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HW_LaTex_thesis_template
========================
Thesis LaTex template based on the submission guidelines of Heriot-Watt University, that I have personally updated.
Aside: these guidelines are mainly for PhD theses but are also valid for non PhD research dissertations/theses (specifically for those writing up an MRes or MPhil).
The template has been updated to support subfiles (for rendering each chapter independently of the full document) - a feature helpful for theses with lots of images, especially large ones. Other small tweaks are applied such as support for using acronyms in the document with the acro package, replacing the more cumbersome glossaries package.
Additionally the university shield is now updated to something I cropped and cleaned myself, rather than the previously included one which looked like it was traced lovingly in microsoft word.
Lastly, links to the university guidance are included, and text in each section describe the relevant portion of the guidance.
November 2021: I have updated the documentation to be clearer about cleveref, and have added biblatex which allows per-chapter bibliographies. To-do notes have also been added. More mathematics support was added in out of the box too.
-Alexandre Coates, November 2021

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Micro indentation tester
Image analysis stuff
PUMA Microscope - https://hackaday.com/2021/09/09/highly-configurable-open-source-microscope-cooked-up-in-freecad/
https://www.sciencedirect.com/science/article/pii/S246806722300007X
Make the damn thing an inverted microscope, for god's sake. I'm so done with irregular samples
https://hackaday.com/2021/04/26/3d-printed-laser-scanning-confocal-microscope-measures-microns/
https://hackaday.com/2020/05/05/lego-microscope-does-research/
Stereo microscope??
https://hackaday.com/2024/04/09/adjustable-lights-help-peer-inside-chips-with-ir/
openflexure but bigger - https://hackaday.com/2024/03/10/%ce%bcreprap-taking-reprap-down-to-micrometer-level-manufacturing/
Electron microscope youtube to watch - https://hackaday.com/2019/02/18/electron-microscopes-are-awesome-everything-you-didnt-know-you-wanted-to-know/
TL;DR a Loadcell for the force and a displacement sensor for the displacement
DIY Hardness testing using a bouncing ball bearing by Tony Foale (Motochassis)
https://www.youtube.com/watch?v=oxT8Uqq88xM
https://www.youtube.com/watch?v=4ghW9RNKiDA
https://s3-us-west-1.amazonaws.com/hmt-forum/tony_foale_hardness_tester.pdf
Michel-Uphoff
https://www.youtube.com/watch?v=CHMexzeWQD8
https://www.youtube.com/watch?v=mtxRkP5UavY
https://www.youtube.com/watch?v=ZBGS0ZLZPTY
Accurate precision level
https://www.youtube.com/watch?v=8F6tnOIg0FA
https://www.youtube.com/watch?v=dhGLn6MObcE
General Infi
https://xometry.pro/en/articles/hardness-testing-of-metals/
LitReview
https://www.technoarete.org/common_abstract/pdf/IJERCSE/v4/i2/2.pdf
https://www.mdpi.com/2073-4352/7/10/258

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\documentclass[../HWThesis.tex]{subfiles}
\begin{document}
\chapter{Foo}
Hi I'm an appendix
Appendices, labelled A, B etc., should be treated as additional chapters and should normally follow the main text. Appendices may consist of supporting material of
considerable length or of lists, documents, commentaries, tables or other evidence that if included in the main text, would interrupt its flow. The style of appendices must be consistent with the style of the main text. Long appendices may be divided into sections, labelled as Appendix A.1 etc., with corresponding subsection numbering, which must be entered in the table of contents. Alternatively, short appendices may be attached to individual chapters, as an extra section with a heading of style 3.7 Appendix.
\end{document}

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\documentclass[../HWThesis.tex]{subfiles} %Copy this at the top of each subfile, then you can render the .tex file on its own
\begin{document}
\begin{refsection}
\chapter{Introduction}
\label{ch:introduction}
% Describe why there is a need to look from both the fluid and solid perspective
Cavitation erosion is a complex phenomenon that results from hydrodynamic elements and material characteristics \cite{Franc2004265}.
% Hydrodynamic POV
From a hydrodynamic standpoint, cavitation erosion results from the formation of and subsequent collapse of vapor bubbles within a fluid medium, due to the local pressure reaching the saturated vapor pressure (due to pressure decrease (cavitation) or temperature increase (boiling)). When these bubbles implode, they emit heat, shockwaves, and high-speed microjets that can impact adjacent solid surfaces, leading to damage to the surface and removal of material due to the accumulation of damage following numerous cavitation events.
The required pressure drop required by cavitation could be provided by the propagation of ultrasonic acoustic waves and hydrodynamic pressure drops, such as constrictions or the rotational dynamics of turbomachinery \cite{GEVARI2020115065}.
% Now do the materials POV
The resultant stress levels, which range from 100 - 1000 MPa, can surpass material resistance thresholds, including yield strength, ultimate strength, or fatigue limit, leading to material removal from the surface and subsequent degradation of industrial sysytems. The high strain rate in cavitation erosion makes it rather comparable to explosions or projectile impacts, albeit with very limited volume of deformation and repeated impact loads. The plastic deformation results in progressive hardening, crack propagation, and local fracture and removal of material, with the damage being a function of intensity and frequency of vapor bubble collapse. The selection of more resistent materials requires investigation of material response to cavitation stresses, with the mechanism of erosion being of particular interest. The resulting reduction of performance \& service life and the increased maintenance and repair costs motivate research into understanding how materials respond to the impact of a cavitating material. Cavitation erosion is a major problem in hydroelectric power plants \cite{Romo201216}, Francis turbines \cite{Kumar2024}, nuclear power plant valves \cite{Kim200685, Gao2024}, condensate and boiler feedwater pumps \cite{20221xix}, marine propellers \cite{Usta2023}, liquid-lubricated journal bearings \cite{Cheng2023}, pipline reducers \cite{Zheng2022, Chen201442, Mokrane2019}.
%The commercial wear resistant Stellite alloys are derived from the Co–Cr–W–C family first investigated by Elwood Haynes in early 1900s [1].
% Stellites
Stellite alloys consist of a cobalt (Co) matrix with solid-solution strengthening of chromium (Cr) and tungsten(W)/moblybdenum(Mo), and hard carbid phases (Co, Cr, W, and/or Mo carbides) \cite{Shin2003117, Crook1992766, Desai198489, Youdelis1983379}. The matrix provides execelent high-temperature performance, while the carbides provide strength, wear resistance and resistance to crack propagation \cite{Ahmed2021, Crook199427}.
% Applications
Stellites are typically used for wear-resistant surfaces in lubrication-starved, high temperature or corrosive environments \cite{Zhang20153579, Ahmed2023, Ahmed20138, Frenk199481, Song1997291}, such as in the nuclear industry \cite{McIntyre1979105, Xu2024, Gao2024}, oil \& gas \cite{Teles2024, Sotoodeh2023929}, marine \cite{Song2019}, power generation \cite{Ding201797}, and aerospace industries \cite{Ashworth1999243}. Hot Isostatic Pressing (HIP) consolidation of Stellite alloys offers significant technological advantages for components operating in aggressive wear environments \cite{Ahmed20138, Ahmed201470, Ashworth1999243, Yu20071385}. Yu et al \cite{Yu2007586, Yu20091} note that HIP consolidation results in superior impact and fatigue resistance over cast alloys.
% Why are stellites OP at cavitation?
% Stellites have good CE resistance due to the low stacking fault energy of the cobalt fcc phase, which favors planar slip dislocations and increases the number of cycles that leads to fatigue failure.
% Understanding the matrix phase
Understanding the cobalt phase is crucial for studying structural changes in Co-based alloys widely used in industry. Cobalt and Co-Cr-Mo alloys undergo thermally induced phase transformation from the high temperature face-centered cubic (fcc) $\gamma$ phase to low temperature hexagonal close-packed (hcp) $\epsilon$ phase at 700 K and strain induced fcc-hcp transition through maretensitic-type mechanism (partial movement of dislocations) \cite{HUANG2023106170}. At ambient conditions, the metastable FCC retained phase in stellites can be transformed into HCP phase by mechanical loading, although any HCP phase is completely transformed into a FCC phase between 673 K and 743 K \cite{DUBOS2020128812}; the metastable fcc cobalt phase in stellite alloys \cite{Rajan19821161} absorbs a large part of imparted energy under the mechanical loading of cavitation erosion. The fcc to hcp transition is related to the very low stacking fault energy of the fcc structure (7 mJ/m2) \cite{Tawancy1986337}. Solid-solution strengthening leads to increase of the fcc cobalt matrix strength (due to distortion of the atomic lattice with the additino of elements of different atomic radiuses), decrease of low stacking fault energy \cite{Tawancy1986337} due to the adjusted electronic structure of the metallic lattice, and inhibition of dislocation cross slip. Given that dislocation cross slip is the main deformation mode in imperfect crystals at elevated temperature, as dislocation slip is a diffusion process that is enhanced at high temperature, this leads to high temperature stability \cite{LIU2022294}. The addition of nickel (Ni), iron (Fe), and carbon (C) stabilize the fcc structure of cobalt (a = 0.35 nm), while chromium (Cr) and tungsten (W), stabilize the hcp structure (a = 0.25 nm and c = 0.41 nm), although Cr and W increases hot corrosion resistance \cite{Vacchieri20171100, Tawancy1986337}.
