Custom Designed Microstructures Using Metamaterials Arthur L. Chait, CEO • EoPlex Technologies, Inc.
Considerable hype has been associated with metamaterials and most of this stems from the speculation, in the popular press, that we may soon see the cloaking devices and invisibility cloaks of Star Trek and Harry Potter. The work done by Duke University’s David R. Smith, Ph.D., lends credibility to this possibility. Dr. Smith was one of the first to use metamaterials with a negative index of refraction, to bend microwave energy around an object – making it appear that the object was not there. [1] Theoretically, it may be possible to do the same thing, with visible light and other forms of radiation and create a true cloaking device. Perhaps, in some government lab, scientists are close to developing metamaterials that will accomplish this task. We will leave cloaking devices to the specialists and focus, in this article, on a new way to alter the microstructure of sintered ceramics and metals to create new metamaterials.
What are metamaterials? Metamaterials are unique arrangements of existing materials that act like entirely new materials, because of their structure. They expand on the “ingredients” that scientists can use in their “recipes” to achieve superior properties. [1] To quote from Duke’s website on metamaterials:
“Nature has provided us a rich palette of material properties from which to engineer useful optical devices. Yet, that palette is limited: Chemical synthesis, the conventional approach to material development, has so far not enabled us to access the entire range of material properties that should be theoretically possible. But chemistry is not the only process by which we can create materials. As an alternative approach, we can artificially structure a material by assembling a collection of objects together. These objects* serve to replace the atoms and molecules of a conventional material, the result being a composite structure that can have electromagnetic properties unlike any naturally occurring or chemically synthesized material. Such composites have been termed metamaterials, because they have properties that extend beyond materials found naturally.” http://people.ee.duke.edu/~drsmith/metamaterials.html
Clarke School of Engineering at the University of Maryland describes the objects referenced above as artificially produced structures or “meta atoms.” [2]
“Metamaterials are composite systems whose properties are dominated not by the individual atoms, but by the properties of larger, artificially produced structures or "meta-atoms". The most famous types of metamaterials are those in which the interaction with light is markedly different than in conventional materials: in some cases the index of refraction which determines the speed of light can even be negative-light bends in the opposite sense from common experience in these materials! Possible applications are invisibility cloaks and aberration free lenses.” http://www.mse.umd.edu/whatismse/metamaterials.html
The key characteristic of metamaterials is that their structure, not just their chemistry, controls the properties of the material. Most definitions of metamaterials also include a statement that these structures do not normally occur in nature. However, we can turn to some naturally occurring non-metamaterials to help illustrate how structure, rather than chemistry, can be the driving element in a material’s properties. A classic example of the dominance of structure over chemistry occurs with carbon. When carbon atoms are arranged in a cubic crystalline structure, the result is diamond, the hardest substance known. The same atoms arranged in hexagonal planes forms graphite, a very soft material that is commonly used as a lubricant. The dramatic difference in these two forms of carbon is completely dependent on how the atoms are arranged rather than any change in the chemistry.
The situation is similar with metamaterials, except that we are not dealing with atomic structure. Instead, metamaterials structures are larger elements, such as individual crystals, clusters of crystals and small grains of matter. Duke and Maryland definitions refer to the structural elements as “objects” or “meta-atoms.” In Dr. Smith’s work at Duke, these objects are millimeter-sized structures, as shown in Figure 1. It is the world of millimeter-sized structures that we will discuss in this article.
Microstructure
Scientists and engineers, working in the fields of metallurgy, ceramics and advance materials, deal with structures that could also be called “objects” or “meta-atoms.” However, it is more common in these fields to refer to the “crystals” and “grains” that make up the microstructure. Figure 2 (left) shows the typical microstructure of steel with individual grains clearly visible. These grains are formed as the steel cools from the molten state. Some ceramics are also processed by melting and form similar structures.
In contrast to melt-processing, most ceramics and powdered metallurgy parts are made by a solid state reaction known as sintering. With sintering, a mixture of grains in a specific particle-sized distribution is mixed and usually combined with a temporary binder. “Green” (meaning unfired) parts are then formed by pressing, casting, extruding or some other method. The green parts are dried and then heated to high temperature to burn away the binder and allow the grains to grow together. An example of this type of structure is represented by the sintered alumina microstructure shown on the right in Figure 2.
