Mechanical Properties of Multifunctional TiF4 from First-Principles

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Mechanical Properties of Multi-Functional TiF4 from First-Principle Calculations Mariyal Jebasty Rethinaraj, and Ravindran Vidya ACS Biomater. Sci. Eng., Just Accepted Manuscript • DOI: 10.1021/acsbiomaterials.8b01391 • Publication Date (Web): 06 Mar 2019 Downloaded from http://pubs.acs.org on March 9, 2019

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ACS Biomaterials Science & Engineering

Mechanical Properties of Multi-Functional TiF4 from First-Principle Calculations. Rethinaraj Mariyal Jebasty†1 and Ravindran Vidya†1* †Department

of Medical Physics, Anna University, Sardar Patel Road, Guindy, Chennai - 600 025, India. *[email protected]

ABSTRACT: Titanium Tetrafluoride (TiF4) plays a crucial role in the pre-restorative dentistry, synthesis of metal fluorides and titanium silicate thin films, enhancing photo-catalytic activity of TiO2, and hydrogen storage applications. Though TiF4 is touted for superior catalytic activity in deflating decomposition temperature of metal hydrides, its fundamental properties have not been studied yet. Compressibility is a vital parameter during mechanical milling and hydrogen cycling process from solid metal hydrides to sustain its stability. Even though many high-pressure studies are available on metal hydrides, similar study on the additive TiF4 has not been made either by theoretical or experimental methods. In an effort to identify the compressibility of the catalyst TiF4, we have performed state-of-theart density functional theory based calculations for three chemical states of TiFx (x= 4, 3, and 2). Mechanical strength of a material is derived from inter-atomic interactions which in turn is influenced by the micro structure and bonding. The results highlight the superior structural, electronic, mechanical, and optical properties of orthorhombic TiF4 which has octahedral columns similar to the bone tissue material

1

These authors contributed equally to this work.

*corresponding author ACS Paragon Plus Environment

ACS Biomaterials Science & Engineering 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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(hydroxyapatite). This perspective highlights the stable iono-covalent F-Ti-F bonding of 4+ state of titanium fluoride. Materials with Young's modulus close to that of bone (20-30 GPa) are intensely searched for bone implants. TiF4 can be used for this purpose, because its average Young's modulus is 47 GPa. Our detailed analysis of charge density in TiF4 throws light on its unique bonding characteristics which result in the extraordinary mechanical properties, making TiF4 a multi-functional material not only for dental filling, but also for orthopedic, and catalytic applications. KEYWORDS: titanium tetrafluoride, Density Functional Theory, columnar structure, elastic constants, anisotropy, dental-filling. INTRODUCTION: TiF4 has been widely used in many technological applications. It is an active precursor to synthesize thin films of metal fluorides and titanium silicate.1,2 When TiF4 is added to TiO2 nanocrystal, photocatalytic hydrogen production is enhanced due to change in surface morphology3. Moreover, TiF4 additive has shown superior catalytic activity on the decomposition of MgH2, Mg(BH4)2 and Mg(AlH4)2 used in hydrogen storage applications.5-8 By application of constant shear stress on TiF4 additives, Ti4+ is reduced to Ti3+ and Ti2+ during mechano-chemical process.6 Upon reacting with metal hydrides, the lower oxidation states of Ti triggers the decomposition kinetics of hydrides. The mechano-chemical action requires optimum compressibility and ductility of the material, which prevents pinning of the catalyst to the milling media and promotes better conversion mechanism.7 However, TiF4 is less studied in this perspective. Besides, TiF4 plays vital role in pre-restorative dentistry in maintaining tooth vitality. Increased demand for aesthetics motivates the material scientists to search for new dental filling materials with properties similar to oral tissues. The required ideal characteristics of a tooth-filling material are: good mechanical strength, corrosion resistance, non-toxicity, compatibility with oral environment and cost-effectiveness.9 Most importantly, the filling material should adhere with the surrounding hard tissue [hydroxyapatite

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(HAp) crystal lattice] so as to avoid structural changes. The efficacy of the filling materials relies primarily on the physical properties which are controlled by microstructure of the material.10 The present status of titanium and its fluoride solution in the field of dentistry is prudent in preventing caries, sealing the pit and fissures, desensitizing the tooth, and corrosion-resistance in various solutions like saliva in oral environment.11-14 It was found that, TiF4 enhances the fluoride uptake15,16 and thereby provides mechanical protection to the teeth.17,18 The pretreatment of 2.5 % TiF4 on dentin was found to increase its hardness and elastic modulus. Moreover the TiF4 layer is erosion resistant, and prevents dentin demineralization thereby enhancing the strength and stability of the dentin surface.12 In addition, TiF4 adheres with the tooth surface19 and topical TiF4 around orthodontic brackets protects the enamel by introducing CaF2-like deposits.20,21 A series of in-vitro studies on various transition metal fluorides underscored the effectiveness of TiF4 on maturing enamel.22 A recent review11 has shown that, TiF4 can be used in various dental treatment techniques, and its impact is especially significant when it is topically applied for anti-caries activity, because TiF4 forms an acid-resistant varnish on the tooth surface.23 Interestingly, the properties of TiF4 are similar to that of the Glass Ionomer Cement (GIC), however with better sealing character. More recently, toxicological study by Alexander et.,al revealed a decrease in the depth of the caries lesion by the application of TiF4 showed no abnormalities in oral soft tissues.24 Despite many technological applications of TiF4, its micro-mechanical properties have not been studied either by theoretical or by experimental methods. Hence we performed state-of theart accurate DFT calculation on mechanical properties of TiF4. We provide a detailed analysis of these properties and elucidate the influence of structural anisotropy. We have also calculated the mechanical property of the trivalent and divalent chemical states of titanium to verify the mechanical stability under various oxidation states of Ti. TiF4 takes up low symmetry orthorhombic structure (here after o-TiF4), whereas TiF3 stabilizes in cubic and rhombohedral structural variants (c-TiF3 and r-TiF3) and TiF2 has cubic structure (c-TiF2). TiF4 could be a better replacement for GIC in the foreseeable future with suitable hardness, elasticity, adhesion and ACS Paragon Plus Environment


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cost-effectiveness in the series of aesthetic fluoride-releasing restorative materials. We show that the unique bonding behavior of TiF4 makes it suitable for catalytic, dental filling and orthopedic applications. Outline of the methodology used for the mechanical property calculation is the consecutive label, followed by Results and Discussion section dealing with energetics of crystal structures and detailed analysis of chemical bonding and mechanical properties. METHODOLOGY Computational Details The Density Functional Theory (DFT) was used to calculate the mechanical properties. The simulations were performed using the quantum engine Vienna Ab-initio Simulation Package (VASP)25 which describes the electron-ion interaction by the projector-augmented-wave (PAW)26 method with plane-wave basis-set cutoff energy of 550 eV. The free energy of the taken primitive unit cell has been calculated as integral over the 8 × 8 × 8 k-point grid with the automatic pack scheme. The stopping criterion for total energy convergence was set to 10-6 eV for the self-consistency cycle to calculate electronic ground state. The exchange correlation energy was calculated using the GGA-PBE functional (PW91).27 Before performing calculations to obtain elastic constants, the structural stability of these compounds were analyzed using complete structural optimization by minimizing the stress and force in the crystal structures, with the tolerance factor for forces to (1 meV / Å) using a conjugate gradient algorithm. Successively, ionic relaxations are applied to the lattice vectors and the resulting stress tensor is calculated from DFT and the resulting 6 × 6 stiffness (elastic) tensor was obtained from stress-strain linear relationship which is explained in detail elsewhere.28-31 The theoretical background and computational parameters used for deducing the stress-strain relations are explained in Appendix-I. Elastic Properties The second order elastic constants (Cij) have great significance in determining the mechanical stability and compressibility of the material. The elastic constants are basic parameters closely related to hardness of the material which inherently depends on the bond distance and micro-structure. In order to describe the elastic behavior of orthorhombic, trigonal and cubic systems completely, nine, six and three single ACS Paragon Plus Environment

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crystal elastic constants are needed, respectively. Concerning the limited studies on the Ti-F variants, the lattice stability has been double checked with the eigenvalue matrix and the Born-stability criteria, elaborated under the label ‘Mechanical Stability’. The necessary Born- stability criteria32 for the material belonging to the orthorhombic, rhombohedral (class-I) and cubic system are given by the equations 2, 3, 4, respectively. C11 > 0 ; C11 C22 > C212

(2a)

C11 C22 C33 + 2 C12 C13 C23 – C11 C223 – C22 C213 – C33 C212 > 0

(2b)

C44 > 0 ; C55 > 0 ; C66 > 0.

