Heat capacity of a five-coordinated iron(III) complex,chlorobis(N,N-dimethyldithiocarbamato) iron(III), between 0.4 and 300 k: New finding of a magnetic phase transition

The heat capacity of the title complex, Fe[S₂CN(CH₃)₂]₂Cl, has been measured between 0.4 and 300 K. A λ -type phase transition with a small shoulder arising from magnetic ordering was found at (0.609 ± 0.005) K. The character of the ordered phase has been suggested to be ferromagnetic on the basis of comparison between the methyl- and ethyl-homologues. The magnetic hyperfine structure of the Mössbauer spectra and the line broadening due to electronic relaxation effects at 1.2 K hitherto reported are concluded to result from a critical slowing-down when the magnetic transition temperature is approached from the high-temperature side. A Schottky-type anomaly arising from the zero-field splitting of a single ferric ion was observed around 2 K. The excess entropy beyond the lattice contribution at low temperatures amounts to (14.05 ±0.27) J K^?1mol^?1, which cannot be accounted for solely by the magnetic entropy of Rln 4 (= 11.53 JK^?1mol^?1) for the intermediate spin of $\text{S =}\text{3}\text{2}$. Two possibilities concerning additional conntribution have been discussed; one is a mixing of spin species of $\text{S =}\text{5}\text{2}$ and the other is a tunnel-splitting of the rotational levels of four methyl-constituents. The present study cannot give a definite conclusion as to the existence of dimeric units suggested from Mössbauer spectroscopy.     

Heat capacity of a five-coordinated iron(III) complex with spin S = 32, bromobis(N,N-diethyldithiocarbamato)iron(III), between 0.4 and 300 K

Heat capacity measurements have been made for six kinds of specimens prepared by different methods. Among them, Sample A exhibited a A-type ferromagnetic pahse transition at 1.347 K and a Schottky-type anomaly due to the zero-field splitting around 9K. The total entropy and enthalpy were (11.05 ± 0.04) J K^?1mol^?1 and (97.0 ± 0.4) J mol^?1, respectively. Sample B exhibited a Sehottky-type anomaly around 0.4 K due to the ferro-magnetic dimeric coupling with $\text{J}{}_{\mathrm{D}}\text{k}\text{= + 0.30}\text{K}$ as well as the Schottky-type anomaly at 9K. The total magnetic entropy and enthalpy were (11.45 ± 0.03) JK^?1 mol^?1 and (93.8 ± 0.8) J mol^?1, respectively. The remaining samples are simple mixtures of the λ-type modification and the dimeric modification. Irrespective of the magnetic behavior at low temperatures, all the samples showed a non-magnetic first-order phase transition around 270 K. The heat capacity and entropy of this phase transition have been accounted for in terms of the Frenkel theory of heterophase fluctuation. Construction of an adiabatic-type calorimeter workable between 1.5 and 393 K has been also presented.     

Heat capacity of a five-coordinated iron(III) complex,iodobis (N,N-Dimethyldithiocarbamato) iron(III), between 0.4 and 300 K

The heat capacity of iodobis (N, N-dimethyldithiocarbamato)iron(III) has been measured between 0.4 and 300 K. Based on the heat capacity and entropy at low temperatures it was found that the present sample consists of a mixture of monomer (ca. 40%) and dinier (ca. 60%); the former brings about a λ-type phase transition from an antiferromagnetic to a paramagnetic state at T_N = (1.65 ±0.04) K while the latter exhibits a Schottky-ype anomaly due to antiferromagnetic dimeric coupling, the effect of which becomes dominant below ca. 0.7 K. The zero-field splitting parameter of a single ferric ion was estimated to be $\text{D}\text{k}\text{=}\text{D}{}_{\mathrm{D}}\text{k}\text{= 14 K}$ for the monometer and the dimer, while the dimeric coupling constant was $\text{J}{}_{\mathrm{D}}\text{k}\text{= ?0.15 K}$. The entropy at low temperatures cannot be accounted for solely by the spin manifold. Additional contribution from a tunnel-splitting of the rotational levels of four constituent methyl-groups has been discussed. In this case, the level splitting of the ground state is 2.5 J mol^?1 and the barrier height of hindering potential is 2.3 kJ mol^?1.     

