Applications of differential geometry to high spin field theories

The main aim of this thesis is to investigate the application of methods of differential geometry to the constraint analysis of relativistic high spin field theories. As a starting point the coordinate dependent descriptions of the Lagrangian and Dirac-Bergmann constraint algorithms are reviewed for general second order systems. These two algorithms are then respectively employed to analyse the constraint structure of the massive spin-1 Proca field from the Lagrangian and Hamiltonian viewpoints. As an example of a coupled field theoretic system the constraint analysis of the massive Rarita-Schwinger spin-3/2 field coupled to an external electromagnetic field is then reviewed in terms of the coordinate dependent Dirac-Bergmann algorithm for first order systems. The standard Velo-Zwanziger and Johnson-Sudarshan inconsistencies that this coupled system seemingly suffers from are then discussed in light of this full constraint analysis and it is found that both these pathologies degenerate to a field-induced loss of degrees of freedom. A description of the geometrical version of the Dirac-Bergmann algorithm developed by Gotay, Nester and Hinds begins the geometrical examination of high spin field theories. This geometric constraint algorithm is then applied to the free Proca field and to two Proca field couplings; the first of which is the minimal coupling to an external electromagnetic field whilst the second is the coupling to an external symmetric tensor field. The onset of acausality in this latter coupled case is then considered in relation to the geometric constraint algorithm.

Mössbauer spectroscopic study of the thermal spin crossover in [Fe(II)(isoxazole)6](ClO4)2

The Fe Mössbauer spectroscopy of mononuclear [Fe(II)(isoxazole)](ClO) has been studied to reveal the thermal spin crossover of Fe(II) between low-spin (S = 0) and high-spin (S = 2) states. Temperaturedependent spin transition curves have been constructed with the least-square fitted data obtained from the Mössbauer spectra measured at various temperatures between 84 and 270 K during a cooling and heating cycle. This compound exhibits an unusual temperature-dependent spin transition behaviour with T(?) = 223 and T(?) = 213 K occurring in the reverse order in comparison to those observed in SQUID observation and many other spin transition compounds. The compound has three high-spin Fe(II) sites at the highest temperature of study of which two undergo spin transitions. The compound seems to undergo a structural phase transition around the spin transition temperature, which plays a significant role in the spin crossover behaviour as well as the magnetic properties of the compound at temperatures below T. The present study reveals an increase in high-spin fraction upon heating in the temperature range below T, and an explanation is provided.

Observation of a 331 K (58 °C) spin transition for bis[hydrotris(1,2,4-triazol-1-yl)borate]iron(II) by variable temperature infrared spectroscopy and magnetic susceptibility measurements

Fe{HB(CHN)} is observed by variable temperature infrared and magnetic studies to have a spin transition between the low spin S = 0 and high spin S = 2 states at 331 K (58 °C) with thermal hysteresis of ~1.5 K. Changes in the triazole ligand IR absorptions demonstrate that distant non-metal-ligand vibrations are altered upon the change in electronic structure associated with the spin-crossover can be used to monitor the the spin-crossover transition.

Study of neutral Fe(III) complexes of pyridoxal-N-substituted thiosemicarbazone with desolvation induced spin-state transformation above room temperature

The preparation and characterization of two new neutral ferric complexes with desolvation-induced discontinuous spin-state transformation above room temperature are reported. The compounds, Fe(Hthpy)(thpy).CH3OH.3H2O (1) and Fe(Hmthpy)(mthpy).2H2O (2), are low-spin (LS) at room temperature and below, whereas their nonsolvated forms are high-spin (HS), exhibiting zero-field splitting. In these complexes, Hthpy, Hmthpy, and thpy, mthpy are the deprotonated forms of pyridoxal thiosemicarbazone and pyridoxal methylthiosemicarbazone, respectively; each is an O,N,S-tridentate ligand. The molecular structures have been determined at 100(1) K using single-crystal X-ray diffraction techniques and resulted in a triclinic system (space group P1) and monoclinic unit cell (space group P21/c) for 1 and 2, respectively. Structures were refined to the final error indices, where RF = 0.0560 for 1 and RF = 0.0522 for 2. The chemical inequivalence of the ligands was clearly established, for the "extra" hydrogen atom on the monodeprotonated ligands (Hthpy, Hmthpy) was found to be bound to the nitrogen of the pyridine ring. The ligands are all of the thiol form; the doubly deprotonated chelates (thpy, mthpy) have C-S bond lengths slightly longer than those of the singly deprotonated forms. There is a three-dimensional network of hydrogen bonds in both compounds. The discontinuous spin-state transformation is accompanied with liberation of solvate molecules. This is evidenced also from DSC analysis. Heat capacity data for the LS and HS phases are tabulated at selected temperatures, the values of the enthalpy and entropy changes connected with the change of spin state were reckoned at DeltaH = 12.5 0.3 kJ mol-1 and DeltaS = 33.3 0.8 J mol-1 K-1, respectively, for 1 and DeltaH = 6.5 0.3 kJ mol-1 and DeltaS = 17.6 0.8 J mol-1 K-1, respectively, for 2