(2c)

C11 > |C12|; C44 > 0

(3a)

1

C213 < 2C33 (C11 + C12)

(3b)

1

C214 < 2C44(C11 − C12) = C44C66

(3c)

C11 - C22 > 0 ; C11 + 2C12 > 0; C44 > 0

(4)

The elastic stiffness constants C11, C22, C33 are the co-efficients of the uniaxial stress along , and direction called principal axis. The shear elastic constant, C44 corresponds to the shear between (100) and (010) planes, C55 corresponds to the shear between (010) and (001) planes and C66 corresponds to the shear between (001) and (100) planes.33 The biaxial elastic constants Cij where, i ≠ j entails normal and shear strains. These compliance constants are fundamental values used to derive the other moduli of elasticity, for instance, Young's modulus (E), shear modulus (G), bulk modulus (B), and Poisson's ratio (ν). In general, crystalline materials are mechanically anisotropic however the extent of their anisotropies has to be quantified with prior knowledge of single-crystal elastic constants.33 The elastic properties play an important role in providing valuable information regarding the binding characteristics between adjacent atomic planes, the anisotropic character of binding and structural stability.



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We have extracted the isotropic elastic moduli such as E, G, B and ν using the homogenization technique called Voigt-Ruess method. It provides theoretical higher (Voigt) and lower (Ruess) bounds. The aforementioned technique assumes uniform strain and uniform stress throughout the crystal, as implemented in the online ELAstic TEnsor analysis (ELATE) tool.34,35 It is appropriate for isotropic materials alone. Therefore, an arithmetic average of these two values called Hill average provides the mechanical properties of poly-crystalline aggregates.36 In addition, the percentage of anisotropy in the elastic properties has been calculated using the equations 5 given below. The interesting observations found from the calculated directional properties are summarized under the label Charge Density and Density of States using the following anisotropy parameters. 𝐴𝐺 = 𝐴𝐵 =

G𝑉 ― G𝑅

(5)

G𝑉 + G𝑅 B𝑉 ― B𝑅 𝐵𝑉 + B 𝑅

where, GV, BV, GR, BR are the theoretical upper and lower bounds on shear (G) and bulk modulus (B), respectively. Finally, the relationship between bonds and mechanical strength has been explicitly brought out in the charge density analysis. RESULTS AND DISCUSSION Crystal Structures We have performed structural optimization in order to find the lowest energy state in which the atoms are arranged in a manner that free energy is minimized. Stability of the considered structures has been confirmed by calculating the formation energy (∇H / formula unit (f.u) and ∇H / atom) which is included in Table 1: ∇𝐻 𝑇𝑖𝐹𝑥 = 𝐸 𝑇𝑖𝐹𝑥 - 𝐸𝑇𝑖 + x𝐸𝐹 ;

(x=4,3, 2)

(6)

where, 𝐸 𝑇𝑖𝐹𝑥, 𝐸𝑇𝑖 and 𝐸𝐹are the optimized total energy of TiFx, metallic Ti and gaseous F, respectively. The optimized crystal structures are shown in Figure 1. Interestingly, o-TiF4 has unusual closely spaced columnar structure similar to the HAp crystal where the atoms are aligned parallel to c-axis in a highly ACS Paragon Plus Environment

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ordered way that could be responsible for the exceptional mechanical property of HAp. TiF4 has the structural environment of corner sharing octahedra described by simple orthorhombic symmetry of space group Pnma. o-TiF4 contains 60 atoms in its primitive cell37(No. of formula unit [Z]=12). While majority of the trifluorides crystallize in rhombohedral structure, TiF3 stabilizes in a simple cubic structure with space group Pn3m (No: 221) at 950 °C. Nevertheless, TiF3 stabilizes at low temperature in rhombohedral structure with space group R3c (No: 167), similar to other tri-halides those stabilize in prototype FeF3 structure. The polymorphic r-TiF3 has metal ion (Ti3+) at the octahedral site.38 We have found that both tri-fluoride structures are energetically stable, with a very small energy difference of ≈ 4 meV / f.u between them, and c-TiF3 is having the lowest energy. c-TiF2 takes up the typical CaF2 type structure (space group Fm3m) at high pressure which has flattened undistorted octahedral coordination.39 The optimized crystal structures are shown in Figure 1 except that of c-TiF3, as it has a well-known simple cubic structure.



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Figure 1. (Color online) Crystal structures of (a) o-TiF4 (b) Ring structure formed by three polyhedra of o-TiF4 (c) Columnar representation of o-TiF4 (for clarity only one half of the cell along the c-axis is shown), (d) r-TiF3 and (e) c-TiF2. ACS Paragon Plus Environment

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The optimized structural parameters are given in Table 1 along with corresponding equilibrium bond lengths, which are in general good agreement with corresponding experimental values. The equilibrium volume is overestimated by 2 % from the experimental volume for o-TiF4, 5 % for r-TiF3, and that for cubic structures have only 1 % deviation from experimental parameters. Table 1. Calculated and experimental equilibrium lattice parameters, bond lengths and heat of formation of o-TiF4, r-TiF3, c-TiF3 and c-TiF2 Compound Lattice Parameter (Å) Bond Distance (Å) Formation Energy (eV)

o-TiF4

Theory

Experiment

Theory

Experiment

∇H/f.u

a=23.504

a=22.811a

Ti-F1 = 1.933

1.932

-16.056

b=3.919

b=3.848

Ti-F2 = 1.775

1.716

c= 9.868

c= 9.568

Ti-F3 = 2.001

1.976

Ti-F4 = 1.982

1.965

Ti-F5 = 1.781

1.719

Ti-F = 1.961

1.966

-12.925

a=b=5.571

a=b=4.767b

c= 13.654

c= 13.990

c-TiF3

a=b=c= 3.941

a=b=c= 3.941

Ti-F = 1.971

1.971

-3.231

c-TiF2

a=b=c= 5.130

a=b=c= 5.156c

Ti-F = 2.221

2.232

-7.326

r-TiF3

aRef.[37],

bRef.[38], cRef.[39],

Especially, TiF4 has highly distorted octahedra with five different Ti-F bonds. As shown in Figure 1(b), there are three types of Ti atoms each with five different nearest neighbor F- ions. Three TiF6 octahedra are connected together to form a ring as shown in Figure 1(b). This leads to Ti3F15 cluster formation. Their respective apical and basal fluorines have almost similar bond distances (the difference is ≈ 0.003 Å). So for clarity, we have displayed five different bond lengths of one polyhedra. The apical octahedral Ti-F bonds are identical marked by F1 in the Figure 1(b). It is apparent that the orthorhombic structure, forms parallel polyhedra layers as shown in Figure 1(c). If TiF4 decomposes at extreme conditions, it will disintegrate into the following fragments, ACS Paragon Plus Environment


