Mssbauer spectra of MnFe_(2-2x)Al_(2x)O_4(0≤x≤0.4) ferrites

The effect of non-magnetic Al3+ ion doping on the magnetic properties of MnFe2-2xAl2xO4(0≤x≤0.4) spinel ferrites was studied using Mssbauer spectroscopy measurements at room temperature.From the Mssbauer study,it is observed that the resolved hyperfine sextets are due to the distribution of Fe ions on the two sublattices of the spinel ferrites.The value of the isomer shift obtained from the fitting of the Mssbauer spectra indicates that Fe ions are in +3 state.A paramagnetic doublet is observed at degree of inversion x=0.4,superimposed on the hyperfine sextets,indicating that the super-exchange interaction A-B decreases due to the dilution of sublattice by Al3+ ions.The hyperfine magnetic field decreases at both interstitial sites of tetrahedral(A) and octahedral(B) with the increase in Al concentration.     

Impedance spectroscopy study on Mn_(1+x)Fe_(2-2x)Ti_xO_4(0≤x≤0.5) ferrites

The complex impedance spectroscopy and surface morphology of Mn1+xFe2-2xTixO4(0≤x≤0.5) system,prepared using a conventional solid state reaction technique,were investigated.The impedance spectroscopy measurements were carried out at room temperature in the frequency range of 42-5 MHz.The electrical processes in the samples were modeled in the form of an equivalent circuit made up of a combination of two parallel RC circuits attributed to grain and grain boundaries.The DC conductivity obtained by extrapolation of AC data using impedance spectroscopy and four-probe method increases at 10% doping of Ti ions.The energy-dispersive X-ray(EDX) pattern confirmed the homogeneous mixing of the Mn,Fe,Ti and O atoms in pure and doped ferrite samples.     

Impedance spectroscopy study on Mn1＋xFe2-2xTixO4 （0≤x≤0.5） ferrites

The complex impedance spectroscopy and surface morphology of Mn_1+x Fe_2−2x Ti _x O₄ (0⩽x⩽0.5) system, prepared using a conventional solid state reaction technique, were investigated. The impedance spectroscopy measurements were carried out at room temperature in the frequency range of 42–5 MHz. The electrical processes in the samples were modeled in the form of an equivalent circuit made up of a combination of two parallel RC circuits attributed to grain and grain boundaries. The DC conductivity obtained by extrapolation of AC data using impedance spectroscopy and four-probe method increases at 10% doping of Ti ions. The energy-dispersive X-ray (EDX) pattern confirmed the homogeneous mixing of the Mn, Fe, Ti and O atoms in pure and doped ferrite samples.     

Phase and Structure in the System Gd_(2-x)Eu_xZr_2O_7 (0.0≤x≤2.0)

Pyrochlore Gd2Zr2O7 are considered as an excellent candidate for treatment of radioactive waste forms, because of its superior physical, chemical and anti-irradiation properties. To investigate the phase and structure of pyrochlore Gd2Zr2O7 used for immobilizing Pu(Ⅲ), trivalent europium was used as the simulacrum for plutonium with trivalence. The compounds of stoichiometry Gd2-xEuxZr2O7(0.0x2.0) synthesized by high temperature solid state reaction method, were analyzed with the help of XRD and Rietveld structural refinement method. The results indicated that the phases of compounds continuously kept the phase of pyrochlore under our experimental condition. The linear relation between a andxwas discovered in the system of Gd2-xEuxZr2O7(0.0≤x≤2.0) at 1 773 K, which accorded with a=10.538 41+0.008 95 x, V=1 170.373 32+2.985 97 x.     

