Analysis¶

Note

This page use the following conventions for output files:

The prefix is set to pcmc (the default)
$b is used to denote the index of a simulation box (meaning there will be multiple files if more than one box)

Radial distribution function¶

Also named g(r).

Switched on by when calculation_period is positive. The interval of the histograms is controlled by rdf_bin_length.

Output files¶

pcmc_box$b_rdf.dat:

Contains the global RDF. Composed of lines of format r g(r).

pcmc_box$b_rdfall.dat

Type-Type RDFS. Composed of line of the form:

r

$g_{11}(r)$

$g_{22}(r)$

…

$g_{12}(r)$

$g_{13}(r)$

…

$g_{23}(r)$

…

Effective structure factor¶

Aka S(q)

Calculated from radial distribution functions, assuming the particles are homogeneous spheres. A “full” S(q) is first computed with a discrete sine transformation, it is then interpolated (see wave_number_interval) to get the final S(q).

Output files¶

pcmc_box$b_seff.dat: Contains the effective structure factor as a function of the wave number. Composed of lines of format q S(q).
pcmc_box$b_sfull.dat: Contains the full effective structure factor as a function of the wave number. Composed of lines of format q S(q).

Swaps¶

When a swaps between two particles is accepted, a counter is incremented for each pair (type of particle #1, type of particle #2). This allows to produce a “map” of relative acceptance of swaps between particle type pairs. For example, this can allow to know if a swaps are performed between particles of not two close sizes, otherwise swaps are not really useful for this simulation.

Output files¶

pcmc_swapmap.dat

Contains relative acceptance a of swaps between particles of two different types. Composed of lines of the form

$R_i$

$R_j$

$a_{ij}$

where $R_i$ is the radius of particles of type i.

pcmc_swapmap.dat

Same as pcmc_swapmap.dat but for swaps betwenn particles of different simulation boxes. See interbox_swap_probability.

Bond-order parameters¶

Bond-order analysis is invoked from the command line like this:

polcolmc bondorder INPUT_FILE [ --bondorder-cfg BOND_ORDER_CONFIG ]

Options¶

`-d FILE`	Get distribution from file FILE (default: distrib)
`-p FILE`	Get parameters from file FILE (default: polcolmc.cfg)
`--box BOX`	(convert) Index of the simulation box to consider (default: 1).
`--bondorder-cfg`
	BOND_ORDER_CONFIG Separate configuration file for bond-order analysis

The bond-order parameters (qₗ) are computed from the input trajectory file INPUT_FILE (eg pcmc_out.inst) and used to determine the composition of crystal phases.

This will produce (too) many files with the bondorder_ prefix, see below.

In the output, phases are referred by the following shortcuts:

phase	Description
fcc	FCC
bcc	BCC
hcp	HCP
big	Laves(big)
small	Laves(small)
flu	fluid

Configuration¶

In ‘polcolmc.cfg’(or file set by option -p), or in a separate file, use a [bondorder] section.

Example:

[bondorder]
# typically determined from the g(r)
cutoff = 55.800000
cutoff_big = 63.388800
cutoff_small = 52.731000
# qₗ limits to separate the phases
# Laves
barq6_small_sup = 0.092
barq6_big_inf = 0.092
barq6_big_sup = 0.177
q6_big_sup = 0.273
q6_small_inf = 0.0354
# others
barq6_bcc_inf = 0.308
barq6_bcc_sup = 0.486
barq4_bcc_inf = 0.
barq4_bcc_sup = 0.0617
barq6_hcp_inf = 0.308
barq6_hcp_sup = 0.486
barq4_hcp_inf = 0.0602
barq4_hcp_sup = 0.124
barq6_fcc_inf = 0.476
barq6_fcc_sup = 0.638
barq4_fcc_inf = 0.124
barq4_fcc_sup = 3.5
barq6_flu_inf = 0.
barq6_flu_sup = 0.308
barq4_flu_inf = 0.
barq4_flu_sup = 0.0617

Parameters of the form (bar)qX_XXX_(inf|sup) determines the bounds of qₗ values for each phase.

bar	average qₗ (if absent, regular qₗ)
XXX	phase
inf	lower bound
sup	upper bound

Output files¶

bondorder_log.txt

Summary of the main results of the computation.

