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Na||Sb-Pb-Sn液态金属电池电极的价电子结构与热-电性能计算

张健 王心桥 苏彤 陈英 郭永权

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Na||Sb-Pb-Sn液态金属电池电极的价电子结构与热-电性能计算

张健, 王心桥, 苏彤, 陈英, 郭永权

Calculation of thermic and electric properties and valence electron structure for metallic electrodes of Na||Sb-Pb-Sn liquid metal battery

Zhang Jian, Wang Xin-Qiao, Su Tong, Chen Ying, Guo Yong-Quan
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  • 应用固体与分子经验电子理论系统地研究液态金属池Na||Sb-Pb-Sn电极的价电子结构与热、电性能. 研究结果表明: 电极合金的价电子结构与其性能密切关联. 阴极合金Na1–xIAx (IA = K, Rb, Cs)的晶格电子随着掺杂量的增加而减少, 诱发合金的熔点、结合能随掺杂量的增加而降低. Na离子输运到阳极, 与阳极Sb-Sn-Pb形成产物NaSb3, NaSn, Na15Sn4, NaPb. 其理论熔点与实验相符. NaSb3的平均晶格电子数最少, 开路电压最高. 研究表明: 对于Na||Sb-Pb-Sn液态金属电池体系而言, 晶格电子扮演重要的角色, 可以调控电极的热、电性能.
    The valence electron structures and thermal and electric properties of Na||Sb-Pb-Sn liquid metal battery are systematically studies with solid and molecular empirical electron theory (EET). The theoretical studies show that the thermal and electric properties are strongly related to the valence electron structure of electrode. The cathodic alloys Na1–xIAx (IA = K, Rb, Cs) are designed by doping IA group alkali metals (K, Rb, Cs) into Na electrode since the melting points of IA group metals (K, Rb, Cs) are all lower than that of sodium. The theoretical bond lengths and cohesive energy of cathodic alloys Na1–xIAx match the experimental ones well. The theoretical studies show the decreasing tendency of melting point, cohesive energy and electric potential with increasing doping content x in Na1–xIAx alloys, which is due to the modulation of valence electron structure of IA group dopants. According to the analyses of valence structures, the number of lattice electrons decreases with the increasing of the doping content x for the cathodic alloy and causes the melting point, electric potential and cohesive energy to decline. It reveals that the IA group dopant modulates the valence electron structure of cathodic alloy, and induces the electron transformation from lattice electron to covalent electron in s orbital. The anode products such as NaSb3, NaSn, Na15Sn4 and NaPb are formed by transporting Na ions into the anode alloy Sb-Sn-Pb. The calculated bond-lengths and melting points fit the observed ones well for these anode products. Owing to their complex structures with various atomic occupations in unit cell, the thermal property or electric property is not only relative to lattice electron, but also depends on the covalent electron. The sublattice plays an important role in the forming of the four anode products. The lattice electrons are supplied by Na at 4f sites in Na3Sb, Na at 16e and Sn at 32g sites in NaSn, Sn at 16c and Na at 48e sites in Na15Sn4, and Na at 16f and Pb at 32g sites in NaPb, respectively. The open-gate voltage is closely related to the lattice electrons and inversely proportional to the average number of lattice electrons per atom. The open-gate voltage of NaSb3 is the largest among the anode products, however, its averaged number of lattice electron per atom is the least. Since the lattice electron number of NaSn is the largest among the anode products, the open-gate voltage of NaSn is the least. It implies that the lattice electron plays a very important role in Na||Sb-Pb-Sn liquid metal battery, which can modulate the valence electron structures and thermal and electric properties.
      通信作者: 郭永权, yqguo@ncepu.edu.cn
    • 基金项目: 国家重点研发计划(批准号: 2018YFB0905600)资助的课题
      Corresponding author: Guo Yong-Quan, yqguo@ncepu.edu.cn
    • Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2018YFB0905600)
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  • 图 1  阴极Na1–xIAx合金的n电子数与熔点的关联图

    Fig. 1.  Correlations between various electron numbers and melting points of Na1–xIAx cathode alloys.

    图 2  阴极Na1–xIAx合金的各种电子数与结合能的关联图

    Fig. 2.  Correlations between various electrons and cohesive energy of Na1–xIAx cathode alloys.

    图 3  阴极Na1–xIAx合金的各种电子数与电势的关联图

    Fig. 3.  Correlations of various electrons and electric potentials for Na1–xIAx anode alloys.

    表 1  Na1–xIAx合金键距计算

    Table 1.  Calculation of bond distances of Na1–xIAx alloy.