Influence of Ti~(4+) doping on hyperfine field parameters of Mg_(0.95)Mn_(0.05)Fe_(2-2x)Ti_(2x)O_4(0≤x≤0.7)

The mixed spinel ferrite system Mg0.95Mn0.05Fe2-2xTi2xO4(0≤x≤0.7) was synthesized by the conventional solid-state reaction technique.The effect of Ti4+ doping was studied by using the Mssbauer spectroscopy measurements at room temperature.From the analysis of the Mssbauer spectra,it is observed that s-electron density,electric field gradient(EFG),quadrupole coupling constant(QCC) and the net hyperfine magnetic fields acting on the M-ssbauer nuclei-FeA3+ and FeB3+ change with the increase of Ti4+ doping in Mg0.95Mn0.05Fe2O4.The hyperfine magnetic field decreases with the increase of Ti4+ doping.     

(1-x)SrZnP_2O_7-xSr_2P_2O_7(0.2≤x≤0.8)陶瓷微波介电性能研究!

采用固相反应法制备了复相体系(1-x)SrZnP2O7-xSr2P2O7陶瓷,研究了该体系的相组成、晶体结构对微波介电性能的影响。研究结果表明,在比例系数x从0.2到0.8的范围内所获得的材料只含有SrZnP2O7和Sr2P2O7两种晶体相,并且当烧结温度合适时所有复相比例的材料均可获得较高的烧结密度。烧结温度的升高会使材料的相对密度和介电常数均有所上升;而随着x值的增大,体系中的Sr2P2O7相含量也逐渐升高,在同样的烧结温度下则伴随着品质因子Q×f值的下降和频率温度系数τf值的上升。在复合比x=0.6时,上述材料具有较优良的微波介电性能:ε=7.44,Q×f=10200GHz,τf=-28.6×10-6/℃。上述结果表明,复合Sr2P2O7相可以有效地使SrZnP2O7材料的负的频率温度系数τf值得到补偿。     

Influence of Ti^4＋ doping on hyperfine field parameters of Mg0.95Mn0.05Fe2-2xTizxO4 （0 ≤x ≤ 0.7）

The mixed spinel ferrite system Mg_0.95Mn_0.05Fe_2−2x Ti_2x O₄ (0⩽x⩽0.7) was synthesized by the conventional solid-state reaction technique. The effect of Ti⁴⁺ doping was studied by using the M?ssbauer spectroscopy measurements at room temperature. From the analysis of the M?ssbauer spectra, it is observed that s-electron density, electric field gradient (EFG), quadrupole coupling constant (QCC) and the net hyperfine magnetic fields acting on the M?ssbauer nuclei-Fe_A ³⁺ and Fe_B ³⁺ change with the increase of Ti⁴⁺ doping in Mg_0.95Mn_0.05Fe₂O₄. The hyperfine magnetic field decreases with the increase of Ti⁴⁺ doping.     

Dy0.65Tb0.25Pr0.1Fex合金的显微组织和磁致伸缩（1.70≤x≤…

采用金相、Ｘ射线衍射、电子探针显微分析、交流初始磁化率和标准应变测试技术研究了Ｄｙ０．６５Ｔｂ０．２５Ｐｒ０．１Ｆｅｘ合金的显微组织、居里温度和磁致伸缩。     

关于丢番图方程x(x+1)(2x+1)=2~kpy~n

利用简洁初等方法,证明了丢番图方程 ｘ（ｘ＋ １）（２ｘ＋ １）＝ ２ｋｐｙｎ在 ｎ＝ ３, ５及 ｎ ≥４为偶数时无正整数解,在ｎ＝２时仅有正整数解在ｎ＞７为奇数时最多有四组正整数解,并且满足（ｋ,ｎ）＝１,从而简洁初等地证明了Ｌｕｃａｓ猜想．     

R(Fe0.95Mn0.05)x合金的显微结构与磁致伸缩的研究(R=Dy0.6Tb0.3Pr0.1,1.7≤x≤2.0)

采用金相、X射线衍射、电子探针显微分析和标准应变测试技术研究了电弧浇铸的R(Fe0.95Mn0.05)x(R=Dy0.6Tb0.3Pr0.1,1.7≤x≤2.0)合金的显微结构与磁致伸缩.结果表明,合金的基体为MgCu2型立方结构的(Dy,Tb,Pr)(Fe,Mn)2相, 当x≤1.8时,第二相为富稀土相,当x>1.85时,变为(Dy,Tb,Pr)(Fe,Mn)3相.合金的磁致伸缩测量表明,当x≤1.80时,磁致伸缩随x的增加而增加,当x>1.85时,磁致伸缩随x的增加而降低.对于采用提拉技术制备的R(Fe0.95Mn0.05)x取向样品,当x=1.85时磁致伸缩呈现出一个峰值.相对于电弧浇铸的样品,取向样品的磁致伸缩特性得到改善.     

