<p>In this work we have investigated the intercalation of electron-donors between NbS₂ slabs in Nb-based layer sulfides.</p><p>Two series of Sr substituted Nb-based misfit sulfides belonging to the 1.5Q/1H and 1Q/1H series of misfit layer compounds have been synthesised. For large lanthanides (Ln=La, Ce), only the 1Q/1H compounds formed whereas for smaller lanthanides and yttrium, both types of phases can be obtained. The crystal structure of misfit sulfide (Pr_0.55Sr_0.45S)_1.15NbS₂ has been refined using the composite approach. In the Q-slab, Pr-atoms are partly replaced by Sr with a random distribution over one cation position. The crystal structure of misfit sulfide [(Sm_1/3Sr_2/3S)_1.5]_1.15NbS₂ belonging to the 1.5Q/1H series have also been determined. The obtained results suggest a preferred occupancy of the cation positions in the slab where Sr atoms mainly occupy positions on the exterior of the slab while Sm atoms are in the center of the slab. The (La_1-xSr_xS)_1.15NbS₂ solid solution (0.1<x<0.9) has also been studied. It was found that the maximum value of Sr substitution is 40-50% and therefore, the minimal value of charge transfer to stabilize this structure type is about 0.6ē per Nb atom. </p><p>An attempt to synthesize Sr_xNbS₂ (0.1≤x≤0.5) intercalates was made but single phases were not obtained and increasing the temperature from 1000^оС to 1100^оС leads to the decomposition of these intercalates. Single crystals of Sr_0.22Nb_1.05S₂ and Sr_0.23NbS₂ were found and their structures were determined. The structures belong to two different types of packings with statistical distribution of Sr between layers.</p><p>A new superconducting sulfide, "EuNb₂S₅", was investigated by ED and HREM and its structure model consisting of Nb₇S₁₄ and (Eu₃S₄)₂ slabs alternating along the c-axis is suggested. An attempt to suggest a model for the structure of "SrNb₂S₅" by means of X-ray single crystal diffraction was made. The proposed structure consists of two types of slabs: a Nb₇S₁₄ and a [Sr₆(NbS₄)₂S] slab with niobium in tetrahedral coordination. It is shown that "SrNb₂S₅" and "EuNb₂S₅" are have similar structures.</p><p>For the first time, single crystals of the complex sulfide BaNb_0.9S₃ have also been studied by means of X-ray single crystal diffraction. The single crystal refinement and EDX analysis showed the existence of cation vacancies at the niobium position. BaNb_0.9S₃ has also been studied by ED and no superstructure was found which implies that and the vacancies are statistically distributed.</p><p>No improvement of the magnetic properties of the studied compounds was observed in comparison to NbS₂.</p>

Atualmente, os implantes são utilizados em diversos tipos de tratamento na reabilitação oral. Para manutenção da osseointegração, é essencial que o conjunto prótese/implante/osso seja submetido a forças às quais estejam aptos a suportar. Os diferentes tipos de desadaptações das infraestruturas das próteses sobre implantes são fatores que podem contribuir para o aumento das tensões na região peri-implantar. Este estudo teve como objetivo avaliar a influência das desadaptações angulares unilaterais na distribuição de tensões na região periimplantar de pilares tipo UCLA, no momento da pré-carga e carga axial. Infraestruturas de CoCr, confeccionadas utilizando-se pilares tipo UCLA, foram divididas em quatro grupos: Grupo A (adaptado), Grupo B, Grupo C e Grupo D (50, 100 e 200 &#x3BC;m de desadaptação unilateral angular por vestibular, respectivamente). Cada grupo foi representado por quatro infraestruturas (n=4). Quatro implantes (4.1mm/15mm) foram posicionados em uma matriz metálica, onde posteriormente foi vazado o poliuretano (PU), com função de simular o tecido ósseo. Quatro extensômetros (strain gauges) foram posicionados na região vestibular, distal, lingual e mesial de cada implante, para aferir a quantidade de deformação; cada grupo foi posicionado em seu respectivo implante. Foram realizados dois testes: o teste de pré-carga com um torque de 32Ncm e o teste de carga com uma força axial estática de 300N. Cada infraestrutura foi sujeita aos dois testes, por cinco vezes. Para análise estatística dos dados, foram utilizados ANOVA (dois critérios) e o teste de Tukey (p<0,05). Os resultados mostraram que os grupos A e B tiveram