Both of the micrographs in Figure 2 show materials, which are considered single phase systems with each grain bonded directly to the others, without a second phase. However, many materials contain a combination of several different phases. Figure 3 shows a typical ceramic material with two distinct phases. The light colored grains are silicon carbide (SiC) and the darker colored areas are a bonding phase of high purity clay. In the manufacturing process, these two materials are blended together to obtain a well-mixed random distribution. The material is formed into the desired shape and then heated to high temperature, bonding the materials together into a dense finished part.
A well mixed, random distribution of materials is very useful for many applications. In other applications a random distribution cannot provide the properties required. Sometimes, the requirements can only be achieved by a very ordered pattern of the components. For example, composites made from fibers, such as Kevlar, graphite and fiberglass, require specific microstructure patterns to optimize their properties. In these composites the fibers are arranged in patterns that take advantage of the strength, stiffness or some other property of the fiber. This fiber pre-form is then combined with a second bonding phase, such as epoxy resin, to create the final part. The resulting composite has a distinct microstructure and properties that may vary in different directions. Applications range from sporting equipment, like golf clubs and tennis rackets, to aircraft parts, body armor and pressure tanks. In all of these products, the arrangement of fibers is relatively simple and can be achieved in a cost effective manner, with processes like weaving or winding. In this article, we will refer to this type of microstructure as a “uniform distribution,” to differentiate from the prior random distribution.
Going Beyond Uniform or Random Distributions
In all previous examples, phases have either been mixed randomly or oriented uniformly to obtain the required properties. Both of these methods work for many applications. However, they do not work when a microstructure, with a specific, non-uniform design, is required. For example, suppose that instead of the random structure of silicon carbide and clay shown in Figure 4 on the left, these phases needed to be in the precise pattern shown on the right. The light squares represent the silicon carbide grains and the dark squares represent the clay phase. These squares are intended to be about 100 microns on a side; about the size of a human hair.
Producing structures like this is sometimes possible with co-extrusion or other methods, but options will be limited and manufacturing will be expensive. The situation becomes even more difficult if the requirement is not a simple two-dimensional pattern, like that in Figure 4, but a 3-D pattern with changes in X, Y and Z directions, like that shown in Figure 5. It is virtually impossible and/or prohibitively expensive, with conventional methods, to produce parts with this microstructure or the microstructure examples shown later in Figure 12.
High Volume Print Forming (HVPF)
The need to create structures, such as those shown in Figure 5, drove the development of a new forming technique by EoPlex Technologies, Inc. [3] The process, called High Volume Print Forming (HVPF), offers a low cost manufacturing solution for 3-D structures, including the manufacture of metastructures in the micron level. [4]
HVPF creates structures by an additive process that builds in layers. At first glance, the process may look like a variation of rapid prototyping (RP). However, HVPF has little in common with RP, with the exception that it builds in layers. In many ways, HVPF is more similar to semiconductor processing, manufacturing thousands of parts simultaneously in large panels similar to silicon wafers. With HVPF, many different materials can be combined into the same structure. Metal and ceramic powders that have a similar sintering temperature are routinely used together. Parts made with HVPF commonly have from two to eight different specific materials in the structure, each serving some critical role. To allow formation of complex open spaces within a part, HVPF incorporates structures made from proprietary fugitive or sacrificial materials that will disappear in the process. Many types of open spaces can be formed including: channels, chambers, cavities, pipes and fluidic designs.
HVPF builds parts in layers that are created using several different types of printing equipment, along with EoPlex proprietary “inks.” Each full and partial layer is given a temporary cure using heat, UV radiation or some other process. This allows layers to be deposited on top of each other at a very high degree of accuracy, precision and speed. The inks decompose later in the process to leave behind specific metals, ceramics, glasses or voids and channels. Panels of parts, with hundreds of layers, are built quickly, with different materials, in the required pattern, to produce thousands of 3-D structures. Green parts are transformed into the finished structures in a final heat treating and sintering process. The concept looks simple, but it took years to perfect the necessary materials and to master the deposition techniques. HVPF uses EoPlex modifications of printing methods that include: offset, screen, stencil, transfer and others to deposit layers of these special “inks” in tiny micro-bricks, to create the required patterns.
Like many high technology companies, EoPlex has technology that is often referred to as “secret sauce.” However, unlike most of these companies, EoPlex actually has materials that look a lot like the sauces in Chapter II of Julia Child’s famous cookbook.
