Data in Brief 48 (2023) 109075 Contents lists available at ScienceDirect Data in Brief journal homepage: www.elsevier.com/locate/dib Data Article Datasets on the elastic and mechanical properties of hydroxyapatite: A first principle investigation, experiments, and pedagogical perspective Obinna A. Osuchukwua , d, Abdu Salihi a , Ibrahim Abdullahia , David O. Obadab , c , d , ∗ , Simeon A. Aboladeb , c b , c , Akinlolu Akande , Stefan Csakie , g, David Dodoo-Arhin f a Department of Mechanical Engineering, Bayero University, Kano, 700241, Nigeria b Mathematical Modelling and Intelligent Systems for Health and Environment Research Group, School of Science, Atlantic Technological University, Ash Lane, Ballytivnan, Sligo, F91 YW50, Ireland c Africa Centre of Excellence on New Pedagogies in Engineering Education, Ahmadu Bello University, Zaria, 810222, Nigeria d Multifunctional Materials Laboratory, Shell Office Complex, Department of Mechanical Engineering, Ahmadu Bello University, Zaria, 810222, Nigeria e Department of Physics, Constantine the Philosopher University in Nitra, Nitra, 949 11, Slovakia f Department of Materials Science and Engineering, University of Ghana, Legon, 25, Ghana g Department of Horticultural Machinery, Faculty of Horticulture, Mendel University in Brno, Valticka 337, Lednice, 691 44, Czech Republic a r t i c l e i n f o a b s t r a c t Article history: The purpose of this data article is to report the quan- Received 6 September 2022 tum mechanical analysis by generalized gradient approxi- Revised 10 March 2023 mation (GGA) exchange-correlation functional using density Accepted 13 March 2023 functional theory (DFT). The predictions were based on the Available online 20 March 2023 elastic constants and mechanical properties of stoichiomet- ric hydroxyapatite (HAp) crystal. The elastic stiffness con- Dataset link: Load and Displacement Curve Datasets for HAp samples (Original data) stants in hexagonal symmetry were obtained by fitting the Hookes’ law for the energy-strain and stress-stain relations. Some of the theoretical datasets were compared to mea- sured mechanical properties of produced HAp pellets ob- tained through micro and nanoindentation experiments. The ∗ Corresponding author. E-mail address: david.obada@atu.ie (D.O. Obada) . https://doi.org/10.1016/j.dib.2023.109075 2352-3409/© 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ) 2 O.A. Osuchukwu, A. Salihi and I. Abdullahi et al. / Data in Brief 48 (2023) 109075 Keywords: datasets show considerable anisotropy in the stress-strain Hydroxyapatite behaviour and are discussed in the context of the me- Mechanical properties chanical properties of HAp which are useful for tis- Elastic Constants sue engineering. We also provide a pedagogical snap- CACPLA Pedagogy shot on the use of the datasets herein to teach and Engineering Education interpret DFT based atomistic simulations in a typi- Nanoindentation Young’s Modulus cal blended online teaching set-up for engineering stu- dents using a new pedagogy, CACPLA (Communicate, Active, Collaborate, Practice, Learning and Assessment). © 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ) S V pecifications Table Subject Engineering Specific subject area Biomedical Materials: Computational Materials Physics; Engineering Education Type of data Table Figure How the data were acquired First principle calculations Micro and nanoindentation experiments Survey links (questionnaire) Data format Raw Analysed (observed/experimental) and Predicted Description of data collection Quantum mechanical calculations from first principles DFT calculations were performed using the resources of the Trinity Centre for High Performance Computing (TCHPC), and Irish Center for High End Computing (ICHEC), Ireland Nanoindentation measurements were performed at the African University of Science and Technology (AUST), Abuja, Nigeria Usage of questionnaire to collect data from respondents (students) Data source location • African University of Science and Technology • Atlantic Technological University, • Africa Centre of Excellence on New Pedagogies in Engineering Education (ACENPEE) • City/Town/Region: Abuja, Zaria, and Sligo • Country: Nigeria and Ireland Data accessibility Repository name: 