稀释晶场对纳米管上Blume-Capel模型磁化性质的研究
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摘要
利用有效场理论研究了纳米管上稀释晶场中Blume-Capel模型格点的磁化强度、内能、比热和自由能,得到了系统格点的磁化强度、内能、比热和自由能与温度和稀释晶场的关系.结果表明:稀释晶场取值概率和晶场强度等诸多因素相互竞争,使系统表现出比含恒定晶场作用的Blume-Capel模型更为丰富的磁学特性;稀释晶场会抑制系统格点的磁化强度,导致其基态饱和值小于1;温度较低时,系统格点的磁化强度表现出复杂性;晶场较强时,系统的内能、比热和自由能也呈现出不同的磁学性质.
The magnetization, internal energy, specific heat and free energy of spin-1 Blume-Capel model on a cylindrical Ising nanotube with distribution of the diluted crystal field are investigated by using the effective field theory. The relationship between the magnetization, internal energy, specific heat and free energy of the system lattice and the temperature and the dilute crystal field is obtained. The results show that many factors such as the probability of the dilution of the crystal field and the intensity of the crystal field are competing with each other, making the system more rich in magnetic properties than the Blume-Capel model containing the constant crystal field. The diluted crystal field will inhibit the magnetization of the system lattice, which leads to the saturation value of the ground state less than 1. When the temperature is low, the magnetization of the system lattice is complex. When the intensity of the crystal field is strong, the internal energy, specific heat and free energy of the system also show different magnetic properties.
The magnetization, internal energy, specific heat and free energy of spin-1 Blume-Capel model on a cylindrical Ising nanotube with distribution of the diluted crystal field are investigated by using the effective field theory. The relationship between the magnetization, internal energy, specific heat and free energy of the system lattice and the temperature and the dilute crystal field is obtained. The results show that many factors such as the probability of the dilution of the crystal field and the intensity of the crystal field are competing with each other, making the system more rich in magnetic properties than the Blume-Capel model containing the constant crystal field. The diluted crystal field will inhibit the magnetization of the system lattice, which leads to the saturation value of the ground state less than 1. When the temperature is low, the magnetization of the system lattice is complex. When the intensity of the crystal field is strong, the internal energy, specific heat and free energy of the system also show different magnetic properties.
引文
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[19] Kaneyoshi T,Fittipaldi I P,Honmura R,et al.New correlated-effective theory in the Ising model [J].Phys.Rev.B,1981,24:481.
[20] Kaneyoshi T,Tucker J W,Ja?cur M.Differential operator technique for higher spin problems [J].Physica A,1992,186:495.
[21] Kaneyoshi T.Differential operator technique in the Ising spin systems [J].Acta Phys.Pol.A,1993,83:703.
[2] Capel H W.On the possibility of first-order phase transitions in Ising systems of triplet ions with zero-field splitting [J].Physica,1966,32:966.
[3] Albayrak E.The spin-1 Blume-Capel model with random crystal field on the Bethe lattice [J].Physica A,2011,390:1529.
[4] Albayrak E.The mixed spin-1/2 and spin-1 Blume-Capel model with random crystal field on the Bethe lattice:Two approaches [J].Solid State Commun.,2013,159:76.
[5] Albayrak E.Spin-1 Blume-Capel model with longitudinal random crystal and transverse magnetic field:A mean-field approach [J].Chin.Phys.B,2013,22:077501.
[6] Ak?nc? ü,Yüksel Y,Polat H.Effects of the bond dilution on the phase diagrams of a spin-1 transverse Ising model with crystal field interaction on a honeycomb lattice [J].Physica A,2011,390:541.
[7] Yigit A,Albayrak E.Bimodal random crystal field distribution effects on the ferromagnetic mixed spin-1/2 and spin-3/2 Blume-Capel model [J].J.Magn.Magn.Mater.,2013,329:125.
[8] Zhou D,Cai L H,Wen F S,et al.Template Synthesis and Magnetic Behavior of FeNi Alloy Nanotube Arrays [J].Chinese J.Chem.Phys.,2007,20:821.
[9] Mao R,Guo H,Tian D X,et al.Hollow Nanotubular SnO2 Templated Cellulose Fibers for Lithium Ion Batteries [J].J.Inorg.Mater.,2013,28:1213 (in Chinese) [毛瑞,郭洪,田冬雪,等.滤纸为模板制备中空SnO2纳米管锂离子电池负极材料 [J].无机材料学报,2013,28:1213]
[10] Kaneyoshi T.Some characteristic properties of initial susceptibility in a Ising nanotube [J].J.Magn.Magn.Mater.,2011,323:1145.
[11] Canko O,Erdin? A,Ta?k?n F,et al.Some characteristic behavior of spin-1 Ising nanotube [J].Phys.Lett.A,2011,375:3547.
[12] Canko O,Erdin? A,Ta?k?n F,et al.Some characteristic behavior of mixed spin-1/2 and spin-2 Ising nano-tube [J].J.Magn.Magn.Mater.,2012,324:508.
[13] Ta?k?n F,Canko O,Erdin? A,et al.Thermal and magnetic of a nanotube with spin-1/2 core and spin-3/2 shell structure [J].Physica A,2014,407:287.
[14] Magoussi H,Zaim A,Kerouad M.Theoretical investigations of the phase diagrams and the magnetic properties of a random field spin-1 Ising nanotube with core/shell morphology [J].J.Magn.Magn.Mater.,2013,344:109.
[15] Li X J,Liu Z Q ,Wang C Y,et al.Effects of bimodal random crystal field on the magnetization and phase transition of Blume-Capel model on nanotube [J].Acta.Phys.Sin.2015,64:247501 (in Chinese) [李晓杰,刘中强,王春阳,等.双模随机晶场对纳米管上Blume-Capel 模型磁化强度和相变的影响 [J].物理学报,2015,64:247501]
[16] Wei D,Kong X M.Thermodynamics and phase transitions of Blume-Emery-Griffiths model on nanotube [J].J.At.Mol.Phys.,2017,34:515 (in Chinese) [魏东,孔祥木.Blume-Emery-Griffiths 纳米管的热力学与相变性质 [J].原子与分子物理学报,2017,34:515]
[17] Wu Y,Hu Y P.Study AI/N co-doping small diameter carbon nanotubes by using the first principles theory [J].J.At.Mol.Phys.,2016,33:259 (in Chinese) [吴楹,胡玉鹏.第一性原理研究铝氮掺杂小半径碳纳米管 [J].原子与分子物理学报,2016,33:259]
[18] Zhang N C,Ren J.First-principles study on the hydrogen storage properties of La doped BN nanotubes [J].J.Sichuan Univ.:Nat.Sci.Ed.,2018,55:105 (in Chinese) [张宁超,任娟.稀土金属La吸附掺杂BN纳米管储氢性能的第一性原理研究 [J].四川大学学报:自然科学版,2018,55:105]
[19] Kaneyoshi T,Fittipaldi I P,Honmura R,et al.New correlated-effective theory in the Ising model [J].Phys.Rev.B,1981,24:481.
[20] Kaneyoshi T,Tucker J W,Ja?cur M.Differential operator technique for higher spin problems [J].Physica A,1992,186:495.
[21] Kaneyoshi T.Differential operator technique in the Ising spin systems [J].Acta Phys.Pol.A,1993,83:703.