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TiF4-nn ↔ TiF3-nn-1 + F- ; (where n=4,3,2) Then, as a fluorine reservoir TiF4 can decompose into TiF3 and F-1, and TiF3 can further decompose into TiF2 and F-1. This can ensure continuous release of fluorine over time which helps in remineralization of the teeth and inhibits secondary caries. Mechanical Properties Mechanical Stability The independent elastic constants also known as stiffness constants (Cij) are obtained from the stressstrain curve fit for the theoretically optimized structural parameters and listed in Table 2. It is clearly seen from this table that the symmetry has influence over the components of elastic tensor matrix in terms of number of independent coefficients. Since no experimental elastic constants are available for the studied Ti-F variants, comparison has been made for c-TiF3, r-TiF3, and c-TiF2 with the previous theoretical results available at Materials Project database40. The calculated elastic constants for TiF3, and TiF2 are somewhat overestimated than the previous theoretical values Ref,40 may be because our optimized structural parameters are overestimated from experimental values by ≈ 5 %. The elastic properties of oTiF4 are hitherto not studied. Hence, we benchmarked our elastic constant calculations for orthorhombic system by calculating the mechanical properties of a well-known orthorhombic TiSi2. The elastic constants of TiSi2 from our calculations are consistent with experimental values41 and within 5\% deviation from previous theoretical values28,43(more details are given in supplementary information).


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Table 2. Calculated stiffness constants (Cij) of o-TiF4, r-TiF3, c-TiF3 and c-TiF2 Propertie o-TiF4 r-TiF3 c-TiF3 c-TiF2 Elastic Present Present Ref.40 Present Ref.40 Present Ref.40 s C11 = 178.22 159 C11 = 319.62 259 C11 = 165.56 201 Constants C11 = 25.97 (Cij ) GPa

C22 = 262.49

C33 = 140.13

129

C12 = 26.84

26

C12 = 104.81

63

C33 = 33.30

C44 = 92.46

76

C44 = 22.73

21

C44 = 16.79

47

C44 = 17.34

C12 = 62.89

58

C55 = 6.50

C13 = 99.95

88

C66 = 11.10

C14 = 51.74

42

C12 = 8.90 C13 = 12.93 C23 = 6.76

More fundamentally, the elastic constants of a solid provide important informations concerning the nature of the forces operating and displacements at all of the structural coordinates in solids. These constants can also play an important role in analyzing phase stability of materials. The mechanically stable crystal system should have positive strain energy (positive Cij).44 The positive coefficients imply that the stability of TiF derivatives are stable on application of strain. The mechanical stability of the respective lattice type has been verified using the eigenvalue matrix (λ) and the Born-stability criteria, further emphasizing the energetic stability of the studied compounds. Table 3: Eigen values of the stiffness matrix for o-TiF4, r-TiF3, c-TiF3 and c-TiF2 𝝀𝟏 Compounds λ2 λ3 λ4 λ5 λ6 λmax/λmin o-TiF4

6.50

11.10

16.158

17.34

42.55

263.05

40.46

r-TiF3

20.47

29.831

40.52

129.65

177.95

340.71

16.62

c-TiF3

22.73

22.73

22.73

292.60

292.60

371.41

16.34

c-TiF2

16.79

16.79

16.79

60.75

60.75

375.18

22.34



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The stiffness matrix for a stable structure must be invertible. In general an n x n matrix deforms into n eigenvalues (λ), any one of its value will be zero for the unstable structure (i.e.,singular matrix). Also, the ratio λmax/λmin governs the stiffness of the material. If the ratio is greater than one, it indicates that the structure is stiffer. Eigenvalue of the studied TiFx compounds are given in Table 3 which fulfills the stiffness condition for stable structures. Further, the calculated Born-stability conditions for the o-TiF4, rTiF3, c-TiF3, and c-TiF2 are given in Table 4. It may be noted that a material is regarded as mechanically stable if it satisfies the Born-stability criteria. Failing the criteria may indicate the onset of structural transformation, melting, polymorphism and pressure induced amorphization etc,.42 Table 4: Born-Stability criteria for o-TiF4, r-TiF3, c-TiF3 and c-TiF2 Compounds Born-Stability criteria Calculated Value o-TiF4

r-TiF3

eqn. 2a

25.97 > 0; 6816.86 > 79.2

eqn. 2b

180848.63 > 0

eqn. 2c

17.34 > 0; 6.50 > 0; 11.10 > 0

eqn. 3a

178.22 > |62:89| ; 92.46 > 0

eqn. 3b

9990.00 < 16893.37

eqn. 3c

2677.02 < 5331.70 = 5331.70

c-TiF3

eqn. 4

292.98 > 0; 373.3 > 0; 22.73 > 0

c-TiF2

eqn. 4

60.75 > 0; 375.18 > 0; 16.79 > 0

Based on these stability criteria we found that the strain energies of all the studied compounds satisfy the conditions given in equations 2, 3, 4, implying that they are mechanically very stable for deformation forces. Single-Crystal Elastic Constants The knowledge of stiffness constant has great significance in defining the mechanical reliability of a material.45 It is informative to look at the normal stress-strain constants C11, C22 and C33 along the principal a, b and c axes as they play a significant role against the deformation.


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The high value of Cij component implies that the structure is less compressible (stiffer) along that direction. For the case of orthorhombic-TiF4, the stiffness constant is of the order C22 > C33 > C11, implying that the material is more resistant to deformation along b-axis compared to that along the a and c axes, accordingly the binding force of the atoms along b-axis is greater. On close observation, we have identified an intriguing feature in o-TiF4 crystal from the rest. On the other hand, C11 is higher in the remaining compounds. This implies that, shorter interatomic distance of Ti-F along b-axes leads to stronger bonding in TiF4, resulting in its incompressbility along the b-axis. The modulus C22 is larger than other Cij components for o-TiF4. The Ti-F bond length in o-TiF4 is shorter (1.72 Å) along b-axis compared to that along other directions (1.98 Å to 2.0 Å). The Ti-F bond lengths in r-TiF3, c-TiF3, and c-TiF2 are 1.96 Å, 1.97 Å, and 2.23 Å, respectively. The shorter bond length along with unique bonding nature of o-TiF4 (discussed in detail in using charge density analysis) make stronger bonding compared to the bonding in r-TiF3, c-TiF3, and cTiF2. The electronic distribution is also highly anisotropic (see Figure 4b) in o-TiF4, whereas r-TiF3, cTiF3, and c-TiF2 have somewhat uniform distribution of charges. Hence, the response of o-TiF4 to external strain along the b-axis is different from that of r-TiF3, c-TiF3, and c-TiF2. This could be the reason for higher stiffness constant of o-TiF4 along the b-axis than that in other systems. It is known that, shear modulus concerns the deformation and fracture behavior of a solid.33 The shear constant C44 corresponds to the shear deformation resistance along (100) plane. The shear deformation resistance is in the order c-TiF2 > o-TiF4 > c-TiF3 > r-TiF3. The shear anisotropic factors (A1, A2, A3) along different crystallographic planes provide a measure of the degree of anisotropy in atomic bonding in different planes which are calculated as given below:

For {100} shear plane between and directions, 𝐴1 = 𝐶11 +

4 𝐶44 𝐶33 ― 2𝐶13

For {010} shear plane between and directions,



𝐴2 = 𝐶22 +

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4 𝐶55 𝐶33 ― 2𝐶23

For {001} shear plane between and directions, 𝐴3 = 𝐶11 +

4 𝐶66 𝐶22 ― 2𝐶12

For an isotropic crystal the factors A1, A2, and A3 must be unity and for anisotropic crystal A ≠ 1. For the case of less symmetric o-TiF4, values of A1 = 2.086, A2 = 0.1151, and A3 = 0.1640 imply its higher degree of anisotropy. The highest value obtained for A1 for shear values between and directions, implies exceptional degree of anisotropy along the (100) shear plane. Poly-Crystalline Elastic Properties Young's modulus is generally used to measure the stiffness of an elastic material. Plastic deformation and fracture behavior can be analyzed with the aid of shear modulus (G) (also known as rigidity modulus) whereas bulk modulus (B) gives a measure of resistance to uniform compression. Both shear modulus and bulk modulus determine the hardness of a material. The Poisson's ratio determines the stability of the crystal against shear and emphasizes the nature of bonding. Table 5: Calculated elastic properties of o-TiF4, r-TiF3, c-TiF3, and c-TiF2 Properties Young’s Modulus (VRH) E

o-TiF4 Present 47.09

r-TiF3 c-TiF3 40 Present Ref. Present Ref. 124.92 139.84 40

c-TiF2 Present Ref.40 60.56 -

Shear Modulus(VRH) G

18.86

47.43

42

53.26

45

21.33

55

Bulk Modulus(VRH) B

31.19

113.58

102

124.44

104

125.06

109

Poisson's ratio (VRH) ν

0.25

0.31

0.31

0.31

0.32

0.41

0.28

AG = 0.41

0.35

0.30

0.35

0.31

0.04

0.01

Anisotropy Average


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Table 5 summarizes the Hill average (arithmetic average) of Voigt-Ruess theoretical limits along with the percentage of anisotropy. In addition, the spatial extent of the Young's modulus (E) is illustrated in Figure 2. The calculated elastic modulus of o-TiF4, r-TiF3, c-TiF3, and c-TiF2 are listed in Table 5. It may be noted that o-TiF4 has the Young's modulus value of 47 GPa which is greater than that of dentin (18 GPa) and other teeth restorative materials commonly used. Hence o-TiF4 is suitable for restoration at the pulp cavity. In addition, for bone implants and repairing bone fractures, materials with Young's modulus close to that of bone (20-30 GPa47) are desired. It is important to reduce elastic mismatch between the bone replacement material and existing bone. When a stiffer implant is used, the physical load on the bone is reduced, leading to drop in the bone density, mineralization, and bone strength. This can eventually result in contact loosening, implant failure, and infections etc. However, implant materials with Young's modulus as high as 110-120 GPa48-50 are frequently used, because finding materials with Young's modulus close to that of bone is still challenging. In this perspective, we propose that o-TiF4 can be considered for the above purposes, owing to its Young's modulus value closer to that of bone than other implant materials and its good bio-compatibility. The hardness of the compounds is usually derived from the shear modulus. The shear modulus value is about 18.86 GPa for o-TiF4 that is reasonable to resist plastic deformation since the stated hardness value is only 3.5 GPa on the surface of enamel46. The higher value of hardness (> 40 GPa) for both the phases of TiF3 indicates that, this compound belongs to the family of hard materials. The fracture resistance of c-TiF2 is close to that of o-TiF4. The o-TiF4 has reasonable value of bulk modulus (31 GPa) implying its high hardness. The other derivatives r-TiF3, c-TiF3, and c-TiF2 have higher value of bulk modulus (> 40 GPa) implying their super hard nature. However, there is a large variation in magnitude for all the derived elastic properties of oTiF4 from the other Ti-F variants. The calculated packing efficiency per unit cell is 54 % for o-TiF4, 66 % for r-TiF3 and 89 % for c-TiF2. Since the density of the material has influence on hardness, the above



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stated difference may be due to the larger voids in o-TiF4 compared to the close packing present in the remaining compounds apart from anisotropic bonding behaviour. Poisson's ratio lesser (greater) than 0.25 signifies the brittle (ductile) nature of the material. The Poisson's ratio of o-TiF4 falls exactly at the critical limit that is very close to the Poisson's ratio of enamel and dentin10 while the other Ti-F compounds have crossed that limit indicating their ductility. In addition, the threshold Poisson's ratio value of 0.20 implies strong covalent bond whereas 0.4 is widely implied to describe metallic nature. This highly validates the dominant role of metallic Ti over fluorine ion in the compounds other than o-TiF4, notably leading to the increase in their hardness values. This elucidated the influence of Ti:F ratio in the bonding feature. The higher mechanical moduli with decreasing fluorine content can be attributed to the less covalent bonding. Elastic Anisotropy The hardness of the material can be deduced more properly from the softest elastic modes than from bulk elastic properties. So we have analyzed the role of elastic anisotropy on the hardness of the material. The extreme minima and maxima of Young's moduli are as follows: 19.42 to 259.24 GPa for o-TiF4; 57.26 to 281.76 GPa for r-TiF3; 64.26 to 314.87 GPa for c-TiF3; and 48.21 to 84.3 GPa for c-TiF2. The directional dependence of Young's moduli for the considered Ti-F compounds are shown in Figure 2. The surface geometry clearly points out the large anisotropy with extreme maxima, minima and average values along with negative values. Figure 2(a) shows that the Young's modulus of o-TiF4 is strongly polarized along b-axis rather than other axes, implying its incompressibility along b-axis. So the shape of the geometry is ellipsoidal along (101) plane perpendicular to b-axis, whereas (110) and (011) planes experience more stress. The other fluorides also show remarkable anisotropy because of their large moduli value along certain crystallographic axis. For instance, r-TiF3 has a range of maximas along different directions exhibiting large anisotropy as shown by Figure 2(b). The Figure 2(c) and 2(d) show Young's modulus for c-TiF3 and c-TiF2 which has a somewhat uniform maxima along the axes. This indicates noticeable directional anisotropy even in isotropic structure itself. High C11 and low C12 values make ACS Paragon Plus Environment

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Young's modulus large along the principal axis and small along the diagonal direction for the cubic compounds.

Figure 2. Color online: Anisotropy in Young's modulus for (a) o-TiF4 (b) r-TiF3 (c) c-TiF3 and (d) cTiF2 The observed minimum and maximum shear strength value of the material is: 6.5 GPa to 23.93 GPa for o-TiF4, 20.33 to 129.65 GPa for r-TiF3, 22.73 to 146.30 GPa for c-TiF3, and 16.79 to 30.375 GPa for cTiF2. The extreme values of bulk modulus (B) must be the same throughout the solid for an isotropic crystal. The observed theoretical upper (BV) and lower bulk modulus (BR) values for the cubic structures ACS Paragon Plus Environment


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are almost equal and explicitly show the sphere-like distribution (shown in Supplementary data). The pictorial representation of the compressive strength shows very high spatial variance for o-TiF4 and somewhat uniform distribution for TiF3 and TiF2. Specifically, for the o-TiF4, the value extends from 2.37 to 28.49 TPa-1. The percentage of anisotropy in the shear modulus (AG) and bulk modulus (AB) are calculated using equation (5) and listed in Table 5. The AB value for o-TiF4 is 0.35 and zero for other Ti-F variants. The zero AG and AB are due to the isotropic nature, and the deviation from zero corresponds to the directional elastic properties. The anisotropic behavior is usually due to the non-uniform distribution of charges. The anisotropy in bulk modulus is nearly 40 % for o-TiF4, indicating the inhomogenity in its charge distribution.

