A neutron diffraction study of structural changes in one-dimensional K2Pt(CN)4Br0.3 · 3H2O from 77–323°K

Single crystal neutron diffraction measurements of K₂Pt(CN)₄Br_0.3 · 3H₂O (KCP) above room temperature, to the point of irreversible crystal breakdown (318–323°K), and at liquid nitrogen temperature (77°K), give no indication of a crystallographic phase change. Full three-dimensional data collected at 77°K ($\text{a = 9.848(5)}\text{A}\text{?}\text{, c = 5.714(3)}\text{A}\text{?}\text{,}\text{and space group}\text{P4mm}$) indicate that the structure is essentially unchanged from that at room temperature except for increased hydrogen bonding association between H₂O(2) and Br(1). The possible relationship between the hydrogen bonding changes and Br(1) site ordering is discussed.     

Renormalization group studies of phase diagrams of Ising and XY-model films of variable thickness

We compare the critical behavior of $\text{spin}\text{-}\text{1}\text{2}$ Ising model (ordinary phase transition in two dimensions) and classical XY-model (topological phase transition in two dimensions) films, with two flat surfaces and nearest neighbor couplings K_S between surface spins and K_B between all others, as a function of film thickness. We carry out a real space Migdal-style renormalization in two stages. In the bulk stage the film is first renormalized towards a double layer, with the renormalized parameters as inter- and intra-layer couplings. Then the double layer is renormalized with those couplings as initial parameters. From the RG-equations for the bulk stage we find a tricritical point, not only for the Ising model (in which case it is well known) but also for the XY-model. It signals the existence of distinct surface and bulk transitions for sufficiently large values of $\text{K}{}_{\mathrm{<mtext>S</mtext>}}\text{K}{}_{\mathrm{<mtext>B</mtext>}}$. For the Ising model the complete program can be carried out and the phase diagram for films of arbitrary thickness is constructed. For the double layer XY-model a sufficiently complex Migdal-style renormalization appears to be unfeasible, presumably due to the possible presence of strings between the layers. Therefore, in an alternative approach, two representations for the partition function of the double layer XY-model are given. The system can be described in terms of its topological excitations, i.e., vortices on each layer and strings, either closed or terminating in vortices, between them. The system is also written as three coupled Coulomb gases. Based on this representation a renormalization group is found, and used, together with a Griffiths inequality for the correlation functions, to obtain information on the phase diagram. If there is a single phase transition, there is one phase where the correlations exhibit power law behavior and another where they fall off exponentially. The transition temperature increases monotonously with interlayer coupling to twice its value in two dimensions, but the nature of the phase transition for any finite inter-layer coupling appears to be different from that at zero coupling. We suggest that this is associated with the behavior of the internal strings. These results should be relevant for the renormalization of the film with isotropic bulk couplings as well as for layered systems of finite thickness, with different inter- and intra-layer couplings.     

Elastic constants of nionium up to the melting point

The elastic constants of a pure niobium single crystal have been measured between 1300 and 2600 K by means of an ultrasonic method and a suitable geometry. We find that the shear constant C₄₄ behaves anomalously up to the melting point and that $\text{1}\text{2}$(C₁₁–C₁₂) decreases monotonically. The anomalous behaviour of C₄₄ associated with the trigonal distortion is explained as an electronic contribution with a (local) degeneracy temperature which is considerably higher than the melting point.     

N2 Monolayers on graphite: Specific heat and vapor pressure measurements — thermodynamics of size effects and steric factors

Calorimetric and vapor pressure measurements of N₂ monolayers on Grafoil have been made in the regions recently explored by neutron scattering. The phase transition at T = 48 K involves approximately symmetric specific heat anomalies of 2&#x0303; K FWHM, and the peak position shifts about 1 K from $\text{1}\text{3}$ to $\text{2}\text{3}$ of one monolayer. In spite of the peak width and temperature shift the transition is intrinsically first order, due to melting of the √3 registered structure into a disordered phase in the presence of 2D vapor. The shift and broadening are shown to be a consequence of size effects primarily due to large edge-to-area ratios of the ordered phase domains. A formula relating the domain size to the shift in transition temperature gives r = 50' A for the mean radius of the domains. At film densities above $\text{2}\text{3}$ monolayer the peak broadens and shifts to a higher temperature until a critical region is reached near T= 85 K. The combined heat capacity and vapor pressure data indicate that there is no two phase region at coverages near monolayer completion and that the transition near T = 85 K is higher than first order. Effects of molecular orientation and surface-normal vibration appear in certain regions of temperature and density. A phase diagram is constructed which is consistent with both calorimetric and neutron scattering results.     

On a modified Lindemann-like criterion for 2D melting

By means of a molecular dynamics simulation the existence of a Lindemann-like criterion for 2D melting is proved. The criterion is the constancy of the value $\text{γ}{}_{\mathrm{<mtext>M</mtext>}}{}^{\mathrm{<mtext>c</mtext>}}\text{≡}\text{〈[}\text{u}\text{(}\text{R}\text{+}\text{a}{}_0\text{)?}\text{u}\text{(}\text{R}\text{)]}{}^2\text{〉}\text{a}{}^2$ along the melting curve; this value being practically independent of the nature of a 2D classical crystal (the Lindemann constant is infinite for a 2D crystal in the thermodynamical limit). For 2D dipole and 2D Lennard-Jones crystals γ_M^c = 0.12. For a 2D electron crystal γ_M^c ≈ 0.10. These values are consistent with the results of calculations in the framework of the phonon-mediated melting theory.     

