Comment on "Structure Prediction of Li-Sn and Li-Sb Intermetallics for Lithium-Ion Batteries Anodes''
Raja Sen Priya Johari

[figure]name=Figure 



In a recently published article Mayo et al.<cit.>
presented the ground state crystal structures of various experimentally
unknown Li-Sn intermetallic compounds at ambient pressure (~
0 GPa) and 0 K temperature using ab-initio random structure searching
method (AIRSS) with high-throughput screening from the Inorganic Crystal
Structure Database (ICSD).<cit.> In their study,<cit.>
besides the experimentally known phases of Li-Sn such as, Li_2Sn_5
(P4/mbm),<cit.> Li_1Sn_1
(P2/m, I4_1/amd),<cit.>
Li_7Sn_3 (P2_1/m),<cit.>
Li_5Sn_2 (R3̅m),<cit.>
Li_13Sn_5 (P3̅m1),<cit.>
Li_7Sn_2 (Cmmm),<cit.>
and Li_17Sn_4 (F4̅3m),<cit.>
Mayo et al. also reported two previously unknown stable phases for
Li-Sn such as, Li_8Sn_3-R3̅m and
Li_7Sn_2-P1̅ along with several Li-Sn
metastable phases (Li_1Sn_2, Li_2Sn_3,
Li_7Sn_9, Li_3Sn_2, Li_5Sn_3,
Li_2Sn_1, Li_3Sn_1, Li_4Sn_1,
Li_5Sn_1, and Li_7Sn_1) which lie
within 20 meV/atom from the convex hull tie-line. However, while going
through their article, we noticed a significant inconsistency and
contradictions in their results. Moreover, a one-to-one comparison
with our published results<cit.> revealed a disagreement
in the symmetry of Li_3Sn_1, Li_7Sn_2,
Li_4Sn_1, Li_5Sn_1, and Li_7Sn_1
discussed by Mayo et al.<cit.> 

Predicting the lowest energy ground state structures
is always an important task, as that is what determines the properties
of any material and specifically, in the context of Li-ion batteries
this is particularly crucial, since the open circuit voltage, Li-diffusivity,
and swelling upon lithiation, etc., depend critically on the crystal
structure and its respective ground state energy. We, therefore, re-calculated
the formation energy of the reported phases (given as CIF files in
the “Supporting Information” by Mayo et al.<cit.>)
and our predicted phases, by considering higher and strict convergence
criteria (see the “Methodology and Computational
Details in SI”) and compared the results on an equal footing by
calculating the formation enthalpy of each Li-Sn compound. Interestingly,
current calculations reveal that Mayo et al.<cit.> not
only predicted completely wrong structures in few cases (much higher
in energy than what we found, in some cases a difference of more than
100 meV/atom), but for many other cases it is not just that they published
a wrong symmetry for the right structure but the structures themselves
are often wrong, which can mislead the scientific community. Through
this comment, we therefore not only highlight several disparities
in reporting the correct crystal structure and describing the proper
symmetry of several Li-Sn compounds by Mayo et al.<cit.>
but, also present the correct ground state structures of Li-Sn compounds
at ambient pressure (~ 0 GPa) and 0 K temperature,
which are extremely important to know, in order to establish an in-depth
understanding of the charge-discharge process in Li-Sn batteries. 



§ LOWEST ENERGY LI-SN STRUCTURES




In search of accurate ground state structures of
the stable and metastable Li-Sn compounds at ambient pressure and
0 K temperature, current calculations following strict convergence
criterion reveal few new phases whose formation enthalpies are either
comparable or lower than the respective phase of the compounds reported
by Mayo et al.<cit.> Also, on comparing our results with
those of Mayo et al.,<cit.> it has been noticed that
in most of the cases, either they have wrongly identified the ground
state structure (symmetry) or there have been involved contradictions
in presenting the proper space group and corresponding crystal structure
of the compounds in their article (Figure <ref> and Table
<ref>). In order to present a concise comparison
and inconsistencies within the results reported by Mayo et al.,<cit.>
we have tabulated the description of crystal symmetry of stable and
metastable Li-Sn compounds in Table <ref>. The
table displays the crystal symmetry reported by Mayo et al. in the
“ABSTRACT”, “Table 1”, “RESULTS”, and “Supporting Information”
of their article<cit.>, together with the symmetry and
their respective fitness (vertical distance from the convex hull tie
line) obtained by present calculations for each composition. The contradicting
results (within their paper and with respect to current work using
better convergence criteria) are highlighted in red colored fonts
in Table <ref>. The CIF files corresponding to
the newly predicted structures from current work have also been supplied
in the Supporting Information of this comment, while correction for
the symmetry and structure of contradicting  Li-Sn compounds (marked
in red in Table <ref>) are given next.



