Na11Ti8(PO4)12

High-Entropy Materials HEA

MP-ID: mp-761068 · Space group: P1 (#1)

Materials Project API

Basic Information

Formula

Na11Ti8(PO4)12

MP-ID

mp-761068

Elements

Sites

Density

2.8991

g/cm³

Volume

1,016.94

Å³

Cell a

8.8820

Cell b

9.0877

Cell c

12.5991

α Angle

89.82

β Angle

89.88

γ Angle

89.75

Space Group

Point Group

Crystal System

Triclinic

Bravais Lattice

Triclinic P

Stability

Packing Fraction

0.5240

X-ray Diffraction

Diffraction Pattern

Target / Radiation

X-axis: 2θ (°); Y-axis: relative intensity; CuKa ; λ=1.5406 Å

Diffraction Peaks (Top 24)

2θ	d (Å)	I	hkl
7.02	12.5990	1.6	(0,0,1)
11.99	7.3813	1.6	(0,1,1)
12.18	7.2666	3.1	(1,0,1)
13.91	6.3660	2.9	(1,1,0)
13.97	6.3379	3.2	(1,-1,0)
14.06	6.2995	2.3	(0,0,2)
15.57	5.6903	6.3	(1,1,1)
15.62	5.6734	5.0	(1,1,-1)
15.65	5.6634	5.9	(1,-1,-1)
15.66	5.6604	2.6	(1,-1,1)
19.54	4.5438	28.4	(0,2,0)
19.79	4.4861	38.7	(1,1,2)
19.86	4.4695	18.3	(1,1,-2)
19.86	4.4695	16.6	(1,-1,-2)
19.88	4.4664	40.1	(1,-1,2)
19.99	4.4409	63.5	(2,0,0)
20.76	4.2786	3.2	(0,2,1)
20.80	4.2701	5.6	(0,2,-1)
22.24	3.9970	23.8	(2,1,0)
22.32	3.9831	33.5	(2,-1,0)
23.03	3.8620	13.0	(1,2,1)
23.08	3.8536	20.6	(1,2,-1)
23.12	3.8473	20.3	(1,-2,-1)
23.14	3.8433	14.2	(1,-2,1)

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Energy Properties

Formation Energy/atom

-2.82551

eV/atom

Energy/atom

-7.64083

eV/atom

Energy above Hull

0.0649

eV/atom

Uncorrected Energy

-7.2234

eV/atom

Volume/atom

12.87

Å³

c/a Ratio

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Yes

Total Mag. Moment

7.0971

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.006980

μB/Å³

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

O · 0.608

Element Family

Metalloid-Nonmetal

Solute Fraction

0.392

Interstitial Fraction

0.152

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.0954

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

9.1072

J/mol·K

Ω Parameter

0.0504

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

49.973%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.9719

smaller = more stable mixing

VEC

3.734

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-59.638

kJ/mol; negative = exothermic mixing

Entropy Norm

0.7902

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (1)

aaaebdui

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-761068

Reference Citation

The crystal structure and related material properties of Na11Ti8(PO4)12 were obtained from the Materials Project database (MP-ID: mp-761068, database version v2026.04.13).

Literature Citation

Horton, M.K., Huck, P., Yang, R.X. et al. Accelerated data-driven materials science with the Materials Project. Nat. Mater. 24, 1522–1532 (2025). https://doi.org/10.1038/s41563-025-02272-0