% Maybe get the size of atoms and show the mismatch?
% Let's now move into the carbides portion.
In addition to solid-solution strengthening, the precipitation of carbides allows stellites to endure mechanical and thermal stresses at high temperature. \cite{Gui20171271,osti_4809456}
% Novelty
% How well was the novelty of the project expressed?
%To date, academic research pertaining to cavitation erosion specifically on HIP'd stellite alloys appears to be absent from the existing literature.
% Novelty - Me jerking off to the novelty of my thesis
Given the detrimental influence of voids and defects on cavitation erosion, the lack of academic investigation into cavitation erosion on HIP (Hot Isostatic Pressing) stellite alloys, underscores the need for further exploration. Moreover, the complexity introduced by blended stellite alloys in the context of cavitation erosion in corrosive enironments adds another layer of intrigue to this research endeavor. By analyzing the interactions between alloy composition, microstructure, and cavitation erosion behavior, this thesis aims to fill a critical gap in the current understanding of material performance under cavitation erosion conditions.
\section{Thesis Structure Details}
\label{sec: thesis details}
For the Degree of Doctor of Philosophy the thesis shall not normally exceed 80,000 words and shall not normally exceed 400 pages in length including Appendices, with a limit of no more than 100,000 words. In exceptional circumstances, the Research Degrees Committee will consider requests for thesis exceeding 100,000 on a case by case basis. The number of pages of a thesis exceeding 80,000 words in length shall be increased on a pro rata basis in accordance with the word limit. For the Degree of Doctor of Philosophy by Published Research, a critical review of the published research which shall be in the range of 10,000 to 25,000 words must be submitted.
Chapter 1 of the thesis must be an Introduction, so headed, defining the relation of the thesis to other work in the same field and referring appropriately to any findings, propositions or new discoveries contained in the thesis and to any important points about sources or treatment.
Thesis guidelines can be found at: \\ \url{https://www.hw.ac.uk/uk/students/doc/guidelinesonsubmissionandformatofthesis.pdf}
Related documents and forms at: \url{https://www.hw.ac.uk/uk/students/studies/examinations/thesis.htm}
\subsection{Layout details}
\label{sec: layout}
In the main tex document \texttt{HWThesis.tex} the margins are set, and the left margin is larger than the right one. This is because the PhD thesis you submit will be printed one-side rather than double sided. So in any two spread the printed page will be the one on the right hand side. Therefore, the left side of every page will connect to the thesis binding, so you need an extra large margin to make sure none of your images or text are hidden by the binding.
\subsubsection{Paragraph indentation} I have turned off the LaTeX default of having the first line of each paragraph be indented. If you want to turn that back on, simply go to the preamble in \texttt{HWThesis.tex} and comment out the line \texttt{\textbackslash usepackage\{parskip\}}.
\section{Template Structure}
This LaTeX template is for you to have the format generally laid out, and an example structure. The main file is \texttt{HWThesis.tex}, that defines the title page, layout, packages, and a few other pieces of information. The file tree is set up for a long project, with a few folders. A \texttt{Figures} folder for all your figures, then a \texttt{Chapters} folder to keep the tex files for each chapter. This is just so you don't accidentally make one massive tex file where it gets really really difficult to correct LaTeX mistakes for example. You can change this structure if you'd like, for example with a different figures folder for every chapter.
I have also tried to make this structure modular. For large Theses, if they have lots of images, it can take a long time for them to render, but you are likely only wanting to update one chapter or appendix at a time. So I have introduced the \texttt{subfiles} package.
\subsection{\texttt{subfiles}}
The subfiles package allows you to render individual subdocuments within a larger document, keeping all the functionality from the main document intact. You can see how I have done this in \texttt{HWThesis.tex} where the introduction is added with the \texttt{subfile} command, rather than \texttt{input} or \texttt{include} command. Then each chapter just begins with one line of text\texttt{ \\documentclass[../HWThesis.tex]\{subfiles\}}, and has \\ \texttt{begin\{document\}, end\{document\}} around the rest of the chapter. See further down for details on generating per-chapter references.
\subsubsection{What is the advantage?}
With this, you can work on each chapter in isolation, and not worry about massively long typesetting times, or breaking the rest of your LaTeX document. The main thing that might not work is the citation numbering. This is done at the end of a document, so won't show the numbers correctly unless you render the whole \texttt{HWThesis.tex}, unless you do some workarounds.
\section{What other features are in this template?}
\subsection{citations with \texttt{biblatex}}
So you can use \texttt{biblatex} to define however you would like your references styled. You will have your bibliography in whatever your software of choice is, and you can use that (for example Zotero or Mendeley) to connect to an Overleaf document, or make BibItems / a big .bib file. This has to be loaded with the \texttt{\textbackslash addbibresource\{...\}} command as I have done in the header. You can do this with multiple files if for example you have different bibliographies per paper.
Note, for the per-chapter features we are talking about, we need \texttt{backend = biber} - so if you are generating things offline, you will need to run biber, instead of bibtex to generate the correct behaviour.
I have also set some default arguments when loading \texttt{biblatex}. Lets talk about your citation options. For more detail, please search for the biblatex documentation.
\subsubsection{citation sorting}
I have set the default sorting=none. This means your bibliography will show things in the order you reference them. If you want them sorted by name, then year, then title, set sorting=nyt. For title, then name, then year, sorting=tny. There are lots of these options listed in the documentation, including sorting citations bby type of document etc.
\subsubsection{formatting citations}
\label{sec: format-citations }
I have set the default style for the citation and the bibliography to numeric-comp, meaning compressed numerical style, similar to Vancouver style citations \cite{gum2}.
This means where possible citations will be numbered. The compressed part means that if you cite a range of numbers with a few of them in a row, so instead of showing [1][2][3][5] it will show ranges as hyphenated like [1-3, 5] for example. You may change this to any style you like, or ideally what is used in your field. Let's see a citation range: \cite{gum2, Maier10, gum}
\subsubsection{Doing bibliographies per chapter, vs for the whole thesis}
For the default whole-thesis bibliography, you just need a \texttt{\textbackslash printbibliography} command at the end of your thesis, before the document ends, I have this set up already for you by default.
But if you have a lot of references and a lot of chapters, you may prefer separate bibliographies per chapter. \texttt{biblatex} makes doing sub-bibliographies very easy. You just need to set up a \texttt{begin refsection and end refsection} at the top and bottom of each chapter, and then have a \texttt{\textbackslash printbibliography[heading=subbibliography]} command inside of it. You can do one of these per chapter (\textit{so one per-subfile}). Lets do that now for this introduction chapter. Things are already set up so we can just print it right here (though normally we'd do that at the bottom of the chapter). You'll see that it doesn't include any citations from the next chapter. \cite{gum2, Talia01}
You can look through the biblatex documentation for how to split the bibliography by document type, keyword and all other sorts of things. But this minimal set up should be enough for you to copy paste and achieve something functional quite quickly.
You can also still print the per-chapter references outside of the refsections, there is an example at the end of this thesis.
You just do \\ \texttt{\textbackslash printbibliography\{section=1,heading=subbibliography\}} where 1 means \textit{the first refsection}. Note, the default title is \textit{References}, to set a custom title, for example the name of the chapter you can set this manually by adding \texttt{title = your custom title}
\subsubsection{Sub-bibliography numbering}
The default for sub-bibliographies is that each \texttt{refsection} starts a new index. So each new bibliography starts from [1] again.
If you want separate sub-bibliographies, but with the numbers to continue between chapters, use \texttt{refsegment} instead of \texttt{refsection}. And similarly for printing bibliographies, swap section for segment e.g. \texttt{\textbackslash printbibliography\{segment=1,heading=subbibliography\}}
\subsection{Linking to figures, equations and sections with \texttt{hyperref}}
We can also reference prior sections, for example you might want to see \cref{sec: thesis details} for specifics on how to set up a thesis. These links should be clickable in the pdf thanks to the \texttt{hyperref} package. These links \textbf{will not show up when printing, they are digital only}. If you want to make them printable, you can do that with the help of the \texttt{hyperref} documentation. To link to anything, it needs a label. So label anything you want to reference with with \texttt{\textbackslash \label{...}} and you will be good to go. You can also look up its documentation to change all kinds of behaviours, for example the default link looks like a box around numbers, you can also set it to be like a webpage where links are different colours, but have no boxes around them. Don't go too wild.
