### Non-Brittle Ceramic Structures

November 21, 2014

A principal difference between triangles and quadrilaterals, aside from the obvious difference that triangles have three sides and quadrilaterals have four, is that a collection of three lengths (the sum of the lengths of two of which necessarily longer than the third) will assemble to a triangle with only one set of angles. As a quadrilateral example, a set of four equal length sides can be assembled into a square having four right angles, or a rhombus having two acute, and two obtuse, angles.

Three equal sides will assemble into only one triangle, but four equal sides can assemble into quadrilaterals of various angles, such as a square (center) and a rhombus (right). The transition from a square to a rhombus is often used as an example of shear. (Inkscape.)

You don't need to be a mechanical engineer to realize that triangles add dimensional stability to structures. In 1839, Camille Polonceau, a French railway engineer, invented the Polonceau truss, as shown in the figure. This truss is a common element of roof construction. For this achievement, his name is engraved among the 72 names on the Eiffel Tower. To realize the importance of this, we need only scan the list of names to find Cauchy, Coriolis, Coulomb, Gay-Lussac, Fourier, Lagrange, Laplace, and Lavoisier.

The power of the triangle. A Polonceau truss.

(Via Wikimedia Commons.)

As I wrote in a previous article (Strong Nano Trusses, September 25, 2013), scientists at the California Institute of Technology (Pasadena, California) and the Jet Propulsion Laboratory (Pasadena, California) created nanoscale truss-like structures of titanium nitride on polymer templates created by two-photon lithography.[1-2]

When the polymer was subsequently removed, the 75 nanometer wall thickness struts withstood a compressive strength of 1.75 GPa without failure, even after many deformation cycles.[1-2] This is remarkable, since the structures were more than 85% air.[2] The Caltech team has continued research on such structures, producing the alumina-coated structure shown in the micrograph earlier this year.[3]

Detail of a nano-truss structure.

The scale bar is 10 micrometers.

(L. Meza, L. Montemayor,
N. Clarke, J. Greer / Caltech
.)[3)]

With a proper truss design, intrinsically brittle materials, such as alumina, can be fabricated into deformable structures that won't shatter when stressed. Instead, they show elastic behavior over a wide range of applied stress.[3] Says Julia R. Greer, professor of materials science and mechanics at Caltech and project leader,
"Having full control over the architecture gives us the ability to tune material properties to what was previously unattainable with conventional monolithic materials or with foams... For example, we can decouple strength from density and make materials that are both strong (and tough) as well as extremely lightweight. These structures can contain nearly 99 percent air yet can also be as strong as steel. Designing them into fractals allows us to incorporate hierarchical design into material architecture, which promises to have further beneficial properties."[3]

The Caltech team has continued to improve their materials, now fabricating alumina nanolattices that are 99.9% air and capable of reversible compressive deformations of 50%.[4-5] These structures were fabricated by the same techniques as for the previous materials; that is, two-photon lithography using focused lasers to form a polymer base, atomic layer deposition of the alumina, and oxygen plasma etching to remove the polymer.

When the ratio of the wall thickness, which was adjusted between 5-60 nanometers, to the beam radius is small enough, the nanobeams comprising the structure can be compressed without breaking. When the compressive forces are removed, nearly all the original shape is recovered.[4]

Compression and recovery.

In this sequence, starting from the upper left and going clockwise, an alumina nanolattice is compressed by more than 50%, and it recovers most of its shape when the compressive stress is removed.

(Lucas Meza/Caltech.)

Alumina wall thickness of 10 nanometers for tubes of about a micrometer diameter produced material that suppressed brittle fracture. Instead, there was elastic shell buckling and a ductile-like deformation.[4-5] Good recovery of shape resulted even after 85% compression. It's conjectured that at the 10 nanometer wall thickness, there are few flaws and their number are small, so the structure is less likely to fail.[5] Says Greer,
"Ceramics have always been thought to be heavy and brittle... We're showing that in fact, they don't have to be either. This very clearly demonstrates that if you use the concept of the nanoscale to create structures and then use those nanostructures like Lego to construct larger materials, you can obtain nearly any set of properties you want. You can create materials by design."[5]

One interesting application for such a strong, lightweight material would be a gas-free balloon, just an evacuated shell that would float in air. It might also be possible to build a biocompatible scaffold that would be infiltrated by cells for bone replacement.[5] This research was funded by the Defense Advanced Research Projects Agency. Greer is on the board of directors of the Kavli Nanoscience Institute at Caltech.[5]

### References:

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