In this section we briefly summarize the color codes of some of the figures
that can be obtained from `thermo_pw`.

- Total energy versus kinetic energy. This is a figure of the total
energy versus wave-functions kinetic energy cut-offs. When the test
requires several charge density cut-offs there is a different curve
for each charge density cut-off. The curve corresponding to the lowest
charge density cut-off is
`red`, the one corresponding to the highest is`blue`, all the others are`green`. Note that the total energy of the last configuration (highest wave function and charge density cut offs) is subtracted from all energies. - Total energy versus size of the
**k**-point mesh. This is a figure of the total energy as a function of the size of the**k**-point mesh. When the test requires several values of`degauss`, there is a different curve for each`degauss`. The curve corresponding to the first`degauss`is`red`, the one corresponding to the last is`blue`, all the others are`green`. Note that the total energy of the last configuration (highest number of points and lowest`degauss`) is subtracted from all energies. - Total energy as a function of volume (
`lmurn=.TRUE.`). This plot is composed of three figures: the total energy as a function of the volume, the pressure as a function of the volume and the enthalpy as a function of pressure. All curves are`red`. The points on the first curve are the energies calculated by`pw.x`, the continuous curve is the fit. - Total energy as a function of one or two crystallographic parameters
(
`lmurn=.FALSE.`). When there is a single parameter the curve is`red`as in the case`lmurn=.TRUE.`. When there are two parameters a contour plot of the energy as a function of two parameters is shown. The contour levels, their number and their colors can be given in input. By default the code shows nine levels with three colors. From the lowest to the highest levels, the colors are`red`,`green`, and`blue`. The energy value of each level is written on output. When the user requests more levels without specifying their colors, the code continues with three`yellow`levels, then`pink`,`cyan`,`orange`,`black`, and when more than 24levels are requested the sequence of colors is repeated. When `lgeo_to_file=.TRUE.`the path written on file is shown in this plot with an`orange`points connected by a line. For orthorhombic solids the code produces many postscript figures, one for each value of*c*/*a*on the grid. In each figure there is a contour plot of the energy as a function of *a*and *b*/*a*. The colors of the levels follow the same conventions of the previous case. When the levels are chosen by the code the entire energy range (for all *c*/*a*) is divided into nine levels so each figure might have less that nine curves. For crystal systems with more crystallographic parameters, this figure is not available. - Elastic constants (elastic compliances) as a function of pressure.
The elastic constants (elastic compliances) are shown in different
plots in red. In a final plot all the elastic constants (elastic
compliances) are shown on the same figure in
`red, green, blue, yellow, pink, cyan, orange and black`with same order of the previous plots. When there are more than eight elastic constants the colors are repeated. - The crystal parameters and the volume as a function of pressure.
When (
`lmurn=.FALSE.`) the code plots the lattice parameters as a function of pressure, as well as the volume as a function of pressure (so far tested only for cubic cases). All plots are`red`. - Energy bands. In this figure the bands have the color of
their irreducible representation. Each line of the path can have a different
point group and set of representations. See the
`point_groups.pdf`file for the list of representations and their color code. When the symmetry analysis is not done all the bands are`red`. - Energy bands with
`enhance_plot=.TRUE.`. In this case the background color of the panels with lines at the zone border are gray, yellow, or pink. Gray means that the point group (or double point group) representations are used, yellow or pink means that a gauge transformation was applied and projective representations might have been used. A yellow background indicates that no switch from the point group to the double point group or viceversa was made, while a pink background means that such a switch was necessary. - Electron density of states. This is a plot composed of two figures,
the first contains the electron density of states, the second the integral
of the density of states up to that energy. The dos is
`red`. In the local spin density case, the dos for spin up is`red`the one for spin down is`blue`and with a negative sign. The integrated density of states is`blue`. In the spin polarized case, the curve shows the integral of the sum of the up and down density of states. - Electronic energy, free energy, entropy, and isochoric heat capacity
(metals only). This plot is composed of four pictures one for each
quantity. There is a single
`blue`curve per plot. - Dielectric constant as a function of frequency (
9#9 = 10#10
). There are two plots, one for the real part and one for the imaginary part. Other two plots contain the real and imaginary part of the complex index of refraction. For cubic solids other two plots show the reflectivity for normal incidence and the absorption coefficient. All curves are in red. For hexagonal, trigonal, and tetragonal systems the *xx*component is in red, while the *zz*component is in green. For orthorombic systems the *xx*component is in red, the *yy*component in green and the *zz*component in blue. For monoclinic and triclinic systems the plot is not available. - Inverse of the dielectric constant as a function of frequency
(
9#9 11#11 10#10
). There are four plots: the real and imaginary part of 12#12(9#9,1#1) and the real and imaginary part of 1/12#12(9#9,1#1) . They are all in red. Note that the latter is really calculated, while the first is just its inverse. - Phonon dispersions. In this figure the phonon dispersions have the color
of their irreducible representations. The same comments made for the plot of
the band structure apply here.
