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Gradient Materials

July 28, 2014

It's unknown who coined the expression, "Change is good," and that's a good thing, since he would be a hated man. No one likes change, and you can be certain that when you hear some corporate manager say, "Change is good," bad things are about to happen. If there must be change, people would like the change to be gradual. A decade time scale, preferably a lifetime, would be nice.

Some things in nature happen abruptly, and some things happen gradually. The universe, itself, started abruptly, with the Big Bang, and the quantum nature of matter is inherently abrupt. The phase transitions of macroscopic systems can be either gradual (first order), or abrupt (second order). An example of a first order phase transition would be melting, and an example of a second order phase transition would be superconductivity. In superconductivity, you're either superconducting, or you're not.

Many useful materials are layers of one material on another. Printed circuit boards, in which a copper layer forms conductive paths on a glass-epoxy or ceramic substrate, are one example. An extreme example is integrated circuitry in which layer after layer of semiconductors and metals are used to form some useful electronics. Since different materials have different mechanical and thermal properties, bad things can happen at the abrupt interface between one layer and another.

You can often eliminate the problems of an abrupt interface by using multiple material layers to approximate a gradual change. A good example of this is the anti-reflection coating on a glass camera lens. The refractive index of glass is about 1.5, so there's quite a bit of reflection of a light wave in air (refractive index, 1.0) as it strikes the lens.

Plugging these values into the reflectance equation,

Figure caption

where n1 and n2 are the two refractive indices (in any order), gives you a reflectance R of about 4% at normal incidence. Adding an intermediate layer with a refractive index of 1.225 gives 1% at each interface, so the reflectance is halved.

A multimode optical fiber with graded-index core.

An example of a graded material. A multimode optical fiber with a graded-index core has lower loss than a step-index fiber. (Illustration by Stanisław Skowron, via Wikimedia Commons.)

One major problem with layered materials is the difference in thermal expansion between layers. This becomes a major problem when the layer is deposited at high temperature, but used at room temperature. At one time, I was developing thick iron garnet layers on transparent garnet substrates formagneto-optical sensors. The layers were prepared at about 800 °C by liquid phase epitaxy, and when they were cooled to room temperature you would often find that the wafers were bowed; or, worse yet, they would crack from the mismatch strain.

Often it's advantageous to have a surface that's highly strained. In a process called shot peening, or ball peening, an alloy's surface is pelted by hard metal balls to induce a compressive surface strain. The strain profile is gradual through the alloy, since there are more impact forces at the surface than below the surface.

The purpose of such a layer is to enhance fracture toughness, since the compression tends to close any cracks at the surface before they can grow larger. Many years ago I was a member of a research team that used compressive layers on articles made from single crystals to increase their fracture toughness.[1-3]

An international team of scientists from the Chinese Academy of Sciences (Beijing, China), North Carolina State University (Raleigh, NC), and the Nanjing University of Science and Technology (Nanjing, China) have recently published their research on the properties of material gradient structures. Their approach was to mimic the microscale-nanoscale change in the grain-size of some biological materials to obtain better mechanical properties for technological materials.[4-6]

As I've often mentioned, a material derives its properties from both its chemical composition and its microstructure. Most materials are polycrystalline; that is, they are composed of a myriad of small single crystals packed together, and the size and orientation of these grains determine many of the material properties, including its strength and fracture toughness. Smaller grains offer hardness, and larger grains offer ductility.

Some natural materials derive their excellent mechanical properties from a hierarchical structure, mixing smaller and larger structures to give both strength and ductility. I wrote about the hierarchical structure of spider silk in a previous article (Spider Silk, March 12, 2012). What the Chinese-North Carolina research team did was to create materials with a gradient in grain size from large grains in the interior to small grains at the surface to derive benefit from their different properties.[6]

Representation of a gradient structured polycrystalline material.

Representation of a gradient structured polycrystalline material

(NCSU image by Yuntian Zhu.)

The research team tried this gradient approach on many metals, including copper, iron, nickel and stainless steel, and the mechanical properties were improved for them all.[6] Experiments were also done for interstitial-free steel. Although this material can be made with 450 MPa tensile strength, it has low ductility, having a strain limit of about 5%. The gradient process produced material with 500 MPa tensile strength, and a 20% rupture strain.[6]

These improved mechanical properties arise from conversion of an applied uniaxial stress to bi-axial stress generated by the gradient. This results in the the accumulation and interaction of dislocations that leads to additional work hardening that supplements that of non-gradient materials. The gradient technique is a novel path to superior mechanical properties for an otherwise optimized material.[4-5]

Says Xiaolei Wu, professor of materials science at the Institute of Mechanics of the Chinese Academy of Sciences and lead author of the two papers on this research,
"We think this is an exciting new area for materials research because it has a host of applications and it can be easily and inexpensively incorporated into industrial processes."[6]

The research team will now investigate whether this gradient structure approach can be used to engineer corrosion resistance in existing materials, and also improve their fatigue and wear properties. This research was funded by the U.S. Army Research Office.[6]


  1. J. Marion, D.M. Gualtieri, and R.C. Morris, "Compressive Epitactic Layers on Single Crystal Components for Improved Mechanical Durability and Strength," J. Appl. Phys., vol. 62, no. 5 (September 1, 1987), pp. 2065-2069.
  2. Robert C. Morris, Devlin M. Gualtieri, Dave Narasimhan, and Philip J. Whalen, "Epitaxially Strengthened Single Crystal Aluminum Garnet Reinforcement Fibers," U.S. Pat. No. 5,572,725, November 5, 1996
  3. Devlin M. Gualtieri, Robert C. Morris, Dave Narasimhan, and Philip J. Whalen, "Single Crystal Oxide Turbine Blades," U.S. Pat. No. 5,573,862, November 12, 1996.
  4. X.L. Wu, P. Jiang, L. Chen, J.F. Zhang, F.P. Yuan, and Y.T. Zhu, "Synergetic Strengthening by Gradient Structure," Materials Research Letters, July 2, 2014, DOI: 10.1080/21663831.2014.935821. This is an open access article with a PDF file available here.
  5. XiaoLei Wua, Ping Jianga, Liu Chena, Fuping Yuana, and Yuntian T. Zhub, "Extraordinary strain hardening by gradient structure," Proceedings of the National Academy of Sciences, May 5, 2014, DOI: 10.1073/pnas.1324069111. This is an open access article with a PDF file available here.
  6. Matt Shipman, "Inspired by Nature, Researchers Create Tougher Metal Materials," North Carolina State University Press Release, July 2, 2014.

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