xraytools.

Interatomic Distances and Angles

This sheet: https://xraytools.com/geometry?atomstyle=ball&cellsc=2&structure=albite

Page: https://xraytools.com/geometry

No diffraction data

The first thing anybody asks of a solved structure: how far apart are the atoms, and at what angles. Give a cell, a space group and the asymmetric unit — the page expands them by the symmetry, finds every neighbour inside a radius you choose, and names each one by the operation that produced it.

Before this
The atoms you supply are the asymmetric unit; the neighbours a distance is measured to are mostly symmetry copies the page generates. A distance to an atom you never typed is the normal case, not an error.
You supply
A unit cell, a space group and one atom per line of the asymmetric unit. Any constant or coordinate may carry its standard uncertainty in brackets, as a CIF writes it, and those are what the uncertainties below are propagated from.
Reading it
Uncertainties are propagated as if the parameters were uncorrelated, because a CIF does not carry the refinement’s variance–covariance matrix. That is not what a refinement program prints: for two atoms of one rigid group the correlation is usually positive, which makes the figure here larger. It is not an upper limit either.

Worked examples: Quartz, with uncertainties supplied · cubic – NaCl, Fm3m · cubic – Cu, Fm3m · cubic – α-Fe, Im3m · cubic – CsCl, Pm3m · cubic – ZnS, F43m · hexagonal – quartz, P3221 · tetragonal – cristobalite, P41212 · hexagonal – berlinite, P3121 · tetragonal – rutile, P42/mnm · orthorhombic – aragonite, Pmcn · monoclinic – ZrO2, P21/c · triclinic – albite, C1 · tetragonal – urea, P421m

Earlier on the path: CIF Parser Next on the path: Displacement Parameters and NPD Atoms On How to read a published structure, step 2 of 4

Notation here: U, B — what each one means here

Terms here: asymmetric unit · setting · zone

See also: CIF Parser · Displacement Parameters and NPD Atoms

What each input changes
How far to look
How far out neighbours are looked for. It decides which contacts are listed and nothing about their values; a bond does not become a bond by raising it.
Atoms in the asymmetric unit
The asymmetric unit. Most of the neighbours in the answer are symmetry copies the page generates, so a distance to an atom you never typed is the normal case.
Teaching with this page
Objective
After this page a learner can decide whether two reported distances are significantly different.
Start from
this worked example
Ask first
Two bonds are reported as 1.943(4) Å and 1.947(4) Å. Are they different?
Watch for
“No — the difference is inside the uncertainty, so they are equal”
Then
Displacement Parameters and NPD Atoms
Check yourself: Two bonds are reported as 1.943(4) Å and 1.947(4) Å. Are they different?

Not resolved, which is not the same as being equal No — the difference is inside the uncertainty, so they are equal

The difference is 0.004 Å against a combined uncertainty near 0.006 — well under the 3 s.u. that is conventionally taken as the threshold for calling a difference real — so the data cannot separate them. That is a statement about the data and not about the bonds: failing to resolve a difference is not evidence that there is none, and better data might resolve it. The combined figure is approximate as well — this page propagates as if the refined parameters were uncorrelated, and a CIF carries no variance–covariance matrix to do better.

Unit cell
Å
Å
Å
°
°
°

A constant may carry its standard uncertainty in brackets, exactly as a CIF writes it — 4.9137(2). That is what the uncertainties below are built from.

Space group

Conditions belong to a setting, not to a space group number. Pnma, Pbnm and Pmcn are one space group with its axes labelled three ways, and the three tables differ: the glide that empties hk0 in one of them empties 0kl in another — a glide, because it is the fractional translation that makes a whole zone cancel, and a pure mirror carries none and empties nothing. Every setting in the International Tables is here with its own operations, so P21/n and P21/a answer for themselves.

Atoms in the asymmetric unit

One atom per line, for example Si 0.4697(1) 0 1/6. This is the same notation the structure factor page reads, so a list works on either — and a coordinate may carry its uncertainty, which only this page uses. A coordinate written as a fraction is one the symmetry fixes, and carries no uncertainty by definition.

How far to look
Å

Every neighbour inside this radius is listed. The angle table grows as the square of the neighbour count, so a small increase here is a large one there.

These are distances and angles, not bonds. Every neighbour inside the radius is listed, whether or not anything holds the two atoms together, and a short contact between ions of the same charge is a repulsion rather than a bond. Contacts are found through every symmetry operation of the space group and across cell boundaries, so the list is the full environment and not only what lies inside one cell. Which of these contacts are bonds is asked separately below, by sorting them on how far each one exceeds the two covalent radii and cutting at the largest gap in that order — and it is that answer, not this table, that the picture draws.

