Updated estimate of the muon magnetic momentusing revised results from <Emphasis Type="Italic">e</Emphasis><Superscript> + </Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>-</Superscript>annihilation

A new evaluation of the hadronic vacuum polarization contribution to the muon magnetic moment is presented. We take into account the reanalysis of the low-energy e ⁺ e ^-annihilation cross section into hadrons by the CMD-2 Collaboration. The agreement between e ⁺ e ^-and spectral functions in the channel is found to be much improved. Nevertheless, significant discrepancies remain in the center-of-mass energy range between 0.85 and , so that we refrain from averaging the two data sets. The values found for the lowest-order hadronic vacuum polarization contributions are where the errors have been separated according to their sources: experimental, missing radiative corrections in e ⁺ e ^-data, and isospin breaking. The corresponding Standard Model predictions for the muon magnetic anomaly read where the errors account for the hadronic, light-by-light (LBL) scattering and electroweak contributions. The deviations from the measurement at BNL are found to be (1.9 ) and (0.7 ) for the e ⁺ e ^-- and -based estimates, respectively, where the second error is from the LBL contribution and the third one from the BNL measurement.Received: 7 September 2003, Published online: 30 October 2003     

On the Best Constant in the Moser-Onofri-Aubin Inequality

Let S ² be the 2-dimensional unit sphere and let J _α denote the nonlinear functional on the Sobolev space H ¹(S ²) defined by

Na‐site energy of P2‐type NaxM O2 (M = Mn and Co)

P2‐type Na_xM O₂ (M = Mn and Co) is a promising cathode material for low‐cost sodium ion secondary batteries. In this structure, there are two different crystallographic Nai (i = 1 and 2) sites with different Coulomb potential $ (\varphi _i)$ provided by M^4–x and O^2–. Here, we experimentally determine a difference ${(\rm \Delta }\varepsilon \equiv \varepsilon _1 - \varepsilon _2)$ of Na‐site energies ${(}\varepsilon _i \equiv e\varphi {\kern 1pt} _i)$ based on the temperature dependence of the site occupancies. We find that ${\rm \Delta }\varepsilon \;{=}\;56\;{K}$ for Na_0.52MnO₂ is significantly smaller than 190 K for Na_0.59CoO₂. We interpret the suppressed ${\rm \Delta }\varepsilon $ in Na_0.52MnO₂ in terms of the screening effect of the Na⁺ charge. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Jet production in charged current deep inelastic <Emphasis Type="Italic">e</Emphasis><Superscript> + </Superscript><Emphasis Type="Italic">p</Emphasis> scatteringat HERA

The production rates and substructure of jets have been studied in charged current deep inelastic e ⁺ p scattering for Q ² > 200 GeV² with the ZEUS detector at HERA using an integrated luminosity of 110.5 pb^-1. Inclusive jet cross sections are presented for jets with transverse energies GeV and pseudorapidities in the range . Dijet cross sections are presented for events with a jet having GeV and a second jet having GeV. Measurements of the mean subjet multiplicity, , of the inclusive jet sample are presented. Predictions based on parton-shower Monte Carlo models and next-to-leading-order QCD calculations are compared to the measurements. The value of , determined from at for jets with GeV, is . The mean subjet multiplicity as a function of Q ² is found to be consistent with that measured in NC DIS.Received: 5 June 2003, Published online: 10 October 2003     