In situ imaging and height reconstruction of phase separation processes in polymer blends during spin coating

Spin coating polymer blend thin films provides a method to produce multiphase functional layers of high uniformity covering large surface areas. Applications for such layers include photovoltaics and light-emitting diodes where performance relies upon the nanoscale phase separation morphology of the spun film. Furthermore, at micrometer scales, phase separation provides a route to produce self-organized structures for templating applications. Understanding the factors that determine the final phase-separated morphology in these systems is consequently an important goal. However, it has to date proved problematic to fully test theoretical models for phase separation during spin coating, due to the high spin speeds, which has limited the spatial resolution of experimental data obtained during the coating process. Without this fundamental understanding, production of optimized micro- and nanoscale structures is hampered. Here, we have employed synchronized stroboscopic illumination together with the high light gathering sensitivity of an electron-multiplying charge-coupled device camera to optically observe structure evolution in such blends during spin coating. Furthermore the use of monochromatic illumination has allowed interference reconstruction of three-dimensional topographies of the spin-coated film as it dries and phase separates with nanometer precision. We have used this new method to directly observe the phase separation process during spinning for a polymer blend (PS-PI) for the first time, providing new insights into the spin-coating process and opening up a route to understand and control phase separation structures. © 2011 American Chemical Society.

A new 3-D polymeric spin transition compound: [tris(1,4-bis-(tetrazol-1-yl) butane-N1,N1′)iron(II)] bis(perchlorate)

A series of novel polymeric compounds of formula [M(btzb)3][ClO4]2 (Mll = Fe, Ni or Cu) with btzb = 1,4-bis-(tetrazol-1-yl)butane have been prepared and their physical properties investigated. The btzb ligand has been prepared and its crystal structure determined, together with a tentative crystal structure of the 3-D compound [Fe(btzb)3][ClO4]2. The model of the latter shows two symmetry-related, interpenetrating Fe-btzb networks in which the iron(II) ions approach each other as close as 8.3 and 9.1 Å. This supramolecular catenane undergoes a sharp thermal spin transition around 160 K with hysteresis (20 K) along with a pronounced thermochromic effect. The spin crossover behaviour has been followed by magnetic, DSC, optical spectroscopy and 57Fe Mössbauer spectroscopy measurements. Irradiation with green light at low temperature leads to population of the metastable high-spin state for the thermally active iron(ll) ions. The nature of the spin crossover behaviour has been discussed in detail.

Structure and physical properties of [µ-Tris(1,4-bis(tetrazol-1-yl)butane-N4,N4‘')iron(II)] Bis(hexafluorophosphate), a new Fe(II) spin-crossover compound with a three-dimensional threefold interlocked crystal lattice