menos deformação da região peri-implantar em ambos os testes, quando comparados aos grupos C e D. A estatística também mostrou que o Grupo A apresentou melhor distribuição de tensões em sua região, peri-implantar quando comparado aos outros três grupos (p<0,05). Como conclusões, este estudo mostrou que as desadaptações influem na distribuição das tensões da região peri-implantar e que quanto maior o nível de desadaptação, mais altas são as tensões geradas. / Nowadays implants are used in several kinds of oral rehabilitation treatments. For the osseointegration maintenance it is important that crow/implant/bone are subjected to forces which are able to withstand. Different kinds of misfit on the crown frameworks are factors that could lead to an increase of strain around the implanted bone. This study aimed to evaluate the influence of the unilateral angular misfit in frameworks made of UCLA on the peri-implant strain distribution, subjected to preload and axial load. Frameworks made of chrome-cobalt were fabricated on UCLA abutments and divided in 4 groups: Group A (no misfit), Group B, Group C, Group D (50, 100, and 200 of unilateral angular misfit by buccal side, respectively). Each group was represented for 4 frameworks (n=4). Four implants (4.1mm/15mm) were positioned in a metallic matrix which was subsequently poured the polyurethane (PU) to simulate the bone. Four strain gauges were positioned on the buccal, distal, lingual and mesial sides of each implant to assess the amount of strain, each group was connected on its respectively implant. It was performed 2 tests: the preload test with a 32Ncm torque and the load test by applying an axial force of 300N. Each framework was subjected to the both test five times. To the statistics analysis ANOVA (2 ways) and Turkeys test were performed. The results showed that the Groups A and B presented less deformation when compared to Groups C and D. The statistics also showed that the Group A presented better distribution of strain on its peri-implant bone when compared to the other three groups (p<0,05). In conclusion this study showed that misfit had influence on the strain distribution on the peri-implant bone and that strain increased on the Groups C and D which presented higher levels of misfit.

O desenvolvimento de novos sistemas cerâmicos propicia a possibilidade de escolha do tipo de restauração que se deseje utilizar. Entretanto, os benefícios advindos deste progresso devem ser avaliados frente à possibilidade de comportamento clínico insatisfatório. Este trabalho se propõe a avaliar infra-estruturas cerâmicas quanto à influência do ajuste interno na adaptação, o desajuste vertical após a simulação da cimentação, a espessura de película nas superfícies axiais e oclusal e a ocorrência de assentamento oblíquo. Um troquel-padrão metálico com preparo para coroa total em pré-molar superior foi confeccionado e trinta troquéis de gesso foram obtidos e dividos em três grupos de dez espécimes cada. Sobre os troquéis de gesso foram confeccionadas infra-estruturas metálicas para o grupo MC, infra-estruturas cerâmicas In-Ceram Zirconia, para o grupo IZ, e Procera AllZircon, para o grupo PZ. As infra-estruturas tiveram sua posição, em relação ao troquel-padrão, mensurada durante ajuste interno e simulação da cimentação com silicone de consistência fluida (cimento-análogo). A película de cimento-análogo abaixo das infra-estruturas foi seccionada no sentido vestíbulo-lingual e mensurada nas paredes axiais e oclusal. A análise dos resultados demonstrou que: 1) o ajuste interno das infra-estruturas metalo-cerâmicas e In-Ceram Zirconia resultou em redução do desajuste vertical; 2) o desajuste vertical das infra-estruturas Procera AllZircon foi estatisticamente diferente das infra-estruturas metalo-cerâmicas e In-Ceram Zirconia; 3) a espessura de película das infra-estruturas Procera AllZircon foi significantemente maior que das infra-estruturas metalo-cerâmicas e In-Ceram Zirconia; 4) todas as infra-estruturas apresentaram assentamento oblíquo. / The development of new ceramic systems creates the possibility of choice above the type of restoration one could mean to choose. Thus, benefits from this progress must be appraised on the possibility of unsatisfactory clinical behavior. This work intends to evaluate