Intermolecular H‐bond in propan‐2‐ol and its solutions with acetonitrile

Formation of propan‐2‐ol–acetonitrile dimers is manifested in the Raman spectra as an appearance of a band of aggregates in the high‐wavenumber side of the CN vibrational band of liquid acetonitrile (∼2 cm⁻¹). The intensity of the band of aggregates changes with a change in the concentration of the mixture (1–0.05 mole fraction). For propan‐2‐ol we carried out nonempirical calculations of a structure of isolated dimer aggregates. The formation of an intramolecular H‐bond between the H and the O atom of the \newbox\osprulebox \newdimen\osprulewd \def\osprule#1#2{ \global\setbox\osprulebox=\hbox{#1} \osprulewd=\wd\osprulebox\advance\osprulewd by ‐8pt \raise0.5pc\hbox{$\matrix{\hskip‐1pt\lower6.5pt\hbox{\vrule height #2pt}\lower4.5pt\hbox to \osprulewd{\hrulefill}\lower6.5pt\hbox{\vrule height #2pt}\cr \noalign{\vskip‐1pt} \hbox{#1}\cr}$} } $\osprule{{\rm HCO}}{2.5} \hbox{H}$ group of length 2.045 Å is possible in the monomer molecule. The CH₃ groups of alcohol are not equivalent. In the dimer formation, intramolecular H‐bond in the \newbox\osprulebox \newdimen\osprulewd \def\osprule#1#2{ \global\setbox\osprulebox=\hbox{#1} \osprulewd=\wd\osprulebox\advance\osprulewd by ‐8pt \raise0.5pc\hbox{$\matrix{\hskip‐1pt\lower6.5pt\hbox{\vrule height #2pt}\lower4.5pt\hbox to \osprulewd{\hrulefill}\lower6.5pt\hbox{\vrule height #2pt}\cr \noalign{\vskip‐1pt} \hbox{#1}\cr}$} } $\osprule{{\rm HCO}}{2.5} \hbox{H}$ group is preserved. An intermolecular H‐bond of length 2.045 Å and energy 15 kJ/mole is formed between the H atom of one molecule and the O atom of another molecule of the O H. The length and energy of the H‐bond for the propan‐2‐ol–acetonitrile dimer formations calculate to 2.27 Å and 12.9 kJ/mole, respectively. The H‐bond is formed by σ‐electrons of nitrogen. The experimental data and the results of calculations are in good agreement. Copyright © 2007 John Wiley & Sons, Ltd.     

Semipolar (11\bar 2\bar 2) ZnO thin films grown on LaAlO3‐buffered LSAT (112) single crystals by pulsed laser deposition

Semipolar (11\bar 2 \bar 2) ZnO was successfully grown on (112) LaAlO₃/(LaAlO₃)_0.29(Sr₂AlTaO₆)_0.35 substrate by pulsed laser deposition. The epitaxial relationship is [11\bar 23]_{\rm ZnO} // [11\bar 1]_{\rm LAO/LSAT} with the polar axis of [000\bar 1]_{\rm ZnO} pointing to the surface. For ZnO films with thickness of 1.6 μm, the threading dislocation density is ～1 × 10⁹ cm^–2, and the density of basal stacking faults is below 1 × 10⁴ cm^–1. The (11\bar 2 \bar 2) ZnO exhibits strong D⁰X emissions with a FWHM of 9 meV and very few green–yellow emissions in the low‐temperature (10 K) and room‐temperature photoluminescence spectra, respectively.

     

Electron tunnelling phase time and dwell time through an associated delta potential barrier

The electron tunnelling phase time τP and dwell time τD through an associated delta potential barrier U(x) = ξδ(x) are calculated and both are in the order of 10^-17～10^-16s. The results show that the dependence of the phase time on the delta barrier parameter ξ can be described by the characteristic length lc = h^2/meξ and the characteristic energy Ec=meξ^2/h^2 of the delta barrier, where me is the electron mass, lc and Ec are assumed to be the effective width and height of the delta barrier with lcEc=ξ, respectively. It is found that TD reaches its maximum and τD = τp as the energy of the tunnelling electron is equal to Ec/2, i.e. as lc =λDB, λDB is de Broglie wave length of the electron.     

Physics beyond the Standard Model through b → s μ ?+? μ ? transition

A comprehensive study of the impact of new-physics operators with different Lorentz structures on decays involving the b ?? s ?? ^?+? ?? ^? transition is performed. The effects of new vector?Caxial vector (VA), scalar?Cpseudoscalar (SP) and tensor (T) interactions on the differential branching ratios, forward?Cbackward asymmetries (A _FB??s), and direct CP asymmetries of ${\bar B}_{\rm s}^0 \to \mu^+ \mu^-$ , ${\bar B}_{\rm d}^0 \to$ $ X_{\rm s} \mu^+ \mu^-$ , ${\bar B}_{\rm s}^0 \to \mu^+ \mu^- \gamma$ , ${\bar B}_{\rm d}^0 \to {\bar K} \mu^+ \mu^-$ , and ${\bar B}_{\rm d}^0\to {\bar{K}^*} \mu^+ \mu^-$ are examined. In ${\bar B}_{\rm d}^0\to {\bar{K}^*} \mu^+ \mu^-$ , we also explore the longitudinal polarization fraction f _L and the angular asymmetries $A_{\rm T}^{(2)}$ and A _LT, the direct CP asymmetries in them, as well as the triple-product CP asymmetries $A_{\rm T}^{\rm (im)}$ and $A^{\rm (im)}_{\rm LT}$ . While the new VA operators can significantly enhance most of the observables beyond the Standard Model predictions, the SP and T operators can do this only for A _FB in ${\bar B}_{\rm d}^0 \to {\bar K} \mu^+ \mu^-$ .     

