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<li class="toctree-l1"><a class="reference internal" href="Section_intro.html">1. Introduction</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_start.html">2. Getting Started</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_commands.html">3. Commands</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_packages.html">4. Packages</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_accelerate.html">5. Accelerating LAMMPS performance</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_howto.html">6. How-to discussions</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_example.html">7. Example problems</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_perf.html">8. Performance &amp; scalability</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_tools.html">9. Additional tools</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_modify.html">10. Modifying &amp; extending LAMMPS</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_python.html">11. Python interface to LAMMPS</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_errors.html">12. Errors</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_history.html">13. Future and history</a></li>
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<li class="toctree-l1"><a class="reference internal" href="tutorials.html">Tutorials</a></li>
<li class="toctree-l1"><a class="reference internal" href="commands.html">Commands</a></li>
<li class="toctree-l1 current"><a class="reference internal" href="fixes.html">Fixes</a><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="fix_adapt.html">fix adapt command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_adapt_fep.html">fix adapt/fep command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_addforce.html">fix addforce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_addtorque.html">fix addtorque command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_append_atoms.html">fix append/atoms command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_atc.html">fix atc command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_atom_swap.html">fix atom/swap command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_atom.html">fix ave/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_chunk.html">fix ave/chunk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_correlate.html">fix ave/correlate command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_correlate_long.html">fix ave/correlate/long command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_histo.html">fix ave/histo command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_histo.html#fix-ave-histo-weight-command">fix ave/histo/weight command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_time.html">fix ave/time command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_aveforce.html">fix aveforce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_balance.html">fix balance command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_bond_break.html">fix bond/break command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_bond_create.html">fix bond/create command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_bond_swap.html">fix bond/swap command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_box_relax.html">fix box/relax command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_colvars.html">fix colvars command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_controller.html">fix controller command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_deform.html">fix deform command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_deform.html#fix-deform-kk-command">fix deform/kk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_deposit.html">fix deposit command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_drag.html">fix drag command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_drude.html">fix drude command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_drude_transform.html">fix drude/transform/direct command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_drude_transform.html#fix-drude-transform-inverse-command">fix drude/transform/inverse command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_dt_reset.html">fix dt/reset command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_efield.html">fix efield command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ehex.html">fix ehex command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_enforce2d.html">fix enforce2d command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_eos_cv.html">fix eos/cv command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_eos_table.html">fix eos/table command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_eos_table_rx.html">fix eos/table/rx command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_evaporate.html">fix evaporate command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_external.html">fix external command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_flow_gauss.html">fix flow/gauss command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_freeze.html">fix freeze command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_gcmc.html">fix gcmc command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_gld.html">fix gld command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_gle.html">fix gle command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_gravity.html">fix gravity command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_gravity.html#fix-gravity-omp-command">fix gravity/omp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_heat.html">fix heat command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_imd.html">fix imd command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_indent.html">fix indent command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ipi.html">fix