[μ-Tris(1,4-bis(tetrazol-1-yl)butane-N4,N4‘)iron(II)] bis(hexafluorophosphate), [Fe(btzb)3](PF6)2, crystallizes in a three-dimensional 3-fold interlocked structure featuring a sharp two-step spin-crossover behavior. The spin conversion takes place between 164 and 182 K showing a discontinuity at about T1/2 = 174 K and a hysteresis of about 4 K between T1/2 and the low-spin state. The spin transition has been independently followed by magnetic susceptibility measurements, 57Fe-Mössbauer spectroscopy, and variable temperature far and midrange FTIR spectroscopy. The title compound crystallizes in the trigonal space group P30¯(No. 147) with a unit cell content of one formula unit plus a small amount of disordered solvent. The lattice parameters were determined by X-ray diffraction at several temperatures between 100 and 300 K. Complete crystal structures were resolved for 9 of these temperatures between 100 (only low spin, LS) and 300 K (only high spin, HS), Z = 1 [Fe(btzb)3](PF  6)2:  300 K (HS), a = 11.258(6) Å, c = 8.948(6) Å, V = 982.2(10) Å3; 100 K (LS), a = 10.989(3) Å, c = 8.702(2) Å, V = 910.1(4) Å3. The molecular structure consists of octahedral coordinated iron(II) centers bridged by six N4,N4‘ coordinating bis(tetrazole) ligands to form three 3-dimensional networks. Each of these three networks is symmetry related and interpenetrates each other within a unit cell to form the interlocked structure. The Fe−N bond lengths change between 1.993(1) Å at 100 K in the LS state and 2.193(2) Å at 300 K in the HS state. The nearest Fe separation is along the c-axis and identical with the lattice parameter c.

A 2D [FeII-bistetrazole] coordination polymer exhibiting spin-crossover properties

The reaction of 1,3-bis(tetrazol-1-yl)-2-propanol (btzpol) with Fe(BF4)2 · 6H2O in acetonitrile yields the remarkable 2D coordination polymer [FeII(btzpol)1.8(btzpol-OBF3)1.2](BF4)0.8 · (H2O)0.8(CH3CN) (1). This compound has been structurally characterized using an X-ray single-crystal synchrotron radiation source. The iron(II) centers are bridged by means of double btzpol bridges along the c direction, and by single btzpol bridges along the b direction. The reaction of part of the ligand with the counterion has forced the compound to crystallize in this extended two dimensional structure. The compound shows spin-transition properties, both induced by temperature and light, with T½ = 112 K and T(LIESST) = 46 K, respectively. The relaxation of the metastable high-spin state created by irradiation is exponential, following an Arrhenius type behavior at high temperature, and dominated by a temperature independent tunneling process at lower temperatures.

Study of thermal spin crossover in [Fe(II)(isoxazole)6](BF4)2 with Mössbauer spectroscopy

57Fe Mössbauer spectroscopy of the mononuclear [Fe(II)(isoxazole)6](BF4) 2compound has been studied to reveal the thermal spin crossover of Fe(II) between low-spin (S = 0) and high-spin (S = 2) states. A temperature-dependent spin transition curve has been constructed with the least-square fitted data obtained from the Mössbauer spectra measured at various temperatures in the 240-60K range during the cooling and heating cycle. The compound exhibits a temperature-dependent two-step spin transition phenomenon with Tsco (step 1) = 92 and Tsco (step2) = 191K. The compound has three high-spin Fe(II) sites at the highest temperature of study; among them, two have slightly different coordination environments. These two Fe(II) sites are found to undergo a spin transition, while the third Fe(II) site retains the high-spin state over the whole temperature range. Possible reasons for the formation of the two steps in the spin transition curve are discussed. The observations made from the present study are in complete agreement with those envisaged from earlier magnetic and structural studies made on [Fe(II)(isoxazole)6](BF4)2, but highlights the nature of the spin crossover mechanism.

One- and two-step spin-crossover behavior of [Fe(II)(isoxazole)6]2+ and the structure and magnetic properties of triangular [Fe(III)3O(OAc)6(isoxazole)3][ClO4)]

