Alan F.
Berndt Textbook Errors, 93
University of Missouri-St. Louis
St. Louis 63121 Binary Phase Diagrams
I n most physical chemistry texts and in
some introductory texts binary phase diagrams are pre-
sented in detail.' I n the discussion of the phase dia-
gram for a binary system having a congruently melting
compound i t is often stated that this diagram can be
thought of as consisting of two juxtaposed simple
eutectic diagrams. This concept is a useful pedagogic
tool for understanding equilibrium relationships among
phases hut leads to erroneous results when applied to a
quantitative description of the slope of the liquidus.
I n a binary eutectic diagram the liquidus has nonzero
slope a t the melting points of the pure components.
Juxtaposition of two diagrams of this type would imply
that the liquidus would similarly have nonzero slope a t Schematic phase d i a g r a m for b i n m y system having a congruently melting
compound, ( o j , correct; (bj, incorrect.
the melting point of the compound. That this is not
true is a well known experimental fact and has been the
subject of a theoretical proof for the general casez in gram for the compound system is therefore not quan-
which no assumptions about the detailed nature of the titatively equivalent to two juxtaposed eutectic dia-
liquid phase are made. The liquidus actually has a grams.
horizontal tangent, i.e., zero slope, a t the melting point This results from the inclusion of the entropy of
of a congruently melting compound. The phase dia- mixing term into the expression for the Gibbs free en-
ergy. The entropy of mixing expressed as a function of
the mole fraction of one component has infinite deriva-
Suggestions of material suitable for this column and guest tive at the composition of the pure components but has
columna suitable for puMicstion directly should be sent with as a finite derivative a t the compound composition.
many details as possible, and particularly with reference to Although this point may be rather subtle the texts
modern textbooks, to W. H. Eberhardt, School of Chemistry, should clarify the difference in order to make the stu-
Georgja Institute of Technology, Atlant,a, Georgia 30332. dent aware of this feature. I n addition many texts add
Since the purpose of this column is to prevent the spread and to the misunderstanding by presenting incorrect illustra-
continuation of errors and not the evaluation of individual tive phase diagrams in which the liquidus is shown to
t,exts, the sources of errors discussed will not be cited. In order have a cusp (point) a t the melting point of a congruently
to be presented, an error must occur in s t l a s t two independent
recent standard books. melting compound (Part (b) of the figure) rather than
%BERNDT, A. F., AND DII,:STLER, D. J., J. Phys. Chem., 72, correctly illustrating the slope of the liquidus (Part (a)
2263 (1968). of the figure).
An additional aspect of phase equilibrium diagrams mechanical properties of the major component. Some
which has been the subject of extensive correspondence presentations accentuate the small solubility of the
to the Editor of This Column concerns partial solid- minor component by plotting the concentration on a
state solubility and the very basic question of whether logarithmic scale so that the range of concentration be-
or not a "pure" solid substance can be present in an tween .001 and .O1 mole % is thc same length as that be-
equilibrium system with a liquid solution containing a tween .Ol and .1 mole % or between 1and 10 mole %.
second component. Whether or not limited solubility is a consequence of
I n particular, Dr. Stig Holmquist of Ferro Corpora- general thermodynamic theory or a specific statistical
tion, Cleveland, Ohio has been most insistent that treat- model is a moot point, but there is little doubt that, ex-
ments are inadequate if they present phase diagrams perimentally, limited solubility is the rule rather than
which do not show such partial solubility or if they do the exception. The implications concerning the word
not make clear in thc text that such solubility exists. "pure" are especially interesting and deserve detailed
The problem becomes particularly interesting and consideration.
acute in systems where very small mole fractions of
minor components alter dramatically thc electrical or
594 / Journal of Chemical Education