Figure 3. (Color online) Spatial variation of (a) shear modulus (b) bulk modulus and (c) Poisson's ratio of o-TiF4 The spatial variations of elastic properties of o-TiF4 have been analyzed in detail. The directional dependence of shear modulus (G), bulk modulus (B), and Poisson's ratio of o-TiF4 are plotted and displayed in Figure 3(a), (b) and (c), respectively. The shear modulus displays larger anisotropy. The (011) plane of o-TiF4 has higher shear modulus indicating more fracture resistance along the (011) plane. The spatial dependence of bulk modulus along (101)-plane is somewhat isotropic and has its peak value along b-axis. This uniform compressibility along (101)-plane is due to the basal TiF4 atoms. Further, the higher bulk modulus along b-axis implies its significant covalent bonding. The bulk modulus is dumbbell ACS Paragon Plus Environment

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shaped along (011) and (110)-planes because of the bonding of Ti with apical octahedral fluorine atoms. The orientation dependence is clearly seen from this Figure 3(b). Eventually, the spatial dependence of Poisson's ratio of o-TiF4 along (110) plane is more directional and reaches the maximum value of 0.4, implying its more ductility. The spatial variations of shear modulus, bulk modulus, and Poisson's ratio for r-TiF3, c-TiF3, and c-TiF2 are consistent with the previous theoretical results40 (given in supplementary data). Furthermore the anisotropy in the elastic properties has also been calculated for all the Ti-F variants and given in supplementary data. The compressibility of materials is connected with anisotropy in the arrangement of atoms. In this elaborate investigation, we have found that the bulk modulus is large enough to withstand load/unload of hydrogenation. As oxidation state of Ti decreases, the hardness value increases. The value of poisson's ratio indicates the ductile nature of all the considered Ti-F variants, which prevents pinning of catalyst to the wall of container during milling process of hydrides thereby enabling efficient release of hydrogen53. Among all fluoride variants, o-TiF4 is more suitable for dental filling because of its moderate strength whereas other variants may crack the enamel walls while chewing force is applied because of their high hardness value. Mechanical and other physical properties of the restorative dental materials are important for both material selection and for analyzing their clinical performance. The o-TiF4 has the advantage of metal added with fluorine which can be responsible for its mechanical reliability, since F-1 ion promotes remineralization and metallic Ti provides the mechanical strength same as that of silver diamine fluoride. The o-TiF4 has elastic modulus greater than that of weakly mineralized intertubular dentin (18 GPa), equal to the highly mineralized pertitubular dentin (40-42 GPa) and lesser than the enamel (80 GPa). It may be noted that, the modulus of elasticity (iE) of o-TiF4 is greater than the other restorative materials employed in daily practice in the restorative dental practice. The Young's modulus of dentin and enamel varies with depth from 18 to 80 GPa, due to the complex structure of HAp and anisotropic mineral composition. On the other hand, o-TiF4 responds differently in ACS Paragon Plus Environment


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different directions with respect to the stiffness. Noticeably, the tight packing of atoms enriches Young's modulus along b-axis. Then this directional property would be appropriate for the mechanical load experienced during mastication. Furthermore, the shear modulus (hardness value) of o-TiF4 is about 18 GPa that is sufficient to withstand the fracture resistance. We can conclude that with increasing F content, the directional covalent interactions and stability are enhanced. Charge Density and Density of States The results of the structural analysis and elastic properties encouraged us to investigate the bonding nature of o-TiF4 along direction by analyzing the spatial charge distribution. The unit cell consists of 60 atoms where each Ti atom is surrounded by six fluorine atoms with five different bond lengths ranging from 1.7 to 2.0 Å. Hence the bonding between Ti and F has mixed bonding character which shows predominant covalent bonding. Smaller distances are indicative of appreciable covalency. It is clear from Figure 4(b) that the Ti bond is slightly polarized towards F. So it gives dominant covalent character. It is apparent from Figure 4(b) that, there are three types of Ti atoms, each surrounded by four F atoms which are connected together in a cyclic manner introducing triangular voids. This cage like appearance builds Ti3F9 cluster of charges along (010) plane. This cluster repetition over the cell leads to columnar structure along b-axis with stripes like interstitial voids as illustrated in Figure 1(c). These voids would be responsible for binding characteristics of TiF4 with tooth structure, further enhancing its mechanical strength. Each Ti is surrounded by six F atoms (bond lengths are given in Table 1). It is intriguing that the F atoms of corner-shared octahedral positions (F3, F4) forming cage-like structure have longer bond lengths (1.98 - 2.0 Å) than those at the unshared corners, F2 and F5 (≈ 1.78 Å). The charge density plot clearly elucidates the directional, covalent bonding between Ti-F3 (F4) by the anisotropic charge distributions with more electrons present in the region between Ti and F3 (F4). The density of electrons around the F atoms at the un-shared polyhedral edges (F2 and F5) is almost uniform indicating its dominant ionic character. The non-directional Ti-F bonds at un-shared corners of octahedra along with the directional bonding within the cage create an unusual iono-covalent behaviour. As valence electrons of Ti are strongly pulled towards ACS Paragon Plus Environment

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F3 and F4, the Ti atoms become more positively charged. Since both F3 and F4 gain electrons from two Ti atoms each, their 2p outer shell becomes filled, making optimum bond lengths of 1.98 - 2.0 Å with the Ti atoms. On the other hand, the F atoms at un-shared corners (F2 and F5) come closer to Ti neighbours in an effort to gain electrons. Moreover, the F2 and F5 atoms face the F3 and F4 atoms of the neighboring cages and situated at the midway between the Ti-F3(F4)-Ti bonds. As all these F atoms have completely filled outer orbital due to the electrons from Ti, their surrounding electron cloud repel each other. So F2 and F5 are further pushed towards Ti resulting in shorter Ti-F bond lengths, thereby creating voids. These voids act as channel and binding site to adhere with the tooth structure or as retention sites in hydrogenstorage metal hydrides. Moreover, the stable cyclic Ti-F-Ti bond formation may pave the way for hydrogen diffusion mechanism. Even though these F atoms are exposed to the interstitial region, they can be unreactive because their outer shells are completely filled with electrons from Ti. In general, F- ion is more reactive, but the peculiar bond formation in TiF4 makes it less reactive as discussed above. In this way, F ions become stable in the TiF4 structure and provide enhanced stability to TiF4.



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Figure 3. (Color online) (a) Representation of 010 lattice plane of o-TiF4 (b) Charge density distribution along 010 plane (c) Total and site-projected Density of states for o-TiF4 In order to gain further insight on bonding, total as well as partial density of states (DOS) are calculated. Evidently, TiF4 has large band gap value of nearly 4 eV (Figure 4(c)) between valence band maximum (VBM) and conduction band minimum (CBM), implying its insulating character. The other studied fluorides are having metallic character. The electronic states crossing the Fermi level (EF) in TiF3 and TiF2 are due to the Ti-d electrons. In o-TiF4 the bonding states are dominated by Ti-s, Ti-d and F-p orbital, and significant hybridization is seen between Ti-d and F-p orbitals. The Ti-d and F-p states are energetically degenerate between the energy range -3.5 eV to -1 eV indicating their directional bonding. Further, there is a degeneracy of Ti-s and F-p states at the energy range -3.5 to -3.0 eV. This increased


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covalent character can give rise to stronger bonds between Ti and F in TiF4 compared to that in TiF2 and TiF3. Beside this, the observation indicates significant electronic states of titanium at the valence band region where fluorine has higher density of states. However, CBM is mainly due to Ti-d orbital states. Since, the top most valence band is dominated by F-p electrons, they have significant effect in determining the electrical conductivity. In addition, o-TiF4 can be considered as a suitable material for dental fillings due to its low thermal conductivity much like HAp crystal. Further, we have calculated the refractive index of o-TiF4 as it is important in determining it's aesthetic nature. The derived refractive index value of 1.75 confirms its translucency which is close to that of enamel (1.65) and higher than other fluoride containing restorative materials (≈ 1.50)51,52. More detailed analysis on optical properties will be published elsewhere. CONCLUSIONS The elastic properties of materials can reliably be predicted using DFT if one takes into account the structural relaxations along with gradient corrections for correlations effects into the calculations. In this sense, we have performed with complete structural optimization and the calculated structural parameters are consistent with the corresponding experimental results for four Ti-F variants o-TiF4, c-TiF3, r-TiF3 and c-TiF2. 1. A remarkable feature in the crystal structure of o-TiF4 was observed. The specific stacking of octahedral network forms columns parallel to b-axis similar to the fibre-like hydroxyapatite structure present in bones. 2. We have calculated the elastic constants for TiF4 for the first time. The observed elastic constants are in good agreement with the previously reported theoretical elastic constants for TiF3 and TiF2. The mechanical stability of the materials has been verified with Born stability criteria and we found that the studied compounds are mechanically very stable and retain their structural stability upon elastic-plastic work during de(hydrogenation).