- Phonon dos. There is one picture with a single
`red`curve. - Vibrational energy, free energy, entropy, and isochoric heat capacity. This plot
is composed of four figures each one showing one quantity. In
`red`the quantities obtained using the phonon density of states, in`blue`those obtained from integration over the Brillouin zone. In some cases the`red`curve is not visible because it is exactly below the`blue`one. - Atomic B factors as a function of temperature. This plot is composed of
one figure for each atom for cubic solids and of two figures for each atom
in the other cases. One figure contains
*B*_{xx}(red, pink), *B*_{yy}(blue, light_blue) and *B*_{zz}(dark_green, green) as a function of temperature. The first color refers to quantities calculated from generalized phonon density of states while the second refers to quantities calculated by Brillouin zone integration. If the curves coincide, only the last one (green) will be visible. The second figure, when plotted shows *B*_{xy}(red, pink), *B*_{xz}(blue, light_blue), and *B*_{yz}(dark_green, green). - Debye vibrational energy, free energy,
entropy, and isochoric heat capacity. This plot is composed of four
figures, one for each quantity. The curves are in
`blue`and the word Debye appears in the*y*axis label. - Crystal parameters as a function of pressure at several temperatures.
Volume as a function of pressure at several temperatures.
The number of plots depends on the crystal system.
In these plots the first temperature is red, the others follow in the
order green, blue, yellow, pink, cyan, orange, black.
If there are more temperatures the sequence is
repeated.
- Helmholtz free energy as a function of volume (
`lmurn=.TRUE.`). The free energy calculated using the phonon dos (integral over the Brillouin zone) is`red`(`blue`). When required in input this figure contains also the free energy as a function of volume for several temperatures. The color sequence`red`,`green`,`blue`,`yellow`,`pink`,`cyan`,`orange`,`black`indicates the different temperatures. In this case the same figure contains also the Gibbs energy as a function of pressure for several temperatures, the vibrational (plus electronic if available) free energy as a function of volume for several temperatures and the electronic free energy as a function of volume for several temperatures. - The equilibrium volume as a function of temperature (
`lmurn=.TRUE.`). The equilibrium volume obtained from the free energy calculated using the phonon dos (integral over the Brillouin zone) is`red`(`blue`). When required in input this figure contains also the volume as a function of temperature at several pressures. The color sequence`red`,`green`,`blue`,`yellow`,`pink`,`cyan`,`orange`,`black`indicates the different pressures. In this figure there is also the equilibrium volume divided by the equilibrium volume at*T*= 300K (and the same pressure) is plotted as a function of temperature. When required in input this figure contains also the equilibrium volume as a function of pressure at several temperatures with the same color sequence. In this case also the equilibrium volume divided by the equilibrium volume at *T*= 300K and zero pressure is plotted as a function of pressure for several temperatures. - When requested in input, the pressure as a function of volume at
several temperatures (
`lmurn=.TRUE.`). The color sequence`red`,`green`,`blue`,`yellow`,`pink`,`cyan`,`orange`,`black`, indicates the different temperatures. In the same figure there is also the thermal pressure as a function of volume for several temperatures with the same color sequence and the thermal pressure as a function of temperature for several volumes with the same color sequence. - The isothermal bulk modulus as a function of
temperature (
`lmurn=.TRUE.`). The isothermal bulk modulus obtained interpolating the free energy calculated using the phonon dos (integral over the Brillouin zone) is`red`(`blue`). When required in input this figure contains also the isothermal bulk modulus as a function of temperature at several pressures. The color sequence`red`,`green`,`blue`,`yellow`,`pink`,`cyan`,`orange`,`black`, indicates the different pressures. When required in input this figure contains also the isothermal bulk modulus as a function of pressure at several temperatures with the same color sequence. The same figure contains also the isoentropic bulk modulus as a function of temperature and the difference between isothermal and isoentropic bulk moduli. When required in input this figure contains also the isoentropic bulk modulus and the difference isoentropic-isothermal bulk moduli as a function of temperature for several pressures or as a function of pressure for several temperatures. - Volume thermal expansion as a function of temperature (
