Pith. sign in

REVIEW 3 major objections 5 minor 112 references

The Recurrent Structural Frameworks of Stable Inorganic Materials

T0 review · 3 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Stable inorganic materials compress into a small set of recurring structural frameworks: 23,160 compounds yield 6,820 frameworks and 2,382 prototypes.

desk verdict Useful recurrence-based prototype catalog, but the paper needs to reconcile its headline numbers with its own filtering step before the abstract can be trusted. read the letter →

arxiv 2607.17911 v1 pith:O25H6CK2 submitted 2026-07-20 cond-mat.mtrl-sci

Roee Asher , Nadav Moav , Lee A. Burton This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords structuralframeworksprototypescrystalstructureclassificationconvexhullmaterialsdiscoveryrecurrenceinorganicspecies-independentmatching
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

The paper tries to show that the vast space of possible crystal structures is not uniformly populated: experimentally realized, thermodynamically stable inorganic materials cluster into a surprisingly small number of recurring geometric frameworks. Analyzing 23,160 experimentally reported ground-state compounds, it finds only 6,820 distinct frameworks, of which 2,382 are shared by two or more chemically distinct materials and are promoted to structural prototypes. Metallic and intermetallic compounds show the strongest reuse (6,270 materials in 535 frameworks), while ionic compounds still concentrate strongly (5,557 materials in 1,704 frameworks). This matters because it replaces a worldview in which every new composition brings a new structure with one in which a limited set of favorable geometries is rediscovered across chemistry, giving structure prediction a quantitative prior. A sympathetic reader would take this as evidence that inorganic structure space is highly compressible and that prototype recurrence, not geometric uniqueness, defines structural families.

What carries the argument

The engine is a species-independent geometric structure comparison that ignores atomic identity and matches occupied crystallographic sites within chosen tolerances (length, angle, and site displacement). Structures are compared only within the same stoichiometric class (ANX notation) so that chemically incompatible geometries, such as CsCl and elemental bcc, are not merged. An iterative clustering against a growing set of representative frameworks (choosing the largest-cell representative) avoids exhaustive pairwise comparison. A framework becomes a prototype only when it is realized by at least two chemically distinct, ground-state materials. Tolerance curves are used to select a plateau w

What would settle it

Apply the same clustering to the 9,190 excluded complex-stoichiometry structures; if they show a frameworks-to-materials ratio close to 1 (much weaker compression), the claim would hold only for simple stoichiometries. A second decisive test: cluster randomly generated, composition-blind arrangements with the same tolerances; if random structures compress as strongly, the effect would reflect the matching algorithm rather than stability.

Watch

Extended reading notes

Core claim

The central claim is that structural frameworks that recur across multiple chemically distinct, thermodynamically stable materials form a small and quantifiable set. Treating crystal structures as species-independent geometric arrangements, and grouping them with a tolerant, atom-identity-agnostic matching procedure, the paper reports that 23,160 experimentally realized ground-state structures reduce to 6,820 frameworks, and that only 2,382 of these appear for more than one chemical composition and thus qualify as prototypes. Recurrence is most dramatic for metallic systems, where 6,270 materials occupy 535 frameworks, and remains strong for ionic compounds. The result is offered as an empir

Load-bearing premise

The claim rests on the assumption that the computationally determined set of experimentally reported ground-state materials used here faithfully represents all thermodynamically stable inorganic materials, despite excluding many complex-stoichiometry compounds.

Editorial extensions

If this is right

  • New compounds should continue to be discovered faster than new frameworks: exploring composition space is predicted to expand the compound count without proportionally expanding structural diversity.
  • Prototype recurrence frequencies give a physically motivated ranking that can seed element-substitution searches and crystal-structure prediction methods with the most probable templates.
  • The recurrence-based catalog supplies a reproducible benchmark for evaluating structure-similarity metrics and machine-learning representations of crystals.
  • Canonical prototypes (rock-salt, spinel, perovskite, rutile, close-packed metals) are recovered automatically from geometry alone, with prevalence counts attached.
  • The ten most common space groups account for more than half of both metals and ionic compounds, indicating that symmetry is also concentrated.