The cell, filled

Al — O3, 1.738 ÅO3 at −0.1875, 0.1103, 0.1906, outside the cell, drawn for a bondAl — O1, 1.739 ÅO1 at 0.0047, 0.131, −0.0322, outside the cell, drawn for a bondAl — O5, 1.727 ÅAl — O7, 1.737 ÅAl — O1, 1.739 ÅAl — O3, 1.738 ÅAl at 0.0088, 0.1685, 0.2084O1 — Na, 2.532 ÅNa at −0.2683, 0.0112, 0.8538, outside the cell, drawn for a bondO7 — Na, 2.441 ÅNa at 0.2683, −0.0112, 0.1462, outside the cell, drawn for a bondO2 — Na, 2.370 ÅNa at −0.2317, 0.4888, 0.1462, outside the cell, drawn for a bondAl — O5, 1.727 ÅSi3 — O5, 1.597 ÅO5 at 0.0132, 0.3018, 0.2703Al — O7, 1.737 ÅSi3 — O7, 1.609 ÅO7 — Na, 2.441 ÅO7 at 0.2064, 0.1091, 0.3888O3 — Na, 2.459 ÅNa at 0.7317, 0.0112, −0.1462, outside the cell, drawn for a bondO2 — Si2, 1.631 ÅSi2 at 0.3081, −0.1101, 0.6853, outside the cell, drawn for a bondO1 — Na, 2.667 ÅO3 — Na, 2.459 ÅNa at 0.2317, 0.5112, −0.1462, outside the cell, drawn for a bondO1 — Al, 1.739 ÅAl at 0.4912, 0.3315, −0.2084, outside the cell, drawn for a bondO1 — Si1, 1.609 ÅO4 — Si1, 1.603 ÅSi1 at −0.0037, 0.1798, 0.7629, outside the cell, drawn for a bondAl — O3, 1.738 ÅO3 at −0.1875, 0.1103, 1.1906, outside the cell, drawn for a bondSi2 — O2, 1.631 ÅO2 at 0.592, −0.0026, 0.2801, outside the cell, drawn for a bondcSi2 — O2, 1.631 ÅSi3 — O2, 1.646 ÅO2 — Na, 2.370 ÅO2 at 0.092, 0.4974, 0.2801O1 — Al, 1.739 ÅO1 — Na, 2.667 ÅO1 — Na, 2.532 ÅO1 — Si1, 1.609 ÅO1 at 0.0047, 0.131, 0.9678Si3 — O2, 1.646 ÅSi3 — O4, 1.616 ÅSi3 — O5, 1.597 ÅSi3 — O7, 1.609 ÅSi3 at 0.181, 0.3817, 0.36Si3 — O4, 1.616 ÅO4 — Si1, 1.603 ÅO4 at 0.1802, 0.1486, 0.7416Si1 — O4, 1.603 ÅSi3 — O4, 1.616 ÅO4 at 0.3198, 0.3514, 0.2584Si1 — O6, 1.630 ÅSi2 — O6, 1.612 ÅO6 at 0.5234, 0.1928, 0.229Si3 — O2, 1.646 ÅSi3 — O4, 1.616 ÅSi3 — O5, 1.597 ÅSi3 — O7, 1.609 ÅSi3 at 0.319, 0.1183, 0.64Si1 — O4, 1.603 ÅO4 at −0.1802, 0.8514, 0.2584, outside the cell, drawn for a bondNa — O1, 2.532 ÅSi1 — O1, 1.609 ÅO1 — Na, 2.667 ÅO1 — Al, 1.739 ÅO1 at 0.4953, 0.369, 0.0322Na — O2, 2.370 ÅSi3 — O2, 1.646 ÅO2 — Si2, 1.631 ÅO2 at 0.408, 0.0026, 0.7199Si1 — O6, 1.630 ÅSi2 — O6, 1.612 ÅO6 at 0.0234, 0.6928, 0.229Na — O1, 2.532 ÅSi1 — O1, 1.609 ÅO1 at −0.0047, 0.869, 0.0322, outside the cell, drawn for a bondNa — O2, 2.370 ÅO2 at −0.092, 0.5026, 0.7199, outside the cell, drawn for a bondNa — O3, 2.459 ÅO3 at 0.6875, 0.3897, −0.1906, outside the cell, drawn for a bondNa — O3, 2.459 ÅO3 at 0.1875, 0.8897, −0.1906, outside the cell, drawn for a bondSi1 — O1, 1.609 ÅSi1 — O4, 1.603 ÅSi1 — O6, 1.630 ÅSi1 — O8, 1.622 ÅSi1 at 0.5037, 0.3202, 0.2371Si2 — O3, 1.592 ÅSi2 — O6, 1.612 ÅSi2 — O8, 1.618 ÅSi2 — O2, 1.631 ÅSi2 at 0.6919, 0.1101, 0.3147O1 — Al, 1.739 ÅAl — O5, 1.727 ÅAl — O7, 1.737 ÅAl — O3, 1.738 ÅAl at 0.0088, 0.1685, 1.2084O1 — Na, 2.532 ÅNa at −0.2683, 0.0112, 1.8538, outside the cell, drawn for a bondSi1 — O6, 1.630 ÅSi1 — O8, 1.622 ÅSi1 — O1, 1.609 ÅSi1 — O4, 1.603 ÅSi1 at 0.0037, 0.8202, 0.2371O1 — Na, 2.667 ÅO7 — Na, 2.441 ÅNa at 0.2683, −0.0112, 1.1462, outside the cell, drawn for a bondSi2 — O2, 1.631 ÅSi2 — O3, 1.592 ÅSi2 — O6, 1.612 ÅSi2 — O8, 1.618 ÅSi2 at 0.1919, 0.6101, 0.3147Si2 — O3, 1.592 ÅO3 — Na, 2.459 ÅO3 — Al, 1.738 ÅO3 at 0.8125, 0.1103, 0.1906O2 — Na, 2.370 ÅNa at −0.2317, 0.4888, 1.1462, outside the cell, drawn for a bondAl — O3, 1.738 ÅSi2 — O3, 1.592 ÅO3 — Na, 2.459 ÅO3 at 0.3125, 0.6103, 0.1906Na — O7, 2.441 ÅO7 at 0.7936, −0.1091, 0.6112, outside the cell, drawn for a bondNa — O7, 2.441 ÅAl — O7, 1.737 ÅSi3 — O7, 1.609 ÅO7 at 0.2936, 0.3909, 0.6112aNa — O1, 2.667 ÅAl — O1, 1.739 ÅO1 at 0.5047, 0.631, −0.0322, outside the cell, drawn for a bondNa — O1, 2.667 ÅO1 at 0.0047, 1.131, −0.0322, outside the cell, drawn for a bondAl — O5, 1.727 ÅSi3 — O5, 1.597 ÅO5 at 0.4868, 0.1982, 0.7297Al — O5, 1.727 ÅSi3 — O5, 1.597 ÅO5 at 0.0132, 0.3018, 1.2703bAl — O7, 1.737 ÅSi3 — O7, 1.609 ÅO7 — Na, 2.441 ÅO7 at 0.2064, 0.1091, 1.3888O3 — Al, 1.738 ÅAl at 1.0088, 0.1685, 0.2084, outside the cell, drawn for a bondNa — O2, 2.370 ÅNa — O3, 2.459 ÅNa — O1, 2.532 ÅNa — O1, 2.667 ÅNa — O7, 2.441 ÅNa at 0.7317, 0.0112, 0.8538Si1 — O8, 1.622 ÅSi2 — O8, 1.618 ÅO8 at 0.8159, 0.1317, 0.5641Al — O3, 1.738 ÅAl — O5, 1.727 ÅAl — O7, 1.737 ÅAl — O1, 1.739 ÅAl at 0.5088, 0.6685, 0.2084O2 — Si2, 1.631 ÅSi2 at 0.3081, −0.1101, 1.6853, outside the cell, drawn for a bondNa — O1, 2.532 ÅNa — O7, 2.441 ÅNa — O1, 2.667 ÅNa — O3, 2.459 ÅNa — O2, 2.370 ÅNa at 0.2317, 0.5112, 0.8538Si1 — O8, 1.622 ÅSi2 — O8, 1.618 ÅO8 at 0.6841, 0.3683, 0.4359Si1 — O8, 1.622 ÅSi2 — O8, 1.618 ÅO8 at 0.3159, 0.6317, 0.5641Na — O1, 2.532 ÅNa — O7, 2.441 ÅNa — O1, 2.667 ÅNa — O2, 2.370 ÅNa — O3, 2.459 ÅNa at 0.7683, 0.4888, 0.1462Al — O3, 1.738 ÅAl — O5, 1.727 ÅAl — O7, 1.737 ÅAl — O1, 1.739 ÅAl at 0.4912, 0.3315, 0.7916Si1 — O8, 1.622 ÅSi2 — O8, 1.618 ÅO8 at 0.1841, 0.8683, 0.4359O1 — Si1, 1.609 ÅO4 — Si1, 1.603 