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<p>Continuum atomistic and mesoscopic models are developed and utilized in the context of studying microstructural evolution and phase selection in materials systems. Numerous phenomena are examined, ranging from defect-solute interaction in solid state systems to microstructural evolution under external driving conditions. Emphasis is placed on the derivation and development of models capable of self consistently describing the intricate mechanisms at work in the systems undergoing these phenomena.</p> <p>Namely, grain growth dynamics are studied in nanocrystalline systems under external driving conditions using a newly developed phase-field-crystal model, which couples an additional free energy source term to the standard phase-field-crystal model. Such external driving can be attributed to incident energetic particles. The nanocrystalline system is found to be susceptible to enhanced grain growth as a function of the intensity/flux associated with the external driving and the energy of driving. Static kinetic phase diagram calculations also seem to confirm that systems under external driving conditions can be forced into long metastable states.</p> <p>Early stage solute clustering and precipitation in Al alloys is also examined with a variant of the phase-field-crystal method, so-called structural phase-field-crystal models for multi-component alloys developed as part of this thesis. We find that clustering is aided by quenched-in defects (dislocations), whereby the nucleation barrier is reduced and at times eliminated, a mechanism proposed by Cahn for a single dislocation for spinodal systems. In a three-component system, we predict a multi-step mechanism for clustering, where the nature and amount of the third species plays an important role in relieving stresses caused by the quenched-in dislocations before clustering, i.e., segregation as predicted by the equilibrium phase diagram, can occur.</p> <p>Finally, we present a new coarse-graining procedure for generating complex amplitude models, i.e., complex order-parameter phase-field models, derived from phase-field-crystal models. They retain many salient atomistic features and behaviours of the original phase-field-crystal model, however is now capable of describing mesoscopic length scales like the phase-field model. We demonstrate the scheme by generating an amplitude model of the two-dimensional structural phase-fieldcrystal model, which allows multiple crystal structures to be stable in equilibrium, a crucial aspect of proper multi-scale modelling of materials systems. The dynamics are demonstrated by examining solidification and coarsening, peritectic growth, along with grain growth and the emergence of secondary phases.</p> / Doctor of Science (PhD)

Dans cette thèse, nous présentons des études théoriques de matériaux pérovskites sous con-trainte mécanique uniaxiale en combinant les calculs de premier principe DFT ainsi quela théorie phénoménologique de type Landau. Les pérovskites ABO3 forment une classetrès importante de matériaux fonctionnels, qui peuvent présenter un large éventail de pro-priétés (e.g., supraconductivité, magnétisme, ferroélectricité, multiferroïcité, transitionsmétal-isolant. . . ) grâce aux petites distorsions d’ une même structure prototype cubique.Bien que ces composés aient été largement étudiés expérimentalement et théoriquement, ilreste encore des questions importantes et non résolues concernant les effets de contraintesuniaxiales. Au cours de ces dernières années, l’ ingénierie de contrainte a été décrite commeune approche originale pour ajuster les propriétés ferroélectriques pérovskites ABO3. Alorsque les effets de tension épitaxié-biaxiale et pression la hydrostatique, sont plutôt bien com-pris dans cette classe de matériaux, très peu est connu en ce qui concerne l’ effet des con-traintes mécaniques uniaxiales. Notre étude est motivée par ce manque de compréhensionactuelle de l’ effet de tension et compression uniaxiale, qui a été jusqu’à présent presquetotalement négligé. Deux composés prototypes sont étudiés dans le détail: PbTiO3 etSrTiO3. Après une introduction générale sur les composés ABO3 et les calculs techniques(ab initio et modèle phénoménologique de Landau), nous avons étudié l’ effet de contraintesmécaniques sur ces matériaux dans notre thèse.PbTiO3 est un composé ferroélectrique prototypique et également l’ un des