The structure and spin-crossover magnetic behavior of [FeII16][BF4]2 (1 = isoxazole) and [FeII16][ClO4]2 have been studied. [FeII16][BF4]2 undergoes two reversible spin-crossover transitions at 91 and 192 K, and is the first two-step spin transition to undergo a simultaneous crystallographic phase transition, but does not exhibit thermal hysteresis. The single-crystal structure determinations at 260 [space group P3̄, a = 17.4387(4) Å, c = 7.6847(2) Å] and at 130 K [space group P1̄, a = 17.0901(2) Å, b = 16.7481(2) Å, c = 7.5413(1) Å, α = 90.5309(6)°, β = 91.5231(6)°, γ = 117.8195(8)°] reveal two different iron sites, Fe1 and Fe2, in a 1:2 ratio. The room-temperature magnetic moment of 5.0 μB is consistent with high-spin Fe(II). A plateau in μ(T) having a moment of 3.3 μB centered at 130 K suggests a mixed spin system of some high-spin and some low-spin Fe(II) molecules. On the basis of the Fe−N bond distances at the two temperatures, and the molar fraction of high-spin molecules at the transition plateau, Fe1 and Fe2 can be assigned to the 91 and 192 K transitions, respectively. [FeII16][ClO4]2 [space group P3̄, a = 17.5829(3) Å, c = 7.8043(2) Å, β = 109.820 (3)°, T = 295 K] also possesses Fe1:Fe2 in a 1:2 ratio, and magnetic measurements show a single spin transition at 213 K, indicating that both Fe1 and Fe2 undergo a simultaneous spin transition. [FeII16][ClO4]2 slowly decomposes in solutions containing acetic anhydride to form [FeIII3O(OAc)613][ClO4] [space group I2, a = 10.1547(7) Å, b = 16.5497(11) Å, c = 10.3205(9) Å, β = 109.820 (3)°, T = 200 K]. The isosceles Fe3 unit contains two Fe···Fe distances of 3.2844(1) Å and a third Fe···Fe distance of 3.2857(1) Å. The magnetic data can be fit to a trinuclear model with ℋ = −2J(S1·S2 + S2·S3) − 2J13(S1·S3), where J = −27.1 and J13 = −32.5 cm-1.

catena-[μ-tris(1,2-bis(tetrazol-1-yl)ethane-N4,N4')iron(II)] bis(tetrafluoroborate): Synthesis, structure, spectroscopic and magnetic characterisation of a chain-type coordination polymer spin-crossover compound.

In analogy to a common synthesis of 1-substituted 5-H tetrazoles (Tetrahedron Lett. 36 (1995)1759; Beloruss. Gos. Univ., Minsk, USSR. Khim. Geterotsikl. Soedin. 11 (1985) 1521; Beloruss. Gos. Univ., Minsk, USSR. Khim. Geterotsikl. Soedin. 1 (1991) 66; BGU, Belarus. Vestsi Akad. Navuk Belarusi, Ser. Khim. Navuk 1 (1992) 73), the new bidentate ligand 1,2-bis(tetrazol-1-yl)ethane [endi] was synthesized and characterized by X-ray diffraction, NMR, IR and UV–Vis spectroscopy. By using iron(II) tetrafluoroborate hexahydrate the complexation with this ligand yields a 1-dimensional linear coordination polymer similar to the recently published chain compound (Inorg. Chem. 39 (2000) 1891) exhibiting a thermally induced spin-crossover phenomenon. Similar to the 1,2-bis(tetrazol-1-yl)propane-bridged compound, our 1,2-bis(tetrazol-1-yl)ethane-bridged compound shows a gradual spin transition, but the spin-crossover temperature T1/2≈140 K is found to be 10 K above the other T1/2. The T1/2 was determined by temperature-dependent 57Fe-Mössbauer, far FT-IR and UV–Vis spectroscopy as well as by temperature-dependent magnetic susceptibility measurements. Single crystals of the complex were grown in situ from a solution of the ligand and iron(II) tetrafluoroborate. The X-ray structure determinations of both the high spin as well as the low spin state of the compound revealed a solid state structure, which is comparable to that of catena-[Fe(1,2-bis(tetrazole-1-yl)propane)3](ClO4)2 (Inorg. Chem. 39 (2000) 1891; 2nd TMR-TOSS Meeting, 4th Spin Crossover Family Meeting, Lufthansa Training Center, Seeheim/Germany, April 30–May 2, 1999). Both the 1,2-bis(tetrazol-1-yl)propane-bridged and our compound do not show a thermal hysteresis effect (J. Am. Chem. Soc. 115 (1993) 9810; Inorg. Chim. Acta 37 (1979) 169; Chem. Phys. Lett. 93 (1982) 567). The synthesis of the complex described in the experimental section yielded a fine powdered product being poorly soluble in most common solvents. The single crystal measurements were done with crystals obtained by various diffusion methods. Most of them yielded either thin needles or small hexagonal prism crystals depending on the specific conditions.

