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本文以原子物理学中电子按能级分布理论为基础,提出一个关于金属磁性的新的巡游电子模型:在形成金属的过程中由于受到电子间泡利排斥力的作用,Fe,Ni,Co原子的大部分4s电子进入3d轨道,只有一少部分4s电子成为自由电子;最外层3d轨道的电子有一定概率在离子实间巡游,形成巡游电子;其余的3d电子为局域电子.因此,由Fe,Ni,Co金属的平均原子磁矩实验值2.22,0.62和1.72 B,计算出Fe,Ni,Co金属中平均每个原子贡献的自由电子数目为0.22,0.62和0.72,从而解释了为什么Fe,Ni,Co金属的电阻率依次减小.应用这个模型计算出的平均每个原子的3d电子数为7.78,9.38和8.28,与金属能带论计算结果(7.4,9.4和8.3)比较接近,但是本文的方法更加简单、有效,易于理解.这为进一步澄清金属与合金的价电子结构提供了新思路.Conventionally, the energy band theory is used to explain the magnetic and electrical transport properties of metals. However, so far, there has been no quantitative explanation of the relations between the average magnetic moment per atom and the resistivity for Fe, nor Ni, nor Co metals. In this paper, a new itinerant electron model for magnetic metal is proposed on the basis of electron distribution theory at the energy level. 1) In the process of free atoms forming the metal solid, most of the 4s electrons of Fe, Ni and Co enter into the 3d orbits subjected to the Pauli repulsive force, and the remaining 4s electrons form free electrons. 2) Since the average number of 3d electrons is not an integer, a part of atoms have one 3d electron more than the other atoms. These excess 3d electrons have a certain probability to itinerate between the 3d orbits of the adjacent atoms as itinerant electrons; and the other 3d electrons are local electrons. 3) The transition probability of itinerant electrons is very low, thus the contribution to metal resistivity from itinerant electrons is far lower than that from free electrons. Resistivity of metal decreases with increasing the number of free electrons. Therefore, using the observed values of average atomic magnetic moments, 2.22, 0.62 and 1.72 B, the average numbers of free electrons in Fe, Ni and Co can be calculated to be 0.22, 0.62 and 0.72, respectively. This is the reason why the electrical resistivities of Fe, Ni and Co (8.6, 6.14 and 5.57 -cm) decease successively. In addition, according to this model, the average number of 3d electrons per atom in Ni metal is 9.38. This indicates that 38% of atoms in Ni metal have ten 3d electrons, forming a full 3d sub-shell, as in Cu or Zn atoms. The 3d electrons in these atoms are difficult to itinerate or exchange. This may be the reason why the Curie temperature of Ni metal (631 K) is far lower than those of Fe and Co metals (1043 and 1404 K). On the basis of the energy band theory, the numbers of 3d electrons in Fe, Ni and Co metals are 7.4, 9.4 and 8.3, which are close to our results (7.78, 9.38 and 8.28), respectively. This indicates that our model is consistent with the energy band theory. Compared with the complex energy band theory, a simple and effective method on investigating valence electron structures through the experimental average magnetic moments per atom in a metal is presented based on our model. Therefore, the new itinerant electron model may be a new clue to understanding the electronic structure of metals and alloys.
[1] Ida S, Ono K, Kozaki H (translated by Zhang Z X) 1979 Data on Physics in Common Use(Beijing:Science Press) p133(in Chinese)[饭田修一, 大野和郎, 神前熙编(张质贤译) 1979物理学常用数表(北京:科学出版社)第133页]
[2] Dai D S, Qian K M 1986 Ferromagnetism (Beijing:Science Press) p320(in Chinese)[戴道生, 钱昆明1986铁磁学(上册) (北京:科学出版社)第320页]
[3] Stöhr J, Siegmann H C (translated by Ji Y) 2012 Magnetism:From Fundamentals to Nanoscale Dynamics (Beijing:Higher Education Press) p450(in Chinese)[Stöhr J, Siegmann H C著(姬扬译) 2012磁学:从基础知识到纳米尺度超快动力学(北京:高等教育出版社)第450页]
[4] Johnson P D 1997 Rep. Prog. Phys. 60 1217
[5] Sánchez-Barriga J, Minár J, Braun J, Varykhalov A, Boni V, Marco I D, Rader O, Bellini V, Manghi F, Ebert H, Katsnelson M I, Lichtenstein A I, Eriksson O, Eberhardt W, Drr H A, Fink J 2010 Phys. Rev. B 82 104414
[6] Stearns M B 1973 Phys. Rev. B 8 4383
[7] Stearns M B 1978 Phys. Today 31(4) 34
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[1] Ida S, Ono K, Kozaki H (translated by Zhang Z X) 1979 Data on Physics in Common Use(Beijing:Science Press) p133(in Chinese)[饭田修一, 大野和郎, 神前熙编(张质贤译) 1979物理学常用数表(北京:科学出版社)第133页]
[2] Dai D S, Qian K M 1986 Ferromagnetism (Beijing:Science Press) p320(in Chinese)[戴道生, 钱昆明1986铁磁学(上册) (北京:科学出版社)第320页]
[3] Stöhr J, Siegmann H C (translated by Ji Y) 2012 Magnetism:From Fundamentals to Nanoscale Dynamics (Beijing:Higher Education Press) p450(in Chinese)[Stöhr J, Siegmann H C著(姬扬译) 2012磁学:从基础知识到纳米尺度超快动力学(北京:高等教育出版社)第450页]
[4] Johnson P D 1997 Rep. Prog. Phys. 60 1217
[5] Sánchez-Barriga J, Minár J, Braun J, Varykhalov A, Boni V, Marco I D, Rader O, Bellini V, Manghi F, Ebert H, Katsnelson M I, Lichtenstein A I, Eriksson O, Eberhardt W, Drr H A, Fink J 2010 Phys. Rev. B 82 104414
[6] Stearns M B 1973 Phys. Rev. B 8 4383
[7] Stearns M B 1978 Phys. Today 31(4) 34
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