composantsmère de la solution solide Pb(Zr,Ti)O3 (PZT), qui est le piézoélectrique le plus largementutilisé dans des applications. Pour PbTiO3, nous avons montré que indépendammentde la contrainte mécanique uniaxiale appliquée, le système conserve un état fondamentalpurement ferroélectrique avec la polarisation alignée, soit le long de la direction de lacontrainte (en phase FEz) ou bien le long d’ un des axes pseudo-cubique, qui lui estperpendiculaire (phase de FEx). Cela contraste avec les cas de contraintes mécaniquesisotropes ou bi-axial, pour qui de nouvelles phases combinant des modes ferroélectriqueset antiferrodistortives ont déjà été décrites. Sous contrainte uniaxiale, PbTiO3 passe d’unétat fondamental FEx sous compression à un état fondamental FEz en tension au-delà d’une tension critique !czz! +1%. Sous contrainte uniaxiale, PbTiO3 présente soit un étatfondamental FEx sous compression ("zz < 0) ou un état fondamental de FEz sous tension("zz > 0). Cependant, ici, un brusque saut des paramètres structuraux est prévu sousdes contraintes de compression et de traction à des valeurs critiques "zz! +2 GPa et −8GPa. Ce comportement semble similaire à celui pré-prédit sous pression isotrope négativeet pourrait se révéler utile en pratique pour améliorer la réponse piézoélectrique dans lesnano-composants.Le deuxième composé intéressant est SrTiO3. Il a été largement étudié au cours desdernières décennies, en raison de ses propriétés exceptionnelles à basse température. Dansce travail, nous avons élargi nos précédentes études de PbTiO3, en explorant théorique-ment les effets de pression sur la perovskite SrTiO3, combinant les premiers principes decalculs et un modèle phénoménologique de type Landau. Nous avons discuté de l’évolutiondes fréquences des phonons de SrTiO3 des trois cas de contraintes isotrope, uniaxial ettensions biaxiaux en utilisant les calculs de premier principe. Nous confirmons des travauxexpérimentaux précédents sur SrTiO3 que ça soit en contrainte épitaxiée ou sous pressionhydrostatique. Enfin, nous avons calculé de diagramme de phase de SrTiO3 sous contrainteuniaxiale, obtenue à partir de la théorie de Landau que nous avons comparé aux calculsde premier principe. / In the present thesis we present theoretical studies of perovskite compounds under uniax-ial mechanical constraints combining first-principles DFT calculations approach and phe-nomenological Landau theory. ABO3 perovskites form a very important class of functionalmaterials that can exhibit a broad range of properties (e.g., superconductivity, magnetism,ferroelectricity, multiferroism, metal-insulator transitions. . . ) within small distortions ofthe same simple prototype cubic structure. Though these compounds have been exten-sively studied both experimentally and computationally, there are still unresolved issuesregarding the effect of pressure. In recent years, strain engineering has reported to bean original approach to tune the ferroelectric properties of perovskite ABO3 compounds.While the effect of epitaxial biaxial strain and hydrostatic strain is rather well understoodin this class of materials, very little is yet known regarding the effect of uniaxial mechanicalconstraints. Our study is motivated by the little existing understanding of the effect ofuniaxial strain and stress, that has been up to now almost totally neglected. Two proto-type compounds are studied in detail: PbTiO3 and SrTiO3. After a general introductionon ABO3 compounds and calculations techniques (ab initio and phenomenological Landaumodel), we studied the effect of mechanical constraints in these compounds in our thesis.PbTiO3 is a prototypical ferroelectric compound and also one of the parent components ofthe Pb(Zr,Ti)O3 solid solution (PZT), which is the most widely used piezoelectrics. ForPbTiO3, we have shown that irrespectively of the uniaxial mechanical constraint applied,the system keeps a purely ferroelectric ground-state, with the polarization aligned eitheralong the constraint direction (FEz phase) or along one of the pseudocubic axis perpen-dicular to it (FEx phase). This contrasts with the case of isotropic or biaxial mechanicalconstraints for which novel phases combining ferroelectric and antiferrodistortive motionshave been previously reported. Under uniaxial strain, PbTiO3 switches from a FEx groundstate under compressive strain to FEz ground-state under tensile strain, beyond a critical strain !czz! +1%. Under