`lmurn=.TRUE.`). The thermal expansion obtained from the free energy calculated using the phonon dos (integral over the Brillouin zone) is`red`(`blue`). The one obtained from the mode Grüneisen parameters is`green`. When required in input this figure contains also the thermal expansion as a function of temperature at several pressures. The color sequence`red`,`green`,`blue`,`yellow`,`pink`,`cyan`,`orange`,`black`, indicates the different pressures. When required in input this figure contains also the thermal expansion as a function of pressure at several temperatures with the same color sequence. - The isochoric heat capacity as a function of temperature
(
`lmurn=.TRUE.`). The isochoric heat capacity calculated using the phonon dos (integral over the Brillouin zone) is`red`(`blue`). When required in input this figure contains also the isochoric heat capacity as a function of temperature for several pressures. The color sequence`red`,`green`,`blue`,`yellow`,`pink`,`cyan`,`orange`,`black`, indicates the different pressures. When required in input this figure contains also the isochoric heat capacity as a function of pressure at several temperatures with the same color sequence. The same figure contains also the isobaric heat capacity as a function of temperature and the difference isobaric-isochoric heat capacity. When required in input this figure contains also the isobaric heat capacity and the difference isobaric-isochoric heat capacity as a function of temperature for several pressures or as a function of pressure for several temperatures. - Average Grüneisen parameter as a function of temperature
(
`lmurn=.TRUE.`). The parameter obtained from phonon dos (integral over the Brillouin zone) is`red`(`blue`). The one obtained from the mode Grüneisen parameters is`green`. When required in input this figure contains also the average Grüneisen parameter as a function of temperature at several pressures. The color sequence`red`,`green`,`blue`,`yellow`,`pink`,`cyan`,`orange`,`black`, indicates the different pressures. When required in input this figure contains also the average Grüneisen parameter as a function of pressure at several temperatures with the same color sequence. - Crystallographic parameters, volume, Helmholtz (or Gibbs at finite pressure)
free energy, thermal expansion tensor, volume thermal expansion, constant
strain heat capacity (
*C*_{13#13}), isobaric heat capacity ( *C*_{P}), difference *C*_{P}-*C*_{V}of isobaric and isochoric heat capacities, difference *C*_{14#14}-*C*_{13#13}of constant stress and constant strain heat capacities (note that *C*_{14#14}=*C*_{P}), difference *C*_{V}-*C*_{13#13}of isochoric and constant strain heat capacities, difference *B*_{S}-*B*_{T}of the isoentropic and isothermal bulk modulus, and average Grüneisen parameter as a function of temperature ( `lmurn=.FALSE.`). The number of figures in this plot depends on the crystal system and on the presence of one or more files with the elastic constants. It shows*a*as a function of temperature for cubic solids, *a*, *c*/*a*, and *c*for tetragonal and hexagonal solids. For orthorhombic solids it shows also *b*/*a*and *b*while for trigonal solids it shows *a*and cos8#8 . For monoclinic solids it shows *a*, *b*/*a*, *b*, *c*/*a*, *c*, and cos8#8 (c-unique) or cos15#15 (b-unique). All the six crystallographic parameters as a function of temperature are shown for triclinic solids. All quantities calculated using the phonon density of states are in `red`, those calculated integrating over the Brillouin zone are in`blue`with the exception of the thermal expansion tensor. When this tensor is diagonal with all identical components it follows the above rules while the tensor computed from mode Grüneisen parameters is in`green`. For hexagonal, tetragonal and trigonal solids 16#16follows the above rules while 17#17 is `pink`,`cyan`, and`orange`when computed from phonon density of states, Brillouin zone integration, or mode Grüneisen parameters, respectively. In the orthorhombic case 16#16and 17#17 have the same colors, while 18#18 is `gold`,`olive`, and`light-blue`in the three cases, respectively. For the other crystal systems the thermal expansion tensor is not given. The thermal expansion tensor from the mode Grüneisen parameters is calculated only when the`elastic_constants`directory contains at least one file with the elastic constants. In this case also*C*_{P}-*C*_{V}, *C*_{14#14}-*C*_{13#13}, *C*_{V}-*C*_{13#13}, and the average Grüneisen parameters are calculated using this thermal expansion tensor and plotted in `green`. The volume used in these calculations is the`blue`curve if`ltherm_freq=.TRUE.`or as in the`red`curve if`ltherm_freq=.FALSE.`and`ltherm_dos=.TRUE.`. When both`ltherm_freq=.FALSE.`and`ltherm_dos=.FALSE.`the volume is kept fixed at the equilibrium volume at*T*= 0K. The same applies for the bulk modulus calculated from a single elastic constant file when the flag `lb0_t=.FALSE.`or computed within the ``quasi-static'' approximation when`lb0_t=.TRUE.`. The*C*_{P}, *C*_{14#14}-*C*_{13#13}, *C*_{V}-*C*_{13#13}, and the average Grüneisen parameter are plotted only in presence of one or more elastic constants file. - Thermal stresses as a function of temperature. This plot is composed of
one figure in cubic solids and of two figures in the other cases.
