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中国物理学会期刊
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Structure and stability of possible new L i-Y-H ternary hydrides

Li Huan ,  Ye Xiao-Qiu ,  Tang Jun ,  Ao Bing-Yun ,  Gao Tao

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Li Huan, Ye Xiao-Qiu, Tang Jun, Ao Bing-Yun, Gao Tao. Structure and stability of possible new L i-Y-H ternary hydrides. Acta Phys. Sin., 2022, 71(1): 017401. doi: 10.7498/aps.71.20210824
Citation: Li Huan, Ye Xiao-Qiu, Tang Jun, Ao Bing-Yun, Gao Tao. Structure and stability of possible new L i-Y-H ternary hydrides. Acta Phys. Sin., 2022, 71(1): 017401. doi: 10.7498/aps.71.20210824
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Structure and stability of possible new L i-Y-H ternary hydrides

Li Huan, Ye Xiao-Qiu, Tang Jun, Ao Bing-Yun, Gao Tao
Acta Phys. Sin., 2022, 71(1): 017401.
doi: 10.7498/aps.71.20210824
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  • Abstract

    The research on the superconductivity of hydrogen-rich compounds has become a hot research topic in the field of high-temperature superconductors in recent years and yttrium hydride YH9+x has been experimentally confirmed to have high temperature superconductivity (near room temperature (Tc = 262 K)), following behind the research of H3S (Tc = 200 K) and LaH10 (Tc = 260 K). The theoretical study of binary hydrogen-rich systems is relatively mature, while the structural characteristics and superconductivity of ternary or quaternary hydrogen-rich compounds are still under exploration. In this paper, nLiH + YH3→LinYHn+3 (n = 1–3) is the synthesis way to explore the stable configuration of ternary hydride LinYHn+3 in a pressure range of 0–300 GPa. The crystal structure, electronic structure, thermodynamic and kinetic stability of LiYH4, Li2YH5 and Li3YH6 in the pressure range of 0–300 GPa are studied based on the structure prediction by particle swarm optimization algorithm and first-principles calculation. The CALYPSO method is used to search for 1–4 times molecular formula structures for Li-Y-H ternary systems with different stoichiometric ratios in the pressure range of 0–300 GPa in steps of 50 GPa. The results show that LiYH4-P4/nmm, Li2YH5-I4/mmm, and Li3YH6-P4/nmm can be respectively synthesized with a certain ratio between LiH and YH3 respectively in a pressure range of 169–221 GPa, 141–300 GPa and 166–300 GPa. The Li2YH5 has the lowest stable pressure and widest range which can be the possible choice in experiment. The results can provide the data support for the superconductivity research and experimental synthesis of hydrides in Li-Y-H ternary system.
      PACS:
      74.70.Dd(Ternary, quaternary, and multinary compounds)
      74.10.+v(Occurrence, potential candidates)
      71.15.-m(Methods of electronic structure calculations)

    Authors and contacts

    • 1.

      Science and Technology on Surface Physics and Chemistry Laboratory, Mianyang 621907, China

    • 2.

      Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China

      • Corresponding author: Ye Xiao-Qiu, xiaoqiugood@sina.com ; Gao Tao, gaotao@scu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 21401173)

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    氢的金属化研究, 是当前凝聚态物理学最重要的研究领域之一, 具有重要的工程意义和科学意义.

    理论和实验均证实, 富氢材料中的氢由于化学或物理预压缩作用, 相比于纯氢, 富氢材料体系可以在较低的压力下金属化并呈现超导电性[1]. Roald Hoffmann、马琰铭、Eremets等研究组[2-5]对各种富氢材料开展了广泛的研究. 在高压下二元富氢材料中已发现了系列高温超导体[6], 特别是首先被理论预测随后被实验证实的新型硫氢化物H3S[7]和镧系氢化物LaH10[8-11], 以及2019年报道的实验已合成并证实超导性的YH6[12]和YH9[12], 它们的超导转变温度均超过200 K; 最近实验证实了钇氢化物(YH9+x)[13]超导温度高达262 K.

