第 55卷 第 4期
20 1 5 年 7月
大连理工大学学报
Journal of Dalian University of Technology
Vol. 55, No. 4
July 2 0 1 5
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去去企金
| 材 料 、机 械 工 程 | 文章编号:1000-8608(2015)04-0366-07
Cluster formulas of Hume-Rothery phases
QIANG Jian-bing1 ? KE Xing1,WANG Ying-mirT1, SUN Ji-zhong2, LIU Tian-wei3, DONG Chuang1
(1 . School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024,China;
2. School of Physics and Optoelectronic Engineering, Dalian University of Technology, Dalian 116024,China;
3.China Academy of Engineering Physics, Mianyang 621900,China )
Abstract : Hume-Rothery phases sharing the same e/a ( electron
concentration,which usually is 1. 50( = 21/14) , 1. 62 ( = 21/13),1.75 ( = 21/
12)) crystallize into many different types of structures based on a common
Bravais lattice, hence the e/a alone can not be used as the finger print
parameter specifying a Hume-Rothery phase. A refined electronic structure
parameter is desirable for the classification of Hume-Rothery phases in a more
rigorous manner. So the cluster-plus-glue-atom model is used to decipher the
structures of Hume-Rothery phases, from which the cluster formula and
relative number of electrons per unit formula,e/m,are derived. Hume-
Rothery phases with an identical e/a are classified by e/u, so e u is a new
parameter to specify Hume-Rothery phase structures.
Key words: Hume-Rothery phases; electron concentration; cluster-plus glue-
atom model; cluster formula
0 Introduction
Hume-Rothery phases, also known as
electron compounds,are formed between metal
elements having close atomic radii and
electronegativity,such as Cu,Zn and A g ,etc..
In these phases, the effect of the valence
electrons on the structure formation is quite
pronounced as compared to the phases composed
of atoms with la rg e atom radius differences,
where g eo m e trica l factor plays an important role,
or to electrochemical compounds ? in which chemical
bonding dominates. Hume-Rothery phases have
distinct el a ( number of valence electron per
atom ),namely,21/14,21/13 and 21/12,
irrespective of their different chemical species
and compositions⑴.
The stabilization mechanism behind the
apparent e/ a rule lies in the Fermi surface-
Brillouin zone (FsBz) effect, due to which the
electron density of states ( eDOS) reaches the
minimum by forming pseudogap across the
Fermi level[2'。. In Mizutani7 s w ork,the first
principles calculations are applied to various
complex metal alloys including some Hume-
Rothery phases,like Cu:,Zns ? Al.i Cu<) ? CuZn,
A gM g, etc. [0. F irstly, they resolved the
problem discovered in Pippard7 s work[a] that
Received by : 2014-06-10; Revised by : 2015-05-20.
Supported by: Fundamental Research Funds for the Central Universities (No. D UT13ZD102) ? Scientific and. Technological Development
Foundation of China Academy of Engineering Physics (No. 2013A0301015) j National Defense Basic Scientific Research ( No.
B1520133007) ; National Magnetic Confinement Fusion Science Program (No. 2013GB107003).
Corresponding authors: Q IA N f j J imi I'iii.l" 1117 i ,M ale ,D oc.,Associa. P ro f.,E-mail : qiang (a ' 1 u t. edu. cn; WA\< > Ymu ruin'"
(1971-),M ale,D o c .,Associa. P ro f.,E-mail : ap\vangym@dlut. edu. cn.