# Fluoride Frameworks as Potential Calcium Battery Cathodes

Dereje Bekele Tekliye  Department of Materials Engineering, Indian Institute
of Science, Bengaluru, 560012, India  Gopalakrishnan Sai Gautam  Department of
Materials Engineering, Indian Institute of Science, Bengaluru, 560012, India
Email<EMAIL_ADDRESS>
###### Abstract

Calcium batteries (CBs) are potential next-generation energy storage devices,
offering a promising alternative to lithium-ion batteries due to their
theoretically high energy density, better safety, and lower costs associated
with the natural abundance of calcium. However, the limited availability of
positive electrode (cathode) materials has constrained the development of CBs
so far. Given the similar ionic radii of Na+ and Ca2+, structures that are
effective at reversibly intercalating Na+ may be able to reversibly
intercalate Ca2+ as well. In this context, transition metal fluorides (TMFs)
exhibiting weberite and perovskite structures that are known for intercalating
Na+ form an interesting set of possible CB cathode frameworks. Thus, we use
first principles calculations to explore weberite and perovskite TMFs as CB
cathodes, of compositions CaxM2F7 and CaxMF3, respectively, where M = Ti, V,
Cr, Mn, Fe, Co, or Ni. We systematically evaluate key cathode properties,
including ground state structure, average Ca-intercalation voltage,
thermodynamic stability (at 0 K), theoretical capacity, and Ca2+ migration
barriers. Importantly, we identify CaxCr2F7 and CaxMn2F7 weberite frameworks
as promising Ca-cathodes. Our study not only unveils potential CB cathodes but
also paves the way for further advancement in TMF-based intercalation
cathodes, diversifying the chemical space for next-generation energy storage
systems.

##  1 Introduction

The ubiquity of rechargeable Li-ion batteries (LIBs), with their high energy
and power density, has emerged as the predominant energy source for numerous
applications ranging from portable electronics, electric vehicles, and
stationary energy storage.[1, 2, 3, 4, 5, 6] However, the growing demand for
LIBs across a wide variety of applications raises concern about Li (also Co
and Ni) resource availability and associated supply-chain constraints[7],
necessitating an exploration of alternate solutions to the LIB technology.
Off-late, there is growing interest in Calcium batteries (CBs) as a potential
next-generation battery technology due to: (i) the low standard reduction
potential of Ca (-2.87 V versus standard hydrogen electrode, SHE) approaching
that of Li (-3.04 V versus SHE), (ii) the multivalent nature of Ca2+, which
shuttles two valence electrons at a time, combined with the use of Ca-metal as
anode, which can result in an increased volumetric energy density[8, 9, 10,
11, 12, 13], (iii) CBs utilize Ca, which is more abundant than Li (Ca: 4.2%
versus Li: 0.002% of earth’s crust[14]), potentially making CBs less expensive
and more sustainable than LIBs.

Despite the inherent advantages, the development of CBs is constrained by the
need for suitable electrolytes and positive electrodes (cathodes). While
stripping and plating Ca-metal at the negative electrode (anode) has
encountered challenges due to electrolyte decomposition [11, 15], recent
advances in the electrolyte design have enabled efficient Ca plating/stripping
with the formation of a protective layer enhancing electrochemical
performance.[16, 17, 18, 19] However, the lack of suitable cathode candidates,
namely lack of thermodynamic and/or cyclic stability,[13] and poor Ca2+
diffusion,[20] continues to hinder the development of practical CBs.

Previous studies have employed both experimental and computational techniques
to explore select chemistries as possible CB cathodes. The set of inorganic
cathodes that have been reported with Ca so far include CaMo6X8 (X = S, Se, or
Te),[21] VOPO4·2H2O[22], CaxV2O5,[23, 24, 25, 26, 27] CaV2O4,[28, 29]
CaMn2O4,[30] MoO3,[31, 32, 33] NH4V4O10,[34] CaCo2O4,[35, 36] NaFePO4F,[37]
TiS2,[38] CaV6O16·2.8H2O,[39] Prussian-blue analogues (PBA)[40, 41, 42, 43,
44], and other polyanionic frameworks.[45, 46, 47, 48] However, only a select
few of these compounds show reasonable electrochemical performance, with most
suffering from inadequate cyclic stability, poor Ca-ion diffusion, and large
volume changes during charge/discharge. For instance, VOPO4·2H2O demonstrates
reasonable electrochemical performance against Ca-containing electrolytes,[22]
yet its susceptibility to proton intercalation and the undesirable effects of
water in organic electrolytes pose challenges for practical cell
applications.[49]

Recently, Chando et al.[30] explored the post-spinel phase of CaMn2O4 as CB-
cathode candidate using both experiments and density functional theory
(DFT[50, 51]) calculations, and reported a low cycling capacity of 52 mAh/g at
a rate of C/33. Prabakar et al.[26] used a water-free $\beta$-phase Ca0.14V2O5
as a Ca-cathode and reported a reversible capacity of $\sim$247 mAh/g. The
authors stated that unlike conventional layered $\beta$-V2O5 and
$\delta$-CaxV2O5·nH2O cathodes, the $\beta$-phase facilitates efficient
insertion/extraction of Ca ions, contributing to improved cyclic stability and
minimal dimensional changes during charge/discharge cycles.[26]

In terms of polyanionic materials, Vaughey and co-workers[45] reported two
phosphates, namely sodium superionic conductor (NaSICON) (NaV2(PO4)3) and
olivine (FePO4), as high-voltage cathodes for room-temperature CBs. NaV2(PO4)3
demonstrates stable cycling with reversible intercalation of $\sim$0.6 mol of
Ca2+ at 3.2 V vs. Ca, while FePO4 exhibits reversible intercalation of
$\sim$0.2 mol of Ca2+ at 2.9 V. Subsequently, Kang and co-workers[47] reported
a successful extraction/insertion of Ca from/into Na0.5VPO4.8F0.7, exhibiting
exceptional cycling stability with 90% capacity retention over 500 cycles and
87 mAh/g capacity. Additionally, Nazar and coworkers[52] investigated the
Ca–Na dual cation system, using experimental and computational methods to
understand the phase evolution and kinetics of CaxNaV2(PO4)3 that takes place
during Ca2+ cycling. The authors reported a reversible Ca2+ cycling capacity
being limited to be x $\approx 0.65$ in CaxNaV2(PO4)3, attributing the limit
due to phase separation into Na-rich and Ca-rich phases. Also, the authors
demonstrated that Na+ migration within the host framework facilitates
neighboring Ca2+ migration, enabling reversible electrochemical activity.

With respect to recent computational identification of promising Ca-cathodes,
Lu et al.[28] identified two promising Ca-cathode compositions through a DFT-
based high-throughput screening considering average voltages, thermodynamic
stability, and migration barriers, namely, post-spinel-CaV2O4 and layered-
CaNb2O4. While a subsequent experimental investigation by Palacín, Arroyo-de
Dompablo and co-workers[29] showed promise for reversible Ca intercalation in
CaV2O4, further optimization of the electrode framework is imperative.
Additionally, we performed an extensive screening study of NaSICON frameworks
as potential Ca-cathodes.[48] Specifically, we used first principles
calculations to determine the ground state structure, average intercalation
voltage, 0 K thermodynamic stability, and migration barrier, using which we
identified three promising candidate Ca-cathodes, namely, CaxV2(PO4)3,
CaxMn2(SO4)3, and CaxFe2(SO4)3. Experimental realization of these predicted
NaSICONs, except for CaxV2(PO4)3, is pending.