BibTeX

@article{Horton2025,
  author  = {Horton, Matthew K. and Huck, Patrick and Yang, Ruo Xi and Munro, Jason M. and Dwaraknath, Shyam and Ganose, Alex M. and Kingsbury, Ryan S. and Wen, Mingjian and Shen, Jimmy X. and Mathis, Tyler S. and Kaplan, Aaron D. and Berket, Karlo and Riebesell, Janosh and George, Janine and Rosen, Andrew S. and Spotte-Smith, Evan W. C. and McDermott, Matthew J. and Cohen, Orion A. and Dunn, Alex and Kuner, Matthew C. and Rignanese, Gian-Marco and Petretto, Guido and Waroquiers, David and Griffin, Sinead M. and Neaton, Jeffrey B. and Chrzan, Daryl C. and Asta, Mark and Hautier, Geoffroy and Cholia, Shreyas and Ceder, Gerbrand and Ong, Shyue Ping and Jain, Anubhav and Persson, Kristin A.},
  title   = {Accelerated data-driven materials science with the Materials Project},
  journal = {Nature Materials},
  year    = {2025},
  volume  = {24},
  number  = {10},
  pages   = {1522--1532},
  month   = {oct},
  doi     = {10.1038/s41563-025-02272-0},
  issn    = {1476-4660},
  url     = {https://doi.org/10.1038/s41563-025-02272-0},
  abstract = {The Materials Project was launched formally in 2011 to drive materials discovery forwards through high-throughput computation and open data. More than a decade later, the Materials Project has become an indispensable tool used by more than 600,000 materials researchers around the world. This Perspective describes how the Materials Project, as a data platform and a software ecosystem, has helped to shape research in data-driven materials science. We cover how sustainable software and computational methods have accelerated materials design while becoming more open source and collaborative in nature. Next, we present cases where the Materials Project was used to understand and discover functional materials. We then describe our efforts to meet the needs of an expanding user base, through technical infrastructure updates ranging from data architecture and cloud resources to interactive web applications. Finally, we discuss opportunities to better aid the research community, with the vision that more accessible and easy-to-understand materials data will result in democratized materials knowledge and an increasingly collaborative community.}
}