ceramic copings to the influence of internal adjustment on adaptation, vertical misfit after cementation, film thickness of axial and occlusal surfaces and occurrence of oblique seating. A metallic superior premolar analogue with full crown preparation was yield and thirty casts were obtained and divided into three groups of ten specimens each. Metal copings were yield for group MC and ceramics copings of In-Ceram Zirconia and Procera AllZircon were yield for group IZ and group PZ, respectively. The copings had their position, in relation to the metallic analogue, measured during adjustment and cementation with light body silicon. Cement film, below the copings, was sectioned and measured at the axial and occlusal surfaces. The analysis of the results demonstrated that: 1) internal adjustment of metal and In-Ceram Zirconia copings reduced the vertical misfit; 2) vertical misfit after cementation of Procera AllZircon copings was statistically different from metal and In-Ceram Zirconia copings; 3) film thickness of Procera AllZircon copings was significantly greater than metal and In-Ceram Zirconia copings; 4) all copings presented oblique seating.

The thermoelectric properties and microstructure of two families of misfit type layered structure cobaltites were investigated for thermoelectric applications. Firstly, Bismuth strontium cobaltite ceramics with the formulations Bi2+xSr2Co2Oy (x=0, 0.1 and 0.2), Bi1.74Sr2Co1.8Oy and Bi2Sr2Co1.8Oy were produced using solid-state reaction (MO) method. The same powders were also used to produce ceramics by Spark Plasma Sintering (SPS) fabrication technique. SEM, high resolution XRD and HRTEM techniques has been employed to characterise the microstructure and crystal structures of the ceramics. Figure of merit (ZT) was also determined from measurement of electrical resistivity, Seebeck coefficient and thermal conductivity. Together with the above, calcium cobaltite of formulation Ca3-xBixCo3O9 (x=0 and 0.3) was also produced via MO and SPS routes. The same characterisation techniques were used for characterisation of calcium cobaltite. For Bi2+xSr2Co2Oy ceramics, it was found that SPS fabrication is essential to obtain high density samples. Excess bismuth has a major role in the adjustment of the microstructure and thermoelectric properties. The room temperature microstructure contains two minor phases with compositions of CoO and Bi0.75Sr0.25O1.26. The crystal structure of the main phase was successfully indexed and refined as misfit type structure having monoclinic symmetry with I2/a space group. A high ZT of 0.12 was achieved in both x=0.1 and 0.2 MO samples. For Bi2Sr2Co1.8Oy ceramics, the microstructure contains only one minor phase, Bi0.75Sr0.25O1.26. A high ZT of 0.16 was obtained at 900 K for this composition. For Bi1.74Sr2Co1.8Oy, it was not possible to obtain high density ceramics by MO route and SPS fabrication was necessary. However, SPS sample showed a low ZT of 0.04 at 900 K.For ceramics of formulation Ca3-xBixCo3O9 (x=0 and 0.3), it was difficult to obtain high density calcium cobaltite ceramics by MO route and SPS fabrication was found to be essential. In addition to improved density, SPS produced textured microstructure. Similar to bismuth strontium cobaltite, excess bismuth played a major role in microstructure development and thermoelectric properties. Single phase and high density Ca3Co4O9 ceramics were obtained by SPS. A minor phase of Bi2Ca2Co2Oy was found in the microstructure of Ca3-xBixCo3O4 (x=0.3) samples. A high ZT of 0.25 was obtained for Ca3Co4O9 SPS samples at 900 K through improvement of power factor. In-situ synchrotron XRD in the temperature range of 300-1223 K was performed on both Bi2Sr2Co2Oy and Ca3Co4O9 to obtain their high temperature structural characteristics. The crystal structure of both compounds remains unchanged till 1223 K. For, Bi2Sr2Co2Oy the CoO and Bi0.75Sr0.25O1.26 minor phases disappear above 1073 K and a new minor phase containing (Bi-Sr-O) or (Bi-Co-O) starts forming. On heating, the lattice volume and coefficient of thermal expansion change linearly for both compounds. Thermal expansion coefficient was found to be 0.0000353-0.0000343 and 0.0000296-0.0000288 K-1 over the temperature range of 300-1223 K for Bi2Sr2Co2Oy and Ca3Co4O9 respectively.

