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Pressure-Induced Irreversible Disorder in $\beta^{\prime}$-Mn$_3$(PO$_4$)$_2$: A High-Pressure X-ray Diffraction and Density-Functional Theory Study

T0 review · 3 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read β′-Mn3(PO4)2 loses crystalline order irreversibly above 14.1 GPa, and density-functional calculations place a mechanical instability at nearly the same pressure, indicating the collapse is intrinsic to the crystal framework.

desk verdict First HP-XRD study of β'-Mn3(PO4)2: the irreversible disorder near 14 GPa looks real, but the elastic-instability claim needs a corrected tensor before it can be used. read the letter →

arxiv 2607.25896 v1 pith:66OIY4QZ submitted 2026-07-28 cond-mat.mtrl-sci physics.chem-phphysics.geo-ph

Ana Melissa P. Brito , Neha Bura , Pablo Botella , Robert Oliva , Alanna Khesley L. da Costa , Fabiana V. da Motta , Mauricio R. D. Bomio , Alfonso Munoz
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Joao Elias Rodrigues Daniel Errandonea
This is my paper · ORCID
classification cond-mat.mtrl-sciphysics.chem-phphysics.geo-ph
keywords high-pressureX-raydiffractionmanganesephosphateirreversiblestructuraldisorderelasticinstabilitycompressibilitytensordensity-functionaltheorypolyhedralcompressionframeworks
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that β′-Mn3(PO4)2, the stable ambient form of manganese phosphate, does not survive compression to 20 GPa as a crystalline material. Instead, near 14.1 GPa it develops irreversible structural disorder: X-ray diffraction peaks broaden and weaken, no known Mn3(PO4)2 polymorph can index the pattern, and the broadened pattern persists after pressure is released. The paper also shows through density-functional calculations that the crystal becomes mechanically unstable near the same pressure, with one elastic eigenvalue turning negative at 14.3 GPa. If true, this means the high-pressure limit of this phosphate is a permanent, partially disordered state rather than a new crystal phase, and it connects that behavior to a specific elastic softening of the polyhedral framework.

What carries the argument

The load-bearing computational object is the pressure-dependent elastic stiffness tensor of the monoclinic P21/c cell, evaluated at each optimized volume. Mechanical stability is judged through the generalized Born stability criteria; at 14.3 GPa one eigenvalue becomes negative, meaning certain strain modes lower the elastic energy and the crystal is unstable to small perturbations. The complementary structural mechanism is the polyhedral-unit analysis: nearly rigid PO4 tetrahedra versus soft, distorting MnO5/MnO6 polyhedra, with three Mn sites switching from five- to six-fold coordination and one Mn–O bond anomalously stretching. This combination is what the paper uses to tie the observed i

What would settle it

Compress a fresh sample to 20 GPa in a quasi-hydrostatic medium such as helium or neon, then decompress to ambient pressure: if the recovered X-ray diffraction pattern is sharp and matches the starting β′ phase, the claimed irreversibility and intrinsic disorder are wrong. A second check would be measuring single-crystal elastic constants near 14 GPa: if all eigenvalues remain positive, the predicted mechanical instability is absent.

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Extended reading notes

Core claim

The central discovery is that β′-Mn3(PO4)2 remains crystalline up to about 14 GPa but then undergoes a loss of long-range crystallographic order that is irreversible upon decompression. The authors report a third-order Birch–Murnaghan equation of state with bulk modulus K0 = 81(2) GPa and strongly anisotropic compression, with the most compressible principal axis lying in the ac plane. Density-functional calculations reproduce the measured compressional behavior and attribute it to distortions of MnO5/MnO6 polyhedra while PO4 tetrahedra remain nearly rigid. Three initially penta-coordinated Mn sites become octahedrally coordinated below 8 GPa, and one MnO6 polyhedron shows anomalous bond len

Load-bearing premise

The quantitative lattice and compressibility results assume that all 117 internal atomic coordinates stay at their ambient-pressure values during compression (Section III.a), because the powder data could not refine them; if those coordinates shift substantially under pressure, as the DFT calculations suggest, the refined lattice parameters and derived elastic quantities could be biased.

