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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
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
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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