A ausência do perfeito ajuste e o assentamento passivo dos pilares sobre implantes podem provocar tensões inadequadas na interface de osseointegração, possibilitando problemas mecânicos e biológicos. A fotoelasticidade é uma técnica experimental para análise de tensões capaz de produzir resultados confiáveis e fiéis aos parâmetros clínicos. Assim, este estudo teve como objetivos avaliar por meio de microscopia ótica a adaptação marginal entre pilares intermediários tipo mini pilar cônico e a estrutura metálica com desenho geométrico em viga I fundida com liga de cobalto-cromo (CoCr). Analisaram-se, também, por meio de fotoelasticidade, as tensões geradas ao redor dos implantes por essa mesma estrutura metálica quando submetida a cargas estáticas em função da variação do número de pilares (4 ou 5) e da inclinação dos implantes distais (para o modelo de 5 implantes). As análises foram feitas antes e após o seccionamento das barras e soldagem a laser. Foram obtidas dez infraestruturas em viga I, fundidas em monobloco, utilizando-se liga de cobalto cromo. A análise da adaptação marginal foi realizada em estereomicroscópio sob aumento de 20X. Modelos fotoelásticos para 4 ou 5 implantes foram confeccionados e realizada a mensuração da tensão ao redor dos implantes. As barras foram seccionadas e soldadas por laser e novas medidas de adaptação marginal foram realizadas, bem como foram confeccionados novos modelos fotoelásticos para as estruturas soldadas. A análise da passividade das vigas I em monobloco não se mostrou estatisticamente significante (p&le;0,05), a passividade no pilar oposto foi sempre menor que a do pilar parafusado antes e após a soldagem a laser, não houve diferença estatística no desajuste vertical entre as vigas I para quatro e cinco implantes, antes e após a soldagem a laser. A soldagem a laser gerou maior passividade e menor desajuste vertical nas vigas I. A análise fotoelástica mostrou que a soldagem a laser ocasionou menor tensão nos implantes quando não há aplicação de carga na viga I para quatro implantes, mas aumentou a tensão em viga I para cinco implantes. Assim, pode-se concluir que a soldagem a laser gerou maior passividade e menor desajuste vertical entre os pilares e o implante, e menor tensão ao redor dos implantes em vigas I de quatro implantes, e maior tensão em viga I para cinco implantes. / The absence of perfect fit and passivity on implants can cause stress on the osseointegration interface, enabling biomechanical problems. Photoelasticity is an experimental technique for stress analysis can produce reliable results and faithful to clinical parameters. Thus, the aim of this study was to assess by light microscopy the marginal adaptation of mini pillar intermediate and superstructure with geometric design I beam with cast cobalt-chromium (CoCr). It was analyzed also by means of photoelasticity, the tensions generated around the implants by the same metal superstructure when subjected to static loads due to the variation in the number of implants (4 or 5) and tilting the distal (for model 5 implants). Analyses were made before and after sectioning of the bars and laser welding. It was obtained ten I-beam superstructure I, cast in cobalt chromium alloy. The analysis of marginal adaptation was performed in a stereomicroscope under magnification 20X. Photoelastic models for 4 or 5 implants were made and carried out the measurement of the tension surrounding the implants. The bars were cut and welded by laser and marginal adaptation of new measures were taken and new photoelastic models were made for welded structures. The analysis of the passivity of the I-beams in a single block was not statistically significant (p&le;0.05), passivity on the pillar opposite was always less than the abutment screws before and after laser welding, there was no statistical difference in the vertical misfit between I-beams for four and five implants before and after laser welding. The laser welding has generated greater passivity and lower beams in vertical misfit I. The photoelastic analysis showed that laser welding caused less stress on the implants when there is no application of load over four implants, but increased the tension for five implants. Thus, it can be concluded that laser welding generated more passivity and less vertical fit between the pillars and the implant, and less tension around the implants in four implants, and higher stress for five implants.

