by Professor Ricardo H. R. Castro
Nanostructured materials already play important roles in our everyday lives.
From sun blockers to anti-scratching paintings, nanomaterials are revolutionizing
how we see materials, improving their performances, and broadening the horizons
of applications. To fully understand the origin of their unique properties and
better utilize them, it is important to realize that nanomaterials are different
from bulk materials not just because they are smaller, but because the small
sizes significantly affect their properties, creating novel and different responses
to the environment. The size effects can be seen as different colors, tastes,
electrical responses, catalytic activities, etc.
Most of this nano-related behavior can be attributed to the fact that a large
fraction of the volume of the material is within the "interface region",
that is, a few nanometers or less from the interface itself (as shown in Figure
1)1,2. Thus, nanomaterials'
properties can be considered a consequence of, and will be strongly influenced
by, their interface features, such as composition3,
and, fundamentally, energetics1,7-10.
Calculus of the fraction of atoms on the surface (within 0.5 nm of the
surface) for a general nanoparticle.
The energetics will rule the stability of a nanomaterial and how its structure
spontaneously grows or responds to a heat treatment. That is, in any system,
micro or nano, the total energy has at least two important contributions: the
bulk energy and the interface energy. The bulk energy is mainly determined by
the crystalline structure and composition of the core of the material. This
energy can be predicted by using regular phase diagrams, with which you can
study phase stability of micro and macro samples.
The interface energy is proportional to the interface area. By definition,
interfaces are unstable as they represent the work needed to create a unit area
by breaking or stretching a material. Logically, the higher the area, the higher
the energy of a system. Hence, systems with high interface areas, such as nanomaterials,
tend to collapse by coarsening, sintering or coalescence to decrease the total
Though this may sound like a bad thing, the tendency of the system to sinter
can be smartly exploited to create controlled nanostructures, offering an alternative
to the time consuming and expensive methodologies to create nanostructures based
on hard templates and complex nanolithography. This thermodynamic control of
nanostructure is based on a manipulation of the interface energetics, which
may force the system to grow only in a desired direction and to stop grow to
retain certain structure.
Controlling Thermodynamics of Nanostructure
Sintering is commonly considered a heat ignited process which driving force
is the surface energy and curvature potentials. However, a new type of interface
is created when necks start to form during sintering. This is generally called
grain boundary (or solid-solid interface) and is shown both schematically and
in a real micrograph in Figure 2.
ZrO2 nanoparticles partially sintered showing grain boundary
The grain boundaries typically have different energies than the surfaces (solid-vapor
interfaces), such that, when the system is transforming surface into grain boundary
during sintering, there is an energy 'cost' which is dependent on
the balance between surface energy and grain boundary energy. This balance will
define the evolution of the nanostructure and can be controlled to provide desirable
For instance, MgO and ZnO have significantly different surface and grain boundary
energies11. A significantly different nanostructure
evolution upon heating is observed in these samples, as shown in Figure 3. Note
that though the starting nanoparticles are similar in size and shape, the ZnO
samples coarse significantly more than the MgO powders. There are certainly
many kinetic concepts to explain this behavior, but the difference in the ratio
between the surface and the grain boundary energy plays an additional significant
role here. Because the grain boundary energy of MgO is relatively high with
relation to its surface energy, there is a relatively high energy cost in creating
a neck. So, the neck formation stops when the energy 'gained' by
the system due to the surface elimination is comparable to the 'needed'
energy to form the boundary. As the surface to grain boundary energy ratio in
ZnO is significantly higher, this energy barrier is not as present, and grain
boundary is more freely formed. This suggests that the absolute energies are
not of prime importance, but the relative energies would be governing nanosintering.
Sintering experiments showing the behavior of MgO, ZnO, and doped MgO
under heat treatment. Though kinetics plays a major role, nanoenergetics
is proven to be way to improve nanosintering. (γS is
surface energy and γGB is grain boundary energy)
The effect of the energy ratio on the nanostructure evolution is clearly seen
when doping MgO samples with CaO. As this dopant is observed to change the interface
energies without significantly changing the kinetics, one can somehow isolate
the energetic effects from kinetics. Observing the microstructure of doped MgO
after sintering and comparing to MgO and ZnO, there are much more similarities
with ZnO microstructure, consistently with the energetics trend.
A logical application of this approach would be in the improvement of sintering
itself. One of the main challenges in ceramic sintering industries is to obtain
dense parts with controlled shrinkage and controlled grain sizes. This control
is currently only done on a kinetic basis, by using dopants to control densification
mechanisms. The thermodynamic approach can help to identify how dopants affect
densification driving forces, providing a tool to further optimize the industrial
composition design of nanoceramics.
