







































Coskun Firat /Future Sustainability                                                                                           August 2025| Volume 03 | Issue 03 | Pages 
26-34 

26 

 

 

 

Article 

Unifying thermodynamic and mechanical stability 

in perovskites: a computational approach for 

advanced applications 
Coskun Firat* 

Istanbul Technical University, Energy Institute, Istanbul, Türkiye 

               A R T I C L E   I N F O 
 

Article history: 
Received 25 March 2025  
Received in revised form 
07 May 2025 
Accepted 15 May 2025 
 
Keywords:  
Perovskite stability, Thermodynamic-mechanical 
integration, combined stability index, 
Computational analysis, Material design for 
durability 
 
*Corresponding author 
Email address: 
coskun.firat@itu.edu.tr 
 
 
DOI: 10.55670/fpll.fusus.3.3.4 
 

A B S T R A C T 
 

Perovskite materials hold immense potential for advanced technologies, yet 

their practical deployment is hindered by an insufficient understanding of the 

interplay between thermodynamic and mechanical stability. This study bridges 

this critical gap by developing a unified computational framework that 

integrates both stability dimensions, enabling the rational design of perovskites 

for demanding applications. Leveraging pre-computed density functional 

theory data from The Materials Project and AFLOW databases, 44 perovskite 

materials are analyzed. Thermodynamic stability is assessed via formation 

energy and energy above hull, while mechanical stability is quantified through 

bulk modulus, shear modulus, and Pugh’s ratio. A novel combined stability 

index is introduced, employing geometric mean aggregation of normalized 

metrics to prioritize balanced performance. Key findings reveal that Ba-based 

perovskites exhibit superior thermodynamic stability and mechanical 

resilience. This work provides a computational blueprint for synthesizing 

perovskites tailored to applications requiring durability under thermal and 

mechanical stress, such as photovoltaics and catalysis. By correlating 

composition-structure-property relationships, the study advances the design of 

next-generation materials, emphasizing the necessity of holistic stability 

metrics. 

 

1. Introduction 
Perovskite materials, with their general formula ABX3, 

have emerged as a cornerstone of modern materials science 
due to their exceptional optoelectronic, catalytic, and 
mechanical properties [1]. These materials underpin 
advancements in solar cells, light-emitting diodes, solid oxide 
fuel cells, and piezoelectric devices, among others. However, 
their practical implementation is often hindered by 
challenges related to stability under operational conditions. 
Thermodynamic stability [2-4] in perovskites has been 
widely studied using metrics such as formation energy and 
energy above the hull. For instance, Ba-based perovskites are 
renowned for their superior thermodynamic stability [5-7], 
whereas materials with high energy above hull values are 
prone to decomposition [8]. However, these studies have 
focused mainly on isolated thermodynamic properties [9-11], 
neglecting how mechanical stability [12-14] influences 
overall performance. Conversely, mechanical stability metrics 
like bulk modulus [15], shear modulus [16], and Pugh’s ratio 

(B/G) [12,17] have been used to classify perovskites as brittle 
or ductile [18-20], with K-based perovskites [21] 
demonstrating excellent mechanical properties. Yet, the 
interplay between thermodynamic and mechanical stability 
remains poorly understood, limiting the rational design of 
perovskites that can withstand real-world stresses such as 
thermal cycling or mechanical loading [22-23]. Previous 
studies have made significant strides in exploring 
thermodynamic or mechanical stability in isolation, but few 
have considered these aspects together in a cohesive 
framework [24-27]. This disconnect is problematic for 
applications where both forms of stability are critical. For 
example, a material with excellent thermodynamic stability 
but poor mechanical properties may fail under stress, while a 
mechanically robust material with poor thermodynamic 
stability may decompose during operation [28]. Bridging this 
gap requires a holistic approach that integrates 
thermodynamic and mechanical stability metrics, enabling 
the design of perovskites with balanced properties. In this 

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August 2025| Volume 03 | Issue 03 | Pages 26-34 

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Coskun Firat /Future Sustainability                                                                                           August 2025| Volume 03 | Issue 03 | Pages 26-34 