ÅSi1 at −0.0037, 0.1798, 1.7629, outside the cell, drawn for a bondNa — O2, 2.370 ÅNa — O1, 2.667 ÅNa — O1, 2.532 ÅNa — O3, 2.459 ÅNa — O7, 2.441 ÅNa at 0.2683, 0.9888, 0.1462O3 — Al, 1.738 ÅAl at −0.0088, 0.8315, 0.7916, outside the cell, drawn for a bondSi2 — O2, 1.631 ÅO2 at 0.592, −0.0026, 1.2801, outside the cell, drawn for a bondSi2 — O2, 1.631 ÅSi3 — O2, 1.646 ÅO2 — Na, 2.370 ÅO2 at 0.092, 0.4974, 1.2801O1 — Na, 2.667 ÅO1 — Na, 2.532 ÅO1 — Al, 1.739 ÅO1 — Si1, 1.609 ÅO1 at 0.0047, 0.131, 1.9678Si3 — O2, 1.646 ÅSi3 — O4, 1.616 ÅSi3 — O5, 1.597 ÅSi3 — O7, 1.609 ÅSi3 at 0.181, 0.3817, 1.36Si3 — O4, 1.616 ÅO4 — Si1, 1.603 ÅO4 at 0.1802, 0.1486, 1.7416Al — O5, 1.727 ÅSi3 — O5, 1.597 ÅO5 at 0.5132, 0.8018, 0.2703Si1 — O4, 1.603 ÅSi3 — O4, 1.616 ÅO4 at 0.3198, 0.3514, 1.2584Na — O1, 2.667 ÅO1 at 0.9953, −0.131, 1.0322, outside the cell, drawn for a bondSi1 — O6, 1.630 ÅSi2 — O6, 1.612 ÅO6 at 0.5234, 0.1928, 1.229Si3 — O2, 1.646 ÅSi3 — O4, 1.616 ÅSi3 — O5, 1.597 ÅSi3 — O7, 1.609 ÅSi3 at 0.319, 0.1183, 1.64Si1 — O4, 1.603 ÅO4 at −0.1802, 0.8514, 1.2584, outside the cell, drawn for a bondNa — O1, 2.667 ÅAl — O1, 1.739 ÅNa — O1, 2.532 ÅSi1 — O1, 1.609 ÅO1 at 0.4953, 0.369, 1.0322Na — O2, 2.370 ÅSi3 — O2, 1.646 ÅO2 — Si2, 1.631 ÅO2 at 0.408, 0.0026, 1.7199Si1 — O6, 1.630 ÅSi2 — O6, 1.612 ÅO6 at 0.0234, 0.6928, 1.229Na — O7, 2.441 ÅAl — O7, 1.737 ÅSi3 — O7, 1.609 ÅO7 at 0.7064, 0.6091, 0.3888Na — O1, 2.532 ÅSi1 — O1, 1.609 ÅO1 at −0.0047, 0.869, 1.0322, outside the cell, drawn for a bondNa — O2, 2.370 ÅO2 at −0.092, 0.5026, 1.7199, outside the cell, drawn for a bondNa — O7, 2.441 ÅO7 at 0.2064, 1.1091, 0.3888, outside the cell, drawn for a bondAl — O3, 1.738 ÅSi2 — O3, 1.592 ÅO3 — Na, 2.459 ÅO3 at 0.6875, 0.3897, 0.8094Si2 — O3, 1.592 ÅO3 — Na, 2.459 ÅO3 — Al, 1.738 ÅO3 at 0.1875, 0.8897, 0.8094Si2 — O2, 1.631 ÅSi2 — O3, 1.592 ÅSi2 — O6, 1.612 ÅSi2 — O8, 1.618 ÅSi2 at 0.8081, 0.3899, 0.6853O1 — Na, 2.667 ÅNa at 0.7317, 1.0112, −0.1462, outside the cell, drawn for a bondSi1 — O1, 1.609 ÅSi1 — O4, 1.603 ÅSi1 — O6, 1.630 ÅSi1 — O8, 1.622 ÅSi1 at 0.5037, 0.3202, 1.2371Si1 — O6, 1.630 ÅSi1 — O8, 1.622 ÅSi1 — O1, 1.609 ÅSi1 — O4, 1.603 ÅSi1 at 0.9963, 0.1798, 0.7629Si2 — O3, 1.592 ÅSi2 — O6, 1.612 ÅSi2 — O8, 1.618 ÅSi2 — O2, 1.631 ÅSi2 at 0.6919, 0.1101, 1.3147O1 — Al, 1.739 ÅAl at 0.0088, 0.1685, 2.2084, outside the cell, drawn for a bondO1 — Al, 1.739 ÅAl at 0.9912, 0.8315, −0.2084, outside the cell, drawn for a bondSi2 — O3, 1.592 ÅSi2 — O6, 1.612 ÅSi2 — O8, 1.618 ÅSi2 — O2, 1.631 ÅSi2 at 0.3081, 0.8899, 0.6853Si1 — O6, 1.630 ÅSi1 — O8, 1.622 ÅSi1 — O1, 1.609 ÅSi1 — O4, 1.603 ÅSi1 at 0.0037, 0.8202, 1.2371Si1 — O1, 1.609 ÅSi1 — O4, 1.603 ÅSi1 — O6, 1.630 ÅSi1 — O8, 1.622 ÅSi1 at 0.4963, 0.6798, 0.7629O1 — Na, 2.667 ÅNa at 0.2683, −0.0112, 2.1462, outside the cell, drawn for a bondSi2 — O2, 1.631 ÅSi2 — O3, 1.592 ÅSi2 — O6, 1.612 ÅSi2 — O8, 1.618 ÅSi2 at 0.1919, 0.6101, 1.3147Na — O3, 2.459 ÅSi2 — O3, 1.592 ÅO3 — Al, 1.738 ÅO3 at 0.8125, 0.1103, 1.1906Na — O3, 2.459 ÅAl — O3, 1.738 ÅSi2 — O3, 1.592 ÅO3 at 0.3125, 0.6103, 1.1906Na — O7, 2.441 ÅO7 at 0.7936, −0.1091, 1.6112, outside the cell, drawn for a bondNa — O2, 2.370 ÅO2 at 1.092, 0.4974, 0.2801, outside the cell, drawn for a bondNa — O1, 2.532 ÅSi1 — O1, 1.609 ÅO1 at 1.0047, 0.131, 0.9678, outside the cell, drawn for a bondNa — O7, 2.441 ÅAl — O7, 1.737 ÅSi3 — O7, 1.609 ÅO7 at 0.2936, 0.3909, 1.6112Si1 — O6, 1.630 ÅSi2 — O6, 1.612 ÅO6 at 0.9766, 0.3072, 0.771Na — O2, 2.370 ÅSi3 — O2, 1.646 ÅO2 — Si2, 1.631 ÅO2 at 0.592, 0.9974, 0.2801Na — O1, 2.532 ÅSi1 — O1, 1.609 ÅO1 — Na, 2.667 ÅO1 — Al, 1.739 ÅO1 at 0.5047, 0.631, 0.9678Si1 — O4, 1.603 ÅO4 at 1.1802, 0.1486, 0.7416, outside the cell, drawn for a bondSi3 — O2, 1.646 ÅSi3 — O4, 1.616 ÅSi3 — O5, 1.597 ÅSi3 — O7, 1.609 ÅSi3 at 0.681, 0.8817, 0.36Si1 — O6, 1.630 ÅSi2 — O6, 1.612 ÅO6 at 0.4766, 0.8072, 0.771Na — O1, 2.667 ÅO1 at 0.0047, 1.131, 0.9678, outside the cell, drawn for a bondSi1 — O4, 1.603 ÅSi3 — O4, 1.616 ÅO4 at 0.6802, 0.6486, 0.7416Al — O5, 1.727 ÅSi3 — O5, 1.597 ÅO5 at 0.4868, 0.1982, 1.7297Si3 — O4, 1.616 ÅO4 — Si1, 1.603 ÅO4 at 0.8198, 0.8514, 0.2584Si3 — O2, 1.646 ÅSi3 — O4, 1.616 ÅSi3 — O5, 1.597 ÅSi3 — O7, 1.609 ÅSi3 at 0.819, 0.6183, 0.64O1 — Na, 2.532 ÅO1 — Na, 2.667 ÅO1 — Al, 1.739 ÅO1 — Si1, 1.609 ÅO1 at 0.9953, 0.869, 0.0322Si2 — O2, 1.631 ÅSi3 — O2, 1.646 ÅO2 — Na, 2.370 ÅO2 at 0.908, 0.5026, 0.7199Si2 — O2, 1.631 ÅO2 at 0.408, 1.0026, 0.7199, outside the cell, drawn for a bondO3 — Al, 1.738 ÅAl at 1.0088, 0.1685, 1.2084, outside the cell, drawn for a bondNa — O2, 2.370 ÅNa — O1, 2.532 ÅNa — O1, 2.667 ÅNa — O3, 2.459 ÅNa — O7, 2.441 ÅNa at 0.7317, 0.0112, 1.8538O1 — Si1, 1.609 ÅO4 — Si1, 1.603 ÅSi1 at 1.0037, 0.8202, 0.2371, outside the cell, drawn for a bondSi1 — O8, 1.622 ÅSi2 — O8, 1.618 ÅO8 at 0.8159, 0.1317, 1.5641O1 — Al, 1.739 ÅAl — O3, 1.738 ÅAl — O5, 1.727 ÅAl — O7, 1.737 ÅAl at 0.5088, 0.6685, 1.2084Na — O1, 2.532 ÅNa — O7, 2.441 ÅNa — O1, 2.667 ÅNa — O2, 2.370 ÅNa — O3, 2.459 ÅNa at 0.2317, 0.5112, 1.8538Si1 — O8, 1.622 ÅSi2 — O8, 1.618 ÅO8 at 0.6841, 0.3683, 1.4359Si1 — O8, 1.622 ÅSi2 — O8, 1.618 ÅO8 at 0.3159, 0.6317, 1.5641O1 — Na, 2.667 ÅO3 — Na, 2.459 ÅNa — O1, 2.532 ÅNa — O7, 2.441 ÅNa — O2, 2.370 ÅNa at 0.7683, 0.4888, 1.1462O2 — Si2, 1.631 ÅSi2 at 0.6919, 1.1101, 0.3147, outside the cell, drawn for a bondAl — O3, 1.738 ÅAl — O5, 1.727 ÅAl — O7, 1.737 ÅAl — O1, 1.739 ÅAl at 0.4912, 0.3315, 1.7916Si1 — O8, 1.622 ÅSi2 — O8, 1.618 ÅO8 at 0.1841, 0.8683, 1.4359O3 — Na, 2.459 ÅNa — O2, 2.370 ÅNa — O1, 2.667 ÅNa — O1, 2.532 ÅNa — O7, 2.441 ÅNa at 0.2683, 0.9888, 1.1462O3 — Al, 1.738 ÅAl at −0.0088, 0.8315, 1.7916, outside the cell, drawn for a bondAl — O7, 1.737 ÅSi3 — O7, 1.609 ÅO7 — Na, 2.441 ÅO7 at 0.7936, 0.8909, 0.6112Al — O5, 1.727 ÅSi3 — O5, 1.597 ÅO5 at 0.9868, 0.6982, 0.7297Al — O5, 1.727 ÅSi3 — O5, 1.597 ÅO5 at 0.5132, 0.8018, 1.2703Na — O1, 2.667 ÅO1 at 0.9953, −0.131, 2.0322, outside the cell, drawn for a bondNa — O1, 2.667 ÅAl — O1, 1.739 ÅO1 at 0.4953, 0.369, 2.0322, outside the cell, drawn for a bondNa — O7, 2.441 ÅAl — O7, 1.737 ÅSi3 — O7, 1.609 ÅO7 at 0.7064, 0.6091, 1.3888Na — O7, 2.441 ÅO7 at 0.2064, 1.1091, 1.3888, outside the cell, drawn for a bondAl — O3, 1.738 ÅSi2 — O3, 1.592 ÅO3 — Na, 2.459 ÅO3 at 0.6875, 0.3897, 1.8094O2 — Na, 2.370 ÅNa at 1.2317, 0.5112, 0.8538, outside the cell, drawn for a bondSi2 — O3, 1.592 ÅO3 — Na, 2.459 ÅO3 — Al, 1.738 ÅO3 at 0.1875, 0.8897, 1.8094Si2 — O2, 1.631 ÅSi2 — O3, 1.592 ÅSi2 — O6, 1.612 ÅSi2 — O8, 1.618 ÅSi2 at 0.8081, 0.3899, 1.6853O7 — Na, 2.441 ÅO1 — Na, 2.667 ÅNa at 0.7317, 1.0112, 0.8538, outside the cell, drawn for a bondSi1 — O6, 1.630 ÅSi1 — O8, 1.622 ÅSi1 — O1, 1.609 ÅSi1 — O4, 1.603 ÅSi1 at 0.9963, 0.1798, 1.7629O1 — Na, 2.532 ÅNa at 1.2683, 0.9888, 0.1462, outside the cell, drawn for a bondAl — O5, 1.727 ÅAl — O7, 1.737 ÅAl — O1, 1.739 ÅAl — O3, 1.738 ÅAl at 0.9912, 0.8315, 0.7916Si2 — O3, 1.592 ÅSi2 — O6, 1.612 ÅSi2 — O8, 1.618 ÅSi2 — O2, 1.631 ÅSi2 at 0.3081, 0.8899, 1.6853Si1 — O1, 1.609 ÅSi1 — O4, 1.603 ÅSi1 — O6, 1.630 ÅSi1 — O8, 1.622 ÅSi1 at 0.4963, 0.6798, 1.7629Na — O3, 2.459 ÅO3 at 0.8125, 0.1103, 2.1906, outside the cell, drawn for a bondNa — O3, 2.459 ÅO3 at 0.3125, 0.6103, 2.1906, outside the cell, drawn for a bondNa — O2, 2.370 ÅO2 at 1.092, 0.4974, 1.2801, outside the cell, drawn for a bondNa — O1, 2.532 ÅSi1 — O1, 1.609 ÅO1 at 1.0047, 0.131, 1.9678, outside the cell, drawn for a bondSi1 — O6, 1.630 ÅSi2 — O6, 1.612 ÅO6 at 0.9766, 0.3072, 1.771Na — O2, 2.370 ÅSi3 — O2, 1.646 ÅO2 — Si2, 1.631 ÅO2 at 0.592, 0.9974, 1.2801Na — O1, 2.532 ÅSi1 — O1, 1.609 ÅO1 — Na, 2.667 ÅO1 — Al, 1.739 ÅO1 at 0.5047, 0.631, 1.9678Si1 — O4, 1.603 ÅO4 at 1.1802, 0.1486, 1.7416, outside the cell, drawn for a bondSi3 — O2, 1.646 ÅSi3 — O4, 1.616 ÅSi3 — O5, 1.597 ÅSi3 — O7, 1.609 ÅSi3 at 0.681, 0.8817, 1.36Si1 — O6, 1.630 ÅSi2 — O6, 1.612 ÅO6 at 0.4766, 0.8072, 1.771Si1 — O4, 1.603 ÅSi3 — O4, 1.616 ÅO4 at 0.6802, 0.6486, 1.7416Si3 — O4, 1.616 ÅO4 — Si1, 1.603 ÅO4 at 0.8198, 0.8514, 1.2584Si3 — O2, 1.646 ÅSi3 — O4, 1.616 ÅSi3 — O5, 1.597 ÅSi3 — O7, 1.609 ÅSi3 at 0.819, 0.6183, 1.64Al — O1, 1.739 ÅO1 — Na, 2.667 ÅO1 — Na, 2.532 ÅO1 — Si1, 1.609 ÅO1 at 0.9953, 0.869, 1.0322Si2 — O2, 1.631 ÅSi3 — O2, 1.646 ÅO2 — Na, 2.370 ÅO2 at 0.908, 0.5026, 1.7199Si2 — O2, 1.631 ÅO2 at 0.408, 1.0026, 1.7199, outside the cell, drawn for a bondAl — O3, 1.738 ÅO3 at 1.1875, 0.8897, 0.8094, outside the cell, drawn for a bondO1 — Si1, 1.609 ÅO4 — Si1, 1.603 ÅSi1 at 1.0037, 0.8202, 1.2371, outside the cell, drawn for a bondO1 — Al, 1.739 ÅAl at 0.5088, 0.6685, 2.2084, outside the cell, drawn for a bondO1 — Na, 2.667 ÅO3 — Na, 2.459 ÅNa at 0.7683, 0.4888, 2.1462, outside the cell, drawn for a bondO2 — Si2, 1.631 ÅSi2 at 0.6919, 1.1101, 1.3147, outside the cell, drawn for a bondO3 — Na, 2.459 ÅNa at 0.2683, 0.9888, 2.1462, outside the cell, drawn for a bondAl — O7, 1.737 ÅSi3 — O7, 1.609 ÅO7 — Na, 2.441 ÅO7 at 0.7936, 0.8909, 1.6112Al — O5, 1.727 ÅSi3 — O5, 1.597 ÅO5 at 0.9868, 0.6982, 1.7297O2 — Na, 2.370 ÅNa at 1.2317, 0.5112, 1.8538, outside the cell, drawn for a bondO7 — Na, 2.441 ÅNa at 0.7317, 1.0112, 1.8538, outside the cell, drawn for a bondO1 — Na, 2.532 ÅNa at 1.2683, 0.9888, 1.1462, outside the cell, drawn for a bondAl — O5, 1.727 ÅAl — O7, 1.737 ÅAl — O1, 1.739 ÅAl — O3, 1.738 ÅAl at 0.9912, 0.8315, 1.7916Al — O1, 1.739 ÅO1 at 0.9953, 0.869, 2.0322, outside the cell, drawn for a bondAl — O3, 1.738 ÅO3 at 1.1875, 0.8897, 1.8094, outside the cell, drawn for a bond
a1+b1+c−2+Atomsball & stickvan der Waalsspace-fillingShowasymmetric unitunit cellBondsshownhiddendrag to rotate · scroll to zoomLook along

