Crystals and figures

Crystals and figures

extensions/chemistry/crystal.mojo reads crystal structures from CIF text and places their atoms. plot.mojo draws charts of process chemistry on a frame. The gallery's chemistry figures use both.

This page is a reference. For the rest of the library, see Process chemistry.

Read a CIF file

CIF is the Crystallographic Information File of the IUCr. A CIF file gives a unit cell, the symmetry operations of its space group, and the atoms of the asymmetric unit. read_cif(text) reads the first data block. It applies each operation to each atom site, and keeps each different position in the cell once.

from std.pathlib import Path
from extensions.chemistry.crystal import bonds, read_cif
from extensions.chemistry.quantities import ANGSTROM
from units.si import GRAM_PER_CUBIC_CENTIMETER, Length64

var diamond = read_cif(Path("diamond.cif").read_text())
diamond.density().to(GRAM_PER_CUBIC_CENTIMETER)   # 3.516
var atoms = diamond.block(1, 1, 1)                 # 18 atoms
var links = bonds(atoms, Length64(1.3, ANGSTROM), Length64(1.6, ANGSTROM))

The reader takes these items:

Item	Use
_cell_length_a, _b, _c	The edges, in angstroms
_cell_angle_alpha, _beta, _gamma	The angles, in degrees
_space_group_symop_operation_xyz or _symmetry_equiv_pos_as_xyz	The operations, such as -y,x-y,z+1/2. Without them, the identity is the only operation
_atom_site_fract_x, _y, _z	The positions, as fractions of the edges
_atom_site_type_symbol or _atom_site_label	The element, from the leading letters, so Ti1 is titanium and O2- is oxygen

A number can carry its uncertainty in parentheses, as in 3.5668(2). The reader ignores the uncertainty and the occupancy. It reads comments, quoted values and text fields, and it refuses an unknown element or a broken loop with the line number.

Place the atoms

A Crystal gives:

• volume(), from the edges and the angles of any cell, triclinic included.
• density(), the mass of the cell's atoms over its volume.
• place(u, v, w), the Cartesian point of a fractional position. Edge a lies along x, and edge b lies in the x-y plane.
• block(na, nb, nc), the atoms of a block of cells. Atoms on the far faces are included, so a block of one cell shows all eight corners.

bonds(positions, shortest, longest) gives each pair of positions in a range of distance, the lower index first.

Crystal	Atoms per cell	Bond	Density
Diamond, a = 3.5668 angstroms	8	a sqrt(3) / 4 = 1.5445 angstroms	3.516 g/cm³, handbook 3.515
Graphite, P6_3/mmc, 24 operations	4	a / sqrt(3) = 1.4226 angstroms	2.261 g/cm³, handbook 2.26
Rock salt, a = 5.64 angstroms	8	a / 2 = 2.82 angstroms

examples/crystal.mojo draws diamond and graphite as spheres and rods. Diamond's bonds go out in four directions, so it is hard. Graphite's bonds lie in flat sheets 3.36 angstroms apart, so the sheets slide.

Charts

An Axes maps a box of data onto a box of pixels, with y up. Its methods draw in data units:

Method	Draws
frame(frame, font, x_title, y_title, size, color)	The box, the ticks, their numbers and the titles
line(frame, xs, ys, width, color)	A line through points
band(frame, x_low, x_high, y_low, y_high, color)	A filled box
cells(frame, map, colors)	Each node of a LabelMap in the color of its label

nice_ticks picks round ticks: steps of 1, 2 or 5 times a power of ten. tick_text writes a tick with the decimals its step needs. The cells of a map fall on whole pixels, so the boxes that touch do not blend twice. The axes do not clip, so keep the data inside the box.

The gallery figures

Image	Example	Page
out/ellingham.png	examples/ellingham.mojo	Process maps
out/predominance.png	examples/predominance.mojo	Process maps
out/process-windows.png	examples/process_windows.mojo	Why a process runs where it does
out/anodizing.png	examples/anodizing.mojo	Electrolysis and film color
out/kroll-loop.png	examples/kroll_loop.mojo	Flowsheets and routes
out/crystal.png	examples/crystal.mojo	This page

make out/NAME.png renders one image and compresses it. The figures share one dark surface and one order of series colors, in tools/_chemistry_figure.mojo. Every series also carries a label, so no reader needs the color alone.