27 

 

study, three key questions are addressed: How can 
thermodynamic and mechanical stability be unified into a 
single framework for perovskites? What composition-
structure-property relationships govern their combined 
stability? And which materials exhibit optimal stability 
profiles for advanced applications? To answer these 
questions, pre-computed DFT data from both The Materials 
Project and AFLOW for 44 perovskites with different crystal 
systems are analyzed [29,30]. Thermodynamic parameters 
(formation energy, energy above hull) and mechanical 
properties (bulk modulus, shear modulus) are evaluated 
using Python-based computational tools. A combined stability 
index is introduced to unify these metrics, enabling 
systematic identification of materials with optimal stability 
profiles. This work makes several key contributions. First, a 
unified stability framework is established, which integrates 
thermodynamic and mechanical metrics, providing a holistic 
view of perovskite stability. Second, the composition-
structure-property relationships are revealed, showing that 
Ba-based perovskites excel in thermodynamic and 
mechanical stability. Notably, tantalum-containing 
compounds consistently outperform their niobium 
counterparts in combined stability metrics. Third, promising 
candidates such as KTaO3 (high mechanical strength), 
Ba2TaInO6 (exceptional thermodynamic stability), and 
Ba2TaInO6, BaNbO3 (balanced stability) are identified. These 
findings offer a computational blueprint for designing next-
generation perovskites, with implications for energy 
conversion, catalysis, and electronics. The practical relevance 
of this work lies in its ability to guide the synthesis of stable 
perovskites for applications requiring both durability and 
performance. For instance, thermodynamically and 
mechanically robust perovskites could enhance the longevity 
of solar cells, improve catalytic efficiency in harsh 
environments, or develop reliable high-temperature sensors. 

2. Methodology 
This study analyzes a dataset of 44 perovskite materials 

with ABX3 and related stoichiometries, leveraging pre-
computed density functional theory (DFT) [31] data from The 
Materials Project and AFLOW databases. The dataset 
comprises materials with cubic, pseudo-cubic, tetragonal or 
trigonal symmetry [32], spanning diverse compositions of A-
site cations (Ba, Sr, Ca, K, Na) [33,34] and B-site cations (Ti, 
Zr, Nb, Ta) [35,36], enabling systematic exploration of 
composition-stability relationships. The DFT calculations 
were performed using the Vienna Ab initio Simulation 
Package (VASP) [37] with the Perdew-Burke-Ernzerhof (PBE) 
exchange-correlation functional [38], ensuring consistency 
with widely accepted computational standards. The dataset 
includes the following key parameters: 

• Material identification: Chemical formula, standardized 
formula notation, and unique material ID. 

• Crystal structure: Space group, lattice parameters, and 
atomic positions. 

• Electronic properties: Bandgap and electronic structure 
classification (metal, semiconductor, or insulator). 

• Thermodynamic stability: Formation energy per atom, 
energy above hull (relative to the convex hull), and 
stability classification. 

• Mechanical properties: Voigt-Reuss-Hill (VRH) averaged 
bulk modulus, shear modulus, and elastic constants 
where available. 

Python-based computational tools (pandas, NumPy, 
matplotlib, seaborn) were employed to process and analyze 

the dataset [39]. Derived mechanical properties, including 
Pugh’s ratio (B/G), Poisson’s ratio, and Vickers hardness, 
were calculated using empirical relationships. A combined 
stability index was developed to unify thermodynamic and 
mechanical stability metrics, enabling quantitative 
comparison of materials. Statistical methods, including 
correlation analysis and classification algorithms, were 
applied to identify trends in composition-structure-property 
relationships. To ensure reproducibility, all computational 
workflows- from data retrieval to visualization- were 
structured using open-source libraries, with custom functions 
validated against reference calculations. The methodology 
emphasizes transparency in parameter derivation and error 
handling, particularly for entries with anomalous mechanical 
properties (e.g., negative shear moduli). 