uniaxial stress, PbTiO3 exhibits either a FEx ground state undercompression ("zz < 0) or a FEz ground state under tension ("zz > 0). Here, however, anabrupt jump of the structural parameters is also predicted under both compressive andtensile stresses at critical values "zz! +2 GPa and −8 GPa. This behavior appears similarto that predicted under negative isotropic pressure and might reveal practically useful toenhance the piezoelectric response in nanodevices.The second compound of interest is SrTiO3. It has been widely studied in the past decadesdue to its unusual properties at low temperature. In this work, we have extended ourprevious investigations on PbTiO3 by exploring theoretically the pressure effects on per-ovskite SrTiO3 combining the first-principles calculations and a phenomenological Landaumodel. We have discussed the evolution of phonon frequencies of SrTiO3 with the threeisotropic, uniaxial and biaxial strains using first-principles calculations. We also reproducethe previous work done in SrTiO3 with epitaxial strain and hydrostatic strain. Finally,we have calculated the phase diagram of SrTiO3 under uniaxial strain, as obtained fromLandau theory and discussed how it compares with the first-principles calculations.

The thesis entitled “In situ crystallography and charge density analysis of phase transitions in complex inorganic sulfates” consists of six chapters. Structural changes exhibited by ferroic and conducting materials are studied as a function of temperature via in situ crystallography on the same single crystal. These unique experiments bring out the changes in the crystal system resulting in subtle changes in the complex polyhedra, distortions in bond lengths and bond angles, rotation of sulfate tetrahedral around metal atoms, phase separations and charge density features. The results provide new insights into the structural changes during the phase transition in terms of coordination changes, variable bond paths and variability in electrostatic potentials while suggesting possible reaction pathways hitherto unexplored. Chapter 1 gives a brief review of the basic features of structural phase transitions in terms of types of phase transitions, their mechanisms and related properties and outlines some of the key characterization techniques employed in structural phase transition studies like single crystal diffraction, thermal analysis, conductivity, dielectric relaxation, Raman spectroscopy and charge density studies. Chapter 2 deals with the group of compounds A3H(SO4)2, where A= Rb, NH4, K, Na which undergoes ferroelastic to paraelastic phase transitions with increase in temperature. Crystal structures of these compounds have been determined to a high degree of accuracy employing the same single crystal at room temperature at 100K and at higher temperatures. The data collection at 100K allows the examination of the ordered and disordered hydrogen atom positions. Rb3H(SO4)2 show two intermediate phases before reaching the paraelastic phase with increase in temperature. However, in case of (NH4)3H(SO4)2 and K3H(SO4)2, the paraelastic phase transition involves a single step. Chapter 3 deals with variable temperature in situ single crystal X-ray diffraction studies on fast super protonic conductors AHSO4, where A= Rb, NH4, K to characterize the structural phase transitions as well as the dehydration mechanism. The structure of KHSO4 at room temperature belongs to an orthorhombic crystal system with the space group symmetry Pbca and on heating to 463K it transforms to a C centered orthorhombic lattice, space group Cmca. The high temperature structure contain two crystallographically independent units of KHSO4 of which one KHSO4 unit is disordered at oxygen and hydrogen sites an shows a remarkable increase of sulfur oxygen bond distance – 1.753(4)Å. On heating to 475K, two units of disordered KHSO4 combine and loose one molecule of water to result in a structure K2S2O7 along with an ordered KHSO4 in a monoclinic system [space group P21/c]. On further heating to 485K two units of ordered KHSO4 combine, again to lose one water molecule to give K2S2O7 in a monoclinic crystal system [space group C2/c]. In the case of RbHSO4, both the high temperature structural phase transition and a serendipitous polymorph have been characterized by single crystal X-ray diffraction. The room temperature structure is monoclinic, P21/n, and on heating the crystal insitu