4TU. ResearchData. Data identification number: https://doi.org/10.4121/20279226.v1 Related research article Osuchukwu, O. A., Salihi, A., Abdullahi, I., Obada, D. O., Abolade, S. A., Akande, A., & Csaki, S. (2022). Structural and Nano-Mechanical Characteristics of a Novel Mixture of Natural Hydroxyapatite Materials: Insights from Ab-initio Calculations and Experiments. Materials Letters , 132977. https://doi.org/10.1016/j.matlet.2022.132977 alue of the Data • The data in this study will be useful for researchers in archiving the mechanical proper- ties of HAp using atomistic simulations without the need to perform expensive and time- consuming experiments. • The additional value of the datasets is inherent in the synergy between theoretically and experimentally derived mechanical properties of HAp to enable a better understanding of the mechanical behavior of HAp. • Datasets in this work will continually justify that the improvement of reliable and ac- curate computational methods are important in quantum mechanical theory and will be useful for ab initio comparisons of similar materials. O.A. Osuchukwu, A. Salihi and I. Abdullahi et al. / Data in Brief 48 (2023) 109075 3 • These data were used to teach and interpret DFT based atomistic simulations to engineer- ing students using a blended online teaching and learning strategy called CACPLA. 1. Objective These datasets were generated to add value to an ongoing research on the structural char- acteristics and mechanical properties of natural HAp materials on a nanoscale [1] . The data complements the results obtained in the study from a theoretical and experimental standpoint allowing a probe into the physics of the biomaterials. In addition, the outcomes of using the datasets as presented in this study for teaching a module on atomistic simulations to engineer- ing students is highlighted. 2. Data Description The dataset available for the calculated/atomistic simulations of the elastic constants and me- chanical properties of hexagonal HAp in addition to nano and micro indentation data derived from experiments on produced HAp pellets from a mixture of two biogenic biowastes [1 , 2] are presented in this article. Elastic constants C ij, bulk mechanical characteristics, and experimen- tal nanoindentation measurement data for HAp are tabulated in Tables 1–3 , respectively. Fig. 1 reflects the deposited raw data in the repository (4TU. ResearchData) that underlines the load and displacement curves for HAp samples obtained using nanoindentation experiments. Fig. 2 shows the Vickers hardness properties of produced HAp pellets obtained using micro indentationTable 1 Elastic constants C ij of hexagonal HAp from atomistic simulations. DFT Code C 11(GPa) C 12(GPa) C 13(GPa) C 33(GPa) C 44(GPa) C 66(GPa) This work VASP 117.6 34.6 72.0 162.5 44.6 41.5 Reported [3] VASP 120.6 32.9 65.9 167.2 35.8 43.8 Reported [4] Quantum Espresso 118.3 31.6 63.7 156.8 33.5 43.4 Reported [5] Quantum Espresso 117.9 30.6 66.4 165.0 38.5 43.7 Reported [6] CRYSTAL17 132.0 36.0 63.0 168.0 39.0 48.0 Reported [7] CASTEP 139.0 49.0 61.0 178.0 47.0 45.0 Reported [8] VASP 140.0 49.0 60.0 179.0 48.0 45.0 Reported [9] CASTEP 149.2 52.5 64.6 180.1 41.0 48.6 Reported [10] VASP 134.4 48.9 68.5 142.5 51.4 42.8 Reported [11] VASP 122.2 34.4 65.2 166.6 42.1 44.4 Reported [12] VASP 117.1 26.2 55.6 231.8 56.4 45.5 Table 2 Bulk mechanical characteristics of hexagonal HAp from atomistic simulations. HAp (Hexagonal) DFT Code B (GPa) G(GPa) E (GPa) B/G ʋ H v (GPa) This work VASP 79.88 39.90 102.61 2.00 0.29 4.64 Reported [3] VASP 78.84 38.83 100.05 2.03 0.29 - Reported [4] Quantum Espresso 76.40 37.1 95.9 2.09 0.29 - Reported [5] Quantum Espresso 77.00 39.40 - 1.95 - - Reported [6] CRYSTAL17 82.00 43.00 110.00 1.91 0.28 - Reported [7] CASTEP 88.70 46.70 118.90 1.90 0.27 - Reported [8] VASP 86.0 - - - - - Reported [9] CASTEP 92.2 45.6 119.2 2.02 0.27 - Reported [10] VASP - - - - - - Reported [11] VASP 79.49 41.73 106.6 1.90 0.28 - Reported [12] VASP 76.00 52.00 - 1.46 - - 4 O.A. Osuchukwu, A. Salihi and I. Abdullahi et al. / Data in Brief 48 (2023) 109075 Table 3 Experimental nano-indentation measurement data for HAp-derived pellets. Samples E r (GPa) E (GPa) B100 0.06 0.06 C100 0.93 0.89 