Heat capacity and phase transition of a five-coordinated antiferromagnet,IODOBIS (N,N-diethyldithiocarbamato) iron (III), in the temperature range from 0.4 TO 300 K

The heat capacity of iodobis (N,N-diethyldithiocarbamato) iron (III) has been measured between 0.4 and 300 K. A phase transition from an antiferromagnetic to a paramagnetic state was found at T_N = (1.937 ± 0.010) K, and a Schottky-type anomaly arising from a zero-field single ion splitting was observed around 12 K. The total magnetic entropy and enthalpy, including the phase transition and the Schottky-type anomaly, are 11.36JK^?1mol^?1 and 134.5 J mol^?1, respectively. The entropy is approximately equal to Rln 4 ( = 11.53 JK^?1mol^?1), confirming that the spin manifold is really a quartet. The entropy and enthalpy due to the phase transition are estimated to be (5.57±0.01)JK^?1mol^?1 and (13.2±0.05)Jmol^?1, respectively. The entropy and enthalpy above t_n are quite large, as in the case of the related compound chlorobis (N,N-diethyldithiocarbamato) iron (III). This fact suggests that the present complex may be considered to have a two-dimensional type of magnetic structure from a thermodynamic point of view. A correlation diagram between the transition entropy and energy is proposed, this being a diagnostic for the determination of the magnetic dimensionality.     

Electron paramagnetic resonance and thermodynamic measurements on a phase transition of tris(acetylacetonato)aluminium(III) and tris(acetylacetonato)cobalt(III)

Pure Al(acac)₃ and Co(acac)₃ exhibit a first-order phase transition at 140 ± l K and 30 ± l K respectively. At the phase transition the unit cell triples, but the space-group remains P₂₁c. The unit cell dimensions at 90 K and at room temperature in parenthesis are: a = 41.17 (14.07) Å; $\text{b = 7.42 (7.57)}\text{A}\text{?}\text{;}$$\text{c = 22.70 (23.20)}\text{A}\text{?}\text{; β = 135.7 (135.8)}$. From epr measurements on Cr doped Al(acac)₃ and Co(acac)₃ it appeared that at the phase transition the molecules in the lattice are rotated over small angles towards new orientations. The paramagnetic parameters showed small deviations from those at room temperature, except for the rhombic parameter E. By calorie methods the transition enthalpy of Al(acac)₃ was determined to be 36.8 ± 0.4J mol^?1. From the T, X phase diagram of the binary system Al(acac)₃-Co(acac)₃ as determined by means of epr measurements for Co(acac)₃ a transition enthalpy of 17.4 ± 4.8J mol^?1 was estimated. The use of a paramagnetic ion as a probe for solid-solid phase transitions may have conceivable wider applications.     

Heat capacity of a cubane-tetramer, [Ni(OCH3) (SAL) (CH3OH)]4, between 0.4 AND 288 K: spin-spin interactions and tunnel-splitting of the internal rotation of methyl-groups2

The heat capacity of a cubane-tetramer, tetra-μ₃-methoxy-tetrakis [salicylaldehydato (methanol) nickel (II)] (abbreviated as [Ni(OCH₃) (SAL) (CH₃OH)]₄), has been measured from 0.4 to 288 K. A broad peak centered at 0.85 K was observed. Subtraction of the lattice heat capacity from the observed one brought about another broad peak centered around 13.5 K. The magnetic anomaly is accounted for by a nearest-neighbor intracluster ferromagnetic exchange interaction characterized by $\text{J}\text{k}\text{= 3.8 K}$ and a single-ion zero-field splitting due to biaxial crystalline anisotropy$\text{(}\text{D}\text{K}\text{= 3.8 K}$ and$\text{E}\text{k}\text{= 1.9 K).}$ The tunnel-splitting of the ground vibrational-rotational state is δ = 2.4 J mol^?1, which corresponds to a potential barrier of V₀ = 2.3 kJ mol^?1 when a three-fold symmetry of a methyl-rotator is assumed. Comparison of the heat capacities between the present compound and a similar cubane-tetramer, [Ni(OCH₃) (acac) (CH₃OH)]₄, indicates that among eight methyl-groups the four belonging to methoxy-ligands are concerned with the tunnel-splitting at low temperatures.     

