 mm diameter and 55-50 mm length. Dimensional changes are detected in the range of 1 pm to 2500 pm. 

Pig. 27. Linear expansion before and after the glass-transition range using TMA-DTMA. Linear expansion coefficient a from TMA trace requires measurement of the slope DTMA allows direct recording of a (64). 

This linear expansion coefficient can be measured either by using a dilatometer or by shift in X-ray diffraction lines as a function of the temperature. 

The true linear expansion coefficient for water absorption, , is measured by experiment. The volume change of the Nation due to water absorption assuming isotropic expansion is given by (2). 

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