\subsection{better internal references with \texttt{cleveref}}
\label{sec: cleveref}
You will notice that when you use a \texttt{ref} command to point to somethign you have labelled (a subsection, figure, equation etc) - you only get the number. It might be more convenient to have it automatically say \textit{eqn 2.2} rather than just \textit{2.2}, forcing you to type eqn, fig, sec every time. That's what this package is here to help. This lets you type \texttt{\textbackslash cref} instead of \texttt{\textbackslash ref}, and it will automatically write eq./fig./sec. as appropriate. To capitalise (if at the beginning of a sentence) use Cref instead of cref.
If you want the full label (figure/equation/section instead of fig./eq./sec. ) then you can add \texttt{[noabbrev]} before the curly brackets when loading cleveref.
So lets use \texttt{\textbackslash ref} to reference a section (\ref{sec: cleveref}), a figure (\ref{fig: black shield}), a table (\ref{tab: example table}), and an equation (\ref{eqn: example equation})
Now the same with cleveref \texttt{\textbackslash cref}: a section (\cref{sec: cleveref}), a figure (\cref{fig: black shield}), a table (\cref{tab: example table}), and an equation (\cref{eqn: example equation})
\subsection{Colors}
You may want to even change the color of text when working on it, you can do that like this \textcolor{red}{there are some colors that are already named in \texttt{graphicx}} but you can also define your own. \definecolor{light-blue}{rgb}{0.8,0.85,1} \textcolor{light-blue}{So now I have a specific light blue color, very nice.} You may want to have colours to highlight sections you are working on, but text needs to be black when you submit!
\subsection{Acronyms, via \texttt{acro}}
This thesis comes set up with acronyms so you can define terms you use repeatedly and make sure they're formatted correctly every time. A simple acronym is \ac{wys}, as this is the first time it is used in the thesis, we get the long version, with the short version following it in brackets. Now it has been used once, we can now simply write the acronym command \texttt{ac\{wys\}} again and we will just get the shortened version. For example: \textit{unlike \LaTeX, Microsoft Word is a \ac{wys} typesetting program. }
These acronyms have to be defined in the preamble of \texttt{HWThesis.tex} . You will want to use these when you just don't want to have to type out a term over and over again, or you can invoke long and hard to spell terms like bacterial names, specific pieces of hardware used in experiments, or even lengthy phrases. This document is set up to include a page that lists used terms. \acl{opt}.
Of course you can choose whether you want the long or short version of an acronym at any point, here is a quick summary of options:
\begin{table}[H]
\begin{tabular}{lll}
first & \texttt{ac\{lol\}} & \ac{lol} \\
second & \texttt{ac\{lol\}}& \ac{lol} \\
long & \texttt{acl\{lol\}} & \acl{lol} \\
short & \texttt{acs\{lol\}} & \acs{lol} \\
full & \texttt{acf\{lol\}} & \acf{lol}
\end{tabular}
\caption{This is also an example of a table}
\label{tab: example table}
\end{table}
This is a very versatile package that saves time and lets you say the important things, whether that is \ac{jau} or \ac{woodchuck}
\section{Symbols}
Top tip, if you are struggling to remember the name of a \LaTeX symbol you need, maybe play around with detexify, where you can draw a symbol, and it will try and find a matching one in \LaTeX: \url{https://detexify.kirelabs.org/classify.html}.
\subsection{Maths}
As a physicist I have included a few packages for maths, these should be standard enough. Specifically I have added \texttt{amsmath} for maths environments and better equations, \texttt{amssymb} for extended mathematical symbols, and \texttt{amsthm} for better maths theorems.
\begin{equation}
e = \sum\limits_{n = 0}^{\infty} \frac{1}{n!} = 1 + \frac{1}{1} + \frac{1}{1\cdot 2} + \frac{1}{1\cdot 2\cdot 3} + \cdots
\label{eqn: example equation}
\end{equation}
An important note here - Thesis guidelines say every equation that appears on its own line, needs an associated number, even if you don't refer to it. So $2 = \sum_i^\infty 2^{-i}$ would not need a number, but the above equation \ref{eqn: example equation} does. I also added in a different fraction option with the \texttt{nicefrac} package. So you can make your fractions like this $\nicefrac{1}{2}$ as compared to the standard $\frac{1}{2}$, up to you!
\subsection{SI Units via \texttt{siunitx}}
The SI unit package is also include, one of the more common usages is to have a proper command for the degree symbol, for example 10 degrees becomes \(\ang{10}\). However the package also includes a lot of functions for using units like grams, candela, moles, electronvolts etc with numbers, so that the unit labels look the same whether in text mode or math mode. If you write a lot of units, maybe look into the documentation.
\textbf{That is everything, the following chapters show some example plots, tables, and then an appendix with details on how an appendix should be set up.}
\section{Keeping Track}
\listoftodos
\subsection{Todo notes}
If while writing you want some very visible coloured boxes to tell you what you have To Do, then use the \todo[color=yellow]{this is a yellow todo note in the margin}todonotes package.
This lets you create todo notes, and empty figures. You can even make a list of your todo notes to see what you have left to do.
Here are some examples.
\todo[inline]{hello, this is a todo note that is inline}
Now lets do a placeholder figure in \cref{fig: missing figure}
\begin{figure}[H]
\begin{center}
\missingfigure[figwidth = .5\linewidth]{one day a nice figure could go here}
\caption{captions still work}
\label{fig: missing figure}%labels work too
\end{center}
\end{figure}
And of course, above this subsection we generated a list of todos.
\subsection{Subfigures and Subcaptions}
I have both of these in the header for the main \texttt{HWThesis.tex} but I have not bothered to test them, play around at your own risk, I don't really like either package honestly.
\section{Logos}
Last last thing, I have included a new university crest for the title page, but you may want an alternative. Here I will quickly show you the ones I have included. You can then choose exactly which one you would like on your title page!
\begin{figure}[H]
\begin{center}
\includegraphics[width=.5\linewidth]{HW_shield.pdf}
\caption{The default HW\_shield, that I cropped from the full logo svg}%make sure to put a \ before any underscores in captions, otherwise it can get nasty
\label{fig:shield}
\end{center}
\end{figure}
\begin{figure}[H]
\begin{center}
\includegraphics [width=0.5\linewidth]{HW_shield_black.pdf}
\caption{The black HW\_shield.pdf, that I also cropped from the full logo svg}
\label{fig: black shield}
\end{center}
\end{figure}
\begin{figure}[H]
\begin{center}
\includegraphics [width=0.5\linewidth]{HW_logo}
\caption{The JPEG HW\_logo from the intranet}
\label{fig: hw logo}
\end{center}
\end{figure}
\begin{figure}[H]
\begin{center}
\includegraphics [width=0.5\linewidth]{HW_logo_black}
\caption{Lastly... the black JPEG HW\_logo from the intranet.}
\label{fig: hw logo black}
\end{center}
\end{figure}
%\printbibtitle
\printbibliography
\end{refsection}
\end{document}

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\documentclass[../HWThesis.tex]{subfiles}
\begin{document}
\begin{refsection}
\chapter{Background}
\label{ch:background}
\begin{figure}[H]
\begin{center}
\includegraphics [width=12cm]{Background/pic.png}
\caption{Figure Caption.}
\label{fig:label}
\end{center}
\end{figure}
Some default citations: \cite{gum, ghc-smp}
\subsection{Subsection}
\begin{table}[H]
\begin{center}
\begin{tabular}{c c c c} % centered columns (4 columns)
\hline\hline %inserts double horizontal lines
Case & Method\#1 & Method\#2 & Method\#3 \\ [0.5ex] % inserts table
%heading
\hline % inserts single horizontal line
1 & 50 & 837 & 970 \\ % inserting body of the table
2 & 47 & 877 & 230 \\
3 & 31 & 25 & 415 \\
4 & 35 & 144 & 2356 \\
5 & 45 & 300 & 556 \\ [1ex] % [1ex] adds vertical space
\hline %inserts single line
\end{tabular}\caption{Table Caption}
\label{tab:lable}
\end{center}
\end{table}
\subsubsection{Subsubsection}
\end{refsection}
\end{document}

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\begin{document}
\chapter{Conclusion and Future Work}
\label{ch:conclusion}
\end{document}

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\begin{document}
\chapter{Design}
\label{ch:design}
Write..
\section{Section}
According to \cite{ghc-pps} ...
\begin{figure}[H]
\begin{center}
\includegraphics [width=12cm]{Design/pic.png}
\caption{Figure Caption.}
\label{fig:label}
\end{center}
\end{figure}
\subsection{Subsection}
\begin{table}[H]
\begin{center}
\begin{tabular}{c rrrrrrr} % creating eight columns
\hline\hline %inserting double-line
Audio Name&\multicolumn{7}{c}{Sum of Extracted Bits} \\ [0.5ex]
\hline % inserts single-line
Police & 5 & -1 & 5& 5& -7& -5& 3\\ % Entering row contents
Midnight & 7 & -3 & 5& 3& -1& -3& 5\\
News & 9 & -3 & 7& 9& -5& -1& 9\\[1ex] % [1ex] adds vertical space
\hline % inserts single-line
\end{tabular}
\caption{Table Caption}
\label{tab:lable}
\end{center}
\end{table}
\subsubsection{Subsubsection}
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%\documentclass[../HWThesis.tex]{subfiles} %Copy this at the top of each subfile, then you can render the .tex file on its own
%\begin{document}
%\begin{refsection}
\chapter{Introduction}
\label{ch:introduction}
% Describe why there is a need to look from both the fluid and solid perspective
%Cavitation erosion is a complex phenomenon that results from hydrodynamic elements and material characteristics \cite{Franc2004265}.