Tuning of the charge in octahedral ferric complexes based on pyridoxal-N substituted thiosemicarbazone ligands

Four novel mononuclear coordination compounds namely: [Fe(Hthpy)2](SO4)1/2·3.5H2O 1, [Fe(Hthpy)2]NO3·3H2O 2, [Fe(H2mthpy)2](CH3C6H4SO3)3·CH3CH2OH 3 and [Fe(Hethpy)(ethpy)]·8H2O 4, (H2thpy = pyridoxalthiosemicarbazone, H2mthpy = pyridoxal-4-methylthiosemicarbazone, H2ethpy = pyridoxal-4-ethylthiosemicarbazone), were synthesized in the absence or presence of organic base, Et3N and NH3. Compounds 1 and 2 are monocationic, and were prepared using the singly deprotonated form of pyridoxalthiosemicarbazone. Both compounds crystallise in the monoclinic system, C2/c and P21/c space group for 1 and 2, respectively. Complex 3 is tricationic, it is formed with neutral bis(ligand) complex and possesses an interesting 3D channel architecture, the unit cell is triclinic, P1 space group. For complex 4, the pH value plays an important role during its synthesis; 4 is neutral and crystallises with two inequivalent forms of the ligand: the singly and the doubly deprotonated chelate of H2ethpy, the unit cell is monoclinic, C2/c space group. Notably, in 1 and 4, there is an attractive infinite three dimensional hydrogen bonding network in the crystal lattice. Magnetic measurements of 1 and 4 revealed that a rather steep spin transition from the low spin to high spin Fe(III) states occurs above 300 K in the first heating step. This transition is accompanied by the elimination of solvate molecules and thus, stabilizes the high spin form due to the breaking of hydrogen bonding networks; compared to 2 and 3, which keep their low spin state up to 400 K.

Crystal structure and magnetic behaviour of a five-coordinate iron(III) complex of pyridoxal-4-methylthiosemicarbazone

The crystal structure and magnetic properties of a penta-coordinate iron(III) complex of pyridoxal-4-methylthiosemicarbazone, [Fe(Hmthpy)Cl](CHCHSO), are reported. The synthesised ligand and the metal complex were characterised by spectroscopic methods (H NMR, IR, and mass spectroscopy), elemental analysis, and single crystal X-ray diffraction. The complex crystallises as dark brown microcrystals. The crystal data determined at 100(1) K revealed a triclinic system, space group P over(1, ¯) (Z = 2). The ONSCl geometry around the iron(III) atom is intermediate between trigonal bipyramidal and square pyramidal (t = 0.40). The temperature dependence of the magnetic susceptibility (5-300 K) is consistent with a high spin Fe(III) ion (S = 5/2) exhibiting zero-field splitting. Interpretation of these data yielded: D = 0.34(1) cm and g = 2.078(3). © 2007 Elsevier B.V. All rights reserved.

Equilibrium properties of disordered spin models with two-scale interactions

Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely connected structure, have become well understood. Many features generalize to sparse Erdös- Rényi graph structures above the percolation threshold and to Bethe lattices when appropriate boundary conditions apply. In this paper, we consider spin states subject to a combination of sparse strong interactions with weak dense interactions, which we term a composite model. The equilibrium properties are examined through the replica method, with exact analysis of the high-temperature paramagnetic, spin-glass, and ferromagnetic phases by perturbative schemes. We present results of replica symmetric variational approximations, where perturbative approaches fail at lower temperature. Results demonstrate re-entrant behaviors from spin glass to ferromagnetic phases as temperature is lowered, including transitions from replica symmetry broken to replica symmetric phases. The nature of high-temperature transitions is found to be sensitive to the connectivity profile in the sparse subgraph, with regular connectivity a discontinuous transition from the paramagnetic to ferromagnetic phases is apparent.

Direct observation of morphological development during the spin-coating of polystyrene-poly(methyl methacrylate) polymer blends

We present results of the direct observation, in real-space, of the phase separation of high molecular weight polystyrene and poly(methyl methacrylate) from ortho-xylene using our newly developed technique of high speed stroboscopic interference microscopy. Taking a fixed concentration (3 wt % in o-xylene) at a fixed composition (1:4 by weight) and by varying the rotational rate during the spin-coating process, we are able to observe the formation of a range of phase separated bicontinuous morphologies of differing length-scales. Importantly, we are able to show that the mechanism by which the final phase separated structure is formed is through domain coarsening when rich in solvent, before vitrification occurs and fixes the phase separated structure. The ability to directly observe morphological development offers a route toward controlling the length-scale of the final morphology through process control and in situ feedback, from a single stock solution. © 2013 Wiley Periodicals, Inc.