Numerical solutions for single passage NMR on nuclei experiencing small electric quadrupole interactions

The adiabatic rapid-passage NMR equations are numerically solved for a small additional quadrupole interaction. The full range of the ratio of rf interaction strengths to quadrupole interactions strengths is considered for any electric field gradient orientation. The results forI=1 are particularly easy to describe and are used to predict the single-passage results for different orientations of the electric field gradient with respect to the static magnetic field.     

The extraction of weak nuclear electric quadrupole splittings of dilute impurities in ferromagnets using modulated Adiabatic Passage NMR/ON

A novel extension of the Single or Adiabatic Fast Passage NMR/ON technique is described. Its principal advantages in extracting the mode magnitudes and distribution widths of weak nuclear electric quadrupole splittings much less than the magnetic inhomogeneous broadening are its simplicity and generality requiring no assumptions on the degree of adiabaticity of the nuclear spin motion during sweep through the quadrupolar split subresonances. The technique is applied to a concentrated single crystal sample of⁶⁰CoFe which failed to yield a well resolved mid passage signal to conventional single passage NMR/ON. The result is an asymmetric frequency distribution of quadrupole frequencies with a mode value of P=3e²qQ/4I (2I-1)=+4.5 ±1.0 kHz and half maxima of +2.5 kHz and +7.0 kHz.     

Studies of weak electric quadrupole interaction in57,60CoFe using modulated adiabatic passage on oriented nuclei

The electric quadrupole interactions at⁵⁷Co and⁶⁰Co in co-diffused^57,60CoFe single crystal have been measured using Modulated Adiabatic Passage on Oriented Nuclei (MAPON). The quadrupole splittings Δν_Q<100> are + 18(2) kHz for⁵⁷Co and +9(2) kHz for⁶⁰Co, corresponding to a principal electric field gradient (efg) tensorV _zz =2.0(5)×10¹⁹ Vm⁻² and 2.5(6)×10¹⁹ Vm⁻², respectively, in broad agreement with previous MAPON results for CoFe. The distributions of the efg’s are very similar for the two isotopes, verifying that previously reported differences in⁵⁸CoFe and⁶⁰CoFe could be attributed to different host preparations. The measurement of such weak efg’s which are not spectroscopically resolved, allows determination of new nuclear electric quadrupole moments, not accessible by other techniques. Applications to other systems are discussed.     

铜铁稀磁合金中铁磁杂质之间相互作用对低温热电势的影响

本文提出在铜铁稀磁合金中高浓度铁磁杂质之间的相互作用对低温热电势的影响巨大, 基于耦合杂质理论, 得出了高浓度铜铁稀磁合金的热电势在4-100 K的温度范围内随温度变化的理论曲线. 理论曲线与铁杂质浓度含量为0.1%(at) Fe, 0.13%(at) Fe和0.15%(at) Fe原子百分比的铜铁合金热电势实验值符合, 为推动低温铜铁稀磁热电偶的应用提供了理论分析基础.     

Investigation of the nuclear indirect interaction by NMR line shape analysis of single crystal molybdenum

NMR signals of⁹⁵Mo and⁹⁷Mo were determined on single crystals of molybdenum. Their absorptive parts were analysed providing information about the indirect spin-spin interaction in spite of the quadrupole interaction. For the indirect exchange interaction the analysis yields |A _ij |=100Hz±5%. An estimation of the upper limit of the indirect dipole-dipole interaction leads to |B _ij |<15 Hz.     

On the interpretation of nuclear quadrupole interaction data for rare-earth nuclei at low symmetry sites

Expressions are given for all tensor components of the lattice- and 4f-shell electric field gradient contributions at a rare-earth nucleus and the influence of local symmetry is discussed. To demonstrate that a full tensor analysis is essential for monoclinic symmetry, the quadrupole splitting data for¹⁶⁹Tm in Tm₂O₃ are re-analyzed, resulting in significantly different shielding factorsR _Q and .     

Powder MAS NMR lineshapes of quadrupolar nuclei in the presence of second-order quadrupole interaction

We derive a complete analytical solution for the powder magic angle spinning (MAS) nuclear magnetic resonance (NMR) lineshape in the presence of second-order quadrupole interaction, considering a radiofrequency (rf) pulse of finite width, a finite MAS frequency, and a non-zero asymmetry parameter. I_x is calculated using two approaches. The first applies time-dependent perturbation theory in the presence of the rf pulse and stationary perturbation theory (SPT) in its absence. The second is based on the Magnus expansion of the density matrix in the interaction representation during the pulse and SPT in its absence. We solve the problem in the laboratory frame using the properties of the Fourier transform and spin operators. Diagonalisation is not required. Both approaches agree well with each other under all conditions and also with the transition probability approach for the central transition. The Magnus expansion exists at all times and the effect of the non-secular terms is negligible. We describe an analytical method of averaging I_x over the Euler angles and simulate the ¹¹B MAS NMR lineshapes for crystalline and vitreous B₂O₃. A critical analysis is given of all earlier calculations of the MAS NMR lineshape.     