Reading between the lines

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

  • The compression ratio may be underestimated: the filters exclude 9,190 structures with stoichiometric coefficients above four, and if those complex chemistries are structurally more diverse, the 6,820-framework count would grow once they are included.
  • Recurrence frequency could be used as a Bayesian prior for ranking candidate structures in discovery pipelines; the paper stops at providing the frequencies, not the probabilistic model.
  • The same recurrence analysis applied to predicted but not-yet-synthesized materials (e.g., from generative models) would test whether computationally proposed structures expand framework space or rediscover the same prototypes — a natural next experiment.
  • Because matching ignores atom identity within a stoichiometry class, frameworks that appear across very different chemistries might occasionally be false merges (e.g., a metal packing and an ionic arrangement with the same site geometry); the reported counts depend on the ANX restriction.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes a recurrence-based classification of stable inorganic materials. Using species-independent geometric matching (StructureMatcher in PyMatGen) on 23,160 Materials Project structures on the thermodynamic convex hull, it reports that these materials collapse to 6,820 distinct structural frameworks, of which 2,382 recur across multiple chemically distinct materials and are designated structural prototypes. The authors further filter the dataset to separately analyze 6,270 metallic/intermetallic and 5,557 ionic compound materials, finding stronger recurrence in metallic systems (535 frameworks, 327 prototypes) than in compounds (1,704 frameworks, 696 prototypes). They validate the catalog against well-known prototype collections, discuss comparisons with AFLOW and ICSD, and propose the recurrence frequencies as empirical priors for structure prediction and materials informatics.

Significance. If the claims are robust, the paper provides a valuable quantitative catalog of recurring structural frameworks and a physically motivated measure of prototype prevalence. The work ships reproducible code and data (GitHub link is provided), and the sensitivity analysis for matching tolerances is a strength. The recurrence-based definition of prototypes is a meaningful conceptual shift from mere structural enumeration. However, the headline counts and the general conclusion that 'stable inorganic materials occupy a highly compressed region of structure space' depend on a dataset definition that is internally inconsistent in the manuscript, and the prototype threshold is ambiguously specified. These issues must be resolved before the significance can be fully assessed.

major comments (3)
  1. [Methods vs. Results; Table 1] The manuscript gives contradictory descriptions of the dataset. Methods states that 'Additional preprocessing excluded structures containing hydrogen, noble gases, structures with more than 100 atoms per unit cell, stoichiometric coefficients exceeding four, and structures containing more than three distinct cation or anion species.' But Results then says that applying the filtering criteria to the 'initial dataset of 23,160' excluded 1,457 hydrogen-containing, 64 noble-gas-containing, 55 miscellaneous, 496 >100-atom, 9,190 >4-coefficient, and 71 >3-species structures, leaving 11,827. These numbers sum to 11,333, exactly 23,160 minus 11,827. Thus the 'full' 23,160 apparently includes structures that Methods claims were already pre-excluded. This is load-bearing: the headline compression (23,160 to 6,820 frameworks, 2,382 prototypes) either includes the 9,190 high-stoichiometry structures
  2. [Results, Figure 2, prototype definition] The recurrence threshold for prototype status is ambiguous. The text defines prototypes as frameworks that 'recur across multiple chemically distinct materials,' which normally implies at least two occurrences. However, Figure 2's workflow shows a decision box labeled '>2 matches?' If the operational criterion is strictly greater than two matches (i.e., at least three materials), then the reported 2,382 prototype count uses a different threshold than the stated definition. This affects the central catalog and the comparison with Table 3. Please specify the exact integer threshold used, justify it, and report whether the counts are sensitive to the choice between '≥2' and '>2'.
  3. [Results, Figure 3, Sensitivity analysis] The sensitivity analysis identifies a plateau near 6,800 frameworks, but all final counts (6,820, 2,382, 1,940, 907, etc.) are presented as exact numbers without uncertainty bounds. Since the paper's central claim is about the degree of compression, the authors should report the range of framework and prototype counts across the plateau (e.g., for length tolerance 0.4–0.6, angle 4°–6°, site 0.2–0.4). This would quantify the robustness that the current text asserts only qualitatively.
minor comments (5)
  1. [Abstract] The phrase 'Within a filtered dataset' is vague. Specify the filtering criteria (e.g., excluding complex stoichiometries, hydrogen-containing, etc.) in the abstract, especially since the filtering is central to the metals/compounds split.
  2. [Table 3] The 'Count' column for elemental frameworks (e.g., Na for HCP, Al for FCC) uses the abundance-based naming convention from Methods, but this may confuse readers who expect conventional prototype names. Add a footnote explaining that the proposed name is the abundance-selected representative formula.
  3. [Discussion, AFLOW comparison] The statement 'AFLOW XtalFinder identifies 15,205 frameworks among 34,820 unique materials that came from 60,390 ICSD entries' lacks a citation for the specific numbers. Either cite the exact table in Ref. [36] or [50], or state that these are from the present analysis of the AFLOW Encyclopedia.
  4. [Figure 3] The plateau near 6,800 is not visually clear in all three panels, particularly in (c). Add gridlines or a shaded region to guide the reader to the claimed plateau.
  5. [General] The term 'stabilized near 6,800' in the Results should be 'stabilizes' for the singular subject 'the number of identified frameworks.'

