sodium_chloride.rst 2.52 KB
 Paul Erhart committed Mar 01, 2017 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 .. _example_sodium_chloride: Molten Sodium Chloride ********************** This example deals with molten sodium chloride in order to illustrate the analysis of multiple component systems and the treatment of partial correlation functions. As in the case of liquid alumnium the analsysi is carried out for a spherically averaged momentum vector **q** The born/coul potential in lammps was used with parameters from Lewis and Singer (1974). The melting point was found to be about 1300 K and the simulations were carried out at 1400 K for 4096 atoms (:math:8\times8\times8 conventional unit cells). The partial correlation functions are denoted :math:S_{AA}(q,\omega) where :math:A is an atomic species and :math:S represents an arbitray correlation function. We define the number correlation :math:S_{NN}(q,\omega), mass correlation :math:S_{MM}(q,\omega) and the charge correlation :math:S_{ZZ}(q,\omega) as .. math:: S_{NN}(q,\omega) = S_{AA}(q,\omega) + S_{BB}(q,\omega) + S_{AB}(q,\omega) S_{MM}(q,\omega) = ( m_A^2 S_{AA}(q,\omega) + m_B^2 S_{BB}(q,\omega) + m_A m_B S_{AB}(q,\omega) ) / (m_A+m_B)^2 S_{ZZ}(q,\omega) = q_A^2 S_{AA}(q,\omega) + q_B^2 S_{BB}(q,\omega) + q_Aq_B S_{AB}(q,\omega), where :math:m_A and :math:q_A denote the mass and charge of atom type :math:A, respectively. These are useful in ionized systems because acoustic type modes show up in the mass correlation and optic type modes can be seen in the charge correlation. For direct comparison with with exprimental data one can compute a linear combination of the partial functions weighted with the appropriate atomic form factors.  Erik Fransson committed Dec 19, 2018 42 43 Structure factors: F(q,t) =========================  Paul Erhart committed Mar 01, 2017 44   Erik Fransson committed Dec 19, 2018 45 The figure below shows the static charge and mass structure factors.  Paul Erhart committed Mar 01, 2017 46   Erik Fransson committed Dec 19, 2018 47 48 .. figure:: figs/NaCl_liquid/NaCl_Sq.png :scale: 40 %  Paul Erhart committed Mar 01, 2017 49 50  :align: center  Erik Fransson committed Dec 19, 2018 51  the static charge and mass structure factors.  Paul Erhart committed Mar 01, 2017 52 53  All structure factors agree well with Figures 10.2 and 10.3 in  Erik Fransson committed Dec 19, 2018 54 :cite:HansenMcDonald.  Paul Erhart committed Mar 01, 2017 55   Erik Fransson committed Dec 19, 2018 56 57 Current correlations: C(q,w) ============================  Paul Erhart committed Mar 01, 2017 58 59  Below the partial, charge, mass and number longitudinal and transverse  Erik Fransson committed Dec 19, 2018 60 current correlation functions are shown.  Paul Erhart committed Mar 01, 2017 61   Erik Fransson committed Dec 19, 2018 62 63 .. figure:: figs/NaCl_liquid/NaCl_partial_heatmaps.png :scale: 40 %  Paul Erhart committed Mar 01, 2017 64 65  :align: center  Erik Fransson committed Dec 19, 2018 66 67  Heatmap of partial current correlations. Top is longitudinal and bottom is transverse.  Paul Erhart committed Mar 01, 2017 68   Erik Fransson committed Dec 19, 2018 69 70 .. figure:: figs/NaCl_liquid/NaCl_charge_mass_heatmaps.png :scale: 40 %  Paul Erhart committed Mar 01, 2017 71 72  :align: center  Erik Fransson committed Dec 19, 2018 73 74  Heatmap of charge and mass current correlations. Top is longitudinal and bottom is transverse.