Investigation of impurity diffusion in dilute alloys by nuclear magnetic resonance

The diffusion of Al in a Cu: 3.8 at % Al alloy has been investigated by observing the rotating-frame nuclear magnetic relaxation time T_1π of ²⁷Al as a function of temperature. It is shown that relaxation measurements of the solute atoms in a dilute alloy provide the correlation time of the diffusive motion of these atoms, if quadrupolar interactions form the main contribution to the relaxation time. From the correlation times the Al-diffusion coefficient in the alloy has been determined.     

Temperature dependence of the electric quadrupole interaction at scandium impurities in titanium

Perturbed angular correlation measurements of the electric field gradient at ⁴⁴Sc impurities in Ti metal show a weak dependence on temperature similar to that previously observed in Ta impurities but much weaker than that at Cd impurities in Ti.     

Electric quadrupole interaction of210Po(6+) in Bi single crystal

The electric quadrupole coupling constant of the²¹⁰Po(6⁺) isomer in a Bi single crystal was measured as a function of the temperature using the time-differential perturbed angular correlations technique. The electric field gradient (EFG) for Po in Bi is found to be temperature independent in the range 77–477 K. Using a calculated value of the nuclear quadrupole moment, the magnitude of the EFG is derived, and in turn serves to re-examine the systematics of quadrupole moments of λh ₉ ^2/2 configurations in the lead region.     

Field dependent nuclear spin-lattice relaxation of cobalt impurities in iron single crystals

Nuclear spin-lattice relaxation (NSLR) of guest atoms in a ferromagnetic host metal is studied by means of nuclear orientation of radioactive isotopes at low temperatures. The sample, a ferromagnetic, tron single crystal containing⁵⁸Co or⁶⁰Co impurities, is cooled to about 20 mK and the lattice is warmed up by r.f. heating, whereafter the nuclear polarization is monitored by gamma-ray intensity measurements versus time. The results show a considerable influence of external magnetic fields and, in particular, also isotope effects. These will be discussed on the basis of second-order magnon processes.     

Niobium hydride studied by the electric quadrupole interaction of100Rh

NbH_x (x=0.83, 0.72) was studied between 90K and 450K by observing the quadrupole interaction of¹⁰⁰Rh with the TDPAC method. The transition from a static interaction at low temperatures to the motional narrowing limit in the non-cubic beta phase and the cubic alpha’ phase is well observed.     

Temperature dependence of the electric quadrupole interaction in PbHfO3

The temperature dependence of the Electric Field Gradient (EFG) in PbHfO₃ was studied in the temperature range 25–225°C by the Differential Perturbed Angular Correlation method. In the two anti-ferroelectric phases below 215°C, not too close to either transition temperature, the EFG decreases as the temperature increases toward T_c. Just above T_c an abrupt rise of EFG was observed indicating a critically behaving contribution to EFG. The results are interpreted in terms of a model based on the local static as well as time-dependent changes of the electric environment, at a lattice site. In accord with the predictions of this model the results exhibit qualitatively the P²_s temperature dependence of EFG far from T_c, where P_s is the sub-lattice polarization, while in close proximity to T_c the dominant contribution to EFG is due to the susceptibility X_q connected with the soft-mode fluctuations. The derived critical exponents are in agreement with previous experimental results on related compounds and with theoretical predictions. A hitherto unobserved additional component of V_zz was established, behaving critically at the antiferro-paraelectric transition at 215°C. This new component is interpreted to originate in local fluctuations connected with the central mode.     

Study of the electric quadrupole interaction at Ta impurities in rare earth metal hosts

The time differential perturbed angular correlation technique has been used to measure the electric fieldgradient (EFG) at the site of¹⁸¹Ta impurities in the heavy Rare Earth metals Gd, Tb, Dy, Ho and Er at room temperature. It is found that the ratio α ≡ ¦V _zz ^eff /V _zz ^lat ¦ between the measured EFGV _zz ^eff and the lattice EFGV _zz ^lat , which is known from lattice sum calculations, is in the order of α?300, suggesting that an important contribution to the EFG is due to electrons localized at the impurity. The ratio α is not constant throughout the Rare Earth series. It decreases from Gd to Tb and increases between Tb and Er. This behaviour is compared to the results of a previous investigation with the impurity Cd in the same hosts.     

Temperature dependence of the electric quadrupole interaction at scandium impurities in zirconium and hafnium

The PAC probe⁴⁴Sc was employed to study the magnitude and temperature dependence of the electric quadrupole interaction at the site of the transition metal Sc in the hexagonal host lattices Zr and Hf. In Zr ∼ 100% of the probe atoms were situated on regular lattice sites and a quadrupole interaction frequency of υ_Q=7.8(1)MHz was measured at room temperature. For Hf the fraction of the probe atoms on regular lattice sites was smaller and a damping of the interaction pattern (υ_Q=9.3(5)MHz at 293 K) could not be excluded. The temperature dependence of the electric field gradient in both host lattices was found to be weak.