A contrastive study on the influences of radial and three-dimensional satellite gravity gradiometry on the accuracy of the Earth's gravitational field recovery

The accuracy of the Earth’s gravitational field measured from the gravity field and steady-state ocean circulation explorer(GOCE),up to 250 degrees,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij from the satellite gravity gradiometry(SGG) are contrastively demonstrated based on the analytical error model and numerical simulation,respectively.Firstly,the new analytical error model of the cumulative geoid height,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij are established,respectively.In 250 degrees,the GOCE cumulative geoid height error measured by the radial gravity gradient V zz is about 2 1/2 times higher than that measured by the three-dimensional gravity gradient V ij.Secondly,the Earth’s gravitational field from GOCE completely up to 250 degrees is recovered using the radial gravity gradient V zz and three-dimensional gravity gradient V ij by numerical simulation,respectively.The study results show that when the measurement error of the gravity gradient is 3×10 12 /s 2,the cumulative geoid height errors using the radial gravity gradient V zz and three-dimensional gravity gradient V ij are 12.319 cm and 9.295 cm at 250 degrees,respectively.The accuracy of the cumulative geoid height using the three-dimensional gravity gradient V ij is improved by 30%-40% on average compared with that using the radial gravity gradient V zz in 250 degrees.Finally,by mutual verification of the analytical error model and numerical simulation,the orders of magnitude from the accuracies of the Earth’s gravitational field recovery make no substantial differences based on the radial and three-dimensional gravity gradients,respectively.Therefore,it is feasible to develop in advance a radial cold-atom interferometric gradiometer with a measurement accuracy of 10 13 /s 2-10 15 /s 2 for precisely producing the next-generation GOCE Follow-On Earth gravity field model with a high spatial resolution.     

DPAC study of radiation damage in178W recoil implanted silicon

The annealing behaviour of radiation damage in¹⁷⁸W recoil implanted n-type Si is studied from 295 to 641 K by the differential perturbed angular correlation method (DPAC), using¹⁷⁸Hf as probe nuclei for the first time. Preliminary results suggest that oxygen-vacancy (O-V) pairs are observed, which give rise to a quadrupole interaction characterized by |V _zz|=5.41×10¹⁸ V/cm² (v _Q=2550 MHz). The probe nuclei also experience an electric field gradient (EFG) due to distant defects.     

Static electric quadrupole interaction of Ta- and Hf-ions in barium and lead titanate

The static electric quadrupole interaction of¹⁸¹Ta and¹⁷⁸Hf in polycrystalline barium and lead titanate at the site of titanium has been measured using time differential PAC and the Mössbauer effect. The electric field gradients (EFG) at room temperature at the¹⁸¹Ta nucleus are ¦V _zz¦=(3.6±0.2)·10¹⁷V/cm² in BaTiO₃ and ¦V _zz¦=(14.6±0.6)·10¹⁷ V/cm² in PbTiO₃. The temperature dependence of the quadrupole interaction has been studied giving the following EFG values: ¦V _zz¦=(2.4±0.2)·10¹⁷ V/cm² in the monoclinic and ¦V _zz¦=(1.1±0.3)·10¹⁷ V/cm² in the rhomboedral phase of BaTiO₃, and ¦V _zz¦=(15.7±0.6)·10¹⁷ V/cm² for¹⁸¹Ta/PbTiO ₃ at 77 °K. The EFG of¹⁷⁸Hf in PbTiO₃ has been derived from a Mössbauer effect experiment to beV _zz=+(10.7±0.5)·10¹⁷ V/cm². The results are compared with EFG's calculated in a point charge model and with experimental EFG's measured at⁴⁴Sc and⁵⁷Fe in the same titanates by other authors. Contributions of covalent bonds to the effective EFG's in perovskit crystals are discussed.     