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the recurrence catalog is computed directly from structural data and validated against external prototype collections.

full rationale

This is a descriptive/analytic study rather than a derivation. The pipeline is: (1) take experimentally reported Materials Project convex-hull structures; (2) filter by explicit criteria; (3) cluster geometries with StructureMatcher using tolerances chosen from a sensitivity plateau; (4) define prototypes as frameworks recurring across chemically distinct materials; (5) validate against known prototype collections. None of these steps takes the target conclusion as an input. The prototype definition is an operational definition, not a self-justifying derivation: recurrence is computed from geometric matching, and the catalog is the output. Tolerance selection is calibrated on the same data, but the paper selects a plateau regime rather than a count that forces a preconceived number; the reported counts are descriptive. The validation in Table 3 is an external benchmark against curated prototype collections, so the recovery of known structures is an independent check. The only author-overlapping citation (Ref. 48, used for assigning cationic/anionic roles) is a methodological detail in the metals-vs-compounds partition and does not bear on the full-dataset compression claim; it is published external work, not a self-imported uniqueness theorem. The dataset-scope concern raised by the skeptic (exclusion of 9,190 high-stoichiometry structures) is a generalizability limitation, not circularity: the paper explicitly states the filtered scope and reports the excluded counts, and the full-dataset framework count (23,160 to 6,820) is also reported independently of that filter. No equation reduces to its own input, no fitted parameter is renamed as a prediction, and no load-bearing conclusion depends on a self-citation chain. No significant circularity.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central counts depend on several hand-chosen thresholds and domain assumptions; each is disclosed in the paper but none is independently calibrated against a ground-truth structural classification.

free parameters (5)
  • StructureMatcher length tolerance = 0.5 (fractional)
    Chosen from sensitivity plateau in Figure 3a; affects number of frameworks.
  • angle tolerance = 5 degrees
    Chosen from plateau in Figure 3b.
  • site tolerance = 0.3 (normalized displacement)
    Chosen from lower end of plateau in Figure 3c to avoid merging.
  • recurrence threshold for prototype = >2 matches (Figure 2); text says 'multiple'
    Defines which frameworks are called prototypes; exact threshold is not stated unambiguously in prose.
  • Filtering thresholds = ≤100 atoms/unit cell; stoichiometric coefficients ≤4; ≤3 distinct cation/anion species; exclude H and noble gases
    Dataset-scope cutoffs remove 9,190 high-stoichiometry structures and others; they shape all reported counts.
assumptions (4)
  • domain assumption Materials Project convex-hull structures are a faithful proxy for experimentally realized, thermodynamically stable inorganic materials.
    The entire dataset is drawn from Materials Project DFT hull predictions (Methods), so computed stability and experimental realization are assumed aligned.
  • domain assumption StructureMatcher with FrameworkComparator correctly identifies geometric equivalence at the chosen tolerances.
    Structural equivalence is defined by this software's matching; no independent check of per-pair equivalence is provided.
  • domain assumption ANX stoichiometric classification with fixed cation/anion assignment (e.g., As always a cation) correctly separates metals from ionic compounds.
    Used to split the dataset into metallic/intermetallic vs compound subsets (Methods).
  • domain assumption The excluded classes (H-containing, noble-gas, >100 atoms, high stoichiometry, >3 cation/anion species) would not overturn the compressibility conclusion.
    The central claim is generalized to 'stable inorganic materials' although 9,190 high-stoichiometry structures and others are excluded from the filtered analysis.

how reviews work

0 comments
Cite this review

Pith. "Pith review of The Recurrent Structural Frameworks of Stable Inorganic Materials." pith.science (2026). https://pith.science/paper/O25H6CK2

@misc{pith2026260717911,
  author       = {Pith},
  title        = {Pith review of: The Recurrent Structural Frameworks of Stable Inorganic Materials},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O25H6CK2}},
  note         = {Machine review of arXiv:2607.17911}
}
read the original abstract

The number of possible crystal structures vastly exceeds the number realized among thermodynamically stable inorganic materials, suggesting that experimentally accessible structure space is organized around a limited set of preferred structural frameworks. Analysis of 23,160 structures on the thermodynamic convex hull identifies 6,820 distinct structural frameworks, of which 2,382 recur across multiple chemically distinct materials and are therefore classified as structural prototypes. Within a filtered dataset, metallic systems exhibit particularly strong structural recurrence, with 6,270 materials grouped into 535 frameworks and 327 prototypes, while 5,557 ionic compounds occupy 1,704 frameworks and 696 prototypes. These results demonstrate that stable inorganic materials occupy a highly compressible region of structure space and establish a recurrence-based catalog of structural prototypes that provides an empirical measure of framework prevalence, enabling the relative likelihood of structural frameworks in future materials to be estimated from their recurrence among known compounds.