    组成元素数量的增加一般会导致多元氢化物中稳定超导化合物的数量迅速增加, 这使得三元氢化物体系比二元氢化物体系更适合用于寻找高温超导体. 2019年, 孙莹等[14]通过理论计算研究发现立方相Li2MgH16氢笼合物(空间群Fd-3m)在250 GPa下具有高达473 K的超导温度; 然而, 该三元化合物是高压亚稳相, 不容易被高压实验制备. 在Li-Mg-H体系中, Li和Mg金属原子作为电子供体, 使H2分子解离为H原子, 形成氢的笼子. 相较于Mg原子, 稀土金属可以提供更多的电子用于H2分子单元的解离, 如将Mg原子换做稀土金属原子有可能设计实现含有更大“氢笼”的氢笼合物高温超导体. 基于此思路, 孙莹[15]将Li2MgH16中的Mg替换成Y, 获得了一种热力学和动力学均稳定的立方Li2YH17新型氢笼合物(空间群Fd-3m), 并预言200 GPa下其超导转变温度约为112 K. 相比于Li2MgH16, Li2YH17将有可能通过高压实验合成.

    目前三元体系的高温超导研究尚处于起步阶段, 设计稳定的、易于合成的三元高温超导体仍然是亟需解决的重要科学问题. 鉴于LiH[4]和YH3[9,16,17]是稳定存在且易于获得的二元氢化物, 本文以nLiH + YH3→LinYHn+3 (n = 1—3)为合成路线, 探索三元氢化物LinYHn+3在0—300 GPa压力范围内的稳定构型, 以期为Li-Y-H三元体系氢化物的超导电性研究及实验合成提供数据支撑.

    基于粒子群优化算法的CALYPSO晶体结构预测方法和软件[18-20]已成功应用于多元体系的高压结构预测, 该方法只需要给定化合物的化学成分即可在给定压力下预测稳定或亚稳定结构. 采用CALYPSO方法在0—300 GPa压力范围内每隔50 GPa针对3种不同化学计量比的Li-Y-H三元体系(LiYH4, Li2YH5, Li3YH6)进行了1—4倍分子式结构搜索.

    在获得晶体结构之后, 利用第一性原理计算软件包VASP(Vienna ab-initio simulation package)[21]进行了结构弛豫、电子局域函数(ELF)、电子能带结构和态密度等方面的计算. 采用梯度校正(Generalized gradient approximation, GGA)[22]下的Perdew-Burke-Ernzerh(PBE)[22,23]方法交换关联泛函. 布里渊区中的K网格的精度选取为2π × 0.03 Å–1 (1 Å = 0.1 nm), 截断能设置为400 eV. ELF分析[24]被用于描述和可视化分子和固体中的化学键. 利用Bader电荷分析方法分析电荷转移[25-27]. 稳定结构的声子色散曲线和声子态密度的计算分别是通过密度泛函微扰理论和有限位移方法结合PHONOPY代码程序[28]来实现的. 电声耦合作用的计算是通过QUANTUM-ESPRESSO软件包[29]来计算的; 选用了Perdew-Wang LDA类型的模守恒赝势, 截断能选取为80 Ry, 第一布里渊区内的q点网格选取为6×6×2.