BC 75/25 0.79 0.76 BC 50/50 4.60 4.43 BC 25/75 4.83 4.65 Fig. 1. Load Vs Displacement curves obtained through nanoindentation experiments for the HAp pellets. Fig. 2. Vickers hardness measurement data for the HAp pellets. O.A. Osuchukwu, A. Salihi and I. Abdullahi et al. / Data in Brief 48 (2023) 109075 5 Fig. 3. Learners Satisfaction Survey (LSS) for a student sample size of N = 45. Fig. 4. Word cloud analysis on the learners satisfaction survey. experimentally. Figs. 3 and 4 show the learners satisfaction survey datasets and the word cloud analysis on the satisfaction survey section, respectively. Typically, the elastic constants and bulk moduli for HAp materials are the mechanical prop- erties that directly influences the strength of HAp scaffolds/implants . The response of the HAp crystal to applied forces on the macroscopic scale can be described by the elastic constants that explain the synergy between the mechanical and dynamical behaviour [5] . The stress and strain forces are characterized by 3 tensile and shear components resulting in 6 components. Therefore, the elastic constants produce a 6 × 6 symmetric matrix which includes 27 different components with 21 of these independent. However, symmetries in the crystal have the tendency to decrease 6 O.A. Osuchukwu, A. Salihi and I. Abdullahi et al. / Data in Brief 48 (2023) 109075 t s c e C t s A s w s m m c d i v w d t T a h o d o t d a f g M a t E t d c p c c 2 w d n b t a p c he number of components. For the hexagonal crystal, there are five independent elastic con- tants. C 11, C 12, C 13, C 33, C 44 = C 55 and a dependent constant C 66 = ( C 11 −C 12)/2 [4] . The elastic onstants C 11 and C 33 describe the elasticity in length while C 12, C 13, C 44, and C 66 represent the lasticity in shape. C 11 and C 33 are typically larger than their C 12, C 13, C 44, and C 66 counterparts. alculated ratio between bulk modulus B and shear modulus G and Poisson’s ratio ν , reveal that he hexagonal HAp behaves as a ductile material. Table 1 lists the calculated elastic constants for HAp in the study, and the estimated con- tants are in acceptable agreement with other computational values by other researchers [3–12] . ny significant deviation from our reported estimates can be ascribed to a variation in the de- cription for charge and geometry of the phosphate polyhedral. The mechanical stability which as evaluated by the Born’s criteria [13] reveals that the HAp crystal is mechanically stable. The calculated estimates obtained for the elastic moduli, the ratio of B (bulk modulus) to hear modulus (G) and Poisson’s ratio for the HAp crystal are tabulated in Table 2 . Generally, ost of the calculated elastic properties are in line with studies elsewhere [3–12] . The bulk odulus describes the resistance of the crystal to volume change when stresses are applied and an be used to measure the average bond strength of the atoms of HAp. The shear modulus escribes how much resistance there is to reversible deformations over shear stress. As reported n Table 2 , the B/G ratio can reveal the brittle or ductile behaviour of a material. The critical alue for this separation is 1.75 [14 , 15] . For the HAp crystal investigated, the B/G ratio is 2.00 hich is higher than 1.75 and indicates the material is ductile. This agrees with the Poisson’ ratio ata obtained. The Poisson ratio for ductile materials is larger than 0.26. The ductile nature of he investigated HAp crystal quantifies the stable nature of the crystal against shear deformation. he stiffness of the HAp crystal represented by the Young’s modulus as calculated is 102.61 GPa nd can favour the applicability of HAp in terms of mechanical characteristics such as wear and ardness when used as fillers and in restorative medicine. However, these results have been btained in the absence of any defects in the bulk HAp crystal which could be vacancies and islocations. Usually, these defects affect the interfacial behaviours with a direct consequence n the mechanical properties [16] . Table 3 presents the elastic deformation that occurs on the sample (HAp pellet) and the tip of he indenter which is the reduced modulus (Er), and the relationship between stress and strain uring elastic deformation which