Editorial extensions

If this is right

  • The crystalline form of β′-Mn3(PO4)2 cannot be used as a stable phase above roughly 14 GPa; any application requiring crystalline integrity would instead produce a permanently disordered material.
  • The reported bulk modulus and full anisotropic compressibility tensor provide quantitative input for modeling the behavior of manganese phosphates in high-pressure and geophysical settings.
  • The correspondence between the predicted elastic instability and the experimental disorder onset suggests that other structurally complex A3(PO4)2 frameworks may similarly degrade irreversibly rather than transform to new crystalline phases.
  • The predicted pressure-driven coordination changes at individual Mn sites offer a microscopic fingerprint that could be observed with element-specific spectroscopies under compression.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The quantitative lattice-parameter, equation-of-state, and compressibility results could be biased if the internal atomic coordinates shift substantially under pressure, as the DFT calculations indicate they do; a high-pressure single-crystal or better-resolved powder study would test this directly.
  • The DFT prediction that three Mn sites become octahedrally coordinated between about 4.7 and 7.6 GPa could be probed with Mn K-edge X-ray absorption spectroscopy under pressure, providing an experimental check of the proposed densification mechanism before the 14 GPa collapse.
  • The anomalous stretching of a single Mn–O bond resembles a soft-mode precursor, so Raman or inelastic X-ray scattering up to 14 GPa might reveal a phonon that softens toward zero frequency, giving a direct dynamical signature of the instability.
  • A separate compression-decompression cycle that stops just below and just above 14.1 GPa could map the irreversibility boundary and test whether crossing the elastic instability is required to produce the permanent disorder.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper reports a combined high-pressure synchrotron XRD and DFT study of β′-Mn₃(PO₄)₂ up to 20 GPa. The experiments show that the monoclinic β′ phase survives to about 13 GPa, but at 14.1 GPa the diffraction peaks broaden and weaken abruptly, and the degraded pattern persists after decompression to 0.7 GPa. The authors fit a third-order Birch–Murnaghan equation of state (K₀ = 81(2) GPa) and derive the compressibility tensor. DFT reproduces the lattice-parameter evolution, shows that compression is accommodated by Mn–O polyhedral distortions while PO₄ tetrahedra remain rigid, and predicts that three penta-coordinated Mn sites become octahedral before the transition. Elastic-constant calculations are used to claim that the crystal becomes mechanically unstable near 14.3 GPa, correlating with the observed loss of crystallinity. The central experimental finding is that compression produces an irreversible, disordered state rather than a crystalline high-pressure phase.

Significance. If the conclusions hold, the paper provides a useful data point for the high-pressure behavior of complex A₃(PO₄)₂ frameworks: structurally complex, distorted frameworks may undergo irreversible loss of long-range order instead of a cooperative crystalline transition. The work combines synchrotron XRD with DFT, and several computational choices are well grounded: U_eff = 4.3 eV is a literature value with a sensitivity test, the magnetic ordering is selected by energy minimization among several configurations, and the experimental/computational comparison is not fitted to the transition pressure. These strengths make the experimental observation credible. However, the computational support for elastic instability rests on elastic tensors that contain internal inconsistencies, so the central mechanistic link requires verification before the conclusions can be accepted in their present form.