    3.1   LiYH4

    LiYH4各结构的焓差曲线如图1所示, 其相变序列为P21/m→P4/nmm→Cmmm, 相转变压力分别为25 GPa和301 GPa. P21/m (Z = 2, 图2(a))为单斜结构, 在YH3[30]中也报道了类似结构; 在结构弛豫的过程中, 当施加的压力增大到150 GPa左右时, 它的对称性转变为P4/nmm. 在这个结构中, Li和Y原子分别被3个氢原子和9个氢原子围绕, Li-H和Y-H最短距离分别为1.88 Å和2.13 Å. 四方结构P4/nmm (Z = 2, 图2(b))中每个Li原子周围有9个氢原子, Y原子周围有12个氢原子, Li-H/Y-H最短距离为1.49 Å/1.87 Å. 正交结构Cmmm (Z = 2, 图2(c)) 中每个Li原子周围有8个氢原子, Y原子周围有14个氢原子, Li-H/Y-H最短距离为1.42 Å/1.69 Å. 可见, 在这些结构中Li-H距离均小于Y-H距离, 且随着压力增大, 金属与氢之间距离逐渐减小.

    图 1 LiYH4每分子式的基态静态焓随压力的变化关系, 以具有P4/nmm空间群的LiYH4结构为基准; 插图为300—330 GPa压力范围内的局部放大图\r\nFig. 1. Ground-state static enthalpy curves per formula unit as a function of pressure (with respect to the P4/nmm structure) for static LiYH4. The inset is a partial enlargement of the pressure range 300−330 GPa.
    图 1  LiYH4每分子式的基态静态焓随压力的变化关系, 以具有P4/nmm空间群的LiYH4结构为基准; 插图为300—330 GPa压力范围内的局部放大图
    Fig. 1.  Ground-state static enthalpy curves per formula unit as a function of pressure (with respect to the P4/nmm structure) for static LiYH4. The inset is a partial enlargement of the pressure range 300−330 GPa.
    下载: 全尺寸图片 幻灯片
    图 2 LiYH4的晶体结构. 绿色、紫色、粉色小球分别代表Li, Y, H原子(Li-H, Y-H和H-H距离分别小于2.20 Å, 2.47 Å和2.00 Å)(a) 101.325 kPa时的P21/m; (b) 压力为150 GPa时的P4/nmm; (c) 压力为300 GPa时的Cmmm\r\nFig. 2. Crystal structures of (a) P21/m LiYH4 at 1 atm, (b) P4/nmm LiYH4 at 150 GPa and (c) Cmmm LiYH4 at 300 GPa. The green, purple and pink spheres represent Li, Y and H atoms, respectively. Lines are drawn for Li-H, Y-H and H-H separations shorter than 2.20 Å, 2.47 Å and 2.00 Å, respectively.
    图 2  LiYH4的晶体结构. 绿色、紫色、粉色小球分别代表Li, Y, H原子(Li-H, Y-H和H-H距离分别小于2.20 Å, 2.47 Å和2.00 Å)(a) 101.325 kPa时的P21/m; (b) 压力为150 GPa时的P4/nmm; (c) 压力为300 GPa时的Cmmm
    Fig. 2.  Crystal structures of (a) P21/m LiYH4 at 1 atm, (b) P4/nmm LiYH4 at 150 GPa and (c) Cmmm LiYH4 at 300 GPa. The green, purple and pink spheres represent Li, Y and H atoms, respectively. Lines are drawn for Li-H, Y-H and H-H separations shorter than 2.20 Å, 2.47 Å and 2.00 Å, respectively.
    下载: 全尺寸图片 幻灯片

    由于氢原子的质量非常小, 且轻元素常伴随高振动频率, 零点振动能 (ZPE, 粒子在绝对零度时的振动所具有的能量; 一般情况下含有氢或氦等元素的材料, 应加上零点能计算总能. 对不同含氢量体系中各相结构的整体稳定压力范围有不同程度的影响. 考虑零点能修正后, P21/m相LiYH4在17 GPa的较低压力下相转变为P4/nmm相(图3(a)); P4/nmm相在301 GPa转化成Cmmm相 (零点能的详细数据参见Table S1).