Magnetization and magnetic phase diagrams of a spin-1/2 ferrimagnetic diamond chain at low temperature

We used the Jordan–Wigner transform and the invariant eigenoperator method to study the magnetic phase diagram and the magnetization curve of the spin-1/2 alternating ferrimagnetic diamond chain in an external magnetic field at finite temperature. The magnetization versus external magnetic field curve exhibits a 1/3 magnetization plateau at absolute zero and finite temperatures, and the width of the 1/3 magnetization plateau was modulated by tuning the temperature and the exchange interactions. Three critical magnetic field intensities H_(CB), H_(CE) and H_(CS) were obtained, in which the H_(CB) and H_(CE) correspond to the appearance and disappearance of the 1/3 magnetization plateau, respectively, and the higher H_(CS) correspond to the appearance of fully polarized magnetization plateau of the system. The energies of elementary excitation ωσ,k(σ = 1, 2, 3) present the extrema of zero at the three critical magnetic fields at 0 K, i.e., [hω_(3,k)(HCB)]_(min)= 0, [hω_(2,k)(H_(CE))]_(max)= 0 and [hω _(2,k)(H_(CS))]_(min)= 0, and the magnetic phase diagram of magnetic field versus different exchange interactions at 0 K was established by the above relationships. According to the relationships between the system's magnetization curve at finite temperatures and the critical magnetic field intensities, the magnetic field-temperature phase diagram was drawn. It was observed that if the magnetic phase diagram shows a three-phase critical point, which is intersected by the ferrimagnetic phase, the ferrimagnetic plateau phase, and the Luttinger liquid phase, the disappearance of the1/3 magnetization plateau would inevitably occur. However, the 1/3 magnetization plateau would not disappear without the three-phase critical point. The appearance of the 1/3 magnetization plateau in the low temperature region is the macroscopic manifestations of quantum effect.     

Lowest- Q2 measurement of the γp → Δ reaction: Probing the pionic contribution

To determine nonspherical angular-momentum amplitudes in hadrons at long ranges (low Q²), data were taken for the p(ˉe, e'p)π⁰ reaction in the Δ region at Q ² = 0.060 (GeV/c)² utilizing the magnetic spectrometers of the A1 Collaboration at MAMI. The results for the dominant transition magnetic dipole amplitude and the quadrupole to dipole ratios at W = 1232 MeV are , Re( )%, and Re( )%. These disagree with predictions of constituent quark models but are in reasonable agreement with lattice calculations with nonlinear (chiral) pion mass extrapolations, with chiral effective field theory, and with dynamical models with pion cloud effects. These results confirm the dominance, and general Q² variation, of the pionic contribution at large distances.     

Effect of substrate temperature on the growth and properties of boron-doped microcrystalline silicon films

Highly conductive boron-doped hydrogenated microcrystalline silicon (\mu c-Si:H) films are prepared by very high frequency plasma enhanced chemical vapour deposition (VHF PECVD) at the substrate temperatures $T_{\rm S})$ ranging from 90$^\circ$C to 270$^\circ$C. The effects of $T_{\rm S}$ on the growth and properties of the films are investigated. Results indicate that the growth rate, the electrical (dark conductivity, carrier concentration and Hall mobility) and structural (crystallinity and grain size) properties are all strongly dependent on $T_{\rm S}$. As $T_{\rm S}$ increases, it is observed that 1) the growth rate initially increases and then arrives at a maximum value of 13.3 nm/min at $T_{\rm S}$=210$^\circ$C, 2) the crystalline volume fraction ($X_{\rm c})$ and the grain size increase initially, then reach their maximum values at $T_{\rm S}$=140$^\circ$C, and finally decrease, 3) the dark conductivity ($\sigma _{\rm d})$, carrier concentration and Hall mobility have a similar dependence on $T_{\rm S}$ and arrive at their maximum values at $T_{\rm S}$=190$^\circ$C. In addition, it is also observed that at a lower substrate temperature $T_{\rm S}$, a higher dopant concentration is required in order to obtain a maximum $\sigma _{\rm d}$.     

