H2在AlnCr(n=1-7)團(tuán)簇上吸附和解離的密度泛函研究

李向富， 李高清

(隴東學(xué)院電氣工程學(xué)院， 慶陽 745000)

H2在AlnCr(n=1-7)團(tuán)簇上吸附和解離的密度泛函研究

李向富， 李高清

(隴東學(xué)院電氣工程學(xué)院， 慶陽 745000)

采用密度泛函理論中的B3LYP方法研究了H2在AlnCr(n=1-7)團(tuán)簇上的吸附和解離.結(jié)果表明：AlnCr團(tuán)簇結(jié)構(gòu)與Aln+1團(tuán)簇結(jié)構(gòu)相似；物理吸附是H2以側(cè)向的形式吸附在Cr原子上，H-H鍵長略微增長，H2的振動(dòng)頻率發(fā)生了紅移；除了n=5外，其它AlnCrH2團(tuán)簇的最穩(wěn)定結(jié)構(gòu)均是AlnCr團(tuán)簇的最穩(wěn)定結(jié)構(gòu)與兩個(gè)氫原子成鍵而成；AlnCr團(tuán)簇向H原子轉(zhuǎn)移了電荷；AlnCrH2團(tuán)簇的平均結(jié)合能，垂直電離勢(shì)和能隙均大于AlnCr團(tuán)簇的，即AlnCrH2團(tuán)簇比AlnCr團(tuán)簇更穩(wěn)定；Al7Cr對(duì)H2的化學(xué)吸附表現(xiàn)出較強(qiáng)的惰性，而AlnCrH2(n=1,2,6)則表現(xiàn)出較強(qiáng)的化學(xué)活性；由化學(xué)反應(yīng)路徑跟蹤可知，通過改變AlnCr團(tuán)簇中Al原子的個(gè)數(shù)可以調(diào)節(jié)H2的物理化學(xué)吸附行為.

AlnCr團(tuán)簇； 氫分子； 吸附； 解離

1 引 言

2 計(jì)算方法

采用用密度泛函理論中的B3LYP方法研究了H2在AlnCr(n=1-7)團(tuán)簇上的吸附和解離.所有計(jì)算均在Gaussian03程序包[12]下完成.Al和H采用全電子基組6-31g*，Cr原子的內(nèi)層電子和價(jià)電子均采用LANL2DZ贗勢(shì).根據(jù)最小振動(dòng)頻率是否為正值判斷所得結(jié)構(gòu)是否為局域穩(wěn)定結(jié)構(gòu).使用QST方法尋找物理吸附到化學(xué)吸附的中間過渡態(tài)，通過計(jì)算反應(yīng)路徑來確認(rèn)過渡態(tài)的正確性.為了使得所得結(jié)構(gòu)盡可能是全局最穩(wěn)定結(jié)構(gòu)，根據(jù)已報(bào)道的Aln和AlnX(X=Cu, Au, Co, V) 團(tuán)簇的幾何結(jié)構(gòu)，通過替換或擔(dān)載的方式獲得豐富的初始結(jié)構(gòu).考慮了自旋多重度的影響.

為了驗(yàn)證所采用計(jì)算方法的可行性，計(jì)算了Cr2, Al2和AlCr二聚體，結(jié)果見表1.由表1可以看出：Cr2和Al2的鍵長、平均結(jié)合能和垂直電離勢(shì)的本文計(jì)算值與實(shí)驗(yàn)值符合得很好；AlCr的鍵長和垂直電離勢(shì)的本文計(jì)算值與理論和實(shí)驗(yàn)值符合得很好，但是，平均結(jié)合能比實(shí)驗(yàn)值小得多，而與理論值符合得很好.綜上所述，本文采用的計(jì)算方法是可行的.