ipi command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_langevin.html">fix langevin command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_langevin.html#fix-langevin-kk-command">fix langevin/kk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_langevin_drude.html">fix langevin/drude command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_langevin_eff.html">fix langevin/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_lb_fluid.html">fix lb/fluid command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_lb_momentum.html">fix lb/momentum command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_lb_pc.html">fix lb/pc command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_lb_rigid_pc_sphere.html">fix lb/rigid/pc/sphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_lb_viscous.html">fix lb/viscous command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_lineforce.html">fix lineforce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_manifoldforce.html">fix manifoldforce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_meso.html">fix meso command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_meso_stationary.html">fix meso/stationary command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_momentum.html">fix momentum command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_move.html">fix move command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_msst.html">fix msst command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_neb.html">fix neb command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh.html">fix nvt command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh.html#fix-nvt-intel-command">fix nvt/intel command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh.html#fix-nvt-kk-command">fix nvt/kk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh.html#fix-nvt-omp-command">fix nvt/omp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh.html#fix-npt-command">fix npt command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh.html#fix-npt-intel-command">fix npt/intel command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh.html#fix-npt-kk-command">fix npt/kk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh.html#fix-npt-omp-command">fix npt/omp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh.html#fix-nph-command">fix nph command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh.html#fix-nph-kk-command">fix nph/kk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh.html#fix-nph-omp-command">fix nph/omp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh_eff.html">fix nvt/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh_eff.html#fix-npt-eff-command">fix npt/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh_eff.html#fix-nph-eff-command">fix nph/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nph_asphere.html">fix nph/asphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nph_asphere.html#fix-nph-asphere-omp-command">fix nph/asphere/omp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nph_body.html">fix nph/body command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nph_sphere.html">fix nph/sphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nph_sphere.html#fix-nph-sphere-omp-command">fix nph/sphere/omp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nphug.html">fix nphug command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nphug.html#fix-nphug-omp-command">fix nphug/omp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_npt_asphere.html">fix npt/asphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_npt_asphere.html#fix-npt-asphere-omp-command">fix npt/asphere/omp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_npt_body.html">fix npt/body command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_npt_sphere.html">fix npt/sphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_npt_sphere.html#fix-npt-sphere-omp-command">fix npt/sphere/omp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve.html">fix nve command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve.html#fix-nve-intel-command">fix nve/intel command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve.html#fix-nve-kk-command">fix nve/kk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve.html#fix-nve-omp-command">fix nve/omp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_asphere.html">fix nve/asphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_asphere.html#fix-nve-asphere-intel-command">fix nve/asphere/intel command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_asphere_noforce.html">fix nve/asphere/noforce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_body.html">fix nve/body command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_eff.html">fix nve/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_limit.html">fix nve/limit command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_line.html">fix nve/line command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_manifold_rattle.html">fix nve/manifold/rattle command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_noforce.html">fix nve/noforce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_sphere.html">fix nve/sphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_sphere.html#fix-nve-sphere-omp-command">fix nve/sphere/omp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_tri.html">fix nve/tri command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvt_asphere.html">fix nvt/asphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvt_asphere.html#fix-nvt-asphere-omp-command">fix nvt/asphere/omp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvt_body.html">fix nvt/body command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvt_manifold_rattle.html">fix nvt/manifold/rattle command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvt_sllod.html">fix nvt/sllod