    Na1–xIAx$ {I}_{\alpha } $$ {D}_{\mathrm{uv}}\left({n}_{\alpha }\right) $/Å ${\bar{D}}_{\mathrm{uv}}\left({n}_{\alpha }\right) $/Å$ {n}_{\rm{A}}$$ { I}_{\alpha } $$ {D}_{\mathrm{uv}}\left({n}_{\alpha }\right) $/${ \text{Å} }$${\bar{D} }_{\mathrm{uv} }\left({n}_{\alpha }\right)/{ \text{Å} }$$ {n}_{\alpha } $|∆D|/${\text{Å} }$
    Na83.72963.75020.0516064.30044.32100.008100.0206
    Na0.99K0.0183.73813.75380.0522064.31034.32600.008200.0157
    Na0.99Rb0.0183.74303.75720.0522064.31574.33000.008200.0143
    Na0.99Cs0.0183.74543.76280.0522064.31874.33610.008100.0175
    Na0.98K0.0283.74653.75740.0529064.32024.33100.008230.0108
    Na0.98Rb0.0283.75643.76430.0529064.33104.33890.008200.0079
    Na0.98Cs0.0283.76113.77550.0529064.33704.35130.008170.0143
    Na0.97K0.0383.75503.76100.0534864.33014.33610.008290.0060
    Na0.97Rb0.0383.76973.77130.0535164.34634.34790.008250.0016
    Na0.97Cs0.0383.77693.78810.0535464.35524.36650.008210.0113
    Na0.96K0.0483.76353.76470.0541164.33994.34110.008340.0012
    Na0.96Rb0.0483.78313.77850.0541564.36164.35700.008290.0047
    Na0.96Cs0.0483.79263.80090.0541964.37354.38180.008240.0082
    Na0.95K0.0583.77193.76840.0547464.34984.34630.008400.0036
    Na0.95Rb0.0583.79653.78560.0547964.37694.36610.008340.0109
    Na0.95Cs0.0583.80843.81360.0548464.39184.39710.008270.0052
    下载: 导出CSV

    表 2  Na阴极合金的价电子结构

    Table 2.  Valence electron structures of cathode Na based alloy.

    Na1–xIAxncnsnpnlR(1)
    Na0.46140.46060.00080.53861.4181
    Na0.99K0.010.46680.46600.00080.53321.4217
    Na0.98K0.020.47220.47130.00080.52781.4254
    Na0.97K0.030.47760.47670.00090.52241.4290
    Na0.96K0.040.48300.48210.00090.51701.4327
    Na0.95K0.050.48840.48750.00090.51161.4363
    Na0.99Rb0.010.46680.46600.00080.53321.4235
    Na0.98Rb0.020.47220.47130.00080.52781.4289
    Na0.97Rb0.030.47760.47670.00090.52241.4343
    Na0.96Rb0.040.48300.48210.00090.51701.4397
    Na0.95Rb0.050.48840.48750.00090.51161.4451
    Na0.99Cs0.010.46680.46600.00080.53321.4263
    Na0.98Cs0.020.47220.47130.00080.52781.4345
    Na0.97Cs0.030.47760.47670.00090.52241.4428
    Na0.96Cs0.040.48300.48210.00090.51701.4510
    Na0.95Cs0.050.48840.48750.00090.51161.4592
    下载: 导出CSV

    表 3  阴极Na1–xIAx合金的熔点、结合能与电势

    Table 3.  Melting point, cohesive energy, and electric potentials of cathode Na1–xIAx alloy.

    掺杂量x原子杂阶掺杂杂阶$ \bar{T}_{\rm{m}} $/K$ {E}_{\mathrm{c}} $/(eV·atom–1)$ {\bar{E}}_{\mathrm{c}} $/(eV·atom–1)$\left| { {\Delta E}_{\mathrm{c} } }/{ {E}_{\mathrm{c} } }\right|/{\%}$电势/V
    0Na3336.761.1131.1654.670.1482
    0.01Na2K4336.641.1111.1644.770.1481
    0.01Na2Rb4336.451.1101.1634.770.1480
    0.01Na2Cs4336.021.1031.1615.260.1478
    0.02Na2K4336.641.1091.1634.390.1481
    0.02Na2Rb4336.141.1081.1614.780.1478
    0.02Na2Cs4335.291.1101.1584.320.1475
    0.03Na2K4336.601.1031.1625.350.1480
    0.03Na2Rb4335.851.1091.1594.510.1476
    0.03Na2Cs4334.581.1081.1544.150.1471
    0.04Na2K4336.571.1071.1624.970.1479
    0.04Na2Rb4335.571.1031.1574.900.1474
    0.04Na2Cs4333.881.1091.1513.790.1467
    0.05Na2K4336.551.1081.1614.780.1478
    0.05Na2Rb4335.301.1071.1564.430.1472
    0.05Na2Cs4333.201.1081.1473.520.1463
    下载: 导出CSV

    表 4  正极合金的晶体结构

    Table 4.  Crystal structures of anode alloys.