表1 Cr2、Al2和AlCr團(tuán)簇的鍵長r、平均結(jié)合能Eb、垂直電離勢(shì)VIP的理論和實(shí)驗(yàn)值

Table 1 Theoretical and experimental values of bond length r, average binding energy Eband vertical ionization potential IP of Cr2, Al2and AlCr clusters

Cr2Al2AlCrthisworkExpt.[13]thisworkExpt.[14]thisworkTheo.15]Expt.[16]r(?)1.6111.6792.5142.5602.7422.742.74Eb(eV)1.5951.420±0.1001.1890.997±0.1081.1251.172.272±0.009IP(eV)6.0996.3046.200±0.2005.9875.945.96±0.04

3 結(jié)果與討論

3.1 AlnCr (n=1-7)團(tuán)簇的基態(tài)結(jié)構(gòu)

圖1(na) 給出了AlnCr (n=1-7)團(tuán)簇的基態(tài)結(jié)構(gòu).表2給出了AlnCr(n=1-7)團(tuán)簇基態(tài)結(jié)構(gòu)的自旋多重度、對(duì)稱性、總能量、能隙、平均結(jié)合能、垂直電離勢(shì)和垂直電子親和勢(shì).AlCr的鍵長為2.611 ?，自旋多重度為6，與文獻(xiàn)[17]的結(jié)果相一致；Al2Cr呈平面等腰三角形，自旋多重度為5，呈C2V對(duì)稱性；Al3Cr是呈CS對(duì)稱性的三棱錐結(jié)構(gòu)，自旋多重度為4；Al4Cr是呈C4V對(duì)稱性的四棱錐結(jié)構(gòu)，自旋多重度為5；Al5Cr是在Al4Cr的四邊形底面一側(cè)鄰接一Cr原子，自旋多重度為4；Al6Cr是在三棱柱Al6團(tuán)簇的四邊形面上鄰接一Cr原子，自旋多重度為5，對(duì)稱性為C2V；Al7Cr 團(tuán)簇是在呈C4V對(duì)稱性的Al6團(tuán)簇上鄰接一Al原子和Cr原子，自旋多重度為6.總之，AlnCr團(tuán)簇的基態(tài)結(jié)構(gòu)均是Cr原子替換Aln+1團(tuán)簇[18]中一個(gè)Al原子而得到.

圖1 AlnCr (na), AlnCr-H2 (nb)和AlnCrH2 (nc)團(tuán)簇的基態(tài)結(jié)構(gòu) (灰、黑、白色小球分別表示Al, Cr, H原子)Fig.1 Ground state structures of AlnCr (na), AlnCr-H2 (nb) and AlnCrH2 (nc) clusters (gray ball: Al, black ball: Cr, white ball: H)

表2 AlnCr(n=1-7)團(tuán)簇基態(tài)結(jié)構(gòu)的自旋多重度M，對(duì)稱性Sym，總能量E，能隙Gap，平均結(jié)合能Eb，垂直電離勢(shì)VIP和垂直電子親和勢(shì)VEA

Table 2 Multiplicities M, symmetries Sym, total energies Et, HOMO-LUMO Gaps Gap, averaged binding energies Eb, Vertical ionization potentials VIP and Vertical electron affinities VEA for the most stable AlnCr(n=1-7) clusters

ClusterMSymEt(eV)Gap(eV)Eb(eV)VIP(eV)VEA(eV)AlCr6C∞V-8943.8141.9051.1245.9950.605Al2Cr5C2V-15540.7011.3861.3946.1981.441Al3Cr4CS-22138.0161.2371.6275.9991.312Al4Cr5C4V-28735.2201.2651.7136.1441.793Al5Cr4C1-35332.0181.1341.6845.8991.902Al6Cr5C2V-41930.1471.2601.8876.2812.159Al7Cr6C1-48527.631271.4201.9395.8921.746

3.2 H2在AlnCr (n=1-7)團(tuán)簇上的物理吸附

考慮了頂位，橋位和面位三種可能的吸附模式.最穩(wěn)定的吸附結(jié)構(gòu)如圖1(nb)所示.吸附能，能隙，H-H鍵長，平均H-Cr鍵長和H-H振動(dòng)頻率如表3所示.吸附能的定義式如下：

ΔEad=E(AlnCr)+E(H2)-E(AlnCr-H2)

(1)

(1)式中E(AlnCr ), E(H2)和E(AlnCr -H2)分別表示AlnCr，自由H2和AlnCr-H2團(tuán)簇的能量.吸附能均為負(fù)值，即都是放熱反應(yīng).H2分子以側(cè)向的形式吸附在Cr原子的頂位上，這是由于Cr原子低配位，化學(xué)鍵未飽和所致.H-H鍵長范圍為0.744—0.751 ?，相對(duì)自由H2鍵長0.7428 ?，略微變長；吸附能的范圍為0.009-0.064 eV，相對(duì)較?。粌蓚€(gè)H原子與Cr原子的平均距離為2.391-3.701 ?，是典型的范德華相互作用；這三點(diǎn)均說明了典型的物理吸附特征.吸附在團(tuán)簇上氫分子的振動(dòng)頻率為4295-4427 cm-1，相對(duì)自由H2的頻率4650 cm-1，發(fā)生了紅移，這是由氫分子鍵長增加所致.

