{
  "counts": {
    "above_hull": 9,
    "entries": 28,
    "intervals": 6,
    "vertices": 7
  },
  "elements": [
    "BA",
    "MG"
  ],
  "flags": [
    "has_intermediate_compounds",
    "theoretical_vertices"
  ],
  "isotherms": [
    {
      "intervals": [
        {
          "intercept": 0.0,
          "kind": "two_phase",
          "left": {
            "phase": "mp-aaaaaaes",
            "x": 0.0
          },
          "mu_a_rel": 0.0,
          "mu_b_rel": -0.1106927299999998,
          "right": {
            "phase": "mp-aaacpilw",
            "x": 0.5
          },
          "slope": -0.1106927299999998,
          "x_hi": 0.5,
          "x_lo": 0.0
        },
        {
          "intercept": -0.005420207500000246,
          "kind": "two_phase",
          "left": {
            "phase": "mp-aaacpilw",
            "x": 0.5
          },
          "mu_a_rel": -0.005420207500000246,
          "mu_b_rel": -0.10527252249999955,
          "right": {
            "phase": "mp-aaaaacwl",
            "x": 0.6666666666666666
          },
          "slope": -0.0998523149999993,
          "x_hi": 0.6666666666666666,
          "x_lo": 0.5
        },
        {
          "intercept": -0.06016269340909014,
          "kind": "two_phase",
          "left": {
            "phase": "mp-aaaaacwl",
            "x": 0.6666666666666666
          },
          "mu_a_rel": -0.06016269340909014,
          "mu_b_rel": -0.07790127954545459,
          "right": {
            "phase": "mp-aaabgizw",
            "x": 0.7931034482758621
          },
          "slope": -0.01773858613636445,
          "x_hi": 0.7931034482758621,
          "x_lo": 0.6666666666666666
        },
        {
          "intercept": -0.21172501678571182,
          "kind": "two_phase",
          "left": {
            "phase": "mp-aaabgizw",
            "x": 0.7931034482758621
          },
          "mu_a_rel": -0.21172501678571182,
          "mu_b_rel": -0.03836328214285761,
          "right": {
            "phase": "mp-aaaaacrt",
            "x": 0.8947368421052632
          },
          "slope": 0.1733617346428542,
          "x_hi": 0.8947368421052632,
          "x_lo": 0.7931034482758621
        },
        {
          "intercept": -0.4003519812811414,
          "kind": "two_phase",
          "left": {
            "phase": "mp-aaaaacrt",
            "x": 0.8947368421052632
          },
          "mu_a_rel": -0.4003519812811414,
          "mu_b_rel": -0.016171874555160004,
          "right": {
            "phase": "mp-aaacpjzl",
            "x": 0.9933333333333333
          },
          "slope": 0.3841801067259814,
          "x_hi": 0.9933333333333333,
          "x_lo": 0.8947368421052632
        },
        {
          "intercept": -2.8099612899999715,
          "kind": "two_phase",
          "left": {
            "phase": "mp-aaacpjzl",
            "x": 0.9933333333333333
          },
          "mu_a_rel": -2.8099612899999715,
          "mu_b_rel": 0.0,
          "right": {
            "phase": "mp-aaacidek",
            "x": 1.0
          },
          "slope": 2.8099612899999715,
          "x_hi": 1.0,
          "x_lo": 0.9933333333333333
        }
      ],
      "temperature_K": 0.0,
      "vertices": [
        {
          "collinear": false,
          "degenerate": [],
          "energy": 0.0,
          "energy_per_atom": -1.91897494,
          "entries_at_x": 11,
          "formula": "Ba",
          "nsites": 2,
          "phase": "mp-aaaaaaes",
          "phase_kind": "structure",
          "spacegroup_number": 229,
          "spacegroup_symbol": "Im-3m",
          "theoretical": false,
          "x": 0.0
        },
        {
          "collinear": false,
          "degenerate": [],
          "energy": -0.0553463649999999,
          "energy_per_atom": -1.81497386,
          "entries_at_x": 1,