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3. The elastic properties such as Young's modulus, shear modulus, bulk modulus, and Poisson's ratio and their directional dependence have been calculated. Though the elastic moduli is low for oTiF4 compared to the other Ti-F variants, they are higher than that of other restorative materials employed in clinical practice. 4. The directional dependence of Young's modulus highlights the ultra-incompressibility along direction. In addition, we found that the TiF4 compound shows significant resistance to plastic deformation. The calculated Young's modulus value of 47 GPa for o-TiF4 is greater than that of dentin and other teeth-restorative materials and close to that of bone, making it attractive for dental restoration as well as orthopedic applications. 5. The linear compressibility is isotropic for all Ti-F entities except for o-TiF4. The Poisson's ratio gives important information on the bonding feature of Ti-F compounds, suggesting that the metallic feature decreases in the following sequence: c-TiF2 > r-TiF3 > c-TiF3 > o-TiF4. 6. Further, the intriguing bonding behavior incites large anisotropy in the elastic properties of TiF4 as revealed by the charge density analysis. The unique bonding nature viz, stronger iono-covalent bonds forming cage-like structures and shorter outer bonds lead to less reactive fluorine in TiF4 which makes it more suitable for dental filling applications. The site projected density of states elucidates the mixed-bonding states and hybridization of Ti-d and F-p states. In conclusion, among the four halides, o-TiF4 has desirable physical properties which combine good structural, mechanical, and electronic properties. The anisotropic mechanical properties strongly recommend the preferential b-axis orientation for the o-TiF4. Therefore, when TiF4 is used for dentalfilling it is essential to fix the columnar structures of o-TiF4 rods parallel to the enamel fiber to withstand the external chewing force. In this perspective of study, all the three chemical states of titanium namely TiF4, TiF3, and TiF2 are mechanically stable. This can stabilize the structure during prolonged milling and decomposition process of metal hydrides when TiF4 is used as catalyst. Noticeably, the aniosotropic charge distribution can give


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rise to preferential growth directions of TiF4 thin films and nano-phases with suitable active sites for catalysis. Though these results are pertinent at the atomic scale, they constitute the first step towards a full understanding on mechanical behavior of o-TiF4, r-TiF3, c-TiF3, and c-TiF2 which can open up new possibilities for utilizing TiF4 in many applications. APPENDIX-I Calculation of Elastic Constants The elastic constants determine the mechanical response of the crystal to external forces, as characterized by Young's modulus, shear modulus, bulk modulus, and Poisson's ratio, which determine the strength of the materials.28 VASP employs stress- strain approach, which is a finite difference method for calculating the above mentioned elastic parameters. Usually materials follow generalized Hook's law at small strain i.e. within elastic limit given by; σi = Cij εi

(1)

where, σi is second rank stress tensor, Cij is fourth rank elastic tensor constant/stiffness constant (elastic coefficient of the material), and εi is second rank strain tensor. Using the matrix notation we can rewrite the above equation for elasticity as:

[] ( 𝜎1 𝜎2 𝜎3 𝜎4 𝜎5 𝜎6

=

𝐶11 𝐶21 𝐶31 𝐶41 𝐶51 𝐶61

𝐶12 𝐶22 𝐶32 𝐶42 𝐶52 𝐶62

𝐶13 𝐶23 𝐶33 𝐶43 𝐶53 𝐶63

𝐶14 𝐶24 𝐶34 𝐶44 𝐶54 𝐶64

𝐶15 𝐶25 𝐶35 𝐶45 𝐶55 𝐶65

)[]

𝐶16 𝐶26 𝐶36 𝐶46 𝐶56 𝐶66

𝜖1 𝜖2 𝜖3 𝜖4 𝜖5 𝜖6

This methodology is straightforward i.e. assumes that stress is directly proportional to the applied strain. In matrix format, the stress and strain relation shows the 36 stiffness coefficients as 6 × 6 symmetric matrix. The elasticity tensor inherits symmetries of the crystal and has some intrinsic degrees of independence of its own. Higher the degree of symmetry, lesser the number of independent elastic constants and vice versa.29 If neither symmetry nor symmetry-axis is present in a crystal, maximum of 21 independent elastic moduli will result as in the case of triclinic crystals.30 More precise DFT parameters ACS Paragon Plus Environment


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were set in order to obtain the accurate elastic constants. Often the displaced configurations require a different k-point grid for the strained cells, depending on their symmetry. VASP allows to change the set of k-points automatically. The Brillouin zone integration was performed over different sets of k -points 6 ×12 × 8 k -points for orthorhombic TiF4, 6 × 6 × 4 mesh for trigonal TiF3, and 8 × 8 × 8 grid points for cubic TiF3 and TiF2 lattices. This lead to 90, 50 and 35 irreducible k -points for the unstrained system respectively. The following six linearly independent finite strains are applied irrespective of the symmetry,

(

)

𝑒1 0 0 0 0 0 0 𝑒2 0 0 0 0 0 0 𝑒3 0 0 0 0 0 0 𝑒4 0 0 0 0 0 0 𝑒5 0 0 0 0 0 0 𝑒6

𝑒1, 𝑒2, and 𝑒3 are normal strains and the rest are shear strains. We have used Voigt notation for singleindex representation as follows, 11 12 13 1 6 5 . 22 23 = . 2 4 . . 33 . . 3 It is possible to calculate single crystal elastic constants, while deforming the system. In general six cell parameters are adjustable in the triclinic system, based on which the number of degrees of freedom will be varying.30 The displacement of the lattice vector after deformation is given by,

(

)

𝜖6 𝜖5 1 + 𝜀1 2 2 𝜖6 𝜖4 R=𝑅 2 1 + 𝜀2 2 𝜖5 𝜖4 2 2 1 + 𝜀3

Two displacements are used for each ion along each direction, with the step size defaulted to 0.015 Å for low symmetry systems and 0.1 Å for high symmetry systems (i.e,. ei = ± 0.015, ± 0.03 ; ± 0.1, ± 0.2).30 For each strained states (e) the resulting stress is calculated and listed together with the stress matrix. Single strain is sufficient to extract the whole row of components, and different strain patterns are not required for various crystal symmetries as in the case of energy-strain approach.31 Once the stress is ACS Paragon Plus Environment

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calculated for each strain, the single-crystal elastic constants are retrieved by linear least-squares fitting of stress-strain data which is explained in detail elsewhere.30 Eventually, the component of the fit gives the element of the elastic tensor matrix. ACKNOWLEDGMENT:

The author R. Mariyal Jebasty is grateful to Centre for Research, Anna University, Chennai for offering Anna Centenary Research Fellowship (Lr. No. CFR/ACRF/2017/41) and thank Prof. P. Ravindran's research group for scientific discussions and hospitality at SCANMAT, Central University of Tamil Nadu. The authors are grateful to DST-SERB, India for the funding under sanction SB/FTP/PS-009/2014 availed for the computer facilities. SUPPORTING INFORMATION: The supplementary information is available. The bench marking calculations and supplementary Figures and Tables. REFERENCES (1) Pilvi, T.; Ritala, M.; Leskelå, M.; Bischoff, M.; Kaiser, U.; Kaiser, N. Atomic layer deposition process with TiF4 as a precursor for depositing metal fluoride thin films. Appl. Opt. 2008, 47(13), 271. DOI: 10.1364/AO.47.00C271. (2) Chang, C. M.; Chang, Y. C.; Chun, Y. A.; Lee, C. Y.; Chen, L. J. Synthesis and Properties of the Low Resistivity TiSi2 Nanowires Grown with TiF4 Precursor. J. Phys. Chem. C. 2009, 113, 17720. DOI: 10.1021/jp906039t. (3) Gordon, T. R.; Cargnello, M.; Paik, T.; Mangolini, F.; Weber, R. T.; Fornasiero, P.; Murray, C. B. Nonaqueus Synthesis of TiO2 Nanocrystals using TiF4 to engineer morphology, oxygen vacancy concentration, and photocatalytic activity. J. Am. Chem. Soc. 2012, 134, 6751. DOI: 10.1021/ja300823a. (4) Grzech, A.; Lafont, U.; Magusin, P. C.; Mulder, F. M. Microscopic Study of TiF3 as Hydrogen Storage Catalyst for MgH2. J. Phys. Chem. C, 2012, 116(49), 26027. DOI: 10.1021/jp307300h. ACS Paragon Plus Environment


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(5) Chen, R.; Zhigang, Z. F.; Chengshang, Z.; Lu, J.; Ren, Y.; Zhang, X.; Luo, X. In situ X‐ray diffraction study of dehydrogenation of MgH2 with Ti‐based additives. Int J Hydrogen Energy. 2014, 39, 5868. DOI: 10.1016/j.ijhydene.2014.01.152. (6) Jian, A.; Agarwal, S.; Kumar, S.; Yamaguchi, S.; Miyaoko, H.; Kojima, Y.; Ichikawa, T. How does TiF4 affect decomposition of MgH2 and its complex Variants? - An XPS investigation. J. Mater. Chem A. 2017, 5, 15543. DOI: 10.1039/C7TA03081A. (7) Hlova, I. Z.; Castle, A.; Jennifer, Goldston, F.; Gupta, S.; Prost, T.; Kobayashi, T.; Chumbley, L. S.; Pruskiab, M.; Pecharskyac, V. K. Solvent- and catalyst-free mechanochemical synthesis of alkali metal monohydrides. J. Mater. Chem. A. 2016, 4, 12188. DOI: 10.1039/C6TA04391G. (8) Jangir, M.; Jain, A.; Agarwal, S.; Zhang, T.; Kumar, S.; Selvaraj, S.; Ichikawa, T.; Jain, I. P. The enhanced de/re-hydrogenation performance of MgH2 with TiH2 additive. Int J Energy Res. 2018, 42, 1139. DOI: 10.1002/er.3911. (9) Swift, E. J; Heymann, H. O.; Roberson, T. Sturdevant's Art and Science of Operative Dentistry. 5th Ed, Mosby:USA, 2006. (10) Anusavice, K.; Shen, C.; Rawls, H. R. Phillips' Science of Dental Materials, 12th Ed, Saunders:China, 2012. (11) Wahengbam, P.; Tikku, A. P.; Lee, W. B. Role of Titanium Tetrafluoride (TiF4) in Conservative Dentistry: A systematic Review. J Conserv Dent. 2011, 14, 98. DOI: 10.4103/0972-0707.82598. (12) Basting, R. T.; Leme, A. A.; Bridi, E. C.; Amaral, F. L.; Franca, F. M.; Turssi, C. P. Nanomechanical properties, SEM, and EDS Microanalysis of Dentin Treated with 2.5 % Titanium Tetrafluoride, before and after an Erosive Challenge. J Biomed Mater B Appl Biomater. 2015, 103, 783. DOI: 10.1002/jbm.b.33254. (13) Hove, L.; Holme, B.; Ogaard, B.; Willumsen, T.; Tveit, A. B. The Protective Effect of TiF4, SnF2 and NaF on Erosion of Enamel by Hydrochloric Acid in vitro Measured by White Light Interferometry. Caries Res, 2006, 40, 440. DOI: 10.1159/000094291.


Page 29 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(14) Exterkate, R. A.; Ten Cate, J. M. Effects of a New Titanium Fluoride Derivative on Enamel De- and Remineralization. Eur J Oral Sci, 2007, 115, 143. DOI: 10.1111/j.1600-0722.2007.00431.x. (15) Wefel, J.S.; Harless, J. D. A Model for Producing Caries-like Lesions in Enamel and Dentin Using Oral Bacteria in vitro. J Dent Res, 1984, 63(11), 1276. DOI: 10.1177/00220345840630100201. (16) Medeiros, M. I. D. D.; Carlo, H. L.; Lacerda-Santos, R.; Bruno, Alessandro, Lima, G. D.; Sousa, F. B. D.; Rodrigues, J. A.; Carvalho, F. G. D. Thickness and nanomechanical properties of protective layer formed by TiF4 varnish on enamel after erosion. Braz. Oral Res. 2016, 30(1), e75. DOI: 10.1590/18073107BOR-2016.vol30.0075. (17) Shrestha, B. M; Mundorff, S. A.; Bibby, B. G. Enamel Dissolution: I. Effects of Various Agents and Titanium Tetrafluoride. J Dent Res, 1972, 51(6), 1561. DOI: 10.1177/00220345720510060901. (18) Mundorff, S.A.; Little, M. F.; Bibby, B. G. Enamel Dissolution: II. Action of Titanium Tetrafluoride. J Dent Res. 1972, 51(6), 1567. DOI: 10.1177/00220345720510061001. (19) Tranquilin, J. B.; Bridi, E. C.; Amaral, F. L. B.; França, F. M. G.; Turssi, C. P.; Basting, R. T. TiF4 improves microtensile bond strength to dentin when using an adhesive system regardless of primer/bond application timing and method. Clin Oral Investig, 2016, 20, 101. DOI: 10.1007/s00784-015-1496-2. (20) Büyükyilmaz, T.; Tangugsorn, V.; Øgaard, B.; Arends, J.; Ruben, J.; Rølla, G. The effect of titanium tetrafluoride (TiF4) application around orthodontic brackets. Am J Orthod Dentofacial Orthop. 1949, 103(1), 293. DOI: 10.1016/S0889-5406(94)70124-5. (21) Yu. H; Attin, T.; Wiegand, A.; Buchalla, W. Effects of Various Fluoride Solutions on Enamel Erosion in vitro. Caries Res, 2010, 44(4), 390. DOI: 10.1159/000316539. (22) Wiegand, A.; Hiestand, B.; Sener, B.; Magalhães, A. C.; Roos, M.; Attin, T. Effect of TiF4, ZrF4, HfF4 and AmF on erosion and erosion/abrasion of enamel and dentin in situ, Arch Oral Biol, 2010, 55(3), 223. DOI: 10.1016/j.archoralbio.2009.11.007. (23) Clarkson, B.; Wefel, J. Titanium and Fluoride Concentrations in Titanium Tetrafluoride and APF Treated Enamel. J Dent Res, 1979, 58, 600, 2. DOI: 10.1177/00220345790580021001.



