Nanoscale Roughness


  • Nanoscale Devices
  • Algebra
  • Dimensions and Units
  • Statistics

MEA Description: Nano Roughness provides students with a hands-on experience with relevant scientific and mathematical concepts used in nanoscale technologies and research. This task requires students to develop a procedure to measure roughness given atomic force microscope (AFM) images of three different samples of gold. The motivation for developing the procedure is established by using a realistic context in which a company specializing in biomedical applications of nanotechnology wishes to start producing synthetic diamond coatings for joint replacements. The company intends to extend its experience with gold coatings for artery stents to this new application. Student teams of four are required to establish a procedure for measuring the roughness of gold samples that could be applied to diamond samples. The students then apply the procedure to three different samples of gold and develop a list of additional information they need to improve their procedure.

Implementation Strategy:

  1. Pre-Reading Activity - A reading introducing students to the vocabulary and functioning of the atomic force microscope is assigned as homework. To hold the student accountable for the reading, the student is required to answer three questions related to the various modes of operation of AFM and resolution of the AFM.
  2. Individual Activity – Students individually begin to articulate how they would define and measure roughness. The focus is at the macro scale – how to measure the roughness of pavement and identify other examples where roughness matters. Students begin to enter the nanoscale context by reading a biomedical company profile.
  3. Team Activity – In teams of four, students read the interoffice memo from the biomedical company client, which establishes the need to create a procedure to measure roughness using AFM images.
  4. MAA Activity - Individually, students develop a sequence of user defined functions in MATLAB to load an AFM Image and quantitatively assess how rough each strip is using statistical analysis and random sampling.

Six Principles:

Principle Description How the principle is addressed in the MEA?
Model Construction Ensures the activity requires the construction of an explicit description, explanation, or procedure for a mathematically significant situation
Describe the mathematical model the students will be developing when solving this MEA:
  • What are the elements?
  • What are the relationships among elements?
  • What are the operations that describe how the elements interact?
The students need to develop a procedure for quantifying roughness (given their own definition of roughness) using AFM images. The data that the students must work with is imbedded in three different monochromatic images. These are two-dimensional images in which the intensity of the color signifies the third dimension – height of the surface. Each image is at a different scale.
Student are expected to apply algebra, dimensions, and units, and perhaps even statistics, to measure roughness.
Reality Requires the activity to be posed in a realistic engineering context and be designed so that the students can interpret the activity meaningfully from their different levels of mathematical ability and general knowledge
Describe the context. What is the story?
What knowledge will students need to bring to this problem?
What background information must be provided?

Describe how the problem is open-ended.
The client in Nano Roughness is a company that produces coatings for biomedical applications. This client needs a procedure for quantifying surface roughness of a new product line.
Knowledge & Background Needed: It is expected that students would apply algebra, dimensions, and units, and perhaps even statistics, to this problem. Few students have been exposed to nanotechnology in high school. Therefore, a pre-lab reading was assigned to provide background on AFM. In addition, it is not known whether students would have been exposed to the concepts of roughness and measuring roughness. So, warm-up questions were used to introduce these concepts at the beginning of the MEA.
Open-ended: The fact that there are a number of established methods for quantifying roughness from AFM data ensures the creation of a very open-ended problem that is mathematically significant.
Self-Assessment Ensures that the activity contains criteria the students can identify and use to test and revise their current ways of thinking
What is provided in this MEA that students can use to test their ways of thinking?
The test cases in the Nano Roughness problem consist of three atomic force microscope (AFM) images of gold coatings. The students must apply their procedure to each of these images. The AFM images are monochromatic pictures of surfaces where the intensity of the color of the surface is an indicator of the height of the surface. The x-y scales on the images are given in micrometers and the surface height (z) is given in nanometers. Each image is a different size – 6x6 micrometers, 2x2 micrometers, and 0.939x1 micrometers. So large features in the 2x2 image, may in fact not be any different from those found in the 6x6 image.
Model-Documentation Ensures that the students are required to create some form of documentation that will reveal explicitly how they are thinking about the problem situation
What documentation are the students being asked to produce in this MEA?
In addition, to answering the individual questions in a traditional manner (to the instructor), student teams are asked to respond to the client in the form of a memo. The memo must include the procedure for quantifying roughness, the results of applying the procedure to the AFM images, and a description of information the team feels it would need to improve the procedure.
Construct Share-Ability and Re-Usability Requires students produce solutions that are shareable with others and modifiable for other engineering situations
What will indicate to the students that a sharable, reusable, or generalizable solution is desired?
Sharable: The student teams are being asked to create their procedure for the biomedical company client.
Re-usable: The implication is that the client will apply this procedure to other AFM images, in particular AFM images of the client’s new diamond coating.
Effective Prototype Ensures that the solution generated must provide a useful prototype, a metaphor, for interpreting other situations
What are other examples of structurally or conceptually similar problems that would required a similar solution?
It is anticipated that students will use the following knowledge and skills imbedded in this MEA in subsequent courses and engineering practice:
  • defining a measurement
  • graphical representation
  • dimensions and unit conversions
  • scaling
  • statistics

Author Information:

  • Original Author(s):
    • Tamara Moore


Tested in ENGR106 - Fall 2003