major comments (3)
  1. [III.e, Tables 2 and 3] The elastic-constant data are internally inconsistent. For monoclinic P2₁/c, the symmetry-allowed constants include C15, C25, C35 and C46, while C45 is symmetry-forbidden. Table 2 lists C45 = 0.4 GPa and omits C35; Table 3 lists C35 = 6.8 GPa and omits C45. Moreover, the text states 'C33 > C11 > C22', but Table 2 gives C22 = 159.7, C11 = 151.5, C33 = 140.6 GPa. These errors directly affect the eigenvalue analysis and the generalized Born criterion, including the expression displayed in the text, which uses C35. The claim that one eigenvalue becomes negative at 14.3 GPa is therefore not currently supported. Please provide the full 6×6 tensors at both pressures, correct the symmetry-allowed entries, and re-evaluate the Born criteria and eigenvalues.
  2. [III.a and III.b] All quantitative experimental results — lattice parameters, EoS parameters, and the compressibility tensor — come from Rietveld refinements in which all 117 internal atomic coordinates were fixed at their ambient-pressure literature values. The paper acknowledges that the DAC data cannot refine these coordinates. Since the DFT calculations show substantial internal rearrangements (e.g., coordination changes at several Mn sites), the fixed-coordinate model may bias the derived unit-cell parameters and hence K₀, K₀′, and the compressibility axes. The qualitative irreversible-broadening result is unaffected, but the claimed quantitative agreement between experiment and DFT (Section III.b, Figure 5) should be either reassessed with a sensitivity test or stated with this caveat.
  3. [III.a, Abstract, and Conclusions] The manuscript’s central claim is phrased as a 'loss of long-range crystallographic order.' The diffraction data demonstrate irreversible peak broadening and weakening, but the authors themselves note that the data do not uniquely distinguish partial amorphization, nanocrystallization, severe microstrain, defect accumulation, or unresolved phase coexistence. The abstract and conclusions nevertheless state the stronger interpretation. Please temper the wording to match the evidence, or provide additional characterization (e.g., recovered-sample TEM, diffuse scattering analysis, or a quantitative strain/size analysis) that discriminates among these possibilities.
minor comments (4)
  1. [II.a] Typo: 'Precipitation was induced by adding by adding ammonium hydroxide' — remove the duplicated 'by adding'.
  2. [III.b] Reference [25] is cited for the bulk modulus of Co₃(VO₄)₂ (122 GPa), but [25] is the PBEsol functional paper. Please check and correct the citation.
  3. [Author contributions] G. Garbarino is listed in the author-contribution statement but does not appear in the author list. Add the author or correct the contribution statement.
  4. [III.e, Table 2 caption] Please state explicitly whether the reported constants are the raw second-order elastic constants or the pressure-corrected constants used in the Born analysis. The text describes a pressure correction, but it is not clear how it was applied to the values in Tables 2 and 3.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the experimental disorder onset and the DFT elastic-instability claim are independent, and no prediction reduces to a fitted input or a self-citation chain.

full rationale

The paper's central derivation is self-contained. The experimental claim of irreversible pressure-induced disorder above 14.1 GPa is based directly on in-situ synchrotron XRD patterns (Figs. 3 and 4), including peak broadening and weakening and their persistence after decompression; it does not depend on any parameter fitted to that outcome. The DFT calculations are independent: U_eff = 4.3 eV is a standard literature value with an explicit sensitivity test, the lowest-energy spin configuration is selected by energy minimization, and the 14.3 GPa elastic instability emerges from diagonalizing the calculated elastic tensor and evaluating generalized Born criteria, with no parameter tuned to match the experimental 14.1 GPa transition. The comparison between DFT and experiment (EoS parameters, unit-cell evolution) is a genuine benchmark rather than a fitted reproduction. Self-citations to related phosphates and pressure-medium behavior are used as supporting context and analogy, not as the load-bearing basis of the present conclusions. The manuscript even includes explicit caveats that the data do not uniquely determine the microscopic nature of the transformed state and that the calculations do not uniquely identify the transformation pathway. The elastic-tensor inconsistencies noted by the skeptic (C45 vs C35 in Tables 2 and 3, and the text statement C33 > C11 > C22 contradicting the tabulated values) are potential numerical or typographical errors that affect reliability of the instability claim, but they are not instances of circular reasoning. No step reduces, by construction or by self-citation, to its own inputs.

