Normal Thermal Expansion

For perovskites that are used in high-temperature applications, such as solid oxide fuel cells that operate above 800°C or so, thermal expansion becomes an important physical property, as mismatch of the thermal expansion of the cell components, cathode, electrolyte and anode, will cause early cell failure. The magnitude of the thermal expansion of many perovskites is rooted in the thermal behaviour of the BXg octahedra and is associated with octahedral tilt, distortion and the bonding between the B-cation and the surrounding anions. These are all susceptible to modification as the temperature rises and can contribute to anomalies in thermal expansion characteristics. 

Perovskites Structure-Property Relationships, First Edition. Richard J. D. Tilley. 2016 John Wiley Sons, Ltd. Published 2016 by John Wiley Sons, Ltd. 

this relative thermal expansion is identical to the change in the apical and equatorial bond lengths over the same temperature range. 

The lowest energy state for the Co cations is the low-spin (LS, tjg) configuration. However, the intermediate-spin (IS, t gC ) and high-spin (HS, t gCg) states are 

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Between 0 °C and the temperature of maximum density (4 °C) the hydrogen bond collapse dominates over the normal thermal expansion. At temperatures above that of the maximum density, thermal expansion dominates, and the density decreases progressively as the temperature rises. 

The former were presumed to have a more complex structure but to be less dense than the latter. Hence, when water at 0° C. is warmed, the equilibrium at 0° is disturbed in the direction of left to right, some ice molecules melting to the more dense water molecules, and the contraction thereby resulting more than counteracts the normal thermal expansion of the liquid with rise of temperature. 

Normal ice is analogous to tridymite water has the quartz structure with a greater density. The occurrence of the density maximum at 4°, a unique property of water, must be attributed to the gradual transition of the tridymite structure into the quartz-like structure, while at higher temperature the normal thermal expansion again gets the upper hand. 

The density of water changes in a complex way. When ice melts at 0°C, the tetrahedral arrangement around each O atom breaks down, and the loosened molecules pack much more closely, filling spaces in the collapsing solid structure. As a result, water is most dense (1.000 g/mL) at around 4°C (3.98°C). With more heating, the density decreases through normal thermal expansion. 

TMA has been employed in criminalistic studies to characterize a single fiber of untextured cellulose triacetate (34). The normal thermal expansion of the material at low temperatures is followed by contraction as water is lost above 100°C. The 5% expansion associated with the Ts at 180CC is followed by contraction before melting/decomposition, properties that are diagnostic of the material. Other major classes of fibers such as Orion, Acrilon, rayon, or cotton show no distinctive features up to 300°C. 

Many anisotropic crystals are known that show a contraction along one or two axes as the temperature increases, although other axes may show normal thermal expansion (Figure 15.8). Some of the most important compounds that reveal this beha-... 

Although the definition of functional materials is not so stringent in general, it is critical that the property variation in these materials must be sufficiently large in amplitude. For example, thermal expansion alone is too small to be utilized for any control purpose therefore, materials with normal thermal expansion properties do not qualify as functional materials. It is very important to understand the fundamental principles that make these materials functional, which can help us to use them properly and to inspire us to create better multifunctional materials based on the same physical principles. 

We have already seen that this model will have a normal thermal expansion coefficient i.e. [see Eq. (4.5.62)],... 

Fig. 149. CuCr2S4. Lattice constant vs. temperature. The dashed line is a normal thermal expansion curve deduced by the Gruneisen relation based on the measuie-...

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