2.1 Thermodynamic and mechanical stability analysis 
Thermodynamic stability was evaluated using two key 

metrics: the formation energy per atom (𝐸𝑓) and the energy 

above hull (𝐸ℎ𝑢𝑙𝑙). The formation energy, defined as [30]:  

𝐸𝑓 =
𝐸𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑−∑ 𝑛𝑖𝐸𝑖𝑖

𝑁
            (1) 

Eq (1) quantifies the energy released or required to form a 
compound from its constituent elements. Here, 𝐸𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑  is 

the total energy of the perovskite, 𝑛𝑖  and 𝐸𝑖  represent the 
number of atoms and reference energy of element i in its 
standard state, and N is the total number of atoms in the 
compound. The energy above the hull (𝐸ℎ𝑢𝑙𝑙), calculated 
as [30]: 

 𝐸ℎ𝑢𝑙𝑙 = 𝐸𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑 − 𝐸𝑐𝑜𝑛𝑣𝑒𝑥 ℎ𝑢𝑙𝑙           (2) 

Eq (2) measures the energy difference between a compound 
and the most stable phase(s) at its composition, 
where 𝐸𝑐𝑜𝑛𝑣𝑒𝑥 ℎ𝑢𝑙𝑙 corresponds to the lowest-energy 
configuration of stable phases. 
Materials were categorized into stability classes based 
on 𝐸ℎ𝑢𝑙𝑙 values:  

• Stable: 𝐸ℎ𝑢𝑙𝑙 = 0 

• Very likely stable: 0 < 𝐸ℎ𝑢𝑙𝑙 < 0.025 eV/atom 

• Likely stable: 0.025 ≤ 𝐸ℎ𝑢𝑙𝑙 < 0.05 eV/atom 

• Potentially metastable: 0.05 ≤ 𝐸ℎ𝑢𝑙𝑙 < 0.1 eV/atom 

• Likely unstable: 𝐸ℎ𝑢𝑙𝑙 ≥ 0.1 eV/atom. 
Statistical analyses, including mean, standard deviation, and 
extreme values, were applied to characterize the distribution 
of thermodynamic parameters. Correlation studies further 
identified relationships between composition and stability 
metrics. 
Mechanical stability is assessed using bulk modulus (B), shear 
modulus (G), and derived parameters. The Voigt-Reuss-Hill 
(VRH) averaging scheme has been employed to compute 
isotropic values of B and G from the anisotropic elastic tensor 
for data in the databases. Pugh’s ratio (𝐵 𝐺⁄ ) classifies 
materials as ductile (𝐵 𝐺⁄ > 1.75) or brittle (𝐵 𝐺⁄ < 1.75). 
Derived mechanical properties included: Young’s modulus 
[40,41]: 

𝐸 =
9𝐵𝐺

3𝐵+𝐺
= 2𝐺(1 + 𝜈)           (3) 

Poisson’s ratio [40,41]: 

𝜈 =
3𝐵−2𝐺

2(3𝐵+𝐺)
            (4) 

 

 



Coskun Firat /Future Sustainability                                                                                           August 2025| Volume 03 | Issue 03 | Pages 26-34 

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Vickers hardness [42]: 

𝐻𝜈 ≈ 0.92 (
𝐺

𝐵
)

1.137
𝐺0.708           (5) 

Simplified elastic anisotropy index (derived from the 
universal anisotropy index [43]): 

𝐴𝑎𝑝𝑝𝑟𝑜𝑥 =
5𝐺

𝐵
+

𝐵

5𝐺
−

6

5
           (6) 

Statistical distributions of mechanical properties were 
analyzed, and correlation matrices were constructed to 
explore relationships between composition and mechanical 
behavior. 