Figures

Figures reproduced from arXiv: 2607.17911 by the authors.

Figure 1
Figure 1. Unit-cell structures of (a) diamond, (b) zinc-blende, and (c) spinel. These examples highlight both [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Workflow for identifying recurrent structural frameworks as prototypes. Crystal structures are [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Sensitivity of framework identification to matching tolerances for the full dataset of 23,160 mate [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: The three most prevalent prototypes among metallic and intermetallic ground-state materials. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: The five most common prototypes among ionic compound ground-state materials. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Compression of experimentally realized ground-state materials within framework and prototype [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

112 extracted references · 13 canonical work pages

  1. [1]

    Zimmermann, Nils E. R. and Jain, Anubhav. Local structure order parameters and site fingerprints for quantification of coordination environment and crystal structure similarity. RSC Adv. 2020. doi:10.1039/C9RA07755C

    doi:10.1039/c9ra07755c 2020

  2. [2]

    and Frost, Jarvist M

    Whalley, Lucy D. and Frost, Jarvist M. and Jung, Young-Kwang and Walsh, Aron , title =. The Journal of Chemical Physics , volume =. 2017 , month =. doi:10.1063/1.4984964 , url =

    work page doi:10.1063/1.4984964 2017

  3. [3]

    and Cordiner, Joan L

    Glasby, Lawson T. and Cordiner, Joan L. and Cole, Jason C. and Moghadam, Peyman Z. , month = oct, year =. Topological. Chemistry of Materials , publisher =. doi:10.1021/acs.chemmater.4c00762 , number =

    work page doi:10.1021/acs.chemmater.4c00762

  4. [4]

    Nature Communications , author =

    Understanding the diversity of the metal-organic framework ecosystem , volume =. Nature Communications , author =. 2020 , pages =. doi:10.1038/s41467-020-17755-8 , abstract =

    doi:10.1038/s41467-020-17755-8 2020

  5. [5]

    The Journal of Physical Chemistry Letters , author =

    Data-. The Journal of Physical Chemistry Letters , author =. 2020 , pages =. doi:10.1021/acs.jpclett.0c02072 , language =

    work page doi:10.1021/acs.jpclett.0c02072 2020

  6. [6]

    Computational Materials Science , volume=

    Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis , author=. Computational Materials Science , volume=. 2013 , publisher=

    2013

  7. [7]

    Carbon , author =

    Effect of lattice stacking orientation and local thickness variation on the mechanical behavior of few layer graphene oxide , volume =. Carbon , author =. 2018 , pages =. doi:10.1016/j.carbon.2018.04.074 , abstract =

    work page doi:10.1016/j.carbon.2018.04.074 2018

  8. [8]

    Nano letters , volume=

    Stacking-dependent electronic structure of trilayer graphene resolved by nanospot angle-resolved photoemission spectroscopy , author=. Nano letters , volume=. 2017 , publisher=

    2017

Show all 112 references
  1. [9]

    NPG Asia Materials , volume=

    Stacking-controllable interlayer coupling and symmetric configuration of multilayered MoS2 , author=. NPG Asia Materials , volume=. 2018 , publisher=

    2018

  2. [10]

    APL Materials , author =

    Commentary:. APL Materials , author =. 2013 , pages =. doi:10.1063/1.4812323 , abstract =

    2013 doi

  3. [11]

    Applied Crystallography , volume=

    Recent developments in the Inorganic Crystal Structure Database: theoretical crystal structure data and related features , author=. Applied Crystallography , volume=. 2019 , publisher=

    2019

  4. [12]

    The Journal of Chemical Physics , author =

    Crystal structure prediction using ab initio evolutionary techniques:. The Journal of Chemical Physics , author =. 2006 , pages =. doi:10.1063/1.2210932 , abstract =

    2006 doi

  5. [13]

    Journal of Physics: Condensed Matter , author =

    Ab initio random structure searching , volume =. Journal of Physics: Condensed Matter , author =. 2011 , pages =. doi:10.1088/0953-8984/23/5/053201 , abstract =

    2011 doi

  6. [14]