Agency theory proposes that the role of the board of directors is to control management (Fama & Jensen 1983). A structurally independent board, one with a high percentage of non-executive directors and a chairperson who is not the CEO, has been used as a proxy for the control role. Therefore, agency theory predicts a positive relationship between independent board structure and firm performance. These predictions have not been confirmed by meta-analytic reviews (Dalton, Daily, Ellstrand, & Johnson 1998; Rhoades, Rechner, & Sundaramurthy 2000). This thesis applies structural contingency theory to provide an alternative explanation for the relationship between board structure and firm performance. Structural contingency theory (Donaldson 2001) proposes that the relationship between an organization???s structure and its performance is moderated by contingencies. In this study the contingency is the salience of the board???s control role. I argue that structural independence of the board has a beneficial effect on performance only if it is in fit with control salience. For example, a firm with an independently structured board that gives high prominence to the control role will perform well. On the other hand, another firm with a less independently structured board that does not see its main role as controlling management will also prosper. Survey data were analyzed to measure the control salience for 98 Australian listed companies. Archival data provided measures of board structure and firm performance. Consistent with the meta-analytic reviews, there was no association between independent board structure and firm performance. There was some evidence that high control salience resulted in high performance, but this effect was evident chiefly when performance was measured by total shareholder returns. This may indicate that the share market was responding to the symbolism of high control salience. In contrast to the symbolic main effect of control salience, the fit between the control salience and the independent structure of the board caused increased return on equity. This reflects the board???s objective effect on profit when its structure is in fit with control salience.

In this work we have investigated the intercalation of electron-donors between NbS2 slabs in Nb-based layer sulfides. Two series of Sr substituted Nb-based misfit sulfides belonging to the 1.5Q/1H and 1Q/1H series of misfit layer compounds have been synthesised. For large lanthanides (Ln=La, Ce), only the 1Q/1H compounds formed whereas for smaller lanthanides and yttrium, both types of phases can be obtained. The crystal structure of misfit sulfide (Pr0.55Sr0.45S)1.15NbS2 has been refined using the composite approach. In the Q-slab, Pr-atoms are partly replaced by Sr with a random distribution over one cation position. The crystal structure of misfit sulfide [(Sm1/3Sr2/3S)1.5]1.15NbS2 belonging to the 1.5Q/1H series have also been determined. The obtained results suggest a preferred occupancy of the cation positions in the slab where Sr atoms mainly occupy positions on the exterior of the slab while Sm atoms are in the center of the slab. The (La1-xSrxS)1.15NbS2 solid solution (0.1&lt;x&lt;0.9) has also been studied. It was found that the maximum value of Sr substitution is 40-50% and therefore, the minimal value of charge transfer to stabilize this structure type is about 0.6ē per Nb atom. An attempt to synthesize SrxNbS2 (0.1≤x≤0.5) intercalates was made but single phases were not obtained and increasing the temperature from 1000оС to 1100оС leads to the decomposition of these intercalates. Single crystals of Sr0.22Nb1.05S2 and Sr0.23NbS2 were found and their structures were determined. The structures belong to two different types of packings with statistical distribution of Sr between layers. A new superconducting sulfide, "EuNb2S5", was investigated by ED and HREM and its structure model consisting of Nb7S14 and (Eu3S4)2 slabs alternating along the c-axis is suggested. An attempt to suggest a model for the structure of "SrNb2S5" by means of X-ray single crystal diffraction was made. The proposed structure consists of two types of slabs: a Nb7S14 and a [Sr6(NbS4)2S] slab with niobium in tetrahedral coordination. It is shown that "SrNb2S5" and "EuNb2S5" are have similar structures. For the first time, single crystals of the complex sulfide BaNb0.9S3 have also been studied by means of X-ray single crystal diffraction. The single crystal refinement and EDX analysis showed the existence of cation vacancies at the niobium position. BaNb0.9S3 has also been studied by ED and no superstructure was found which implies that and the vacancies are statistically distributed. No improvement of the magnetic properties of the studied compounds was observed in comparison to NbS2.

