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Solid Solution
MSE 528
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solid-state solution of one or more solutes in a solvent.
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Such a mixture is considered a solution rather than a compound when the crystal
structure of the solvent remains unchanged by addition of the solutes, and when
the mixture remains in a single homogeneous phase.
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The solute may incorporate into the solvent crystal lattice substitutionally, by
replacing a solvent particle in the lattice, or interstitially, by fitting into the space
between solvent particles.
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Both of these types of solid solution affect the properties of the material by
distorting the crystal lattice and disrupting the physical and electrical homogeneity
of the solvent material.
Some mixtures will readily form solid solutions over a range of concentrations,
while other mixtures will not form solid solutions at all. The propensity for any two
substances to form a solid solution is a complicated matter involving the chemical,
crystallographic, and quantum properties of the substances in question.
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Solid solutions, in accordance with the Hume-Rothery rules, may form if the solute
and solvent have:
Similar atomic radii (15% or less difference)
Same crystal structure
Similar electronegativities
Similar valency
• Hume-Rothery (1899-1968) was a metallurgist who studied the
alloying of metals. His research was conducted at Oxford University
where in 1958, he was appointed to the first chair in metallurgy.
• His research led to some simple and useful rules on the extent to
which an element might dissolve in a metal . The rules that he
derived are paraphrased here. The rules are still used widely. For
example, the miscibility gap in Au-Ni is correlated with the fact that
the lattice parameter of Au is 1.15 times that of Ni, thus acting
maximally according to Hume-Rothery .
• If a solute differs in its atomic size by more than about 15% from the
host, then it is likely to have a low solubility in that metal. The size
factor is said to be unfavourable.
• If a solute has a large difference in electronegativity (or
electropositivity) when compared with the host, then it is more likely
to form a compound. Its solibility in the host would therefore be
limited.
• A metal with a lower valency is more likely to dissolve in one which
has a higher valency, than vice versa.
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The phase diagram in Fig. 1 displays
an alloy of two metals which forms a
solid solution at all relative
concentrations of the two species. In
this case, the pure phase of each
element is of the same crystal
structure, and the similar properties of
the two elements allow for unbiased
substitution through the full range of
relative concentrations.
Solid solutions have important
commercial and industrial
applications, as such mixtures often
have superior properties to pure
materials. Many metal alloys are solid
solutions. Even small amounts of
solute can affect the electrical and
physical properties of the solvent.
•The binary phase diagram in Fig. 2
at right shows the phases of a
mixture of two substances in varying
concentrations, alpha and beta. The
region labeled "alpha" is a solid
solution, with beta acting as the
solute in a matrix of alpha. On the
other end of the concentration scale,
the region labeled "beta" is also a
solid solution, with alpha acting as
the solute in a matrix of beta. The
large solid region in between the
alpha and beta solid solutions,
labeled "solid alpha and beta", is not
a solid solution. Instead, an
examination of the microstructure of
a mixture in this range would reveal
two phases — solid solution alphain-beta and solid solution beta-inalpha
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Hume-Rothery rules
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The Hume-Rothery rules are a set of basic rules describing the conditions
under which an element could dissolve in a metal, forming a solid solution.
There are two sets of rules, one which refers to substitutional solid
solutions, and another which refers to interstitial solid solutions.
Substitutional Solid Solution Rule for substitutional solid solutions,
the Hume-Rothery rules are:
– 1. The atomic radii of the solute and solvent atoms must differ by no more than
15%:
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– 2. The crystal structures of solute and solvent must match.
– 3. Maximum solubility occurs when the solvent and solute have the same
valency. Metals with lower valency will tend to dissolve metals with higher
valency.
– 4. The solute and solvent should have similar electronegativity. If the
electronegativity difference is too great, the metals will tend to form
intermetallic compounds instead of solid solutions.
Interstitial Solid Solution Rules
• For interstitial solid solutions, the Hume-Rothery rules are:
– 1. Solute atoms must be smaller than the pores in the solvent lattice.
– 2. The solute and solvent should have similar electronegativity.