command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvt_sllod.html#fix-nvt-sllod-intel-command">fix nvt/sllod/intel command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvt_sllod.html#fix-nvt-sllod-omp-command">fix nvt/sllod/omp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvt_sllod_eff.html">fix nvt/sllod/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvt_sphere.html">fix nvt/sphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvt_sphere.html#fix-nvt-sphere-omp-command">fix nvt/sphere/omp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_oneway.html">fix oneway command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_orient.html">fix orient/fcc command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_orient.html#fix-orient-bcc-command">fix orient/bcc command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_phonon.html">fix phonon command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_pimd.html">fix pimd command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_planeforce.html">fix planeforce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_poems.html">fix poems</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_pour.html">fix pour command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_press_berendsen.html">fix press/berendsen command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_print.html">fix print command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_property_atom.html">fix property/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_qbmsst.html">fix qbmsst command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_qeq.html">fix qeq/point command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_qeq.html#fix-qeq-shielded-command">fix qeq/shielded command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_qeq.html#fix-qeq-slater-command">fix qeq/slater command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_qeq.html#fix-qeq-dynamic-command">fix qeq/dynamic command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_qeq.html#fix-qeq-fire-command">fix qeq/fire command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_qeq_comb.html">fix qeq/comb command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_qeq_comb.html#fix-qeq-comb-omp-command">fix qeq/comb/omp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_qeq_reax.html">fix qeq/reax command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_qeq_reax.html#fix-qeq-reax-kk-command">fix qeq/reax/kk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_qmmm.html">fix qmmm command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_qtb.html">fix qtb command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_reax_bonds.html">fix reax/bonds command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_reax_bonds.html#fix-reax-c-bonds-command">fix reax/c/bonds command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_reaxc_species.html">fix reax/c/species command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_recenter.html">fix recenter command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_restrain.html">fix restrain command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_rigid.html">fix rigid command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_rigid.html#fix-rigid-nve-command">fix rigid/nve command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_rigid.html#fix-rigid-nvt-command">fix rigid/nvt command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_rigid.html#fix-rigid-npt-command">fix rigid/npt command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_rigid.html#fix-rigid-nph-command">fix rigid/nph command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_rigid.html#fix-rigid-small-command">fix rigid/small command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_rigid.html#fix-rigid-nve-small-command">fix rigid/nve/small command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_rigid.html#fix-rigid-nvt-small-command">fix rigid/nvt/small command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_rigid.html#fix-rigid-npt-small-command">fix rigid/npt/small command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_rigid.html#fix-rigid-nph-small-command">fix rigid/nph/small command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_rx.html">fix rx command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_saed_vtk.html">fix saed/vtk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_setforce.html">fix setforce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_setforce.html#fix-setforce-kk-command">fix setforce/kk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_shake.html">fix shake command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_shake.html#fix-rattle-command">fix rattle command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="fix_spring.html">fix spring command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_spring_chunk.html">fix spring/chunk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_spring_rg.html">fix spring/rg command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_spring_self.html">fix spring/self command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_srd.html">fix srd command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_store_force.html">fix store/force command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_store_state.html">fix store/state command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_temp_berendsen.html">fix temp/berendsen command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_temp_csvr.html">fix temp/csvr command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_temp_csvr.html#fix-temp-csld-command">fix temp/csld command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_temp_rescale.html">fix temp/rescale command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_temp_rescale_eff.html">fix temp/rescale/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_tfmc.html">fix tfmc command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_thermal_conductivity.html">fix thermal/conductivity command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ti_rs.html">fix ti/rs command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ti_spring.html">fix ti/spring command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_tmd.html">fix tmd command</a></li>