Si Z 14 · rcov 1.11 Å Al Z 13 · rcov 1.21 Å Na Z 11 · rcov 1.66 Å O Z 8 · rcov 0.66 Å

Hover an atom to name it. Click one to pin it and mark every copy of that site.

Every atom of the cell is drawn, including the symmetry-equivalent ones. An atom lying on a face, an edge or a corner belongs to each cell it touches and is drawn in all of them, so counting the spheres overcounts the contents of one cell. Colours are the standard CPK ones, and spheres are drawn at half the covalent radius (Cordero et al., 2008), reduced further only if that would make two of them run into each other — at full size two bonded atoms touch by definition. These are not ionic radii: in a salt the cation is drawn larger than the anion, which is the opposite of the ionic picture. A stick is drawn where both atoms' own bond ladders put the other below their cut, so every bond here is one the table above lists — and where the two ladders disagree the table is the fuller answer, not this picture. A sphere outside the cell is drawn only because a bond from inside reaches it, and its own bonds are not completed in turn.

The symmetry the atoms obey

The atoms obey exactly the 4 operations of the space group given, and no others that this cell would permit.

Distances

Interatomic distances, in Å. CSV
atomneighbourdistancesymmetry of the neighbour
NaO22.3697x,y,z
O72.4411x,y+1,z
O32.4585-x+1,-y+1,-z
O12.5325-x,-y+1,-z+1
O12.6671x,y+1,z-1
O52.9701x+1/2,y+1/2,z
O82.9960x,y,z
Al3.1710-x,-y+1,-z
Al3.1990x,y+1,z
AlO51.7266x,y,z
O71.7370x,y,z
O31.7382x-1,y,z
O11.7391x,y,z-1
Si33.0133x-1/2,y-1/2,z
Si33.0835-x+1,-y+1,-z+1
Si23.1279x-1,y,z
Si13.1587-x,-y+1,-z
Na3.1710-x,-y+1,-z
Na3.1990x,y-1,z
Si1O41.6027x-1,y,z
O11.6087-x,-y+1,-z+1
O81.6219x,y,z
O61.6296x,y,z
Si22.9995x-1/2,y+1/2,z
Si23.1401-x+1,-y+1,-z+1
Al3.1587-x,-y+1,-z
Si33.1759x-1,y,z
Si2O31.5917x,y,z
O61.6125x+1/2,y-1/2,z
O81.6179-x+1,-y+1,-z+1
O21.6310x,y-1,z
Si32.9713x,y-1,z
Si12.9995x+1/2,y-1/2,z
Al3.1279x+1,y,z
Si13.1401-x+1,-y+1,-z+1
Si3O51.5971x+1/2,y+1/2,z
O71.6089-x+1,-y+1,-z+1
O41.6165x,y,z
O21.6456x,y,z
Si22.9713x,y+1,z
Al3.0133x+1/2,y+1/2,z
Al3.0835-x+1,-y+1,-z+1
Si13.1759x+1,y,z
O1Si11.6087-x,-y+1,-z+1
Al1.7391x,y,z+1
Na2.5325-x,-y+1,-z+1
O82.5958-x,-y+1,-z+1
O42.6197-x+1,-y+1,-z+1
Na2.6671x,y-1,z+1
O62.6933-x,-y+1,-z+1
O32.7184x-1,y,z+1
O72.7409x,y,z+1
O52.9391x,y,z+1
O2Si21.6310x,y+1,z
Si31.6456x,y,z
Na2.3697x,y,z
O62.5548x+1/2,y+1/2,z
O52.5950x+1/2,y+1/2,z
O82.6112-x+1,-y+2,-z+1
O42.6229x,y,z
O72.6419-x+1,-y+1,-z+1
O32.6627x,y+1,z
O3Si21.5917x,y,z
Al1.7382x+1,y,z
Na2.4585-x+1,-y+1,-z
O82.6551-x+1,-y+1,-z+1
O62.6566x+1/2,y-1/2,z
O22.6627x,y-1,z
O12.7184x+1,y,z-1
O72.8659x+1,y,z
O52.8757x+1,y,z
O4Si11.6027x+1,y,z
Si31.6165x,y,z
O12.6197-x+1,-y+1,-z+1
O62.6226x+1,y,z
O22.6229x,y,z
O52.6382x+1/2,y+1/2,z
O72.6386-x+1,-y+1,-z+1
O82.6621x+1,y,z
O5Si31.5971x-1/2,y-1/2,z
Al1.7266x,y,z
O22.5950x-1/2,y-1/2,z
O42.6382x-1/2,y-1/2,z
O72.6963-x+1/2,-y+1/2,-z+1
O72.8398x,y,z
O32.8757x-1,y,z
O12.9391x,y,z-1
Na2.9701x-1/2,y-1/2,z
O6Si21.6125x-1/2,y+1/2,z
Si11.6296x,y,z
O22.5548x-1/2,y-1/2,z
O42.6226x-1,y,z
O82.6359x,y,z
O82.6541-x+1/2,-y+3/2,-z+1
O32.6566x-1/2,y+1/2,z
O12.6933-x,-y+1,-z+1
O7Si31.6089-x+1,-y+1,-z+1
Al1.7370x,y,z
Na2.4411x,y-1,z
O42.6386-x+1,-y+1,-z+1
O22.6419-x+1,-y+1,-z+1
O52.6963-x+1/2,-y+1/2,-z+1
O12.7409x,y,z-1
O52.8398x,y,z
O32.8659x-1,y,z
O83.1433x,y-1,z
O8Si21.6179-x+1,-y+1,-z+1
Si11.6219x,y,z
O12.5958-x,-y+1,-z+1
O22.6112-x+1,-y+2,-z+1
O62.6359x,y,z
O62.6541-x+1/2,-y+3/2,-z+1
O32.6551-x+1,-y+1,-z+1
O42.6621x-1,y,z
Na2.9960x,y,z
O73.1433x,y+1,z

Which of these are bonds

Contacts ranked by slack against the covalent radii, in Å. The rule marks the largest gap. CSV
atomneighbourdistanceradius sumslackgap
NaO22.36972.32000.0497—
O72.44112.32000.12110.0714
O32.45852.32000.13850.0174
O12.53252.32000.21250.0740
Al3.17102.87000.30100.0886
Al3.19902.87000.32900.0279
O12.66712.32000.34710.0182
O52.97012.32000.65010.3030
O82.99602.32000.67600.0259
Na: 7 neighbours below the cut — O2, O7, O3, O1, 2 × Al, O1. The gap is 0.3030 Å, 3.42 times the next largest.
AlO51.72661.8700−0.1434—
O71.73701.8700−0.13300.0104
O31.73821.8700−0.13180.0012
O11.73911.8700−0.13090.0009
Na3.17102.87000.30100.4320
Na3.19902.87000.32900.0279
Si33.01332.32000.69330.3643
Al: 4 neighbours below the cut — O5, O7, O3, O1. The gap is 0.4320 Å, 1.19 times the next largest; 3 further contacts inside this radius are not shown.
Si1O41.60271.7700−0.1673—
O11.60871.7700−0.16130.0060
O81.62191.7700−0.14810.0132
O61.62961.7700−0.14040.0077
Si22.99952.22000.77950.9199
Al3.15872.32000.83870.0592
Si23.14012.22000.92010.0814
Si1: 4 neighbours below the cut — O4, O1, O8, O6. The gap is 0.9199 Å, 11.31 times the next largest; 1 further contact inside this radius is not shown.
Si2O31.59171.7700−0.1783—
O61.61251.7700−0.15750.0208
O81.61791.7700−0.15210.0054
O21.63101.7700−0.13900.0130
Si32.97132.22000.75130.8903
Si12.99952.22000.77950.0282
Al3.12792.32000.80790.0284
Si2: 4 neighbours below the cut — O3, O6, O8, O2. The gap is 0.8903 Å, 7.93 times the next largest; 1 further contact inside this radius is not shown.
Si3O51.59711.7700−0.1729—
O71.60891.7700−0.16110.0118
O41.61651.7700−0.15350.0076
O21.64561.7700−0.12440.0291
Al3.01332.32000.69330.8177
Si22.97132.22000.75130.0580
Al3.08352.32000.76350.0122
Si3: 4 neighbours below the cut — O5, O7, O4, O2. The gap is 0.8177 Å, 4.25 times the next largest; 1 further contact inside this radius is not shown.
O1Si11.60871.7700−0.1613—
Al1.73911.8700−0.13090.0303
Na2.53252.32000.21250.3434
Na2.66712.32000.34710.1347
O82.59581.32001.27580.9287
O42.61971.32001.29970.0239
O62.69331.32001.37330.0736
O1: 4 neighbours below the cut — Si1, Al, 2 × Na. The gap is 0.9287 Å, 2.70 times the next largest; 3 further contacts inside this radius are not shown.
O2Si21.63101.7700−0.1390—
Si31.64561.7700−0.12440.0146
Na2.36972.32000.04970.1741
O62.55481.32001.23481.1851
O52.59501.32001.27500.0402
O82.61121.32001.29120.0162
O2: 3 neighbours below the cut — Si2, Si3, Na. The gap is 1.1851 Å, 6.81 times the next largest; 3 further contacts inside this radius are not shown.
O3Si21.59171.7700−0.1783—
Al1.73821.8700−0.13180.0465
Na2.45852.32000.13850.2703
O82.65511.32001.33511.1966
O62.65661.32001.33660.0015
O22.66271.32001.34270.0061
O3: 3 neighbours below the cut — Si2, Al, Na. The gap is 1.1966 Å, 4.43 times the next largest; 3 further contacts inside this radius are not shown.
O4Si11.60271.7700−0.1673—
Si31.61651.7700−0.15350.0138
O12.61971.32001.29971.4532
O62.62261.32001.30260.0029
O22.62291.32001.30290.0003
O4: 2 neighbours below the cut — Si1, Si3. The gap is 1.4532 Å, 61.84 times the next largest; 3 further contacts inside this radius are not shown.
O5Si31.59711.7700−0.1729—
Al1.72661.8700−0.14340.0295
Na2.97012.32000.65010.7936
O22.59501.32001.27500.6249
O42.63821.32001.31820.0432
O5: 2 neighbours below the cut — Si3, Al. The gap is 0.7936 Å, 1.27 times the next largest; 4 further contacts inside this radius are not shown.
O6Si21.61251.7700−0.1575—
Si11.62961.7700−0.14040.0171
O22.55481.32001.23481.3752
O42.62261.32001.30260.0678
O82.63591.32001.31590.0133
O6: 2 neighbours below the cut — Si2, Si1. The gap is 1.3752 Å, 20.30 times the next largest; 3 further contacts inside this radius are not shown.
O7Si31.60891.7700−0.1611—
Al1.73701.8700−0.13300.0281
Na2.44112.32000.12110.2541
O42.63861.32001.31861.1975
O22.64191.32001.32190.0033
O52.69631.32001.37630.0544
O7: 3 neighbours below the cut — Si3, Al, Na. The gap is 1.1975 Å, 4.32 times the next largest; 4 further contacts inside this radius are not shown.
O8Si21.61791.7700−0.1521—
Si11.62191.7700−0.14810.0040
Na2.99602.32000.67600.8241
O12.59581.32001.27580.5998
O22.61121.32001.29120.0155
O8: 2 neighbours below the cut — Si2, Si1. The gap is 0.8241 Å, 1.37 times the next largest; 5 further contacts inside this radius are not shown.

