This problem is to be completed individually. Complete this problem before working on Part B.

This is a continuation of the Nano Roughness MEA in which your engineering team developed a procedure to measure surface roughness at the nanoscale from AFM images.. Interoffice Memo: Li

Model-Eliciting & Exploration Activity

Nano Roughness – Homework Part A

This problem is to be completed individually Complete this problem before working on Part B.

This is a continuation of the Nano Roughness MEA in which your engineering team developed a procedure to measure surface roughness at the nanoscale from AFM images

A profile is a two-dimensional picture of a three dimensional surface that may be thought of as the result of a sectioning place cutting the surface Profiles are ordinarily taken perpendicular to the lay as shown in Figure 1

Figure 1: Extraction of a two-dimensional profile from a three dimensional surface.

Consider graphs A through D below These are profile graphs of a topographical image The x-axis represents the position on the image in the x-direction; the z-x-axis represents the height

In a Word document, answer the following questions:

 Of these 4 graphs, which would you characterize as the most rough and why?

 What assumptions have you made about these graphs?

 If you consider your procedure for roughness from Lab 10, would your answer for which graph was the most rough be the same as in the first question? Why or why not?

Model-Eliciting & Exploration Activity

Nano Roughness – Homework Part B

This problem is to be completed by your team.

Read the memo below and complete the assignment presented to your team by the

Vice President of Research, Kerry Prior

Interoffice Memo: Liguore Labs

To: Nanosurface Engineering Team

From: Kerry Prior, Vice President of Research

RE: Surface roughness update

The research laboratory scientists spoke to me today about the surface

roughness issue One of the newer scientists on the team believed that

methods to measure surface roughness already exist After looking into this issue, I found there are many methods that are commonly used to measure roughness on the nanoscale A method that is used for surfaces in which wear

and friction are an issue is called the Average Maximum Profile The

attachment has a description of how to calculate the Average Maximum Profile Study the method carefully and compare your team’s procedure to the Average Maximum Profile.

Please reply in a memo that answers the following questions:

1 How is the Average Maximum Profile similar to the procedure your team produced?

2 How is the Average Maximum Profile different from your team’s

procedure?

3 How rough are the three samples of gold (A, B, and C) attached to this memo using the Average Maximum Profile procedure? Compare this to your roughness findings using your procedure.

4 In your opinion, which method better quantifies roughness and why?

5 In what ways does the Average Maximum Profile lend itself to the

development of a software tool?

6 Does your team’s method lend itself to the development of a software tool? If so, how? If not, why not?

Your team has given a great effort thus far Keep up the good work!

Kerry Prior

Attachments: Average Maximum Profile tutorial, AFM images of gold with cross-sectional data graphs

Average Maximum Profile Method (AMP):

The Average Maximum Profile Method is an average of the difference between the heights of the ten highest peaks and the ten deepest valleys It is used for evaluating surface texture on limited-access surfaces where the presence of high peaks or low valleys is of functional significance

10 10

1 1

1

 

=  − 

 ∑ ∑ 

Each team member is to use the AMP method to approximate the roughness of the three sample cross-sectional graph of gold Each team member is to find his or her own 10 peaks

and valleys, determine the height value for each of those points, and calculate the roughness value Mini tables are provided with each sample When all of your team members have

completed their measurements, compare your answer with those of your teammates Please note that no answer is better than any other Thus, there is no need to change your answers based on what other team members found

The team is to complete the summary tables by entering each member's name and measurements for his or her peaks and valleys, along with his or her calculated roughness value At the top of each table, include the roughness value measured using your procedure from the Nano

Roughness MEA

SAMPLE A:

Member Name Peaks Valleys

Roughness:

where p i represents the ith highest peak and v j represents the jth deepest valley

Copyright © 2004 Purdue University 4

SAMPLE B:

Member Name Peaks Valleys

Roughness:

SAMPLE C:

Member Name Peaks Valleys

Roughness:

Roughness Measurement Summary Tables:

SAMPLE A:

Your Procedure Roughness Value:

Member 1 Name Member 2 Name Member 3 Name Member 4 Name

Peaks Valleys Peaks Valleys Peaks Valleys Peaks Valleys

AMP

Roughness:

AMP Roughness:

AMP Roughness:

AMP Roughness:

SAMPLE B:

Your Procedure Roughness Value:

Member 1 Name Member 2 Name Member 3 Name Member 4 Name

Peaks Valleys Peaks Valleys Peaks Valleys Peaks Valleys

AMP

Roughness:

AMP Roughness:

AMP Roughness:

AMP Roughness:

SAMPLE C:

Your Procedure Roughness Value:

Member 1 Name Member 2 Name Member 3 Name Member 4 Name

Peaks Valleys Peaks Valleys Peaks Valleys Peaks Valleys

AMP

Roughness: AMPRoughness: AMPRoughness: AMPRoughness: