The omega phase is a metastable phase which forms in alloys of titanium and zirconium with most transition metals. In this paper the available data from both alloy systems on the occurrence, the structure, the mechanism of formation, and the morphology of the phase are reviewed and compared. The effect of omega phase on the mechanical behaviour and on the superconducting properties is then discussed. It is concluded that uncertainties still exist on the mechanism of the omega transformation during quenching and on the mechanism of the effect of omega on the mechanical properties.

Progress in Low Temperature Physics. Vol. 2

The formation of omega phase in titanium and zirconium alloys: A review

In order to clarify the compositional effect on the superconductivity of zirconium-transition metal (M) binary amorphous alloys, the superconducting properties and electrical resistance of the alloys were examined as functions of the concentration, group number and periodicity of the M elements.T
c for Zr75M25 alloys rises in the order Ru > Rh > Ir > Co > Os > Ni > Pt > Cu > Pd > Fe > Au, i.e. as the group number decreases when the periodicity belongs to the 5th period, and with decreasing M content for Zr100−X
M
 X
 alloys. The highT
c attained in the present work is 4.55 K for Zr80Rh20, 4.38 K for Zr75Rh25 and 4.47 K for Zr75Ru25. The temperature gradient of the upper critical magnetic field (H
c2) near the transition temperature (T
C) tends to increase with increasing zirconium content, and the resistive state due to the flux flow phenomena appears in a wide sweeping field. Following the sharp and large decrease of the flux flow resistance due to a peak effect, the resistance recovers sharply nearH
c2. The peak effect was found to occur more distinctly for the alloys containing a magnetic element of iron or cobalt, probably because of the suppression of the pair-breaking effect due to magnetic scattering by the application of the high field nearH
c2. The dominating factor for the compositional effect onT
C is inferred to originate from the variation ofλ throughω for Zr100−x
M
 X
 alloys and from that of λ through N(Ef) for Zr75M25 alloys. Additionally, it has been found for the Zr-M amorphous alloys that the electrical resistivityρ(T) exhibits a maximum value at temperature ranging from 2T
C to 3T
C, suggesting that the hump phenomenon in ρ(T) appeared through the generation of the superconducting fluctuations. The temperature coefficient of resistivity (tcr) defined by 1/R250(dR/dT) shows negative values ranging from 1.05×10−4 to 1.75×10−4
K
−1 andT
C was found to rise through the increase inλ with the increase in the negative value of the tcr.

Superconducting and electrical properties of amorphous zirconium-transition metal binary alloys