Another application would be to induce particular shapes and long range ordering
of nanoparticles as a consequence of interface energy minimizing. This can be
driven by changing the energetics of selected planes to force certain preferential
growth. The idea lies on the fact that the surface energies are not unique on
a particle, meaning that, because of the crystal structure, different crystal
facets are present at the surface of a particle. Each of those facets has a
different energy, and could be independently controlled. Since the higher energy
surfaces grow faster, a fine control of those energies by using specific atmospheres,
liquid phases, or dopants can promote the growth of different morphologies,
such as star-like and nanowires12(Figure 4).
Faceted nanoparticles with exposed planes of different interface energies
can rearrange or grow to distinct shapes and rearrange spontaneously.
Measuring Interface Energies
The measurement of interface energies is not a simple task at all, and therefore
limited data is available in the literature to be exploited in the nano-control
strategy discussed here. Thermochemistry has been proposed as a very powerful
technique to determine accurate interface energies for nanoceramics13,14.
Briefly, the idea of these calorimetric measurements is to evaluate the heat
released during the dissolution of samples with similar shapes, but different
interface areas (Figure 5).
(Left) Typical result of surface energy measurements using DS. The surface
gives an excess energy that is proportional to the surface area and
measured as a difference in the enthalpy of DS. (Right) Setup for the
measurement of enthalpy of drop solution (DS). Solvent is kept at 702
°C and sample is dropped from room temperature to be dissolved.
A thermochemical cycle accounts for the reactions during dissolution.
As the excess energy is directly proportional to the interface areas, a good
characterization of the samples will provide absolute values for the interface
energies. This technique can be used to virtually any crystalline material,
as the only requirement is a relatively high interface area to make it measurable.
The perspectives are that this technique will be able to provide lots of data
to improve the control of nanostructure on a thermodynamics basis. This may
be a breakthrough in the nanotechnology, but is still in the beginning of its
potentials. We may dream however on being capable of tuning the interface energies
of nanomaterials such that they can assemble themselves spontaneously the way
we want them to, promoting macro organized shapes, with mesopores for catalysis
applications, controlled contacts for battery cathodes, aligned channels for
molecular filtering, etc. Well, perhaps this dream is not that far away of becoming
- Navrotsky, A., Thermochemistry of nanomaterials, in Reviews
in Mineralogy and Geochemistry: Nanoparticles and the Environment, Banfield,
J.F. and Navrotsky, A., Editors. 2001, Mineralogical Society of America and
the Geochemical Society: Washington. p. 73-103.
- Cao, G., Nanostructures and Nanomaterials: Synthesis, Properties,
and Applications. 1st ed. 2004, Danvers: Imperial College Press. 433.
- Castro, R.H.R., Ushakov, S.V., Gengembre, L., Gouvea,
D., and Navrotsky, A., Surface energy and thermodynamic stability of gamma-alumina:
Effect of dopants and water. Chemistry of Materials, 2006. 18: p. 1867-1872.
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formulation for surface stress effects on the coupled thermomechanical behavior
of nanomaterials. Computer Methods in Applied Mechanics and Engineering, 2008.
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Gengembre, L., Roussel, P., and Gouvea, D., Interface Excess and Polymorphic
Stability of Nanosized Zirconia-Magnesia. Chemistry of Materials, 2008. 20:
- Navrotsky, A., Energetics of nanomaterials:
The competition between polymorphism and surface energy. Abstracts of Papers
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- Hill, T.L., Perspective: Nanothermodynamics.
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to include a one-dimensional surface excess. Nano Letters, 2001. 1(3): p.
- Rusanov, A.I., Nanothermodynamics.
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D., Interface Energy Measurement of MgO and ZnO: Understanding the Thermodynamic
Stability of Nanoparticles. Chemistry of Materials, 2010. 22(8): p. 2502-2509.
- Zhang, P., Xu, F., Navrotsky, A., Lee, J.S., Kim, S.,
and Liu, J., Surface enthalpies of nanophase ZnO with different morphologies.
Chemistry of Materials, 2007. 19: p. 5687-5693.
- McHale, J.M., Auroux, A., Perrotta, A.J., and Navrotsky,
A., Surface energies and thermodynamic phase stability in nanocrystalline
aluminas. Science, 1997. 277(5327): p. 788-791.
- Costa, G.C.C., Ushakov, S.V., Castro, R.H.R., Navrotsky,
A., and Muccillo, R., Calorimetric Measurement of Surface and Interface Enthalpies
of Yttria-Stabilized Zirconia (YSZ). Chemistry of Materials, 2010. 22(9):
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