Figure 252b shows bond energy curves for two

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Unformatted text preview: the average separation distance increases as energy (temperature) increases. (b) Comparison of the bond-energy curves for two materials: material A has a deeper and more symmetric bond-energy well so that the locus of midpoints on the constanttemperature line segments changes less rapidly for material A. This means that th (A) th (B). line segments and connecting their midpoints, we see that the average atomic-separation distance increases as the temperature increases. For many materials this relationship can be represented over a limited temperature range by the linear equation xe x0 th x0 T T0 (2.5–4) | v v where xe is the equilibrium spacing at temperature T , x 0 is the equilibrium spacing at the reference temperature T0 , and t h is the coefficient of linear expansion. Figure 2.5–2b shows bond-energy curves for two materials with approximately the same equilibrium separation distance. The curve for material A is nearly symmetric in the vicinity of x0 while that for material B is highly asymmetric. The midpoints of the constant-temperature line segments for each curve show that the bond length changes more rapidly with temperature for material B than A. Since t h is a measure of the normalized change in dimensions with temperature, the magnitude of t h increases as the bond-energy curve becomes more asymmetric. We can combine this observation with another, that deeper energy wells tend to be more symmetric, and predict that materials with high bond energies— those with deep and symmetric wells—should have low t h values. This prediction is supported by the data in Table 2.5–1. The elements with higher melting temperatures have stronger primary bonds and lower coefficients of thermal expansion. It is important to recognize that the relationships between the bond-energy curve and macroscopic properties developed in this section show general trends. They are extremely helpful in understanding and predicting relative differences in properties between different materials. However, the constant...
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This note was uploaded on 02/25/2013 for the course PHYS 2202 taught by Professor Sowell during the Spring '10 term at Georgia Institute of Technology.

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