% Why is the above important?
Cavitation erosion occurs when vapor bubbles form and collapse within a fluid due to local pressure reaching the vapor pressure threshold \cite{knapp1970cavitation, brennen1995cavitation, Lauterborn_Bolle_1975}. The implosion emits heat \cite{doi:10.1126/science.253.5026.1397}, shockwaves \cite{10.1115/1.4049933}, and microjets \cite{XIONG2022105899} that damage adjacent solid surfaces, leading to material removal due to cumulative cavitation events \cite{Franc2004265, karimi1986cavitation}. The resulting stress levels, as seen in Figure \ref{fig:cavitation_damage}, can exceed material thresholds, causing surface damage and system degradation \cite{Pereira1998}. Understanding material response to cavitation stresses is crucial for selecting resistant materials and minimizing maintenance costs.
\begin{figure}[h]
\centering
\includegraphics[width=0.98\textwidth]{Figures/the-damage-mechanism-of-cavitation.png}
\label{fig:cavitation_damage}
\caption{Damage mechanism of cavitation}
\end{figure}
Stellites are cobalt-chromium alloys that are typically used for surfaces in lubrication-starved, high temperature or corrosive environments \cite{Zhang20153579, Ahmed2023, Ahmed20138, Frenk199481, Song1997291}, such as in the nuclear industry \cite{McIntyre1979105, Xu2024, Gao2024}, oil \& gas \cite{Teles2024, Sotoodeh2023929}, marine \cite{Song2019}, power generation \cite{Ding201797}, and aerospace industries \cite{Ashworth1999243}. The wear resistance of different stellite alloys manufactured by casting, forging, laser cladding, and hot isostatic pressing (HIP) has been investigated extensively, \cite{Opris2007581, Engqvist2000219, Antony198352, Crook1992766, Desai198489, Yang1995196, DeMolVanOtterloo19971225, Frenk199481, Ahmed20138, Yu2007586, KRELL2020203138, Yu2007586, KRELL2020203138}. The cavitation erosion of stellites has been investigated in experimental studies \cite{Wang2023, Szala2022741, Mitelea2022967, Liu2022, Sun2021, Szala2021, Zhang2021, Mutascu2019776, Kovalenko2019175, E201890, Ciubotariu2016154, Singh201487, Hattor2014257, Depczynski20131045, Singh2012498, Romo201216, Hattori20091954, Ding201797, Guo2016123, Ciubotariu201698}, along with investigations into cobalt-based alloys \cite{Lavigne2022, Hou2020, Liu2019, Zhang20191060, E2019246, Romero2019581, Romero2019518, Lei20119, Qin2011209, Ding200866, Feng2006558}.
Ahmed et al. have investigated the impact of HIP'ing on stellite alloys, finding superior impact and fatigue resistance compared to cast stellite alloys \cite{Ahmed2021, Ahmed2017487,Ahmed201470,Ahmed201498,Yu20071385,Yu20091}. They also explored blended alloys formed by consolidating two stellite powders, resulting in unique microstructures influenced by the different diffusion rates of added elements. Depending on the composition of the stellite powders used, the blended alloys possess uniform microstructure or regions that are similar to the constituent powders \cite{Ahmed2023,Ahmed2021}. This is due to the different diffusion rates of the added elements - carbon diffuses through the blended alloys while tungsten cannot diffuse due to its high atomic radius \cite{Ahmed2023,Ahmed2021}.
%Ahmed et al investigate the influence of the HIP'ing process on stellites \cite{Ahmed2021,Ahmed2017487,Ahmed201470,Ahmed201498,Yu20071385, Yu20091}, and conclude that HIP consolidation of Stellite alloys offers significant technological advantages for components operating in aggressive wear environments due to superior impact and fatigue resistance over cast alloys \cite{Ahmed20138, Ahmed201470, Ashworth1999243, Yu20071385}. In order to achieve unique microstructures from existing stellite alloys, Ahmed et al investigate the performance of blended alloys \cite{Ahmed2023,Ahmed2021}, which are formed through the consolidation of a mixture of two stellite powders. During the HIP'ing process, carbides are precipitated, in addition to reduction of supersaturation of the matrix.
%The powders are created through gas atomization, in which a stream of liquid stellite alloy is disrupted and atomized into tiny molten droplets by a high-pressure inert gas flow. The free-falling molten droplets rapidly solidify into spherical particles before being collected, forming high quality stellite powders with controllable size \cite{Ahmed2023,Ahmed2021}.
%The rapid cooling of the powder during atomization leads to reduced precipitation of carbides and supersaturation of the metallic matrix with other elements, as seen in the reduced proportion of carbide phases detected in the XRD performed on powders, compared to XRD of HIP'd samples \cite{Ahmed2023,Ahmed2021}.
%The mixing of powders is conducted in a powder hopper that ensures uniform distribution of powder mixtures. The HIP treatment was conducted at a temperature of 1200 C and a pressure of 100 MPa for a duration of 4 hours, resulting in full dense blended stellite alloys \cite{Ahmed2023,Ahmed2021}.
% The use of blended stellite
% Stellite alloys can be manufactured by casting, deposition welding, laser cladding, forging, or hot isostatic pressing (HIP). These different processes result in different microstructures.
% Why are stellites OP at cavitation?
% Stellites have good CE resistance due to the low stacking fault energy of the cobalt fcc phase, which favors planar slip dislocations and increases the number of cycles that leads to fatigue failure.
% Novelty
% How well was the novelty of the project expressed?
%To date, academic research pertaining to cavitation erosion specifically on HIP'd stellite alloys appears to be absent from the existing literature.
% Novelty - Me jerking off to the novelty of my thesis
In light of the advantageous impact of fine carbide structure and microstructure on cavitation erosion, the lack of academic investigation into cavitation erosion on HIP'ed stellite alloys highlights the imperative for additional research. Investigating the effects of alloy composition \& microstructure of blended alloys on their cavitation erosion behaviour promises to yield deeper insights into stellite performance under such conditions.
\section{Aims and Objectives}
% Were the aims of the project clearly expressed?
% Were they specific and measurable?
% Were they realistic?
% Were adequate timescales referred to?
Cavitation erosion impacts various industrial components, lowering their service life and increasing overall costs. In order to minimize damage \& losses due to cavitation, the mechanisms by which materials degrade under cavitation erosion need to be understood. This work aims at identifying the most relevant factors to the cavitation erosion of base and blended stellite alloys, with a focus on how composition and microstructure affect cavitation resistance. The objectives of this work are to:
\begin{enumerate}
\item \textbf{Design and develop} an experimental rig capable of accurately simulating cavitation erosion conditions in distilled water \& artificial seawater and achieving measurable \& replicable erosion rates, \textbf{by end of May}.
\item \textbf{Quantify} cavitation erosion resistance of stellite materials in distilled water and artificial seawater \textbf{by end of June}.
\item \textbf{Investigate} the morphology, microstructure, chemical composition, and surface characteristics of eroded stellite samples \textbf{by end of July}.
\begin{enumerate}
\item \textbf{Acquire} Optical Microscopy images of eroded stellite samples at different stages of testing, in order to track changes of overall morphology of eroded surface.
\item \textbf{Acquire} Scanning Electron Microscopy (SEM) images of eroded stellite samples to analyze the microstructural changes and phase composition resulting from cavitation erosion.
\item \textbf{Acquire} Energy Dispersive X-ray Spectrometry (EDS) images and scans to analyze the elemental composition of specific regions on the eroded stellite samples (elemental composition of matrix, carbides, and interfaces)
\end{enumerate}
\item \textbf{Develop} mathematical models for cavitation erosion of stellite alloys \textbf{by end of July}.
\begin{enumerate}
\item \textbf{Investigate} the relationship between composition and previously reported structure-property relationships to cavitation erosion rates.
\item \textbf{Assess} the applicability of parameter-models of cavitation erosion to experimental data of the cumulative mass loss of stellites.
\end{enumerate}
\item \textbf{Understand} the cavitation mechanism in stellite alloys and describe a phenomological model of CE in stellite alloys and provide actionable recommendations for enhancing cavitation resistance in stellite alloys
\end{enumerate}
Finite element simulations (FEA) and other numerical simulation techniques are outside the the scope of this thesis.
\section{Gantt Chart}
\includepdf[pages=-,landscape=true,angle=-180]{Ganttv2.pdf}
\clearpage
\section{Resources}
% In this section, you list what resources you require to do the project.
% Do you need lab access?
% Do you require access to archives?
