the researchers noted that given the vast number of elements that can be used to make max phases and an even greater number of ways of combining them the task of experimentally verifying how each composite will behave at high temperatures becomes impractical on the other hand computational techniques such as purely machine-learning algorithms have not been as robust at predicting the materials behavior at nonzero temperatures as an alternative to experiments and machine learning physics-based mathematical models offer a rigorous method to evaluate the properties of max phases at different temperatures among these models the most established one called density functional theory can account for the behavior of materials with minimal input data but this theory best applies to materials at their lowest energy state called the ground state to predict their behavior at elevated temperatures more complex and time-consuming calculations are needed these calculations scale very poorly said arróyave for perspective if we want to use density functional theory to calculate the properties of a candidate material at the lowest temperature of zero kelvins that is at the ground state it might take about a day of computational time but now if you want to calculate the same properties at a finite temperature say 1000 kelvins it can take weeks further he noted that predicting the behavior of materials when exposed to oxygen at elevated temperatures is more complicated and may take months or longer even when using thousands of supercomputer processors at a time hence instead of relying solely on just one method arróyave and his team used a three-pronged approach that included a combination of density functional theory machine learning and computational thermodynamics the researchers first calculated some fundamental properties of max phases at zero kelvins with density functional theory next those calculations were used as inputs to a machine-learning model in this way the researchers replaced otherwise computationally expensive calculations from density functional theory with machine-learning models then they used computational thermodynamics to determine the most stable compounds for a given temperature and a certain max phase composition lets consider a max phase made of titanium aluminum and carbon at higher temperatures we could have for example carbon dioxide carbon monoxide and other combinations of carbon and oxygen that might compete to exist said arróyave using our framework one can now determine which phases or combinations we can expect at that temperature how much of it and whether that can be detrimental simply put we can now quickly tell whether the material will decompose at a given temperature the researchers noted that although they tested their computational framework on a few candidate max phases the algorithm can be used for gauging the behavior of other existing or novel materials as well the research will help in rapidly ruling out those elements that might form unstable oxides at the material design phase said arróyave we can then use these materials to build superior gas turbines and other machines that can withstand even the harshest environmental conditions with minimal wear and tear over time these high-performance turbines will benefit not just the aviation and energy industry but also consumers who will see reduced costs this research is funded by the designing materials to revolutionize and engineer our future grant from the national science foundation