Assumptions & free parameters 5 free parameters · 9 assumptions · 0 invented entities

No new particles, forces, or entities are introduced. The disordered state is an interpretation of existing XRD data, not a new entity. The main input choices are the DFT+U parameter, the BM3 fit parameters, and the coordination-shell cutoff.

free parameters (5)
  • Ueff (GGA+U effective Hubbard parameter) = 4.3 eV
    Standard literature value chosen for Mn 3d electrons; sensitivity analysis (2-8 eV) changes bulk modulus by <5%, so weakly dependent.
  • V0 (BM3 equation-of-state ambient volume) = 1861(1) Å3 (exp); 1869(1) Å3 (DFT)
    Fitted in third-order Birch-Murnaghan fit to P-V data; anchors the reported compressibility.
  • K0 (BM3 bulk modulus) = 81(2) GPa (exp); 86(3) GPa (DFT)
    Fitted parameter; primary reported elastic result, compared across experiment and DFT.
  • K0' (BM3 pressure derivative) = 3.3(2) (exp); 2.9(4) (DFT)
    Fitted parameter; constrained by data only up to ~13 GPa.
  • Mn-O first-coordination-shell cutoff = 2.75 Å
    Hand-chosen threshold from Stephens & Calvo (1969); determines which Mn sites are classified as penta- vs octa-coordinated and the reported coordination transitions.
assumptions (9)
  • standard math Third-order Birch-Murnaghan equation of state describes the pressure-volume data.
    Used in Sec. III.b to extract V0, K0, K0'.
  • domain assumption PBEsol+U (Ueff=4.3 eV) adequately captures Mn 3d electron correlation and structural energetics.
    Sec. II.d; the U sensitivity test covers bulk modulus only, not elastic constants or the disorder mechanism.
  • domain assumption The ++−− antiferromagnetic spin arrangement is the true ground state at all pressures.
    Sec. II.d; lowest among arrangements examined, but the search is not exhaustive and spin state is not measured experimentally.
  • domain assumption Static 0 K DFT can be compared directly with room-temperature XRD.
    Sec. II.d; authors justify by prior phosphate studies, but no phonon or thermal corrections are included.
  • domain assumption The 4:1 methanol-ethanol medium remains effectively hydrostatic through 14.1 GPa.
    Sec. III.a; known hydrostatic limit ~10 GPa, authors argue FWHM and prior neon studies support intrinsic behavior.
  • standard math Generalized Born stability criteria and the Le Page elastic-constant method are valid for this monoclinic system.
    Sec. II.d and Sec. III.e; criteria taken from Wu et al. (2007).
  • domain assumption The 2.75 Å Mn-O cutoff defines the coordination shell; bonds beyond it are not part of the first shell.
    Sec. I and Sec. III.c; coordination-evolution claims depend on this threshold.
  • domain assumption Copper pressure scale (Dewaele et al. 2004) yields accurate pressures.
    Sec. II.c; all pressure values rely on the Cu equation of state.
  • domain assumption Decomposition products MnO + P2O5 and known Mn3(PO4)2 polymorphs cannot explain the high-pressure XRD patterns.
    Sec. III.a; authors state patterns are inconsistent with these phases, but no detailed fit is shown.

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Pith. "Pith review of Pressure-Induced Irreversible Disorder in $\beta^{\prime}$-Mn$_3$(PO$_4$)$_2$: A High-Pressure X-ray Diffraction and Density-Functional Theory Study." pith.science (2026). https://pith.science/paper/66OIY4QZ

@misc{pith2026260725896,
  author       = {Pith},
  title        = {Pith review of: Pressure-Induced Irreversible Disorder in $\beta^\prime$-Mn$_3$(PO$_4$)$_2$: A High-Pressure X-ray Diffraction and Density-Functional Theory Study},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/66OIY4QZ}},
  note         = {Machine review of arXiv:2607.25896}
}
abstract

