### updated figs

parent 0b559420
 ... ... @@ -5,7 +5,7 @@ Liquid and solid aluminum In this first example aluminium will be studied. An EAM potential was used [Phys. Rev. B 59, 3393 (1999)] to describe both the solid and liquid phases. The melting point was found to be about 930 K. The liquid phases. The melting point was found to be about 1000 K. The lattice parameters used for the NVT MD simulations were found running NPT and averaging the box length. ... ... @@ -31,8 +31,8 @@ below if running the :program:dynasor scripts as are. In the figure the structure factor :math:S(q) is shown. .. figure:: figs/Al_liquid/Al_liquid_static.png :scale: 120 % .. figure:: figs/Al_liquid/Al_liquid_Sq.png :scale: 15 % :align: center Structure factor :math:S(q) computed by running ... ... @@ -58,7 +58,7 @@ Figure 3 of :cite:Mokshin. The clear dispersion in of :cite:Mokshin. .. figure:: figs/Al_liquid/Al_liquid_heatmap.png :scale: 120 % :scale: 100 % :align: center Dynamical structure factor (a), longitudinal current (b) and ... ... @@ -73,51 +73,35 @@ of :cite:Mokshin. Crystalline =========== .. todo:: Update these old figures. In this example we look at alumnium below the melting point at :math:T=300K. The crystal structure is face-centered-cubic (fcc) and :math:q-space sampling was done along three paths .. math:: L=\frac{2\pi}{a} \Big(\frac{1}{2},\frac{1}{2},\frac{1}{2}\Big) \quad , \quad K=\frac{2\pi}{a} \Big(\frac{3}{4},\frac{3}{4},0\Big) Since the sampling along a path is much faster than doing a spherical average the number of atoms used here is 6912 (12x12x12 fcc). In this example we look at alumnium (FCC) below the melting point at :math:T=300K. Since the sampling along a path is much faster than doing a spherical average the number of atoms used here is 6912 (12x12x12 fcc). The transverse and longitudinal current correlation is shown both in time and frequency between :math:\Gamma and K. Here the :math:q-value is between 0 and 1 and represent how far along the path you are. time and frequency for a single q-point. Fits to the analytical functions are also shown. .. figure:: figs/Al_solid/C_ktw_GK.png :scale: 50 % .. figure:: figs/Al_solid/fit_illustration.png :scale: 80 % :align: center Current correlations between :math:\Gamma and K in both time (top) and frequency . Longitudinal and transverse current correlations in both time and frequency. Looking at the current correlations in time we see that the longitudinal is oscillating with one frequency and the transverse with many. This agrees with what is seen in the frequency domain. two. This agrees with what is seen in the frequency domain. The sum of the longitudinal and transverse current correlation is seen below together with the phonon dispersion calculated, using the same potential, by phonopy. .. figure:: figs/Al_solid/dispersion_T300.png :scale: 50 % .. figure:: figs/Al_solid/current_heatmap_T300.png :scale: 70 % :align: center Sum of the longitudinal and transverse current show along the path L to :math:\Gamma to K. The black dots indicate the results from phonopy calculations. Sum of the longitudinal and transverse current heatmaps. The agreement with the phonon dispersion calculated with phonopy is very good. The fact that there is discrete :math:q-values which give rise to high intensitiy is due to the finite supercell size not supporting all kinds of oscillations.

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 ... ... @@ -12,8 +12,6 @@ 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). .. todo:: Insert proper reference via references.bib. The partial correlation functions are denoted :math:S_{AA}(q,\omega) where :math:A is an atomic species and :math:S represents an ... ... @@ -41,86 +39,36 @@ combination of the partial functions weighted with the appropriate atomic form factors. Structure factors: F(q,t) and S(q,w) ==================================== Structure factors: F(q,t) ========================= The figure below shows the static structure factors. The figure below shows the static charge and mass structure factors. .. figure:: figs/NaCl_liquid/structureFactor.png :scale: 50 % .. figure:: figs/NaCl_liquid/NaCl_Sq.png :scale: 40 % :align: center Number-number and charge-charge structure factor (left) and partial structure factors (right). the static charge and mass structure factors. All structure factors agree well with Figures 10.2 and 10.3 in :cite:HansenMcDonald. The normalization differs by a factor of two, which is simply a matter of choice if the normalization for the partial structure factor should be done with :math:N_A or :math:N_A+N_B. :cite:HansenMcDonald. Below the partial intermediate scattering functions and dynamical structure factors are shown. .. figure:: figs/NaCl_liquid/S_partial.png :scale: 50 % :align: center Partial :math:F(q,t) and :math:S(q,\omega) for two different **q**-values. .. figure:: figs/NaCl_liquid/S_CMN.png :scale: 50 % :align: center Mass charge and number computed from partial :math:F(q,t) and :math:S(q,\omega). Note the logged scale for :math:S(q,\omega) in order to resolve some peaks. .. figure:: figs/NaCl_liquid/S_partial_map.png :scale: 50 % :align: center Map of logged partial dynamical structure factors. .. figure:: figs/NaCl_liquid/S_CMN_map.png :scale: 50 % :align: center Map of logged charge, mass and number dynamical structure factors. Charge correlation: C(q,t) and C(q,w) ===================================== Current correlations: C(q,w) ============================ Below the partial, charge, mass and number longitudinal and transverse current correlation functions are shown. Note that the peaks in the frequency domain are much more easily seen compared to the dynamical structure factors. These figures show four modes (TA, TO, LA, LO). .. figure:: figs/NaCl_liquid/C_partial.png :scale: 50 % :align: center Partial current correlations :math:C(q,t) and :math:C(q,\omega). .. figure:: figs/NaCl_liquid/C_CMN.png :scale: 50 % :align: center Mass, charge and number current correlations :math:C(q,t) and :math:C(q,\omega). Below maps of the current correlations are shown. current correlation functions are shown. .. figure:: figs/NaCl_liquid/C_partial_map.png :scale: 50 % .. figure:: figs/NaCl_liquid/NaCl_partial_heatmaps.png :scale: 40 % :align: center Map of partial current correlations. Heatmap of partial current correlations. Top is longitudinal and bottom is transverse. .. figure:: figs/NaCl_liquid/C_CMN_map.png :scale: 50 % .. figure:: figs/NaCl_liquid/NaCl_charge_mass_heatmaps.png :scale: 40 % :align: center Map of current, mass and number current correlations. Heatmap of charge and mass current correlations. Top is longitudinal and bottom is transverse.
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