Measurements of charged kaon semileptonic decay branching fractions K±→π0μ±ν and K±→π0e±ν and their ratio

Measured ratios of decay rates for , and are presented. These measurements are based on K^± decays collected in a dedicated run in 2003 by the NA48/2 experiment at CERN. The results obtained are and . Using the PDG average for the K^±→π^±π⁰ normalisation mode, both values are found to be larger than the current values given by the particle data book and lead to a larger magnitude of the |V_us| CKM element than previously accepted. When combined with the latest particle data book value of |V_ud|, the result is in agreement with unitarity of the CKM matrix. In addition, a new measured value of is compared to the semi-empirical predictions based on the latest form factor measurements. An erratum to this article can be found at     

Influence of reducing anneal on the ferromagnetism in single crystalline Co-doped ZnO thin films

This paper reports that the high-quality Co-doped ZnO single crystalline films have been grown on $a$-plane sapphire substrates by using molecular-beam epitaxy. The as-grown films show high resistivity and non-ferromagnetism at room temperature, while they become good conductive and ferromagnetic after annealing in the reducing atmosphere either in the presence or absence of Zn vapour. The x-ray absorption studies indicate that all Co ions in these samples actually substituted into the ZnO lattice without formatting any detectable secondary phase. Compared with weak ferromagnetism (0.16~$\mu _{\rm B}$/Co$^{2 + })$ in the Zn6110M, 7550P, 7280E, 7870Dhttp://cpb.iphy.ac.cn/CN/10.1088/1674-1056/19/5/056101https://cpb.iphy.ac.cn/CN/article/downloadArticleFile.do?attachType=PDF&id=111756Co-doped ZnO, diluted magnetic semiconductors, x-ray absorption fine structure, single crystalline thin filmsProject partially supported by National Science Foundation of China (Grant No.~10804017), National Science Foundation of Jiangsu Province of China (Grant No.~BK2007118), Research Fund for the Doctoral Program of Higher Education of China (Grant No.~20070286037), Cyanine-Project Foundation of Jiangsu Province of China (Grant No.~1107020060), Foundation for Climax Talents Plan in Six-Big Fields of Jiangsu Province of China (Grant No.~1107020070) and New Century Excellent Talents in University (NCET-05-0452).This paper reports that the high-quality Co-doped ZnO single crystalline films have been grown on $a$-plane sapphire substrates by using molecular-beam epitaxy. The as-grown films show high resistivity and non-ferromagnetism at room temperature, while they become good conductive and ferromagnetic after annealing in the reducing atmosphere either in the presence or absence of Zn vapour. The x-ray absorption studies indicate that all Co ions in these samples actually substituted into the ZnO lattice without formatting any detectable secondary phase. Compared with weak ferromagnetism (0.16~$\mu _{\rm B}$/Co$^{2 + })$ in the Zn$_{0.95}$Co$_{0.05}$O single crystalline film with reducing annealing in the absence of Zn vapour, the films annealed in the reducing atmosphere with Zn vapour are found to have much stronger ferromagnetism (0.65~$\mu _{\rm B}$/Co$^{2 + })$ at room temperature. This experimental studies clearly indicate that Zn interstitials are more effective than oxygen vacancies to activate the high-temperature ferromagnetism in Co-doped ZnO films, and the corresponding ferromagnetic mechanism is discussed.Co-doped;ZnO;diluted;magnetic;semiconductors;x-ray;absorption;fine;structure;single;crystalline;thin;filmsThis paper reports that the high-quality Co-doped ZnO single crystalline films have been grown on a-plane sapphire substrates by using molecular-beam epitaxy.The as-grown films show high resistivity and non-ferromagnetism at room temperature,while they become more conductive and ferromagnetic after annealing in the reducing atmosphere either in the presence or absence of Zn vapour.The x-ray absorption studies indicate that all Co ions in these samples actually substituted into the ZnO lattice without formatting any detectable secondary phase.Compared with weak ferromagnetism(0.16 μB/Co2+) in the Zn0.95Co0.05O single crystalline film with reducing annealing in the absence of Zn vapour,the films annealed in the reducing atmosphere with Zn vapour are found to have much stronger ferromagnetism(0.65 μB/Co2+) at room temperature.This experimental studies clearly indicate that Zn interstitials are more effective than oxygen vacancies to activate the high-temperature ferromagnetism in Co-doped ZnO films,and the corresponding ferromagnetic mechanism is discussed.     