The high-pressure structural behavior of $\beta^\prime$-Mn$_3$(PO$_4$)$_2$ was investigated using synchrotron X-ray diffraction up to 20 GPa combined with density-functional theory calculations. At ambient conditions, $\beta^\prime$-Mn$_3$(PO$_4$)$_2$ crystallizes in a monoclinic structure that exhibits strongly anisotropic compression. The pressure dependence of the unit-cell volume was described using a third-order Birch--Murnaghan equation of state, and the principal axes of compressibility were determined. Above 14.1 GPa, significant broadening and weakening of the diffraction peaks are attributed to the onset of irreversible pressure-induced structural disorder associated with the loss of long-range crystallographic order. The disordered state persists after decompression to ambient pressure, demonstrating the irreversible nature of the transformation. The calculations accurately reproduce the experimental compressional behavior and provide insights into the microscopic structural evolution under pressure. Compression is mainly accommodated through distortions of the Mn--O polyhedra, whereas the PO$_4$ tetrahedra behave as comparatively rigid units. Several initially penta-coordinated Mn sites progressively evolve toward octahedral coordination under compression, while selected MnO$_6$ polyhedra exhibit anomalous distortions and elastic softening preceding the onset of disorder. Elastic constant calculations further reveal that the crystalline phase becomes mechanically unstable near the experimentally observed transition pressure. The combined experimental and computational results suggest that the HP response of $\beta^\prime$-Mn$_3$(PO$_4$)$_2$ is influenced by the interplay between framework complexity, anisotropic polyhedral compressibility, and elastic instability, providing new insight into pressure-induced structural degradation in structurally complex phosphate frameworks.

Figures

Figures reproduced from arXiv: 2607.25896 by the authors.

Figure 1
Figure 1. XRD pattern measured at ambient conditions. The dots represent the experiment. The red line is the Rietveld refinement, the blue line the residual, and the green ticks identify the Bragg peak positions. R-values of the refinement are given in the plot. The refinement was performed assuming the atomic positions reported in the literature.20 Selected high￾intensity Bragg reflections are labeled with their Miller indic… view at source ↗
Figure 2
Figure 2. Crystal structure of β’-Mn3(PO4)2. MnO6 octahedra are represented in yellow and MnO5 polyhedra in blue. The PO4 tetrahedra are shown in green. Red spheres represent oxygen atoms [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 4
Figure 4. Full width at half maximum (FWHM) of XRD peaks identified in [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figures from the paper (2 more)
Figure 8
Figure 8. Figure 8: Electron localization function (ELF) maps of β′-Mn₃(PO₄)₂ at 0 GPa (top) and 14 GPa (bottom). The color scale ranges from 0 (blue) to 1 (red). Strong electron localization around the oxygen atoms indicates the highly covalent nature of the P–O bonds, while the lower lo…
Figure 9
Figure 9. Figure 9: Spin-polarized total density of states (DOS, black lines) and projected density of states (PDOS) of the Mn 3d (blue lines) and O 2p (red lines) orbitals of β′-Mn₃(PO₄)₂ at 0 GPa (top) and 14 GPa (bottom). Positive and negative values correspond to the spin-up and spin￾…

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Works this paper leans on

42 extracted references

  1. [1]

    X. Ye, X. Wang, Z. Liu, B. Zhou, L. Zhou, H. Deng and Y . Long, Dalton Trans., 2022, 51, 1745-1753

    2022

  2. [2]

    Muñoz, S

    A. Muñoz, S. Radescu, A. Mujica and D. Errandonea, J. Phys. Chem. C, 2026, 130, 3201-3225

    2026

  3. [3]

    H. K. Mao, B. Chen, J. Chen, K. Li, J. F . Lin, W. Yang and Q. Zeng, Matter and Radiation at Extremes, 2018, 3, 141-207

    2018

  4. [4]

    Y . Ding, D. Haskel, Y . C. Tseng, E. Knoesel, J. Liu, J. C. Lang, J. Poole, and H. K. Phys. Rev. Lett., 2005, 94, 157202