<li class="toctree-l2 current"><a class="current reference internal" href="#">fix ttm command</a></li>
<li class="toctree-l2"><a class="reference internal" href="#fix-ttm-mod-command">fix ttm/mod command</a><ul>
<li class="toctree-l3"><a class="reference internal" href="#syntax">Syntax</a></li>
<li class="toctree-l3"><a class="reference internal" href="#examples">Examples</a></li>
<li class="toctree-l3"><a class="reference internal" href="#description">Description</a></li>
<li class="toctree-l3"><a class="reference internal" href="#restrictions">Restrictions</a></li>
<li class="toctree-l3"><a class="reference internal" href="#related-commands">Related commands</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="fix_tune_kspace.html">fix tune/kspace command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_vector.html">fix vector command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_viscosity.html">fix viscosity command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_viscous.html">fix viscous command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_wall.html">fix wall/lj93 command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_wall.html#fix-wall-lj126-command">fix wall/lj126 command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_wall.html#fix-wall-lj1043-command">fix wall/lj1043 command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_wall.html#fix-wall-colloid-command">fix wall/colloid command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_wall.html#fix-wall-harmonic-command">fix wall/harmonic command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_wall_gran.html">fix wall/gran command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_wall_piston.html">fix wall/piston command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_wall_reflect.html">fix wall/reflect command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_wall_reflect.html#fix-wall-reflect-kk-command">fix wall/reflect/kk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_wall_region.html">fix wall/region command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_wall_srd.html">fix wall/srd command</a></li>
</ul>
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<li class="toctree-l1"><a class="reference internal" href="computes.html">Computes</a></li>
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<div class="section" id="fix-ttm-command">
<span id="index-0"></span><h1>fix ttm command</h1>
</div>
<div class="section" id="fix-ttm-mod-command">
<h1>fix ttm/mod command</h1>
<div class="section" id="syntax">
<h2>Syntax</h2>
<pre class="literal-block">
fix ID group-ID ttm seed C_e rho_e kappa_e gamma_p gamma_s v_0 Nx Ny Nz T_infile N T_outfile
fix ID group-ID ttm/mod seed init_file Nx Ny Nz T_infile N T_outfile
</pre>
<ul class="simple">
<li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><span class="doc">fix</span></a> command</li>
<li>style = <em>ttm</em> or <em>ttm_mod</em></li>
<li>seed = random number seed to use for white noise (positive integer)</li>
<li>remaining arguments for fix ttm:</li>
</ul>
<pre class="literal-block">
C_e = electronic specific heat (energy/(electron*temperature) units)
rho_e = electronic density (electrons/volume units)
kappa_e = electronic thermal conductivity (energy/(time*distance*temperature) units)
gamma_p = friction coefficient due to electron-ion interactions (mass/time units)
gamma_s = friction coefficient due to electronic stopping (mass/time units)
v_0 = electronic stopping critical velocity (velocity units)
Nx = number of thermal solve grid points in the x-direction (positive integer)
Ny = number of thermal solve grid points in the y-direction (positive integer)
Nz = number of thermal solve grid points in the z-direction (positive integer)
T_infile = filename to read initial electronic temperature from
N = dump TTM temperatures every this many timesteps, 0 = no dump
T_outfile = filename to write TTM temperatures to (only needed if N &gt; 0)
</pre>
<ul class="simple">
<li>remaining arguments for fix ttm/mod:</li>
</ul>
<pre class="literal-block">
init_file = file with the parameters to TTM
Nx = number of thermal solve grid points in the x-direction (positive integer)
Ny = number of thermal solve grid points in the y-direction (positive integer)
Nz = number of thermal solve grid points in the z-direction (positive integer)
T_infile = filename to read initial electronic temperature from
N = dump TTM temperatures every this many timesteps, 0 = no dump
T_outfile = filename to write TTM temperatures to (only needed if N &gt; 0)
</pre>
</div>
<div class="section" id="examples">
<h2>Examples</h2>
<pre class="literal-block">
fix 2 all ttm 699489 1.0 1.0 10 0.1 0.0 2.0 1 12 1 initialTs 1000 T.out
fix 2 all ttm 123456 1.0 1.0 1.0 1.0 1.0 5.0 5 5 5 Te.in 1 Te.out
fix 2 all ttm/mod 34277 parameters.txt 5 5 5 T_init 10 T_out
</pre>
</div>
<div class="section" id="description">
<h2>Description</h2>
<p>Use a two-temperature model (TTM) to represent heat transfer through
and between electronic and atomic subsystems. LAMMPS models the
atomic subsystem as usual with a molecular dynamics model and the
classical force field specified by the user, but the electronic
subsystem is modeled as a continuum, or a background &#8220;gas&#8221;, on a
regular grid. Energy can be transferred spatially within the grid
representing the electrons. Energy can also be transferred between
the electronic and the atomic subsystems. The algorithm underlying
this fix was derived by D. M. Duffy and A. M. Rutherford and is