表3 H2物理吸附在AlnCr(n=1-7)團(tuán)簇上的吸附能△Ead，能隙Gap，H-H鍵長DH-H，平均H-Cr鍵長DH-Cr和H-H振動(dòng)頻率ωH-H

Table 3 Adsorption energies △Ead, HOMO-LUMO gaps Gap, H-H bond lengths DH-H, averaged H-Cr bond lengths DH-Crand H-H vibration frequencies ω for the physisorption of H2on AlnCr(n=1-7) clusters

Cluster△Ead(eV)Gap(eV)DH-H(?)DH-Cr(?)ωH-H(cm-1)AlCr-H2-0.0121.9160.7463.7014393Al2Cr-H2-0.0151.5720.7483.4284351Al3Cr-H2-0.0091.5350.7443.3044427Al4Cr-H2-0.0111.2740.7443.1144419Al5Cr-H2-0.0121.1320.7443.1254415Al6Cr-H2-0.0131.2570.7462.7874391Al7Cr-H2-0.0641.4120.7512.3914295

3.3 H2在AlnCr (n=1-7)團(tuán)簇上的化學(xué)吸附

AlnCrH2的最穩(wěn)定吸附結(jié)構(gòu)如圖1(nc)所示.AlCrH2是平面結(jié)構(gòu)，H-Al鍵長均為1.609 ?，H原子獲得等量電荷(0.116e).Al2CrH2是兩個(gè)氫原子分別鄰接在Al-Al鍵橋位上，H-Al鍵長幾乎相等(1.786 ?,1.787 ?)，H原子獲得等量電荷(0.122e).Al3CrH2是兩個(gè)氫原子分別鄰接在兩個(gè)Al原子的頂位上，H-Al鍵長均為1.597 ?，H原子獲得等量電荷(0.061e).Al4CrH2是兩個(gè)氫原子分別鄰接在相對(duì)的兩個(gè)Al原子的頂位上，H-Al鍵長均為1.591 ?，H原子獲得等量電荷(0.058e).Al5CrH2的基態(tài)結(jié)構(gòu)相對(duì)Al5Cr發(fā)生了根本性變化，不是在Al5Cr基礎(chǔ)上鄰接H原子，而是在Al5Cr亞穩(wěn)定結(jié)構(gòu)基礎(chǔ)上鄰接H原子，一個(gè)H位于Al-Al鍵橋位上，另一個(gè)H位于Al-Cr橋位上，兩個(gè)H原子得到電荷分別為0.118e和0.124e.Al6CrH2是兩個(gè)H原子分別接在相對(duì)的兩個(gè)Al原子的頂位上，H-Al鍵長均為1.592 ?，H原子獲得等量電荷(0.058e).Al7CrH2團(tuán)簇中一個(gè)H原子接在Al的頂位上，一個(gè)H原子接在Cr的頂位上；H-Al鍵長為1.589 ?，H-Cr鍵長為1.713 ?；H分別獲得電荷(0.056e, 0.132e).總之，n=5的最穩(wěn)定結(jié)構(gòu)不是由Al5Cr的最穩(wěn)定結(jié)構(gòu)吸附兩個(gè)H原子，其它AlnCrH2的最穩(wěn)定結(jié)構(gòu)均是在最穩(wěn)定的AlnCr團(tuán)簇上吸附兩個(gè)氫原子；AlnCr向H原子轉(zhuǎn)移了電荷.