In the context of using anion chemistry to boost energy density of cathodes,
Fluorine’s high electronegativity triggers a strong inductive effect on
transition-metal (TM) ions within the cathode.[53] As a result of this
inductive effect, the electron density on the TM redox center reduces,
resulting in a better response to addition or removal of electrons, or a
higher voltage with the (de)intercalation of an electroactive ion.[54] In
addition, the lower molar mass of F compared to polyanionic groups (e.g.,
phosphates) can enhance the gravimetric capacity of a given cathode. Thus,
fluorine-based frameworks can exhibit higher voltages, on average, compared to
oxide or other halide frameworks. As a result, researchers typically utilize
F- to substitute anionic sites or polyanionic groups, completely/partially,
yielding better cathode materials with enhanced properties.[47, 55, 56, 57,
58]

Fluorides as a chemical space are a promising, yet overlooked class of host
materials as cathodes in intercalation-based electrochemical energy storage
systems, especially in CBs. A few fluoride compounds, such as perovskite-type
NaMF3 (M = Fe, Mn, Ni, and Co), have been investigated as cathodes for sodium-
ion batteries (NIBs).[59, 60] NaFeF3 showed an initial capacity of 130 mAhg-1,
yet suffered from high polarization and capacity fading, while the initial
charge capacity of NaMnF3, NaNiF3 and NaCoF3 was limited to 40 mAhg-1, largely
attributable to side reaction as later demonstrated by Dimov et al.[61] While
Ca is known to occupy the perovskite framework among oxides,[62, 63] fluorine-
based perovskites have not been rigorously explored for CBs.

Weberite-type fluorides (typically Fe-containing), known for their robust
three-dimensional open framework interconnected by FeF6 octahedra, have been
explored computationally as NIB cathodes by Euchner et al.[64] Moreover,
weberites can be synthesized from fluoride precursors using topochemical wet
chemistry routes, which employ lower temperatures compared to solid-state
synthesis routes.[65, 66] Recently, Park et al.[67] investigated trigonal-type
fluoride weberite (Na2Fe2F7), using experimental and computational methods.
The authors demonstrated a high capacity of 184 mAh/g at C/20 (1C = 184 mA
g-1), which approaches the theoretical capacity of the weberite and reported a
capacity retention over 88% of the initial capacity at 2C after 1000 cycles
along with an average operating voltage of $\sim$3.1 V. Park et al. attributed
this exceptional electrochemical performance to preventing structural changes
during Na (de)intercalation and facile Na+ diffusion. Note that the similarity
in size between Na+ and Ca2+ (116 and 114 pm in an octahedral coordination
environment surrounded by O2-, respectively[68, 69]) indicates that cathodes
with reversible Na-intercalation may hold promise as CB cathodes as well.
Thus, fluoride frameworks, specifically with the weberite and perovskite
structures, could be potential Ca-cathodes.

In this work, we use DFT-based calculations to systematically explore the
chemical space of weberite- and perovskite-type fluorides, with chemical
formula of CaxM2F7 and CaxMF3, respectively, as potential CB cathodes. Here, M
represents a redox active 3d transition metal, including Ti, V, Cr, Mn, Fe,
Co, or Ni, while x represents the Ca composition within a range of $0\leq$ x
$\leq 1.5$ for weberites and $0\leq$ x $\leq 0.5$ for perovskites. We
calculate the ground state structure (including the stable Ca-vacancy
arrangement), 0 K thermodynamic stability, average Ca intercalation voltage
and Ca2+ migration barriers upon Ca (de)insertion in the weberite and
perovskite fluorides. Importantly, our systematic screening identifies
CaxCr2F7 and CaxMn2F7 weberites as promising cathode candidates for CBs. Our
study marks the first extensive exploration of fluoride frameworks as
potential intercalation-type Ca-cathode materials, which can hopefully aid in
the practical development of energy dense CBs.

##  2 Results

###  2.1 Structural Features

####  2.1.1 Weberites

Figure 1: The crystal structure of the conventional cell (panel a) and
primitive cell (panel b) of orthorhombic weberite, and conventional cell of
trigonal weberite (panel c). Green and purple polyhedra indicate MF6
octahedral for divalent (M2+) and trivalent (M3+) transition metals,
respectively, where oxygen atoms are represented by grey spheres. Orange, and
light blue spheres in panel a, b, c indicate Na1 and Na2 sites (equivalent to
Ca1 and Ca2 in Ca-based weberites), respectively, and maroon spheres in panel
c indicate Na3 sites (equivalent to Ca3). Dashed black lines indicate the
extent of the unit cell.

The weberite structure derives its name from the parent compound, namely the
mineral Na2MgAlF7, and typically crystallizes in an orthorhombic structure[70]
with a space group of Imma (panels a and b of Figure 1). The weberite
framework is considered as a type of anion-deficient fluorite superstructure
with a general stoichiometry of A(4a)A'(4d)M(4b)M'(4c)F7(4e,8h,16j). A and A'
usually represent Na occupying two different crystallographic sites,
represented by orange (Na1 or 4a sites) and blue (Na2 or 4d) spheres in Figure
1a and b. M and M' represent TM cation with a +2 and a +3 oxidation state,
respectively, and are represented by green and purple octahedra in Figure 1.
Note that the A and A' represent possible sites for Ca occupation in Ca-
containing weberites. The conventional cell of the orthorhombic weberite
(Figure 1a) consists of four A2M2F7 (A = Na/Ca) formula units, with the MF6
and M'F6 octahedra sharing corners to form a three-dimensional framework. The
primitive cell of the orthorhombic weberite (Figure 1b) has two A2M2F7 formula
units. The fluorine atoms, which are represented by grey spheres, occupy three
different Wykoff positions, namely F1 (4e), F2 (8h) and F3 (16j).

Both Na1 and Na2 sites coordinate with 6+2 with neighboring fluorine atoms,
with Na1 exhibiting a hexgonal bipyramidal coordination and Na2 displaying a
distorted cubic (or square prism) coordination. While Na1 coordinates with all
three types of F sites, Na2 coordinates with only F1 and F2. The Na2 polyhedra
are interconnected via edge-sharing, resulting in a series of chains along
[100], as shown in Figure S1a of the supporting information (SI). On the other
hand, the Na1 polyhedra share corners among each other along [010] (Figure
S1b), with the Na1 polyhedra also sharing some of their edges with Na2
polyhedra (Figure S1a). Note that there exists another orthorhombic weberite
structure, with space group Pmnb, which is considered to be a modification of
the Imma weberite via tilting of the Na1 polyhedra resulting in a set of non-
corner-sharing pentagonal bipyramidal polyhedra (Figure S1c). We will not be
considering the distorted Pmnb version of the weberite structure further in
our work.

Interestingly, the Imma weberite framework can be considered as a repeated
stacking of slabs made of (011) planes. Each slab consists of two distinct
layers, namely A3M (A-rich layer) and AM3 (TM-rich layer), forming an ‘AA’
stacking sequence, as depicted in Figure S2a. In turn, each layer exhibits a
Kagome-like network where majority cations (A in A3M and M in AM3) form a
continuous network, while minority cations occupy the Kagome ring centers as
illustrated in Figure S2b,c.

In addition to the orthorhombic crystal structure, weberite can exist as a
trigonal and a monoclinic polymorph, which differ in their stacking sequence
of the Kagome-type layers.[71, 72] Figure 1c depicts the conventional cell of
trigonal weberite of space group P3121 and consisting of six formula units of
A2M2F7, depicted including the Wyckoff notation as
A2(6c)M(3a)M'(3b)M''(6c)F7(6c). In trigonal weberites, there are two distinct
sites for trivalent cations M/M' sitting at 3a/3b sites (purple polyhedra in
Figure 1c), while the divalent cations (M'') sit in 6c sites (green
polyhedra). The TM-F polyhedra are connected to each other through corner
sharing to form a three-dimensional open framework. There are 3 distinct sub-
sites for Na occupation, namely Na1 (orange spheres in Figure 1c), Na2 (half-
blue spheres), and Na3 (half-maroon spheres). There are 6 Na sites of each
type in the conventional trigonal cell, with the Na2 and Na3 sites being half-
occupied in the stoichiometric (i.e., A2M2F7) weberite. All three Na sites in
the trigonal structure can be occupied by Ca, and denoted as Ca1, Ca2, and Ca3
sites in the Ca-containing structures.