    图 3 考虑零点能(ZPE) 修正后不同LiYH4结构的焓值在　(a) 0−35 GPa范围内和 (b) 290−325 GPa范围内随压力的变化关系\r\nFig. 3. Change of enthalpy of different LiYH4 structures with pressure in the range of (a) 0−35 GPa and (b) 290−325 GPa after the correction of zero point energy (ZPE) was considered.
    图 3  考虑零点能(ZPE) 修正后不同LiYH4结构的焓值在　(a) 0−35 GPa范围内和 (b) 290−325 GPa范围内随压力的变化关系
    Fig. 3.  Change of enthalpy of different LiYH4 structures with pressure in the range of (a) 0−35 GPa and (b) 290−325 GPa after the correction of zero point energy (ZPE) was considered.
    下载: 全尺寸图片 幻灯片

    LiYH4的P21/m、P4/nmm、Cmmm结构中最短的H-H距离分别为2.35 Å, 1.89 Å、1.31 Å, 随压力的增大, 结构中H-H距离减小趋势明显. 三维电子局域函数(ELF)(图4)显示, LiYH4高压相Cmmm在300 GPa下H1和H6原子之间存在较弱的相互作用(图4(c)), 实际上, H1和H6原子之间相交的区域(绿色区域)ELF数值较小, 不足0.5, 不能判断它们之间是否形成了共价键; 而如图4(a)和4(b)所示, 当ELF图的等值面值设置为0.5时, 低压相P21/m和P4/nmm中H原子之间不存在相互作用, 在3.5节中Bader电荷分析P4/nmm结构中H呈离子性, 进一步说明该结构中H原子之间没有共价相互作用.

    图 4 不同LiYH4结构　(a) P21/m (1 atm), (b) P4/nmm (150 GPa)和 (c) Cmmm (300 GPa)的等值面值为0.5的三维电子局域函数(ELF)\r\nFig. 4. Three-dimensional electron local function (ELF) with anisosurface value of 0.5 for different LiYH4 phase structures (a) P21/m (101.325 kPa), (b) P4/nmm (150 GPa) and (c) Cmmm (300 GPa).
    图 4  不同LiYH4结构　(a) P21/m (1 atm), (b) P4/nmm (150 GPa)和 (c) Cmmm (300 GPa)的等值面值为0.5的三维电子局域函数(ELF)
    Fig. 4.  Three-dimensional electron local function (ELF) with anisosurface value of 0.5 for different LiYH4 phase structures (a) P21/m (101.325 kPa), (b) P4/nmm (150 GPa) and (c) Cmmm (300 GPa).
    下载: 全尺寸图片 幻灯片

    3.2   Li2YH5

    对于Li2YH5, 压力低于14 GPa时, Cmc21 (Z=4, 图5(a))、Pmn21 (Z=4, 图5(b))和Pmmn (Z = 4, 图5(c))结构在焓上非常接近. 如图6中插图所示, 8 GPa以下, Cmc21结构焓值最低; 8—14 GPa, Pmmn结构最稳定; 压力高于14 GPa时, I4/mmm (Z = 2, 图5(d))结构最稳定. Cmc21, Pmn21和Pmmn相的焓值在0—80 GPa压力范围内非常接近, 压力高于80 GPa时, Cmc21和Pmn21相的焓值明显低于Pmmn的焓值. 从图6中插图可以看出, 零点振动能对其稳定压力范围影响不大, 且不影响整体相变序列. Cmc21和Pmmn相均为正交结构, 其中每个Li原子周围有6个氢原子, Y原子周围分别有10个氢原子和9个氢原子, Li-H/Y-H最短距离为1.88 Å/2.19 Å (Cmc21相)、1.86 Å/2.22 Å (Pmmn相). I4/mmm为四方结构, 其中每个Li原子周围有9个氢原子, Y原子周围有12个氢原子, Li-H/Y-H最短距离为1.38 Å/1.77 Å.