The cut is where the largest gap falls, not a criterion anyone chose. Slack is the contact's length less the sum of the two covalent radii, so a bond has little of it and a passing neighbour has a great deal; sorting by slack puts the coordination shell at the top whatever elements it is made of. Nothing here decides that a contact is a bond — it shows you where the evidence changes, and you decide.

A covalent radius is the wrong radius for a large ion, and that is where this fails. Where a published coordination number exists to compare against, the cut reproduces it for 26 of 35 atoms at a 5 Å radius, and 5 of the 9 misses have a soft cation — rock salt's sodium, caesium chloride's caesium, rutile's titanium, aragonite's calcium, baddeleyite's zirconium. The radius decides as much as the chemistry: the same 35 atoms give 23 right at 3.2 Å and 25 at 4 Å. A wrong cut usually has a gap barely bigger than the next one, so the ratio beside each cut is worth reading — but it is an association and not a test, and albite's sodium breaks it at 3.2 Å with a gap 3.4 times the next and the wrong answer.

Angles

Angles at each atom, in degrees. CSV
atbetweenangle
NaO2 and O7102.855
O2 and O3100.728
O2 and O1145.462
O2 and O1131.427
O2 and O556.824
O2 and O8108.160
O2 and Al128.642
O2 and Al125.788
O7 and O3154.418
O7 and O198.626
O7 and O164.724
O7 and O5124.514
O7 and O869.782
O7 and Al127.711
O7 and Al32.479
O3 and O165.983
O3 and O192.090
O3 and O577.285
O3 and O8111.760
O3 and Al32.988
O3 and Al122.660
O1 and O182.321
O1 and O588.706
O1 and O855.241
O1 and Al33.166
O1 and Al85.797
O1 and O5168.258
O1 and O8109.922
O1 and Al84.199
O1 and Al32.929
O5 and O870.334
O5 and Al84.149
O5 and Al154.090
O8 and Al84.500
O8 and Al85.857
Al and Al104.142
AlO5 and O7110.149
O5 and O3112.194
O5 and O1116.004
O5 and Si323.938
O5 and Si394.112
O5 and Si298.295
O5 and Si197.448
O5 and Na135.666
O5 and Na139.106
O7 and O3111.113
O7 and O1104.095
O7 and Si390.803
O7 and Si321.934
O7 and Si2106.116
O7 and Si1113.842
O7 and Na114.184
O7 and Na48.996
O3 and O1102.843
O3 and Si3134.660
O3 and Si3105.853
O3 and Si219.158
O3 and Si1111.436
O3 and Na50.361
O3 and Na108.516
O1 and Si3109.734
O1 and Si3125.643
O1 and Si2121.733
O1 and Si118.578
O1 and Na52.812
O1 and Na56.481
Si3 and Si379.813
Si3 and Si2118.299
Si3 and Si193.180
Si3 and Na151.472
Si3 and Na115.542
Si3 and Si294.599
Si3 and Si1132.855
Si3 and Na128.306
Si3 and Na70.900
Si2 and Si1128.249
Si2 and Na69.502
Si2 and Na120.117
Si1 and Na64.931
Si1 and Na70.637
Na and Na75.858
Si1O4 and O1109.321
O4 and O8111.289
O4 and O6108.458
O4 and Si2125.763
O4 and Si2101.467
O4 and Al117.323
O4 and Si39.446
O1 and O8106.930
O1 and O6112.542
O1 and Si2112.481
O1 and Si2120.786
O1 and Al20.146
O1 and Si3117.276
O8 and O6108.325
O8 and Si287.849
O8 and Si214.236
O8 and Al116.691
O8 and Si3103.085
O6 and Si222.182
O6 and Si2103.241
O6 and Al92.428
O6 and Si3107.962
Si2 and Si285.404
Si2 and Al94.392
Si2 and Si3122.496
Si2 and Al130.822
Si2 and Si392.563
Al and Si3126.563
Si2O3 and O6112.012
O3 and O8111.628
O3 and O2111.426
O3 and Si3100.590
O3 and Si1103.120
O3 and Al21.001
O3 and Si198.603
O6 and O8110.490
O6 and O2103.939
O6 and Si3128.625
O6 and Si122.430
O6 and Al111.829
O6 and Si1112.367
O8 and O2106.975
O8 and Si391.578
O8 and Si196.770
O8 and Al93.307
O8 and Si114.271
O2 and Si325.049
O2 and Si1125.914
O2 and Al129.101
O2 and Si1118.757
Si3 and Si1149.799
Si3 and Al112.464
Si3 and Si1100.096
Si1 and Al96.021
Si1 and Si194.596
Al and Si179.491
Si3O5 and O7114.495
O5 and O4110.362
O5 and O2106.302
O5 and Si2131.098
O5 and Al26.017
O5 and Al114.281
O5 and Si1115.324
O7 and O4109.785
O7 and O2108.530
O7 and Si294.501
O7 and Al110.738
O7 and Al23.784
O7 and Si1100.437
O4 and O2107.034
O4 and Si293.843
O4 and Al89.129
O4 and Al88.879
O4 and Si19.365
O2 and Si224.811
O2 and Al128.819
O2 and Al127.558
O2 and Si1111.684
Si2 and Al151.914
Si2 and Al107.782
Si2 and Si195.366
Al and Al100.187
Al and Si192.060
Al and Si179.607
O1Si1 and Al141.275
Si1 and Na108.191
Si1 and O836.708
Si1 and O435.264
Si1 and Na116.350
Si1 and O633.976
Si1 and O3143.542
Si1 and O7146.216
Si1 and O5109.433
Al and Na94.021
Al and O8145.584
Al and O4143.312
Al and Na90.589
Al and O6107.337
Al and O338.567
Al and O737.926
Al and O531.869
Na and O871.483
Na and O4122.493
Na and Na97.679
Na and O6120.779
Na and O355.701
Na and O7105.284
Na and O5113.002
O8 and O461.382
O8 and Na121.577
O8 and O659.751
O8 and O3116.758
O8 and O7174.323
O8 and O5125.529
O4 and Na81.778
O4 and O659.139
O4 and O3178.053
O4 and O7118.454
O4 and O5120.407
Na and O6135.158
Na and O399.060
Na and O753.644
Na and O5111.763
O6 and O3120.751
O6 and O7125.521
O6 and O575.580
O3 and O763.330
O3 and O560.953
O7 and O559.873
O2Si2 and Si3130.140
Si2 and Na120.278
Si2 and O637.775
Si2 and O5166.295
Si2 and O836.342
Si2 and O4107.311
Si2 and O7107.059
Si2 and O333.811
Si3 and Na108.756
Si3 and O6166.462
Si3 and O536.206
Si3 and O8104.724
Si3 and O436.104
Si3 and O735.270
Si3 and O3112.136
Na and O682.538
Na and O573.329
Na and O8127.993
Na and O4128.384
Na and O7117.423
Na and O3133.215
O6 and O5155.867
O6 and O861.817
O6 and O4140.480
O6 and O7133.007
O6 and O361.175
O5 and O8135.183
O5 and O460.741
O5 and O761.969
O5 and O3138.484
O8 and O4101.895
O8 and O773.503
O8 and O360.445
O4 and O760.155
O4 and O379.374
O7 and O3109.051
O3Si2 and Al139.841
Si2 and Na123.459
Si2 and O834.505
Si2 and O634.245
Si2 and O234.764
Si2 and O1174.066
Si2 and O7123.761
Si2 and O5112.613
Al and Na96.651
Al and O8108.406
Al and O6130.975
Al and O2161.283
Al and O138.590
Al and O734.430
Al and O533.774
Na and O8150.866
Na and O6113.494
Na and O293.081
Na and O158.316
Na and O7103.659
Na and O5117.618
O8 and O659.957
O8 and O258.818
O8 and O1146.282
O8 and O789.754
O8 and O591.491
O6 and O257.410
O6 and O1140.218
O6 and O7142.484
O6 and O597.223
O2 and O1149.460
O2 and O7127.380
O2 and O5147.223
O1 and O758.719
O1 and O563.316
O7 and O559.285
O4Si1 and Si3161.189
Si1 and O135.416
Si1 and O636.115
Si1 and O2149.022
Si1 and O5151.719
Si1 and O7126.201
Si1 and O834.589
Si3 and O1158.527
Si3 and O6139.455
Si3 and O236.861
Si3 and O534.578
Si3 and O735.013
Si3 and O8128.431
O1 and O661.829
O1 and O2121.683
O1 and O5147.731
O1 and O7150.289
O1 and O858.867

Every pair of neighbours inside the radius is here, which is more than the bond angles: two atoms that are not bonded to each other still subtend an angle at the middle one, and a small value usually means the two legs are of very different length. The distance table above is what says which neighbours are close enough to be bonds.