2.2 Combined stability assessment 
To holistically evaluate both thermodynamic and 

mechanical stability, a combined stability index integrating 
normalized values of 𝐸ℎ𝑢𝑙𝑙 , B, G, and Pugh’s ratio is developed. 
This index enables systematic ranking of materials based on 
their ability to balance competing stability requirements, 
critical for applications demanding both long-term phase 
persistence and mechanical resilience. The assessment 
framework follows four key steps: 
Normalization: Each parameter (𝐸ℎ𝑢𝑙𝑙 , B, G, B/G) was scaled 
to a 0–1 range using min-max normalization to eliminate unit 
dependency and ensure equal weighting. For a parameter X, 
the normalized value 𝑋𝑛𝑜𝑟𝑚 is calculated as: 

𝑋𝑛𝑜𝑟𝑚 =
𝑋−𝑋𝑚𝑖𝑛

𝑋𝑚𝑎𝑥−𝑋𝑚𝑖𝑛
            (7) 

where 𝑋𝑚𝑖𝑛  and 𝑋𝑚𝑎𝑥  represent the minimum and maximum 
values of 𝑋 across the dataset. For 𝐸ℎ𝑢𝑙𝑙 , lower values indicate 
greater stability, so the normalization was inverted (1 −
𝑋𝑛𝑜𝑟𝑚). 
Weighting: Parameters were assigned weights reflecting 
their relevance to specific applications. For general-purpose 
evaluation, equal weights (𝜔𝑖 = 0.25) were applied to all 
parameters, ensuring unbiased prioritization of 
thermodynamic and mechanical stability. 
Aggregation: The weighted parameters were combined 
using the geometric mean to compute the stability index 
(𝑆𝑖𝑛𝑑𝑒𝑥) for each material [44]: 

𝑆𝑖𝑛𝑑𝑒𝑥 = (∏ 𝑋𝑖,𝑛𝑜𝑟𝑚
𝜔𝑖𝑛

𝑖=1 )
1

∑ 𝜔𝑖
⁄

           (8) 

Unlike arithmetic averaging, the geometric mean penalizes 
materials with extreme weaknesses in any stability 
dimension, favoring balanced performance. 
Classification: Materials were categorized into four stability 
classes: For classification, thresholds were defined for each 
property (𝐸ℎ𝑢𝑙𝑙 , 𝐸𝑓, B, G, and Pugh’s ratio). These thresholds 

are used to classify materials into different stability 
categories. A categorization function was defined to evaluate 
each material based on the defined thresholds. The function 
first categorizes the material based on 𝐸ℎ𝑢𝑙𝑙 . Then, it adjusts 
the stability category based on mechanical properties (B, G, 
and Pugh’s ratio). Finally, it considers 𝐸𝑓 to provide a holistic 

assessment. The combined stability category will be like: 
Stable (Strong Mechanical Properties) (Low Formation 
Energy), Very Likely Stable (Moderate Mechanical 
Properties) (Moderate Formation Energy), Likely Stable 
(Brittle) (Low Formation Energy), Potentially Metastable 
(Brittle) (Low Formation Energy), Likely Unstable (Weak 
Mechanical Properties) (High Formation Energy), 
Unknown (for materials with missing data). 

 

3. Computational details and the results 
The dataset for this study originated from the Materials 

Project and AFLOW databases, from which 1070 cubic 
perovskite materials with ABX3 and related stoichiometries 
were initially extracted. However, only 44 of these materials 
contained complete mechanical property data (bulk modulus, 
shear modulus, etc.), necessitating a focused analysis on this 
subset to unify thermodynamic and mechanical stability 
metrics. All computational workflows, including data 
processing, statistical analysis, and visualization, were 
implemented in Python 3.8 using the following libraries: 

• Pandas and NumPy for data manipulation and numerical 
computations. 

• Matplotlib and seaborn for generating visualizations. 

• Custom functions for specialized calculations, such as the 
combined stability index and normalized parameter 
aggregation. 

Key visualization techniques were employed to elucidate 
structure-property relationships: 
a. Scatter plots to examine correlations between 

thermodynamic and mechanical parameters.  
b. Heatmaps to visualize multivariate relationships across 

stability metrics.  
c. Bar charts to compare key properties (e.g., formation 

energy, bulk modulus) across materials.  
d. Radar plots for multi-parameter comparison of top-

performing candidates. 
The computational workflow was designed for 
reproducibility: 

• Data processing steps were systematically documented, 
including handling of missing values and normalization 
procedures. 