% Do you need to establish a budget?
% How will you procure the required resources?
The designed rig will require the use of the following equipment
\begin{itemize}[noitemsep]
\item Q500 Sonicator (existing)
\item Vacuum Pump and Dessicator (purchased)
\item Chilled Water Supply (existing)
\item Coiled heat exchanger (purchased)
\item Air Compressor (existing)
\end{itemize}
This work will require access to the following Heriot-Watt University laboratories.
\begin{itemize}[noitemsep]
\item Energy Laboratory \\
Location of relevant existing equipment (sonotrode, microscope, precision balance). There are two computers in the Energy Lab, the first to control the microscope and to handle image processing through ImageJ, and second for general purpose computing. The second computer has an automated backup, in addition to version control on all data stored.
\item Chemical Laboratory \\
Acetone is stored in Flammable Liquid Storage Cabinet in Chemical Lab, with purchase of more acetone available through vendors registered with Procurement. Distilled water is provided by Type 1 water purification system in the Chemical Laboratory.
\item Fabrication \& Automotive Laboratory \\
Access to tools for modification of equipment.
\item Electronics Laboratory \\
Access to soldering equipment for work on unpowered equipment.
\end{itemize}
In addition to the above, the following items are required:
\begin{itemize}[noitemsep]
\item Specimens of Blended Stellite Alloys (provided by Dr Rehan Ahmed)
\item Access to material characterization equipment (SEM, EDS, and XRD) through MoU w/ University of Sharjah.
\end{itemize}
\section{Risks}
The major obstacle for this project is the potential for time constraints and delays, especially those that were not adequately accounted for during the initial project planning phase.
\subsection{Experimental setup complexity risks}
Experimental setup could pose unexpected issues due to lack of planning. In order to mitigate the risk of unexpected design changes, the following strategies are to be employed:
\begin{itemize}[noitemsep]
\item Detailed Planning and Design in CAD \\
The rig is to be designed in CAD to ensure all subsystems meet spatial, power, and I/O requirements.
\item Expert Consultation \& Review \\
The rig design is to be reviewed by supervisor and other expereinced researchers \& engineers. Feedback is to be recorded and designed altered to alleviate concerns. Identified people for review are Dr Rehan Ahmed, Dr Mohammed Al-Musleh, Muhsin Aykapaddatu
\item Functionality/performance is not as expected or to specification \\
Pilot testing of the rig to ASTM G32 standards using known materials (e.g., 316L stainless steel) will verify functionality and performance, comparing results with existing data.
\item Documenting Procedures and Troubleshooting Protocols \\
Detailed documentation of components and development of a Standard Operating Procedure (SOP) aligned with ASTM G32 standards will be maintained. Troubleshooting protocols will be established for unforeseen issues.
\item Modular Design \& Redundancies \\
The rig will feature a modular design for easy component adjustment. Spare parts will be readily available for quick replacement or repair, minimizing downtime.
\end{itemize}
\subsection{Health \& Safety risks}
% TODO Link to appendix
The primary H\&S risks are Noise Exposure and Chemical Hazards (exposure to acetone). Both of these risks have been investigated in existing risk assessments for equipment have been attached to the appendix for the reader's perusal. Unlike the proposed additions, these equipment involve human interaction, requiring the need for a more comprehensive risk assessment. The risk assessments were written by the author, with feedback from project supervisor and lab manager.
\begin{itemize}
\item Grinder-Polisher, available at Appendix \ref{RA_GrinderPolisher}
\item Ultrasonic Bath, available at Appendix \ref{RA_UltrasonicBath}
\item Cavitation Equipment, available at Appendix \ref{RA_Cavitation}
\end{itemize}
\section{Beneficiaries \& Stakeholders}
% Applications for CE research
Industrial manufacturers and technology providers will benefit from improved understanding of cavitation erosion in stellite alloys, enabling the development of more durable materials for applications in harsh environments, such as hydroelectric power plants \cite{Romo201216}, Francis turbines \cite{Kumar2024}, nuclear power plant valves \cite{Kim200685, Gao2024}, condensate and boiler feedwater pumps \cite{20221xix}, marine propellers \cite{Usta2023}, liquid-lubricated journal bearings \cite{Cheng2023}, pipline reducers \cite{Zheng2022, Chen201442, Mokrane2019}.
The project supervisor and academic faculty represent the primary stakeholders, whose critique will be necessary for attaining project \& academic objectives. Apart from serving as mentor, the project supervisor has provided rare specimens and leveraged inter-university connections to access material characterization facilities, enhancing the project's resources and capabilities. Other stakeholders are:
\begin{itemize}
\item Peer Researchers: offer peer review and collaboration, in addition to being users of similar equipment. Undergraduate students are unlikely to be present during project duration, although they are likely to be end users of equipment after project close.
\item Research Community: contribute to understanding of cavitation erosion and benefit from data. Project outcomes generate data and contribute to understanding of cavitation erosion.
\item Lab Management: ensure compliance with health and safety requirements. Additionally, the lab management consists of doctoral students working on other research equipment; their advice will helpful when troubleshooting issues that arise.
\end{itemize}
%\end{refsection}
%\end{document}

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%\documentclass[../HWThesis.tex]{subfiles} %Copy this at the top of each subfile, then you can render the .tex file on its own
%\begin{document}
%\begin{refsection}
\chapter{Literature Review}
\label{ch:literature_review}
% Describe why there is a need to look from both the fluid and solid perspective
Cavitation erosion is a complex phenomenon that results from hydrodynamic elements and material characteristics \cite{Franc2004265}. When components are exposed to sustained cavitation erosion, the component surface is degraded and material is progressively lost.
% Hydrodynamic POV
From a hydrodynamic standpoint, cavitation erosion results from the formation of and subsequent collapse of vapor bubbles within a fluid medium, due to the local pressure reaching the saturated vapor pressure (due to pressure decrease (cavitation) or temperature increase (boiling)). When these bubbles implode, they emit heat, shockwaves, and high-speed microjets that can impact adjacent solid surfaces, leading to damage to the surface and removal of material due to the accumulation of damage following numerous cavitation events \cite{Yu2024771, Niedzwiedzka201671, Micu2017894}. The required pressure drop required by cavitation could be provided by the propagation of ultrasonic acoustic waves and hydrodynamic pressure drops, such as constrictions or the rotational dynamics of turbomachinery \cite{GEVARI2020115065}. Impurities in the fluid, such as solid particles and nanobubbles with a radius of 500nm can significantly reduce the cavitation threshold leading to increased cavitation intensity \cite{Bai2020}. When these bubbles collapse near walls, the concentration of energy on very small areas of the wall result in high stress levels on the wall \cite{Karimi19861}.
% Now do the materials POV
The resultant stress levels, which range from 100 - 1000 MPa, can surpass material resistance thresholds, including yield strength, ultimate strength, or fatigue limit, leading to material removal from the surface and subsequent degradation of industrial systems \cite{Yu2024771, Niedzwiedzka201671, Micu2017894}. The high strain rate in cavitation erosion makes it rather comparable to explosions or projectile impacts, albeit with very limited volume of deformation and repeated impact loads \cite{Meged2002914, Hattori2010855, Steller2021, Steller2020, Meged2015262, FortesPatella2013205}. The plastic deformation results in progressive hardening, crack propagation, and local fracture and removal of material, with the damage being a function of intensity and frequency of vapor bubble collapse \cite{KARIMI19871, Meng1995443, Berchiche2002601}. The selection of more resistent materials requires investigation of material response to cavitation stresses, with the mechanism of erosion being of particular interest \cite{Meged2003277, Soyama200427, Meged200642}. The resulting reduction of performance \& service life and the increased maintenance and repair costs motivate research into understanding how materials respond to the impact of a cavitating material.
\section{Measuring cavitation erosion through ASTM G32}
% Let's describe the ultrasonic cavitation setup and go deeper
% Why is thin layer stuff so important?
The ASTM G32 standard defines the study of cavitation performance of materials by placing an ultrasonic sonotrode above a stationary specimen, forming a thin liquid layer between the two solid walls, as seen in Figure \ref{fig:ASTMG32_fig}. The sonotrode horn emits an acoustic wave into the fluid and causes cavitation when the pressure amplitude is sufficiently high. Due to the reflection and superposition of ultrasound in the thin liquid layer, the intensity of cavitating bubbles is increased, leading to accelerated cavitation erosion \cite{ASTMG32, Bai2020, Hammitt1980}.
\begin{figure}[h!]
\centering
\label{fig:ASTMG32_fig}
\includegraphics[width=0.98\textwidth]{Figures/ASTMG32_important_parameters.png}
\caption{Important parameters of experimental apparatus from ASTM G32. From \cite{ASTMG32}}
\end{figure}
\subsection{Effect of distance between sonotrode and specimen}
Endo et al \cite{Endo1967229} found that the extent of damage depends upon the thickness of the thin liquid layer, Kikuchi et al \cite{Kikuchi1985211} find that the extent of damage is a function of the reciprocal of the thickness of the liquid layer. For thicknesses $h < 0.5mm$, numerous bubbles coalese into several large bubble clusters in contact with the horn tip and the staionary specimen, while for thicknesses $h > 0.5mm$, the numerous bubbles produced are isolated \cite{Me-Bar1996741,Abouel-Kasem201221702, Wu201775}.