is the Young’s Modulus ( E). The importance of E for biomedical pplications cannot be overemphasized. However, there are different elastic properties of HAp ound in the literature ranging from 3 to 180 GPa [12 , 17-22] . The factors responsible for these radients are the porosity, morphology, crystallinity, purity, and the grain size of HAp [12 , 33] . ost of the reports do not report the E of HAp with a complete description of the sample char- cteristics in terms of the chemical composition, calcium to phosphate ratio (Ca/P), density and he structure, and this leads to a difficulty in terms of the evaluation of the datasets. The highest reported in this study is 4.65 GPa for the BC 25/75 HAp sample and this value is compara- ively lower than the E reported during atomistic simulations. This variation can be ascribed to efects in the bulk crystal during the sintering process which could cause vacancies and dislo- ations. Usually, these defects affect mechanical properties of the materials. The low compaction ressure used in preparing the samples and the loading during nanoindentation experiments ould also cause reduced mechanical properties. Fig. 1 represents the typical force-depth curves obtained during nanoindentation tests for the ompact HAp pellets with an applied load of 100 μN, a hold time of 2 s and a loading rate of 0 μN/s. The low holding time was used to minimize the creep effect. The curve for BC 25/75 hich produced the highest E was characterized by a substantial continuity, as there were no iscontinuities in the curve during loading and unloading. The results indicate that E and hard- ess could decrease with increased loading as noticed in this study. Such characteristics could e ascribed to the indentation size effect (ISE). Typically, for higher contact loads, a larger plas- ic core that is generated causes some damage at the surface in the form of cracks/fractures nd leads to reduced mechanical properties [23] . The Vickers microhardness data for the HAp ellets is presented in Fig. 2 . The obtained micro hardness values are low as compared to mi- rohardness (H v ) values calculated by atomistic simulations ( Table 2 ), and this can be ascribed O.A. Osuchukwu, A. Salihi and I. Abdullahi et al. / Data in Brief 48 (2023) 109075 7 to defects in the bulk crystal during the sintering process and the low compaction pressure (500 Pa) used in fabricating the pellets. Higher sintering temperature could increase the mechanical characteristics of the bio-ceramics samples [24,25 , 26 , 34-37] . The learning sessions on elastic constants were accessed by the engineering stu- dents of ACENPEE through this link: https://compmatphys.epotentia.com/topic/elastic-constants -definition/ . The learner’s satisfaction survey link was administered to the students at the end of the teaching sessions using a five-point Likert scale with responses from strongly agree to strongly disagree as shown in Fig. 3 . Forty-five (45) students with an average age of 27 partic- ipated in the survey, and from the survey plots, it can be observed that students agreed that the jigsaw approach under the collaborate section of the CACPLA pedagogy [38 , 39] aided their understanding of the subject and enhanced their proof-reading skills, motivation, importance of participation, shared responsibility, and cooperation amongst students in their various jig- saw groups. The percentage of students that “agreed” and “strongly agreed” to all the markers (proof reading skills, motivation etc) in the survey questions outweighs the other responses on the Likert scale. This means that when students are grouped to discuss learning outcomes, and the groups are mid-sized (in this case, 10 per group), the motivation to study, the essence of proof-reading, shared responsibility and cooperation amongst the students is enhanced, conse- quently impacting on their experiential learning experience. This result is also supported by the word cloud of the feedback received from the students as shown in Fig. 4 . The word “good”, “method”, “courses”, and “thank you” etc. were mentioned frequently as a result of the feedback of the students on the effectiveness of the CACPLA pedagogy and the need to apply the method to other courses. The word “network” was also mentioned frequently, and this can be ascribed to some limitations in the internet infrastructure which can be improved. 