Mayo et al. have described the symmetry of Li_2Sn_3
to be triclinic with space group P1 everywhere
in the article. But, in the “Supporting Information”, they have
provided the CIF file for P4/mmm phase. Thus, the structural
information described in the manuscript mislead the exact crystallographic
symmetry. Present calculations, however, predict the correct ground
state structure of Li_2Sn_3 to be P4/mmm,
which is shown in Figure <ref> (b). The atomic arrangement
of Li_2Sn_3 - P4/mmm is very similar to
Li_1Sn_2 -P4/mmm. The only difference
is, instead of double layers of four-membered rings of Sn, single
layers of four-membered rings of Sn can also be found in the Li_2Sn_3
- P4/mmm structure in an alternative sequence, as shown
in Figure <ref> (b). The absence of imaginary phonon frequency
in the whole Brillouin zone as shown in Figure S1 (a) in SI represents
the dynamical stability of Li_2Sn_3 -P4/mmm
at ambient pressure condition.



In their article, Mayo et al. have described Li_7Sn_9
to exhibit P4_2/n symmetry, with ground state formation
enthalpy lying about 19 meV/atom above the convex hull tie-line. However,
in the CIF file they have provided the structure for C222
symmetry. On the contrary, current calculations discovered a new structure
having symmetry P2/m. This structure has been found to
be energetically much stable than C222 phase (with 159
meV/atom difference in formation energy). Additionally, this structure
has been found just 7 meV/atom above the convex hull tie line (Figure
<ref>). In this structure, 1D infinite atomic chains of
pure Li and Sn, can be found to run along [010] direction (Figure
<ref> (c)). Phonon dispersion curve (See Figure S1 (b)
in SI) represents Li_7Sn_9 - P2/m is also
dynamically stable.

In case of Li_3Sn_2, P2_1/m
symmetry is predicted by Mayo et al.<cit.> While, our
calculations predict the ground state structure of Li_3Sn_2
to exhibit Cmcm phase. It is found that in a tight relaxation
of Hellmann-Feynman forces, P2_1/m symmetry transforms
into Cmcm symmetry. In Li_3Sn_2-Cmcm
structure, Li atoms can be seen to intercalate between 1D zigzag chains
and 2D buckled layer of Sn ions (Figure <ref> (d)). Absence
of imaginary frequency in phonon dispersion curve revels the dynamical
stability of Li_3Sn_2-Cmcm phase, shown
in Figure S1 (c) in SI.

The described symmetry of Li_5Sn_3
highly misleads the actual crystallographic informations of the structure.
In the “ABSTRACT” and “Table 1” of their article, Mayo et
al. have described the symmetry to be Im3m,
while in “RESULTS” section, they discussed the P43m
symmetry of Li_5Sn_3, and have provided its CIF file.
Interestingly, on relaxing the Li_5Sn_3-P43m
structure provided by Mayo et al.,<cit.> it has been
found energetically unstable (Figure <ref>). On the other
hand, current calculations predict a new phase having space group
R32 within the rhombohedral symmetry. The formation enthalpy
of this phase is found to be lower than both, Im3m
and P43m phase of Li_5Sn_3
(Table <ref>). Other than this, one more polymorph
of Li_5Sn_3 having symmetry Fmm2 is found,
whose formation enthalpy is as comparable as R32 phase
of Li_5Sn_3. In R32 phase, two different
type of 1D atomic chains, one with pure Li another having an alternative
sequence of Li and Sn atoms, can be seen to run along c-axis (shown
in Figure <ref> (e)). While, the crystal structure of Fmm2
is very much unusual, where bent trimers of pure Sn stacked one after
another along crystallographic a-axis, are surrounded by Li atoms
(Figure <ref> (f)). The phonon dispersion curves of both
of these newly predicted phases (R32 and Fmm2)
are provided in SI (Figure S1 (d) & (e)). It should also be noted
here that few years back, Courtney et al.<cit.> revealed
through experimental study that all known phases of Li-Sn do not always
form in the electrochemical cell of Sn anode, operating at room temperature.
Their investigation indicates that for x>2.5 in Li_xSn,
one of the unknown phases of Li-Sn adopts cubic like structure. In
predicting new stable and metastable Li-Sn compounds, Mayo et al.
therefore suggest that this cubic like arrangement may arise due the
formation of Li_5Sn_3, as they have showed that the
ground state structure of Li_5Sn_3 would be Im3m.
But, in this comment, it has been showed that the ground state structure
of Li_5Sn_3 is rhombohedral and not cubic. Moreover,
in our recent work,<cit.> we have showed that at ambient
pressure and room temperature, Li_3Sn_1 forms a cubic
phase (P2/m 311K⟶Fm3m),
which is also consistent with results of Thackeray et al.<cit.>
Therefore, it may be concluded in this comment that the formation
of cubic like arrangements in electrochemical cell may appears due
to the formation of Li_3Sn_1-Fm3m
phase, where Li atoms form a bcc-like sub-lattice.