• Validation against reference calculations (e.g., cross-
checking DFT-derived properties with literature values) 
ensured robustness. 

• The final dataset of 44 materials, along with analysis 
scripts, is archived to facilitate reproducibility. 

This approach enabled the integration of thermodynamic 
stability (formation energy, energy above hull) 
and mechanical stability (bulk modulus, shear modulus, 
Pugh’s ratio) into a unified framework. By focusing on 
materials with complete datasets, the combined stability 
index could be rigorously applied to identify candidates with 
balanced performance for advanced applications. The results 
for the first five stable materials are given in Table 1. 
In Figure 1, the thermodynamic stability distribution of 44 
perovskite materials based on their 𝐸ℎ𝑢𝑙𝑙 values are 
illustrated. 

The distribution shows a sharp decline in frequency as 

𝐸ℎ𝑢𝑙𝑙 increases, indicating that most materials are stable or 

very likely stable, with fewer materials being metastable or 

unstable. The dashed lines provide clear visual thresholds for 

the stability categories, aiding in the quick assessment of 

material stability. Figure 2 indicates the Pugh’s ratio 

distribution of 44 materials. It can be seen that most materials 

have a Pugh’s ratio clustered around 2, indicating a tendency 

towards ductility. The red dashed line at 1.75 clearly marks 

the boundary between ductile and brittle materials, making it 

easy to identify the classification of each material. The 

distribution shows a sharp peak around the ductile region, 

with a rapid decline in frequency as the ratio increases, 

indicating that most materials are ductile. A few materials 

have significantly higher Pugh’s ratios, suggesting they are 

exceptionally ductile. 



Coskun Firat /Future Sustainability                                                                                           August 2025| Volume 03 | Issue 03 | Pages 26-34 

29 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
Figure 1. Thermodynamic stability distribution of perovskites based 

on 𝐸ℎ𝑢𝑙𝑙 

 

 
Figure 2. Distribution of Pugh’s ratio of the perovskite materials 

Figure 3 illustrates the relationship between Pugh's ratio 

(B/G) and elastic anisotropy for various materials. In Figure 

3, the red dashed line at B/G = 1.75 separates ductile 

materials (right) from brittle ones (left). Most stable materials 

have low anisotropy and are near the ductile-brittle 

threshold. A few outliers show significant anisotropy or 

extreme Pugh's ratios. Figure 4 shows the relationship 

between the bulk modulus (B) and shear modulus (G) for 

various materials. 

 

 

 

 

 

 

 

 

 

 
Figure 3. Relationship between Pugh's ratio (B/G) and elastic 

anisotropy for various materials 

 

 
Figure 4. The relationship between the bulk modulus and shear 

modulus for various materials 

 

Most materials are clustered between 100-200 GPa for 

bulk modulus and 50-150 GPa for shear modulus. A few 

outliers have significantly higher or lower values, indicating 

unique mechanical properties. Stable materials tend to have 

higher values of both moduli, indicating good mechanical 

resilience. The correlation between bulk and shear moduli 

suggests that materials with high resistance to compression 

also resist shape changes well. Figure 5 shows the combined 

stability of the materials.  

Table 1. Thermodynamic, mechanical properties, and combined index for some stable materials 

Code Formula 
Crystal 
system 

Ehull 

(eV/atom) 
Ef (eV/atom) B (Gpa) G (Gpa) 

Pugh’s 
ratio 

Combined 
index 

M7 Ca2Ta2O7 Cubic 0.000789 -3.4826 148.2 97.79 1.5155 78 

M13 BaTiO3 Cubic 0.014788 -3.4775 160 106.6 1.5009 74 

M18 KTaO3 Cubic 0 -3.0716 184.6 121.3 1.5218 44.5 

M19 BaZrO3 Cubic 7.17E-05 -3.6392 147.6 91.03 1.6214 78 

M28 SrFeO3 Cubic 0 -2.223 128.6 80.35 1.6004 99.5 

 



Coskun Firat /Future Sustainability                                                                                           August 2025| Volume 03 | Issue 03 | Pages 26-34 