discussed in two J Physics: Condensed Matter papers: <a class="reference internal" href="#duffy"><span class="std std-ref">(Duffy)</span></a>
and <a class="reference internal" href="#rutherford"><span class="std std-ref">(Rutherford)</span></a>. They used this algorithm in cascade
simulations where a primary knock-on atom (PKA) was initialized with a
high velocity to simulate a radiation event.</p>
<p>The description in this sub-section applies to both fix ttm and fix
ttm/mod. Fix ttm/mod adds options to account for external heat
sources (e.g. at a surface) and for specifying parameters that allow
the electronic heat capacity to depend strongly on electronic
temperature. It is more expensive computationally than fix ttm
because it treats the thermal diffusion equation as non-linear. More
details on fix ttm/mod are given below.</p>
<p>Heat transfer between the electronic and atomic subsystems is carried
out via an inhomogeneous Langevin thermostat. This thermostat differs
from the regular Langevin thermostat (<a class="reference internal" href="fix_langevin.html"><span class="doc">fix langevin</span></a>) in three important ways. First, the
Langevin thermostat is applied uniformly to all atoms in the
user-specified group for a single target temperature, whereas the TTM
fix applies Langevin thermostatting locally to atoms within the
volumes represented by the user-specified grid points with a target
temperature specific to that grid point. Second, the Langevin
thermostat couples the temperature of the atoms to an infinite heat
reservoir, whereas the heat reservoir for fix TTM is finite and
represents the local electrons. Third, the TTM fix allows users to
specify not just one friction coefficient, but rather two independent
friction coefficients: one for the electron-ion interactions
(<em>gamma_p</em>), and one for electron stopping (<em>gamma_s</em>).</p>
<p>When the friction coefficient due to electron stopping, <em>gamma_s</em>, is
non-zero, electron stopping effects are included for atoms moving
faster than the electron stopping critical velocity, <em>v_0</em>. For
further details about this algorithm, see <a class="reference internal" href="#duffy"><span class="std std-ref">(Duffy)</span></a> and
<a class="reference internal" href="#rutherford"><span class="std std-ref">(Rutherford)</span></a>.</p>
<p>Energy transport within the electronic subsystem is solved according
to the heat diffusion equation with added source terms for heat
transfer between the subsystems:</p>
<img alt="_images/fix_ttm.jpg" class="align-center" src="_images/fix_ttm.jpg" />
<p>where C_e is the specific heat, rho_e is the density, kappa_e is the
thermal conductivity, T is temperature, the &#8220;e&#8221; and &#8220;a&#8221; subscripts
represent electronic and atomic subsystems respectively, g_p is the
coupling constant for the electron-ion interaction, and g_s is the
electron stopping coupling parameter. C_e, rho_e, and kappa_e are
specified as parameters to the fix. The other quantities are derived.
The form of the heat diffusion equation used here is almost the same
as that in equation 6 of <a class="reference internal" href="#duffy"><span class="std std-ref">(Duffy)</span></a>, with the exception that the
electronic density is explicitly reprensented, rather than being part
of the the specific heat parameter.</p>
<p>Currently, fix ttm assumes that none of the user-supplied parameters
will vary with temperature. Note that <a class="reference internal" href="#duffy"><span class="std std-ref">(Duffy)</span></a> used a tanh()
functional form for the temperature dependence of the electronic
specific heat, but ignored temperature dependencies of any of the
other parameters. See more discussion below for fix ttm/mod.</p>
<p>These fixes require use of periodic boundary conditions and a 3D
simulation. Periodic boundary conditions are also used in the heat
equation solve for the electronic subsystem. This varies from the
approach of <a class="reference internal" href="#rutherford"><span class="std std-ref">(Rutherford)</span></a> where the atomic subsystem was
embedded within a larger continuum representation of the electronic
subsystem.</p>
<p>The initial electronic temperature input file, <em>T_infile</em>, is a text
file LAMMPS reads in with no header and with four numeric columns
(ix,iy,iz,Temp) and with a number of rows equal to the number of
user-specified grid points (Nx by Ny by Nz). The ix,iy,iz are node
indices from 0 to nxnodes-1, etc. For example, the initial electronic
temperatures on a 1 by 2 by 3 grid could be specified in a <em>T_infile</em>
as follows:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mi">0</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mf">1.0</span>
<span class="mi">0</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mf">1.0</span>
<span class="mi">0</span> <span class="mi">0</span> <span class="mi">2</span> <span class="mf">1.0</span>
<span class="mi">0</span> <span class="mi">1</span> <span class="mi">0</span> <span class="mf">2.0</span>
<span class="mi">0</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mf">2.0</span>
<span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mf">2.0</span>
</pre></div>
</div>
<p>where the electronic temperatures along the y=0 plane have been set to
1.0, and the electronic temperatures along the y=1 plane have been set
to 2.0. The order of lines in this file is no important. If all the
nodal values are not specified, LAMMPS will generate an error.</p>
<p>The temperature output file, <em>T_oufile</em>, is created and written by
this fix. Temperatures for both the electronic and atomic subsystems
at every node and every N timesteps are output. If N is specified as
zero, no output is generated, and no output filename is needed. The
format of the output is as follows. One long line is written every
output timestep. The timestep itself is given in the first column.