          "formula": "BaMg",
          "nsites": 4,
          "phase": "mp-aaacpilw",
          "phase_kind": "structure",
          "spacegroup_number": 51,
          "spacegroup_symbol": "Pmma",
          "theoretical": true,
          "x": 0.5
        },
        {
          "collinear": false,
          "degenerate": [],
          "energy": -0.07198841749999978,
          "energy_per_atom": -1.7785000975,
          "entries_at_x": 1,
          "formula": "BaMg2",
          "nsites": 12,
          "phase": "mp-aaaaacwl",
          "phase_kind": "structure",
          "spacegroup_number": 194,
          "spacegroup_symbol": "P6_3/mmc",
          "theoretical": false,
          "x": 0.6666666666666666
        },
        {
          "collinear": false,
          "degenerate": [],
          "energy": -0.07423122724137919,
          "energy_per_atom": -1.7404481510344827,
          "entries_at_x": 1,
          "formula": "Ba6Mg23",
          "nsites": 29,
          "phase": "mp-aaabgizw",
          "phase_kind": "structure",
          "spacegroup_number": 225,
          "spacegroup_symbol": "Fm-3m",
          "theoretical": false,
          "x": 0.7931034482758621
        },
        {
          "collinear": false,
          "degenerate": [],
          "energy": -0.05661188578947387,
          "energy_per_atom": -1.6904387663157896,
          "entries_at_x": 1,
          "formula": "Ba2Mg17",
          "nsites": 19,
          "phase": "mp-aaaaacrt",
          "phase_kind": "structure",
          "spacegroup_number": 166,
          "spacegroup_symbol": "R-3m",
          "theoretical": false,
          "x": 0.8947368421052632
        },
        {
          "collinear": false,
          "degenerate": [],
          "energy": -0.018733075266666597,
          "energy_per_atom": -1.6211377578666666,
          "entries_at_x": 1,
          "formula": "BaMg149",
          "nsites": 150,
          "phase": "mp-aaacpjzl",
          "phase_kind": "structure",
          "spacegroup_number": 187,
          "spacegroup_symbol": "P-6m2",
          "theoretical": true,
          "x": 0.9933333333333333
        },
        {
          "collinear": false,
          "degenerate": [],
          "energy": 0.0,
          "energy_per_atom": -1.60028005,
          "entries_at_x": 8,
          "formula": "Mg",
          "nsites": 1,
          "phase": "mp-aaacidek",
          "phase_kind": "structure",
          "spacegroup_number": 225,
          "spacegroup_symbol": "Fm-3m",
          "theoretical": true,
          "x": 1.0
        }
      ]
    }
  ],
  "mp_agreement": {
    "comparable": true,
    "comparable_note": "",
    "max_abs_delta_energy_above_hull": 1.1102230246251565e-16,
    "only_mp_stable": [],
    "only_ours_stable": [],
    "stable_sets_match": true
  },
  "provenance": {
    "above_hull_window_eV": 0.05,
    "builder_version": 1,
    "collinear_tol": 1e-12,
    "correction_model": "MP2020 (applied upstream by the Materials Project; none added)",
    "degenerate_tol": 1e-06,
    "entry_pool": "all_nondeprecated",
    "is_stable_source": "upstream_flag",
    "observed_at": "2026-09-01T20:54:47Z",
    "snapshot_scope_elements": [],
    "snapshot_scope_kind": "full",
    "snapshot_sha256": "b6deba8ecf1b67211b3d89cd33a5f98a1939d4bcd92db561818195e55187492a",
    "source_release": "2026.04.13",
    "stability_tol": 0.0001,
    "thermo_type": "GGA_GGA+U",
    "upstream_energy_corrections": "MP2020 compatibility corrections (anion and GGA/GGA+U mixing corrections), applied by the Materials Project to its GGA_GGA+U thermo energies"
  },
  "reference": {
    "kind": "dft_elemental_ground_state_0K",
    "per": "atom",
    "temperature_K": 0.0,
    "units": "eV/atom"
  },
  "schema_version": 1,
  "system_id": "BA-MG",
  "x_element": "MG"
}
