[an error occurred while processing this directive]
<img src="/summerschool/2005/photos/instructors/anton.jpg" width="125" height="154" hspace="10" align="right"><h2>Kinetics and Kinetic MC via the CE</h2>
<p><span style="font-weight: bold">Anton van der Ven</span><br>
Materials Science<br>
University of Michigan<br>
Phone: 1-734-615-3834<br>
Email: avdv --&gt; umich.edu </p>
<h3 class="stb">Lectures</h3>
<ul>
  <li>Diffusion | <a href="/summerschool/2005/week_two_lectures/anton_van_der_ven/SS05_VanDerVen_Diffusion.pdf">PDF</a> (8.8 MB) | <a href="/summerschool/2005/week_two_lectures/anton_van_der_ven/SS05_VanDerVen_Diffusion.ppt">PPT</a> (3.6 MB) </li>
  <li>Kinetic | <a href="/summerschool/2005/week_two_lectures/anton_van_der_ven/SS05_VanDerVen_kineticMC.pdf">PDF</a> (3.9 Kb) | <a href="/summerschool/2005/week_two_lectures/anton_van_der_ven/SS05_VanDerVen_kineticMC.ppt">PPT</a> (3.1 MB) </li>
</ul>
<h3 class="stb">Computer Lab </h3>
<ul>
  <li><a href="/summerschool/2005/week_two_lectures/anton_van_der_ven/SS05_VanDerVen_LabNotes.txt">Lab Notes</a> (3Kb, .txt) -- helper notes for running the lab materials </li>
</ul>
<h3 class="stb">References</h3>
<ul class="plain">
  <li>Van der Ven, A. and Ceder, G., &quot;First principles calculation of the interdiffusion coefficient in binary alloys&quot; Phys. Rev. Lett. 94 (4) 045901 (2005).</li>
  <li>Van der Ven, A. and Ceder, G., &quot;Vacancies in ordered and disordered binary alloys treated with the cluster expansion&quot; Phys. Rev. B 71 (5), 054102 (2005)</li>
  <li>F. M. Bulnes, V. D. Pereyra, and J. L. Riccardo, <span style="font-style: italic">Phys. Rev. E</span>, 58:1 (1998) (.<a href="/summerschool/2005/week_two_lectures/anton_van_der_ven/Paper_bulnes.pdf">pdf</a>, 166Kb) </li>
</ul>
<h3 class="stb">Other review type articles</h3>
<ul>
  <li>D. de Fontaine, &quot;Cluster Approach to Order-Disorder Transformations in Alloys&quot;, <i>Solid State Physics</i>, Vol. 47, H. Ehrenreich and D.Turnbull, eds., Academic Press. pp. 33-176 (1994).</li>
  <li> F&auml;hnle, M., &ldquo;Thermodynamic properties from ab-initio calculations: New theoretical developments, and applications to various materials systems,&rdquo; <i>Phys. Stat. Sol. (b)</i><b>242</b>, 1159&ndash;73 (2005).</li>
</ul>
<h3 class="stb">Details about Lectures and Computer Lab </h3>
<p>Kinetics in alloys systems and the use of the Cluster Expansion for the energetics will be presented. In addition, the use of CE within a Kinetic Monte Carlo framework will be explored. We discuss diffusion, energy barriers for atomic diffusion, and effects of vacancy ordering in alloys.</p>
<h5>Diffusion | <a href="/summerschool/2005/week_two_lectures/anton_van_der_ven/SS05_VanDerVen_Diffusion.pdf">PDF</a> (8.8 MB) | <a href="/summerschool/2005/week_two_lectures/anton_van_der_ven/SS05_VanDerVen_Diffusion.ppt">PPT</a> (3.6 MB) </h5>
<ul class="inline">
  <li class="first">Diffusion in multicomponent solids
  <li>Coarse graining time-Diffusion in a crystal
  <li>Interstitial diffusion
  <li>C diffusion in bcc Iron (steel)
  <li>Li diffusion in transition metal oxide host
  <li>O diffusion on Pt-(111) surface
  <li>Irreversible thermodynamics: -interstitial diffusion of one component
  <li>Notation
  <li>M = number of lattice sites
  <li>N = number of diffusing atoms
  <li>vs = volume per lattice site
  <li>x = N/M
  <li>C=x/vs
  <li>Interstitial diffusion: -one component
  <li>Trajectories
  <li>More familiar form
  <li>Common approximation
  <li>Interstitial diffusion -(two components)
  <li>C & N diffusion in bcc Iron (steel)
  <li>Li & Na diffusion in transition metal oxide host
  <li>O & S diffusion on Pt-(111) surface
  <li>Diffusion of two species on a lattice
  <li>Alternative factorization
  <li>Kinetic coefficients -(fcc lattice in dilute vacancy limit, ideal solution)
  <li>Diffusion in an alloy:-substitutional diffusion
  <li>Not interstitial diffusion
  <li>Instead, diffusing atoms form the lattice
  <li>Dilute concentration of vacancies
  <li>Thermodynamic driving forces for substitutional diffusion
  <li>Textbook treatment of substitional diffusion-Not Rigorous
  <li>Lattice frame and laboratory frame of reference
  <li>Diagonalize the D-matrix
  <li>Physical meaning of modes l+ and l-
  <li>Comparisons of different treatments 
  <li>Intercalation Oxide as Cathode in Rechargeable Lithium Battery
  <li>Cluster Expansions
  <li>First principles energies (LDA)-of different lithium-vacancy configurations
