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For small molecules, NIST has a database of experimentally determined geometries here, and ab initio geometries here. I wonder if there is something similar for materials?

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2DMatPedia

An open computational database of two-dimensional materials. A large dataset of 2D materials, with more than 6,000 monolayer structures, obtained from both top-down and bottom-up discovery procedures

2D structures and layered materials

Results from screening all known 3D crystal structures finding those that can be computationally exfoliated producing 2D materials candidates.

TopoMat database

The database contains the results of high-throughput first-principles screening of known crystal structures for topological materials (topological insulators, Dirac and Weyl semimetals, etc.).

Update

I recently came across the publication Data‐Driven Materials Science: Status, Challenges and Perspectives by Himanen et. al featuring this list of current major materials data infrastructures.

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References:

  1. Himanen, Lauri, et al. "Data‐Driven Materials Science: Status, Challenges, and Perspectives." Advanced Science 6.21 (2019): 1900808.
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  • $\begingroup$ I already gave a +1 back in April, but which of these "materials data infrastructures" are databases? All of them? $\endgroup$
    – Nike Dattani - No Free Time
    Commented Jul 17, 2020 at 22:15
  • $\begingroup$ Most of them provide some sort of database/repository/properties. The details are given in the overview tab. Hence I thought it was better to add the entire list. Even if a few of them are not strictly a database, the info might be useful for some one. $\endgroup$
    – Thomas
    Commented Jul 18, 2020 at 14:07
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    $\begingroup$ Just an FYI, the Materials Project stat in that table is out of date, MP now has 130k compounds of which 70k have band structures, plus many associated properties (10k elastic tensors, dielectric, piezoelectric, phonon band structures, surfaces and grain boundaries for elemental materials, etc). Disclaimer: commenting as a representative of Materials Project. The database is open access with a Python API client in pymatgen. $\endgroup$
    – Matt Horton
    Commented Sep 17, 2020 at 23:43
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    $\begingroup$ @Matthew. Thanks for the information. I will try to update the information in the answer. Planning to rewrite the answer in full instead of screen shot $\endgroup$
    – Thomas
    Commented Sep 18, 2020 at 1:30
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I agree with the other answer but there are many other resources:

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There is the Materials Project:

https://materialsproject.org/

From the site: Harnessing the power of supercomputing and state of the art electronic structure methods, the Materials Project provides open web-based access to computed information on known and predicted materials as well as powerful analysis tools to inspire and design novel materials.

From the experimental view, there are databases like ICDD (http://www.icdd.com/) with the x-ray crystallographic determined structures.

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    $\begingroup$ Wow! Thank you! During the "Definition" stage this Example Question of mine got 14 upvotes, so I thought a database like this was hard to come by, but you have so much knowledge that you were able to give some great examples! I initially accepted your answer, but now that there's some others, I will wait until we see more! $\endgroup$
    – Nike Dattani - No Free Time
    Commented Apr 28, 2020 at 19:26
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    $\begingroup$ I also recommend here. $\endgroup$
    – exsonic01
    Commented Apr 29, 2020 at 0:12
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    $\begingroup$ If theoretically computed geometries are the desire, other entries include OQMD, AFLOWlib, Catalysis-Hub, the CMR, and NOMAD to name a few. $\endgroup$
    – Andrew Rosen
    Commented Apr 30, 2020 at 18:30
  • $\begingroup$ Commenting as a representative of Materials Project, but I would vote for us :-) We have good coverage of experimental materials without a strong bias towards a particular structure type, plus we have a Pythonic API to do large-scale queries, and many analysis tools available (phase diagrams, Pourbaix etc.), we have a discussion forum at matsci.org for any questions $\endgroup$
    – Matt Horton
    Commented Sep 17, 2020 at 23:41
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Depending on what kind of materials looking for the following crystallographic databases can be relevant, too (unfortunately, for a cost):

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    $\begingroup$ CCDC now also includes the ICSD structures. Also note that you can search for free and also access and dowload the single structures from these results. In contrast to many other sources the database is curated by an editorial team. $\endgroup$
    – Gerhard Goldbeck
    Commented Apr 29, 2020 at 7:21
  • $\begingroup$ @GerhardGoldbeck I didn't know that. Thanks, it is a very convenient way to reach ICSD. $\endgroup$
    – Greg
    Commented Apr 29, 2020 at 20:55
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    $\begingroup$ One caveat to CCDC is that the reuse of derived data requires permission. $\endgroup$
    – Geoff Hutchison
    Commented May 2, 2020 at 19:39
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In addition to above recommendations, I also use American Mineralogist Crystal Structure Database.

http://rruff.geo.arizona.edu/AMS/amcsd.php

The good thing about this place is that you can check the publications related to a specific geometry.

I usually use AMCSD and Materialsproject.

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Awesome Materials Informatics

The community-edited awesome materials informatics list has a section on "machine-readable datasets", many of which contain atomic structures of materials.

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    $\begingroup$ +100 That has to be bookmarked! $\endgroup$
    – Camps ♦
    Commented Jun 16, 2020 at 17:52
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As an additional comment, the OPTIMADE consortium is developing a standard REST API to query many different databases with the same API. Version 1.0 of the specs is out (on GitHub, and a version with DOI for 1.0 on Zenodo). Many of the DBs mentioned earlier are now working to expose their data via OPTIMADE.

Beside performing the queries with any browser or command-line tool (wget, curl, ...), there are two "web" clients I am aware of:

[Disclaimer: I am actively involved with the OPTIMADE consortium]

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