The Kagome-type stacking in trigonal weberite follows an ‘ABCABC’ sequence,
compared to the AA sequence in orthorhombic weberite, as depicted in Figure
S3a. The A3M layer in trigonal weberite, which is constructed with four half
occupied Na2 and four fully occupied Na1 sites forming an octagonal ring with
a trivalent TM at the center is shown in Figure S3b. The AM3 layer consists of
four divalent and two trivalent TMs forming a hexagonal ring with two half-
occupied Na3 sites within the ring, as displayed in Figure S3c. For a point of
comparison with the orthorhombic structure, the trigonal weberite with
stoichiometric Na site occupancy (i.e., containing 2 Na per formula unit) is
illustrated in Figure S4a, and the corresponding Kagome-type stacking is
depicted in Figure S4b-c. The distinctions among the A-, B-, and C-type
stacking layers lie in the orientation of the TMs and/or the arrangement of Na
sites. For instance, Na1 sites are arranged in identical zigzag fashion along
the [100], [110], and [010] directions in the A3M layer, within the A-, B-,
and C-type stacking slabs, respectively (Figure S4b). Note that the monoclinic
weberite is reported to exist in two different Kagome-type staking sequences,
namely ABAB and AABBAABB with both phases crystallizing in the C2/c space
group.[73] However, we do not include the monoclinic structure in our study
since only the orthorhombic and trigonal weberites have demonstrated
electrochemical activity in NIBs.[65, 67]

For Ca-containing weberites, we generated the corresponding orthorhombic
(O-weberite) and trigonal (T-weberite) compositions and structures (i.e.,
CaxM2F7) by substituting Ca2+ at the Na+ sites and utilising a redox-active
3$d$ TM (Ti, V, Cr, Mn, Fe, Co, or Ni) at the M sites. We considered the
charged and discharged weberite compositions to be M2F7 (TM oxidation state of
+3.5) and Ca1.5M2F7 (TM oxidation state of +2) to account for charge-
neutrality of the overall composition given most TMs can reversibly access
oxidation states between +2 and +4 during a redox reaction.[48] We utilised
the primitive cell of O-weberite and conventional cell of T-weberite to
calculate the the ground state structure at both charged and discharged
compositions.

Based on calculated DFT total energies, we find the O-weberite to be
energetically more favorable than the T-weberite at the charged compositions
for V, Fe, and Co compounds, while the T-weberite is more favorable for
charged Ti, Cr, Mn, and Ni compounds. In the case of discharged weberite
compositions, we find the T-weberite structure to be energetically more
favorable for all TMs considered. We have compiled the relative energies
between O- and T-weberite structures at both the charged and discharged
compositions in Table S2 of the SI. The occupancy of individual Ca sites in
the ground state weberite configurations (i.e., T-weberite for discharged
compositions), as calculated by DFT, is compiled in Table 1, while a schematic
of all ground state configurations is compiled in Figure S5. Interestingly, at
the discharged composition, we find Ca to partially occupy all three
crystallographic sites for all TMs, indicating the lack of a strong preference
for a specific site. Note that although the Ca occupancies are identical for
Ti and V/Cr/Co T-weberites (Table 1), the specific Ca-vacancy arrangements are
different (Figure S5).

Table 1: Site occupancy of the Ca1, Ca2, and Ca3 sites in the calculated T-weberite ground states. Compositions | Ca site occupancy
---|---
Ca1 | Ca2 | Ca3
Ca1.5Ti2F7 | 1/3 | 2/3 | 1/2
Ca1.5M2F7, M = V, Cr, Co | 1/3 | 2/3 | 1/2
Ca1.5M2F7, M = Mn, Fe | 2/3 | 1/3 | 1/2
Ca1.5Ni2F7 | 1/2 | 1/2 | 1/2

####  2.1.2 Perovskites

Similar to weberites, we consider perovskites of composition, CaxMF3, obtained
by inserting Ca at possible Na sites in prototypical structures. The charged
and discharged compositions of Ca-containing perovskites are MF3 (TM oxidation
state of +3), and Ca0.5MF3 (TM oxidation state of +2), respectively, which
satisfies the charge neutrality constraint. Note that Na-containing
perovskite-type TM fluorides exhibit different polymorphs depending on the TM.
For our investigation, we considered three different perovskite polymorphs,
namely cubic (Pm$\bar{3}$m space group), orthorhombic (Pnma), and triclinic
(P$\bar{1}$). While we used the conventional perovskite cell (containing four
CaxMF3 formula units) for calculations involving orthorhombic and trigonal
polymorphs, we used a $2\times 2\times 2$ supercell (with eight formula units)
for the cubic polymorph. The set of perovskite structures we considered, along
with the calculated ground state Ca-vacancy configurations are compiled in
Figure S6.

For each TM, we considered the experimentally known ground state[61] of the
corresponding Na-containing perovskite for creating the corresponding Ca-
perovskite structure. For example, we used the cubic and triclinic structures
for CaxVF3 and CaxCrF3, respectively, since the ground states of the
corresponding Na-containing perovskites (i.e., NaVF3 and NaCrF3) are cubic[74]
and triclinic[75]. Similarly, we used the orthorhombic polymorph for Mn,[76]
Fe,[77] Co,[78] and Ni[78] containing perovskites. For the case of CaxTiF3, we
calculated the total energies of the cubic, orthorhombic, and triclinic
structure with composition of Ca0.5TiF3, as the ground state of the analogous
Na-containing composition is unknown. Subsequently, we found the orthorhombic
structure to be energetically preferred for Ti-based perovskite (16.7 and 0.1
meV/atom lower than cubic and triclinic, respectively). For each discharged
Ca0.5MF3 polymorph, we constructed the corresponding charged structure by
removing all Ca2+ from the discharged structure.

###  2.2 Thermodynamic Stabilities

Figure 2: DFT-calculated energy above or below the ground-state convex hull
(EHull) for charged and discharged weberites (first two rows), and perovskites
(last two rows). Each column corresponds to a specific 3d TM. Blue (red)
squares indicate high degrees of stability (instability), with the specific
EHull value of each composition listed as text annotation within each square.
The green line on the legend bar indicates the rule-of-thumb EHull$\sim$50
meV/atom threshold for experimental synthesizability.

Figure 2 presents the 0 K calculated thermodynamic (in)stability, quantified
using energy above or below the convex hull (EHull[62]), of the charged and
discharged weberite (first two rows) and perovskite (last two rows) fluorides,
for all TM-containing systems considered. The EHull value for each composition
is indicated using a text annotation in the corresponding square of Figure 2,
where blue (red) squares indicate stable/metastable (unstable) compositions.
Note that values of EHull $\geq$ 100 meV/atom (EHull $\leq$ 0 eV/atom) are
depicted by fully red (blue) squares. Given that metastable compounds at 0 K
can be synthesized under different experimental conditions, we have used a
rule-of-thumb synthesizability threshold of EHull$\sim$50 meV/atom,[79] as
indicated by the green line on the legend bar of Figure 2. Typically
compositions with 0$<$EHull$\leq$50 meV/atom are referred to as metastable,
while compositions with EHull$>$50 meV/atom are considered unstable. The 0 K
convex hull of all ternary Ca-M-F weberites and perovskites, which comprise of
possible all unary, binary, and ternary compositions that are known to exist
in addition to the weberites and perovskites considered here, are compiled in
Figures S7, S8. The compounds that are ‘adjacent’ on the convex hull for all
weberites and perovskites, i.e., compounds that thermodynamically compete with
stable weberites/perovskites for existence and compounds that are the
decomposition products of unstable weberites/perovskites, are compiled in
Table S3.

