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The third term in Eq. 1 is the sum of n-body interactions (n > 3) within the centrally symmetric approach.
Quality of fitting the universal equations of state for B2 and L12 model structures is illustrated in Figure 1.
The binding energy between two defects (A, B = solute, SIA or vacancy): E(A,B) b = EA(VN−1 + A) + EB(VN−1 + B) − EA+B(VN−2 + A + B) − E(VN), (2) where E(VN) is the energy of the perfect supercell with N vanadium atoms, EV ac(VN−1) is the energy of the supercell with monovacancy, EA(VN−1 + A) and EB(VN−1 + B) are energies of the supercell with A and B type defect, respectively, and finally EA+B(VN−2 + A + B) is energy of the supercell containing both A and BFigure 2: The considered nearest-neighboring (nn) atomic configurations: a) 1nn-3nn positions (black atoms) near the vacancy (white atom); b) 1nn-4nn positions near the ⟨111⟩ dumbbell highlighted with space diagonal defects.
That may elucidate nature of the swelling reduction of vanadium doped with titanium.References [1] D.
Katahara, Phase transformations in the ti-v system under high pressure up to 25 gpa, Acta Metallurgica 29 (3) (1981) 479-485

References [1] G.
Constr., vol. 50, no. 1, pp. 1–11, 2017, doi: 10.1617/s11527-016-0926-1
July, pp. 472–479, 2017, doi: 10.4028/www.scientific.net/KEM.747.472
[16] IS 3495:Parts 1-4 Methods of Tests of Burnt Clay building brick. 1992, pp. 1–7
Constr., vol. 52, no. 2, pp. 1–12, 2019, doi: 10.1617/s11527-019-1333-1.

For a set of alternatives X is represented by matrix A=[aij]ÌX×X, aij=[1/9, 9] and aij∙aji =1 for i,jÎ{1. …, n}.
The relative weights wi for all alternative i can be obtained by using Eq. 1: . (1) Previous studies [16] have given significant attention to fuzzy preference relations.
This study adopt linguistic terms are { AH (Absolutely highly important), VH (Very highly important), SH (Strongly highly important), WH (Weakly highly important), EQ (Equally important), WL (Weakly lowly important), SL (Strongly lowly important), VL (Very strongly lowly important), AL (Absolutely lowly important)} and the intensity of linguistic terms are {AH (9), VH (7), SH (5), WH (3), EQ (1), WL (1/3), SL (1/5), VL (1/7), AL (1/9)}.
References [1] I.
Fazio, DBID: Analogy-based DSS for bidding in construction, Journal of Construction Engineering and Management. 119 (1993) 466-479

Table 1.
Figure 1.
References [1] E.M.
Polym., 242 (2017) 1-15
Process., 7 (2020) 479-492

Tampone [1] and Rotafix [2] report some of the advantages of this strengthening technique: 1.
Table 1 – Beams characteristics, recorded defects and assigned grade.
International Journal of Architectural Heritage 1, no. 1 (2007) 60–81
Materials and Structures, 43(1-2) (2010) 141–150
Teil 1: Nadelschnittholz

Table 1.
The miller indices for the river sand at 2θ = 26.90° is (1 0 1).
(a) (b) Fig. 1.
References [1] J.
Soc., vol. 93, no. 4, pp. 479–487, Apr. 2016

The chemical composition of the mineral ilmenite is shown in Table 1.
Table 1.
(a) (b) (c) (e) (d) Fig. 1.
The decrease in particle size correlates with increased titanium content, extracted using concentrated sulfuric acid, resulting in concentration values of 1229 ppm, 574 ppm, 596 ppm, and 479 ppm, respectively.
References [1] S.

The fractography details are also presented. 1.
Full annealing and Table 1.
Fig. 1.
References [1] K.
Sci., 15 (2010) 479-483

Fig. 1.
Table 1.
The impact of nanoparticles on the elastic modulus is presented in table 1.
References [1] H.
Okamoto, Polymer nanocomposites, Eng, 4 (2023) 457–479

Worldwide, more than 10 billion tons are produced each year [1].
Accoridng this defination, eco-fridenly concete is classified as shown in Table 1.
ALC is a cellular concrete wiht weights ranging from 1/5 to 1/3 of that of concrete, or approximately 480 to 800 kg/m3 with strengths typically in 3.5 to 4.1MPa range.
References [1] C.
Boddy, et al., in: Cement & Concrete Composites, Vol. 23(2001), pp.479-484 [9] G.