    Measurement of the sodium chloride structure factors , author=

    Accuracy of an automatic diffractometer. Measurement of the sodium chloride structure factors , author=. Acta Crystallographica , volume=. 1965 , publisher=

    1965

  7. [15]

    Proceedings of the Japan Academy, Series B , author =

    X-. Proceedings of the Japan Academy, Series B , author =. 1979 , pages =. doi:10.2183/pjab.55.43 , number =

    1979 doi

  8. [16]

    Physical Review B—Condensed Matter and Materials Physics , volume=

    Geometrical magnetic frustration in rare-earth chalcogenide spinels , author=. Physical Review B—Condensed Matter and Materials Physics , volume=. 2005 , publisher=

    2005

  9. [17]

    Nature , volume=

    Unconventional superconductivity in magic-angle graphene superlattices , author=. Nature , volume=. 2018 , publisher=

    2018

  10. [18]

    Science , volume=

    Tuning superconductivity in twisted bilayer graphene , author=. Science , volume=. 2019 , publisher=

    2019

  11. [19]

    Scientific

    Steudel, Annett and Rühl, Stephan and Hinek, Roland and Rehme, Silke , organization =. Scientific. 2021 , url =

    2021

  12. [20]

    Physical Review Letters , volume=

    Band structure and optical properties of diamond , author=. Physical Review Letters , volume=. 1966 , publisher=

    1966

  13. [21]

    Physical Review B , volume=

    Electronic band structure and optical properties of graphite from a variational approach , author=. Physical Review B , volume=. 1970 , publisher=

    1970

  14. [22]

    Physical review , volume=

    Band structure of graphite , author=. Physical review , volume=. 1958 , publisher=

    1958

  15. [23]

    The Journal of Physical Chemistry , volume=

    The band structure of diamond , author=. The Journal of Physical Chemistry , volume=. 1996 , publisher=

    1996

  16. [24]

    Proceedings of the Royal Society of London

    Elastic constants of diamond , author=. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences , volume=. 1946 , publisher=

    1946

  17. [25]

    Journal of Applied Physics , author =

    Elastic. Journal of Applied Physics , author =. 1970 , pages =. doi:10.1063/1.1659428 , abstract =

    1970 doi

  18. [26]

    Computational Materials Science , volume=

    The AFLOW library of crystallographic prototypes: part 1 , author=. Computational Materials Science , volume=. 2017 , publisher=

    2017

  19. [27]

    1931 , publisher =

    Strukturbericht 1913--1928 , editor =. 1931 , publisher =

    1913

  20. [28]

    2022 , publisher =

    The Structure of Crystals , author =. 2022 , publisher =

    2022

  21. [29]

    1958 , publisher =

    A Handbook of Lattice Spacings and Structures of Metals and Alloys , author =. 1958 , publisher =

    1958

  22. [30]

    1991 , publisher =

    Pearson's Handbook of Crystallographic Data for Intermetallic Phases , author =. 1991 , publisher =

    1991

  23. [31]

    Applied Crystallography , volume=

    The crystal chemistry and physics of metals and alloys by WB Pearson , author=. Applied Crystallography , volume=. 1973 , publisher=

    1973

  24. [32]

    Computational Materials Science , author =

    The. Computational Materials Science , author =. 2024 , keywords =. doi:10.1016/j.commatsci.2024.112988 , abstract =

    2024

  25. [33]

    Nature , volume=

    Scaling deep learning for materials discovery , author=. Nature , volume=. 2023 , publisher=

    2023

  26. [34]

    Materials Today: Proceedings , author =

    Supercapacitor:. Materials Today: Proceedings , author =. 2021 , keywords =. doi:10.1016/j.matpr.2021.02.526 , abstract =

    2021 doi

  27. [35]

    Angewandte Chemie International Edition , volume=

    Mixed transition-metal oxides: design, synthesis, and energy-related applications , author=. Angewandte Chemie International Edition , volume=. 2014 , publisher=

    2014

  28. [36]

    Journal of the European Ceramic Society , author =

    Transferring lead-free piezoelectric ceramics into application , volume =. Journal of the European Ceramic Society , author =. 2015 , keywords =. doi:10.1016/j.jeurceramsoc.2014.12.013 , abstract =

    2015 doi

  29. [37]

    Chemistry of Materials , volume=

    Artificial intelligence driving materials discovery? perspective on the article: Scaling deep learning for materials discovery , author=. Chemistry of Materials , volume=. 2024 , publisher=

    2024

  30. [38]