bondorder_phase_fractions.dat

first column is volume fraction, other columns give the fraction of each phase:

Φ

bcc

hcp

fcc

fluid

laves(big)

laves(small)

bondorder_phase_fractions_traj.dat

Fraction of each phase for each step. Columns of the form:

radius

all

bcc

hcp

fcc

fluid

laves(big)

laves(small)

bondorder_histo_qx.dat

Contains an histogram of the qx parameter where qx can be: q4, q4, bq4, bq6, the last two being the neighbor-averaged q’s.

bondorder_mean_pops.dat

Size distribution of the phases phase.

bondorder_sel_phase.xyz

Coordinates of particles in the phase phase, in the XYZ format.

Warning

The calculations described below are experimental or broken.

Energy ergo analysis¶

Switched on by energy_ergo_analysis.

Each energy_output_period, it computes the mean particle energy for type j and the variance of particle energy.

The mean energy at step s ($n_s$ sampled steps) for particle i:

\[\bar{e}_i = \frac{1}{n_s} \sum_{s'=0}^{s} e_i(s'),\]

where $e_i(s)$ is the potential energy of particle i at step s.

The mean energy at steps s for type j is therefore:

\[\bar{E}_j(s) = \frac{1}{N_j} \sum_{i \in J} \bar{e}_j\]

The variance at step s is

\[\sigma_j(s) = \frac{1}{N_j} \sum_{i \in J} (e_i(s) - \bar{E_j}(s))^2\]

Output file¶

pcmc_box$b_nrgergo.dat

Mean and variance of potential energy per particle (for each type) computed at several steps.

step (relative)

variance (type 1)

…

mean (type 1)

…

Switched on by

Configurational temperature¶

Switched on by configurational_temperature.

Calculates the configurational temperature $T_c$.

\[T_c = \frac{\langle \vec{\nabla} V^2 \rangle}{k_B \langle \Delta V \rangle}\]

Output file¶

pcmc_conftemp.dat

Contains the relative configurational temperature $T_c/T$ , squared force F² and second derivate potential V’’ for each box and for each step.

step

$T_c/T$ (box 1)

F² (box 1)

V’‘(box 1)

…

Average Z-density¶

Calculates average particle density along the z axis for each particle type. It is controlled by z_density_period.

Output files¶

pcmc_box$b_zdens.dat

Density as a function of the position of the interval sampled. Composed of lines of the form:

z

d₁

d₂

…

where dᵢ is the density for type i.

3D S(q)¶

Computes directly $S(\vec{q})$ from input $\vec{q}$. Period of the calculation is set by full_structure_period.

Input file¶

qvals.dat: Contains lines of the form q_x q_y q_z.

Output file¶

pcmc_bigseff.dat

contains the structure factor as a function of $\vec{q}$. Composed of lines of the form:

q_x

q_y

q_z

S(q)

P(q)

P(q) is the form factor.

Density fluctuations¶

Fluctuation of the number of particles in small volumes. Activated by density_fluctuations. Period of the calculation is set by fluctuations_period.

Input file¶

fluctuations_input.txt

Can be set by the parameter density_fluctuations_file.

Format:

{random seed}

{number of tests}

{number of radii}
{option (RR ⇒ use relative radius, R ⇒ no)}
{radius 1}
...
{radius {number of radii}}

{minimum density}
{maximum density}
{number of densities}

Output files¶

pcmc_denses.dat

Grace file containing the histograms of densities (XY sets) for each small volume.

pcmc_rad_denses.dat

Grace file containing the histograms of mean particle radius (XY sets) for each small volume.

pcmc_phi_denses.dat

Grace file containing the histograms of mean particle volume fraction (XY sets) for each small volume.

pcmc_cov_denses.dat

Contains covariances of particle numbers.

Fluctuations of families: cov(Ni,Nj)
Nb radii:" ${number of small volumes}
Nb families: ${number of families}
${volume radius #1}
1 ${cov(1,1)}
2 ${cov(2,2)}
...
1 2 ${cov(1,2)}
....
2 3 ${cov(1,2)}
...
${volume radius #2}
...