由表4和圖1(nc)可以看出，AlnCrH2團(tuán)簇中H-H距離遠(yuǎn)遠(yuǎn)大于H2分子中的H-H鍵長，即H2發(fā)生了解離化學(xué)吸附.化學(xué)吸附能大小反應(yīng)了H2與團(tuán)簇間的化學(xué)反應(yīng)活性，其定義式如下：

ΔECE=E(AlnCr)+E(H2)-E(AlnCrH2)

(2)

(2)式中E(AlnCr )，E(H2)，E(AlnCrH2)分別表示AlnCr團(tuán)簇，自由H2和AlnCrH2團(tuán)簇的能量.由表4可以看出Al7CrH2的化學(xué)吸附能最小，即Al7Cr與H2相互作用時(shí)表現(xiàn)出較強(qiáng)的惰性；而AlCrH2，Al2CrH2和Al6CrH2的化學(xué)吸附能相對(duì)較大，對(duì)H2的化學(xué)吸附表現(xiàn)出較強(qiáng)的化學(xué)活性.

表4 AlnCrH2團(tuán)簇的吸附能△ECE、平均結(jié)合能Eb、能隙Gap、H-H距離DH-H、垂直電離勢(shì)VIP和垂直親和勢(shì)VEA

Table 4 Adsorption energies △ECE, average binding energies Eb, HOMO-LUMO gaps, distances between H-H DH-H, Vertical ionization potentials VIP and Vertical electron affinities VEA for the most stable AlnCrH2(n=1-7) clusters

Cluster△ECE(eV)Eb(eV)Gap(eV)DH-H(?)VIP(eV)VEA(eV)AlCrH21.0646.9493.3012.7207.6060.319Al2CrH21.0404.2921.7222.2196.2281.160Al3CrH20.5883.4071.3861.5976.3301.580Al4CrH20.8063.1041.4097.1626.2711.706Al5CrH20.4882.7341.4092.5266.2521.936Al6CrH20.9002.8301.6636.8106.4711.886Al7CrH20.2952.6621.6284.2036.4632.083

3.4 AlnCr與AlnCrH2的穩(wěn)定性比較

通過計(jì)算平均結(jié)合能、能隙、垂直電離勢(shì)和垂直親和勢(shì)比較了AlnCr與AlnCrH2的穩(wěn)定性.平均結(jié)合能的定義式如下：

Eb(AlnCr)=[nE(Al)+E(Cr)-E(AlnCr)]/n

(3)

Eb(AlnCrH2)=[nE(Al)+E(Cr)+

2E(H)-E(AlnCrH2)]/n

(4)

由表2，表4和圖2可以看出，AlnCr 和AlnCrH2團(tuán)簇的平均結(jié)合能變化范圍分別為：1.124-1.939 eV，2.662-6.949 eV，很明顯AlnCrH2團(tuán)簇的平均結(jié)合能大于AlnCr團(tuán)簇，即AlnCrH2團(tuán)簇更穩(wěn)定；隨著團(tuán)簇尺寸的增加，AlnCrH2團(tuán)簇的平均結(jié)合能逐漸減小，AlnCr團(tuán)簇的平均結(jié)合能逐漸增加；可以推測(cè)出當(dāng)團(tuán)簇尺寸大于某一臨界值時(shí)，二者的平均結(jié)合能幾乎相等，因?yàn)槟菚r(shí)H2分子的影響可以忽略了.

圖2 AlnCr和AlnCrH2團(tuán)簇平均結(jié)合能隨團(tuán)簇尺寸的變化Fig.2 Average binding energies per atom of AlnCr and AlnCrH2 versus cluster size

圖3 AlnCr和AlnCrH2團(tuán)簇垂直電離勢(shì)和垂直親和勢(shì)隨團(tuán)簇尺寸的變化Fig.3 Vertical ionization potentials and Vertical electron affinities of AlnCr and AlnCrH2 versus cluster size

保持陰陽離子團(tuán)簇結(jié)構(gòu)與中性團(tuán)簇結(jié)構(gòu)相同的情況下，計(jì)算的電離勢(shì)或親和勢(shì)稱為垂直電離勢(shì)或垂直親和勢(shì).由圖3可以看出AlnCrH2的電離勢(shì)均大于AlnCr團(tuán)簇的電離勢(shì)，這也說明AlnCrH2團(tuán)簇更加穩(wěn)定，較不容易電離電子；AlnCrH2和AlnCr的電子親和勢(shì)隨團(tuán)簇尺寸變化趨勢(shì)相似，表現(xiàn)出奇偶振動(dòng)現(xiàn)象.由圖4可以看出AlnCrH2和AlnCr的能隙隨團(tuán)簇尺寸變化趨勢(shì)相同，且AlnCrH2的能隙值均大于AlnCr，即AlnCrH2比AlnCr更穩(wěn)定.