3D Crystal Structure Rendering

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Raw CIF Data

# generated using pymatgen
data_Na11Ti8(PO4)12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.88197600
_cell_length_b   9.08770384
_cell_length_c   12.59910295
_cell_angle_alpha   89.82029285
_cell_angle_beta   89.87846054
_cell_angle_gamma   89.74665506
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Na11Ti8(PO4)12
_chemical_formula_sum   'Na11 Ti8 P12 O48'
_cell_volume   1016.94166025
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Na  Na0  1  0.28565400  0.79577000  0.82980900  1.0
  Na  Na1  1  0.72489200  0.28737600  0.82708300  1.0
  Na  Na2  1  0.43474500  0.46892500  0.69120400  1.0
  Na  Na3  1  0.16744100  0.27603400  0.68550100  1.0
  Na  Na4  1  0.78621800  0.78640200  0.67477900  1.0
  Na  Na5  1  0.22645100  0.21121500  0.32966000  1.0
  Na  Na6  1  0.82900800  0.71683200  0.32449300  1.0
  Na  Na7  1  0.56362000  0.53585300  0.30870300  1.0
  Na  Na8  1  0.93821300  0.03347100  0.19123600  1.0
  Na  Na9  1  0.27586400  0.71620300  0.17083900  1.0
  Na  Na10  1  0.67243600  0.21516900  0.17324100  1.0
  Ti  Ti11  1  0.24054300  0.46533700  0.89666100  1.0
  Ti  Ti12  1  0.75060400  0.96127000  0.89346000  1.0
  Ti  Ti13  1  0.75967200  0.45853300  0.60487300  1.0
  Ti  Ti14  1  0.25602600  0.96436100  0.60741400  1.0
  Ti  Ti15  1  0.23971600  0.53987700  0.39576600  1.0
  Ti  Ti16  1  0.73999100  0.03547600  0.39935700  1.0
  Ti  Ti17  1  0.26130700  0.04151700  0.10082600  1.0
  Ti  Ti18  1  0.75906000  0.53694300  0.10142000  1.0
  P  P19  1  0.03031600  0.75415900  0.99966800  1.0
  P  P20  1  0.96823700  0.24996100  0.99913900  1.0
  P  P21  1  0.61020600  0.61016500  0.85403000  1.0
  P  P22  1  0.39399100  0.11412500  0.84923300  1.0
  P  P23  1  0.11028400  0.61041700  0.64856800  1.0
  P  P24  1  0.88738400  0.10288600  0.64745100  1.0
  P  P25  1  0.46616600  0.25139700  0.50092000  1.0
  P  P26  1  0.53140100  0.74939900  0.50166400  1.0
  P  P27  1  0.11581600  0.89603700  0.35585600  1.0
  P  P28  1  0.88894300  0.38600700  0.34938400  1.0
  P  P29  1  0.38675500  0.39560900  0.14512500  1.0
  P  P30  1  0.61292300  0.88606300  0.14863300  1.0
  O  O31  1  0.68006800  0.55259000  0.95816600  1.0
  O  O32  1  0.32782900  0.05737800  0.95661100  1.0
  O  O33  1  0.86562600  0.14606200  0.93594600  1.0
  O  O34  1  0.13631500  0.65405400  0.93350700  1.0
  O  O35  1  0.05883900  0.34456500  0.91969100  1.0
  O  O36  1  0.93125500  0.84172900  0.92132600  1.0
  O  O37  1  0.43613600  0.59232800  0.85591200  1.0
  O  O38  1  0.56659200  0.09521600  0.85416900  1.0
  O  O39  1  0.35317500  0.27972300  0.83030300  1.0
  O  O40  1  0.64798000  0.77433400  0.83407200  1.0
  O  O41  1  0.32367200  0.01850900  0.76122800  1.0
  O  O42  1  0.67164300  0.51135900  0.76196500  1.0
  O  O43  1  0.81687700  0.01439100  0.73959800  1.0
  O  O44  1  0.18573400  0.51289100  0.73595100  1.0
  O  O45  1  0.86483700  0.27210400  0.66485600  1.0
  O  O46  1  0.15194900  0.77335200  0.66572000  1.0
  O  O47  1  0.05874300  0.07128700  0.64189100  1.0
  O  O48  1  0.93806800  0.58967100  0.64945600  1.0
  O  O49  1  0.57074300  0.33648900  0.57624600  1.0
  O  O50  1  0.43990200  0.84760600  0.57880300  1.0
  O  O51  1  0.62953500  0.64332900  0.56960800  1.0
  O  O52  1  0.35394900  0.16175700  0.56942100  1.0
  O  O53  1  0.17464200  0.55082500  0.54166700  1.0
  O  O54  1  0.81322200  0.05214700  0.54359900  1.0
  O  O55  1  0.18989400  0.94941600  0.45784900  1.0
  O  O56  1  0.82325600  0.44258300  0.45641000  1.0
  O  O57  1  0.37219700  0.35912400  0.43133700  1.0
  O  O58  1  0.64144200  0.83980600  0.43089100  1.0
  O  O59  1  0.42825200  0.66206400  0.42630100  1.0
  O  O60  1  0.55708000  0.15341000  0.42192900  1.0
  O  O61  1  0.06174600  0.40554800  0.34906200  1.0
  O  O62  1  0.94245200  0.92352500  0.35916100  1.0
  O  O63  1  0.14028300  0.72841400  0.33541900  1.0
  O  O64  1  0.84764700  0.22244800  0.32870300  1.0
  O  O65  1  0.17733000  0.98849700  0.26049200  1.0
  O  O66  1  0.81309500  0.48550200  0.26334400  1.0
  O  O67  1  0.32297300  0.49066900  0.23824100  1.0
  O  O68  1  0.68905600  0.98381200  0.23490500  1.0
  O  O69  1  0.36130400  0.22863500  0.16520700  1.0
  O  O70  1  0.65082100  0.72154400  0.17163300  1.0
  O  O71  1  0.43975200  0.90742500  0.14851700  1.0
  O  O72  1  0.55883300  0.42323100  0.14288500  1.0
  O  O73  1  0.07274100  0.16349700  0.07572800  1.0
  O  O74  1  0.93642000  0.66181600  0.07945400  1.0
  O  O75  1  0.12993800  0.85849700  0.06619200  1.0
  O  O76  1  0.86104200  0.34433800  0.07028600  1.0
  O  O77  1  0.31423100  0.44860600  0.04136400  1.0
  O  O78  1  0.67849800  0.93961000  0.04139000  1.0

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