For Li_3Sn_1, we again notice a
huge inconsistency in the results. Mayo et al. described the symmetry
to be P3_2 in the “RESULTS” section and Table 1
of their manuscript,<cit.> while provided the structure
for P3m1 symmetry in the “Supporting Information”
and haven't discussed its structure at all. This structure, however,
on relaxation is found unstable. In contrast, our search predicts
P2/m symmetry for Li_3Sn_1 to be much
more energetically stable than P3m1 phase. The Li_3Sn_1-
P2/m structure is found to lie just 7 meV/atom above our
convex hull tie line (Figure<ref> and Table <ref>).
The structure of Li_3Sn_1-P2/m has been
described in our recent work.<cit.> A one-to-one comparison
with Li_3Sn_1-P3_2 could not be made
on the basis of formation enthalpy because of unavailibity of its
crystal structure. However, we are confident that the lowest energy
structure will correspond only to the Li_3Sn_1- P2/m
symmetry,

In case of Li_7Sn_2, experimentally
known phase is Cmmm, while we found P3m1
phase (Figure <ref> (a)) to be more stable than Cmmm.<cit.>
Though the difference in the enthalpy for both phases is just 6
meV/atom, which is also in agreement with results of Geneser et al.<cit.>
The structure is also shown to be dynamically stable in our recent
article.<cit.> On the contrary, Mayo et al.<cit.>
predicted Li_7Sn_2 to be stable under P1
symmetry, which they also claim to be 6 meV/atom lower in formation
energy than the experimentally reported Cmmm
phase. However, it has been noticed that the format of the CIF file
is completely wrong (it is in “SHELX” format). On analyzing the
given format, it is found that the structure given in their CIF file
is actually representing the P3m1 phase. Therefore,
the discussion about Li_7Sn_2 in the Ref. [1]
remains irrelevant, as it is providing a misleading crystallographic
information. 

In case of Li_4Sn_1, Mayo et al.
have mentioned the P2_1 symmetry in the Abstract and
Table1 but provided the CIF file for the R3m
phase, which is the lowest energy structure. Thus, their paper provide
a wrong and contradicting information about the symmetry in the text. 

The information provided for Li_5Sn_1,
is again highly contradictory. In “Abstract” Mayo et al. have
described the symmetry to be P6/mmm (19 meV/atom above
the convext hull tie line) and have provided its CIF file as well.
However, in “Table 1” of their article they presented the structure
symmetry to be Pmma. In contract, we found the symmetry
of structures to be C2/m, which is found 11 meV/atom above
from the convex-hull tie line. This clearly indicates C2/m
phase to be energetically favorable, as compared to P6/mmm
phase. 

In case of Li_7Sn_1, Mayo et al.
described the symmetry to be C2, while in “Table 1”,
as well as in the CIF file, they represented the Fmmm
phase for this compound. On the other hand, our calculation predicted
C2/m phase for Li_7Sn_1.<cit.>
The formation enthalpy of our predicted structure (C2/m)
is found to be as comparable as the Fmmm structure, reported
by Mayo et al.<cit.> The C2/m phase is also
shown to be dynamically stable in our recent study.<cit.>

It is also noteworthy to mention here that Mayo
et al. described Li_15Sn_4 as a known phase in the
Li-Sn binary phase diagram. But, to the best of our knowledge, we
did not find any such compound for Li-Sn from our calculations. The
same has not even be available in the ICSD database, as well. However,
in cross verification of the reference Li_15Sn_4,<cit.>
given by Mayo et al., it has been observed that the reference is actually
describing the structure of Na_15Sn_4, rather than
Li_15Sn_4.



§ CONCLUSIONS 


In summary, crystal structure and symmetry of several
Li-Sn compounds reported by Mayo et al.<cit.> are not
only contradicting within the article (e.g., Li_2Sn_3,
Li_7Sn_9, Li_5Sn_3, Li_3Sn_1,
Li_7Sn_2, Li_4Sn_1, Li_5Sn_1,
and Li_7Sn_1,) but in many cases (e.g., Li_7Sn_9,
Li_5Sn_3, Li_3Sn_1 and Li_5Sn_1)
they are wrong as well. Thus, their claim of understanding the lithiation
mechanism in Sn anode is incorrect and the conclusions are questionable.
We hope that this comment will be helpful for the community to identify
the correct ground state structure and phase of various Li-Sn compounds
that may appear during lithiation-delithiation of Sn anode.

P. J. acknowledges the support provided by Grant No. SR/FTP/PS-052/2012
from Department of Science and Technology (DST), Government of India.
R.S. wants to thank Mr. Dwaipayan Chakroborty for critical reading
of the manuscript. The high performance computing facility and workstations
available at the School of Natural Sciences, Shiv Nadar University,
were used to perform all calculations.


Methodology and Computational Details, Phonon dispersion
curves of Li-Sn compounds (pdf), CIF files of newly predicted structures
(ZIP)