\subsection{Effect of liquid temperature}
The test water temperature affects the degree of cavitation erosion \cite{Singer1979147, Ahmed1998119}, with mass loss rate initially increasing with increase in temperature, peaking at an optimum temperature $T_m$, then decreasing with further increase in temperature \cite{Peng2020}, with bulk liquid temperatures above 50 C not altering erosion rate significantly \cite{Singer1979147, Nagalingam20182883}. However, it must be noted that the temperature of the liquid film between the ultrasonic tip and sample rises rapidly, regardless of the bulk liquid temperature \cite{Endo1967229, Abouel-Kasem201221702}, with maximum erosion rates observed with film temperatures at temperatures 30-35 C \cite{Singer1979147, Priyadarshi2023}.
\section{Stellite}
% Stellites
Stellite alloys belong to the cobalt-chromium family, with the addition of tungsten or molybdenum as the main alloying elements.
The matrix in stellite alloys consist of cobalt (Co) with solid-solution strengthening of a substantial amount of chromium (Cr) and tungsten(W)/moblybdenum(Mo), resulting in high hardness \& strength at high temperature, with carbide precipitations (Co, Cr, W, and/or Mo carbides) adding strength and wear resistance \cite{Shin2003117, Crook1992766, Desai198489, Youdelis1983379, Ahmed2021, Crook199427}. Stellites are typically used for wear-resistant surfaces in lubrication-starved, high temperature or corrosive environments \cite{Zhang20153579, Ahmed2023, Ahmed20138, Frenk199481, Song1997291}, such as in the nuclear industry \cite{McIntyre1979105, Xu2024, Gao2024}, oil \& gas \cite{Teles2024, Sotoodeh2023929}, marine \cite{Song2019}, power generation \cite{Ding201797}, and aerospace industries \cite{Ashworth1999243}.
The wear resistance of different stellite alloys manufactured by casting, forging, laser cladding, and hot isostatic pressing (HIP) has been investigated extensively, \cite{Opris2007581, Engqvist2000219, Antony198352, Crook1992766, Desai198489, Yang1995196, DeMolVanOtterloo19971225, Frenk199481, Ahmed20138, Yu2007586, KRELL2020203138, Yu2007586, KRELL2020203138}. Hot Isostatic Pressing (HIP) consolidation of Stellite alloys offers significant technological advantages for components operating in aggressive wear environments \cite{Ahmed20138, Ahmed201470, Ashworth1999243, Yu20071385}. Yu et al \cite{Yu2007586, Yu20091} note that HIP consolidation results in superior impact and fatigue resistance over cast alloys. The cavitation erosion of stellites has been investigated in experimental studies, as seen in Table \ref{tab:stellite}, \cite{Wang2023, Szala2022741, Mitelea2022967, Liu2022, Sun2021, Szala2021, Zhang2021, Mutascu2019776, Kovalenko2019175, E201890, Ciubotariu2016154, Singh201487, Hattor2014257, Depczynski20131045, Singh2012498, Romo201216, Hattori20091954, Ding201797, Guo2016123, Ciubotariu201698}, along with investigations into cobalt-based alloys \cite{Lavigne2022, Hou2020, Liu2019, Zhang20191060, E2019246, Romero2019581, Romero2019518, Lei20119, Qin2011209, Ding200866, Feng2006558}. However the cavitation erosion mechanism has not been fully established, particularly with the effect of microstructure due to different fabrication techniques, as seen in Figure \ref{fig:stellite_microstructure}.
In addition to the energy absorbing effect of phase transformation of the cobalt matrix \cite{Feng2006558}, Heathcock et al \cite{Heathcock1981597} find that finer carbide structure leads to increased cavitation erosion resistance, an observation ratified by Garzon et al \cite{Garzon2005145}. Cavitation erosion of stellite coatings is improved in seawater, when compared to distilled water \cite{Hou2020}, likely due to the protective effect of chromium oxides inhibiting formation of erosion pits \cite{Liu2019}.
\begin{figure}[h!]
\centering
\label{fig:stellite_microstructure}
\includegraphics[width=0.98\textwidth]{Figures/microstructure.jpg}
\caption{Microstructure of Stellite alloys 1, 12, 6, \& 21 due to casting, welding, and HIP'ing. From \cite{KRELL2020203138}.}
\end{figure}
% Insert table of stellite compositions here
% Why are stellites OP at cavitation?
% Stellites have good CE resistance due to the low stacking fault energy of the cobalt fcc phase, which favors planar slip dislocations and increases the number of cycles that leads to fatigue failure.
\begin{table}[ht]
\centering
% To place a caption above a table
\caption{Operating parameters used in ASTM G32 tests on Stellite specimens}
\label{tab:stellite}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline
\multirow{3}{*}{\rotatebox{-90}{\bf Indirect}} & \multirow{3}{*}{\rotatebox{-90}{\bf Water}} & HIP'ed Stellite 6 & 50 & - & 0.5 & 1.5 & 24 & 2.09 & \cite{Szala2022741} \\
& & $5 \times 10^{16} \frac{Mn^{+}}{cm^{2}}$ HIP'ed Stellite 6 & 50 & - & 0.5 & 1.5 & 24 & 2.07 & \cite{Szala2022741} \\
& & $10 \times 10^{16} \frac{Mn^{+}}{cm^{2}}$ HIP'ed Stellite 6 & 50 & - & 0.5 & 1.5 & 24 & 1.88 & \cite{Szala2022741} \\
\hline
\hline
\multirow{10}{*}{\rotatebox{-90}{\bf Direct}} & \multirow{3}{*}{\rotatebox{-90}{\bf Water}} & LC Stellite 6 & 50 & 25 & - & 1 & 14 & 2.7 & \cite{Sun2021} \\
& & SLD Stellite 6 & 50 & 25 & - & 1 & 14 & 0.77 & \cite{Sun2021} \\
& & HVOF Stellite 21 & 25 & 25 & - & 0.5 & 8 & - & \cite{Liu2022} \\ \cline{2-10}
& \multirow{7}{*}{\rotatebox{-90}{\bf 3.5 wt\% NaCl}} & Stellite 728 & 50 & 25 & - & 5 & 50 & 1.012 & \cite{Wang2023} \\
& & Stellite 6 & 50 & 25 & - & 5 & 50 & 2.841 & \cite{Wang2023} \\
& & Stellite 6B & 50 & 25 & - & 5 & 50 & 2.018 & \cite{Wang2023} \\
& & HVOF Stellite 21 & 25 & 25 & - & 0.5 & 8 & - & \cite{Liu2022} \\
& & LC Stellite 6 & 50 & 25 & - & 1 & 14 & 0.044 & \cite{Zhang2021} \\
& & SLD-1.0kW Stellite 6 & 50 & 25 & - & 1 & 14 & 0.017 & \cite{Zhang2021} \\
& & SLD-1.0kW Stellite 6 & 50 & 25 & - & 1 & 14 & 0.017 & \cite{Zhang2021} \\
\hline
\multicolumn{2}{l}{} & & & & & & & & \\
\cline{1-3}
\multicolumn{3}{|l}{Peak to Peak Amplitude (\SI{}{\micro\metre}) } & & & & & & & \\
\cline{1-4}
\multicolumn{4}{|l}{Water Temperature (\SI{}{\celsius})} & & & & & & \\
\cline{1-5}
\multicolumn{5}{|l}{Standoff Distance (\SI{}{\milli\metre})} & & & & & \\
\cline{1-6}
\multicolumn{6}{|l}{Test Duration (hr)} & & & & \\
\cline{1-7}
\multicolumn{7}{|l}{Total Duration (hr)} & & & \\
\cline{1-8}
\multicolumn{8}{|l}{Terminal Erosion Rate for Eroded Area \SI{199}{\milli\metre\squared} (\SI{}{\milli\gram\per\hour})} & & \\
\cline{1-9}
\multicolumn{9}{|l}{References} & \\
\hline
\end{tabular}
\end{table}
Corrosion studies conducted on stellites find high corrosion resistance. The matrix is preferentially attacked, with the dissolution of $Co$ into $Co^{2+}$, while a surface layer comprised of chromium-rich oxides (Cr2O3 \& Cr(OH)3) prevents further corrosion in chloride-rich environments. Zhang et al find that stellite alloys with higher carbon content have less corrosion resistance \cite{Zhang20153579}. Malayoglu et al find improved erosion and corrosion resistance of HIP'ed Stellite 6 over cast Stellite 6, due to lessened removal of Co-rich matrix in HIP'ed material. \cite{MALAYOGLU2003181}. Mohamed et al report similar improved performance of HIP'ed Stellite 6 and attribute it to the fine grain size of carbides in HIP'ed materials \cite{Mohamed1999195}.