    图 5 Li2YH5的晶体结构. 绿色、紫色、粉色小球分别代表Li, Y, H原子(Li-H, Y-H和H-H距离分别小于2.20 Å, 2.47 Å和2.00 Å)(a) 101.325 kPa下的Cmc21; (b) 101.325 kPa下的Pmn21; (c) 101.325 kPa下的Pmmn; (d) 300 GPa下的I4/mmm\r\nFig. 5. The crystal structures of (a) Cmc21 Li2YH5 at 101.325 kPa, (b) Pmn21 Li2YH5 at 101.325 kPa, (c) Pmmn Li2YH5 at 1 101.325 kPa and (d) I4/mmm Li2YH5at 300 GPa. The green, purple and pink spheres represent Li, Y and H atoms, respectively. Lines are drawn for Li-H, Y-H and H-H separations shorter than 2.20 Å, 2.47 Å and 2.00 Å, respectively.
    图 5  Li2YH5的晶体结构. 绿色、紫色、粉色小球分别代表Li, Y, H原子(Li-H, Y-H和H-H距离分别小于2.20 Å, 2.47 Å和2.00 Å)(a) 101.325 kPa下的Cmc21; (b) 101.325 kPa下的Pmn21; (c) 101.325 kPa下的Pmmn; (d) 300 GPa下的I4/mmm
    Fig. 5.  The crystal structures of (a) Cmc21 Li2YH5 at 101.325 kPa, (b) Pmn21 Li2YH5 at 101.325 kPa, (c) Pmmn Li2YH5 at 1 101.325 kPa and (d) I4/mmm Li2YH5at 300 GPa. The green, purple and pink spheres represent Li, Y and H atoms, respectively. Lines are drawn for Li-H, Y-H and H-H separations shorter than 2.20 Å, 2.47 Å and 2.00 Å, respectively.
    下载: 全尺寸图片 幻灯片
    图 6 Li2YH5每分子式的基态静态焓随压力的变化关系, 以具有I4/mmm空间群的Li2YH5结构为基准; 插图为考虑零点能 (ZPE) 修正后焓随压力的变化\r\nFig. 6. Ground-state static enthalpy curves per formula unit as a function of pressure (with respect to the I4/mmm structure) for static Li2YH5. The inset shows a modified enthalpy curve considering zero point energy (ZPE).
    图 6  Li2YH5每分子式的基态静态焓随压力的变化关系, 以具有I4/mmm空间群的Li2YH5结构为基准; 插图为考虑零点能 (ZPE) 修正后焓随压力的变化
    Fig. 6.  Ground-state static enthalpy curves per formula unit as a function of pressure (with respect to the I4/mmm structure) for static Li2YH5. The inset shows a modified enthalpy curve considering zero point energy (ZPE).
    下载: 全尺寸图片 幻灯片

    Li2YH5的Cmc21, Pmmn, I4/mmm结构中最短的H-H距离分别为2.04 Å, 2.36 Å, 1.48 Å, 比H2分子本身的H-H键长(0.74 Å)和单原子氢在500 GPa时的H-H距离(0.98 Å)[31]要长得多, 从它们的ELF图(图7) 可看出, Cmc21和Pmmn结构中H原子之间没有相互作用, I4/mmm结构中部分H原子与其最邻近的一个H原子之间存在较弱的相互作用.

    图 7 不同Li2YH5结构　(a) Cmc21 (101.325 kPa), (b) Pmmn (101.325 kPa)和 (c) I4/mmm (300 GPa)的等值面值为0.5的三维电子局域函数(ELF)\r\nFig. 7. Three-dimensional electron local function (ELF) with anisosurface value of 0.5 for different Li2YH5 phase structures (a) Cmc21 (101.325 kPa), (b) Pmmn (101.325 kPa) and (c) I4/mmm (300 GPa).
    图 7  不同Li2YH5结构　(a) Cmc21 (101.325 kPa), (b) Pmmn (101.325 kPa)和 (c) I4/mmm (300 GPa)的等值面值为0.5的三维电子局域函数(ELF)
    Fig. 7.  Three-dimensional electron local function (ELF) with anisosurface value of 0.5 for different Li2YH5 phase structures (a) Cmc21 (101.325 kPa), (b) Pmmn (101.325 kPa) and (c) I4/mmm (300 GPa).
    下载: 全尺寸图片 幻灯片

    3.3   Li3YH6

    Li3YH6的相变序列为单斜P21/m (Z = 2, 图8(a))→正交Cmcm (Z = 4, 图8(b))→四方P4/nmm (Z = 2, 图8(c))结构, 如图9所示, 各相之间转变压力分别为11 GPa和82 GPa. 考虑零点能修正后, 正交Cmcm相Li3YH6在55 GPa的较低压力下相转变为P4/nmm相.

    图 8 Li3YH6的晶体结构. 绿色、紫色、粉色小球分别代表Li, Y, H原子(Li-H, Y-H和H-H距离分别小于2.20 Å, 2.47 Å和2.00 Å)(a) P21/m (101.325 kPa); (b) Cmcm (100 GPa); (c) P4/nmm (300 GPa)\r\nFig. 8. Crystal structures of (a) P21/m Li3YH6 at 101.325 kPa, (b) CmcmLi3YH6 at 100 GPa and (c) P4/nmn Li3YH6 at 300 GPa. The green, purple and pink spheres represent Li, Y and H atoms, respectively.Lines are drawn for Li-H, Y-H and H-H separations shorter than 2.30 Å, 2.47 Å and 2.00 Å, respectively.
    图 8  Li3YH6的晶体结构. 绿色、紫色、粉色小球分别代表Li, Y, H原子(Li-H, Y-H和H-H距离分别小于2.20 Å, 2.47 Å和2.00 Å)(a) P21/m (101.325 kPa); (b) Cmcm (100 GPa); (c) P4/nmm (300 GPa)
    Fig. 8.  Crystal structures of (a) P21/m Li3YH6 at 101.325 kPa, (b) CmcmLi3YH6 at 100 GPa and (c) P4/nmn Li3YH6 at 300 GPa. The green, purple and pink spheres represent Li, Y and H atoms, respectively.Lines are drawn for Li-H, Y-H and H-H separations shorter than 2.30 Å, 2.47 Å and 2.00 Å, respectively.
    下载: 全尺寸图片 幻灯片
    图 9 Li3YH6的每个公式单位的焓值随压力的变化关系, 以P4/nmm结构的焓值为基准(考虑ZPEs的影响)\r\nFig. 9. Eenthalpy curves per formula unit as a function of pressure with respect to the predicted P4/nmm structure for static Li3YH6, ZPEs included.
    图 9  Li3YH6的每个公式单位的焓值随压力的变化关系, 以P4/nmm结构的焓值为基准(考虑ZPEs的影响)
    Fig. 9.  Eenthalpy curves per formula unit as a function of pressure with respect to the predicted P4/nmm structure for static Li3YH6, ZPEs included.
    下载: 全尺寸图片 幻灯片

    Li3YH6的P21/m, Cmcm, P4/nmm结构中Li-H/Y-H最短距离分别为1.81 Å/2.22 Å, 1.51 Å/1.94 Å, 1.39 Å/1.75 Å, 其中H原子与H原子的最小间距分别为2.17 Å, 1.84 Å, 1.50 Å, 均大于笼形稀土氢化物ReH6, ReH9, ReH10 (高温超导候选材料, Re为稀土元素) 结构中的H-H间距(约1 Å)[8]. 同其他两种配比化合物 (LiYH4和Li2YH5) 一样, 随着压力升高, 金属与氢之间的距离以及氢与氢之间的距离均逐渐减小. 电子局域函数ELF可进一步分析上述结构中原子间的成键情况. 如图10所示, Li/Y和H之间没有局域电荷, 表明了Li/Y原子与H原子之间的化学成键是纯离子键; 由于H-H距离太远, 最近邻的H原子之间也没有局域电荷, 表明H原子之间没有共价相互作用.