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Most materials are clustered near the origin, indicating 

both high thermodynamic stability and ductility. A few 

outliers show distinct properties, for example, BaTiO3 (M26) 

having high ductility and Ba2NbO (M17) being less stable 

thermodynamically. Stable and ductile materials are near the 

origin with low 𝐸ℎ𝑢𝑙𝑙 and high Pugh’s ratio. Stable and brittle 

materials have low 𝐸ℎ𝑢𝑙𝑙 but lower Pugh’s ratio. This index is 

useful for identifying materials that balance both 

thermodynamic and mechanical stability, which is crucial for 

applications requiring durability and resilience. Figure 6 

shows the radar plot for KTaO3 (M18), which provides a visual 

representation of its key properties. 

Bulk Modulus VRH (GPa) indicates the material's 

resistance to uniform compression. The plot shows a 

moderate to high value, suggesting good mechanical stability. 

Shear Modulus VRH (GPa) reflects resistance to shape 

changes. The value is also moderate, supporting mechanical 

resilience. Energy Above Hull (eV/atom) represents 

thermodynamic stability. The plot shows a relatively low 

value, indicating good stability. Pugh's Ratio indicates 

ductility. The plot shows a moderate value, suggesting a 

balance between ductility and brittleness. The plot is fairly 

balanced, with no extreme values, indicating that the material 

has a good balance of properties. The shaded area represents 

the overall performance across these parameters, with a 

larger area generally indicating better combined stability. 

Figure 7 shows the grid radar plot for material indices 14, 23, 

35, and 39, as well as other candidates with good combined 

indices. 

 

 

 

 

 

 
Figure 6. Radar plot of the combined index for KTaO3 

 

 

4. Discussion 
Integrating thermodynamic and mechanical stability 

metrics into a unified framework has revealed critical insights 

into the design of perovskites for advanced applications. By 

analyzing 44 perovskites with complete datasets, this study 

demonstrates that materials such as KtaO3, Ba2TaInO6, and 

BaNbO3 exhibit balanced stability profiles, positioning them 

as promising candidates for applications requiring both 

durability and performance.  

Figure 5. Combined thermodynamic and mechanical stability of materials 

 



Coskun Firat /Future Sustainability                                                                                           August 2025| Volume 03 | Issue 03 | Pages 26-34 

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The combined stability index successfully identifies 

materials that excel in both thermodynamic and mechanical 

stability. For instance, KtaO3 (M18) achieves low energy 

above hull (0 eV/atom) and moderate mechanical properties 

(bulk modulus = 184.6 GPa, shear modulus = 121.3 GPa), 

reflecting its resistance to decomposition and mechanical 

stress. This balance is critical for applications like solar cells, 

where operational stresses (e.g., thermal cycling) demand 

materials that remain structurally intact over time. The 

dominance of Ba-based perovskites (e.g., BaTiO3, BaZrO3) in 

the top candidates aligns with prior studies highlighting the 

stabilizing role of large A-site cations like Ba²⁺, which reduce 

lattice distortions and enhance mechanical resilience [5,7]. 

Tantalum-containing perovskites (e.g., Ba2TaInO6) 

consistently outperform their niobium counterparts (e.g., 

BaNbO3) in combined stability metrics.  

 

 

 

 

 

 

 

This is attributed to Ta⁵⁺’s higher electronegativity and 

stronger metal-oxygen bonding, which enhances both 

thermodynamic stability (lower 𝐸ℎ𝑢𝑙𝑙) and mechanical 

properties (higher bulk/shear moduli) [26]. These findings 

underscore the importance of B-site cation selection in 

tailoring stability. The Pugh’s ratio distribution (Figure 2) 

reveals that most materials (∼70%) are ductile (B/G>1.75), a 

desirable trait for flexible electronics. However, brittle 

materials like Ca2Ta2O7 (M7) still rank highly due to 

exceptional thermodynamic stability (𝐸ℎ𝑢𝑙𝑙 = 0.0008 

eV/atom), illustrating that application-specific requirements 

should guide material selection. For instance, brittle but 

thermodynamically stable perovskites may suffice for rigid 

photovoltaic panels, while ductile materials are preferable for 

wearable devices. The geometric mean-based combined 

index penalizes extreme weaknesses in any stability 

dimension, favoring balanced performance.  