    Chinese Physics Letters , volume=

    Influence of Local Cation Order on Electronic Structure and Optical Properties of Cation-Disordered Semiconductor AgBiS2 , author=. Chinese Physics Letters , volume=. 2024 , publisher=

    2024

  31. [39]

    Progress in Materials Science , author =

    Atomic-level structure and structure–property relationship in metallic glasses , volume =. Progress in Materials Science , author =. 2011 , pages =. doi:10.1016/j.pmatsci.2010.12.002 , abstract =

    2011 doi

  32. [40]

    Nature materials , volume=

    A complete representation of structure--property relationships in crystals , author=. Nature materials , volume=. 2008 , publisher=

    2008

  33. [41]

    Structural Science , volume=

    Crystal structure--physical property relationships in perovskites , author=. Structural Science , volume=. 1989 , publisher=

    1989

  34. [42]

    The International Journal of Advanced Manufacturing Technology , author =

    Friction capabilities of graphite-based lubricants at room and over 1400. The International Journal of Advanced Manufacturing Technology , author =. 2019 , keywords =. doi:10.1007/s00170-019-03290-4 , abstract =

    2019 doi

  35. [43]

    Journal of Applied Physics , author =

    Thermal. Journal of Applied Physics , author =. 1964 , pages =. doi:10.1063/1.1713251 , abstract =

    1964 doi

  36. [44]

    Chemistry--A European Journal , volume=

    Metastable MoS2: crystal structure, electronic band structure, synthetic approach and intriguing physical properties , author=. Chemistry--A European Journal , volume=. 2018 , publisher=

    2018

  37. [45]

    Foundations of Crystallography , volume=

    A unified algorithm for determining the reduced (Niggli) cell , author=. Foundations of Crystallography , volume=. 1976 , publisher=

    1976

  38. [46]

    Foundations of Crystallography , volume=

    The introduction of structure types into the Inorganic Crystal Structure Database ICSD , author=. Foundations of Crystallography , volume=. 2007 , publisher=

    2007

  39. [47]

    Structural Science , volume=

    The perils of Cc: comparing the frequencies of falsely assigned space groups with their general population , author=. Structural Science , volume=. 1992 , publisher=

    1992

  40. [48]

    PRX Energy , volume=

    Challenges in high-throughput inorganic materials prediction and autonomous synthesis , author=. PRX Energy , volume=. 2024 , publisher=

    2024

  41. [49]

    Physical Review Letters , volume=

    Characteristic structural phase transition in perovskite-type compounds , author=. Physical Review Letters , volume=. 1968 , publisher=

    1968

  42. [50]

    The Journal of Physical Chemistry , volume=

    Structures of the ferroelectric phases of barium titanate , author=. The Journal of Physical Chemistry , volume=. 1993 , publisher=

    1993

  43. [51]

    2016 , publisher=

    CRC handbook of chemistry and physics , author=. 2016 , publisher=

    2016

  44. [52]

    Physical Review B , volume=

    Structural studies of charge disproportionation and magnetic order in CaFeO 3 , author=. Physical Review B , volume=. 2000 , publisher=

    2000

  45. [53]

    doi:doi:10.1351/goldbook.C01433 , edition =

    2025 , title =. doi:doi:10.1351/goldbook.C01433 , edition =

    2025 doi

  46. [54]

    Journal of Physics: Conference Series , volume=

    A brief history of strukturbericht symbols and other crystallographic classification schemes , author=. Journal of Physics: Conference Series , volume=. 2019 , organization=

    2019

  47. [55]

    Computational Materials Science , volume=

    AFLOW: An automatic framework for high-throughput materials discovery , author=. Computational Materials Science , volume=. 2012 , publisher=

    2012

  48. [56]

    Journal of Materials Science , volume=

    Review of computational approaches to predict the thermodynamic stability of inorganic solids , author=. Journal of Materials Science , volume=. 2022 , publisher=

    2022

  49. [57]

    and Görne, Arno L

    Popov, Ilya V. and Görne, Arno L. and Tchougréeff, Andrei L. and Dronskowski, Richard , title =. Physical Chemistry Chemical Physics , year =

  50. [58]

    and Ong, Shyue Ping and Hautier, Geoffroy and Jain, Anubhav and Richards, William D

    Sun, Wenhao and Dacek, Stephen T. and Ong, Shyue Ping and Hautier, Geoffroy and Jain, Anubhav and Richards, William D. and Gamst, Anthony C. and Persson, Kristin A. and Ceder, Gerbrand , title =. Science Advances , year =

  51. [59]

    Substantia , volume=

    Early contributions of crystallography to the atomic theory of matter , author=. Substantia , volume=. 2019 , publisher=