164 further angles are not shown — the table stops at 300. An angle table grows as the square of the neighbour count, so a small reduction in the radius removes a great many.

Torsions

Torsion angles about each bond, in degrees. CSV
aboutchaintorsionsectorchains
Na-AlAl–Na–Al–O1+−58.422−sc1
Al–Na–Al–O1+−54.496−sc1
Al–Na–Al–O3+38.906+sc1
Al–Na–Al–O3+129.345+ac1
Al–Na–Al–O5+−149.050−ac1
Al–Na–Al–O5+−146.702−ac1
Al–Na–Al–O7+31.256+sc1
Al–Na–Al–O7+141.157+ac1
Na-O1Al–Na–O1–Al+−124.072−ac1
Al–Na–O1–Al0.000sp4
Al–Na–O1–Al+124.072+ac1
Al–Na–O1–Al+127.489+ac2
Al–Na–O1–Na+−94.138−ac2
Al–Na–O1–Na+−91.139−ac1
Al–Na–O1–Na+−32.933−sc1
Al–Na–O1–Na+32.933+sc1
Al–Na–O1–Na+33.352+sc2
Al–Na–O1–Na+91.139+ac1
Al–Na–O1–Si1+−147.815−ac1
Al–Na–O1–Si1+−88.114−sc1
Al–Na–O1–Si1+−81.376−sc2
Al–Na–O1–Si1+88.114+sc1
Al–Na–O1–Si1+147.815+ac1
Al–Na–O1–Si1+151.135ap2
Na-O2Al–Na–O2–Si2+−29.615sp2
Al–Na–O2–Si2+134.530+ac2
Al–Na–O2–Si3+−54.859−sc2
Al–Na–O2–Si3+140.995+ac2
Na-O3Al–Na–O3–Al+−62.966−sc1
Al–Na–O3–Al0.000sp2
Al–Na–O3–Al+62.966+sc1
Al–Na–O3–Si2+−177.922ap1
Al–Na–O3–Si2+−119.111−ac1
Al–Na–O3–Si2+119.111+ac1
Al–Na–O3–Si2+177.922ap1
Na-O7Al–Na–O7–Al+−50.244−sc2
Al–Na–O7–Al0.000sp2
Al–Na–O7–Si3+126.660+ac2
Al–Na–O7–Si3+176.904ap2
O1-NaAl–O1–Na–O1+−91.139−ac1
Al–O1–Na–O1+91.139+ac1
Al–O1–Na–O1+94.138+ac2
Al–O1–Na–O2+−94.140−ac2
Al–O1–Na–O2+−77.884−sc1
Al–O1–Na–O2+77.884+sc1
Al–O1–Na–O3+−4.621sp1
Al–O1–Na–O3+4.621sp1
Al–O1–Na–O3+159.562ap2
Al–O1–Na–O7+−153.996ap1
Al–O1–Na–O7+−9.220sp2
Al–O1–Na–O7+153.996ap1
O1-Si1Al–O1–Si1–O4+−117.166−ac1
Al–O1–Si1–O4+117.166+ac1
Al–O1–Si1–O6+−3.416sp1
Al–O1–Si1–O6+3.416sp1
Al–O1–Si1–O8+−122.244−ac1
Al–O1–Si1–O8+122.244+ac1
O3-NaAl–O3–Na–O1+−75.997−sc1
Al–O3–Na–O1+−4.643sp1
Al–O3–Na–O1+4.643sp1
Al–O3–Na–O1+75.997+sc1
Al–O3–Na–O2+−151.098ap1
Al–O3–Na–O2+151.098ap1
Al–O3–Na–O7+−51.956−sc1
Al–O3–Na–O7+51.956+sc1
O3-Si2Al–O3–Si2–O2+−150.254ap2
Al–O3–Si2–O6+93.785+ac2
Al–O3–Si2–O8+−30.718−sc2
O5-Si3Al–O5–Si3–O2+152.849ap2
Al–O5–Si3–O4+37.121+sc2
Al–O5–Si3–O7+−87.342−sc2
O7-NaAl–O7–Na–O1+−67.893−sc2
Al–O7–Na–O1+9.334sp2
Al–O7–Na–O2+139.333+ac2
Al–O7–Na–O3+−17.424sp2
O7-Si3Al–O7–Si3–O2+−146.469−ac1
Al–O7–Si3–O2+146.469+ac1
Al–O7–Si3–O4+−29.795sp1
Al–O7–Si3–O4+29.795sp1
Al–O7–Si3–O5+−94.973−ac1
Al–O7–Si3–O5+94.973+ac1
O1-AlNa–O1–Al–O3+−103.868−ac2
Na–O1–Al–O3+−6.128sp2
Na–O1–Al–O5+−128.967−ac2
Na–O1–Al–O5+133.293+ac2
Na–O1–Al–O7+12.119sp2
Na–O1–Al–O7+109.859+ac2
O1-NaNa–O1–Na–O10.000sp4
Na–O1–Na–O2+−169.024ap1
Na–O1–Na–O2+169.024ap1
Na–O1–Na–O2+171.722ap2
Na–O1–Na–O3+−95.760−ac1
Na–O1–Na–O3+65.425+sc2
Na–O1–Na–O3+95.760+ac1
Na–O1–Na–O7+−103.357−ac2
Na–O1–Na–O7+−62.857−sc1
Na–O1–Na–O7+62.857+sc1
O1-Si1Na–O1–Si1–O4+−120.978−ac1
Na–O1–Si1–O4+−12.332sp1
Na–O1–Si1–O4+12.332sp1
Na–O1–Si1–O4+120.978+ac1
Na–O1–Si1–O6+−132.914−ac1
Na–O1–Si1–O6+−118.440−ac1
Na–O1–Si1–O6+118.440+ac1
Na–O1–Si1–O6+132.914+ac1
Na–O1–Si1–O8+−108.258−ac1
Na–O1–Si1–O8+−0.388sp1
Na–O1–Si1–O8+0.388sp1
Na–O1–Si1–O8+108.258+ac1
O2-Si2Na–O2–Si2–O3+−123.583−ac2
Na–O2–Si2–O6+−2.770sp2
Na–O2–Si2–O8+114.157+ac2
O2-Si3Na–O2–Si3–O4+130.335+ac2
Na–O2–Si3–O5+12.381sp2
Na–O2–Si3–O7+−111.235−ac2
O3-AlNa–O3–Al–O1+6.340sp2
Na–O3–Al–O5+131.698+ac2
Na–O3–Al–O7+−104.501−ac2
O3-Si2Na–O3–Si2–O2+32.947+sc2
Na–O3–Si2–O6+−83.014−sc2
Na–O3–Si2–O8+152.484ap2
O7-AlNa–O7–Al–O1+−13.410sp2
Na–O7–Al–O3+96.626+ac2
Na–O7–Al–O5+−138.415−ac2
O7-Si3Na–O7–Si3–O2+−29.252sp1
Na–O7–Si3–O2+29.252sp1
Na–O7–Si3–O4+−145.926−ac1
Na–O7–Si3–O4+145.926+ac1
Na–O7–Si3–O5+−89.306−sc1
Na–O7–Si3–O5+89.306+sc1
Al-NaO1–Al–Na–O1+−84.833−sc1
O1–Al–Na–O1+−82.356−sc1
O1–Al–Na–O10.000sp2
O1–Al–Na–O2+112.792+ac1
O1–Al–Na–O2+134.789+ac1
O1–Al–Na–O3+−24.487sp1
O1–Al–Na–O3+172.233ap1
O1–Al–Na–O7+−33.225−sc1
O1–Al–Na–O7+164.347ap1
Al-O3O1–Al–O3–Si2+−170.972ap2
Al-O5O1–Al–O5–Si3+−80.041−sc2
Al-O7O1–Al–O7–Si3+170.040ap2
Na-AlO1–Na–Al–O3+−172.233ap1
O1–Na–Al–O3+11.045sp1
O1–Na–Al–O3+93.402+ac1
O1–Na–Al–O3+102.934+ac1
O1–Na–Al–O5+−175.461ap1
O1–Na–Al–O5+−174.562ap1
O1–Na–Al–O5+−92.206−ac1
O1–Na–Al–O5+−90.628−ac1
O1–Na–Al–O7+−164.347ap1
O1–Na–Al–O7+4.844sp1
O1–Na–Al–O7+89.677+sc1
O1–Na–Al–O7+113.296+ac1
Na-O1O1–Na–O1–Si1+−121.046−ac1
O1–Na–O1–Si1+−114.728−ac2
O1–Na–O1–Si1+121.046+ac1
Na-O2O1–Na–O2–Si2+12.327sp2
O1–Na–O2–Si2+177.751ap2
O1–Na–O2–Si3+−177.062ap2
O1–Na–O2–Si3+−11.638sp2
Na-O3O1–Na–O3–Si2+−173.279ap1
O1–Na–O3–Si2+−106.081−ac1
O1–Na–O3–Si2+106.081+ac1
O1–Na–O3–Si2+173.279ap1
Na-O7O1–Na–O7–Si3+−173.762ap2
O1–Na–O7–Si3+109.011+ac2
Si1-O4O1–Si1–O4–Si3+−148.399−ac2
Si1-O6O1–Si1–O6–Si2+94.505+ac2
Si1-O8O1–Si1–O8–Si2+167.390ap2
Na-AlO2–Na–Al–O3+−153.806ap1
O2–Na–Al–O3+−37.444−sc1
O2–Na–Al–O5+20.586sp1
O2–Na–Al–O5+44.161+sc1
O2–Na–Al–O7+−135.533−ac1
O2–Na–Al–O7+−51.555−sc1
Na-O1O2–Na–O1–Si1+−69.930−sc1
O2–Na–O1–Si1+56.995+sc2
O2–Na–O1–Si1+69.930+sc1
Na-O3O2–Na–O3–Si2+−26.825sp1
O2–Na–O3–Si2+26.825sp1
Na-O7O2–Na–O7–Si3+−43.763−sc2
Si2-O6O2–Si2–O6–Si1+169.319ap2
Si2-O8O2–Si2–O8–Si1+−147.181−ac1
O2–Si2–O8–Si1+147.181+ac1
Si3-O4O2–Si3–O4–Si1+121.134+ac2
Al-NaO3–Al–Na–O30.000sp1
O3–Al–Na–O3+68.914+sc1
O3–Al–Na–O7+−102.251−ac1
O3–Al–Na–O7+154.542ap1
Al-O1O3–Al–O1–Si1+119.882+ac2
Al-O5O3–Al–O5–Si3+162.176ap2
Al-O7O3–Al–O7–Si3+−79.924−sc2
Na-AlO3–Na–Al–O5+−116.693−ac1
O3–Na–Al–O5+81.605+sc1
O3–Na–Al–O7+−98.090−ac1
O3–Na–Al–O7+171.165ap1
Na-O1O3–Na–O1–Si1+−143.194−ac1
O3–Na–O1–Si1+−49.303−sc2
O3–Na–O1–Si1+143.194+ac1