On the diffractometer to 460K the structure changes to an orthorhombic system [space group Pmmn]. On keeping the crystallization temperature at 80°C polymorph crystals of RbHSO4 were grown. In case of NH4HSO4 both the room temperature and high temperature structures are structurally similar to those in RbHSO4, but the transition temperature is found to be 413K. Chapter 4 deals with the crystal structure, ionic conduction, dielectric relaxation, Raman spectroscopy phase transition pf a fast ion conductor Na2Cd(SO4)2. The structure is monoclinic, space group C2/c, and is built up with inter connecting CdO6 octahedra and SO4 tetrahedra resulting in a framework structure. The mobile Na atoms are present in the framework, resulting in a high ionic conductivity. The conductivity measurement shows two phase transitions one at around 280°C, which was confirmed later from DTA, dielectric relaxation, high temperature powder diffraction and Raman spectroscopy. Chapter 5 describes the structure and in situ phase separation in two different bimetallic sulfates Na2Mn1.167(SO4)2S0.33O1.1672H2O and K4Cd3(SO4)5.3H2O. These compounds were synthesized keeping them as mimics of mineral structures. The structure of Na2Mn1.167(SO4)2S0.33O1.1672H2O is trigonal, space group R . The stiochiometry can be viewed as a combination of Na2Mn(SO4)22H2O resembling the mineral Krohnkite with an additional (Mn0.167S0.333O1.167) motif. On heating the parent compound on the diffractometer to 500K and keeping the capillary at this temperature for one hour, a remarkable structural phase separation occurs with one phase showing a single crystal-single crystal transition and the other generating a polycrystalline phase. The resulting single crystal spots can be indexed in a monoclinic C2/c space group and the structure determination unequivocally suggests the formation of Na2Mn(SO4)2, isostructural to Na2Cd(SO4)z. The mechanism follows the symmetry directed pathway from the rhombohedral → monoclinic symmetry with the removal of symmetry subsequent to the loss of the two coordinated water molecules. In case of K4Cd3(SO4)5.3H2O the structure belongs to the space group P21/n at room temperature and on heating to 500K and holding the capillary at this temperature for 60 minutes as before, the CCD images can be indexed in a cubic P213 space group after the phase separation, generating K2Cd2(SO4)3, belonging to the well known Langbeinite family, while the other phase is expected to be the sought after K2Cd(SO4)2. The possible pathways have been discussed. Chapter 6 reports the charge density studies of phase transitions in a type II langbeinite, Rb2Mn2(SO4)3. The structure displays two different phases, cubic at 200K, orthorhombic at 100K respectively. After multiple refinements it is found that there are significant differences in the actual bond path (Rij) and the conventional bond length. In the cubic phase the distortions in sulfate tetrahedral are more than in the orthorhombic phase which could be the expected driving force for the phase transition to occur. Appendix contains reprints of the work done on the structures of the following: a) Rb2Cd3(SO4)3(OH)2.2H2O: structural stability at 500 K b) Structure of (NH4)2Cd3(SO4)4.5H2O c) Structure of Rb2Cd3(SO4)4.5H2O

Elastic properties of carbon nanotubes (CNT), boron nitride nanotubes (BNNT), double stranded DNA (dsDNA), paranemic-juxtapose crossover (PX-JX) DNA and dendrimer bound DNA are discussed in this thesis. Structural phase transitions of nucleic acids induced by external force, carbon nanotubes and graphene substrate are also studied extensively. Electrostatic interactions have a strong effect on the elastic properties of BNNTs due to large partial atomic charges on boron and nitrogen atoms. We have computed Young’s modulus (Y ) and shear modulus (G) of BNNT and CNT as a function of the nanotube radius and partial atomic charges on boron and nitrogen atoms using molecular mechanics calculation. Our calculation shows that Young’s modulus of BNNTs increases with increase in magnitude of the partial atomic charges on B and N atoms and can be larger than the Young’s modulus of CNTs of same radius. Shear modulus, on the other hand depends weakly on the magnitude of partial atomic charges and is always less than the shear modulus of the CNT. The values obtained for Young’s modulus and shear modulus are in excellent agreement with the available experimental results. We