  <li>Cluster expansion for LixCoO2
  <li>Calculated LixCoO2 phase diagram
  <li>Predicted phases confirmed experimentally
  <li>Effect of metal insulator transition
  <li>Diffusion
  <li>Interstitial diffusion and configurational disorder-
  <li>Individual hops:-Transition state theory
  <li>Kinetically resolved activation barrier
  <li>Migration mechanism in LixCoO2
  <li>Migration barriers depend configuration and concentration
  <li>Local Cluster expansion for divacancy migration barrier
  <li>Calculated diffusion coefficient-(First Principles cluster expansion + kinetic Monte Carlo)
  <li>Available migration mechanisms for -each lithium ion
  <li>Diffusion occurs with a divacancy mechanism
  <li>Diffusion and phase transformations in Al-Li alloys
  <li>fcc Al-Li alloy
  <li>Calculated thermodynamic and kinetic properties of Al-Li alloy
  <li>Expand environment dependence of vacancy formation energy
  <li>Equilibrium vacancy concentration-(Monte Carlo applied to cluster expansion)
  <li>Vacancy surrounds itself by Al-Short range order around a vacancy
  <li>Vacancies reside on lithium sublattice in L12
  <li>Migration barriers for lithium and aluminum differ by ~150 meV
  <li>Calculated interdiffusion coefficient
  <li>Hop mechanisms
  <li>Frequency of hop angles between successive hops
  <li>Conclusion
  <li>Green-Kubo formalism yields rigorous expressions for diffusion coefficients
  <li>Discussed diffusion formalism for both interstitial and substitutional diffusion
  <li>Intriguing hop mechanisms in multi-component solids that can depend on ordering
  <li>Thermodynamics plays a crucial role!  
</ul>
<h5>Kinetic | <a href="/summerschool/2005/week_two_lectures/anton_van_der_ven/SS05_VanDerVen_kineticMC.pdf">PDF</a> (3.9 Kb) | <a href="/summerschool/2005/week_two_lectures/anton_van_der_ven/SS05_VanDerVen_kineticMC.ppt">PPT</a> (3.1 MB) </h5>
<ul class="inline">
  <li class="first">Kinetic Monte Carlo
  <li>Triangular lattice
  <li>Diffusion
  <li>Standard Monte Carlo to study diffusion
  <li>Pick an atom at random
  <li>Pick a hop direction
  <li>Calculate 
  <li>Consider all hops simultaneously
  <li>Time
  <li>After hop k we need to update the time
  <li>Two independent stochastic variables: the hop k and the waiting time 
  <li>Kinetic Monte Carlo
  <li>Hop every time
  <li>Consider all possible hops simultaneously
  <li>Pick hop according its relative probability
  <li>Update the time 
  <li>Triangular 2-d lattice, 2NN pair interactions
  <li>Activation barrier
  <li>Thermodynamics
  <li>Kinetics
</ul>
<h3>Computer Lab </h3>
<ul>
  <li>Diffusion in alloys based on CE will be explored in simplified simulation, such as 2D Kinetic Monte Carlo</li>
  <li><a href="/summerschool/2005/week_two_lectures/anton_van_der_ven/SS05_VanDerVen_LabNotes.txt">Lab Notes</a> (3Kb, .txt) -- helper notes for running the lab materials </li>
</ul>
</div> 

<div id="footer">
		<div id="footer_links" class="footer links">
			<div id="navigation">
			<ul class="bottomnav"  id="myBottomnav">
				<li><a href="http://mcc.illinois.edu">Materials Computation Center</a> </li>
				<li><a href="/summerschool/" title="Travel Award Program" accesskey="t">Travel Award Program</a></li>
				<li><a href="/summerschool/" title="Schools and workshops MCC supports" accesskey="w">Schools &amp; Workshops</a></li>
				<li><a href="/research/" title="Research: publications, posters, nuggets" accesskey="r">Research</a></li>
				<li><a href="/software/" title="Downloadable codes for materials computation and simulation" accesskey="a">Software Archive</a></li>
				<li><a href="https://www.vpaa.uillinois.edu/resources/web_privacy" title="Privacy Notice" accesskey="p">Privacy Notice</a></li>
				 <li class="icon">
    <a href="javascript:void(0);" onclick="myFunctionBottom()">&#9776;</a>
  </li>
			</ul>
			</div>
		</div>
		<div class="footer stationid">
			<p>
				 <a href="https://illinois.edu" title="University of Illinois"><img style="width:8%" src="/common/images/Illinois-Wordmark-Horizontal-Full-Color-RGB.png" 
				 alt="University of Illinois at Urbana-Champaign"/></a>  
			 <a href="http://mrl.illinois.edu/">Frederick Seitz Materials Research Laboratory</a> &middot;
				 <a href="https://grainger.illinois.edu/">The Grainger College of Engineering</a> &middot; 

				 The Materials Computation Center was supported by <a href="https://www.nsf.gov/div/index.jsp?div=DMR">NSF DMR</a> 03-25939.
			</p>
		</div>
</div>
</div>
</body>
</html>