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(24) Alexandria, A. K.; Nassur, C.; Nóbrega, C. B. C.; Branco-de-Almeida, L. S.; dos Santos, K. R. N.; Vieira, A. R.; Neves, A. M.; Rosalen, P. L.; Valença, A. M. G.; Maia, L. C. Effect of TiF4 varnish on microbiological changes and caries prevention: in situ and in vivo models, Clin Oral Invest, 2018, 1-9. DOI: 10.1007/s00784-018-2681-x. (25) Kresse, G.; Hafner, J. Ab-initio molecular dynamics for liquid metals. Phys. Rev. B. 1993, 47, 558; Ibid. 1994, 49(14), 251. DOI: 10.1103/PhysRevB.47.558. (26) Kresse G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B. 1999, 59, 1758. DOI: 10.1103/PhysRevB.59.1758. (27) Perdew, J. P.; Burke, .K; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett, 1996, 77, 3865. DOI: 10.1103/PhysRevLett.77.3865. (28) Ravindran, P.; Fast, L.; Korzhavyi, P. A.; Johansson, B. Density Functional Theory for Calculation of Elastic Properties of Orthorhombic Crystals: Application to TiSi2. J. Appl. Physics, 1998, 84, 9. DOI: 10.1063/1.368733. (29) Nye, J. F. Physical Properties of Crystals: Their Representation by Tensors and Matrices, Clarendon Press:Oxford, 1985. (30) Le Page, Y.; Saxe, P. W. Symmetry-general least-squares extraction of elastic data for strained materials from ab initio calculations of stress. Phys. Rev. B. 2002, 65, 10410. DOI: 10.1103/PhysRevB.65.104104. (31) Le Page, Y.; Saxe, P. W. Symmetry-general least-squares extraction of elastic coefficients from ab initio total energy calculations. Phys. Rev. B, 2001, 63, 174103. DOI; 10.1103/PhysRevB.63.174103. (32) Mouhat, F.; Coudert, F. X. Necessary and Sufficient Elastic Stability Conditions in Various Crystal Systems. Phys. Rev. B, 2014, 90, 224104. DOI: 10.1103/PhysRevB.90.224104 (33) Ghosh, G. A first-principles study of cementite Fe3C and its alloyed counterparts: Elastic constants, elastic anisotropies, and isotropic elastic moduli. AIP Advances, 2015, 5, 087102. DOI: 10.1063/1.4928208.


Page 31 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(34) Gaillac, R.; Pullumb, P.; Coudert, F. X. ELATE: an open-source online application for analysis and visualization of elastic tensors, J. Phys. Condens. Matter. 2016, 28, 27; http://progs.coudert.name/elate. DOI: 10.1088/0953-8984/28/27/275201. (35) Evans, J. D.; Coudert, F. X. Predicting the Mechanical Properties of Zeolite Frameworks by Machine Learning. Chem. Mater. 2017, 29, 7833. DOI; 10.1021/acs.chemmater.7b02532. (36) Huanga, B.; Duan, Y. H.; Hu, W. C.; Sun, Y.; Chen, S. Structural, anisotropic elastic and thermal properties of MB (M=Ti, Zr and Hf) monoborides. Ceram. Int. 2015, 41, 6831. DOI: 10.1016/j.ceramint.2015.01.132. (37) Bialowons, H.; Müller, M.; Müller, B. G. Titantetrafluorid - Eine uberraschend einfache Kolumnarstruktur. Z. Anorg. Allg. Chem. 1995, 621, 1227. (38) Ehrlich, P.; Pietzka, G. Titanium Trifluoride. Z. Anorg. Allg. Chem. 1954, 275, 121e140. (39) Morita, N.; Endo, T.; Sato, T.; Shimada, M. TiF2 with fluorite structure-a new compound. J Mater Sci Lett, 1987, 6, 859. DOI: 10.1007/BF01729038. (40) Jain, A.; Ong, S.P.; Hautier, G.; Chen, W.; Richards, W.D.; Dacek, S.; Cholia, S.; Gunter, D.; Skinner, D.; Ceder, G.; Persson, K.A. Commentary: The Materials Project: A materials Genome Approach to Accelerating Materials Innovation. APL Materials. 2013, 1, 011002. DOI: 10.1063/1.4812323. (41) Nakamura, M. Elastic Constants of Some Transition-Metal-Disilicide Single Crystals. Metall Mater Trans A. 1994, 25A, 331; DOI; 10.1007/BF02647978. (42) Jia, J.; Liang, Y.; Tsuji, T.; Murata, S.; Matsuoka, T. Elasticity and Stability of Clathrate Hydrate: Role of Guest Molecule Motions. Scientific Reports. 2017, 7, 1290. DOI: 10.1038/s41598-017-01369-0. (43) Ravindran, P.; Vajeeston, P.; Vidya, R.; Kjekshus, A.; Fjellvåg, H. Detailed electronic structure studies on superconducting MgB2 and related compounds. Phys. Rev. B. 2001, 64(22), 224509. DOI: 10.1103/PhysRevB.64.224509. (44) De, Jong, M.; Chen W.; Angsten, T.; Jain, A.; Notestine, R.; Gamst, A.; Sluiter, M.; Ande, C. K.; Van der, Z. S.; Plata, J. J.; Toher, C.; Curtarolo, S.; Ceder, G.; Persson K. A.; Asta, M. Charting the ACS Paragon Plus Environment


Page 32 of 33

Complete Elastic Properties of Inorganic Crystalline Compounds. Scientific Data, 2015, 2, 150009. DOI: 10.1016/j.commatsci.2013.09.010. (45) Peskersoy, C.; Culha, O. Comparative Evaluation of Mechanical Properties of Dental Nanomaterials. J. Nanomater. 2017, 1, 6171578. DOI: 10.1155/2017/6171578. (46) Zhang, Y. R.; Du, W.; Zhou, X. D.; Yu, H. Y. Review of Research on the Mechanical Properties of the Human Tooth. Int J Dent Oral Sci. 2014, 6, 61. DOI: 10.1038/ijos.2014.21. (47) Friàk, M.; Counts, W. A.; Ma; D.; Sander, B.; Holec, D.; Raabe, D.; Neugebauer, J. Theory-Guided Materials Design of Multi-Phase Ti-Nb Alloys with Bone-Matching Elastic Properties. Materials, 2012, 5, 1853. DOI: 10.3390/ma5101853. (48) Wang, K. The use of titanium for medical applications in the USA, Materials Science and Engineering: A, 1996, 213, 134-137. DOI: 10.1016/0921-5093(96)10243-4. (49) Niinomi, M. Mechanical properties of biomedical titanium alloys, Materials Science and Engineering: A, 1998, 243, 231-236. DOI: 10.1016/S0921-5093(97)00806-X. (50) Long, M.; Rack, H. J. Titanium alloys in total joint replacement — a materials science perspective, Biomaterials, 1998, 18, 1621-1639. DOI: 10.1016/S0142-9612(97)00146-4. (51) Duminis, T.; Shahid, S.; Karpukhina, N. G.; Hill, R.G. Predicting Refractive Index of Fluoride Containing Glasses for Aesthetic Dental Restorations. Dent Mater, 2018, 34, e83. DOI: 10.1016/j.dental.2018.01.024. (52) Jibran, M.; Murtaza, G.; Khan, M. A.; Khenata, R.; Muhmmada , S.; Ali, R. First principle study of MF2 (M = Mg, Ca, Sr, Ba, Ra) compounds. Comput. Mater. Sci. 2014, 81, 575. DOI: 10.1016/j.commatsci.2013.09.010. (53) Pivak, Y.; Schreuders, H.; Dam, B. Thermodynamic Properties, Hysteresis Behavior and StressStrain Analysis of MgH2 Thin Films, Studied over a Wide Temperature Range. Crystals. 2012, 2, 710. DOI: 10.3390/cryst2020710.


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Mechanical Properties of Multi-Functional TiF4 from First-Principle Calculations. Rethinaraj Mariyal Jebasty and Ravindran Vidya Table of Contents (TOC) Graphic


Mechanical Properties of Multifunctional TiF4 from First-Principles

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