Forming structures of different materials with tiny micro-bricks, in almost any pattern, and with many layers, opens the capability to create new, complex microstructures that were impossible or too expensive before. Two of the most promising applications of this technology are the ability to engineer transitions between two different materials and to manufacture a new class of low cost metamaterials.
Engineered Transitions
HVPF builds parts in layers from tiny micro-bricks of matter. We refer to these micro-bricks as voxels, which are the 3-D equivalent of 2-D pixels. In a digital photo, the 2-D image is formed by the arrangement of different-colored pixels. In a similar manner, HVPF can form 3-D parts by placing thousands of voxels of different materials into complex patterns. Both the patterns and compositions of the voxels can be varied in each layer of a part. These voxels are the micron-sized equivalent of the “meta-atoms” that were discussed earlier. They can be visualized as something similar to tiny Lego blocks. The sculpture of Einstein, in Figure 6, is made from Lego blocks and is on display at a Lego theme park.
This sculpture can further serve to illustrate how HVPF works. With HVPF, Einstein’s head would be built starting with the back of the head and progressing to the tip of the nose. The process would begin by printing a layer of white voxels for the hair and this pattern would be varied as layers are added, to produce the shape of the hair. At the proper height, grey voxels would be deposited in varying layers to build the face and its required contours. At the right time, brown and black voxels would be added for the eyes. More grey and white voxels would then complete the eyebrows and mustache, and, finally, the tip of the nose. With HVPF, each voxel could be composed of various ceramics, glasses, metals or polymers.
Thousands of tiny versions of this sculpture could be produced on a single substrate and then sintered into finished products. The process could even go further to build structures within Einstein’s head, including features to represent nerves, blood vessels, and, of course, the famous brain. Voxels of fugitive materials would be used to create sinus cavities. These fugitive materials would decompose and diffuse through the structure during sintering, to leave behind precise, open spaces.
This model shows the power of HVPF and it also illustrates some limitations for building in layers. Making curved surfaces with blocks requires designs that use steps, like the steps on a contour map. With HVPF, Einstein’s round eyes could be printed with very fine resolution, but his nose requires about nine steps and would not be smooth. If a very smooth structure is necessary, HVPF will require many steps and, even then, may not be suitable for some applications that require a mirror finish.
Lego blocks simply snap together, whereas, the HVPF layers are sintered together. Sintering of ceramic or metal powders can be done in the solid state, with no liquid phase, or with a small amount of liquid phase to enhance the reactions. During sintering, the high temperature provides enough atomic mobility for the materials to densify, shrink and form strong bonds.
However, bonding different materials by sintering sometimes presents challenges, especially if there is a large difference in shrinkage or expansion between two or more materials. In the Einstein example, if his hair shrinks more than his face, it will distort the image. Even after the part is sintered successfully, there could be problems, if there is a significant difference in thermal expansion between materials. A large enough difference may crack or warp the part as it cycles through changes in temperature during service.
Overcoming CTE Mismatches
HVPF offers a breakthrough in extending the number and type of different materials that can be used together, by the creation of a “metastructure transition zone” (MTZ). The “coefficient of thermal expansion” (CTE) measures the change in dimensions with changing temperature. If the CTE of two materials is very different, it is usually impossible to bond them together and use them over a wide range of temperatures. The CTE difference will cause stresses at the interface between the two materials, resulting in distortion or failure.
HVPF provides engineers with a new technique that can help overcome CTE mismatches, especially in cases where the difference is not too great. With this technology, the interface between two different materials can be changed from an abrupt transition to an engineered MTZ specifically designed to balance and smooth out the changes. The MTZ approach creates an opportunity to build parts from several different materials that normally would not work well together.
An example of an abrupt transition vs. an MTZ is shown in Figure 7.
The structure on the left shows a single layer of a 3-D part, with an abrupt transition between two materials, represented by yellow and grey regions. The structure on the right shows the same two materials, with an MTZ that has been engineered to manage the transition from yellow to grey. The ability of engineers, to use HVPF, to create this transition zone, can make it possible to manufacture complex components that require the bonding of structures made from incompatible materials. For example, the component shown in Figure 8 is a prototype hydrogen reformer for use in a specialized portable fuel cell. This part requires several different materials and 30 different internal features. The part on the left was made with conventional processes and shows typical catastrophic failure during the firing cycle. The part on the right was successfully made with HVPF.