Magnetic and electric hyperfine interactions of181Ta implanted in thulium

The magnetic and electric hyperfine interaction at the site of dilute¹⁸¹Ta impurities in the rare earth metal Tm has been investigated as a function of temperature by TDPAC measurements. The samples were prepared by ion implantation of radioactive¹⁸¹Hf. In the paramagnetic phase between 100 K and 700 K the electric fieldgradient is a linear function of temperature: V_zz(T)=V_zz(O)·(1-A·T) with A=4.6·10^?4K^?1 and V_zz(293K)=6.4 (4)·10¹⁷v/cm². The TDPAC spectrum observed at 4.2 K reflects the 4 magnetically non-equivalent sites for an impurity in magnetically ordered Tm. The relative values and amplitudes of the corresponding 4 magnetic hyperfine fields are consistent with the predictions of the RKKY theory.     

Hyperfine interaction of ZrO2 — Tetragonal phase

The quadrupole hyperfine interaction of the tetragonal phase of the zirconium oxide has been measured at 1523 K using the time-differential perturbed angular correlation technique. The electric field gradient at zirconium sites was determined to beV _zz =(17.5±0.4)·10¹⁷ Vcm⁻² and axially symmetric.     

XRD, TDPAC and LAPW study of Hf10B2 under high pressure

The crystallographic structure and electronic properties of Hf¹⁰B₂ were studied as a function of pressure by combining X-ray diffraction measurements with full potential linearized augmented plane wave (LAPW) calculations. No phase transition was observed up to a pressure of 30.8 GPa, with a total volume contraction of V/V ₀?=?0.85 and a bulk modulus value of B ₀?=?232 ±13 GPa. The calculated V _zz value at the hafnium site is linearly increasing as a function of the pressure induced volume reduction, while the V _zz value at the boron site stays almost zero. The major contribution to the V _zz value at the hafnium site comes from a p–p contribution next to the probe nucleus, with a relatively large d–d contribution of about 25%. This unusual large d–d contribution arises from the hafnium p–d electrons coupling.     

The magnetic hyperfine field and the electric field gradient at181Ta impurities in Gd metal

The magnetic hyperfine fieldH _hf and the electric field gradientV _zz at¹⁸¹Ta impurties in metallic Gd were determined by time differential perturbed angular correlation measurements with the 133 keV K-conversion electron 482 keV -cascade of¹⁸¹Ta. The sources for these measurements were prepared by implantation of radioactive¹⁸¹Hf ions into Gd. The results are: |H _hf(TaGd; 77 K)|=285(14)kG, and |V _zz(TaGd; 330 K)|=5.32(15)·10¹⁷V/cm². The value ofH _hf fits well into the systematics for 5d impurities in Gd and indicates a positive core polarisation contribution, which is expected if the conduction electrons of Gd have to a large extent d-character. The electric field gradients of the 5d impurities in Gd are not consistent with a proportionality between the ionic and the electronic contribution.     

The quadrupole interaction of100Rh in various intermetallic compounds of palladium

The nuclear quadrupole interaction of the 75 keV excited state of¹⁰⁰Rh in the ordered intermetallic compounds PdHg, PdPb₂ PdSb and PdTe was measured. Using an estimate for the nuclear quadrupole moment of the 75 keV state in¹⁰⁰Rh and point ion lattice sums for the lattice electric field gradient (EFG) at the Rh site, the electronic contributionV _zz ^el to the total EFG was derived.V _zz ^el was found to be correlated with the average valence electron concentration in the compounds studied. In the case of PdPb₂, the temperature dependence of the quadrupole interaction was also studied and found not to follow theT ^3/2 rule which is observed in virtually all pure noncubic metals.Work partially supported by U.S. Department of Energy.     

Electric quadrupole nuclear orientation of182Ta as graphite intercalation compound TaCl5

Nuclear orientation of¹⁸²Ta achieved by electric quadrupole interaction in TaCl₅ molecules intercalated in oriented graphite crystals has been observed. Assuming the electric field gradient V_zz along the c-axis and proper intercalation yields V_zz=+0.32 (4)×10¹⁸V/cm². Other possibilities and sources of reduction of the nuclear orientation effect are considered.     

