The Free Energy and Thermal Expansion of MgO


INTRODUCTION TO STATISTICAL MECHANICS LAB


Instructions

The following exercises are to be completed in the computational laboratory.
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.
The start date is given in the table below according to the session.
There is an introductory lecture to the lab in Room 235 at 10:00 on the Start Date of your session.

The deadline is at 12:00 of the day indicated in the table below ("Report Deadline").
Work submitted late will be penalised.
There's a link set up on Blackboard for submitting a wiki the report for this experiment.
Blackboard is bb.imperial.ac.uk, and the link is in folder
3rd Year Chemistry Laboratories (2017 - 2018) / Y3C Third Year Computaqtional Laboratory / Wiki submission.

Session Start Date End Date Report Deadline
1 16 / 10 / 2017 20 / 10 / 2017 25 / 10 / 2017
2 30 / 10 / 2017 03 / 11 / 2017 08 / 11 / 2017
3 13 / 11 / 2017 17 / 11 / 2017 22 / 11 / 2017
4 27 / 11 / 2017 01 / 12 / 2017 06 / 12 / 2017
5 11 / 12 / 2017 15 / 12 / 2017 20 / 12 / 2017
6 22 / 01 / 2018 26 / 01 / 2018 31 / 01 / 2018
7 05 / 02 / 2018 09 / 02 / 2018 14 / 02 / 2018
7 19 / 02 / 2018 23 / 02 / 2018 28 / 02 / 2018
9 05 / 03 / 2018 09 / 03 / 2018 14 / 03 / 2018
10 19 / 03 / 2018 23 / 03 / 2018 28 / 03 / 2018

In each exercise there are a number of explicit Questions and often also an opportunity to Speculate on the results obtained. The final report will be expected to contain answers to these questions and, where you feel able, further speculation.

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


Introduction & Background Material

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 !


The Software: RedHat Linux, DLVisualize and GULP

DLVisualize is a general purpose graphical user interface for modelling. It will give you relatively easy access to a number of quantum mechanical and empirical simulation codes. In this case the interface to the molecular modelling code GULP (General Utility Lattice Program) will be used.

Linux provides an excellent environment for numerical simulations so the first step is to reboot your computer into RedHat Linux.

The environment is not hugely dissimilar to that provided by Microsoft Windows. You will find a web browser (Mozilla) on the tool bar and under the Start Menu you will find some office tools (Writer, Math etc.) which are similar to those in Microsoft Office (Word, Excel etc.) and you may find them useful in plotting your data and writing your report.

Starting DLVisualize

There are web sites devoted to both DLV and GULP where you can find some additional information.

Further information about DLV

Further information about GULP


Exercises

The exercises below should be completed in sequence. Although there will be supervisors present during the laboratory the exercises are designed to facilitate self study - there are many extensions of the exercises that might occur to you !

  1. Calculating the internal energy of an MgO crystal
  2. Lattice Vibrations - Computing the Phonons
  3. Calculating the Free Energy in the Harmonic Approximation
  4. The Thermal Expansion of MgO
  5. Molecular Dynamics

How to start DLVisualize

How to save a picture for your report


Additional material.

  1. Vibrations in crystals by Prof. Nicholas Harrison
  2. Introduction