The next Nx*Ny*Nz columns contain the temperatures for the atomic
subsystem, and the final Nx*Ny*Nz columns contain the temperatures for
the electronic subsystem. The ordering of the Nx*Ny*Nz columns is
with the z index varing fastest, y the next fastest, and x the
slowest.</p>
<p>These fixes do not change the coordinates of their atoms; they only
scales their velocities. Thus a time integration fix (e.g. <a class="reference internal" href="fix_nve.html"><span class="doc">fix nve</span></a>) should still be used to time integrate the affected
atoms. The fixes should not normally be used on atoms that have their
temperature controlled by another fix - e.g. <a class="reference internal" href="fix_nh.html"><span class="doc">fix nvt</span></a> or
<a class="reference internal" href="fix_langevin.html"><span class="doc">fix langevin</span></a>.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">The current implementations of these fixes create a copy of the
electron grid that overlays the entire simulation domain, for each
processor. Values on the grid are summed across all processors. Thus
you should insure that this grid is not too large, else your
simulation could incur high memory and communication costs.</p>
</div>
<hr class="docutils" />
<p><strong>Additional details for fix ttm/mod</strong></p>
<p>Fix ttm/mod uses the heat diffusion equation with possible external
heat sources (e.g. laser heating in ablation simulations):</p>
<img alt="_images/fix_ttm_mod.jpg" class="align-center" src="_images/fix_ttm_mod.jpg" />
<p>where theta is the Heaviside step function, I_0 is the (absorbed)
laser pulse intensity for ablation simulations, l_skin is the depth
of skin-layer, and all other designations have the same meaning as in
the former equation. The duration of the pulse is set by the parameter
<em>tau</em> in the <em>init_file</em>.</p>
<p>Fix ttm/mod also allows users to specify the dependencies of C_e and
kappa_e on the electronic temperature. The specific heat is expressed
as</p>
<img alt="_images/fix_ttm_ce.jpg" class="align-center" src="_images/fix_ttm_ce.jpg" />
<p>where <em>X</em> = T_e/1000, and the thermal conductivity is defined as
kappa_e = D_e*rho_e*C_e, where D_e is the thermal diffusion
coefficient.</p>
<p>Electronic pressure effects are included in the TTM model to account
for the blast force acting on ions because of electronic pressure
gradient (see <a class="reference internal" href="#chen"><span class="std std-ref">(Chen)</span></a>, <a class="reference internal" href="#norman"><span class="std std-ref">(Norman)</span></a>). The total force
acting on an ion is:</p>
<img alt="_images/fix_ttm_blast.jpg" class="align-center" src="_images/fix_ttm_blast.jpg" />
<p>where F_langevin is a force from Langevin thermostat simulating
electron-phonon coupling, and nabla P_e/n_ion is the electron blast
force.</p>
<p>The electronic pressure is taken to be P_e = B*rho_e*C_e*T_e</p>
<p>The current fix ttm/mod implementation allows TTM simulations with a
vacuum. The vacuum region is defined as the grid cells with zero
electronic temperature. The numerical scheme does not allow energy
exchange with such cells. Since the material can expand to previously
unoccupied region in some simulations, the vacuum border can be
allowed to move. It is controlled by the <em>surface_movement</em> parameter
in the <em>init_file</em>. If it is set to 1, then &#8220;vacuum&#8221; cells can be
changed to &#8220;electron-filled&#8221; cells with the temperature <em>T_e_min</em> if
atoms move into them (currently only implemented for the case of
1-dimensional motion of flat surface normal to the X axis). The
initial borders of vacuum can be set in the <em>init_file</em> via <em>lsurface</em>
and <em>rsurface</em> parameters. In this case, electronic pressure gradient
is calculated as</p>
<img alt="_images/fix_ttm_blast1.jpg" class="align-center" src="_images/fix_ttm_blast1.jpg" />
<p>where lambda is the electron mean free path (see <a class="reference internal" href="#norman"><span class="std std-ref">(Norman)</span></a>,
<a class="reference internal" href="#pisarev"><span class="std std-ref">(Pisarev)</span></a>)</p>
<p>The fix ttm/mod parameter file <em>init_file</em> has the following syntax/
Every line with the odd number is considered as a comment and