Quadrupole interaction studies of Hg in Sb

Time differential perturbed angular correlation and nuclear orientation studies of the electric quadrupole interaction for Hg in Sb have been performed. The effective field gradients |V _zz ^eff (HgSb)|=1.43(18)×10¹⁷V cm^–2 at room temperature andV _zz ^eff (HgSb)=+1.8(2) × 10¹⁷V cm^–2 below 0.05 K have been derived. These two values are no indication for an anomalous temperature dependence of the effective field gradient for Hg in Sb. The value of the electric field gradient fits well into the systematics for Hg in other hosts. It is shown that the electronic enhancements of the field gradients are correlated to the valence of the impurities and are rather insensitive to the host properties.On leave of absence from: University of Lisboa, Portugal     

High Pressure Study of HfNi Crystallographic and Electronic Structure

The crystallographic structure and electronic properties of HfNi were studied as a function of pressure by combining X-ray diffraction results with the full potential linearized augmented plane wave (LAPW) calculations. No phase transition was observed up to a pressure of 35.3 GPa, with a total volume contraction of V/V ₀ = 0.85, a bulk modulus value of B ₀ = 52 ± 3 GPa and B ₀ ^′ = 1.29 ± 0.26. The calculated linear increase in the V _zz value as a function of the pressure induced volume reduction at the hafnium site was attributed mainly to the p–p contribution, while in the nickel site, a non negligible d–d contribution to V _zz is also observed, and attributed to the high 3d-partial DOS near the nickel nucleus. Based on the total electronic DOS at E _Fermi calculated for 0 K (N(E ⁰ _Fermi)), a value of 6.85 and 5.03 (mJ/mol/k²) was calculated for the band contribution (γ _band) to the electronic specific heat coefficient (γ) at a pressure of 0 and 35.3 GPa, respectively.     

The electric field gradient at188Os nuclei in Re metal

The electric quadrupole interaction of the first excited 2⁺ state of¹⁸⁸Os in hexagonal rhenium metal was investigated by means of the time-differential perturbed angular correlation technique. From the observed quadrupole frequencyV _Q=170(7) MHz, we deduce an electric field gradient value of |V_zz|=4.77(23)·10²¹V/m² for the system OsRe. The half-life of the 2⁺ state was measured to be 641(4)ps.     

Synthesis and Mössbauer Study of Maghemite Nanowire Arrays

An analytical formula for the distance dependence of the electric field gradient produced by a Gaussian charge density distribution n(r) is derived. This charge density is displaced by z ₀ along the z-axis. The system has cylindrical symmetry; hence it suffices to calculate V _zz(0). It turns out that V _zz(0) is always smaller than the value with the total charge shrunk into a point. For distances larger than about four times the Gaussian width σ the expression approaches the point charge value. For z₀ → 0, i.e. a spherically symmetric charge distribution around the origin, V _zz(0) vanishes quadratically, as required by symmetry. A slab-wise calculation in cylindrical coordinates is presented which shows the contribution to V _zz(0) for infinitesimally thin slabs as a function of distance from the origin. This analytical formula allows for a fast computation of electric field gradients from a given charge density distribution for Gaussian expansions of Slater-type orbitals. An example for a hydrogen atom will be given.     

TDPAC studies on181Hf implanted into diamond

¹⁸¹Hf ions were implanted at (900±10)K into (100) cleaved single crystal diamonds. After subsequent annealing residence site parameters were determined for the implanted ions employing the (133 keV)–(482 keV) cascade in¹⁸¹Ta in TDPAC technique. Fractions of 5% each were determined that experience axially symmetric electric field gradients (EFG) V_zz(1)=5.5×10¹⁷ V cm^–2 and V_zz(2)=9.6×10¹⁷ V cm^–2, respectively. The bulk of the ions are strongly disturbed by still higher electric field gradients.     