    图 10 不同Li3YH6结构　(a) P21/m(101.325 kPa), (b) Cmcm (100 GPa)和 (c) P4/nmm (300 GPa)的等值面值为0.5的三维局域函数 (ELF)\r\nFig. 10. Three-dimensional electron local function (ELF) with an isosurface value of 0.5 for different Li3YH6 phase structures (a) P21/m (1 101.325 kPa), (b) Cmcm (100 GPa) and (c) P4/nmm (300 GPa).
    图 10  不同Li3YH6结构　(a) P21/m(101.325 kPa), (b) Cmcm (100 GPa)和 (c) P4/nmm (300 GPa)的等值面值为0.5的三维局域函数 (ELF)
    Fig. 10.  Three-dimensional electron local function (ELF) with an isosurface value of 0.5 for different Li3YH6 phase structures (a) P21/m (1 101.325 kPa), (b) Cmcm (100 GPa) and (c) P4/nmm (300 GPa).
    下载: 全尺寸图片 幻灯片

    3.4   LinYHn+3(n = 1—3)的热力学稳定性和动力学稳定性

    通过nLiH + YH3→LinYHn+3 (n = 1—3) 合成途径来分析LinYHn+3的热力学稳定性. 对于LiYH4的P21/m, P4/nmm, Cmmm3个结构, 将它们的焓值分别与LiH + YH3的焓值作差, 得到如图11所示的这3个结构相对于LiH + YH3的焓差曲线. 图11中焓差为负的区域为LiYH4的热力学稳定区域, 焓差为正则表示LiYH4会分解成LiH和YH3. 从图中可以看出LiYH4的P4/nmm相在169—221 GPa压力范围内是稳定的, 可以由LiH和YH3按1∶1配比加压合成. 考虑LiYH4-P4/nmm的零点能修正后, 其热力学稳定压力范围为169—209 GPa.

    图 11 LiYH4的不同结构(P21/m, P4/nmm和Cmmm)相对于LiH + YH3的焓随压力的变化曲线(包含ZPEs的影响)\r\nFig. 11. Enthalpy curves of various structures (P21/m, P4/nmm and Cmmm) of LiYH4 relative to the products LiH + YH3 as functions of pressure, ZPEs included.
    图 11  LiYH4的不同结构(P21/m, P4/nmm和Cmmm)相对于LiH + YH3的焓随压力的变化曲线(包含ZPEs的影响)
    Fig. 11.  Enthalpy curves of various structures (P21/m, P4/nmm and Cmmm) of LiYH4 relative to the products LiH + YH3 as functions of pressure, ZPEs included.
    下载: 全尺寸图片 幻灯片

    图12给出了Li2YH5各压力区间内稳定结构相对于2LiH + YH3的焓差曲线. 从图中可以看出, I4/mmm相Li2YH5结构可由LiH和YH3按2∶1配比在141 GPa以上合成. 图13则显示P4/nmm相Li3YH6在未考虑ZPE的影响时可以由LiH和YH3按3∶1配比在166 GPa以上合成, 当考虑ZPE后, P4/nmm相结构在173 GPa以上是稳定的, 不会分解为LiH和YH3.