We observe that most of the charged compositions of weberites (first row in
Figure 2) are metastable with EHull (in meV/atom) of 13 (Ti2F7), 11 (V2F7), 11
(Cr2F7), 13 (Mn2F7), and 26 (Ni2F7), suggesting that these compounds are
potentially synthesizable. In contrast, the charged Fe- and Co-weberites are
unstable, exhibiting high EHull of 114 and 78 meV/atom, respectively. Note
that Fe2F7 is thermodynamically driven to decompose into the stable adjacent
compounds on the Ca-Fe-F convex hull, namely F2 and FeF3 (Table S3 and Figure
S8). Similarly, Co2F7 is expected to decompose into F2 and CoF3.

Interestingly, most of the discharged weberites (second row in Figure 2) are
stable compounds with large negative EHull (in meV/atom) of -585 (Ca1.5V2F7),
-170 (Ca1.5Mn2F7), -95 (Ca1.5Fe2F7), -565 (Ca1.5Co2F7), and -573 (Ca1.5Ni2F7),
suggesting that these compositions should be experimentally synthesizable
given their large thermodynamic driving force for formation. While discharged
Ti-weberite is metastable (EHull$\sim$44 meV/atom), the discharged Cr-weberite
is marginally unstable (EHull$\sim$57 meV/atom, marginally higher than our
synthesizability threshold). Nevertheless, both Ca1.5Ti2F7 and Ca1.5Cr2F7 may
be experimentally accessible.

In the case of perovskites, most of the charged fluorides lie marginally above
the convex hull and are likely synthesizable, including TiF3, VF3, CrF3, FeF3,
CoF3 and NiF3, with EHull (in meV/atom) of 1, 35, 7, 22, 35, and 7,
respectively. Note that these charged perovskites are metastable with respect
to their corresponding known trigonal trifluoride polymorphs (with space group
of R$\bar{3}$cR), as compiled in Table S3.[80] The only charged perovskite
that is thermodynamically stable at 0 K is MnF3, with EHull of -4 eV/atom. On
the other hand, several discharged perovskites are unstable, with Ca0.5TiF3,
Ca0.5CrF3, and Ca0.5FeF3 exhibiting large EHull values of 97, 110, and 86
meV/atom, respectively. The metastable discharged perovskites include
Ca0.5VF3, Ca0.5CoF3, and Ca0.5NiF3, with EHull of 7, 20, and 29 meV/atom,
respectively. Similar to charged perovskites, the only discharged perovskite
composition that is thermodynamically stable is the Mn-version, with EHull of
-1 meV/atom.

Generally, it is preferable that both the charged and discharged compositions
of an intercalation system are thermodynamic stable (or metastable) to prevent
undesirable decomposition or conversion reactions.[81] Thus, we identify
CaxMnF3 as a potential Ca-cathode, under the constraint of both charged and
discharged phases being stable. Given that there are several examples of
metastable cathodes that show good electrochemical performance,[82, 83, 84,
85] we can use a constraint of both charged and discharged compositions being
at most metastable for identification of candidates. In this context, we
identify the following compositions to be candidate cathodes for CBs solely
based on our 0 K stability calculations, namely, CaxTi2F7, CaxV2F7, CaxCr2F7,
CaxMn2F7, and CaxNi2F7 within weberites and CaxVF3, CaxMnF3, CaxCoF3, and
CaxNiF3 among perovskites. The other compounds that we predict to be stable,
such as Ca1.5Fe2F7, and Ca1.5Co2F7, may be relevant for other non-CB
applications.

###  2.3 Average Voltages and Theoretical Capacities

Figure 3: Computed average voltage as a function of transition metal, between
the fully charged and discharged orthorhombic weberite (O-weberite,
represented by orange triangles), trigonal weberite (T-weberite, purple
squares) and perovskite (green circles) fluorides.

The electrochemical performance of a battery system is primarily quantified by
its energy density, a metric determined by the voltage and capacity of
electrodes utilised. Thus, we calculated the average Ca-intercalation voltage
of the weberites and perovskites considered using DFT. Note that we computed
the average voltage and theoretical capacity irrespective of thermodynamic
(in)stabilities of all compositions to analyze the overall voltage-capacity
trends. The calculated voltages (versus Ca) and gravimetric capacities are
summarized in Table 2. The theoretical capacities are calculated with
reference to the charged compositions, i.e., MF3 for perovskites and M2F7 for
weberites. Note that the calculated capacities decrease monotonically from Ti
to Ni for both fluoride frameworks, namely from 351 to 320 mAh g-1 in
weberites, and 255 to 231 mAh g-1 in perovskites, due to the increase in
atomic mass from Ti to Ni. Also, the weberites show higher theoretical
capacities compared to the perovskites, due to the higher quantity of Ca2+
(1.5 moles in weberites versus 0.5 moles in perovskites) per formula unit that
can be intercalated.

Table 2: The calculated average intercalation voltage (in Volts versus Ca) and the theoretical gravimetric capacity (in mAh g-1) of the weberites and perovskites considered. O-Weberites and T-weberites represent voltages calculated for topotactic intercalation within the orthorhombic and trigonal weberite polymorphs, respectively. The theoretical capacities are computed with respect to the molar mass of M2F7 for weberites and MF3 for perovskites (M = 3$d$ TM). M |  | Average Voltage (V) |  | Theoretical Capacity (mAhg-1)
---|---|---|---|---
O-Weberites | T-Weberites | Perovskites | Weberites | Perovskites
Ti | 2.4 | 2.5 | 1.7 | 351 | 255
V | 3.6 | 3.6 | 2.8 | 342 | 248
Cr | 3.1 | 3.2 | 1.8 | 339 | 246
Mn | 4.8 | 4.7 | 4.2 | 331 | 239
Fe | 4.5 | 4.5 | 3.2 | 328 | 237
Co | 5.5 | 5.6 | 4.9 | 320 | 231
Ni | 5.6 | 5.5 | 5.0 | 320 | 231

Figure 3 displays the calculated average intercalation voltages (in Volts
versus Ca metal) for all fluoride frameworks considered here. O-weberite
(orange symbols), T-weberite (purple symbols) and perovskite (green symbols)
represent the calculated voltages for a topotactic intercalation within the
orthorhombic weberite, trigonal weberite, and perovskite polymorphs,
respectively. The average voltage is calculated across the entire Ca content
range, i.e., M2F7 $\leftrightarrow$ Ca1.5M2F7 for weberites and MF3
$\leftrightarrow$ Ca0.5MF3 for perovskites. Notably, we predict the Ca
intercalation voltage (in V vs. Ca) to be within the range of 2.4 (Ti) – 5.6
(Ni) for O-weberites, 2.5 V (Ti) -5.6 V (Co) for T-weberites, and 1.7 V (Ti) -
5.0 V (Ni) for perovskites. Clearly, the calculated voltages and trends for
both O-weberite and T-weberite are similar across the 3d series, suggesting
that both polymorphs may exhibit similar Ca intercalation phase behavior.
Additionally, both weberites display consistently higher voltages (by at least
0.5 V) than the corresponding perovskites, which predominantly originates from
the charge/discharge process accessing higher TM oxidation states in weberites
(+3.5) compared to perovskites (+3).