Structural phase transitions in Pd0.8 Si0.2 and Pd0.75 Si0.20 Ag0.05 alloys observed by pac

The phase transition in the alloys Pd_0.8 Si_0.2 and Pd_0.75 Si_0.20 Ag_0.05 have been investigated through the quadrupole interaction of¹¹¹Cd impurities. The quadrupole interactions were measured by means of the TDPAC technique from room temperature up to about 870 K. The variation of the quadrupole interaction with temperature in the alloy PdSiAg shows aT ^3/2 dependence below and above 629 K, with coefficientsB=5.43(25)·10⁻⁵ K^−3/2 andB=3.70(15)·10⁻⁵ K^−3/2, respectively. This demonstrates that the alloy undergoes a phase transition around 629 K. The existence of two electric field gradients observed in the alloy PdSi,V _zz (1)=3.47(54)·10¹⁷ V/cm² andV _zz (2)=2.29(36)·10¹⁷ V/cm², indicates that there are two different¹¹¹Cd sites. The corresponding fractionsf ₁ andf ₂ strongly depend on temperature. Below 520 K, most¹¹¹Cd nuclei are subject to the higher EFGV _zz (1) (f ₁≈70%), whereas above 520 Kf ₁ falls rapidly to zero andV _zz (2) becomes dominant. The temperature dependences of thef ₁ andf ₂ reveal a picture of the phase transition between the two crystal structures.     

Hyperfine interactions of111Cd impurities in Cr2O3

The electric and (antiferro-)magnetic hyperfine interaction of¹¹¹Cd in α-Cr₂O₃ after¹¹¹In implantation was studied via PAC. Two fractions with axially symmetric electric field gradients were observed having antishielding factors of V_zz/V_zz ^pc=79(12) and 106(16), respectively. From the line broadening of the Fourier components of the first fraction its supertransferred magnetic field was estimated as B_loc (20 K)≤0.41 T, about two orders of magnitude smaller than for substitutional¹¹¹Cd in NiO and CoO.     

Orientation of the oxygen-induced non-axially symmetric electric field gradient at181Ta in Ta

The interaction of dilute¹⁸¹Ta in Ta with interstitial oxygen has been investigated via the γ-γ TDPAC-technique applied to the 482 keV state in¹⁸¹Ta. The trapping of Oxygen leading to a quadrupole interaction frequency ν_Q=580(5) MHz with an asymmetry parameter of η-0.37 (1) has been observed after melting the radioactive parent isotope¹⁸¹Hf with Ta. The temperature dependence of the quadrupole interaction frequency between 17 K and 293 K was found to be very weak whereas η varied by about 10%. In a single crystal experiment the orientation of the three principal axes of the electric field gradient leading to ν_Q was determined. The V_zz-axis points in <110>, the V_yy-axis in <100> and the V_xx-axis in <110> direction. These results can be understood in the charge cloud model, suggested by Wrede et al. /1/ for a similar situation found in the HfNb system.     

Determination of the (Na) Sternheimer antishielding factor by Na NMR spectroscopy on sodium oxide chloride, Na3OCl

The (Na⁺) Sternheimer antishielding factor γ_∞ (Na⁺) was determined by ²³Na NMR spectroscopy on sodium oxide chloride, Na₃OCl. The quadrupolar coupling constant of the sodium ion in Na₃OCl was determined to QCC=11.34 MHz, which presents the largest coupling constant of a sodium nucleus observed so far. Applying a simple point charge model, the largest principal value of the electric field gradient at the sodium site was calculated to V_zz=−6.76762·10²⁰ V/m². From these values we calculated the (Na⁺) Sternheimer antishielding factor to γ_∞ (Na⁺)=−5.36. In sodium oxide, Na₂O, we observed an isotropic chemical shift of δ_CS=55.1 ppm, referenced to 1 M aqueous NaCl (δ=0 ppm).