A New Class of Low Cost Metamaterials
The unique capability ofHVPF, to vary the structure of tiny voxels of material in order to manage a CTE mismatch, is actually a simple example of the application of metamaterials. Beyond that, HVPF allows engineers to create far more complex structures and introduce a new class of low cost metamaterials with “meta-atoms” in the 100 micron range. A promising application is in the design of small, high performance ceramic antennas, like those used in cell phones, GPS devices, Blue Tooth units and other portable electronics.
HVPF is currently being used to build ceramic antennas for advanced cell phones and other RF devices. Ceramic antennas give excellent performance in a very small size. These antennas consist of a small ceramic chip with a certain dielectric constant and a specific pattern of conductors both on the surfaces and embedded within the chip. Until now, the ceramics used in these devices have been chips of only one dielectric material. With HVPF, it is possible to build these antennas with several dielectrics in the same chip. HVPF also gives designers great freedom to utilize all the surfaces and to bury radiating and conducting patterns of different metals within the chip. This design freedom lets RF engineers create antennas with improved performance, in small form factor and at low cost. Figure 9 shows examples of these types of advanced miniature antennas. Full production-sized substrates are shown in Figure 10.
With HVPF, engineers can now go even further than the advanced designs in Figure 9 and create metamaterial composites that could offer a large increase in bandwidth, efficiency and performance. A study, by Dimitrios Psychoudakis, Ph.D., at Ohio State University and John L. Volakis, Ph.D., at the University of Michigan, shows that metamaterials could allow improved performance in small structures.5. One simulation started with a relatively large patch antenna with a uniform dielectric and achieved a bandwidth of 1.3 percent (at -10dB) as the control. This antenna was reduced to a 10th of the size of the control and the bandwidth fell to 0.26 percent. The antenna was held at this small size and a metamaterials dielectric was substituted for the uniform dielectric in the control. The bandwidth increased from 0.26 percent to 1.76 percent - a gain of 6.7 times. Results of this work are summarized in Figure 11.
HVPF offers a unique, low cost, way to manufacture metamaterials, like those used in the above study. Additionally, HVPF allows structures that are designed specifically to achieve optimum performance, even if they are more complex, and still keeps costs low. Some of the variables that can be adjusted with HVPF are shown in Figure 12.
The large number of variables that can be adjusted with the EoPlex process allows the creation of a wide range of metamaterials and metastructures. Examples of some structures that would be possible are shown in Figure 13.
Conclusion
HVPF is already being utilized by customers to create advanced, low cost antennas for cell phones and other devices. These customers are taking advantage of the increased design freedom and material combinations which HVPF makes available. The new metamaterials capability, described in this article, was introduced in Q2 of 2010 and is now being studied by some customers who have the necessary design expertise. Taking advantage of this unprecedented design freedom requires close collaboration between EoPlex and our customers’ RF design experts. This collaboration will result in EoPlex customers developing their own proprietary designs that can now be produced in high volume and low cost due to this new metamaterials capability.
Charles S. Taylor, Paul Cherkas, Hilary Hampton, John J. Frantzen, Bob O. Shaw, Dr. William B. Tiffany, Dr. Leonard Nanis, Dr. Philip Booker, Amr Salahieh, Richard Hansen, “Spatial Forming, A Three Dimensional Printing Process,” January 1995; IEEE Publication.
Arthur L. Chait, “High-Volume Print Forming (HVPF®), A New Method for Manufacturing Large Volumes of Complex Metal-Ceramic and Hybrid Components” August 2006, EoPlex Technologies, Inc. http://www.eoplex.com/images/eoplex_whitepaper_hvpf.pdf
Psychoudakis at Ohio State University and Volakis at University of Michigan
D. Psychoudakis and J.L. Volakis, "Enhancing UHF antenna functionality through dielectric inclusions and texturization," IEEE Transactions on Antennas Propagation, vol. 54, issue 2, pp 317-329, February 2006.
Arthur L. Chait is President and CEO of EoPlex Technologies, Inc. He is a materials engineer with broad experience in all facets of manufacturing, including operations, engineering design and business. Chait was previously a senior executive of Solectron Corp. Chait had responsibility for Solectron’s Global Account Organization, representing more than 70 percent of the company’s revenue. Chait’s career includes senior management, marketing and consulting roles with: SRI International, Zitel Corporation, Booz Allen & Hamilton, The PA Consulting Group and Dresser/Halliburton. Mr. Chait is a past recipient of the Steinmetz Medal from GE. He holds two degrees: a BS degree in Ceramic and Materials Engineering from Rutgers University and an MBA in Strategy from the University of Pittsburgh. Mr. Chait’s affiliations include IEEE and the American Ceramic Society. He serves on the Boards of Blue Iguana Networks and TechVenture Networks. He can be reached at achait@eoplex.com.