40 further torsions are not shown — the table stops at 200 of the 240 this structure has. A torsion table grows with the product of the two coordination numbers on either side of a bond, so a small reduction in the radius removes a great many.

A torsion angle is measured looking along the middle bond: it is the angle from the first atom to the fourth, projected onto the plane across that line. It is the first quantity on this page whose sign carries information no distance or angle does — mirror a crystal and every distance and every angle is unchanged, while every torsion changes sign. Quartz is the example: its two enantiomorphs give an identical set of bond lengths and the exactly opposite set of torsions. Two values are their own opposite and so carry no sign here: 0, where the chain is eclipsed, and 180, where it is anti. Each of those is superimposable on its own mirror image, so there is no hand to report.

The sign follows the convention of Klyne and Prelog, which IUPAC adopted as the standard for describing conformation: look from the first atom along the middle bond towards the fourth, and the torsion is positive when the near bond has to turn clockwise, through less than 180°, to eclipse the far one. Which end you look from does not change the answer — reading the chain backwards gives the same number, sign included, which is why a chain and its reverse are one row above. The form of it a reader can check against a picture rather than against algebra: a right-handed helix has positive torsions.

What this page computes, with b1 = B−A, b2 = C−B and b3 = D−C:

τ = atan2( |b2| b1·(b2×b3), (b1×b2)·(b2×b3) )

Two arguments rather than one, which is the whole point: an arc cosine of the angle between the two planes gives the size and throws the sign away, and a sign applied afterwards is a second convention to get wrong. Here it comes out of the arithmetic.

The sector column names the range, in IUPAC's terms:

  • sp synperiplanar, 0–30°
  • ±sc synclinal, 30–90°
  • ±ac anticlinal, 90–150°
  • ap antiperiplanar, 150–180°

IUPAC gives those ranges with shared endpoints — 0 to ±30 synperiplanar, 30 to 90 synclinal — so a torsion of exactly 30° is in two of them and the recommendation does not settle which. This page gives a boundary to the sector nearer zero; that is a choice, not a standard. The sign goes on sc and ac because +sc and −sc are two different sectors, while sp is one sector straddling zero and ap one straddling 180° — a sign on those would only repeat the number beside it.

Each of the three bonds in a chain comes from the ladder above, so every reservation there applies here three times over. Where a cut runs through a large soft cation the chains built on it are numerous and the least trustworthy on the page: read the ladder before the table.

Hydrogen bonds

This structure has no hydrogen in it, so it has no hydrogen bonds. Every other worked example below is an inorganic solid without hydrogen; load urea to see this table with something in it.

A hydrogen bond D–H···A is a hydrogen held between the atom it is covalently bonded to and a second one it is not. This table takes every hydrogen, finds its covalent bond from the ladder above, and keeps the contacts with the hydrogen genuinely between the two — which is the D–H···A angle exceeding 90°, and needs no cutoff to say. What survives is ranked by the same ladder, so the cut here and the cut above are one rule. One thing here is a convention rather than a measurement, and it is the elements: the donor must be N, O, F or S and the acceptor one of those or a halogen, because a hydrogen bond needs a polarised bond at one end and a lone pair at the other and neither is visible in a list of coordinates. That excludes C–H···O, which is a real if weaker interaction — the contact is still in the distance table above, it is only the name that is withheld. Urea is the example the page ships: each of its four N–H donates to a carbonyl oxygen, and each oxygen accepts four.

Every row rests on the ladder twice — once for the D–H bond it starts from and once for the cut among what is left — so each reservation there applies here twice. And the shortest contact of a hydrogen is often not its hydrogen bond: in urea the two closest neighbours of H1 are the other hydrogen on the same nitrogen and the carbon two bonds away, both of which sit beside it rather than in front of it.

Packing and voids

Empty space against probe radius, cell volume 664.1 Å3. CSV
probe radius / Åvoid fractionvoid volume / Å3
0.00.033722.3
0.20.00372.4
0.40.00020.1
0.60.00000.0
0.80.00000.0
1.20.00000.0

Packing fraction 0.9663 — that fraction of the cell is inside an atom.

The packing fraction is the row at a probe radius of zero: how much of the cell lies inside an atom. The rows below it ask a different question — how much space is left for a sphere of that radius to sit in without overlapping anything, which is what a crystallographer means by a void. A water molecule is usually given 1.2 Å.

Measured by sampling 110,592 points on a grid of 483, offset from the cell origin by an irrational fraction. The offset is not cosmetic: a grid that lines up with the lattice samples whole planes of points onto sphere boundaries, and its error then depends on the arithmetic relationship between the grid and the cell rather than on the resolution — refining it does not help. Against the four lattices whose packing fraction is an exact constant, this grid is right to about 5×10−4, so the fourth decimal above is the last one worth reading.

Radii are van der Waals radii from Alvarez (2013), the revision of Bondi's set derived from the Cambridge Structural Database. That choice is a convention and it is the only one on this table — the volumes themselves are geometry. A van der Waals radius describes how close a non-bonded neighbour comes, so in a metal or an ionic solid, where every contact is a bond, the spheres overlap and the packing fraction is 1 by construction. The number means what it says for molecular crystals.

About the uncertainties

No uncertainties are quoted, because none were given. Nothing in the cell or the coordinates above carries a bracket, so there is nothing to propagate. An absent uncertainty is not a zero one.

Write a constant as 4.9137(2) or a coordinate as 0.4697(1) and every distance and angle below will carry its own, split into the part that comes from the cell and the part that comes from the coordinates.

Contacts were searched out to 3.2 Å. A neighbour is named by the operation that produces it from the atom in the list above, written out in full rather than as a numbered code.

Where this comes from