Calorimetric study of proton ordering in hexagonal ice catalyzed by hydrogen fluoride

Heat capacities of hexagonal ices doped with 2.6, 26 and 260 m mol dm^?3 HF were measured with an adiabatic calorimeter. The HF doping accelerated proton ordering which has been known to take place sluggishly around 100 K. The ice containing 26 m mol dm^?3 HF showed the largest excess entropy ((0.102±0.01) J K^?1 mol^?1) and the shortest relaxation time. The relaxation time at 90 K was about $\text{1}\text{30}$ of that of the pure ice I_h at the same temperature. The activation enthalpies obtained were the same for all of the doped ices, (23.5±2.0) J mol^?1, which is approximately equal to the activation energy of the mobility of the Bjerrum L-defect.     

Heat capacity of [Ni(OCH3)(acac)(CH3OH)]4 from 0.4 to 285 K: Spin interaction and tunnel-splitting of internal rotation of methyl group

The heat capacity of the tetranuclear nickel cluster complex, tetrakis [μ₃-methoxo-2,4-pentanedionato (methanol) nickel (2)], has been measured from 0.4 to 285 K. Contrary to the previous prediction by Bertrand et al.[6], that this complex exhibits an intercluster ferromagnetic spin coupling, the present heat capacity measurement shows no indication of the spin-ordering effect caused by the intercluster interaction at least down to 0.4 K. Instead, a heat capacity anomaly centered around 1.5 K with a shoulder at 0.5 K has been observed. This anomaly is well accounted for in terms of both a level splitting of the ground S = 4 state due to a uni-axial crystalline anisotropy and a tunnel-splitting of the rotational levels of methyl groups. The intracluster spin exchange constant J and the single-ion zero-field splitting parameter D are determined to be $\text{J}\text{hc}\text{= 7.0 cm}{}^{\mathrm{?1}}$ and $\text{D}\text{hc}\text{= 3.65 cm}{}^{\mathrm{?1}}$ (h being the Planck constant and c the speed of light in a vacuum). The temperature dependence of the effective Bohr magneton [6] is also satisfactorily accounted for on the basis of this model. The tunnel-splitting δ of the lowest rotational level of the four methyl groups belonging to methoxides is estimated to be $\text{δ}\text{hc}\text{= 0.4–0.7 cm}{}^{\mathrm{?1}}$ and the corresponding potential barrier V_o is found to be V_o = 1.9–1.5 kJmol^?1.     

Particle-hole states in 42K studied by the 44Ca(d, α)42K reaction

The ⁴⁴Ca(d, α)⁴²K reaction was studied at a bombarding energy of 11 MeV using a broadrange magnetic spectrograph and solid-state detectors. About thirty energy levels were identified in ⁴²K, up to an excitation energy of 3.5 MeV. Excitation functions corresponding to some of the low-lying energy states of ⁴²K were measured in the incident energy range from 10.4 to 11.6 MeV. Angular distributions of the α-particle groups corresponding to the excitation of about twenty energy levels in ⁴²K have been measured. DWBA calculations were performed and L-values for most of the above transitions were deduced. The results were compared with previous information and possible spin and configuration assignments are proposed for some of the states. Centroids of states interpreted as belonging to the (1d_{$\text{3}\text{2}$}^?1)_p (1f_{$\text{7}\text{2}$}³)_n, (2s_{$\text{1}\text{2}$}^?1)_p (1f_{$\text{7}\text{2}$}³)_n and the (1d_{$\text{3}\text{2}$}^?1)_P (1d_{$\text{3}\text{2}$}^?1 1f_{$\text{7}\text{2}$}⁴)_n configurations were found to be in good agreement with calculations based on the weak-coupling model.     