ignored. The lines with the even numbers are treated as follows:</p>
<pre class="literal-block">
a_0, energy/(temperature*electron) units
a_1, energy/(temperature^2*electron) units
a_2, energy/(temperature^3*electron) units
a_3, energy/(temperature^4*electron) units
a_4, energy/(temperature^5*electron) units
C_0, energy/(temperature*electron) units
A, 1/temperature units
rho_e, electrons/volume units
D_e, length^2/time units
gamma_p, mass/time units
gamma_s, mass/time units
v_0, length/time units
I_0, energy/(time*length^2) units
lsurface, electron grid units (positive integer)
rsurface, electron grid units (positive integer)
l_skin, length units
tau, time units
B, dimensionless
lambda, length units
n_ion, ions/volume units
surface_movement: 0 to disable tracking of surface motion, 1 to enable
T_e_min, temperature units
</pre>
<hr class="docutils" />
<p><strong>Restart, fix_modify, output, run start/stop, minimize info:</strong></p>
<p>These fixes write the state of the electronic subsystem and the energy
exchange between the subsystems to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a>. See the <a class="reference internal" href="read_restart.html"><span class="doc">read_restart</span></a> command
for info on how to re-specify a fix in an input script that reads a
restart file, so that the operation of the fix continues in an
uninterrupted fashion.</p>
<p>Because the state of the random number generator is not saved in the
restart files, this means you cannot do &#8220;exact&#8221; restarts with this
fix, where the simulation continues on the same as if no restart had
taken place. However, in a statistical sense, a restarted simulation
should produce the same behavior.</p>
<p>None of the <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></a> options are relevant to these
fixes.</p>
<p>Both fixes compute 2 output quantities stored in a vector of length 2,
which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span class="std std-ref">output commands</span></a>. The first quantity is the
total energy of the electronic subsystem. The second quantity is the
energy transferred from the electronic to the atomic subsystem on that
timestep. Note that the velocity verlet integrator applies the fix ttm
forces to the atomic subsystem as two half-step velocity updates: one
on the current timestep and one on the subsequent timestep.
Consequently, the change in the atomic subsystem energy is lagged by
half a timestep relative to the change in the electronic subsystem
energy. As a result of this, users may notice slight fluctuations in
the sum of the atomic and electronic subsystem energies reported at
the end of the timestep.</p>
<p>The vector values calculated are &#8220;extensive&#8221;.</p>
<p>No parameter of the fixes can be used with the <em>start/stop</em> keywords
of the <a class="reference internal" href="run.html"><span class="doc">run</span></a> command. The fixes are not invoked during
<a class="reference internal" href="minimize.html"><span class="doc">energy minimization</span></a>.</p>
</div>
<div class="section" id="restrictions">
<h2>Restrictions</h2>
<p>Fix <em>ttm</em> is part of the MISC package. It is only enabled if LAMMPS
was built with that package. Fix <em>ttm/mod</em> is part of the USER-MISC
package. It is only enabled if LAMMPS was built with that package.
See the <a class="reference internal" href="Section_start.html#start-3"><span class="std std-ref">Making LAMMPS</span></a> section for more
info.</p>
<p>These fixes can only be used for 3d simulations and orthogonal
simlulation boxes. You must also use periodic
<a class="reference internal" href="boundary.html"><span class="doc">boundary</span></a> conditions.</p>
</div>
<div class="section" id="related-commands">
<h2>Related commands</h2>
<p><a class="reference internal" href="fix_langevin.html"><span class="doc">fix langevin</span></a>, <a class="reference internal" href="fix_dt_reset.html"><span class="doc">fix dt/reset</span></a></p>
<p><strong>Default:</strong> none</p>
<hr class="docutils" />
<p id="duffy"><strong>(Duffy)</strong> D M Duffy and A M Rutherford, J. Phys.: Condens. Matter, 19,
016207-016218 (2007).</p>
<p id="rutherford"><strong>(Rutherford)</strong> A M Rutherford and D M Duffy, J. Phys.:
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