One figure contains
*b*_{xx}(red, pink), *b*_{yy}(blue, light_blue) and *b*_{zz}(dark_green, green) as a function of temperature. The first color refers to quantities calculated from phonon density of states while the second refers to quantities calculated by Brillouin zone integration. If the curves coincide, only the last one (green) will be visible. The second figure, when plotted, shows *b*_{xy}(red, pink), *b*_{xz}(blue, light_blue), and *b*_{yz}(dark_green, green). - Mode Grüneisen parameters. In this plot the mode Grüneisen parameters have
the color of the irreducible representation of the phonon dispersion curve
of which they are the derivative.
The same comments made for the band structure plot apply here.
- Generalized average Grüneisen parameters as a function of temperature.
This plot is composed of one figure in cubic solids and of two figures in
the other cases.
One figure contains
19#19
(red, pink), 20#20 (blue, light_blue) and 21#21 (dark_green, green) as a function of temperature. The first color refers to quantities calculated from phonon density of states while the second color refers to quantities calculated by Brillouin zone integration. If the curves coincide, only the last one (green) will be visible. The second figure, when plotted shows 22#22 (red, pink), 23#23 (blue, light_blue), and 24#24 (dark_green, green). - Phonon dispersions at the geometry that corresponds to a given temperature.
The colors are assigned on the basis of the irreducible representation of
each mode. The same comments made for the band structure plot apply here.
- Temperature dependence of the isothermal and isoentropic elastic constants
within the ``quasi-static'', ``fixed geometry quasi-harmonic'' or
``quasi-harmonic'' approximation. There is a plot for each non-zero
elastic constant and a plot of the bulk modulus. The number of plots
depends on the Laue class.
Elastic constants
interpolated at the geometry computed using the phonon density of states
are in
`red`(isothermal) and`green`(isoentropic), those calculated from integration over the Brillouin zone are in`blue`(isothermal) and`orange`(isoentropic). - Temperature dependence of the isothermal and isoentropic elastic compliances
within the ``quasi-static'', ``fixed geometry quasi-harmonic'' or
``quasi-harmonic'' approximation. There is a plot for each non-zero
elastic compliance and a plot of the compressibility. The number of plots
depends on the Laue class.
Elastic compliances
interpolated at the geometry computed using the phonon density of states
are in
`red`(isothermal) and`green`(isoentropic), those calculated from integration over the Brillouin zone are in`blue`(isothermal) and`orange`(isoentropic). - Temperature dependence of the isothermal elastic constants within the
``fixed geometry quasi-harmonic'' approximation for all the geometries of
the mesh. There is a plot for each non-zero
elastic constant and a plot of the bulk modulus. The number of plots
depends on the Laue class.
Elastic constants of the different geometries are in the sequence
`red`,`green`,`blue`,`yellow`,`pink`,`cyan`,`orange`,`black`. When there are more than eight geometries the sequence is repeated. The same colors are used for the elastic constants obtained with the phonon density of states or from the integration over the Brillouin zone. - Temperature dependence of the isothermal elastic compliances within the
``fixed geometry quasi-harmonic approximation'' for all the geometries of
the mesh. There is a plot for each non-zero
elastic compliance and a plot of the compressibility. The number of plots
depends on the Laue class.
Elastic compliances of the different geometries are in the sequence
`red`,`green`,`blue`,`yellow`,`pink`,`cyan`,`orange`,`black`. When there are more than eight geometries the sequence is repeated. The same colors are used for the elastic compliances obtained with the phonon density of states or from the integration over the Brillouin zone. - Anharmonic quantities as a function of temperature (pressure)
plotted for several pressures (temperatures) chosen using
`npress_plot`(`ntemp_plot`). Each pressure (temperature) is plotted with a different color, in the sequence`red`,`green`,`blue`,`yellow`,`pink`,`cyan`,`orange`,`black`from`press_plot`(1)to `press_plot`(`npress_plot`). If there are more than eight pressures (temperatures) the sequence of colors is repeated.