    2005

  5. [5]

    Zhong, H

    W. Zhong, H. Zhang, E. Karaca, J. Zhou, S. Kawaguchi, H. Kadobayashi, X. Yu, D. Errandonea, B. Yue and F . Hong, Phys. Rev. Lett., 2024, 133, 066001

    2024

  6. [6]

    S. Guo, Y . Zhang, K. Bu, Y . Zhan and X. Lü, Chem. Commun., 2025, 61, 1773-1789

    2025

  7. [7]

    Zhang, Y

    L. Zhang, Y . Wang, J. Lv and Y . Ma, Nature Reviews Materials, 2017, 2, 17005. 31

    2017

  8. [8]

    Grèbol-Tomàs, J

    P . Grèbol-Tomàs, J. Ibáñez-Insa, J. M. Trigo-Rodríguez, E. Peña-Asensio, R. Oliva, D. Díaz-Anichtchenko, P . Botella, J. Sánchez-Martín, R. Turnbull, D. Errandonea, A. Liang, C. Popescu and J. Sort, Geoscience Frontiers, 2025, 16, 102110

    2025

Show all 42 references
  1. [9]

    Errandonea and F

    D. Errandonea and F . J. Manjon, Prog. Mat. Sci., 2008, 53, 711-773

    2008

  2. [10]

    Errandonea and A

    D. Errandonea and A. B. Garg, Prog. Mat. Sci., 2018, 97, 123-169

    2018

  3. [11]

    Errandonea, J

    D. Errandonea, J. Appl. Phys., 2020, 128, 040903

    2020

  4. [12]

    Kesari, A

    S. Kesari, A. B. Garg, O. Clemens, B. Joseph and R. Rao, ACS Omega, 2022, 7, 3099–3108

    2022

  5. [13]

    Diaz-Anichtchenko, R

    D. Diaz-Anichtchenko, R. Turnbull, E. Bandiello, S. Anzellini and D. Errandonea, Crystals, 2020, 10, 910

    2020

  6. [14]

    Díaz-Anichtchenko, R

    D. Díaz-Anichtchenko, R. Turnbull, E. Bandiello, S. Anzellini, S. N. Achary and D. Errandonea, J. Mater. Chem. C, 2021, 9, 13402-13409

    2021

  7. [15]

    Turnbull, J

    R. Turnbull, J. Sánchez Martín, A. Liang, D. Díaz -Anichtchenko, C. Popescu, K. S. Rao, S. N. Achary, A. Muñoz, V . Panchal and D. Errandonea, Dalton Trans., 2024, 53, 14278-14288

    2024

  8. [16]

    Gauvin, F

    M. Gauvin, F . Dassenoy, C. Minfray, J. M. Martin, G. Montagnac and B. Reynard, J. Appl. Phys., 2007, 101, 063505

    2007

  9. [17]

    Jaulmes, A

    S. Jaulmes, A. Elfakir, M. Quarton, F . Brunet and C. Chopin, J. Solid State Chem. 1997, 129, 341-345

    1997

  10. [18]

    A. G. Nord and H. Annersten, Acta Chem. Scand. A, 1987, 41, 56-58

    1987

  11. [19]

    O. S. Volkova, L. V . Shvanskaya, E. A. Ovchenkov, E. A. Zvereva, A. S. Volkov, D. A. Chareev, K. Molla, B. Rahaman, T. Saha- Dasgupta and A. N. Vasiliev, Inorg. Chem., 2016, 55, 10692−10700

    2016

  12. [20]

    J. S. Stephens and C. Calvo, Canadian Journal Chem., 1969, 47, 2215-2225

    1969

  13. [21]

    Klotz, J

    S. Klotz, J. C. Chervin, P . Munsch and G. Le Marchand, J. Physics D: Applied Physics, 2009, 42, 075413

    2009

  14. [22]

    Dewaele, P

    A. Dewaele, P . Loubeyre and M. Mezouar, Phys. Rev. B, 2004, 70, 094112

    2004

  15. [23]

