Computational Approach to Materials Science and Engineering

Transcription

1 Computational Approach to Materials Science and Engineering Prita Pant and M. P. Gururajan January, 2012 Copyright c 2011, Prita Pant and M P Gururajan. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back- Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. 1

2 Module: Introduction Materials science and engineering is a cross-disciplinary area. It incorporates into itself sections of condensed matter physics, physical chemistry, solid state chemistry, metallurgy, polymer physics, polymer chemistry, ceramics and glasses, composites, and to some extent, even biology. The fascination with materials science and engineering lies in the fact that, as a subject, it transcends its constituent parts and gives a perspective which is unique and its own. In fact, we believe that a basic understanding of certain concepts of materials science and engineering are essential for everybody. In this course (aptly called Computational approach to materials science and engineering), we take a computational approach to materials science and engineering. The learning goals that we have in mind in taking such an approach are three-fold: 1. To take a hands-on approach to the learning of concepts from materials science and engineering; 2. To be able to use computers and freely available open source software to (a) deal with data, (b) understand concepts and (c) solve problems of engineering interest; and, 3. To develop the mathematical and computational skills that are essential for any engineer. Keeping the above goals in mind, we have organised our course material into four different parts: 1. The tools of the trade In this section, we give short, tutorial introductions to the C programming language and a few open source software for numerical computations and visualization (gnuplot, GNU Octave, Scilab); we also introduce the L A TEXsoftware for report preparation along with other miscellaneous software and programs. 2. Dealing with data In this section, we show how to plot data, fit data to given functional forms, interpolate data, and to integrate it. For doing these operations, 2

3 we use examples of some very basic concepts and ideas from materials science and engineering. 3. Concepts from Structure, Thermodynamics, Kinetics and Phase Transformations In this section, we use certain general concepts from the areas of structure of materials, materials thermodynamics, kinetics of transformations, and phase transformations to introduce linear algebra, partial differential equations, numerical solutions of partial differential equations and simulation techniques. 4. Concepts from Structure, Defects and Mechanical Behaviour of Materials In this section, we use certain general concepts from the areas of structure of materials, defects, and mechanical behaviour of materials to introduce partial differential equations and numerical/simulation techniques. As is clear from the description above, both the selection of material and its presentation have been highly influenced both by our expertise and our interests. 1 Pre-requisites In general, the entire material can be separated into three broad categories: the first is the concepts from materials science and engineering; the second is the mathematical basics and preliminaries; and, the third is the numerical methods and their implementation. We believe that if the students have undergone an introductory materials science and engineering course, they will be able to follow all the material in these notes; if not, we recommend the use of Introduction to materials science and engineering of Raghavan (or, any book of the same difficulty level) to go with these notes. We also expect the students to have undergone a basic course in mathematics (at the level of Kreyzig s Engineering mathematics). 3

4 We expect the students to have undergone a basic programming course; we would prefer if it is a C/C++ programming course. We believe that even those who have learnt a programming language other than C/C++ can still pick enough of C by simply going through all the code and the accompanying commentary. In order to make this course material complete (and for the sake of ready reference), we have given a tutorial introduction chapter on C. In the numerical implementation section, we give more than one way of solving the problem. We believe that the user can choose the method that she/he finds interesting and useful. Further, if the instructor chooses one methodology for classroom instruction, the others can be used by students to learn on their own. Finally, a word about the recommended software to be used with this course material is also in order. We strongly believe in the open source and freeware philosophy. We have made sure that anybody with a computer running the Linux operating system (specifically, Ubuntu), will be able to load and use all the software and programs that we use and recommend. We have also tried to make sure that majority of these freeware are also available for other operating systems (such as WINDOWS). However, owing to our philosophy, knowledge and expertise, we have not ventured to give any technical support to the users of operating systems other than Ubuntu. 2 Loading Ubuntu and applications on to your computer Ubuntu 1 is an operating system (based on Linux kernel and) ideal for use on personal computers, laptops and desktops. It is free and is frequently updated. It has a committed group of volunteers and supports plenty of other educational and development programs and software. Hence, it is an ideal platform for developing expertise in computational skills. 1 A rough translationof the principle of Ubuntu is humanity towardsothers. Another translation could be: the belief in a universal bond of sharing that connects all humanity. A person with ubuntu is open and available to others, affirming of others, does not feel threatened that others are able and good, for he or she has a proper self-assurance that comes from knowing that he or she belongs in a greater whole and is diminished when others are humiliated or diminished, when others are tortured or oppressed. Archbishop Desmond Tutu (This and more are available at 4

