In 1960, Roy introduced the thermodynamic argument for using metastable immiscibility as
an indicator of the parent liquids likely nanoheterogeneity [13]. Actual unmixing is a later
stage in the development of heterogeneity, liquids manifesting their nascent heterogeneity by
actually separating into different phases in their supercooled regimes (see Fig. 3). The
structure of the liquid, say at point 1, can be inferred to have had nascent heterogeneity or
proto-phase separated regions or clusters, which actually form say, at point 2. The
thermodynamics of the non-ideal liquidus shape provides an indicator of possible phase
separation (of course, this is in a 2-component system and easier to image). 

Fig. 3 The first presentation by Roy (1960) of the theoretical argument that the non-ideality of the liquidus
(clearly shown in its shape) indicated that the liquid phase itself was “heterogeneous” in structure, and could be
induced to phase-separate in a temperature region where it was metastable (left hand figure) [13]. Porai-
koshits and Averjanov experimentally demonstrated exactly such an example in 1968 [14].

The inherent “tendency” to inhomogeneity has since been greatly extended and completely
verified in hundreds of cases (see comprehensive summary by Mazurin and Porai-koshits)
[11, 15]. Today, extensive and definitive experimental evidence exists for great
heterogeneity of nano- or microstructure, indeed for a multiplicity of distinct regions,
even Gibbsian phases in at least hundreds of common quenched liquids or glasses.

An important observation about possible water structure and the kinetics of bond breakage,
etc., and their relevance to structure can be drawn from the phase diagrams in Fig. 3. This is
the phenomenon of “consolute points” as appears at the top of the (metastable) two liquids
region in the left-hand phase diagram. First we note that phase relations involving consolute
points in unmixing liquids are quite common in simple binary systems involving water, e.g.
the classic examples of phenol and water, nicotine and water, etc., treated in detail by Ricci in
his textbook on the phase rule [16]. Immediately above the consolute temperature we have a
single phase; immediately below there are two phases of infinitesimally different composition.
Hence below the consolute temperature it is absolutely certain that we have two phases with
different structures which are stable together “forever”. Now consider what changes when we
go infinitesimally above the consolute temperature at exactly the same temperature? The key
logic of this paper proposes that the structure of this liquid is nano-heterogeneous , containing
regions, or clusters, or “oligomers”, reflecting the different structures which form just one
degree Celsius below the consolute temperature. This is evidenced by the gentle continuous
slope of the highly non-ideal shape of the liquidus curve.

Turning from the possible nanoheterogeneity of structure, to kinetics , we examine the
argument that the “rapid breaking and remaking of bonds” excludes the possibility of different
structures co-existing in liquid water. One can safely assume that these kinetics do not change
just because phase separation may be involved at essentially a single temperature. Obviously
these very fast kinetics of breaking and re-formation of bonds are irrelevant since they take
place within each structural arrangement of units, without statistically affecting the structure
of the units themselves.

In the long tradition in classical chemistry and materials research circles, it has been assumed,
and hence become a part of the canon, that liquids of a fixed composition could not occur in
two phases. This assumption has been disproved experimentally since the 1970’s. It was then
shown that in P-T (pressure-temperature) space, even in the liquid-stable region (not just
metastable glasses), one finds a variety of different structures in liquids, in oxide melts, and
even in monatomic systems such as elemental S, Se and Te [17—19]. Figure 4 shows the
phase diagram for S with distinct phase regions for several different liquids taken from their
work. In the jargon of the two decades later work on polyamorphism of H2O-glass, this is
polyamorphism of stable liquids of S, Se, Te. We show later (Fig 6) how this key finding has
specifically been extended to H2O itself.


Fig. 4 P-T Phase Diagrams for sulfur (S). On the left is the subliquidus region showing the many crystalline
structures. On the right is the liquid stable region showing at least 5 different liquid structures separated by a
phase boundary.


In Fig. 4, the left image shows the P-T phase diagrams for sulfur (S) by Vezzoli et al. in with
12 crystalline phases [17]. Note the clear discontinuities in the liquidus. The right half from
the paper by the same authors shows the phase diagram of the liquid-stable region [20]. At
this time (1969) it was universally accepted that only one liquid phase was possible. Yet the
authors provided, probably for the first time ever, experimental evidence for differently-
this time (1969) it was universally accepted that only one liquid phase was possible. Yet the
authors provided, probably for the first time ever, experimental evidence for differently-
structured liquid phases A, B, C, D, E separated by somewhat fuzzy (second order?) P-T
boundaries. Another relevant example, albeit metastable, is that of glassy carbon. TEM
studies (Fig. 5)show that in glassy carbon, interlocking mixtures of 1—2 nm regions of sp2
bonded graphite are mixed with sp3-bonded diamond regions [21]. 

Fig. 5 TEM image and model therefrom of glassy carbon structure showing 1 nm intergrowth of diamond-like
and graphite-like regions after Noda and Inagaki [21].

As we will see later, the relevance of this line of argument by analogy has now been
established beyond any doubt. That different structures of stable liquid water exist has now
been fully confirmed experimentally by Kawamoto et al. using the very same P-T equilibria
approach for water itself (See Fig. 6) [22].