Stability of higher-dimensional Einstein-Yang-Mills theories on symmetric spaces

We study (4 + d)-dimensional Einstein-Yang-Mills theories with arbitrary gauge groups, G_YM. The theory is compactified on a d-dimensional symmetric coset space $\text{G}\text{H}$ with a symmetric, topologically non-trivial classical gauge field, embedded in an H-subgroup of the Yang-Mills group. These theories are known to be classically stabilized by gravity if G_YM = H, $\text{G}\text{H}$ is a sphere and d ≠ 3. We study classical instabilities caused by embedding H in a larger gauge group. The small fluctuation spectrum is completely calculable, and leads to a stability condition. For two-dimensional spheres this condition is precisely the Brandt-Neri stability condition for non-abelian monopole fields. For four-spheres we find stability for SU(2) instantons embedded in arbitrary gauge groups and we reproduce the fluctuation spectrum around instantons. For higher-dimensional spheres the stable solutions of this type are completely classified, and occur only for d = 5, 6, 8, 9, 10, 12 and 16. The results show a remarkable agreement with expected topological stability. We also give a few examples with other symmetric spaces, such as CP_n, where the stability criterion appears less restrictive.     

Magnetic field dependent optical dephasing in LaF3:Er3+

Optical dephasing of the 5388 Å transition between the lowest Kramers doublets of the ⁴S_{$\text{3}\text{2}$} and ⁴I_{$\text{15}\text{2}$} multiplets of Er³⁺:LaF₃ has been studied by photon echo, optical phase switching and optical free induction decay. Er³⁺?¹⁹F hyperfine interactions produce dephasing which is two orders of magnitude faster than in previously studied non-Kramers systems, but at high field changes in the spin dynamics result in microsecond dephasing. For the lower Zeeman component of ⁴S_{$\text{3}\text{2}$}, T₂ (=6μs) is independent of H₀ whereas for the upper component the dephasing is rapid and strongly field dependent. This is quantitatively accounted for by spin lattice relaxation of the upper component of ⁴S_{$\text{3}\text{2}$}. Below 20 kG concentration and temperature dependent dephasing due to electron spin diffusion is observed.     

Equilibrium of three liquid phases and approach to the tricritical point in benzene-ethanol-water-ammonium sulfate mixtures

We have determined the region of coexistence of three liquid phases in the system C₆H₆-EtOH-H₂O-(NH₄)₂SO₄ at 21°, 45°, 48° and 48.6°C, and have located the tricritical point. The temperature and composition at the tricritical point are T_t = 48.9°C and mass fractions x_salt = 0.0175, x_water = 0.351, x_ethanol = 0.450, x_benzene = 0.181. This composition is inferred to lie outside the three-phase region at 21° and 45°, in agreement with the phenomenological theory of Griffiths. The locus of the three liquid phases in the isothermal composition tetrahedron has the parabolic, inflected (cubic), and cusped aspects predicted by the theory. For the three exponents β₁, β₂, and β₃ associated with the vanishing of the three characteristic dimensions of the coexistence region, we find β₁ = 0.4, β₂ = 1.0, β₃ = 1.5, compared to the theoretical $\text{β}{}_1\text{=}\text{1}\text{2}\text{, β}{}_2\text{= 1, β}{}_3\text{=}\text{3}\text{2}$. We verify that the algebraic degree 1/β′ of the coexistence curve near the two critical end points exceeds its classical value of 2.     

NMR investigation of the structure of NiZrF6·.6H2O at low temperatures

Previous studies have shown that NiZrF₆.6H₂O can be described by an axial spin Hamiltonian with parameters g = 2.33 and $\text{D}\text{k}\text{= ?3.14}\text{K}$, and exhibits ferromagnetic ordering at T_c = 164mK. Our room temperature X-ray measurements confirm that NiZrF₆·.6H₂O is isomorphous with NiSnCl₆·.6H₂O and give lattice parameters of $\text{a = 6.55}\text{A}\text{?}$ and α = 96°09′. Proton NMR measurements show that there exist important molecular motions at room temperature and that the space group remains $\text{R}\text{3}$ down to liquid helium temperatures. The positions of all twelve protons have been determined and are found to lie on a sphere of radius 2.9 Å centered on the nickel ion.     

Soft phonon mode at the martensitic phase transformation of AuCuZn2

The lattice dynamical property of AuCuZn₂ has been investigated by means of inelastic neutron scattering technique in connection with its martensitic phase transformation. The temperature dependent soft phonon was observed transformation. The temperature dependent soft phonon was observed around $\text{q =}\text{2}\text{3}\text{[110]}$ of TA₂ phonon branch. We have also found a premartensitic metastable phase, in which new satellite reflections at (H± $\text{2}\text{3}$, K ? $\text{2}\text{3}$, 0) have been observed around fundamental reflections with H + K = 4n. The atomic displacements of the soft phonon mode correspond to the atomic arrangement of the premartensitic phase.     

