Materials follow the ‘Rule of Four,’ but scientists don’t know why yet
April 18, 2024
by National Centre of Competence in Research (NCCR) MARVEL
<div data-thumb="https://scx1.b-cdn.net/csz/news/tmb/2024/materials-follow-the-r.jpg" data-src="https://scx2.b-cdn.net/gfx/news/2024/materials-follow-the-r.jpg" data-sub-html="Percentage of RoF structures that become labeled non-RoF as a function of the symmetry tolerance parameter used for reduction to the primitive cell. The black and green lines correspond to structures in the MP and MC3D-source datasets, respectively. At typical symmetrization parameters, there is little to no change in the number of RoF structures (roughly 1% of RoF structures go to non-RoF). At larger symmetrization parameters (≈1 Å), this increases to roughly 6% based upon the large deviations allowed in considering sites as symmetrically equivalent. Credit: npj Computational Materials (2024). DOI: 10.1038/s41524-024-01248-z”>
Scientists are normally happy to find regularities and correlations in their data—but only if they can explain them. Otherwise, they worry that those patterns might just be revealing some flaw in the data itself, so-called experimental artifacts.
The two collections include over 80,000 electronic structures of experimental as well as predicted materials, and in principle, all types of structures should be equally represented. However, scientists noticed that around 60 percent of structures in both databases have primitive unit cells (the smallest possible cell in a crystal structure) made out of a multiple of 4 atoms. The scientists named this recurrence the “Rule of Four” and started looking for an explanation.
“A first intuitive reason could come from the fact that when a conventional unit cell (a larger cell than the primitive one, representing the full symmetry of the crystal) is transformed into a primitive cell, the number of atoms is typically reduced by four times,” says Elena Gazzarini, a former INSPIRE Potentials fellow in the Laboratory of Theory and Simulation of Materials (THEOS) at EPFL and now at CERN in Geneva.
“The first question we asked was whether the software used to ‘primitivize’ the unit cell had done it correctly, and the answer was yes.”
From a chemical point of view, another possible suspect was the coordination number of silicon (the number of atoms that can bind to its atom), which is four. “We could expect to find that all the materials following this Rule of Four included silicon,” says Gazzarini. “But again, they did not.”
The formation energies of the compounds could not explain the Rule of Four either. “The materials that are most abundant in nature should be the most energetically favored, which means the most stable ones, those with negative formation energy,” says Gazzarini. “But what we saw with classic computational methods was that there was no correlation between the Rule of Four and negative formation energies.”
Because the materials space covered by the two databases is huge, going from small units to very large cells with dozens of different chemical species, there was still a chance that a more refined analysis looking for a correlation between formation energies and chemical properties may provide an explanation.
So, the team involved Rose Cernosky, a machine-learning expert at the University of Wisconsin, who developed an algorithm to group structures according to their atomic properties and look at formation energies within classes of materials sharing some chemical similarities. But again, this method did not provide a way to distinguish the Rule-of-Four compliant materials from the non-compliant ones.
Similarly, the abundance of multiple of fours does not even correlate with highly symmetric structures but rather with low symmetries and loosely packed arrangements.
In the end, the resulting article in npj Computational Materials is the rare example of a scientific paper describing a negative result: the researchers could only describe the phenomenon and rule out several possible causes, without finding one.
But negative results can be just as important as positive ones for scientific advancement, because they point to difficult problems—which is why scientists often complain that journals should publish more such studies.
The failure to find a compelling explanation did not prevent the group from predicting, through a Random Forest algorithm, with an accuracy of 87% whether a given compound will follow the Rule of Four or not. “This is interesting because the algorithm uses only local rather than global symmetry descriptors, which suggests that there may be small chemical groups in the cells (still to be found) that may explain the Rule of Four,” says Gazzarini.
More information:
Elena Gazzarrini et al, The rule of four: anomalous distributions in the stoichiometries of inorganic compounds, npj Computational Materials (2024). DOI: 10.1038/s41524-024-01248-z
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National Centre of Competence in Research (NCCR) MARVEL
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Materials follow the ‘Rule of Four,’ but scientists don’t know why yet (2024, April 18)
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United Methodist Church lifts 40-year ban on LGBTQ clergy – CNN
CNN
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The United Methodist Church overturned its 40-year ban on gay clergy Wednesday, marking a historic shift in the church’s stance on homosexuality.
The church has long been divided into factions over LGBTQ inclusion and even weighed splitting into two separate churches over the issue, CNN previously reported.
In 1984, the church banned “self-avowed practicing homosexuals” from becoming members of the clergy, and later added performing or celebrating same-sex unions to “a list of chargeable offenses that could result in a church trial,” according to a timeline of the church’s history with the LGBTQ community.
The Methodist community spent the ensuing decades debating, fighting and praying over their stance on gay clergy and LGBTQ members. But Wednesday’s vote by the church’s top legislative body signaled a historic shift toward acceptance and inclusion.
In a 692-51 vote, church leaders passed several rules without debate, including overturning both its ban on gay clergy and the penalties for holding same-sex marriages, according to the United Methodist News service.
After the vote, Hope Morgan Ward, a retired bishop in the United Methodist Church, prayed the church would be used as “peacemakers and servants” and be “welcoming of all people into the embrace of God.”
According to the Methodist news service, members cheered, cried and hugged after the vote.
“We’ve been going on like this since the ’70s and, finally, in just a brief few minutes with no debate, it was gone. And now we can get on about the business of the church,” Marilyn Murphy, an observer from the church’s South Carolina conference, told the news service.
LGBTQ advocates within the church hailed the decision.
Matt Patrick, co-pastor at the University United Methodist Church in Tulsa, Oklahoma, told CNN he became emotional after the church announced the decision.
“I did tear up this morning at the announcement of the vote because it was just a huge relief to see justice had been done after so many years,” he said. “There’s just been a lot of pain in order to get us to this place.”
Though the prohibition on gay clergy has been removed from the church bylaws, Patrick said the work will continue to ensure the Methodist church is as an inclusive place for everyone.
“Where we go from here, God only knows,” he said.
More changes are expected as the legislative conference continues in Charlotte, North Carolina.
This is a developing story. Please check back for the latest updates.
Corruption’s Grip on Road Infrastructure Slows Malawi’s Development – VOA Zimbabwe
Economic and accountability bodies in Malawi urge the government to address flaws in the public procurement system. A 2021 Malawi Assurance Report on Public Infrastructure Projects suggests pervasive corruption in Malawi’s public sector. The construction industry is particularly affected.
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