ESPEI Dataset Schema

Formatting JSON Files for ESPEI

ESPEI has a single input style in JSON format that is used for all data entry. For those unfamiliar with JSON, it is fairly similar to Python dictionaries with some rigid requirements

All string quotes must be double quotes. Use "key" instead of 'key'.

Numbers should not have leading zeros. 00.123 should be 0.123 and 012.34 must be 12.34.

Lists and nested key-value pairs cannot have trailing commas. {"nums": [1,2,3,],} is invalid and should be {"nums": [1,2,3]}.

These errors can be challenging to track down, particularly if you are only reading the JSON error messages in Python. A visual editor is encouraged for debugging JSON files such as JSONLint. A quick reference to the format can be found at Learn JSON in Y minutes.

ESPEI has support for checking all of your input datasets for errors, which you should always use before you attempt to run ESPEI. This error checking will report all of the errors at once and all errors should be fixed. Errors in the datasets will prevent fitting. To check the datasets at path my-input-data/ you can run espei --check-datasets my-input-data.

Non-equilibrium Thermochemical Data

Non-equilibrium thermochemical data is used where the internal degrees of freedom for a phase are known. This type of data is the only data that can be used for parameter generation, but it can also be used in Bayesian parameter estimation.

Two examples follow. The first dataset has some data for the formation heat capacity for BCC_B2.

The components and phases keys simply describe those found in this entry.
Use the reference key for bookkeeping the source of the data.
The comment key and value can be used anywhere in the data to keep notes for your reference. It takes no effect.
The solver the internal degrees of freedom and and site ratios are described for the phase.

sublattice_configurations is a list of different configurations, that should correspond to the sublattices for the phase descriptions. Non-mixing sublattices are represented as a string, while mixing sublattices are represented as a lists. Thus an endmember for BCC_B2 (as in this example) is ["AL", "NI", VA"] and if there were mixing (as in the next example) it might be ["AL", ["AL", "NI"], "VA"]. Mixing also means that the sublattice_occupancies key must be specified, but that is not the case in this example. It is important to note that any mixing configurations must have any ideal mixing contributions removed. Regardless of whether there is mixing or not, the length of this list should always equal the number of sublattices in the phase, though the sub-lists can have mixing up to the number of components in that sublattice. Note that the sublattice_configurations is a list of these lists. That is, there can be multiple sublattice configurations in a single dataset. See the second example in this section for such an example.
The conditions describe temperatures (T) and pressures (P) as either scalars or one-dimensional lists.
The type of quantity is expressed using the output key. This can in principle be any thermodynamic quantity, but currently only CPM*, SM*, and HM* (where * is either nothing, _MIX or _FORM) are supported. Support for changing reference states is planned but not yet implemented, so all thermodynamic quantities must be formation quantities (e.g. HM_FORM or HM_MIX, etc.). This is tracked by ESPEI issue #85 on GitHub.
values is a 3-dimensional array where each value is the output for a specific condition of pressure, temperature, and sublattice configurations from outside to inside. Alternatively, the size of the array must be (len(P), len(T), len(subl_config)). In the example below, the shape of the values array is (1, 12, 1) as there is one pressure scalar, one sublattice configuration, and 12 temperatures.
There is also a key, excluded_model_contributions, which will make those contributions of pycalphad's Model not be fit to when doing parameter selection or MCMC. This is useful for cases where the type of data used does not include some specific Model contributions that parameters may already exist for. For example, DFT formation energies do not include ideal mixing or (Calphad-type) magnetic model contributions, but formation energies from experiments would include these contributions so experimental formation energies should not be excluded.

{
  "reference": "Yi Wang et al 2009",
  "components": ["AL", "NI", "VA"],
  "phases": ["BCC_B2"],
  "solver": {
    "mode": "manual",
      "sublattice_site_ratios": [0.5, 0.5, 1],
      "sublattice_configurations": [["AL", "NI", "VA"]],
      "comment": "NiAl sublattice configuration (2SL)"
  },
  "conditions": {
      "P": 101325,
      "T": [  0,  10,  20,  30,  40,  50,  60,  70,  80,  90, 100, 110]
  },
  "excluded_model_contributions": ["idmix", "mag"],
  "output": "CPM_FORM",
  "values":   [[[ 0      ],
                [-0.0173 ],
                [-0.01205],
                [ 0.12915],
                [ 0.24355],
                [ 0.13305],
                [-0.1617 ],
                [-0.51625],
                [-0.841  ],
                [-1.0975 ],
                [-1.28045],
                [-1.3997 ]]]
}