2. Experimental Design, Materials and Methods Ab initio calculations were performed by solving density functional theory Kohn Sham equa- tions [40] . All properties were investigated using standard Perdew-Burke-Ernzerhof (PBE) version of Generalised Gradient Approximation (GGA) alongside projector augmented wave (PAW) which was used as exchange-correlation functional as implemented in VASP [27 , 28] with a cutoff en- ergy of 520 eV. Dense Monkhorst-Pack k-point meshes of 2 × 2 × 2 was utilized for the Brillouin zone sampling. The relaxation of the atoms was conducted until the atomic forces were smaller than 0.01 eV Å−1 . The initial geometry of Ca 10(PO 4) 6(OH) 2 was retrieved from the Materials Project Database (MPD). During the mechanical testing of the materials, a low cold compaction pressure of 1 MPa was used for pelletizing the sample powders. Nanoindentation was performed using the TI 950 Hysitron Tribo-Indenter at 25 °C equipped with a Berkovich tip. The peak load was 100 μN with a hold time of 2 s and a loading rate of 20 μN/s. The Young’s modulus E, and hardness H v , of the pellets were estimated using the method of Oliver and Pharr [29] . The preparation of HAp samples (powders and pellets) were produced from non-separated animal bones and catfish bones at the Multifunctional Materials Laboratory (MFML), Ahmadu Bello Uni- versity, Zaria, Nigeria, which has extensive experience in synthesizing biomaterials [1 , 2 , 34 , 41] . The raw bones were deproteinized and subjected to heat treatment at 900 °C for 2 h. The pow- ders produced after heat treatment were weighed and mixed in different proportions totaling 100 g. The powders were uniaxially pressed in a 25 mm diameter cylindrical die under 500 Pa compaction pressure and sintered in air atmosphere [34] . and the Vickers microhardness of the samples was determined with a microhardness tester. Young’s modulus after nanoindentation was obtained from [the reduced M]odulus using Eq. (1) [29] ( ) −1 = − 2 1 2 E 1 υ − 1 − υi (1) E r E i Where Er is the reduced modulus, υ is the Poisson’s ratio of the sample (taken as 0.2 for ceramics), Ei is the Young’s Modulus of the indenter (taken as 1,141 GPa or 1,141,0 0 0 MPa for diamond), and υi is the Poisson’s ratio of the indenter (taken as 0.07 for diamond). 8 O.A. Osuchukwu, A. Salihi and I. Abdullahi et al. / Data in Brief 48 (2023) 109075 t p H l d t b c 7 a The elastic constants are described by the stress-strain relation for the hexagonal structures: ⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎢σ1 ⎢⎢σ 2⎥ C 11 C 12 C 13 0 0 0 ε 1 ⎥⎥ ⎢⎢⎢C 12 C 11 C 0 0 ⎥⎢ ⎥ 0 ε 13 ⎥⎢ 2 ⎢ ⎥ ⎢ ⎥ σ3 = C 13 C 13 C 33 0 0 0 ε ⎥⎢ ⎥ ⎢ ⎥ ⎣σ 4⎦ ⎣⎢ 0 0 0 C 0 0 44 ⎥ ⎥⎢⎢ 3 ⎥ ε ⎥ 4 σ 5 0 0 0 ⎦⎣ 0 C 44 0 ε ⎦ 5 σ6 0 0 0 0 0 C ε 66 6 C 66 = (C 11 −C )/ 2 12 To describe polycrystalline constants, there are three types of algorithms which corresponds o different bounds and are based on the elastic constant of a single crystal. Voigt and Reuss ex- ressed stress in terms of a given strain and the strain in terms of the given stress, respectively. ill established that approximations made by Voigt [30] and Reuss [31] consider the upper and ower bounds of the elastic constants, respectively. Hence, Hills’ [32] averages are used to pre- ict bulk (B) and shear (G) moduli of the polycrystalline aggregates. For hexagonal structures, hese equations Eqs. 2 - (7) are: B v = 1 [2 (C + C )+ C + 4C ], (2) 11 44 33 13 9 = 1 G v [7C 11 − 5C 12 + 12C 44 + 2C 33 − 4C 13 ], (3) 30 [ ] B R = (C 11 + C 12 )C 33 − 2C2 13 / [C 11 + C 12 + 2C 33 − 4C 13 ], (4) 5{[ ] [ ] ]} G 2 2 R = [C 11 + C 12 )C 33 − 2C 13 C 44 C 66]/ [3 B C v 44 C 66 + (C 11 + C 12)C 33 − 2C 13 (C 44 + C 66) , 2 (5) Hill’s averages are used to predict bulk (B) and shear (G) moduli = 1 1 B (B R + B v) and G = (G R + G v) (6) 2 2 The Young’s modulus (E) and Poisson’s ratio ( ν), major elasticity-related parameters are given y the following formulas: = 9 GB = 3 B − 2 G E + and ν (7)3 B G 2 (3 B + G ) To evaluate the mechanical stability, the Born stability criteria [13] is used as shown in Eq. 8 : C 11 > |C 2 12 |, (C 11 + 