How to Interpret and Understand Villars Distinct Phase Labels

by P. Villars, H. Okamoto, and K. Cenzual

Distinct Phase Labels Concept

A phase label is defined by the chemical system and the crystal structure and has been given a unique name by the combination of its formula and its modification.

This unique name has been used through the “ASM Alloy Phase Diagrams Center” as phase labels in the phase diagrams. In addition, each crystal data entry has been grouped to such a phase label. These distinct phase labels make it possible to link directly any phases in the phase diagrams to its crystallographic data, if any are available.

The crystal structure is defined referring to a prototype, if known. For not yet (fully) investigated structures, partial structural information is given if available, e.g. the complete Pearson symbol may be replaced by t** (tetragonal) or cI* (cubic body centered). Information about colloquial names and stability with respect to temperature, pressure, or composition, has been used to assign a phase label to entries with no structural data.

• Phases that crystallize with the same prototype, but are separated by a two-phase region in phase diagrams, have been distinguished. The same is true for temperature- or pressure-induced isostructural phase transitions where a discontinuity in the cell parameters is reported. On the contrary, the terminal solid solution of (Fe) with bcc structure has been considered as a single phase, since in some systems there exists a continuous solid solution ranging from α-Fe to δ-Fe.
• Structures with different degrees of ordering have in some cases been considered separately, in others not, depending on the possibility of assigning unambiguously one or the other modification to the data sets. More ”detailed” structure refinements, considering for instance split atom positions, have often been grouped under the simplest type.
• Structure proposals stated to be incorrect in later literature have been grouped under a phase identifier in agreement with more recent reports. A Structure data set reporting a hexagonal cell may in such a case, for instance, be grouped under an orthorhombic phase.
• Terminal solid solutions include also solid solutions of interstitial character.
• The definition of a prototype applied here makes that a continuous solid solution may smoothly shift from one type to another. A typical case is the progressive transition of a phase A_xB from a NiAs type to a Ni₂In-type structure by filling progressively first one A site, then a second one. Refinements considering one or the other type have here been grouped together.

It follows that there is a certain amount of subjectivity when assigning a phase identifier, and there may be errors in the assignment. We believe, however, that this approach represents a substantial advantage for the user.

Chemical Formulae and Phase Label

The chemical formulae have been standardized so that the chemical elements are always written in the same order, an order that corresponds roughly to the order of the groups in the periodic system. Chemical units, such as water molecules, azide ions, etc., are distinguished and written within square brackets. Deuterium and tritium are considered as distinct chemical elements.

Whenever a prototype has been assigned to the published data, the chemical formula is written so that the number of formula units per cell is the same as for the type-defining compound. A phase containing 50 at.% A and 50 at.% B, for instance, will be called A_0.50B_0.50 if the structure type is Cu,cF4,Fm3m (Z = 4), but AB if it is CuAu,tP2,P4/mmm (Z = 1) and A₂B₂ if it is Cu₃Au,cP4,Pm3m (Z = 1). Such conventions imply a certain hypothesis on the atom distribution in case of off-stoichiometric formulae. In particular it is necessary to choose between a formula assuming a structure with vacancies and one with mixed occupation, e.g between A_0.9B and A_0.95B_1.05. Adding to this the uncertainty on the chemical composition itself, especially when the authors did not recognize the crystal structure, this must be taken as a formal way of writing and no claims are made on its correctness.

Each phase is assigned a phase label, which, in the general case, is a representative chemical formula, written as described above. A chemical element in parentheses indicates a limited terminal solid solution, whereas for complete solid solutions the two chemical elements are written within the parentheses, separated by comma. Whenever several phases are known for the same chemical composition, a short code specifying the modification is added. Preference is given to terms such as rt (room-temperature), ht (high-temperature), lt (low-temperature) or hp (high-pressure), possibly followed by a digit when several temperature- or pressure induced phase transitions are known. If only one modification, stable at room temperature, is known, the field modification is left blank. The term ht is in principle added for phases that are only stable above room temperature, and by analogy, the term lt for phases that are only stable below room temperature. The specification rt means that a phase stable under ambient conditions decomposes or undergoes a structural transition before reaching the melting point, or on cooling below room temperature. In cases where contradictory information is found in the literature, a specification like cub (cubic), rhom (rhombohedral), orth (orthorhombic), etc., may have been preferred. Ramsdell notations are used for polytypic compounds such as CdI. Mineral names are abbreviated to the first three letters, when several minerals with the same chemical composition are known. A chemical element followed by a plus sign means that the phase probably contains more of that element than indicated in the chemical formula; an additional chemical element written within parentheses has a stabilizing effect.

Prototype Assignment

The prototype is a well-known concept in inorganic chemistry where often a large number of compounds crystallize with very similar atom arrangements. The compilation Strukturbericht started to catalogue crystal structures into types, named by codes such as A1, B1, or A15. These notations are still in use; however, nowadays prototypes are generally referred to by the name of the compound for which this particular kind of atom arrangement was first identified, i.e. for the types enumerated above: Cu, NaCl, Cr₃Si. This product uses a longer notation, which includes also the Pearson symbol and the space group number: Cu,cF4,Fm3m, NaCl,cF8,Fm3m, Cr₃Si,cP8,Pm3n. In a few cases several prototypes correspond to the same code, e.g. several polytypes of CdI have the same notation. A similar situation occurs for the old, wrong, and the correct structure proposals for FeB, which have the same Pearson code and space group. In these cases a letter is added after the type-defining compound, assigned in chronological order, e.g. the correct FeB type will be referred to as FeB-b,oP8,62.

All data sets with published coordinates are classified into prototypes, following criteria defined in TYPIX.* According to this definition, isotypic compounds must crystallize in the same space group, have similar cell parameter ratios, and occupy the same Wyckoff positions in the standardized description with the same or similar values of the atom coordinates. If all these criteria are fulfilled, the atomic environments should be similar. No distinction is made between structures with fully and partly occupied atom sites.

When possible, a prototype has been assigned also to data sets without atom coordinates. The prototype is often stated in the publication, in other cases it has been assigned. The assigned type may in some cases be an approximation of the real structure, ignoring for instance a certain disorder. The exact space group setting to which the cell parameters refer has been added when this was not published.

The term filled-up is used for unrefined structures that are either partly or fully filled versions of refined structures. These are treated as unfilled structures. For example, Ru₂Sm has a crystal structure of the MgZn₂ prototype. H₅Ru₂Sm has similar cell parameters and belongs to the same space group, but the hydride belongs surely to a different prototype. Therefore to show its structural relation, we classify it as filled-up Mg₂Zn prototype.