In the second example below, there is formation enthalpy data for multiple sublattice configurations. All of the keys and values are conceptually similar. Here, instead of describing how the output quantity changes with temperature or pressure, we are instead only comparing HM_FORM values for different sublattice configurations. The key differences from the previous example are that there are 9 different sublattice configurations described by sublattice_configurations and sublattice_occupancies. Note that the sublattice_configurations and sublattice_occupancies should have exactly the same shape. Sublattices without mixing should have single strings and occupancies of one. Sublattices that do have mixing should have a site ratio for each active component in that sublattice. If the sublattice of a phase is ["AL", "NI", "VA"], it should only have two occupancies if only ["AL", "NI"] are active in the sublattice configuration.

The last difference to note is the shape of the values array. Here there is one pressure, one temperature, and 9 sublattice configurations to give a shape of (1, 1, 9).

{
  "reference": "C. Jiang 2009 (constrained SQS)",
  "components": ["AL", "NI", "VA"],
  "phases": ["BCC_B2"],
  "solver": {
      "sublattice_occupancies": [
                     [1, [0.5, 0.5], 1],
                     [1, [0.75, 0.25], 1],
                     [1, [0.75, 0.25], 1],
                     [1, [0.5, 0.5], 1],
                     [1, [0.5, 0.5], 1],
                     [1, [0.25, 0.75], 1],
                     [1, [0.75, 0.25], 1],
                     [1, [0.5, 0.5], 1],
                     [1, [0.5, 0.5], 1]
                    ],
      "sublattice_site_ratios": [0.5, 0.5, 1],
      "sublattice_configurations": [
                        ["AL", ["NI", "VA"], "VA"],
                        ["AL", ["NI", "VA"], "VA"],
                        ["NI", ["AL", "NI"], "VA"],
                        ["NI", ["AL", "NI"], "VA"],
                        ["AL", ["AL", "NI"], "VA"],
                        ["AL", ["AL", "NI"], "VA"],
                        ["NI", ["AL", "VA"], "VA"],
                        ["NI", ["AL", "VA"], "VA"],
                        ["VA", ["AL", "NI"], "VA"]
                       ],
      "comment": "BCC_B2 sublattice configuration (2SL)"
  },
  "conditions": {
      "P": 101325,
      "T": 300
  },
  "output": "HM_FORM",
  "values":   [[[-40316.61077, -56361.58554,
             -49636.39281, -32471.25149, -10890.09929,
             -35190.49282, -38147.99217, -2463.55684,
             -15183.13371]]]
}

Equilibrium Thermochemical Data

Equilibrium thermochemical data is used when the internal degrees of freedom are not known. This is typically true for experimental thermochemical data. Some cases where this type of data is useful, compared to non-equilibrium thermochemical data are:

Activity data
Enthalpy of formation data in region with two or more phases in equilibrium
Enthalpy of formation for a phase with multiple sublattice, e.g. the σ phase

This type of data can not be used in parameter selection, because a core assumption of parameter selection is that the site fractions are known.

Activity data is similar to non-equilibrium thermochemical data, except we must enter a reference state and the solver key is no longer required, since we do not know the internal degrees of freedom. A key detail is that the phases key must specify all phases that are possible to form.

An example for Mg activties in Cu-Mg follows, with data digitized from S.P. Garg, Y.J. Bhatt, C. V. Sundaram, Thermodynamic study of liquid Cu-Mg alloys by vapor pressure measurements, Metall. Trans. 4 (1973) 283–289. doi:10.1007/BF02649628.

{
  "components": ["CU", "MG", "VA"],
  "phases": ["LIQUID", "FCC_A1", "HCP_A3"],
  "reference_state": {
    "phases": ["LIQUID"],
    "conditions": {
      "P": 101325,
      "T": 1200,
      "X_MG": 1.0
    }
  },
  "conditions": {
    "P": 101325,
    "T": 1200,
    "X_CU": [0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.0]
  },

  "output": "ACR_MG",
    "values":   [[[0.0057,0.0264,0.0825,0.1812,0.2645,0.4374,0.5852,0.7296,0.882,1.0]]],
  "reference": "garg1973thermodynamic",
  "comment": "Digitized Figure 3 and converted from activity coefficients."
}

Phase Diagram Data

ESPEI can consider multi-component phase diagram data with an arbitrary number of phases in equilibrium. Phase diagram data JSON datasets are distingished by using "output": "ZPF"¹. Each entry in the JSON values corresponds to a phase region where one or more phases are participating in equilibrium under the given temperature and pressure conditions.