圖4 AlnCr和AlnCrH2團(tuán)簇的能隙隨團(tuán)簇尺寸的變化Fig.4 Energy gaps of AlnCr and AlnCrH2 versus cluster size

3.5 H2分子在AlnCr (n=1-7)團(tuán)簇上的解離機(jī)制

以自由AlnCr和H2的能量之和作為勢(shì)能零點(diǎn)，以此得出反應(yīng)物(H2在AlnCr團(tuán)簇上的物理吸附)，過渡態(tài)和產(chǎn)物(H2在AlnCr團(tuán)簇上的化學(xué)吸附)的相對(duì)能量.反應(yīng)物、過渡態(tài)和產(chǎn)物的能量，反應(yīng)能(產(chǎn)物與反應(yīng)物的能量之差)以及反應(yīng)勢(shì)壘(過渡態(tài)與反應(yīng)物能量之差)的計(jì)算結(jié)果見表5.反應(yīng)能均為負(fù)值，說明H2的解離為放熱過程.AlCrH2、Al2CrH2和Al6CrH2的反應(yīng)勢(shì)壘較小，反應(yīng)能較大，化學(xué)吸附能也較大(見表4)；說明AlCrH2、Al2CrH2和Al6CrH2較容易與H2發(fā)生化學(xué)反應(yīng)，當(dāng)H2與它們相互作用時(shí)，H-H鍵較容易斷裂.Al7CrH2團(tuán)簇有最大的反應(yīng)勢(shì)壘(17.154 kcal/mol)，H2不容易發(fā)生化學(xué)吸附.詳細(xì)分析了H2在AlnCr團(tuán)簇上的解離反應(yīng)路徑，即H2+AlnCr→AlnCrH2，搜尋了中間產(chǎn)物和過渡態(tài).圖5給出了H2在AlnCr團(tuán)簇上的解離反應(yīng)路徑以及反應(yīng)物，過渡態(tài)(只有一個(gè)虛頻，其值見表5)和產(chǎn)物的幾何結(jié)構(gòu).對(duì)于AlnCr(n=1-7,n≠4)團(tuán)簇，H2由物理吸附到化學(xué)吸附經(jīng)歷了一個(gè)過渡態(tài)(TS)，跨越的勢(shì)壘值分別為：9.507, 8.070, 5.103, 11.989, 0.821, 17.154 kcal/mol；對(duì)于Al4Cr團(tuán)簇，H2由物理吸附到化學(xué)吸附經(jīng)歷了兩個(gè)過渡態(tài)(TS1和TS2)，首先由反應(yīng)物R經(jīng)過渡態(tài)TS1生產(chǎn)中間產(chǎn)物IM，跨越的勢(shì)壘值為27.928 kcal/mol，中間產(chǎn)物H-H間距離為1.242 ?(產(chǎn)物中H-H距離值見表4)，H-H鍵已斷裂，兩個(gè)氫原子分別與相鄰的兩個(gè)Al原子成鍵；然后由中間態(tài)IM反應(yīng)至最后產(chǎn)物P，跨越的勢(shì)壘值為11.542 kcal/mol，產(chǎn)物P中的兩個(gè)H原子處在相對(duì)的兩個(gè)Al原子上，產(chǎn)物P的能量比中間產(chǎn)物IM低了3.733 kcal/mol.上述結(jié)果表明，H2在不同尺寸AlnCr團(tuán)簇上的反應(yīng)路徑是不同的，故可通過改變AlnCr團(tuán)簇中Al原子的個(gè)數(shù)來調(diào)節(jié)H2的物理化學(xué)吸附行為.