Commercial off-the-shelf enterprise resource planning (ERP) systems have been adopted by large companies to support their inter- and intra-business processes. Midsize market firms are now investing in ERP systems too. However, research has indicated that about three quarters of attempted ERP projects turned out to be unsuccessful. A common problem encountered in adopting ERP software has been the issue of fit or alignment. This paper presents an ERP misfit analysis methodology, grounded on the task-technology fit theory and cognitive fit theory, for measuring misfits between ERP candidates and enterprise¡¦s requirements in ex-ante implementation. A decision support system prototype embedded the approach has been developed. A usability evaluation is performed on the prototype to demonstrate the approach. With this approach, organizations can more easily and systematically determine where the misfits are and the degree of misfits, thereby reducing the risks in implementing ERP systems. Our research contributes to the practical solution of the problem of misfit analysis.

We present a general approach for determining the equilibrium shape of isolated, coherent, misfitting particles by minimizing the sum of elastic and interfacial energies using a synthesis of finite element and optimization techniques. The generality derives from the fact that there is no restriction on the initial or final shape, or on the elastic moduli of the particle and matrix, or on the nature of misfit. The particle shape is parameterized using a set of design variables which are the magnitudes of vectors from a reference point inside the particle to points on the particle/matrix interface. We use a sequential quadratic programming approach to carry out the optimization. Although this approach can be used to find equilibrium shapes of particles in three dimensional systems, we have presented the details of our formulation for two dimensional systems under plane strain conditions. Using our formulation, we have studied the equilibrium shapes in two dimensional systems with cubic anisotropy; the precipitate and matrix phases may have different elastic moduli, and the misfit may be dilatational or non-dilatational. The equilibrium shapes and their size dependence are analysed within the framework of symmetry-breaking shape transitions. These transitions are further characterized in terms their dependence on the cubic elastic anisotropy parameter, defined by A = 2C44/(C11 – C12), and on the modulus mismatch, defined by δ=μp/μm, where /μp and μm are the effective shear moduli of the precipitate and matrix phases, respectively. Depending on the type of misfit, the systems may be classified into the following four cases: Case A: For dilatational misfit, the equilibrium shapes in isotropic systems are circular (with an isotropic or I symmetry) at small sizes and undergo a transition at a critical size to become ellipse-like (with an orthorhombic or O symmetry). This I --O transition is continuous and is obtained only when the precipitate phase is softer than the matrix. These results are in good agreement with the analytical results of Johnson and Cahn. In cubic systems with dilatational misfit, the particles exhibit a transition from square-like shapes (with a tetragonal or T symmetry) at small sizes to rectangle-like shapes (with an O symmetry) at large sizes. This T -- O transition is continuous. It occurs even in systems with stiffer precipitates; however, it is forbidden for systems with δ >δC, where δ C represents a critical modulus mismatch. The critical size decreases with increasing cubic anisotropy (i.e., with increasing values of (A-1)/(A+1). The sides of the square-like and rectangle-like shapes are along the elastically soft directions. Case B: In these systems, the principal misfits e*xx and e*yy differ in magnitude but have the same sign. The precipitates at small sizes become elongated along the direction of lower misfit; this shape has an O symmetry. In systems with A > 1, they continue to become more elongated along the same direction, exhibiting no symmetry-breaking transition. However, in systems with A < 1, particles at large sizes are elongated along an intermediate direction between the direction of lower misfit and one of the elastically soft <11> directions; this shape has only a monoclinic or M symmetry. This O - M transition, in which the mirror symmetries normal to the x and y axes are lost, may be discontinuous or continuous. The critical size increases with δ (in the range 0.8 < δ <1.25), indicating that this transition would also be forbidden for systems with δ > δC. In systems with A < 1, the critical size decreases with increasing values of A-1/ A+1 Case C: In these systems, the principal misfits differ in both magnitude and sign, and the misfit strain tensor allows an invariant line along which the normal strain is zero. The precipitates at small sizes are elongated along the direction of lower absolute misfit, and possess an 0 symmetry. At large sizes, the mirror symmetries normal to the x and y axes are broken to yield shapes which are elongated along a direction between that of lower misfit and the invariant line. This 0 -> M transition is continuous and occurs in all the systems irrespective of the value of A The critical size increases with A and decreases with δ. Case D; The misfit in this case is a special form of that in Case C; the principal misfits have the same magnitude but opposite signs. The precipitates at small sizes have a square-like shape with its sides normal to the < 11 > axes, irrespective of the type of cubic anisotropy. At large sizes, they become rectangle-like with the long axis oriented along one of the <11> directions. Similar to Case C, this T - 0 transition is continuous and occurs in all the systems irrespective of the values of A. The critical size increases with A and decreases with δ. Thus, we have identified all the symmetry-breaking transitions in equilibrium shapes of coherent precipitates in two dimensional systems. We have identified their origin and nature, and characterized them in terms of their dependence on the anisotropy parameter and modulus mismatch.

Many technologically important alloys such as Ni base superalloys and Ti-Al base alloys benefit from the precipitation of an ordered β phase from a disordered α matrix. When the crystallographic symmetry of the β phase is a subgroup of that of the disordered α phase, the microstructure may contain multiple orientational variants of the β phase, each with its own (anisotropic, crystallographically equivalent) misfit (lattice parameter mismatch) with the matrix phase. Examples include orthorhombic precipitates in a hexagonal matrix in Ti-Al-Nb alloys, and tetragonal precipitates in a cubic matrix in ZrO2-Y2O3. We have studied two-phase microstructures containing multiple variants of the precipitate phase. In particular, we have used phase field simulations to study the effect of elastic stresses in a two dimensional system containing a disordered matrix and three different orientational variants of the precipitate phase, with a view to elucidate the effect of different levels of anisotropy in misfit. We consider a two dimensional, elastically homogeneous and isotropic model system in which the matrix (α) and precipitate (β) phases have hexagonal and rectangular symmetries, respectively, giving rise to three orientational variants of the β phase. Therefore, our phase field model has composition (c) and three order parameters (η1, η2, η3) as the field variables.Due to the difference in crystallographic symmetry, the precipitate-matrix misfit strain tensor, ε*, can be anisotropic. ε*maybe represented in its principal form as ε *= (ε xx 0 ) 0 εyy where ε xx and ε yy are the principal components of the misfit tensor. We define t= εyy/εxx as the parameter representing anisotropy in the misfit. In this thesis, we report the results of our systematic study of microstructural evolution in systems with different values of t, representing different levels of anisotropy in misfit: •Case A: t=1 (dilatational or isotropic misfit) • Case B: 0 <t<1 (principal misfit components are unequal but have the same sign) • Case C: t=0 (the principal misfit along the y direction is zero) • Case D: -1 <t<0 (principal misfit components have opposite signs and unequal magnitudes) • Case E: t= -1 (principal misfit components are equal, but with opposite signs; pure shear) In Cases D and E, there is an invariant line along which the normal misfit is zero. In Case D, this invariant line is at ±54.72◦, and in Case E, it