    Kresse and J

    G. Kresse and J. Furthmüller, Comput. Mat. Sci. 1996, 6, 15-50

    1996

  16. [24]

    P. E. Blöchl, Phys. Rev. B 1994, 50, 17953-17979

    1994

  17. [25]

    J. P . Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Phys. Rev. Lett. 2008, 100, 136406

    2008

  18. [26]

    H. J. Monkhorst and J. D. Pack, Phys. Rev. B 1976, 13, 5188-5192

    1976

  19. [27]

    S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P . Sutton, Phys. Rev. B 1988, 57, 1505-1509

    1988

  20. [28]

    Le Page and P

    Y. Le Page and P. Saxe, Phys. Rev. B 2002, 65, 104104. 32

    2002

  21. [29]

    Z. Wu, E. Zhao, K. Xiang, X. Hao, X. Liu, and J. Meng, Phys . Rev. B 2007, 76, 054115

    2007

  22. [30]

    Funamori, M

    N. Funamori, M. Funamori, R. Jeanloz and N. Hamaya, J. Appl. Phys., 1997, 82, 142–146

    1997

  23. [31]

    Lacomba-Perales, D

    R. Lacomba-Perales, D. Errandonea, Y . Meng and M. Bettinelli, Phys. Rev. B. 2010, 81, 064113

    2010

  24. [32]

    Sánchez-Martín, J

    J. Sánchez-Martín, J. Pellicer-Porres, A. Liang, J. Ibáñez, R. Oliva, C. Popescu, Z. He, P . Rodríguez -Hernández, A. Muñoz and D. Errandonea, J. Phys. Chem. C , 2023,127, 21684-21694

    2023

  25. [33]

    Birch, Phys

    F . Birch, Phys. Rev., 1947, 71, 809–824

    1947

  26. [34]

    G. I. Csonka, J. P . Perdew, A. Ruzsinszky, P . H. T. Philipsen, S. Lebègue4 J. Paier, O. A. Vydrov and J. G. Ángyán, Phys. Rev. B, 2009, 79, 155107

    2009

  27. [35]

    Zhai and X

    S. Zhai and X. Wu, Solid State Communications, 2010, 150, 443-445

    2010

  28. [36]

    Sánchez -Martín, D

    J. Sánchez -Martín, D. Errandonea, H. S. R. Mosafer, W. Paszkowicz, R. Minikayev, R. Turnbull, M. Berkowski, J. Ibáñez -Insa, C. Popescu, A. Fitch, P . Rodríguez-Hernández and A. Muñoz, CrystEngComm, 2023, 25, 1240-1251

    2023

  29. [37]

    Errandonea, C

    D. Errandonea, C. Popescu, S. N. Achary, A. K. Tyagi and M. Bettinelli, Mater. Res. Bull., 2014, 50, 279– 284

    2014

  30. [38]

    Lertkiattrakul, M

    M. Lertkiattrakul, M. L. Evans and M. J, Cliffe, JOSS, 2023, 8, 5556

    2023

  31. [39]

    Gomis, B

    O. Gomis, B. Lavina, P . Rodríguez -Hernández, A. Muñoz, R. Errandonea, D. Errandonea and M Bettinelli, J. Phys.: Condens. Matter, 2017, 29, 095401

    2017

  32. [40]

    Z. J. Wu, E. J. Zhao, H. P . Xiang, X. F . Hao, X. J. Liu and J. Meng, Phys. Rev. B, 2007, 76, 054115

    2007

  33. [41]

    Hill, Proc

    R. Hill, Proc. Phys. Soc. A, 1952, 65, 349-354

    1952

  34. [42]

    Pugh, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1954, 45, 823–843

    F . Pugh, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1954, 45, 823–843. 33 Table of contents entry Framework complexity and elastic instability govern the high-pressure response of β′-Mn₃(PO₄)₂, leading to irreversible degradation of cryst...

    1954

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