Across the 3$d$ series, both weberites and perovskites show similar non-
monotonic trends, i.e., the voltages generally increase from Ti to Ni with
local minima at Cr and Fe compositions, similar to trends observed in sulfate-
NaSICONs for Ca intercalation.[48] In the case of T-weberites, there is a
marginal dip in voltage from Co to Ni (by 0.1 V). The likely reason for the
local minima in calculated voltages at Cr and Fe is the high stability of the
Cr3+ and Fe3+ oxidation states, which are accessed as Ca is deintercalated.
Note that Cr3+ and Fe3+ are stable due to their high-spin half-filled
$t_{\textsubscript{2g}}^{\textsuperscript{3}}$ and half-filled $d$ shell
($t_{\textsubscript{2g}}^{\textsuperscript{3}}e_{\textsubscript{g}}^{\textsuperscript{2}}$)
electronic configurations, respectively.[86, 87]

In addition to the topotactic voltage, we calculated the non-topotactic
average voltage for select weberites that exhibit different ground state
polymorphs in their charged and discharged states. For instance, the ground
state of charged weberites V2F7, Fe2F7, Co2F7 are orthorhombic, while the
ground state of their corresponding discharged weberites (Ca1.5V2F7,
Ca1.5Fe2F7, Ca1.5Co2F7) are the trigonal. Hence, we calculated the average
voltage of V-, Fe-, and Co-based weberites between a charged orthorhombic and
a discharged trigonal structure, resulting in values of 3.6, 4.5, 5.5 V vs.
Ca, respectively. Importantly, the computed non-topotactic voltages are
similar to the corresponding topotactic voltages ($<$0.1 V difference),
suggesting insignifcant driving force for any phase transition between the
trigonal and orthorhombic structures during Ca (de)intercalation. The
similarity between the non-topotactic and topotactic voltages can also be
rationalised via the ‘small’ differences in the DFT-calculated total energies
between the orthorhombic and trigonal structures for all TMs (see Table S2).
Given the marginal thermodynamic driving force for a phase transition between
orthorhombic and trigonal weberites during Ca (de)intercalation, we expect the
topotactic pathway to be active under electrochemical conditions. Therefore,
we take into account topotactic Ca (de)intercalation in the trigonal weberite
for further discussions in this manuscript, given the trigonal structure is
energetically preferred at the Ca1.5M2F7 composition for all TMs considered.

Given the lower voltages with Ti-based weberites and perovskites, and the Cr-
perovskite ($\leq$2.5 V), these compositions are better suited for anode
applications, while the high voltages of Co- and Ni-based fluorides ($>$5 V)
may be beyond the stability limits of available Ca-electrolytes. Despite this
concern, it may be possible to operate the Co and Ni fluorides at a reduced
voltage by extracting a lower amount of Ca from the cathode, albeit reducing
the energy density. For example, the calculated voltage of 4.5 V for Fe2F7
$\leftrightarrow$ Ca1.5Fe2F7 decreases to 3.4 V when considering Ca0.5Fe2F7
$\leftrightarrow$ Ca1.5Fe2F7, where only one mole of Ca is extracted per
weberite formula unit. Thus, all weberites except Ti and all perovskites
except Ti and Cr are candidate CB cathodes, based solely on our voltage
calculations.

However, including both voltage and stability data reduces the set of possible
candidates. For example, the low voltages of Ti- and Cr-perovskites may appear
to be suitable for anode applications, but the high thermodynamic instability
of the discharged Ti- and Cr-perovskites (EHull$>$95 meV/atom, Figure 2) may
impede any practical deployment. Similarly, Fe-based weberites and perovskites
are constrained by high instabilities of the charged and discharged
compositions, respectively. In contrast, Mn-weberite, Mn-perovskite, and Ni-
weberite are highly promising both due to their high voltages ($>$4 V) and
thermodynamic (meta)stabilities. Thus, combining our voltage and stability
data, we identify weberites containing Ti, V, Cr, Mn, and Ni, and perovskites
containing V, Mn, Co, and Ni to be suitable for CB electrode applications.
Nevertheless, the practical feasibility of any of these identified materials
to function as a CB electrode depends on their corresponding bulk Ca2+
diffusivities (vide infra).

###  2.4 Migration Barriers

Figure 4: Calculated Ca2+ Em in the Ti-, V-, Cr-, Mn-, and Ni-weberite frameworks, indicated as text annotations. In each weberite structure, we calculated the Em across three different migration pathways, namely Path1 (top row), Path2 (middle row), and Path3 (bottom row). Bottom and top triangles within each square indicate high (charged state) and low (discharged) Ca-vacancy concentrations. Green line on the legend bar indicates the tolerance limit on Em ($\sim$1000 meV) for enabling Ca2+ diffusion. Due to convergence difficulties, we are unable to calculate a Em for V2F7 along Path3 (solid black line). Table 3: Calculated Ca2+ Em in perovskites considered, at charged and discharged states. Solid lines represent absence of reliable Em for MnF3 and Ca0.5CoF3 due to convergence difficulties. Compounds | Migration energy (meV)
---|---
Charged | Discharged
CaxVF3 | 2875 | 1832
CaxMnF3 | — | 1980
CaxCoF3 | 1666 | —
CaxNiF3 | 2445 | 2120

Typically, the mobility of Ca2+ in solids is lower compared to monovalent
active ions, such as Li+, and Na+, due to the strong electrostatic interaction
of the divalent Ca2+ with the neighboring anions while migrating through a
host framework.[20] Subsequently, we computed the migration barriers (Em) of
Ca2+ using the nudged elastic band (NEB[88, 89]) framework and the generalized
gradient approximation (GGA[90]) exchange-correlation functional in the five
weberite and four perovskite candidates that we had shortlisted based on our
voltage and stability calculations. Note that the diffusivity of Ca2+ depends
exponentially on Em, via the well-known Arrhenius relationship.[91]

Figure 4 depicts the calculated Em in weberites across three different
migration pathways, namely Path1 (top row), Path2 (middle row) and Path3
(bottom row) at the charged (bottom triangles) and discharged (top triangles)
compositions. The individual pathways are depicted in Figure 5, wherein any of
the three pathways can facilitate macroscopic Ca2+ diffusion within the three-
dimensional trigonal weberite framework. The green line on the legend bar
indicates the tolerance limit of $\sim$1000 meV for the Em, which corresponds
to maintaining a reasonable electrochemical rate performance in a potential
Ca-cathode.[48] A brown (purple) triangle in Figure 4 represents a low (high)
Em thereby indicating a facile (poor) Ca2+ migration. The calculated Em in
perovskites are compiled in Table 3. Due to convergence difficulties with our
NEB calculations, we are unable to provide an accurate Em for the charged
CaxV2F7 weberite along Path3 (solid black line). The minimum energy pathways
for all weberite and perovskite structures are presented in Figure S9 and S10
of the SI, respectively.

Unsurprisingly, our calculations predict fairly high Ca2+ Em for most of the
weberites considered. For instance, the Em across all three paths in CaxV2F7,
at both the charged and discharged compositions are above the 1000 meV
threshold, suggesting that the V-weberite is likely infeasible to be used as a
CB cathode. In the case of Ti-weberite, the Em along Path1, Path2, and Path3
are within a wide range of 641 to 1929 meV. Particularly, the Em of the
charged CaxTi2F7 along Path2 (641 meV) and Path3 (880 meV), are well within
the tolerance limit. However, the Em at the discharged limit are above the
1000 meV tolerance for all three paths in the discharged CaxTi2F7 weberite,
suggesting limitations with using the Ti-weberite as a CB anode. Similarly,
the Ni-weberite shows reasonable Em in its charged state along Path1 (881 meV)
and Path2 (1042 meV), but the Em is above the 1000 meV tolerance in the
discharged state of the Ni-weberite for all pathways, making it unsuitable as
a CB cathode.