The axial anomaly for spin 32 fields

The axial anomaly for a Majorana spin $\text{3}\text{2}$ loop with external gravitons in supergravity is ?_μJ^μ₅ = (192π²)^??^αβ?σR?σ^μνRμναβ. This is twice the value of the corresponding anomaly for a Dirac spin $\text{1}\text{2}$ loop.     

On the phase transition in α-NH4HgCl3, a two-dimensional version of ammonium chloride

Heat capacity of α-NH₄HgCl₃ crystal has been measured with an adiabatic calorimeter from 11 to 300 K. A sharply peaked anomaly due to an order-disorder change of the ammonium ions was found at 54.97 ± 0.04 K. The entropy and enthalpy changes were estimated to be ΔS = 5.2 ± 1.0JK^?1 mol^?1 and ΔH = 342 ± 65 J mol^?1. In accordance withthe structural two-dimensionality of α-NH₄HgCl₃ crystal, Onsager's solution of the two-dimensional Ising model was used in calculation of the transition temperature. On the assumption that the octopole-octopole interaction is responsible for the ordering of the ammonium ions in the present crystal and in ammonium chloride, the calculation gives 74.44 K for the transition temperature. Several possibilities were discussed for explaining the remaining discrepancy between the observed and calculated transition temperatures.     

Electronic transition moments between excited singlet states of the H2 molecule

The twelve transition moments which connect each of the three ¹Σ_g⁺ states EF, GK, and $\text{H}\text{H}$ with the three ¹Σ_u⁺ states B,B′, $\text{B″}\text{B}$ and with the state C¹Π_u were computed in the range of internuclear distances 1.25 ≤ R ≤ 15 a.u. using accurate electronic wavefunctions. The relative phases of the wavefunctions, which determine the signs of the transition moments, were consistently defined at all R values. The strong R dependences of the transition moments reflect the R-dependent changes in electronic character of the states involved in these transitions. At large R values the ¹Σ_g⁺-¹Σ_u⁺ transition moments are dominated by the two-electron charge resonance in the ionic configuration H⁺ + H^? whose transition moment is $\text{M(R) ? R}$.     

Heat capacities of the electron acceptor 7,7,8,8-tetracyano- quinodimethane (TCNQ) and its radical-ion salt NH4(TCNQ) showing spin-Peierls transition

Heat capacities of the electron acceptor 7,7,8,8-tetracyanoquinodimethane (TCNQ) and its radical-ion salt NH₄-TCNQ have been measured at temperatures in the 12-350 K range by adiabatic calorimetry. A λ-type heat capacity anomaly arising from a spin-Peierls (SP) transition was found at 301.3 K in NH₄-TCNQ. The enthalpy and entropy of transition are Δ_trsH=(667±7) J mol⁻¹ and Δ_trsS=(2.19±0.02) J K⁻¹ mol⁻¹, respectively. The SP transition is characterized by a cooperative coupling between the spin and the phonon systems. By assuming a uniform one-dimensional antiferromagnetic (AF) Heisenberg chains consisting of quantum spin (S=1/2) in the high-temperature phase and an alternating AF nonuniform chains in the low-temperature phase, we estimated the magnetic contribution to the entropy as Δ_trsS_mag=0.61 J K⁻¹ mol⁻¹ and the lattice contribution as Δ_trsS_lat=1.58 J K⁻¹ mol⁻¹. Although the total magnetic entropy expected for the present compound is R ln 2 (=5.76 J K⁻¹ mol⁻¹), a majority of the magnetic entropy (∼4.6 J K⁻¹ mol⁻¹) persists in the high-temperature phase as a short-range-order effect. The present thermodynamic investigation quantitatively revealed the roles played by the spin and the phonon at the SP transition. Standard thermodynamic functions of both compounds have also been determined.     