\subsection{Matrix phase}
% Understanding the matrix phase
% Understanding the cobalt phase is crucial for studying structural changes in Co-based alloys widely used in industry.
Cobalt and Co-Cr alloys undergo thermally induced phase transformation from the high temperature face-centered cubic (fcc) $\gamma$ phase to low temperature hexagonal close-packed (hcp) $\epsilon$ phase at 700 K and strain induced fcc-hcp transition through maretensitic-type mechanism (partial movement of dislocations) \cite{HUANG2023106170, Wang2023}. At ambient conditions, the metastable FCC retained phase in stellites can be transformed into HCP phase by mechanical loading, although any HCP phase is completely transformed into a FCC phase between 673 K and 743 K \cite{DUBOS2020128812, Liu2022}; the metastable fcc cobalt phase in stellite alloys \cite{Rajan19821161, Sun2021} absorbs a large part of imparted energy under the mechanical loading of cavitation erosion. The fcc to hcp transition is related to the very low stacking fault energy of the fcc structure (7 mJ/m2) \cite{Tawancy1986337, Szala2022741, DeMolVanOtterloo1997239}.
% Let's talk about the addition of other elements
Solid-solution strengthening leads to increase of the fcc cobalt matrix strength (due to distortion of the atomic lattice with the addition of elements of different atomic radii), and decrease of low stacking fault energy \cite{Tawancy1986337} due to the adjusted electronic structure of the metallic lattice. Dislocation motion in stellites is discouraged by solute atoms of Mo and W, due to the large atomic sizes. Given that dislocation cross slip is the main deformation mode in imperfect crystals at elevated temperature, as dislocation slip is a diffusion process that is enhanced at high temperature, this leads to high temperature stability \cite{LIU2022294}. In addition, nickel (Ni), iron (Fe), and carbon (C) stabilize the fcc structure of cobalt (a = 0.35 nm), while chromium (Cr) and tungsten (W), stabilize the hcp structure (a = 0.25 nm and c = 0.41 nm) \cite{Vacchieri20171100, Tawancy1986337}.
% Maybe get the size of atoms and show the mismatch?
\subsection{Carbide phase}
The amount and types of carbides dispersed in the stellite matrix are primarily determined by the carbon content, with higher carbon content encouraging carbides with higher C/M ratios, while the size of carbides is determined by the cooling rate \cite{Desai198489, DeMolVanOtterloo19971225}. Carbon content can be used to distinguish between different stellite alloys: high-carbon stellites designed for high wear resistance, abrasion, \& severe galling, medium-carbon (0.5 - 1.6\% wt) stellites used for high temperature service, and low-carbon (<0.5\% wt) stellites used primarily for corrosion resistance, cavitation, \& sliding wear \cite{kapoor2013microstructure, Szala2021}. Low-carbon stellites depend primarily of solid-solution strengthening for their mechanical properties. As the carbon content increases, the W/Mo content is usually also increased to prevent depletion of Cr from matrix solid solution strengthening \cite{Zhang20153579, Mohamed1999195}. Chromium is the predominant carbide former, with M7C3 and M23C6 phases, in addition to providing corrosion resistance and strength to the stellite matrix \cite{Singh201487, Hattor2014257, Depczynski20131045}. Difference between the M7C3 and M23C6 phases is not readily visible under SEM. In tungsten-containing alloys, carbides of type M7C3 and M6C are formed in addition to the matrix. Ahmed et al report on the identification of intermetallic Co3W and Co7W6 phases through XRD, although these phases are not identified in SEM observations \cite{DeBrouwer1966141, Crook1990446, KRELL2020203138}.
\subsection{Blended Stellite Alloys}
Ahmed et al investigate the influence of the HIP'ing process on stellites \cite{Ahmed2021,Ahmed2017487,Ahmed201470,Ahmed201498,Yu20071385, Yu20091}, and conclude that HIP consolidation of Stellite alloys offers significant technological advantages for components operating in aggressive wear environments due to superior impact and fatigue resistance over cast alloys \cite{Ahmed20138, Ahmed201470, Ashworth1999243, Yu20071385}. In order to achieve unique microstructures from existing stellite alloys, Ahmed et al investigate the performance of blended alloys \cite{Ahmed2023,Ahmed2021}, which are formed through the consolidation of a mixture of two stellite powders.
% The heck is a blended stellite alloys
A blended stellite alloy is formed by hot isostatic pressing of a mixture of two stellite powders. The powders are created through gas atomization, in which a stream of liquid stellite alloy is disrupted and atomized into tiny molten droplets by a high-pressure inert gas flow \cite{Atkinson20002981, Ahmed2023, Yu2007, Ahmed2021}. The free-falling molten droplets rapidly solidify into spherical particles before being collected, forming high quality stellite powders with controllable size. The rapid cooling of the powder during atomization leads to reduced precipitation of carbides and supersaturation of the metallic matrix with other elements, as seen in the reduced proportion of carbide phases detected in the XRD performed on powders, compared to XRD of HIP'd samples. The mixing of powders is conducted in a powder hopper that ensures uniform distribution of powder mixtures \cite{Ahmed2023, Ahmed2021}. The HIP treatment was conducted at a temperature of 1200 C and a pressure of 100 MPa for a duration of 4 hours, resulting in full dense blended stellite alloys \cite{Li19872831, Ashworth2000351, Atkinson1991}. During the HIP'ing process, carbides are precipitated, in addition to reduction of supersaturation of the matrix \cite{Li19931345, Li19891645}. Depending on the composition of the stellite powders used, the blended alloys could possess uniform microstructure or regions that are similar to the constituent powders. This is due to the different diffusion rates of the added elements - carbon diffuses through the blended alloys while tungsten cannot diffuse due to its high atomic radius \cite{Speight1964683, Coble19704798, Ahmed2023, Ahmed2021}.
In summary, the literature review underscores the necessity for additional academic inquiry into the cavitation erosion resistance of HIP'ed stellite alloys, particularly focusing on the influence of composition on microstructure and cavitation erosion behavior. This thesis endeavors to address this gap in knowledge by conducting a comprehensive investigation.
% Novelty
% How well was the novelty of the project expressed?
%To date, academic research pertaining to cavitation erosion specifically on HIP'd stellite alloys appears to be absent from the existing literature.
% Novelty - Me jerking off to the novelty of my thesis
%Given the detrimental influence of voids and defects on cavitation erosion, the lack of academic investigation into cavitation erosion on HIP (Hot Isostatic Pressing) stellite alloys, underscores the need for further exploration. Moreover, the complexity introduced by blended stellite alloys in the context of cavitation erosion in corrosive enironments adds another layer of intrigue to this research endeavor. By analyzing the interactions between alloy composition, microstructure, and cavitation erosion behavior, this thesis aims to fill a critical gap in the current understanding of material performance under cavitation erosion conditions.