Each phase in the phase region must give its phase composition, i.e. the internal composition of that phase (not the overall composition). The "phase composition" is the same as a "tie-line composition" in a two-phase region of a binary phase diagram, but is a more general term for cases where the meaning of a tie-line is ambiguous like a single phase equilibrum or an equilibrium with three or more phases.

Sometimes there may be a phase equilibrium where one or more of the phase compositions are unknown. This is especially common for phase diagram data determined by equilibrated alloys or by scanning calorimetry in binary systems, where one phase composition is determined, but the phase composition of the other phase(s) in equilibrium are not. In these cases, phase compositions can be given as null and ESPEI will estimate the phase composition.

Important

Each phase region must have at least one phase with a prescribed phase composition. If all phases in a phase region have null phase compositions, the target hyperplane (described by Figure 1 in (Bocklund et al. 2019)) will be undefined and no driving forces will be computed.

Important

For a dataset with c components, each phase composition must be specified by c-1 components. There is an implicit N=1 condition.

Example

{
  "components": ["AL", "NI"],
  "phases": ["AL3NI2", "BCC_B2", "LIQUID"],
  "conditions": {
    "P": 101325,
     "T": [2500, 1348, 1176, 977]
  },
  "output": "ZPF",
  "values": [
    [["LIQUID", ["NI"], [0.5]]],
    [["AL3NI2", ["NI"], [0.4083]], ["BCC_B2", ["NI"], [0.4340]]],
    [["AL3NI2", ["NI"], [0.4114]], ["BCC_B2", ["NI"], [null]]],
    [["BCC_B2", ["NI"], [0.71]], ["LIQUID", ["NI"], [0.752]], ["FCC_L12", ["NI"], [0.76]]]
  ],
  "reference": "37ALE"
}

Each entry in the values list is a list of all phases in equilibrium in a phase region. There are four phase regions:

[["LIQUID", ["NI"], [0.5]]]: Single phase equilibrium with LIQUID having a phase composition of X(NI,LIQUID)=0.5.
[["AL3NI2", ["NI"], [0.4083]], ["BCC_B2", ["NI"], [0.4340]]]: Two phase equilibrium between AL3NI2 and BCC_B2, which have phase compositions of X(NI,AL3NI2)=0.4083 and X(NI,BCC_B2)=0.4340, respectively.
[["AL3NI2", ["NI"], [0.4114]], ["BCC_B2", ["NI"], [null]]]: Two phase equilibrium between AL3NI2 and BCC_B2 where the phase composition of BCC_B2 is unknown.
[["BCC_B2", ["NI"], [0.71]], ["LIQUID", ["NI"], [0.752]], ["FCC_L12", ["NI"], [0.76]]]: Eutectic reaction between LIQUID, BCC_B2 and FCC_L12.

Tip: Multi-component phase regions

To describe multi-component phase regions, simply include more components and compositions in each phase composition. For example, a two-phase equilibrium in a three component system could be described by [["ALPHA", ["CR", "NI"], [0.1, 0.25]], ["BETA", ["CR", "NI"], [null, null]]]

Common Mistakes and Notes

A single element sublattice is different in a phase model ([["A", "B"], ["A"]]]) than a sublattice configuration ([["A", "B"], "A"]).
Make sure you use the right units (J/mole-atom, mole fractions, Kelvin, Pascal)
Mixing configurations should not have ideal mixing contributions.
All types of data can have a weight key at the top level that will weight the standard deviation parameter in MCMC runs for that dataset. If a single dataset should have different weights applied, multiple datasets should be created.

References

Bocklund, Brandon, Richard Otis, Aleksei Egorov, Abdulmonem Obaied, Irina Roslyakova, and Zi-Kui Liu. 2019. “ESPEI for Efficient Thermodynamic Database Development, Modification, and Uncertainty Quantification: Application to Cu–Mg.” MRS Communications 9 (2): 618–27. https://doi.org/doi:10.1557/mrc.2019.59.

Footnotes

ZPF after the "Zero Phase Fraction" method (Bocklund et al. 2019) used to compute the likelihood. "Zero phase fraction" is a little misleading as a name, since the prescribed phase compositions in the datasets actually correspond to the overall composition where the phase fraction of the desired phase should be one.↩︎