5 There are a couple of easy ways of loading Ubuntu on your desktop or laptop. It can be done via a CD (compact discs) or Universal Serial Bus (USB, stick, or, memory stick); Ubuntu can also be loaded on a machine running another operating system (such as WINDOWS) either separately, or as an application on the desktop. The instructions for loading Ubuntu are available at the Ubuntu site with screen shots ( Loading Ubuntu typically consists of the following three steps. 1. Download the software. We recommend that you choose the Long Term Support (LTS) version; Ubuntu LTS (Long Term Support) the Lucid Lynx which was released in April 2010; it will be supported until April, Depending on your hardware (computer architecture), you also need to choose the 32-bit or 64-bit version. Typically, for AMD Athlon 64, AMD Opteron, AMD Sempron, AMD Turion 64, AMDD Athlon II, and AMD Phenom II, Intel Celeron (newer), Intel Pentium (newer), Intel Xeon processors in Intel Core i2/i3/i5/i7 and Itanium processors, the 64-bit version should be used. 2. Burn your CD or create a bootable USB stick The creation of bootable CD or USB can be done on any operating system (Linux, Mac and WINDOWS); hence, depending on your requirement you should choose the appropriate procedure; there are stepby-step screenshots available for each of these options at 3. Install Optionally, beforeinstalling, youcantryoutubuntu. If youwant to do an installation, again, instructions are available with screenshots every step of the way at Loading freeware: the example of gnuplot Once the basic operating system is loaded, there are three ways in which a freeware can be loaded onto the computer. They are, in the order of 5

6 increasing complexity, (a) using a program called Synaptic Package Manager; or, (b) using a terminal based command called apt-get; or, (c) directly from the source code. As an example, we show here the loading of the freeware gnuplot using all these three methods. Note that for doing any of these operations, you should have administrator privileges on the machine; typically, if you have created your account at the time of installation of Ubuntu, you will have administrator privileges Using synaptic package manager Here are the instructions as to how to load gnuplot using the synaptic package manager graphical user interface (GUI) tool. On your Ubuntu desktop (typically at the left top) find the system button, to go from System Administration Synaptic Package Manager. Click on the Synaptic Package Manager. The system tells you Enter your password to perform administrative tasks. The application Synaptic Package Manager lets you modify essential parts of your system. Enter the password and click OK. The Synaptic Package Manager window is opened and it looks as shown in Figure. 1 At the top of the window, in the quicksearch box, type gnuplot and enter search. In the listing below, now you can see gnuplot (see Figure. 2). If gnuplot is already installed (as in this case), the box is shown in green. Otherwise, it would be shown with a star. One can point the mouse at the starred box, right-click and select the software for installation. Note that it is also possible to uninstall installed software using the same procedure, namely, by right-clicking at the green box. 6

7 Figure 1: The screenshot of Synaptic Package Manager. Once any application is chosen for loading, the Apply button (Third from left, with a tick sign on as seen in the Figures. 1 and 2) gets activated and is highlighted with green. By clicking on the Apply button, the process of installation can be completed. Note that if you are in a network that uses proxy, then you have to set up your computer and Synaptic Package Manager for proxy. The screenshots explaining how to do this are found at Using apt-get The apt-get program is a command line based utility. Simply by typing sudo apt-get install gnuplot, one can install gnuplot. Note that you should be an user with administrative privileges for this to work; you will also be asked your password before the installation can start. 7

8 Figure 2: Searching for gnuplot in Synaptic Package Manager: the screenshot. 8

9 2.1.3 Loading from the source One can also download the source code for gnuplot; it typically comes as a tarred, gzipped file. One needs to gunzip (gunzip gnuplot tar.gz) and untar (tar -xvf gnuplot tar) to obtain the gnuplot directory. In this directory, issue the commands,./configure, make and sudo make install (optionally, followed by a make clean command) to install gnuplot. More information on this type of installation is available at the gnuplot page 3 Copyright and Licenses Note that all the codes and this course material are copyrighted to Prita Pant and M P Gururajan and are distributed under the GNU Public license and GNU Free Documentation license, respectively. 4 References and further reading 1. The C programming language, Brian W Kernighan and Dennis M Ritchie, Second edition, PHI Learning Private Limited, Materials science and engineering: a first course, VRaghavan, Fifth edition, PHI Private Limited, Physical metallurgy principles, Robert E. Reed-Hill, Second edition, Affiliated East-West Press Pvt. Limited, Materials science and engineering: an introduction, William D Callister, Sixth edition, John Wiley & Sons, An introduction to materials science and engineering, Kenneth M Ralls, Thomas H Courtney, and John Wulff, Wiley India Pvt. Ltd., Advanced engineering mathematics, Erwin Kreyzig, 8th edition, Wiley- India, Student edition,

10 7. Ubuntu: 8. Thinking in C++, Java and Python. Free books can be downloaded from 10