ThirdYearMgOExpt-1415

Thermal Expansion of MgO

This is the welcome page for the elective MgO component of the third year computational chemistry labs for 2019/20.

The computational lab will be from 10:00 to 17:00 on Monday, Tuesday, Thursday and Friday. During these 4 days demonstrators will be available in the computer room to answer all your questions.

There is an introductory lecture to the lab at 10:00 on the Start Date of your session. You will received and email with the location of this lecture.

The deadline is at 12:00 of the day indicated in the table below ("Report Deadline").

Work submitted late will be penalised according to the Late Submission Policy.

There's a link set up on Blackboard for submitting the report in PDF and the Jupyter notebooks as a .zip folder in 3rd Year Chemistry Laboratories (2019 - 2020) / Y3C Third Year Computational Laboratory/.

In each exercise there are a number questions and sub-questions. The final report will be expected to contain answers to these questions.

Questions related to this computational experiment can be directed to the demonstrators, Dr Giuseppe Mallia and Prof. Nicholas Harrison.

Introduction

The properties of materials (solids, liquids, gasses) are a statistical average over the many different energy states of the molecules making up the material. The vibrational free energy of H₂ can be computed analytically by summing over the harmonic vibrations of the molecule. This cannot be done by hand for a real material containing many atoms.

In this laboratory you will use a simple model of atomic interactions to calculate the energy and vibrations of a crystal of MgO. These vibrational energy levels will then be used to compute the free energy of the crystal and to predict how the material expands when heated. In the last final stage you will go beyond the harmonic (and quasi-harmonic) approximation and expand the crystal using a technique called molecular dynamics - essentially reproducing the actual vibration motions of the atoms. Fortunately the computer will do most of the work !

Instructions

- Download all the Jupyter Notebooks as a .zip file.

- On the Software Hub run Anaconda.

- In Anaconda, open Jupyter Notebook.

- Run the The_lab.ipynb

- Follow the instructions in the notebook.

Please, make a copy of the Jupyter notebooks, just in case you mess up with the code.

Previous years related contents

- Maths and Physics for Chemist

- Thermodynamics

- Statistical thermodynamics

- Python

Good skills on python is not a requirement. All the scripts are written in a way where you only need to write an input value (e.g. Temperature = 300 K). However, feel free to edit and play with the scripts.

New contents

- Phonons and reciprocal space

- Quasi-Harmonic approximation

- Molecular dynamics

Submission

The report will be written in a PDF document and submitted via Blackboard.

Additionally, all the files (including the lab notebooks) will be also submitted via Blackboard as a .zip folder.

Write up

The report structure will consist on three sections:

• Introduction/Summary (Half-page)
• Questions & answers (No page limit)
• Conclusions (Half-page)

Tips to write a report:

• The golden rule: Aim for clarity
  • Structured statements that flow in a logical manner.
  • Good use of diagrams and appropriate level of theory.
  • Careful choice of content.

• Keep your language clear and simple.
• Label all tables and figures. Labels should be self-contained, which means that tables and figures should be interpretable by themself.
• Appropriate referencing of figures and tables.
• Cite previous works (with an accepted citation style) whenever is appropriate.

Introduction/Summary:

• The purpose of the Introduction/Summary is to put the reader in the context of the experiment and to explain how the experiment was carried in the lab. It may contain a brief review of previous research, why the research was undertaken, an explanation of the techniques and why they are used and why it is important in a broader context.

Questions & Answers:

• There are a number of questions in the lab script that has to be answered in this section of the report.
• Depending on the nature of the question, it might be appropriate to use figures or tables to give a proper answer.
• It is highly encourage to rationalise the answers.

Conclusions:

• The Conclusions gives a general description of the results and findings and it should be related back to the Introduction. If appropriate, suggest improvements or additional experiments.

Suggested Time Frame

Try to finish all the calculations by Thursday. All the calculations takes seconds, however, it takes time to analyse the results and understand all the new concepts that you will learn in this lab.

Mark Scheme

The break-down for the marks for this lab are as follows:

Introduction/Summary	20%
Questions & Answers	60%
Conclusions	20%

Plagiarism

Submissions are checked for plagiarism. External images may be used if correctly cited, but it's always better to create your own.

Demonstrators

The demonstrators will be Victor Chang (v.chang16@imperial.ac.uk) and Carles Rafols i Belles (c.rafols-i-belles16@imperial.ac.uk). They will be available in the computer room from 10:00 to 11:00 (Tue, Thur) and from 2:00 to 3:00 (Fri).

Feel free to contact them in the lab or via email.

Related literature

How Chemistry and Physics meet in the Solid State by Roald Hoffman

Introduction to the theory of Lattice Dynamics

Introduction to Lattice Dynamics. Dove, Martin T. (ebook available in the library)