1. In this age, we are in constant search for new
materials to use in evolving technology.
Finding materials that work in technology
such as solar cells and batteries can take a lot
of guess work. We can do smarter guessing
and checking if we can predict key properties
of materials, such as melting point and ion
conductivity. Finding this information,
especially for new or uncommon materials,
can take weeks of experimentation or
simulation. These methods are very accurate
and time consuming, which is unnecessary
for information that only needs to be within
the ballpark. Using materials informatics, we
sacrifice some accuracy but gain speed.
• Split unit cell volume into many elements on a grid system
• Each grid point considered accessible if:
o within a certain range of distance away from each atom
o the bond valence (v) for the hypothetical atom deviates by less
than a certain amount from the ideal BV value
MOTIVATION
SOLUTION
BOND VALENCE THEORY as a new descriptor
PREDICTING MELTING POINTS
CONCLUSION
Materials Informatics Approach to Predicting Melting Points in Solids
Sidney Lam, Austin Sendek, Qian Yang, Evan Reed
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Conductivity
Volume Fraction
Correlation Between Volume Fraction and
Conductivity of Li Containing Materials
ACKNOWLEDGEMENT
QSPR uses a linear regression of known
properties (descriptors) to predict the
properties of new materials.
We used 14 descriptors:
• Unit cell volume
• Atoms per cell
• Average atomic mass
• Average atomic volume
• Lattice ionicity
• Variance in lattice ionicity
• Lattice coordination
• Variance in lattice coordination
• Density
• Average electronegativity
• variance in average electronegativity
• Lattice packing fraction
• Empty space spread
• Bond valence
Our work is unique in that we used
descriptors that are rapidly calculable if just
given the material structure. These
descriptors may not have high correlations
individually (Figure 3), but in a linear
combination can create a much better
model. We are looking to find the right
number of descriptors as to not underfit or
overfit the data.
Figure 2: This single descriptor had a correlation coefficient of 0.3047.
Goal: Calculate the volume of an ion transport channel that runs through the entire material
Figure 1 (a) and (b): A filled in grid point represents an accessible site for an ion. Adding
up the number of accessible sites over the total volume gives the volume fraction. Figure
1 (a) has a smaller number of grid points and a higher ∆V, therefore it is less detailed and
has higher volume fraction.
After developing the code that calculated the volume
fraction of a material given the structure, we search
for a correlation among volume fractions and ionic
conductivity values across a broad range of structures.
Equation (a) calculates the bond
valence (v) at each grid point. R0
is a atom-atom pair specific value,
R is the distance from the grid
point to an atom, and b is
accepted to be 0.37 across all
atoms. The bond valence value at
each grid point is given by
equation (b). Each grid point is
considered accessible if equation
(c) is true, 𝑉𝑖𝑑𝑒𝑎𝑙 being 1, and ∆𝑉
arbitrarily picked, generally
around 0.05.
-0.0440
0.0467
-0.0941
-0.3346
-0.1487
0.2867
0.0197
0.1429
0.1367
-0.1087
-0.1040
0.3412
-0.1543
-0.1357
We then put together descriptors that were
known to work in predicting ion conductivity with
the newly calculated bond valence values. Of our
starting 400 materials, 130 had non-zero bond
valence values, and the model was created off
these 130 materials and their known melting
points (MP). Although the correlation between
single descriptors and observed MPs is low
(Figure 3), when put together in various
combinations of features, the correlation is much
higher (Figure 4). Taking the optimal number of
features from Figure 4, we graph the predicted
versus observed MPs, to get a correlation of
0.5349, much higher than any single feature and
useful for predictive purposes.
Bond valence theory does have a significant correlation with melting point and ionic
conductivity, and including it into our model will allow for less guessing and checking.
Although we did not know if these simple descriptors would add to our model, it was
important to try them nonetheless. The next step would be to work with increasingly
complex descriptors, but that would be after our current model meets QSPR standards.
In the future, we will need to fine tune the bond valence code until all the materials have
a non-zero volume fraction, find more relevant descriptors, and possibly run other types
of statistical analyses.
Figure 3: The correlation
between descriptors and
observed MPs, in the
same order as the list
given previously.
Figure 5: Graph of observed MP vs predicted MP of the
best 9 features. Axis values are normalized. There is a
correlation of 0.5349.
Figure 4: Graph of correlational coefficient (left
axis) and error in predicting a material not in the
given set (right axis) versus the number of features.
The arrow points to where there is an optimal
combination of high correlation and low error.
𝑣𝑖 = 𝑒[
𝑅0,𝑖𝑗−𝑅
𝑏
]
𝑉 =
𝑖
𝑣𝑖
∆𝑉 = 𝑉 − 𝑉𝑖𝑑𝑒𝑎𝑙
(a)
(b)
(c)
We thank Stanford REU
for providing financial
support, and Alexander
Duerloo for helping
compiling the database
of materials and their
melting points.