In the case of Cr- and Mn-weberites, we find at least one pathway within the
corresponding structures that can facilitate Ca2+ diffusion. For instance, the
Em in CaxCr2F7 exceeds the 1000 meV threshold along both Path1 (842-1376 meV)
and Path3 (1238-1992 meV), suggesting the unavailability of these pathways for
Ca2+ motion. However, the Em along Path2 is in the range of 877-1052 meV,
which is only marginally above the 1000 meV tolerance, suggesting that Path2
may be open for Ca2+ diffusion within the Cr-weberite. Considering the ground-
state Ca-vacancy configuration of Ca1.5Cr2F7 trigonal weberite (Figure S5d),
the fact that only Path2 remains open for Ca2+ diffusion possibly limits the
amount of Ca that can be reversibly exchanged with the weberite structure to
0.83 moles per formula unit, corresponding to a capacity of $\sim$164 mAhg-1,
instead of the full 1.5 moles of Ca ($\sim$339 mAhg-1).

In the Mn-weberite, the Em along both Path1 (1025-1045 meV) and Path2
(1020-1051 meV) are only marginally above the threshold, suggesting the
feasibility of Ca2+ migration along both paths. However, Path3 is likely
closed for Ca2+ motion in the Mn-weberite, since the Em in the charged state
(1810 meV) is significantly above the threshold despite the low Em in the
discharged state (704 meV). Given that two out of three pathways are active
for Ca2+ motion in the Mn-weberite, based on the Ca-vacancy ground state
configuration of Ca1.5Mn2F7 (Figure S5g), we conclude that the amount of Ca
that can be reversibly exchanged is 1 mole per formula unit, corresponding to
a capacity of $\sim$212 mAhg-1) instead of the maximum of 1.5 moles ($\sim$331
mAhg-1). Thus, we find both Cr-, and Mn-based weberites to be feasible to be
used as CB cathodes, based on our combined set of thermodynamic stability,
voltage, and Ca-mobility calculations.

With respect to perovskites, we find that the calculated Em in the V-, Mn-,
Co-, and Ni-based fluorides are all significantly above the 1000 meV
threshold, namely 1832-2875 meV, 1980 meV, 1666 meV, and 2120-2455 meV.
Therefore, despite their promising thermodynamic stability, average voltage,
and theoretical capacity, we don’t expect any of the perovskite fluorides to
be CB cathode candidates due to their prohibitive Ca2+ Em. Note that we are
unable to obtain reliable Em values for charged CaxMnF3 and discharged CaxCoF3
compositions, due to convergence difficulties, but we do not expect any Em
that is eventually calculated for these compositions to change our
conclusions.

##  3 Discussion

In this work, we used DFT-based calculations to explore the chemical space of
3$d$ TM-containing weberite and perovskite fluoride frameworks as potential
intercalation cathodes for CBs. Specifically, we calculated the ground state
Ca-vacancy configurations, 0 K thermodynamic stabilities, average
intercalation voltages, theoretical capacities, and Ca2+ Em in several
weberite and perovskite fluorides. We considered compositions of CaxM2F7 for
weberites (with 0$\leq$x$\leq$1.5), and CaxMF3 for perovskites (with
0$\leq$x$\leq$0.5), where M = Ti, V, Cr, Mn, Fe, Co, or Ni. Besides obtaining
several qualitative trends in stabilities, voltages, and Ca2+ mobilities, we
identify two weberite frameworks, namely Cr- and Mn-based compositions, to be
promising Ca-cathodes.

While we employed the SCAN+U functional for average voltage and thermodynamic
stability calculations, we chose GGA for Em calculations, due to lower
computational costs, better numerical convergence, and reliability in
providing qualitative trends compared to SCAN.[92] For calculating the Em in
Ca1.5V2F7 along Path3 and Cr2F7 along Path2, we initialized our NEB with five
instead of the typical seven images since we experienced convergence
difficulties with seven images. Further, in Mn2F7 (along Path2), Ni2F7 (all
paths), Ca0.5VF3 and MnF3 we used a higher spring force constant of 10 eV/Å
between images than the usual value of 5 eV/Å to mitigate convergence
difficulties. Note that the Em usually does not change significantly with
varying the spring force constant, as demonstrated by our calculations in the
discharged CaxNi2F7 system, which displays near-identical Em of 2190 and 2189
meV (along Path3) using force constants of 5 and 10 eV/Å, respectively.

Recently, Long et al., demonstrated that SCAN+U exhibits good qualitative
trends in average voltages, but tends to overestimate the absolute voltage
values and also the thermodynamic instabilities in Li-ion cathodes.[93] We
expect similar overestimation of voltages and instabilities to extend to
fluoride Ca-cathodes as well, which is why we used a slightly higher EHull
stabilization threshold ($\sim$50 meV/atom) compared to previous studies
($\sim$25 meV/atom). Nevertheless, the majority of the fluorides considered
here ($\sim$57%) exhibit EHull lower than 25 meV/atom, suggesting that these
fluorides should be synthesizable experimentally.

In terms of structures considered for the fluorides, we included orthorhombic
and trigonal polymorphs for weberites and cubic, orthorhombic, and triclinic
polymorphs for perovskites. The choice of the polymorphs for both weberites
and perovskites was largely motivated by experimental and/or electrochemical
observations in the Na-systems. Another constraint influencing the choice of
polymorphs is the computational cost of considering different combinations of
TMs and Ca-vacancy arrangements in each structure. For instance, perovskites
in general can exist in tetragonal, rhombohedral, hexagonal, and monoclinic
polymorphs as well,[62] which were not considered as possible structures here.
While we hope to extend our Ca-cathode search space to other possible
polymorphs in the fluoride chemical space in the future, we are optimistic
that our search strategy and identification of candidates in this work are
quite useful.

Although Fe-based fluoride weberite exhibits attractive electrochemical
performance as a NIB cathode,[67] we do not find the Fe-based weberite to be a
feasible candidate for CB, largely due to the instability of the charged
(Fe2F7) phase, which exhibits a high EHull of 114 meV/atom. The instability of
the Fe2F7 composition can be rationalised based on the instability of the 4+
oxidation state of Fe. Hence, we explored the stability of the charged Fe-
weberite state with Ca already present in it such that the 4+ oxidation state
is not accessed, i.e., a charged composition of Ca0.5Fe2F7. Although the EHull
reduces to 71 meV/atom with increasing Ca content in the charged state, the
Ca0.5Fe2F7 phase remains above the stability threshold of $\sim$50 meV/atom,
highlighting the instability of Fe-weberite even with introduction of
significant residual Ca content in the structure.

Given the electrochemical accessibility of the charged phase, NaFe2F7 in NIBs,
and the stability of the discharged phase, Ca1.5Fe2F7, in the Ca-Fe-F ternary
space, insertion of Na within the Fe-weberite as a ‘stuffing’ cation may
stabilize Ca-deficient compositions and enable electrochemical exchange of Ca.
This is similar to the role that Na plays in the exchange of Ca in V-based
NaSICON electrodes.[52] Also, we predict a drop in average Ca
(de)intercalation voltage from 4.5 V in the Fe2F7 $\leftrightarrow$ Ca1.5Fe2F7
range to 3.4 V in the Ca0.5Fe2F7 $\leftrightarrow$ Ca1.5Fe2F7 range, which
should be in line with stability windows of existing Ca electrolytes. Thus,
systems containing residual Na and/or Ca in the weberite structure may be
worth exploring both computationally and experimentally.