    合金空间群a/$\text{Å}$b/$\text{Å}$c/$\text{Å}$原子占位xyz
    Sb2c0.33330.66660.2500
    Na3SbP63mmc (194)5.3555.3559.496Na12b000.2500
    Na24f0.33330.66660.5830
    NaSnI41/acd (142)10.46010.46017.390Sn32g0.06960.12600.9362
    Na116f0.62580.87580.1250
    Na216e0.872400.2500
    Sn16c0.20830.20830.2083
    Na15Sn4I43d (220)13.14013.14013.140Na112a0.375000.2500
    Na248e0.12700.15480.9670
    Pb32g0.06960.11860.9383
    NaPbI41/acd (142)10.58010.58017.746Na116e0.25000.12500.5000
    Na216f0.12500.37500.6250
    下载: 导出CSV

    表 5  阳极合金的键距

    Table 5.  Bond distances of the anode alloy.

    合金键序成键原子$ {I}_{\alpha } $$ {D}_{\mathrm{uv}}\left({n}_{\alpha }\right) $/$\text{Å}$$ {\bar{D}}_{\mathrm{uv}}\left({n}_{\alpha }\right)/$$\text{Å}$$ {n}_{\alpha } $|ΔD|/$\text{Å}$
    Na3Sb1Sb-Na263.09753.09100.390550.0065
    2Sb-Na143.16853.16200.194160.0065
    3Na1-Na243.17803.17150.180300.0065
    4Na1-Na163.47693.47040.037380.0065
    5Sb-Na1123.48133.47480.058460.0065
    6Na2-Na1123.48133.47480.056300.0065
    7Na2-Na1124.43104.42450.001470.0065
    8Na2-Na224.75754.75100.000640.0065
    NaSn1Sn-Sn22.97483.02010.426500.0453
    2Sn-Sn42.99253.03780.398490.0453
    3Na1-Sn43.33553.38080.075060.0453
    4Na1-Sn43.35923.40450.068540.0453
    5Na2-Sn43.39743.44270.130640.0453
    6Na2-Sn43.42313.46840.118370.0453
    7Na1-Sn43.48703.53230.041970.0453
    8Na2-Sn23.52253.56780.080830.0453
    9Na2-Sn43.54823.59350.073240.0453
    10Na1-Na243.61483.66010.039850.0453
    11Na1-Na243.66583.71110.032770.0453
    12Na1-Na113.72183.76710.011970.0453
    13Sn-Sn23.74063.78590.022570.0453
    14Sn-Sn24.37804.42330.001960.0453
    15Na1-Na244.49194.53720.001380.0453
    16Na1-Sn44.66744.71270.000450.0453
    17Na2-Na214.70954.75480.001320.0453
    Na15Sn41Sn-Na2243.23783.28540.208500.0476
    2Na2-Na2243.26243.31000.194990.0476
    3Na1-Na2243.34253.39010.110170.0476
    4Na2-Na2123.34683.39440.148300.0476
    5Sn-Na2243.40493.45250.121270.0476
    6Sn-Na2243.41893.46650.115890.0476
    7Na1-Na2243.50263.55020.065550.0476
    8Sn-Na1243.54823.59580.055820.0476
    9Na2-Na2243.81383.86140.032610.047
    10Na2-Na2243.97944.02700.019060.0476
    11Na2-Na2124.17124.21880.010230.0476
    NaPb1Pb-Pb23.14643.14520.334770.0013
    2Pb-Pb43.16183.16060.315560.0013
    3Pb-Na243.36533.36410.198950.0013
    4Pb-Na143.38883.38760.082370.0013
    5Pb-Na243.42153.42030.160350.0013
    6Pb-Na243.48473.48350.125820.0013
    7Pb-Na143.49293.49170.055240.0013
    8Pb-Na143.55493.55370.043540.0013
    9Pb-Na143.61723.61600.034280.0013
    10Pb-Pb23.64183.64060.050010.0013
    11Na1-Na283.69673.69550.034790.0013
    12Na2-Na213.74063.73940.064880.0013
    13Pb-Pb24.40084.39960.002720.0013
    14Na1-Na244.54554.54430.001340.0013
    15Pb-Na244.75134.75010.000970.0013
    下载: 导出CSV

    表 6  阳极产物的价电子结构

    Table 6.  Valence electron structures of anode products

    合金原子杂阶ncnsnpnlR(1)
    Na3SbSb23.00000.56942.430601.4279
    Na141.00000.99820.001801.3070
    Na220.46140.46060.00080.53861.4181
    NaSnSn12.000002.00002.00001.3990
    Na111.00000.99820.001801.3070
    Na240001.00001.5133
    Na15Sn4Sn43.66380.83192.83190.33621.3990
    Na141.00000.99820.001801.3070
    Na230.53500.53400.00100.46501.4029
    NaPbPb22.09620.04812.04811.90381.4300
    Na141.00000.99820.001801.3070
    Na210001.00001.5133
    下载: 导出CSV

    表 7  正极合金的熔点、结合能与电势

    Table 7.  Melting point, cohesive energy, and electric potentials of anode alloy.