2C 12 )C 33 > 2C 13, C 44 > 0 , (8) The students were asked to watch a video and study the downloadable slides at: https:// ompmatphys.epotentia.com/topic/elastic-constants-definition/ Next, the students were split into groups of 10 students each to discuss subtopics per the Jigsaw Strategy, and specific tasks were llotted. Each group was assigned a subtopic under elasticity as follows: Group 1: Stress and strain in engineering materials Group 2: Elastic Hysteresis Group 3: Hooke’s law Group 4: Stress Tensors O.A. Osuchukwu, A. Salihi and I. Abdullahi et al. / Data in Brief 48 (2023) 109075 9 Group 5: Bulk Modulus Group 6: Modulus of Elasticity Group 7: Young Modulus Each group was expected to come up with three power point slides that summarizes the core concept of the subtopics assigned. This way, when the slides (jigsaw pieces) were put together by the overall champions of all groups, it gives a full picture of elasticity. The learners satisfac- tion survey (LSS) questionnaires were designed to understand the opinion of the students on the impact of the jigsaw strategy (a part of the collaborate section of the CACPLA pedagogy) used during the blended online teaching and learning strategy. The LSS was made using the google form and composed mainly of Likert scale questions that required the participants to indicate their level of agreement or disagreement on statements that cover general feedback on the var- ious aspects of the strategy used. The questionnaire was based on a 5-point Likert scale which is as follows: 1 (strongly disagree), 2 (disagree), 3 (neutral), 4 (agree), and 5 (strongly agree). Ethics Statements Students filled in a consent form, and the learners satisfaction survey link which was was administered to the students used a five-point Likert scale through the use of google forms. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal rela- tionships that could have appeared to influence the work reported in this paper. Data Availability Load and Displacement Curve Datasets for HAp samples (Original data) (4TU.ResearchData). CRediT Author Statement Obinna A. Osuchukwu: Methodology, Data curation; Abdu Salihi: Supervision; Ibrahim Ab- dullahi: Supervision; David O. Obada: Conceptualization, Methodology, Data curation, Writing – original draft, Investigation, Writing – review & editing, Supervision; Simeon A. Abolade: Methodology, Data curation; Akinlolu Akande: Writing – review & editing, Supervision; Stefan Csaki: Writing – review & editing; David Dodoo-Arhin: Writing – review & editing. Funding Statement The authors wish to acknowledge funding from Tertiary Education Trust Fund (TETFund), Nigeria under grant Ref: NRF_SETI_HSW_00714, 2020, and the Africa Centre of Excellence on New Pedagogies in Engineering Education Acknowledgments The authors acknowledge the Multifunctional Materials Laboratory, Shell Office in Mechan- ical Engineering, Ahmadu Bello University, Zaria, Nigeria, the Department of Metallurgical and Materials Engineering, Ahmadu Bello University, Zaria, Nigeria and the Department of Mechani- cal Engineering, Bayero University, Kano, Nigeria, for providing facilities to carry out this study. 10 O.A. Osuchukwu, A. Salihi and I. Abdullahi et al. / Data in Brief 48 (2023) 109075 I r N P s t H u C s R [ [ [ [ n addition, the authors acknowledge the Tertiary Education Trust Fund (TETFund) in Nige- ia for funding this study under the National Research Fund category with grant reference: RF_SETI_HSW_00714, 2020, and the Irish Research Council for funding granted to DOO with roject ID GOIPD/2021/28. SAA thanks the Atlantic Technological University, Sligo, President Bur- ary Award for funding support. Most of the calculations were performed on the Kelvin clus- er maintained by the Trinity Centre for High Performance Computing (TCHPC) (Project codes: PC_22_01254 and HPC_21_01219). This cluster was funded through grants from the Higher Ed- cation Authority, through its PRTLI program. The authors also wish to acknowledge the Irish entre for High-End Computing (ICHEC) (Project codes: isphy005c and isphy006c) for the provi- ion of computational facilities and support. eferences [1] O.A . Osuchukwu, A . Salihi, I. 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