also study the elasticity of dsDNA using equilibrium fluctuation methods as well as nonequilibrium stretching simulations. The results obtained from both methods quantitatively agree with each other. The end-to-end length distribution P(ρ) and angle distribution P(θ) of the dsDNA has a Gaussian form which gives stretch modulus (γ1) to be 708 pN and persistence length (Lp) to be 42 nm, respectively. When dsDNA is stretched along its helix axis, it undergoes a large conformational change and elongates about 1.7 times its initial contour length at a critical force. Applying a force perpendicular to the DNA helix axis, dsDNA gets unzipped and separated into two single-stranded DNA (ssDNA). DNA unzipping is a fundamental process in DNA replication. As the force at one end of the DNA is increased the DNA starts melting above a critical force depending on the pulling direction. The critical force fm , at which dsDNA melts completely decreases as the temperature of the system is increased. The melting force in the case of unzipping is smaller compared to the melting force when the dsDNA is pulled along the helical axis. In the case of melting through unzipping, the double-strand separation has jumps which correspond to the different energy minima arising due to sequence of different base-pairs. Similar force-extension curve has also been observed when crossover DNA molecules are stretched along the helix axis. In the presence of mono-valent Na+ counterions, we find that the stretch modulus (γ1 ) of the paranemic crossover (PX) and its topoisomer juxtapose (JX) DNA structure is significantly higher (30 %) compared to normal B-DNA of the same sequence and length. When the DNA motif is surrounded by a solvent of divalent Mg2+ counterions, we find an enhanced rigidity compared to in Na+ environment due to the electrostatic screening effects arising from the divalent nature of Mg2+ counterions. This is the first direct determination of the mechanical strength of these crossover motifs which can be useful for the design of suitable DNA motifs for DNA based nanostructures and nanomechanical devices with improved structural rigidity. Negatively charged DNA can be compacted by positively charged dendrimer and the degree of compaction is a delicate balance between the strength of the electrostatic interaction and the elasticity of DNA. When the dsDNA is compacted by dendrimer, the stretch modulus, γ1 and persistence length, Lp decreases dramatically due to backbone charge neutralization of dsDNA by dendrimer. We also study the effect of CNT and graphene substrate on the elastic as well as adsorption properties of small interfering RNA (siRNA) and dsDNA. Our results show that siRNA strongly binds to CNT and graphene surface via unzipping its base-pairs and the propensity of unzipping increases with the increase in the diameter of the CNTs and is maximum on graphene. The unzipping and subsequent wrapping events are initiated and driven by van der Waals interactions between the aromatic rings of siRNA nucleobases and the CNT/graphene surface. However, dsDNA of the same sequence undergoes much less unzipping and wrapping on the CNT/graphene due to smaller interaction energy of thymidine of dsDNA with the CNT/graphene compared to that of uridine of siRNA. Unzipping probability distributions fitted to single exponential function give unzipping time (τ) of the order of few nanoseconds which decrease exponentially with temperature. From the temperature variation of unzipping time we estimate the free energy barrier to unzipping. We have also investigated the binding of siRNA to CNT by translocating siRNA inside CNT and find that siRNA spontaneously translocates inside CNT of various diameters and chiralities. Free en- ergy profiles show that siRNA gains free energy while translocating inside CNT and the barrier for siRNA exit from CNT ranges from 40 to 110 kcal/mol depending on CNT chirality and salt concentration. The translocation time τ decreases with the increase of CNT diameter having a critical diameter of 24 A for the translocation. After the optimal binding of siRNA to CNT/graphene, the complex is very stable which can serve as siRNA delivery agent for biomedical applications. Since siRNA has to undergo unwinding process in the presence of RNA-induced silencing complex, our proposed delivery mechanism by single wall CNT possesses potential advantages in achieving RNA interference (RNAi).