Phase transitions accompanied by spontaneous breaking of continuous symmetries have been studied extensively in condensed matter and high energy physics. In this thesis we investigate the spontaneous breaking of discrete symmetries, specifically in spin models with three-fold, four-fold and higher discrete symmetries. We show that an interplay between the topological defects domain walls and vortices in these models drives the discrete symmetry to be completely broken, partially broken and even enhanced to a continuous U(1) symmetry. We show that in two dimensions, percolation of domain walls drives a transition from a symmetry broken ordered phase to a symmetry enhanced quasi long range ordered phase which, in turn, undergoes a transition to the symmetry restored disordered phase when vortices proliferate. We highlight a flaw in the standard method for calculating winding numbers and propose a new method which correctly identifies vortices. We show that suppression of vortices in models with even number of states leads to an intermediate partially ordered phase and that additional suppression of domain walls, separating opposite spin states, is required to manifest the symmetry enhanced phase. We show that spin models with three or higher number of states exhibit a partial symmetry broken phase instead of symmetry enhanced phase in three dimensions as individual types of domain walls are able to percolate on their own. We also obtain a variety of phases by suppressing defects belonging to subgroups of the model’s symmetry. Upon enhancing the formation of vortices instead of suppressing them, we obtain a vortex-antivortex lattice phase in two dimensions and a vortex condensate phase in three dimensions. List of Publications arising from the thesis • Journal 1. “Quasi-Long-Range Order and Vortex Lattice in the Three-State Potts Model” Soumyadeep Bhattacharya and Purusattam Ray Physical Review Letters, 2016, 116, 097206. • Conferences 1. “Emergence of U(1) symmetry in Z(q) clock model” Soumyadeep Bhattacharya and Purusattam Ray AIP Conference Proceedings, 2012, 1447, 91. • Others 1. “U(1) Emergence versus Chiral Symmetry Restoration in the Ashkin Teller Model” Soumyadeep Bhattacharya arXiv:1601.02755. 2. “Partial Breaking of Three-Fold Symmetry via Percolation of a Domain Wall” Soumyadeep Bhattacharya and Purusattam Ray arXiv:1608.05901. List of Conferences Attended 1. FracMeet 2011 The Institute of Mathematical Sciences, Chennai, January 2011 2. DAE Symposium on Solid State Physics SRM University, Chennai, December 2011 3. FracMeet 2012 The Institute of Mathematical Sciences, Chennai, January 2012 4. INCF Workshop on Neuroinformatics of Sensory-Motor Integration The Institute of Mathematical Sciences, Chennai, November 2012 5. Bayes by the Bay Pondicherry, January 2013 6. Diversity and Complexity Saha Institute of Nuclear Physics, Kolkata, January 2013 7. FracMeet 2013 The Institute of Mathematical Sciences, Chennai, January 2013 8. Thermalization: From Black Holes to Glasses International Centre for Theoretical Sciences, Bengaluru, June 2013 9. Growing Length Scale Phenomena in Condensed Matter Physics Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru, October 2015 List of changes as suggested by Examiners Overall • Added missing page numbers. • Made some of the figure captions more self-contained. • Corrected some cross-references within the document. Chapter 1 • Modified the description of phases in models of crystal surfaces in Sec. 1.1 to highlight the equilibrium nature of the roughening and pre-roughening transition. • Added clarification about dimensionality in Sec. 1.1: The models show only these two phases on the square lattice when n ≤ 4. • Changed snapshots of typical spin configurations in Fig. 1.2 from that of the Z4 ferromagnet to that of the Z6 ferromagnet, as the latter model exhibits an intermediate U(1) phase without the need for vortex suppresion. • Added clarification about ordering in the 2D XY model, in Sec. 1.5.5: Since the model does not exhibit symmetry breaking at any non-zero temperature, . . . Chapter 2 • Added clarification regarding the n-fold symmetric order parameter distribution in Sec. 2.1.3: The n-fold symmetry in the distribution appears because the distribution is an accumulation of results from an ensemble of simulations, each starting from a completely ordered configuration belonging to one of the n states. • Added clarification in Sec. 2.2.2 regarding the gradual variation of order-parameter and possibility of a higher-order transition in the Z3 ferromagnet with weak suppression of vortices. • Added quantitative estimates of transition temperatures and defect proliferation temperatures in Sec. 2.2.3, Sec. 3.5. • Added clarification in Sec. 2.3.1 that the domain wall percolation temperature in the vortex suppressed Z3 ferromagnet on the square lattice is estimated to be very close, but not necessarily equal to, the thermodynamic transition between the symmetry enhanced and symmetry restored phases. • Added discussion on the change in behavior of specific heat in Sec. 2.2.3 as the order-disorder transition in the 2D Z3 model splits into two transitions with suppression of vortices. Chapter 3 • Added plots for two-point correlations establishing the QLRO nature of the intermediate phase uncovered by vortex (and ±π domain wall) suppression: in the 2D Z5 ferromagnet in Fig. 3.6, in the 2D Z4 ferromagnet in Fig. 3.7 and in the 2D Z6 ferromagnet in Fig. 3.9. • Added clarification regarding the use of the new method for calculating winding number in Sec. 3.3.3 and Sec. 1.5.3. • Added text in Sec. 3.8 stating that the disordered phase for λ = 0 occurs for T > 0. Chapter 4 • Added text in the introduction of Chapter 4 to highlight the study of models in three dimensions. • Added λ = 0 to the caption of Fig. 4.1. • Changed color scheme to better distinguish between the three spin states in Fig. 4.1a, Fig. 4.1b and Fig. 4.5b. • Added analysis of percolation properties for (0 | 1) domain walls in the QLRO phase of the 2D Z3 ferromagnet in Sec. 4.4.4, establishing the percolation threshold behavior across all temperatures in that phase. Chapter 5 • Modified the text in Sec. 5.1.2 to show how the six-fold states map onto the effective three-fold states and how the corresponding six-fold angles θ map onto the effective three-fold angles θ3. Chapter 7 • Added a table summarizing the different phases obtained by manipulating the defects in all the models discussed in this thesis.

Role of topological defects in breaking and enhancing discrete symmetries[HBNI Th111]

of the Dissertation Quantum Critical Behaviors in Magnetic Systems: Yb3Pt4, YFe2Al10, and Yb2Pt2Pb

Progress in Low Temperature Physics. Vol. 2

Citations

The formation of omega phase in titanium and zirconium alloys: A review

Superconducting and electrical properties of amorphous zirconium-transition metal binary alloys

Role of topological defects in breaking and enhancing discrete symmetries[HBNI Th111]

Quantum Critical Behaviors in Magnetic Systems: Yb3Pt 4, YFe2Al10 and Yb2Pt2Pb

Collective Classical And Quantum Fields: In Plasmas, Superconductors, Superfluid 3he, And Liquid Crystals

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