Custom Designed Microstructures Using Metamaterials
The key characteristic of metamaterials is that their structure, not just their chemistry, controls the properties of the material. Most definitions of metamaterials also include a statement that these structures do not normally occur in nature. However, we can turn to some naturally occurring non-metamaterials to help illustrate how structure, rather than chemistry, can be the driving element in a material’s properties. A classic example of the dominance of structure over chemistry occurs with carbon. When carbon atoms are arranged in a cubic crystalline structure, the result is diamond, the hardest substance known. The same atoms arranged in hexagonal planes forms graphite, a very soft material that is commonly used as a lubricant. The dramatic difference in these two forms of carbon is completely dependent on how the atoms are arranged rather than any change in the chemistry. 
Scientists and engineers, working in the fields of metallurgy, ceramics and advance materials, deal with structures that could also be called “objects” or “meta-atoms.” However, it is more common in these fields to refer to the “crystals” and “grains” that make up the microstructure. Figure 2 (left) shows the typical microstructure of steel with individual grains clearly visible. These grains are formed as the steel cools from the molten state. Some ceramics are also processed by melting and form similar structures.
A well mixed, random distribution of materials is very useful for many applications. In other applications a random distribution cannot provide the properties required. Sometimes, the requirements can only be achieved by a very ordered pattern of the components. For example, composites made from fibers, such as Kevlar, graphite and fiberglass, require specific microstructure patterns to optimize their properties. In these composites the fibers are arranged in patterns that take advantage of the strength, stiffness or some other property of the fiber. This fiber pre-form is then combined with a second bonding phase, such as epoxy resin, to create the final part. The resulting composite has a distinct microstructure and properties that may vary in different directions. Applications range from sporting equipment, like golf clubs and tennis rackets, to aircraft parts, body armor and pressure tanks. In all of these products, the arrangement of fibers is relatively simple and can be achieved in a cost effective manner, with processes like weaving or winding. In this article, we will refer to this type of microstructure as a “uniform distribution,” to differentiate from the prior random distribution.
In all previous examples, phases have either been mixed randomly or oriented uniformly to obtain the required properties. Both of these methods work for many applications. However, they do not work when a microstructure, with a specific, non-uniform design, is required. For example, suppose that instead of the random structure of silicon carbide and clay shown in Figure 4 on the left, these phases needed to be in the precise pattern shown on the right. The light squares represent the silicon carbide grains and the dark squares represent the clay phase. These squares are intended to be about 100 microns on a side; about the size of a human hair. 
Producing structures like this is sometimes possible with co-extrusion or other methods, but options will be limited and manufacturing will be expensive. The situation becomes even more difficult if the requirement is not a simple two-dimensional pattern, like that in Figure 4, but a 3-D pattern with changes in X, Y and Z directions, like that shown in Figure 5. It is virtually impossible and/or prohibitively expensive, with conventional methods, to produce parts with this microstructure or the microstructure examples shown later in Figure 12. 
Engineered Transitions
An example of an abrupt transition vs. an MTZ is shown in Figure 7.
The structure on the left shows a single layer of a 3-D part, with an abrupt transition between two materials, represented by yellow and grey regions. The structure on the right shows the same two materials, with an MTZ that has been engineered to manage the transition from yellow to grey. The ability of engineers, to use HVPF, to create this transition zone, can make it possible to manufacture complex components that require the bonding of structures made from incompatible materials. For example, the component shown in Figure 8 is a prototype hydrogen reformer for use in a specialized portable fuel cell. This part requires several different materials and 30 different internal features. The part on the left was made with conventional processes and shows typical catastrophic failure during the firing cycle. The part on the right was successfully made with HVPF.
The unique capability ofHVPF, to vary the structure of tiny voxels of material in order to manage a CTE mismatch, is actually a simple example of the application of metamaterials. Beyond that, HVPF allows engineers to create far more complex structures and introduce a new class of low cost metamaterials with “meta-atoms” in the 100 micron range. A promising application is in the design of small, high performance ceramic antennas, like those used in cell phones, GPS devices, Blue Tooth units and other portable electronics.
Conclusion
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