 

Figure 7. The grid radar plot for material index-14, 23, 35 and 39 

 



Coskun Firat /Future Sustainability                                                                                           August 2025| Volume 03 | Issue 03 | Pages 26-34 

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For example, SrFeO3 (M28) achieves the highest 

combined index (99.5) due to its moderate 𝐸ℎ𝑢𝑙𝑙 (0 eV/atom) 

and exceptional mechanical properties 

(B=128.6 GPa, G=80.35 GPa). However, outliers like BaTiO3 

(M13) with higher 𝐸ℎ𝑢𝑙𝑙 (0.0148 eV/atom) but superior 

ductility (B/G=1.62) highlights the need for customizable 

weighting schemes in the index to prioritize specific 

properties for targeted applications. 

5. Limitations and future work 
This study offers valuable insights into the stability of 

perovskite materials, yet several limitations must be 
acknowledged: The analysis does not account for the 
influence of temperature and pressure on material stability, 
which can be significant in real-world applications, the impact 
of defects, which can greatly affect stability, is not included in 
this study, the dataset is limited to a few materials, restricting 
the exploration of other potentially stable structures. 
Expanding the dataset to thousands of perovskites using high-
throughput DFT could uncover novel candidates with rare 
stability profiles, such as materials combining ultralow 𝐸ℎ𝑢𝑙𝑙

 and extreme ductility. While DFT-derived metrics provide 
valuable insights, experimental validation of mechanical 
properties (e.g., nanoindentation for hardness) and 
thermodynamic stability (e.g., calorimetry) is essential to 
confirm computational predictions. Training machine 
learning models on stability metrics could accelerate the 
discovery of composition-structure-property relationships, 
particularly for non-cubic perovskites [12]. 
Customizing the combined index weights (e.g., prioritizing 
mechanical stability for aerospace materials or 
thermodynamic stability for high-temperature catalysts) 
would enhance its practical utility. 

6. Conclusions 

This comprehensive investigation into perovskite 
materials has provided valuable insights into the interplay 
between composition, structure, thermodynamic stability, 
and mechanical properties. Through systematic 
computational analysis of 44 distinct perovskite 
compositions, several promising candidates for technological 
applications were identified. The analysis highlights the 
superior stability profiles of tantalum-containing materials, 
suggesting that 5d transition metals may enhance both 
thermodynamic and mechanical stability due to stronger and 
more directional bonding characteristics. This trend 
underscores the potential advantages of incorporating such 
elements into perovskite structures. The observed 
relationships between formation energy and mechanical 
properties, such as bulk modulus, suggest fundamental 
structure-property correlations that can guide future 
material design. Materials with more negative formation 
energies tend to exhibit higher elastic moduli, indicating that 
stronger bonding contributes to both thermodynamic and 
mechanical stability. This work lays the groundwork for 
targeted experimental validation of the identified promising 
compositions. Future efforts should focus on synthesizing and 
characterizing these top candidates, particularly those 
containing tantalum, to verify the predicted properties and 
assess their performance under application-relevant 
conditions. Additionally, extending this computational 
framework to include dopants and defects could further 
enhance the stability and functional properties of these 
promising perovskite materials. By this work, the combined 
stability assessment approach has successfully identified 
materials that balance thermodynamic and mechanical 

stability, providing a rational basis for the development of 
next-generation perovskite materials for diverse 
technological applications. 

Ethical issue 
The author is aware of and complies with best practices in 
publication ethics, specifically with regard to authorship 
(avoidance of guest authorship), dual submission, 
manipulation of figures, competing interests, and compliance 
with policies on research ethics. The author adheres to 
publication requirements that the submitted work is original 
and has not been published elsewhere. 

Data availability statement 
The manuscript contains all the data. However, more data will 

be available upon request from the author. 

Conflict of interest 

The author declares no potential conflict of interest. 

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