is at ±45◦, with respect to the x-axis. Our simulations of microstructural evolution in this system are based on numerical integration of the Cahn-Hilliard and Cahn-Allen equations which govern the evolution of composition and order parameter fields, respectively. In each case, we have studied two different situations: isolated particle (single variant) and many interacting particles (multivariant). Dynamical growth shape of an isolated precipitate In systems with an isotropic misfit (Case A), the precipitate shape remains circular at all sizes. In Cases B and C, the precipitate shape is elongated along the y-axis, which is also the direction in which the magnitude of the misfit strain is lower. In all these cases, the symmetry of the particle shape remains unaltered at all sizes. In contrast, in Cases D and E, the particle shape exhibits a symmetry-breaking transition. In Case D, the precipitate elongates initially along the y direction (i.e. the direction of lower absolute misfit), before undergoing a transition in which the mirror symmetry normal to x and yaxes is lost. In Case E, the particle has an initial square-like shape (with its sides normal to the 11directions) before losing its four-fold rotation axis to become rectangle-like with its long axis along one of the the 11directions. The critical precipitate size at which the symmetry-breaking shape transition occurs is obtained using bifurcation diagrams. In both Cases D and E, the critical size for the dynamical growth shapes is larger than those for equilibrium shapes[1].This critical size is larger when the matrix supersaturation is higher or shear modulus is lower. Microstructural Evolution In all the five cases, the elastic stresses have a common effect: they lead to microstructures in which the precipitate volume fraction is lower than that in a system with no misfit. This observation is consistent with the results from the thermodynamics of stressed solids that show that a precipitate-matrix misfit increases the interfacial composition in both the matrix and the precipitate phase. In systems with isotropic misfit (Case A), the microstructure consists of isolated circular domains of the precipitate phase that retain their circular shape during growth and subsequent coarsening. In Cases B and C with anisotropic misfit with t≥0, the three orientational variants of the precipitate phase are elongated along the directions of lower misfit (y-axis and ±120◦to y-axis). At a given size, particles in Case C (in which one of the principal misfits is zero) are more elongated than those in Case B. Systems with a higher shear modulus enhance the effect of misfit stresses, and therefore, lead to thinner and longer precipitates. When the precipitate volume fraction is increased, these elongated precipitates interact with (and impinge against) one another to a greater extent, and acquire a more jagged appearance. For Cases D and E, each orientation domain is associated with an invariant line along which the normal misfit is zero. Thus, in Case D, early stage microstructures show particles elongated along directions of lower absolute misfit (y-axis and ±120°to y-axis). At the later stages, the domains of the precipitate phase tend to orient along the invariant lines; this leads some of the particles to acquire a ‘Z’ shape before they completely re-orient themselves along the invariant line. In Case E, each variant grows as a thin plate elongating along the invariant line. The growth and impingement of these thin plates leads to a microstructure exhibiting complex multi-domain patterns such as stars, wedges, triangles, and checkerboard. These patterns have been compared (and are in good agreement) with experimental observations in Ti-Al-Nb alloys containing the precipitate (O) and matrix (α2)phases[2]. Since in Case E the sum of misfit strains of the three variants is zero, elastic energy considerations point to the possibility of compact, self-accommodating clusters of the three variants, sharing antiphase boundaries (APBs). Thus, if the APB energy is sufficiently low, the microstructure may consist of such compact clusters. Our simulations with such low APB energy do show triangle shaped clusters with six separate particles (two of each variant)in a self-accommodating pattern. (Refer PDF file)