Phonon coupled cooperative low-spin 1A1high-spin 5T2 transition in [Fe(phen)2(NCS)2] and [Fe(phen)2(NCSe)2] crystals

Heat capacities of [Fe(phen)₂(NCS)₂] and [Fe(phen)₂(NCSe)₂] were measured between 13⁵ and 375 K. A heat capacity anomaly due to the spin-transition from low-spin ¹A₁ to high-spin π₂ electronic ground state was found at 176·29 K for the SCN-compound and at 231·26 K for the SeCN-compound, respectively. Enthalpy and entropy of transition were determined to be ΔH = 8·60 ± 0·14 kJ mol^?1 and ΔS = 48·78 ± 0·71 J K^?1 mol^?1 for the SCN-compound and ΔH = 11·60 ± 0·44 kJ mol^?1 and ΔS = 51·22 ± 2·33 J K^?1 mol^?1 for the SeCN-compound. To account for much larger value of ΔS compared with the magnetic contribution, we suggest that there is significant coupling between electronic state and phonon system. We also present a phenomenological theory based on heterophase fluctuation. Gross aspects of magnetic, spectroscopic, and thermal behaviors were satisfactorily accounted for by this model. To examine closely the transition process, infrared spectra were recorded as a function of temperature in the range 4000 ? 30 cm^?1. The spectra revealed clearly the coexistence of the ¹A₁, and the ⁵T₂ ground states around T_c.     

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.     

The ground-state rotational band in 159Tb

162 MeV ⁴⁰Ca ions have been used to Coulomb excite the ground-state band of ¹⁵⁹Tb up to spin $\text{25}\text{2}$. Lifetimes for levels up to spin $\text{25}\text{2}$ have been determined with DSA and recoil distance methods. Multipole mixing ratios for several cascade transitions were extracted from an analysis of γ-ray angular correlation data. Reduced transition probabilities thus deduced in a model-independent way were found to be in agreement with the rotational model with Q₀ = 7.41 ± 0.06 e · b and g_K?g_R = 1.377 ± 0.010.     

The reactions 2H(40Ar,n)41K and 2H(40Ar,p)40Ar and electromagnetic decays of low-lying states in 41K and 41Ar

The γ-decay of states in ⁴¹K and ⁴¹Ar populated in the reactions ²H(⁴⁰Ar, n)⁴¹K and ²H(⁴⁰Ar, p)⁴¹Ar has been investigated at a bombarding energy of 56 MeV. Using the Doppler shift attenuation method and three different stopping materials, mean lifetimes were determined for the states in ⁴¹K at 980 keV (0.5±0.2 ps), 1560 keV (0.6_?0.2^+0.3ps), 1698 keV (0.1_?0.1^+0.2ps), 2144 keV (0.8_?0.2^+0.3ps) and in ⁴¹Ar at 1354 keV (0.664_?0.08^+0.09ps). Shell-model calculations have been performed for the positive parity states in ⁴¹K using a model space of a proton hole in the $\text{1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ orbits and two neutrons in the $\text{1}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ orbit. The resulting excitation energies and electromagnetic properties of the low-lying states are in good agreement with experiment. An empirical value for a [Y₂s]₁ contribution in the effective M1 operator is obtained.     

Spin waves in an Invar alloy (Fe0.65Ni0.35)

The spin wave dispersion relation in an Invar alloy Fe_0.65Ni_0.35 has been measured at 4.2 K in the [111] direction by neutron inelastic scattering.Well defined magnon groups have been observed up to an energy transfer of about 80 meV. The spin wave dispersion is well described by ?ω=Dq²(1?βq²) with $\text{D=143}\text{meV}\text{A}\text{?}$ and $\text{β=0.12}\text{A}\text{?}{}^2$. The value of D is in accord with the value extrapolated from other neutron scattering results at higher contents of Ni and disagrees with spin wave resonance results.No trace of γ-iron type antiferromagnetic order could be detected at 4.2 K in this alloy by elastic neutron scattering measurements.     

Spin selectivity of the polarised (d, 2p) reaction

Tensor polarisation observables in intermediate energy $\text{(}\text{d}\text{, 2}\text{p}\text{)}$ charge exchange on 0⁺ nuclei are investigated. It is shown that for small excitation energies of the di-proton the polarisation can help to distinguish between 0^?, 1^? and 2^? final nuclear states produced through ΔL = 1, ΔS = 1 transitions. The information to be obtained is similar to that inherent in $\text{(}\text{p}\text{,}\text{n}\text{)}$ spin transfer experiments but the deutron-induced experiments should have much higher efficiency.