    2019

  52. [60]

    Crystal Research and Technology , year =

    Hildebrandt, Gerd , title =. Crystal Research and Technology , year =

  53. [61]

    Borisov, S. V. and Podberezskaya, N. V. , title =. Journal of Structural Chemistry , year =

  54. [62]

    2005 , publisher =

    Charles Kittel , title =. 2005 , publisher =

    2005

  55. [63]

    Callister and David G

    William D. Callister and David G. Rethwisch , title =. 2018 , publisher =

    2018

  56. [64]

    2016 , edition =

    International Tables for Crystallography, Volume A: Space-group symmetry , editor =. 2016 , edition =. doi:10.1107/97809553602060000114 , isbn =

    2016 doi

  57. [65]

    Wyckoff position — Online Dictionary of Crystallography , year =

  58. [66]

    M. V. Talanov and V. A. Talanov , title =. Phys. Chem. Chem. Phys. , year =

  59. [67]

    Ralph W. G. Wyckoff , title =. 1963 , publisher =

    1963

  60. [68]

    An Introduction to Mineral Sciences , publisher=

    Putnis, Andrew , year=. An Introduction to Mineral Sciences , publisher=

  61. [69]

    and Ng, Kwok K

    Sze, Simon M. and Ng, Kwok K. , title =. 2007 , publisher =

    2007

  62. [70]

    and Pfister, H

    Giesecke, G. and Pfister, H. , title =. Acta Crystallographica , volume =. doi:https://doi.org/10.1107/S0365110X58000979 , url =. https://onlinelibrary.wiley.com/doi/pdf/10.1107/S0365110X58000979 , year =

    doi

  63. [71]

    , address =

    De Graef, Marc and McHenry, Michael E. , address =. Structure of materials : an introduction to crystallography, diffraction, and symmetry , year =. Structure of materials : an introduction to crystallography, diffraction, and symmetry , edition =

  64. [72]

    Journal of Applied Physics , volume=

    Novel silicon allotropes: Stability, mechanical, and electronic properties , author=. Journal of Applied Physics , volume=. 2015 , publisher=

    2015

  65. [73]

    1928 , publisher=

    Krystallographische und strukturtheoretische Grundbegriffe , author=. 1928 , publisher=

    1928

  66. [74]

    Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography , volume=

    Determination of reduced cells , author=. Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography , volume=. 1970 , publisher=

    1970

  67. [75]

    JOM , volume=

    The role of materials innovation in overall technological development , author=. JOM , volume=. 2012 , publisher=

    2012

  68. [76]

    Nature Energy , volume=

    Performance and cost of materials for lithium-based rechargeable automotive batteries , author=. Nature Energy , volume=. 2018 , publisher=

    2018

  69. [77]

    2008 , publisher=

    The Superalloys: Fundamentals and Applications , author=. 2008 , publisher=

    2008

  70. [78]

    Journal of Propulsion and Power , volume=

    Nickel-based superalloys for advanced turbine engines: chemistry, microstructure and properties , author=. Journal of Propulsion and Power , volume=

  71. [79]

    MRS Bulletin , volume=

    Opportunities and challenges for a first-principles materials database , author=. MRS Bulletin , volume=. 2011 , publisher=

    2011

  72. [80]

    Nature Materials , volume=

    The high-throughput highway to computational materials design , author=. Nature Materials , volume=. 2013 , publisher=

    2013

  73. [81]

    Journal of Physics D: Applied Physics , volume=

    The 2019 materials by design roadmap , author=. Journal of Physics D: Applied Physics , volume=. 2018 , publisher=

    2019

  74. [82]

    1922 , publisher=

    The Analytical Expression of the Results of the Theory of Space Groups , author=. 1922 , publisher=

    1922

  75. [83]

    2001 , publisher=

    Elements of X-ray Diffraction , author=. 2001 , publisher=

    2001

  76. [84]

    Die Gitterkonstanten von Ca O, Ca S, Ca Se, Ca Te

    Oftedal, I. Die Gitterkonstanten von Ca O, Ca S, Ca Se, Ca Te. Zeitschrift fuer Physikalische Chemie (Leipzig). 1927

    1927

  77. [85]

    Inorganic chemistry , volume=

    Some statistics on intermetallic compounds , author=. Inorganic chemistry , volume=. 2015 , publisher=

    2015

  78. [86]

    Foundations of Crystallography , volume=

    More statistics on intermetallic compounds--ternary phases , author=. Foundations of Crystallography , volume=. 2015 , publisher=

    2015

  79. [87]