%\end{refsection}
%\end{document}

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Heriot-Watt University Thesis Template
% Created by : Majed Al Saeed
% Date: June 2012
% Department of Computer Science
% Heriot-Watt University
%
% Updated by: Alexandre Coates
% Date: February 2021
% Institute of Photonics and Quantum Sciences
% Heriot-Watt University
%
% Used by: Vishakh Pradeep Kumar
% Date: April 2024
% School of Engineering and Physical Sciences
% Heriot-Watt University
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[a4paper,12pt]{report}
%==============================title page info=================================
% Name of the author
\newcommand{\auth}{Vishakh Pradeep Kumar}
% Title of Thesis
\newcommand{\thesistitle}{Cavitation Erosion of Blended Stellite Alloys}
% Degree
\newcommand{\degree}{MSc. Mechanical Engineering}
% Date submitted
\newcommand{\supdate}{April 2024}
%===================================packages===================================
\usepackage[top=20mm, bottom=20mm, left=40mm, right=20mm]{geometry}
\usepackage{setspace}
\usepackage{fancyhdr} %fancy headers
\usepackage{acro} %acronyms
\usepackage{graphicx} %graphics
%\usepackage{subfigure}%
%\usepackage{subcaption} %subcaptions for subfigures
\usepackage{xspace}
\usepackage{listings}
\usepackage{pdfpages}
\usepackage{alltt}
\usepackage{float} % to use [H]
\usepackage[notindex, nottoc, notlof, notlot]{tocbibind} %table of content options
%\usepackage{lscape} % if you want to use land scape in one paper
%...\begin{landscape}\end{landscape}
\usepackage{amsmath} %mathematical environments for equations etc
\usepackage{amssymb} %mathematical symbols
\usepackage{amsthm} %for defining mathematical theorems
\usepackage{siunitx} %mainly for producing the degrees symbol using \ang{}, but contains SI units obviously
\usepackage{braket} %for BraKet notation
\usepackage{nicefrac} %a nice fraction, side by side rather than top to bottom
\usepackage{hyperref} %in-document links between references and sections/figures/equations
\usepackage{wrapfig} %figure placement
\usepackage[counterclockwise]{rotating}
\usepackage{booktabs} %better tables
\usepackage{graphicx}
\usepackage{xcolor}
\usepackage{multirow}
\usepackage{amsfonts}
\usepackage{cleveref} %more internal referencing behaviour, lets you use \cref instead of \ref, MUST BE AFTER HYPERREF
%\usepackage[utf8]{inputenc} %related to encoding %not needed as of 2018/9 I think
\usepackage{parskip} % OPTIONAL - removes paragraph indentation
\usepackage[colorinlistoftodos]{todonotes} % to do notes, might help you keep track of things
\reversemarginpar
\setlength{\marginparwidth}{35mm}
%\reversemarginpar %force todonotes into the left margin, as it defaults to the right hand margin
\usepackage{enumitem}
%%% Citations %%%
\usepackage[backend=biber,style=numeric-comp, sorting=none]{biblatex} %using biblatex for citations, style is set to numeric-comp by default, and sorting is set to none so the bibliography prints references in the order of their appearance. See more details in the main document
\addbibresource{literature_review.bib} %add a source for references here
%if you want to load from multiple bib files then do \addbibresource{file1,file2,file3} - no spaces, and you may need the .bib or whatever you file extension is
%%% other things %%%
\graphicspath{{Figures/}{../Figures/}} %sets path for figures for two levels of nesting the fig folder
\setcounter{tocdepth}{3} %set how many subsections your table of contents will show down to
\setcounter{secnumdepth}{3} %set how many levels deep your section numbering will go, 3 means going to subsubsection
\date{\today}
%=========================== define acronyms ===============
%list the command to type, the short version, and the long version at a minimum
%for more advanced features like grouping, tagging or setting capitalisation, see the acro documentation on CTAN
%\DeclareAcronym{lol}{short = lol, long = laughing out loud}
%\DeclareAcronym{www}{short = WWW , long = World-Wide Web}
%\DeclareAcronym{wys}{short=WYSIWYG, long = What you see is what you get}
%\DeclareAcronym{woodchuck}{short = HMWWAWCIAWCCW, long= How much wood would a woodchuck chuck if a woodchuck could chuck wood?}
%\DeclareAcronym{opt}{short = Optional, long = Including a list of used terms/acronyms is totally optional}
%\DeclareAcronym{jau}{short = JAU, long = Join a Union}
%\input {Acronyms} %or you can list your acronyms in a separate file, but it is more work to sort out with subfiles
\usepackage{subfiles} %this need to be the LAST package you include
%===================================Document===================================
\begin{document}
\doublespacing
%==================================Title page==================================
\pagestyle{empty}
\begin{center}
\begin{spacing}{2}
{\large{\ \\ \vspace{1.5cm}\textbf{\MakeUppercase{Research Proposal}}}}\\
{\Large{\ \\ \vspace{0.05cm}\textbf{\MakeUppercase{\thesistitle}}}}\\
\end{spacing}
\vfill
{\Large\textit{by}}\\\vspace{0.2cm}
{\Large\upshape{\auth}}\\\vspace{1.0cm}
\includegraphics[width=5cm]{HW_shield}\\
\vspace{1cm}
{\large Submitted for the degree of \\ \degree}\\
\vspace{1cm}
{\large\textsc{School of Engineering and Physical Sciences}\\
\textsc{Heriot-Watt University}}\vfill
{\large{\supdate}}
\end{center}
%===================================Abstract=================================
\clearpage
\begin{center}
\LARGE\textbf {Abstract}
\end{center}
\vspace{1cm}
\begin{spacing}{1}
\noindent
%Write the abstract here.
%In accordance with the Academic Regulations the thesis must contain an abstract preferably not exceeding 200 words, bound in to precede the thesis. The abstract should appear on its own, on a single page. The format should be the same as that of the main text. The abstract should provide a synopsis of the thesis and shall state clearly the nature and scope of the research undertaken and of the contribution made to the knowledge of the subject treated. There should be a brief statement of the method of investigation where appropriate, an outline of the major divisions or principal arguments of thework and a summary of any conclusions reached. The abstract must follow the Title Page.
% TODO
Cavitation erosion is a complex phenomenon influenced by the intensity of cavitating bubbles and material resistance, leading to performance degradation through material loss. This research endeavors to evaluate the resistance of blended stellite alloys to cavitation erosion.
%Simulation of cavitation phenomena will be achieved using ultrasonic vibrating probes positioned consistently from the material.
The study will investigate the synergy between cavitation and corrosion through in-situ electrochemical measurements. Experimental procedures will involve an ultrasonic vibratory horn operating at a fixed frequency of 20 kHz, with adjustable peak-to-peak amplitude. Microstructural characterization of cavitated sample surfaces and underlying cross-sections affected by cavitation will be conducted using scanning electron microscopy.
\end{spacing}
%==================================frontmatter================================
\clearpage
\pagestyle{plain}
\clearpage\pagenumbering{roman}
%\noindent
%{\LARGE\textbf{Acknowledgements}}
%\vspace{1cm}
%\begin{spacing}{1}
%\noindent
%You can write whatever you want to in the Acknowledgements, I have seen thanks to videogames, rubber ducks, takeaway restaurants, Karl Marx and so on. Some people even go as far as to put down things or people that got in the way of their thesis. If you consider going that route, keep things civil! Still, this is your space, there's no real guidelines, include a fancy quote then several paragraphs about ghosts if you like, or maybe a poem that speaks to you. Have a think about it.
%After this comes the mandatory table of contents.
%\textbf{Lists of Tables and Figures, Glossary, List of Publications by the Candidate}
%It is \textit{optional} to provide these lists. If provided, then they should start on the page following the table of contents and be in the order: Tables, Figures, Glossary (list of abbreviations), Publications.
%Items in lists of Tables and Figures should be in the order in which they occur in the text.
%\end{spacing}
\tableofcontents
%\listoftables %optional
%\listoffigures %optional%
%\printacronyms %OPTIONAL prints used acronyms wherever you put this
%===================================headings=================================
\clearpage
\pagestyle{fancy}
\pagenumbering{arabic}
\fancyhead{}
\lhead{\slshape \leftmark}
\cfoot{\thepage}
\renewcommand{\headrulewidth}{0.4pt}
\renewcommand{\footrulewidth}{0.0pt}
\renewcommand{\chaptermark}[1]{\markboth{\chaptername\ \thechapter:\ #1}{}}
%===================================Chapters================================
\input{Chapter_Introduction}
\input{Chapter_LitReview}
%\subfile{Chapter_Archive}
%\subfile{Chapter_Background}
%\subfile{Chapter_Design}
%\subfile{Chapter_Conclusion}
%=================================Bibliography================================
%If you just need super simple references you can remove all the biblatex stuff and have this for a lump of references at the end, but it's less flexible than biblatex. Remember, you can just remove all of the refsections and biblatex will work with just a \printbibliography command wherever you'd like.
%\bibliographystyle{abbrv}
%\bibliography{Bibliography.bib}
%print bibliography for whole thesis (not obligatory, you can do per-chapter bibliographies if you want)
%\printbibliography[section=1,heading=subbibliography, title= Introduction] %print references for the 1st refsection, custom title for references
%\printbibliography[section=2,heading=subbibliography, title = some random custom title] %print references for the 2nd refsection,
%\printbibheading %print the heading that say BIBLIOGRAPHY
\printbibliography % print ALL references
%===================================Appendix================================
\appendix
%\subfile{Chapters/Appendix1}
\renewcommand{\chaptermark}[1]{\markboth{Appendix \thechapter.\ #1}{}}
\chapter{Risk Assessments}
The following risk assessments are:
\begin{itemize}
\item Grinder-Polisher \ref{RA_GrinderPolisher}
\item Ultrasonic Bath \ref{RA_UltrasonicBath}
\item Cavitation Equipment \ref{RA_Cavitation}
\end{itemize}
\section{Risk Assessment - Grinder Polisher}
\label{RA_GrinderPolisher}
\includepdf[pages=- pagecommand={\section{Risk Assessment Grinder Polisher}\label{RA_GrinderPolisher}\thispagestyle{plain}}]{equipment_manuals/RA_GrinderPolisher.pdf}
\section{Risk Assessment - Ultrasonic Bath}
\label{RA_UltrasonicBath}
\includepdf[pages=- pagecommand={\section{Risk Assessment - Ultrasonic Bath }\label{RA_UltrasonicBath}\thispagestyle{plain}}]{equipment_manuals/RA_UltrasonicBath.pdf}
\section{Risk Assessment - Cavitation Equipment}
\label{RA_Cavitation}
\includepdf[pages=- pagecommand={\section{Risk Assessment - Cavitation }\label{RA_Cavitation}\thispagestyle{plain}}]{equipment_manuals/RA_Cavitation.pdf}
%\printbiblist
%the sorting order of your bibliography is determined by the arguments in the square brackets when importing biblatex, can sort by year or name if preferred
\end{document}

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