Unfortunately, a **lattice description** with and without knowledge of structure and symmetry** is not uniform**.

No crystal structure data available (e.g. CALM)

If one determines only the lattice parameters, e.g. by means of XRD, then the recommendation for **triclinic** applies:

\begin{align*} a \leq b \leq c \quad \textrm{and} \quad \alpha, \beta, \gamma >90\degree \end{align*}

For **monoclinic** the **physical axes setup** is **valid**:

\begin{align*} a\leq b \quad \textrm{and} \quad \gamma>90\degree \end{align*}

although more common is still the mineralogic axes setup with β different from 90°.

The internationally accepted recommendation for **orthorhombic** is:

\begin{align*} a\leq b\leq c \end{align*}

For all higher-symmetric crystal systems no rules are required since there are no reasonable axes permutations.

The reason for these rules is that a phase search in tables (Hanawalt or Fink index) or databases can be significantly shortened [1].

In addition, (phase-specific) information such as the lattice parameter ratios a / b : 1 : c / b are then unambiguous.

Data from crystal structure databases

However, **if** the **crystal structure** of a phase **is known**, **the upper rules are obsolete**.

Then the **definition** of axes and angle definition **follows** the alignment of the symmetry elements, as specified in the **standard settings** of the space-group types **in the International Tables for Crystallography (Vol. A)**.

Since also **in CALM** only the crystal lattice is determined, this means that the rules listed above are followed.

Thus, even for correctly described lattices of low-symmetry phases, there **will inevitably be differences from **their **descriptions** listed **in databases**.

*Thus, for orthorhombic phases, a, b and c can be interchanged arbitrarily, while the output in CALM will always show:**a < b < c.*

[1] Faber, J.; Weth, C. & Jenkins, R.:PCSIWIN: A Windows-Based Index Program with Hanawalt, Fink and Alphabetic Search Capabilities for Use with the ICDD Powder Diffraction File (PDF), *Mater. Sci. Forum, 378-381 *(2001), 106-111