Crossing relations for deep-inelastic and annihilation processes

We calculate in a model field theory [φ³]_σ the structure functions $\text{F}\text{?}\text{(ω), F(ω)}$ for the processes e⁺+e^?→h+X and e^?+h→e^?+X in the next to leading logarithm approximation. We find that $\text{F}\text{(ω) and F(ω)}$ satisfy the analytic continuation relation but not the Gribov-Lipatov reciprocity relation.     

Spin anisotropy effects on the dimerization of the magnetostrictive quasi-one-dimensional XY model

The one-dimensional first-neighbour spin - $\text{1}\text{2}$ magnetostrictive XY model (with crystalline degrees of freedom assumed three- dimensional) with $\text{different}$ X and Y spin coupling constants presents a quite rich spin-Peierls dimerization phase diagram. In the (low anisotropy) - (low temperature) region we recover previous results (in particular the possibility for a first-order phase transition in the absence of external magnetic field); in the other three regions of the temperature-anisotropy space interesting branches of the phase diagram (including the tricritical line) are exhibited (for the first time as far as we know).     

X-ray diffraction of the smectic phases of N-(p-n-heptyloxybenzylidene)-p′-n-pentylaniline

Using X-ray diffraction the various smectic phases of N-($\text{p}$-$\text{n}$-heptyloxybenzylidene)-$\text{p}$′-$\text{n}$-pentylaniline can be classified (with increasing temperature) as S_H, S_B, S_C and S_A, respectively. The long molecular axes are probably tilted with respect to the normal to the layers in the S_A, S_C and S_H phases, and perpendicular to the layers in the S_B phase.     

Magnetic Phase transitions and hysteresis in FeCl2 · 2H2O

The magnetic phase diagram of FeCl₂ · 2H₂O has been determined by means of single crystal neutron diffraction experiments. Isothermal and isobaric measurements reveal the existence of first order and second order phase transitions separated by tricritical points at $\text{t}{}_1{}^1\text{= 0.5, h}{}_1{}^1\text{= 0.91}\text{and}\text{t}{}_2{}^1\text{= 0.39, h}{}_2{}^1\text{= 0.99}$. Considerable hysteresis effects were observed at the antiferro—ferrimagnetic phase boundary at temperatures t < 0.33.     

N.M.R. study of self-diffusion in solid N2

From the measurement of the N.M.R. relaxation times T₂ in ¹⁵N₂ and in ¹⁴N₂ containing Ar impurities we extract the self diffusion coefficient D $\text{i}$n h.c.p. N₂. We find that self-diffusion is a thermally activated process with an activation enthalpy δH¹/k = 1030 ± 25 K. We discuss the diffusion process and conclude that it can be related to the motion of thermally activated vacancies.     

The dynamical image potential for tunneling electrons

The exchange-correlation (XC) potential (image potential) felt by an electron tunneling from a metal through a classically forbidden region into vacuum is calculated by a Green's function technique. The resulting XC-potential reduces to the classical image potential if x, where $\text{x}\textcolor{red}{}\text{2}\text{m}\text{ω}{}_{\mathrm{s}}\text{κ}$ and $\text{κ = {2}\text{m}\text{(}\text{V}\text{?ω)}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, is large. For small x dynamical corrections to the classical result become important.     

Analysis of the two-state model and its application for amorphous iron alloys

The magnetic phase diagram for the two-state Weiss model is calculated in the mean field approximation (MFA) for low spin S₀ = $\text{1}\text{2}$ and high spin S₁ = $\text{3}\text{2}$. We show that the two-state model together with the assumption of the strong shor t range order (SRO) can account for the observed Curie temperature data in amorphous Fe_1-xA_x (A = B, Hf, Ti, Zr) alloys.     

Transport properties of alkali metal-graphite intercalation compounds

Basal resistivity ?_a has been measured $\text{in situ}$ on MC₈ compounds (M=K, Rb, Cs) from 5–300K. We find ?_a(T) = A+BT+CT², in agreement with Suematsu et. al., except our value of A is ～200 times smaller implying fewer defects. In MC₈ compounds R_H at 5K is positive and increases linearly with magnetic field, suggesting a complex Fermi surface. On the other hand, R_H for RbC₂₄ is negative and field-independent but the magnitude is inconsistent with a simple one-carrier model (assuming one free electron per Rb).     

Effective Hamiltonian for polyatomic linear molecules

The leading terms of an effective Hamiltonian for a linear molecule in a given vibrational state are presented up to κ¹⁰T_v order of magnitude, whereby higher-order l-dependent terms such as $\text{H}\text{?}{}_{12.0}$, $\text{H}\text{?}{}_{8.0}$, and $\text{H}\text{?}{}_{8.2}$ have been neglected because in spectroscopic application they are of minor importance. This Hamiltonian therefore includes all those l-type interactions which could contribute to the fitting procedure, within a vibrational state where one or more bending vibrations are excited.