    Villars, Pierre and Cenzual, Karin , title =

  80. [88]

    Applied Crystallography , volume=

    Comparison of structures applying the tools available at the Bilbao Crystallographic Server , author=. Applied Crystallography , volume=. 2016 , publisher=

    2016

  81. [89]

    Crystallography online: Bilbao crystallographic server , author=. Bulg. Chem. Commun , volume=

  82. [90]

    Databases and crystallographic computing programs , author=

    Bilbao Crystallographic Server: I. Databases and crystallographic computing programs , author=. Zeitschrift f. 2006 , publisher=

    2006

  83. [91]

    Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups , author=. Foundations of Crystallography , volume=. 2006 , publisher=

    2006

  84. [92]

    EPJ Web of Conferences , volume=

    An introduction to the tools hosted in the Bilbao Crystallographic Server , author=. EPJ Web of Conferences , volume=. 2012 , organization=

    2012

  85. [93]

    Structural Science , volume=

    The classification of tilted octahedra in perovskites , author=. Structural Science , volume=. 1972 , publisher=

    1972

  86. [94]

    Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography , volume=

    Simple ways of determining perovskite structures , author=. Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography , volume=. 1975 , publisher=

    1975

  87. [95]

    Science and Technology of Advanced Materials: Methods , volume=

    Spglib: a software library for crystal symmetry search , author=. Science and Technology of Advanced Materials: Methods , volume=. 2024 , publisher=

    2024

  88. [96]

    Naval Research Logistics Quarterly , volume=

    The Hungarian method for the assignment problem , author=. Naval Research Logistics Quarterly , volume=. 1955 , publisher=

    1955

  89. [97]

    npj Computational Materials , volume=

    AFLOW-XtalFinder: a reliable choice to identify crystalline prototypes , author=. npj Computational Materials , volume=. 2021 , publisher=

    2021

  90. [98]

    Computer Physics Communications , volume=

    Identifying duplicate crystal structures: XTALCOMP, an open-source solution , author=. Computer Physics Communications , volume=. 2012 , publisher=

    2012

  91. [99]

    Journal of Physics: Condensed Matter , volume=

    Construction of crystal structure prototype database: methods and applications , author=. Journal of Physics: Condensed Matter , volume=. 2017 , publisher=

    2017

  92. [100]

    Journal of Applied Crystallography , volume=

    CMPZ an algorithm for the efficient comparison of periodic structures , author=. Journal of Applied Crystallography , volume=. 2006 , publisher=

    2006

  93. [101]

    Acta Crystallographica Section B , volume=

    Method of crystal-structure similarity searching , author=. Acta Crystallographica Section B , volume=. 1994 , publisher=

    1994

  94. [102]

    Journal of Applied Crystallography , volume=

    STRUCTURE TIDY a computer program to standardize crystal structure data , author=. Journal of Applied Crystallography , volume=. 1987 , publisher=

    1987

  95. [103]

    2014 , publisher=

    Fundamentals of Engineering Thermodynamics , author=. 2014 , publisher=

    2014

  96. [104]

    Bravais, Auguste , journal=. M

  97. [105]

    Lonie and Eva Zurek , keywords =

    David C. Lonie and Eva Zurek , keywords =. XtalOpt: An open-source evolutionary algorithm for crystal structure prediction , journal =. 2011 , issn =. doi:https://doi.org/10.1016/j.cpc.2010.07.048 , url =

    2011 doi

  98. [106]

    and Lyakhov, Andriy O

    Oganov, Artem R. and Lyakhov, Andriy O. and Valle, Mario , title =. Accounts of Chemical Research , volume =. 2011 , doi =

    2011

  99. [107]

    Physical Review B , volume=

    Ab initio molecular dynamics for liquid metals , author=. Physical Review B , volume=. 1993 , publisher=

    1993

  100. [108]

    Computational Materials Science , volume=

    Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set , author=. Computational Materials Science , volume=. 1996 , publisher=

    1996

  101. [109]

    Physical Review B , volume=

    Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set , author=. Physical Review B , volume=. 1996 , publisher=

    1996

  102. [110]

    Physical Review B , volume=

    Projector augmented-wave method , author=. Physical Review B , volume=. 1994 , publisher=

    1994

  103. [111]

    Physical Review B , volume=

    From ultrasoft pseudopotentials to the projector augmented-wave method , author=. Physical Review B , volume=. 1999 , publisher=

    1999

  104. [112]

    Physical Review Letters , volume=

    Generalized gradient approximation made simple , author=. Physical Review Letters , volume=. 1996 , publisher=

    1996

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.