钙钛矿结构锰氧化物Pr_(1-x)Ca_xMnO_3(0.4≤x≤0.5)纳米材料的磁性质研究

采用溶胶凝胶法制备了Pr1-xCaxMnO3(0.4≤x≤0.5)系列纳米样品,对其磁性质进行了研究.所有样品在M-T曲线中250K附近的电荷有序转变和170K附近的顺磁-反铁磁转变都消失,与Dong等人的理论模拟计算相符.所有样品在40K都出现了Reentrant spin glass(RSG)态.随着Ca2+掺杂浓度的增加,Mn3+/Mn4+的比例迅速变小,破坏了Mn-O-Mn导电通道,导致磁化强度M逐渐变小.     

关于丢番图方程x（x＋1）（2x＋1）=2^kpy^n

利用简洁初等方法,证明了丢番图方程x(x 1)(2x 1)=2^kpy^n在n=3,5及n≥4为偶数时无正整数解,在n=2时仅有正整数解在n≥7为奇数时最多有四组正整数解,并且满足（k,n)=1,从而简洁初等地证明了Lucas猜想。     

Sylow子群的秩≤2的有限群

本文对Ｓｙｌｏｗ子群的秩≤２的有限群结构进行讨论，得到了关于这类群的一系列很好的性质。     

Influence of Ca_xSr_(1-x)(0≤x≤1) Substitution for Zn on Microwave Dielectric Properties of Li_2ZnTi_3O_8 Ceramic as Temperature Stable Materials

A temperature stable Li_2Zn_(0.95)(Sr_xCa_(1-x))_(0.05)Ti_3O_8 (0≤x≤1) ceramics were fabricated using a conventional solid-state route sintered at 1100 ℃ for 4 h.The XRD results indicate that the main phase Li_2ZnTi_3O_8 and secondary phase including Sr_xCa_(1-x)TiO_3 (0≤x≤1) solid solution and TiO_2 co-exist in composite and form a stable composite system when the (Ca_xSr_(1-x)) (0≤x≤1) substitutes for Zn of Li_2ZnTi_3O_(8 )ceramic.As x is increased from 0 to 1,the relative permittivity (ε_r) increases from 26.65 to 27.12,and the quality factor (Q×f) increases from 63 300 to 66 600 GHz.With the increased of x,the temperature coefficient of resonant frequency (τ_f) increases from 0.27 to 8.23 ppm/℃,and then decreases to 3.51 ppm/℃.On the whole,the Li_2Zn_(0.95)(Sr_xCa_(1-x))_(0.05)Ti_3O_8 (0≤x≤1) ceramics show excellent comprehensive properties of middle ε_r=25-27,higher Q×f ≥ 60000 GHz and τ_f ≤±8.5 ppm/℃.     

丢番图方程x3＋x2＋x=y2-4y＋3的整数解

利用奇偶分析、因式分解等初等方法证明了丢番图方程x3＋x2＋x=y2-4y＋3的整数解为：（x,y）=（-1,2）,（0,1）,（0,3）,（1,4）,（1,0）,（7,22）,（7,-18）。     

关于丢番图方程x2+by2＝z2n及x2+by2＝bz2n的整数解

本文作者证明了丢番图方程x^2＋by^2=z^2^n及x^2＋by^2=bz^2^n都有无穷多组整数解，同时给出了逐步递推求出其全部整数解的方法。