One strategy to further explore for designing CB cathodes utilising fluoride
frameworks is to explore oxyfluoride compositions, i.e., substitution of O2-
on F- sites. Introducing a mixed anion system unlocks the potential for
voltage modulation and fine-tuning other properties (such as phase behavior).
Also, substituting O at F sites will likely increase the theoretical
concentration of Ca2+ that can be accommodated in a weberite structure and
potentially lower the Em due to slightly weaker Ca-O ionic bonds than Ca-F.
Another strategy is to utilise weberite structures with multiple TMs present,
similar to prior studies on Na-based weberites.[64, 94, 95] For instance, Ni
addition to the Cr-weberite, which is a candidate identified in this work,
could enhance the voltage and mitigate Em of Ca2+ since the Ni-weberite
exhibits high voltage and reasonable Em along Path1 and Path2 at the charged
limit.

##  4 Conclusion

As an alternative to the state-of-the-art LIBs, Ca-based electrochemical
systems are a promising pathway to develop batteries with high energy density,
safety, and lower cost. However, the development of practical CBs so far has
been limited by the lack of suitable cathodes. Hence, we have used DFT-based
calculations to systematically explore TMFs exhibiting weberite and perovskite
structures, as potential CB cathodes. Specifically, we evaluated key metrics,
such as thermodynamic stabilities, average Ca-intercalation voltages,
theoretical capacities, and Ca2+ migration barriers, across weberites of
composition CaxM2F7 and perovskites of composition CaxMF3, where M = Ti, V,
Cr, Mn, Fe, Co, or Ni. Notably, we predict a majority of the TMFs to be
stable/metastable at 0 K, indicating the potential synthesizability of the
TMFs considered. Our calculated average voltages exhibit higher values in
weberites than perovskites, since we access higher TM oxidation states in the
weberite (up to 4+) compared to perovskies (3+). Combining our stability and
voltage data, we shortlisted Ti, V, Cr, Mn, and Ni weberites, and V, Mn, Co,
and Ni perovskites for Ca-mobility evaluation. Subsequently, our Em
calculations indicate potential for trigonal weberites, CaxCr2F7 and CaxMn2F7,
to be candidate CB cathodes, while none of the perovskites can facilitate Ca
diffusion under reasonable electrochemical conditions. We hope that our work
will inspire further computational and experimental efforts into the usage of
TMFs for CB cathodes, eventually resulting in the practical deployment of CBs.

##  5 Methods

###  5.1 First Principles Calculations

We used spin-polarized DFT[50, 51]) and projector augmented wave (PAW[96, 97])
potentials, as implemented in the Vienna ab initio Simulation Package
(VASP[98, 99]) in all our calculations. The list of PAW potentials used in our
calculations are compiled in Table S1 of the SI. We described the valence
electrons using a plane-wave basis, expanded up to a kinetic energy cutoff of
520 eV. We employed $\Gamma$-point-centered, Monkhorst-Pack[100] $k$-point
meshes with a minimum of 48 subdivisions along each unit reciprocal lattice
vector for geometry relaxations and a Gaussian smearing (of 0.05 eV) to
integrate the Fermi surface. We used a Hubbard U corrected strongly
constrained and appropriately normed (i.e., SCAN+U[101, 102, 103, 104, 105])
functional to describe the electronic exchange and correlation. We used U
values of (in eV) 4.5 (Ti), 4.2 (V), 1.5 (Cr), 3.8 (Mn), 5.6 (Fe), and 4.0
(Co), as derived in our previous work.[80] We utilised total energy and force
convergence criteria of 10-5 eV and $|0.03|$ eV/Å. For all structure
relaxations, we relaxed the cell shape, volume, and ionic positions, without
preserving any underlying symmetry.

###  5.2 Structure Generation

We have generated crystal structures for weberites and perovskites considered
in this work by including the constraint of charge neutrality. Note that
stable ionic crystals are typically charge neutral. In intercalation systems
that contain 3$d$ TMs, the oxidation state of the TM sets the limits on the
content of the intercalant ion within the structure. Given that 3$d$ TMs can
reversibly change their oxidation states from +4 to +2 during
(de)intercalation, the Ca content corresponding to a +4 (+2) oxidation state
represents the charged (discharged) composition of the structure. For example,
the highest oxidation state that a TM can acquire in a weberite is +3.5,
corresponding to a composition of Ca0M2F7, which in turn represents the
charged state. Similarly, the lowest (+2) oxidation state that a TM can
exhibit in a weberite is at a composition of Ca1.5M2F7, which represents the
discharged state. In the case of perovskites, MF3 (M3+), and Ca0.5MF3 (M2+)
represent the charged and discharged compositions, respectively. Thus, the
maximum amount of Ca that can be exchanged per formula unit of weberite and
perovskite is 1.5 and 0.5 moles, which is the value we have used in our
theoretical capacity calculations of Table 2.

To generate structures for our DFT calculations, we obtained starting
configurations from the international crystal structure database (ICSD[106]).
Specifically, we used the conventional cell of Na2Fe2F7[67] as a template for
trigonal weberites, while we employed the primitive cell of Na2NiFeF7[107] as
a template for orthorhombic weberites. We substituted Fe/Ni cites in our
template structures with the relevant 3$d$ TM, while Na sites were substituted
with Ca. After performing elemental substitutions, we scaled the lattice
parameters of the theoretically generated structures using the
“RLSVolumePredictor”[108] class of the pymatgen package.[109] Subsequently, we
used the “enumlib” library[110, 111, 112, 113] to generate symmetrically
distinct Ca-vacancy arrangements within each structure. In total, we generated
70 trigonal-Ca1.5M2F7 (10 per TM), 7 trigonal-M2F7 (one per TM), 14
orthorhombic-Ca1.5M2F7 (2 per TM), and 7 orthorhombic-M2F7 (one per TM) Ca-
vacancy weberite configurations.

Similar to weberites, we followed the elemental substitution, lattice
parameter scaling, and Ca-vacancy ordering enumeration to generate Ca-
containing fluoride perovskites. In total, we generated 35 configurations for
Ca0.5MF3 compositions, including 13 for Ti, 6 for V, 4 for Cr, and 3 each for
Mn, Fe, Co, and Ni and 7 MF3 (one per TM) configurations. Note that the
discharged phase of perovskites exhibit different number of distinct Ca-
vacancy configurations depending on the crystal structure. For instance, the
orthorhombic Ca0.5MF3 perovskite with (M = Ti, Mn, Fe, Co, or Ni) exhibits
three possible Ca-vacancy configurations, while the cubic and triclinic
versions exhibit six and four distinct configurations, respectively. We
obtained a total of 13 Ca0.5TiF3 configurations since we considered all three
polymorphs (i.e., cubic, orthorhombic, and triclinic) for identifying the
ground state configuration of the Ti-perovskite.

###  5.3 Average Voltage Calculations

In a reversible intercalation battery, where Ca2+ is inserted/extracted
into/from a cathode material of composition CayM2F7 (in a weberite structure)
or CayMF3 (in a perovskite structure), the overall redox reaction can be
expressed as Eq. 1 and Eq. 2, respectively.