    合金Tm/K [35]$ \bar{T}_{\rm{m}} $/K|${\Delta {T}_{\mathrm{m} } }/{ {T}_{\mathrm{m} } }$|/%电势/VnβEc/(eV·atom–1)
    Na3Sb11291142.961.21.152040.601.766
    NaSn851813.164.40.734350.602.103
    Na15Sn4681746.169.60.907430.711.318
    NaPb645630.682.20.826360.601.559
    下载: 导出CSV

    表 8  电池的开路电压

    Table 8.  Open gate voltages of the battery.

    Na1–xIAx开路电压/V
    Na3SbNaSnNa15Sn4NaPb
    Na1.00380.58610.75920.6781
    Na0.09K0.011.00390.58620.75930.6782
    Na0.98K0.021.00390.58620.75930.6782
    Na0.97K0.031.00400.58630.75940.6783
    Na0.96K0.041.00410.58640.75950.6784
    Na0.95K0.051.00420.58650.75960.6785
    Na0.99Rb0.011.00400.58630.75940.6783
    Na0.98Rb0.021.00420.58650.75960.6785
    Na0.97Rb0.031.00440.58670.75980.6787
    Na0.96Rb0.041.00460.58690.76000.6789
    Na0.95Rb0.051.00480.58710.76020.6791
    Na0.99Cs0.011.00420.58650.75960.6785
    Na0.98Cs0.021.00450.58680.75990.6788
    Na0.97Cs0.031.00490.58720.76030.6792
    Na0.96Cs0.041.00530.58760.76070.6796
    Na0.95Cs0.051.00570.58800.76110.6800
    nl/atom0.26931.25000.36451.0682
    下载: 导出CSV

    表 A1  IA族元素的乙种杂化表

    Table A1.  B type hybrid table of IA group

    σ1234
    Chσ10.53860.46500
    Ctσ00.46160.53501
    nTσ1111
    nlσ10.53860.46500
    ncσ00.46160.53501
    Rσ(1)H0.37080.32890.32220.2800
    Li1.32601.20891.14400.9860
    Na1.51331.45511.43081.3070
    K1.96281.87941.86011.7820
    Rb2.08702.02702.01751.9570
    Cs2.21402.22602.22792.2400
    注: $ l, \; m, \;n, \; \tau $: 1 0 0 0
      $l{'}, \; m{'}, \;n{'}, \; \tau {'}$: 0.9982 0.0018 0 0
    下载: 导出CSV

    表 A2  VA族元素的甲种杂化表

    Table A2.  A type hybrid table of VA group

    σ1234
    Chσ10.56940.19830
    Ctσ00.43060.80171
    nTσ3 or 53 or 53 or 53 or 5
    nlσ0000
    ncσ3 or 53 or 53 or 53 or 5
    Rσ (1)N0.70000.75170.79730.8200
    P1.09801.11731.13431.1428
    As1.18001.23901.29111.3170
    Sb1.35601.42791.49191.5230
    Bi1.39901.44551.50441.5290
    注: $ l, \; m, \; n, \; \tau $: 1 2 0 1; $ l{'}, \; m{'}, \; n{'}, \; \tau {'} $: 0 3 0 1
    下载: 导出CSV

    表 A3  IVA族元素的甲种杂化表

    Table A3.  A type hybrid table of IVA group

    σ123456
    Chσ10.95020.83200.16810.04810
    Ctσ00.04980.16800.83190.95191
    nTσ444444
    nlσ21.90401.66400.33600.09600
    ncσ22.09602.33603.66403.90404
    Rσ(1)C0.76300.76300.76300.76300.76300.7630
    Si1.17001.17001.17001.17001.17001.1700
    Ge1.22301.22301.22301.22301.22301.2230
    Sn1.39901.39901.39901.39901.39901.3990
    Pb1.43001.43001.43001.43001.43001.4300
    注: $ l, \; m, \; n, \; \tau $; 2 2 0 0; $ l{'}, \; m{'}, \; n{'}, \; \tau {'}; $ 1 3 0 1
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-09-30
  • 修回日期:  2020-12-01
  • 上网日期:  2021-04-02
  • 刊出日期:  2021-04-20

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