Page 95 - Materials Chemistry, Second Edition

82 2 Solid-State Chemistry

during nucleation/growth (e.g., impurity incorporation during slow cooling) or from
the application of an external force (stress). The twin boundary is a highly symmet-
rical interface, often with the crystal pairs related to one another by a mirror plane or
rotation axis. Accordingly, twinning poses a problem in determining the correct
crystal structure via X-ray diffraction due to the complexity created by overlapping
reciprocal lattices. [45] Due to the symmetric equivalence of the polycrystals, twin
boundaries represent a much lower-energy interface than typical grain boundaries
formed when crystals of arbitrary orientation grow together.
A stress exerted on a material results in a structural deformation referred to as
strain, whose magnitude is related to the bonding interactions among the atoms
comprising the solid. For example, a rubbery material will exhibit a greater strain
than a covalently bound solid such as diamond. Since steels contain similar atoms,
most will behave similarly as a result of an applied stress. There are four modes of
applying a load, referred to as tension, compression, shear, and torsional stresses
(Figure 2.52). Both tension and compression stresses are applied parallel to the long
axis of the material, resulting in elongation or contraction of the material along the
direction of the stress, respectively. In contrast, shear stress is applied at some angle
with respect to the long axis, and will cause the material to bend. The resultant flex is
referred to as shear strain.
For small stresses, a material will generally deform elastically, involving no
permanent displacement of atoms and reversal of the deformation upon removal
of the shear stress. The linear relationship between stress and strain in these systems
is governed by Hooke’s law (Eq. 28). The stiffer the material, the greater will be its
Young’s modulus, or slope of the stress vs. strain curve. It should be noted that some
materials such as concrete do not exhibit a linear stress/strain relationship during
elastic deformation. In these cases, the modulus is determined by taking the slope of
a tangential line drawn at a specific level of stress.

ð28Þ s ¼ Ee;
2
where: s ¼ tensile stress, in units of force per unit area (S.I. unit: 1 Pa ¼ 1 N/m );
E ¼ Young’s modulus, or modulus of elasticity (e.g., 3 GPa for Nylon,
69 GPa for aluminum, and 407 GPa for W)
e ¼ strain, defined as the geometrical change in shape of an object in
response to an applied stress
Poisson’s ratio is used to describe the lateral distortion that is generated in
response to a tensile strain. The values for elastomeric polymers are ca. 0.5, metals

0.25–0.35, polymeric foams 0.1–0.4, and cork is near zero. Interestingly, auxetic
materials exhibit a negative Poisson’s ratio, becoming thicker under tension
(Figure 2.53). Though this phenomenon was first discovered for foam-like struc-
tures, [46] there are now many classes of materials such as bcc metals, silicates, and
polymers [47] that exhibit this property. Such materials exhibit interesting mechanical
properties such as high-energy absorption and fracture resistance, which may prove
useful for applications such as packing material, personal protective gear, and body
®
armor. The waterproof/breathable fabric Gore-Tex is an auxetic material, com-
prised of a fluorinated polymeric structure (see Chapter 5).