$\ce{Ca_{y}M_{2}F_{7}+(x-y)Ca^{2+}+2(x-y)e^{-}\rightleftharpoons
Ca_{x}M_{2}F_{7}}$ (1)

$\ce{Ca_{y}MF_{3}+(x-y)Ca^{2+}+2(x-y)e^{-}\rightleftharpoons Ca_{x}MF_{3}}$
(2)

y and x are the concentrations of Ca in the charged and discharged weberite or
perovskite fluorides, respectively. The average intercalation voltage for a
given cathode material upon intercalation of (y-x) moles of Ca can be
calculated using the Nernst equation (Eq. 3), as below.[114]

$\begin{split}\langle V\rangle=-\frac{\Delta G}{2(x-y)F}\\\
\approx-\frac{E(\ce{Ca_{x}M_{2}F_{7}/Ca_{x}MF_{3}})-[E(\ce{Ca_{y}M_{2}F_{7}/Ca_{y}MF_{3}})+(x-y)\mu_{\ce{Ca}}]}{2(x-y)F}\end{split}$
(3)

$\Delta$G is the Gibbs energy change of the redox reaction, which is
approximated as the total energy calculated using DFT ($\Delta G\approx\Delta
E$), ignoring the $p-V$ and entropic contributions. F in Eq. 3 is the Faraday
constant and $\mu_{Ca}$ is the Ca chemical potential in pure Ca metal (i.e.,
in its ground state face-centered-cubic structure).

###  5.4 Ab initio Thermodynamics

The 0 K thermodynamic stability of the weberite and perovskite fluorides
considered were evaluated with respect to the corresponding elemental, binary,
and ternary compounds, as obtained from the ICSD, followed by DFT total energy
calculations. For estimating stability, we exclusively considered only ordered
structures that are available in the ICSD, to reduce computational complexity.
In addition to the ICSD compounds, we included the theoretically obtained
weberite (perovskite) compositions for estimating the stability of perovskite
(weberite) compositions, since both weberites and perovskites occupy the same
Ca-TM-F ternary chemical space. We used the pymatgen[109] package to construct
the 0 K convex hull and calculate the EHull for all Ca-TM-F ternary systems.
Note that we used the SCAN functional without any $U$ corrections for total
energy calculations of all unary systems (i.e., Ca, TMs, and F2).

###  5.5 Migration Barrier Calculations

Figure 5: Ca2+ migration pathways in trigonal weberite, including Path1, Path2
(panel a), and Path3 (panels b and c). Purple polyhedra indicate MF6 octahedra
and F atoms are represented by grey spheres. Orange, and light blue spheres in
panel a, b, c indicate Ca1 and Ca2 sites, respectively, while maroon spheres
in panel b and c indicate Ca3 sites.

We used DFT-based NEB[88, 89] to evaluate the Ca2+ Em in select weberite and
perovskite fluorides. We used the GGA exchange-correlation functional instead
of SCAN/SCAN+U to calculate Em to minimize computational costs and mitigate
convergence difficulties.[92] For all structures, we calculated Em at both the
charged (low Ca concentration) and the discharged (high Ca concentration)
states. We considered a vacancy-mediated Ca2+ migration mechanism in all
structures. We converged the atomic forces to $|0.03|$ eV/Å within the
endpoint structures of each NEB. Subsequently, we initialized the minimum
energy path (MEP) of the NEB calculation by linearly interpolating the lattice
vectors and atomic positions to create seven intermediate images between the
endpoints, with a spring constant of 5 eV/Å between images. For select
structures, we used five intermediate images and/or a spring constant of 10
eV/Å (see Section 3). We sampled the irreducible Brillouin zone of all
endpoint and NEB calculations with $\Gamma$-centered Monkhorst-Pack[100]
$k$-point meshes with a minimum of 32 sub-divisions across each unit
reciprocal lattice vector. The NEB calculations were converged until the
perpendicular component of the band force between images reduced to $<$
$|0.05|$ eV/Å.

Within the trigonal weberite, we identified three possible Ca2+ migration
pathways with distinct local environments, namely Path1 (Ca1-Ca1), Path2
(Ca2-Ca1), and Path3 (Ca3-Ca1), as depicted in Figure 5. The same pathways for
Na+ migration were explored by Lu et al.[94] in a recent study. Note that the
Na arrangement along the B-type slab (within the ABCABC stacking sequence) is
equivalent to the Na arrangement in the A- and C-type slabs, but along
different directions. Therefore, the type of paths considered change their
direction depending on the type of slab considered. For example, Path1 is
along the $a$-axis or [100] direction in the A3M layer of the B-type slab,
which is analogous to Path1 along the [110] direction in the A-type and [010]
direction in the C-type slabs.

Notably, Path1 and Path2 migration pathways lie on the $a-b$ plane (across all
A-, B-, and C-type slabs) allowing accessibility of Ca2+ at the Ca1 and Ca2
sites (within the A3M layers), as shown in Figure 5a. Specifically, all the
Ca1 sites can be accessed through Path 1, while the Ca at Ca2 sites can be
accessed through Path2. The Ca2+ at Ca3 sites on the AM3 layer can migrate
along Path3, if both Em from Ca3 to Ca1 and Ca3 to Ca2 are reasonable. Note
that the Ca1-Ca3-Ca2 chains along the $c$-axis are connected via Path3, which
is independent of Path1 and Path2. In case only one Em, i.e., Ca3-Ca1 or
Ca3-Ca2, is reasonable, Ca2+ at Ca3 sites can migrate to available Ca1 or Ca2
sites on the A3M layer, and subsequently use Path1 or Path2 for macroscopic
diffusion. However, Lu et al.[94] have shown that the MEP and Em for a Na hop
from Na3 to Na1 sites are similar to a Na hop from Na3 to Na2 sites. Given the
similarity between the migration paths from Na3 (Ca3) to Na1 (Ca1) and Na2
(Ca2) sites, we evaluated the Em for Ca2+ migration from Ca3 to Ca1 sites
along Path3 (see panels b and c of Figure 5). Thus, depending upon the
magnitude of Em, we can conclude that either Path3 will be fully open or fully
closed to Ca-diffusion.

## Acknowledgments

G.S.G. acknowledges financial support from the Indian Institute of Science
(IISc) and support from the Science and Engineering Research Board (SERB) of
Government of India, under Sanction Numbers SRG/2021/000201 and
IPA/2021/000007. D.B.T. acknowledges financial support from Indian Institute
of Science. The authors acknowledge the computational resources provided by
the Supercomputer Education and Research Centre (SERC), IISc. A portion of the
calculations in this work used computational resources of the supercomputer
Fugaku provided by RIKEN through the HPCI System Research Project (Project ID
hp220393). We acknowledge National Supercomputing Mission (NSM) for providing
computing resources of ‘PARAM Siddhi-AI’, under National PARAM Supercomputing
Facility (NPSF), C-DAC, Pune, and the resources of ‘Param Utkarsh’ at CDAC
Knowledge Park, Bengaluru. Both PARAM Siddhi-AI and PARAM Utkarsh are
implemented by CDAC and supported by the Ministry of Electronics and
Information Technology (MeitY) and Department of Science and Technology (DST),
Government of India. The authors gratefully acknowledge the computing time
provided to them on the high-performance computer noctua1 and noctua2 at the
NHR Center PC2. This was funded by the Federal Ministry of Education and
Research and the state governments participating on the basis of the
resolutions of the GWK for the national high-performance computing at
universities (www.nhr-verein.de/unsere-partner). The computations for this
research were performed using computing resources under project hpc-prf-emdft.

### Author Contributions

GSG: Conceptualization, Supervision, Methodology, Writing, and Editing. DBT:
Data generation and curation, Visualization, Writing, and Editing.

### Conflicts of Interest

There are no conflicts to declare.

## Supplementary Materials

Electronic Supporting Information is available online at , Projector augmented
wave potentials used, structural features of orthorhombic and trigonal
weberites, ground state Ca-vacancy configurations in both weberites and
perovskites, 0 K phase diagrams, and minimum energy pathways of Ca2+ migration
in select structures.

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