Page 92 - Materials Chemistry, Second Edition

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2.3. The Crystalline State

2. The crystal structures of the dopant and solvent atoms must be matched. That is,
the density of the host solvent unit cell must be voluminous enough to accom-
modate the solute atoms.
3. In order for dopant atoms to be stabilized within a host lattice, both solvent/solute
species must have similar electronegativities. If this prerequisite were not met,
electron density would transfer to the more electronegative atoms, forming a
compound with an entirely new lattice structure and distinct properties. For
instance, the reaction of metallic aluminum and nickel results in nickel alumi-
nide, Ni 3 Al, a compound with both ceramic and metallic properties. Such
transformational alloys are in contrast to interstitial and substitutional alloys,
in which the original solvent lattice framework is not significantly altered.
4. The solute and solvent atoms should have similar valences in order for maximum
solubility, rather than compound formation. In general, a greater solubility will
result from the dissolution of a higher-valence solute species in a lower-valence
solvent lattice, than vice versa. For instance, the solubility limit of Zn in Cu is
38.4 at.% Zn, but only 2.3 at.% Cu for Cu in Zn. Solubilities also decrease with an
increase in periodic separation; for example, the solubility maximum is 38.4% Zn
in Cu, 19.9% Ga in Cu, 11.8% Ge in Cu, and only 6.9% As in Cu.
In contrast to substitutional solid solutions, there must be a significant size differ-
ence between solute and solvent species for appreciable interstitial solubility
(Eq. 27). Accordingly, the most common interstitial solutes are hydrogen, carbon,
nitrogen, and oxygen. If the dopant species is identical to the lattice atoms, the
occupancy is referred to as self-interstitial. This will result in a large local distortion
of the lattice since the lattice atom is significantly larger than intersitial sites.
Consequently, the energy of self-interstitial formation is ca. three times greater

than that required to form vacancies, resulting in a very low concentration (i.e.,
3
<1/cm at room temperature).
r solute
ð27Þ Interstitial solubility = b0:59
r solvent
As one would expect, smaller atoms diffuse more readily than larger ones. For

instance, the interdiffusion of a carbon impurity atom within an a-Fe lattice at 500 C
2
2
is 2.4 10 12 m /s, relative to 3.0 10 21 m /s for self-diffusion of Fe atoms
within the iron lattice. Whereas carbon is able to migrate via interstitial diffusion
requiring minimal lattice distortion, Fe diffusion occurs via vacancy diffusion,
which necessitates a much greater perturbation of the lattice since strong Fe-Fe
metallic bonds must first be broken.
The migration of a lattice atom/ion into an available interstitial site will leave
behind a vacancy (Figure 2.49); the formation of such an interstitial/vacancy pair is
known as a Frenkel defect. In contrast, Schottky defects are formed through the
migration of a cation–anion pair from the crystal lattice framework, leaving behind
two vacant lattice sites. For ionic crystals, the overall charge of the crystal must be
charge-balanced. That is, if trivalent ions such as La 3þ are substituted with divalent
cations such as Ca , there must be concomitant placements of divalent anions
2þ