(a)AlCrH2

(b)Al2CrH2

(c)Al3CrH2

(d)Al4CrH2

(e) Al5CrH2

(f) Al6CrH2

(g) Al7CrH2圖5 H2分子在AlnCr團(tuán)簇上的解離反應(yīng)路徑Fig.5 The dissociation reaction pathway of H2 on AlnCr clusters

表5 H2分子在AlnCr團(tuán)簇上解離過程中的反應(yīng)物能量ER、過渡態(tài)能量ETS、產(chǎn)物能量EP、反應(yīng)能ERe、反應(yīng)勢(shì)壘EAc、過渡態(tài)的虛頻ωTS

Table 5 Energies of reactant ER, energies of transition state ETS, energis of product EP, reaction energies ERe, activation barriers EAcand imaginary frequencies of transition state ωTSfor H2dissociation process on AlnCr clusters

ClusterER(kcal/mol)ETS(kcal/mol)EP(kcal/mol)ERe(kcal/mol)EAc(kcal/mol)ωTS(cm-1)AlCrH2-0.2799.227-25.544-25.2649.507-1199Al2CrH2-0.3477.723-23.973-23.6268.070-1113Al3CrH2-0.2084.894-13.559-13.3515.103-463Al4CrH2-0.25827.670-3.315-18.591-18.33327.92811.542-1299-329Al5CrH2-0.27511.714-11.248-10.97311.989-33Al6CrH2-0.3030.518-20.751-20.4480.821-232Al7CrH2-1.47915.676-6.793-5.31417.154-1047

4 結(jié) 論

采用密度泛函理論中的B3LYP方法研究了H2在AlnCr(n=1-7)團(tuán)簇上的吸附和解離.結(jié)果表明：AlnCr團(tuán)簇結(jié)構(gòu)與Aln+1團(tuán)簇結(jié)構(gòu)相似；物理吸附是H2以側(cè)向的形式吸附在Cr原子的頂位上，H-H鍵略微增長，H2的振動(dòng)頻率發(fā)生了紅移；n=5的最穩(wěn)定結(jié)構(gòu)不是Al5Cr的最穩(wěn)定結(jié)構(gòu)吸附兩個(gè)H原子，其它AlnCrH2的最穩(wěn)定結(jié)構(gòu)均是在最穩(wěn)定的AlnCr團(tuán)簇上吸附兩個(gè)氫原子；AlnCr向氫原子轉(zhuǎn)移了電荷；AlnCrH2的平均結(jié)合能，垂直電離勢(shì)和能隙均大于AlnCr的，即AlnCrH2比AlnCr更穩(wěn)定；Al7Cr對(duì)H2的化學(xué)吸附能最小，表現(xiàn)出較強(qiáng)的惰性，而AlnCrH2(n=1,2,6)對(duì)H2的化學(xué)吸附能較大，表現(xiàn)出較強(qiáng)的化學(xué)活性；H2在不同尺寸AlnCr團(tuán)簇上的反應(yīng)路徑是不同的，故可通過改變AlnCr團(tuán)簇中Al原子的個(gè)數(shù)來調(diào)節(jié)H2的物理化學(xué)吸附行為.

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Density functional theoretical investigation for the adsorption and dissociation of molecular hydrogen on AlnCr(n=1-7) clusters

LI Xiang-Fu, LI Gao-Qing

(College of Electrical Engineering, Longdong University, Qingyang 745000, China)

The adsorption and dissociation of molecular hydrogen on AlnCr(n=1-7) clusters are investigated by using the method of B3LYP in density functional theory. The results show that the structures of AlnCr clusters are similar to those of Aln+1clusters. H2is easily adsorbed physically on Cr atom with a side-on orientation. The bond length of H-H increases slightly. The vibration frequency of H2adsorbed is smaller than that of free molecular H2, namely, a red-shift occurs. Except forn=5, the most stable structures of the other AlnCrH2clusters are composed by the most stable structures of AlnCr clusters and two H atoms. Charge transfers from AlnCr clusters to H atoms. Average binding energy, vertical ionization potential and energy gap of AlnCrH2clusters are all greater than those of AlnCr clusters, namely AlnCrH2clusters are more stable than AlnCr clusters. Al7Cr cluster shows stronger inertness for chemical adsorption of H2, while AlnCrH2(n=1,2,6) show stronger chemical activity. The physical and chemical adsorption behavior of H2on AlnCr clusters can be adjusted by changing the number of Al atom in AlnCr clusters from tracking the chemical reaction path.

AlnCr clusters; Molecular hydrogen; Adsorption; Dissociation

李向富(1982—)，男，甘肅環(huán)縣人，理學(xué)碩士，主要從事團(tuán)簇結(jié)構(gòu)及性質(zhì)的研究.

李高清. E-mail: lgaoq@163.com

103969/j.issn.1000-0364.2015.10.010

O641

A

1000-0364(2015)05-0775-08

投稿日期:2015-03-21