The role of hydrogen in hydrogenated microcrystalline silicon film and in deposition process with VHF-PECVD technique

The role of hydrogen in hydrogenated microcrystalline silicon ($\mu $c-Si:H) thin films in deposition processes with very high frequency plasma-enhanced chemical vapour deposition (VHF-PECVD) technique have been investigated in this paper. With \textit{in situ} optical emission spectroscopy (OES) diagnosis during the fabrication of $\mu $c-Si:H thin films under different plasma excitation frequency $\nu _{\rm e }$ (60MHz--90MHz), the characteristic peak intensities ($I_{{\rm SiH}^*}$, $I_{{\rm H}\alpha^*}$ and $I_{{\rm H}\beta ^*}$) in SiHVHF-PECVD技术 氢化微晶硅 光发射光谱 薄膜学VHF-PECVD technique, hydrogenated microcrystalline silicon, role of hydrogen, optical emission spectroscopyProject supported by the Natural Science Foundation of Guangdong Province, China (Grant No 05300378), the State Key Development Program for Basic Research of China (Grant Nos G2000028202 and G2000028203) and the Program on Natural Science of Jinan University, Guangzhou, China (Grant No 51204056).2005-11-252005-11-252006-01-05The role of hydrogen in hydrogenated microcrystalline silicon （μc-Si：H） thin films in deposition processes with very high frequency plasma-enhanced chemical vapour deposition （VHF-PECVD） technique have been investigated in this paper. With in situ optical emission spectroscopy （OES） diagnosis during the fabrication of μc-Si：H thin films under different plasma excitation frequency Ve （60MHz-90MHz）, the characteristic peak intensities （IsiH＊, IHα＊ and IHβ＊ ） in SiH4＋H2 plasma and the ratio of （IHα＊ ＋ IHβ＊ ） to IsiH＊ were measured; all the characteristic peak intensities and the ratio （IHα＊ ＋ IHβ＊ ）/IsiH＊ are increased with plasma excitation frequency. It is identified that high plasma excitation frequency is favourable to promote the decomposition of SiH4＋H2 to produce atomic hydrogen and SiHx radicals. The influences of atomic hydrogen on structural properties and that of SiHx radicals on deposition rate of μc-Si：H thin films have been studied through Raman spectra and thickness measurements, respectively. It can be concluded that both the crystalline volume fraction and deposition rate are enhanced with the increase of plasma excitation frequency, which is in good accord with the OES results. By means of FTIR measurements, hydrogen contents of μc-Si：H thin films deposited at different plasma excitation frequency have been evaluated from the integrated intensity of wagging mode near 640 cm^-1. The hydrogen contents vary from 4% to 5%, which are much lower than those of μc-Si：H films deposited with RF-PECVD technique. This implies that μc-Si：H thin films deposited with VHF-PECVD technique usually have good stability under light-soaking.     

High energy electron radiation effect on Ni/4H-SiC SBD and Ohmic contact

The Ni/4H-SiC Schottky barrier diodes (SBDs) and transfer length method (TLM) test patterns of Ni/4H-SiC Ohmic contacts were fabricated, and irradiated with 1~MeV electrons up to a dose of 3.43× 10¹⁴~e/cm^-2. After radiation, the forward currents of the SBDs at 2~V decreased by about 50%, and the reverse currents at -200~V increased by less than 30%. Schottky barrier height (φ _B ) of the Ni/4H-SiC SBD increased from 1.20~eV to 1.21~eV under 0~V irradiation bias, and decreased from 1.25~eV to 1.19~eV under -30~V irradiation bias. The degradation of φ _B could be explained by the variation of interface states of Schottky contacts. The on-state resistance (R_s) and the reverse current increased with the dose, which can be ascribed to the radiation defects in bulk material. The specific contact resistance (\rho_c) of the Ni/SiC Ohmic contact increased from 5.11× 10⁵~Ωega.cm² to 2.97× 10^-4~Ωega.cm².     

Muonic Anti-hydrogen {(\bar{\rm H}_{\mu}}) Formation in Low-energy Three-body Reactions

A few-body type computation is performed for a three-charge-particle collision with participation of a slow antiproton ${\bar{\rm{p}}}$ and a muonic muonium atom (true muonium), i.e. a bound state of two muons ${(\mu^{+}\mu^{-})}$ in its ground state. The total cross section of the following reaction ${\bar{\rm p}+(\mu^{+}\mu^{-}) \rightarrow \bar{\rm{H}}_{\mu} + \mu^{-}}$ , where muonic anti-hydrogen ${\bar{\rm{H}}_{\mu}=(\bar{\rm p}\mu^{+})}$ is a bound state of an antiproton and positive muon, is computed in the framework of a set of coupled two-component Faddeev-Hahn-type equation. A better known negative muon transfer low energy three-body reaction: ${{\rm t}^{+} + ({\rm d}^{+}\mu^{-})\rightarrow ({\rm t}^{+}\mu^{-}) + {\rm d}^{+}}$ is also computed as a test system. Here, t⁺ is triton and d⁺ is deuterium.     

