Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

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Thesis (M.S.)--George Mason University, 2009. / Vita: p. 164. Thesis director: Daniel Anderson. Submitted in partial fulfillment of the requirements for the degree of Master of Science in Mathematics. Title from PDF t.p. (viewed Oct. 12, 2009). Includes bibliographical references (p. 163). Also issued in print.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1993. / Vita. Abstract. Includes bibliographical references (leaves 224-239). Also available via the Internet.

Thesis (Ph. D.)--University of Chicago, 1936. / Vita. "Private edition, distributed by the University of Chicago libraries, Chicago, Illinois." "Reprinted from Travaux de l'Institut mathématique de Tbilissi, vol. 5, 1938."

M.Sc. / Alloying Cr with non-magnetic Ru, results in unusual magnetoelastic effects due to strong magnetic interactions with the lattice. In the low concentration region, Ru increases the Neél temperature TN due to the enhancement of the spin density wave (SDW). The temperature dependence of the thermal expansion coefficient (a) of Cr o.997Ru0.003 displays Invar behaviour within a small temperature region (7.-: 5 K) of the magnetic transition at TN 390 K). This alloy is of little practical use since the Invar behaviour is well above room temperature. Mo, which is isoelectronic with Cr, is known to vary the strength of the SDW in Cr without changing its basic nature. It reduces and broadens the magnetic transition at TN of Cr and its alloys. Therefore Mo seems to be suitable for tayloring the Cr 0.997R110.003 alloy system, reducing the temperature region, in which the Invar effects are observed, down to room temperature. The temperature dependence of the thermal expansion and of the elastic constants were measured for (Cr i _rMor )0.997Ruo.003 and (Cri _yMoy )0.995Ru0.005 in the temperature range between 77 K and 450 K so that the effects of Mo on the Invar behaviour of Cr 0.997Ru0.003 and on the magnetoelasticity in (Cr i„Moz )0.997Ru0.003 and (Cr i _yMoy )0.995Ru0.005 could be studied. From the Invar-study we learn that although the addition of Mo to Cro.997Rno.003 succesfully decreased the Neel temperature down to room temperature, it simultaneously increased the coefficient of thermal expansion to much larger values. We were therefore not successful in our effort to improve the Invar type properties of the Cr0.997R110.003 alloy by the addition of Mo. Although the study was mainly focussed on tayloring the antiferromagnetic Invar Cr o.997Ru0.003 alloy with Mo, we also theoretically analysed the effects on the magnetoelasticity of Cr0.997Ru0.003, in terms of the temperature dependences of the thermal expansion and elastic constants in (Cri_xMox)0.997Ruo.003 and (Cri— yMoy )o.99sRuo.00s alloy systems when some of Cr atoms are replaced by those of Mo. In both Cr-Ru-Mo alloy systems, a(T) showed well defined anomalies with a minimum at the commensurate (C) SDW to paramagnetic (P) phase transition at TN and a maximum in the incommensurate (I) SDW-CSDW transition at T IC for x < 0.015 and y = 0.01. For x > 0.015, the CSDW state is completely suppressed and only the ISDW-P phase transition at TN is observed. The temperature dependence of the elastic constants in (Cri,M0x)o.997Ruo.003 with x = 0.015 and 0.07 showed only the ISDW-P phase transition, while the alloy with x = 0.007 showed both the CSDW-P at TN and a very small ISDW-CSDW transition at Ti.c . In general: Mo decreases the magnetic contributions to the volume and to the bulk modulus of Cr0.997Ru0.003 below TN . Mo completely suppresses the CSDW state of Cr0.997R11 0.003. The (Cri„Mos )0.997Ruo .003 and (Cri _yMoy )0 .995Ru0.005 show a second order phase transition at TN . Hysteresis effects were observed in (Cri—xMox)o.997Ruo.003 at the ISDW-CSDW phase transition implying a first order phase transition at T1c.. The fact that the transitions at TN are of second order, together with the effect of Mo on Cr0.997R110.003 completely suppressing the CSDW state, make it possible to theoretically analyse the temperature dependence of the magnetic contributions to the thermal expansion and elastic constants of the (Cri_xMoz)o.997Ruo.003 samples showing only the ISDW-P phase transition. From the application of the theories we learn that: There is a mutual dependence between the reduced temperature dependences of the magnetic contribution to volume expansivity, A i3(t) and to the bulk modulus, AB(t). A phenomenological thermodynamic model is found to define the temperature dependence of the magnetic contribution to the volume and to the bulk modulus quite well, for the samples showing no ISDW-CSDW, but only the ISDW-P phase transition, with an increase in temperature. The Griineisen parameters are defined reasonably well within the framework of the phenomenological approach of Fawcett and Alberts. The Mo atomic concentration dependence of the magnetic transition temperature was studied from the magnetic phase diagram of (Cri—xMos)o.997Ruo.00s alloys in terms of the two-band imperfect nesting model of Machida and Fujita. From the magnetic phase diagram: A magnetic triple point where the ISDW, CSDW and P states coexist can clearly be observed. The ISDW-CSDW, CSDW-P and ISDW-P transition boundaries were calculated. The theoretical model describes the ISDW-CSDW and CSDW-P boundaries reasonably well, while there is a significant deviation in the ISDW-P phase line which can probably be ascribed to the fact that impurity scattering effects are not incorporated into the theory.

M.Sc. (Physics) / Please refer to full text to view abstract

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