ALLOY DATABASE (definitions)

This page defines various terms used in the Alloy database.

Pearson Symbol

The Pearson symbol indicates a type of structure. The notation is in the form pTnn. Here p labels the point symmetry and takes values a,m,o,t,h,c for asymmetric, monoclinic, orthorhombic, tetragonal, hexagonal and cubic. T describes translational symmetry and can be P,A,B,C,I,F,R for Primitive, (A,B,C) centered, Body centered, Face centered and Rhombahedral. The final segment, nn, gives the number of atomic sites per unit cell.


The prototype is the name of a familiar compound that illustrates a given structure. For instance "ClNa" with Pearson symbol cF8 is the prototype for all structures based on the sodium-chloride structure. In constrast, "C" with Pearson symbol cF8 is the prototype for all examples of the diamond structure.

Structure file

For each structure listed in the energy database we provide the following information:

Coordinates file

The coordinates file gives explicit relaxed coordinates of each atom in the calculation. The first three lines give the unit cell vectors a,b,c on consecutive lines, in units of angstroms. The following line gives the number of atoms. The remaining lines give the "direct" coordinates &alpha,&beta,&gamma of each atom followed by: the atomic number (e.g. 1=H, 6=C, etc.); the orbit number as given in the structure file; orbit labels as given in the structure file. Cartesian coordinates are obtained from direct coordinates via r=&alphaa+&betab+&gammac.


Several types of energy are reported in our database. All are based on the cohesive energy E0 (units eV per cell) reported by VASP, as listed in the structure file. Cohesive energy is the energy of a fully relaxed structure relative to the energy of its constituent atoms widely separated in a vacuum. Units of cohesive energy are eV/cell. The enthalpy of formation "dH" is the cohesive energy of a compound relative to the composition-weighted average cohesive energies of its pure elements. Compound formation is favored when dH is negative. Units of dH are eV/atom.

The stability energy "dE" is the difference between the enthalpy of formation of a structure and the convex hull of enthalpies of formation of all structures in a given alloy system. By definition it vanishes for stable structures and otherwise must be positive. WARNING: The value of dE is accurate only when all competing stable structures are present in the database. Many alloy systems have not been completely evaluated so their dE values only indicate stability relative to a limited set of alternatives.

Search results

For a given search the result page lists matching structures and associated data. The output includes: structure and coordinates file links, the structural prototype and Pearson symbol, energy data for stability and enthalpy of formation, chemical composition, and pseudopotential type.

Wyckoff coordinates

Wyckoff coordinates describe a representative position for symmetry-related groups of atoms. When transformed by space group operations this representative position generates the direct coordinates of all related atoms within the unit cell.


Displacements are in units of Angstroms. "dri" measures displacements that preserve the symmetry of the initial Wyckoff class, whild "drb" measures the components of displacements that break the initial symmetry. Indeed, drb=0 except in cases where we deliberately break the structural symmetry, for example in the case of partial occupancy or chemical disorder.


Chemical composition of a given structure is described by the number of atoms in the calculated cell ("nat"), the number of atoms of each species present ("nn_spec") and the chemical species themselves ("ch_spec"). Certain of the chemical species are followed by an underscore and additional information (e.g. Y_sv and Ce_3). These specify the the title of the actual VASP potential (POTCAR) file used. The number of atoms can be lower than indicated by the Pearson symbol if (1) there is partial occupancy or (2) the calculation employs a primitive cell.

Pseudopotential type

VASP allows calculations using either ultrasoft pseudopotentials ("uspp") or projector augmented-wave potentials ("paw"). Calculations can be done in the local density approximation (LDA) or using a generalized gradient approximation (GGA or PBE). The majority of our database utilizes paw_GGA potentials. Even for a given potential type, multiple potentials are sometimes available for a given element. In these cases the chemical species name gives the actual name of the VASP potential (POTCAR) file. When evaluating structural stability it is crucial to work with a consistent set of potentials.


This entry lists the plane wave energy cutoff (ENCUT) of the calculation in units of eV (electron volts). Preceding the cutoff energy is a single letter indicating the VASP "Precision" setting. The precision governs the energy cutoff and sets Fourier Transform grids and other parameters consistently. Possible values are l (low, careful not to confuse the letter l with the number 1), m (medium, our default), h (high), n (normal) and a (accurate).


Energy diagram plots identify stable structures (those on the convex hull of energy vs. composition) and unstable structures (those lying above the convex hull). The energy diagram predicts the stable phases and coexistence regions of an alloy system in the limit of low temperature.

Plotting symbols used in binary diagrams are: heavy circles for known low temperature phases, light circles for known high temperature phases, diamonds for known metastable phases, triangles for high pressure phases, square boxes for hypothetical structures or unclassified structures. Our notation for ternary diagrams is similar except that we use heavy circles for experimentally observed structures whose stability is unknown. Additionally we color-code the symbols according to our calculated energies, using black for stable, blue for low energy unstable and red for high energy unstable. Perfect agreement between experiment and calculation thus requires that all heavy circles appear in black and all other symbols appear in blue or red.