Temperature dependence of the quenching of N<Subscript>2</Subscript> (C <Superscript>3</Superscript>Π<Subscript>u</Subscript>) by N<Subscript>2</Subscript> (X) and O<Subscript>2</Subscript> (X)

The temperature dependences of the quenching rate constants of the states N₂ (${\rm C} \ {^{3}{ \rm \Pi }_{u}}${\rm C} \ {^{3}{ \rm \Pi }_{u}} v^′=0,1) by N₂ (X) and of the state N₂ (${\rm C} \ {^{3}{ \rm \Pi }_{u}} \ v^{\prime}=0${\rm C} \ {^{3}{ \rm \Pi }_{u}} \ v^{\prime}=0) by O₂ (X) are studied. Time-resolved light emission from the gas was analyzed in the temperature range from 300 K to 210 K keeping the gas at constant density. In case of quenching by N₂ (X), the quenching rate constant for the vibrational level v^′= 0 increases by (13 ±3)% with gas cooling whereas the quenching rate constant for v^′= 1 decreases by (5.0 ±2.5)% in this temperature range. For quenching by O₂ (X), the quenching rate constant decreases by (3 ±2)% with gas cooling. The temperature variation of the N₂ (C ³Π_u v^′=0) emission intensity for pure nitrogen and dry air are calculated using the obtained quenching rate constants and is compared with the experimental data available in the literature.     

Co-Al-W基高温合金的团簇成分式

Co-Al-W基高温合金具有类似于Ni基高温合金的γ+γ'相组织结构.根据面心立方固溶体的团簇加连接原子结构模型,Ni基高温合金的成分式即最稳定的化学近程序结构单元可以描述为第一近邻配位多面体团簇加上次近邻的三个连接原子.本文应用类似方法,首次给出了Co-Al-W基高温合金的团簇成分式.利用原子半径和团簇共振模型,可计算出Co-Al-W三元合金的团簇成分通式,为[Al-Co_(12)](Co,Al,W)_3,即以Al为中心原子、Co为壳层原子的[Al-Co_(12)]团簇加上三个连接原子.对于多元合金,需要先将元素进行分类:溶剂元素——类Co元素Co (Co, Cr, Fe, Re, Ni,Ir,Ru)和溶质元素——类Al元素Al (Al,W,Mo, Ta,Ti,Nb,V等);进而根据合金元素的配分行为,将类Co元素分为Co~γ(Cr, Fe, Re)和Co~(γ')(Ni, Ir, Ru);根据混合焓,将类Al元素分为Al, W (W, Mo)和Ta (Ta, Ti, Nb, V等).由此,任何多元Co-Al-W基高温合金均可简化为Co-Al伪二元体系或者Co-Al-(W,Ta)伪三元体系,其团簇加连接原子成分式为[Al-Co_(12)](Co_(1.0)Al_(2.0))(或[Al-Co_(12)] Co_(1.0)Al_(0.5)(W,Ta)_(1.5)=Co_(81.250)Al_(9.375)(W,Ta)_(9.375) at.%).其中,γ与γ'相的团簇成分式分别为[Al-Co_(12)](Co_(1.5)Al_(1.5))(或[Al-Co_(12)] Co_(1.5)Al_(0.5)(W,Ta)_(1.0)=Co_(84.375)Al_(9.375)(W,Ta)_(6.250) at.%)和[Al-Co_(12)](Co_(0.5)Al_(2.5))(或[Al-Co_(12)] Co_(0.5)Al_(0.5)(W, Ta)_(2.0)=Co_(78.125)Al_(9.375)(W,Ta)_(12.500)at.%).例如,Co_(82)Al_9W_9合金的团簇成分式为[Al-Co_(12)]Co_(1.1)Al_(0.4)W_(1.4)(～[Al-Co_(12)]Co_(1.0)Al_(0.5)W_(1.5)),其中γ相的团簇成分式为[Al-Co_(12)]Co_(1.6)Al_(0.4)W_(1.0)(～[Al-Co_(12)]Co_(1.5)Al_(0.5)W_(1.0)),γ'相的团簇成分式为[Al-Co_(12)]Co_(0.3)Al_(0.5)W_(2.2)(～[AlCo_(12)]Co_(0.5)Al_(0.5)W_(2.0)).