A single example of the materials science use of the term, may be used to illustrate the
difference. We recognize that this example may be of limited relevance to the water issue,
since it is crystalline and ionic, but it illustrates the difference in terminology for the non-
specialist. The structure of garnet, whether as a semi-precious mineral (e.g. Ca3Cr2Al3O12) or
as high tech magnetic materials (with a formula such as Y3Fe2Ga3O12) is an example because
it contains 3 different sized units or “molecules”, which are called coordination polyhedra by
crystal chemists, Al-O (or Ga-O) tetrahedra, Cr-O (or Fe-O) octahedra, and Ca-O (or Y-O)
cubes (see Fig 10). (These garnet “molecules” are somewhat analogous to the smaller
“molecules” in water.) Figure 10 and Fig. 11, however, also show what the materials scientist
calls the “structure of garnet”. It will be seen that, in 3-D space, these polyhedra (“molecules”)
are not entirely separate, but have a specific relation to each other. Indeed they interpenetrate
completely sharing the same oxygen ions among the three cations. Moreover, this “unitcell”
is repeated precisely throughout the entire crystal, or stock- bottle or drum or tiny single
crystal more or less exactly as shown. 

Fig. 10 Two of the “molecules” in inorganic materials, illustrated in the garnet structure by the 4-coordinated
(cornered) tetrahedral (colored yellow and orange in the middle of the four quadrants, and the 6-coordinated or
cornered octahedra.


Fig. 11 The final “molecule” in the structure, the eight coordinated, or cornered, green cubes, is added, and
knitted into a fixed position. The relationship of the atoms and polyhedra within the outlined (unit cell)
boundaries are fixed; and repeated ad-infinitum in 3-D space, illustrating what materials scientists call
“structure.”

How do we know? By the use of x-ray (or electron or neutron) diffraction, and transmission
electron microscopy (TEM).

The TEM image in Fig. 12, by the leading nanocomposite lab in Japan, shows just how
precisely materials scientists today can know the structure of (crystalline) materials [45]. Of
course this is vastly simpler for a solid phase. One can literally define the position and
composition of every atom, as shown in this TEM example, selected because it also shows
what occurs when crystallinity or periodicity is lost. The so-called grain-boundary material is
non- crystalline (glassy, liquid-like) and one can see immediately that all the atom by atom
precision is gone. Instead we see the size and number of aggregates of various sizes without
any regular arrays of atoms (cf – the cartoon version of Fig. 3 from 1971 [15]). That is
precisely how every structure of covalently (strongly) bonded liquids, including water, is
likely to appear. thin amorphous layer at two phase boundaries

Fig. 12 Routine, typical TEM image of a complex crystalline composite at the nanometer level. Note the
individual atoms all lined up in different arrangements, demanded by the structure. Specifically also note the
intergranular matter, fuzzy and disordered. In the higher resolution blow up, one can see exactly what a typical,
albeit multi-component, non-crystalline (like all liquids) area contains – disordered assemblages of different size
(and composition, as revealed in the differences in contrast) typical of liquids. (From Niihara et al. [45]).

Of course some of the best known water-structure research groups, such as that under
Nemethy and Scheraga and G.W. Robinson, had concluded on the basis of calculation that
there was a “distribution” of two “states” or “five kinds” of molecules respectively, which
varied with “P” or “T”, but no one ever described how they are distributed in space [39, 46]. 

Van der Waals bonds in Liquid Water Structure 

A second aspect of the structure emphasized in materials research is the strengths of all the
bonds involved. Some materials where all the bonds (and their strengths) are identical, say
NaCl, are called isodesmic. In anisodesmic “structures”, different bonds have different
strengths; e.g. in CaCO3, the C-O bond is much stronger than the Ca-O bonds. Much is made
in the chemical literature of the (strong) hydrogen bonds in water. However, the significant
role of the van der Waals bonds (the weak but ubiquitous inter-neutral molecule bonds in
water) is ignored. A key principle in materials science is that the weakest bonds determine the
(interesting) properties, while the strongest bonds determine the structure. An illustrative
example exists in some common crystalline materials. Talc and graphite are both very soft
made up of sheets, because the inter-plane forces are only van der Waals bonds and slide apart
with finger pressure. Indeed, in graphite the in-plane covalent bonds are even stronger than in
diamond, but the enormous anisodesmicity results from the very, very weak inter-plane bonds.
This bond weakness also makes possible very soft phases and the entire world of different
buckyballs and nano-tubes and their radical difference from diamond, the hardest material.
The analogy to the rich diversity of structures possible in liquid water is obvious. Indeed the
universally accepted presence of a wide variety of molecules in H2O no doubt contributes to
the enormous range of van der Waals bonds present, with the weakest ones being most
susceptible to change by very weak forces.

What is proposed here is in many ways simply a modification of G. Wilse Robinson’s series
of papers developed to justify what he called the two-state model of the structure of liquid
water [39]. Indeed, Robinson based his analyses on crystal chemistry and structure analyses.
He took his two state prototypes as ice-II, the high pressure dense ice with a density of 1.18
gm/ml, and ice-Ih with a density of 0.92 gm/ml, a huge difference of 32%. 

Water’s changing properties which demand a multi-structural model 

The absolute reason why only models which posit a wide range of structure, and their
distribution in space can have any value in describing the structure of liquid water, is the well-
known unique range of anomalous physical property changes in the most encountered
temperature range (0—50 °C).


Table I
Changes in different water properties, each requiring a
change of structure, each at a different temperature
Property Comment
Density Maximum at 4 °C
Refractive index Thermal maximum near 0 °C
Thermal expansion coefficient Changes from extremely high up to 6—7 °C
to low (normal) above 12 °C
Isothermal compressibility Minimum at 50 °C
Isothermal piezo-optic coefficient Maximum near 50 °C
Specific heat of water Minimum at 35 °C


Fig. 13. Comparison of changes in normal (dashed lines) liquids with highly anomalous changes in water’s
properties as related to temperature. Such changes in property demand the existence of many structural changes
of different kinds and at different temperatures. Notice in (a), (b) and (c), the radical difference from normal
liquids. Notice the 308—319 K difference between (a) and (b). The most dramatic departure from typical liquid
behavior is shown in (c). (Modified from DeBenedetti and Stanley (Physics Today 6 2003 p 41) [4]


Table I and Fig. 13 show the extreme degree to which water’s properties are
anomalous. Note first in the figure that the properties of the vast majority of liquids have
monotonic, linear, changes with some variable. Next, note the very, very different behavior of
water. Next, note that it is not just one property in which very anomalous changes are found,
but such changes are found in many properties. Note that the kink point or maxima or minima
are all at different temperatures. These anomalies clearly tell the materials scientist that there
is no way to achieve these phenomena except by a combination of two of our key conclusions
about the structure of water. Across the transition point in properties there has to be a change
of structure. Secondly, there must be several quite separate structural transitions to account
for just the property changes noted. There is no prima facie way of telling whether such
absolutely confirmed familiar behavior can be explained by complex rearrangement of just
two (or five) states or clusters, or whether it requires simpler re-arrangements of many
different states. The crystal chemical connection invoked by Robinson is certainly operative,
but it is not necessary that water consists of a mixture of only “two states”, which by some
juggling could be adjusted to try to explain the plethora of anomalies by utilizing only two
structures. Our proposal is simply to posit that there are many possible structures.