    图 12 Li2YH5的不同结构(Cmc21, Pmmn和I4/mmm)相对于2 LiH + YH3的焓随压力的变化曲线(包含ZPEs的影响)\r\nFig. 12. Enthalpy curves of various structures (Cmc21, Pmmn and I4/mmm) of Li2YH5 relative to the products 2 LiH + YH3 as functions of pressure, ZPEs included.
    图 12  Li2YH5的不同结构(Cmc21, Pmmn和I4/mmm)相对于2 LiH + YH3的焓随压力的变化曲线(包含ZPEs的影响)
    Fig. 12.  Enthalpy curves of various structures (Cmc21, Pmmn and I4/mmm) of Li2YH5 relative to the products 2 LiH + YH3 as functions of pressure, ZPEs included.
    下载: 全尺寸图片 幻灯片
    图 13 Li3YH6的不同结构(P21/m, Cmcm和P4/nmm)相对于3 LiH + YH3的焓随压力的变化曲线(包含ZPEs的影响)\r\nFig. 13. Enthalpy curves of various structures (P21/m, Cmcm and P4/nmm) of Li3YH6 relative to the products 3 LiH + YH3 as functions of pressure, ZPEs included.
    图 13  Li3YH6的不同结构(P21/m, Cmcm和P4/nmm)相对于3 LiH + YH3的焓随压力的变化曲线(包含ZPEs的影响)
    Fig. 13.  Enthalpy curves of various structures (P21/m, Cmcm and P4/nmm) of Li3YH6 relative to the products 3 LiH + YH3 as functions of pressure, ZPEs included.
    下载: 全尺寸图片 幻灯片

    利用公式

    ΔH=h(LinYHn+3)−nh(LiH)−h(YH3)n+1, (1)

    计算了LinYHn+3 (n = 1—3) 相对于LiH和YH3的形成焓, 其中h代表化合物的绝对焓值. 通过形成焓的计算结果, 绘制LinYHn+3 (n = 1—3) 3种不同配比化合物的热力学凸包图, 如图14所示, 落在凸包线上的结构 (实心标志) 是热力学稳定的, 原则上在实验上是可以被合成的; 而不在凸包线上的结构 (空心标志) 则是亚稳的或者是不稳定的. 从图14可以看出, LiYH4在200 GPa时是稳定的; Li2YH5在150, 200和250 GPa压力下均保持热力学稳定性; Li3YH6则在250和300 GPa下是热稳定的; 它们在上述各自稳定压力下相对于图中已知的任何分解路径都是稳定的化学配比. 显然, 该结果与图11—13的结果相符. 然而, 还可以从图14看出, 相较于其他两种配比三元氢化物, Li2YH5稳定压力范围更广, 而且最低稳定压力更低.

    图 14 LinYHn+3 (n = 1—3) 在不同压力下相对于LiH和YH3的形成焓. 实心的标志表明氢化物在对应的压力下稳定, 而空心的标志表明是亚稳或者不稳定\r\nFig. 14. Enthalpy of formation of LinYHn+3 (n = 1−3) with respect to LiH and YH3 at different pressures. The solid mark indicates that the hydride is stable at the corresponding pressure, while the hollow mark indicates that it is metastable or unstable.
    图 14  LinYHn+3 (n = 1—3) 在不同压力下相对于LiH和YH3的形成焓. 实心的标志表明氢化物在对应的压力下稳定, 而空心的标志表明是亚稳或者不稳定
    Fig. 14.  Enthalpy of formation of LinYHn+3 (n = 1−3) with respect to LiH and YH3 at different pressures. The solid mark indicates that the hydride is stable at the corresponding pressure, while the hollow mark indicates that it is metastable or unstable.
    下载: 全尺寸图片 幻灯片

    对于热力学稳定的LiYH4-P4/nmm, Li2YH5-I4/mmm, Li3YH6-P4/nmm结构, 进一步计算其在200 GPa压力下的声子色散曲线和态密度, 如图15所示. 分析得知, 整个布里渊区并没有虚频振动模式出现, 说明上述结构是动力学稳定的. 可以看出, 低频区 (< 10 THz) 振动模式主要来源于Y原子的振动; 中频区 (10—30 THz) 的振动主要来自于Li原子的振动, 其中少部分来自H原子的振动; 高频区的振动 (≥ 45 THz) 主要来自于H原子的振动, 这主要是由于H原子的质量比Li/Y原子的质量小而造成的. 同时以发现, 3个结构中的振动最高频率分别为约70 THz(2335 cm–1), 约65 THz(2168 cm–1), 小于500 GPa下“金属”氢的振动频率2600 cm–1[32], 但与300 GPa下LaH10 (Fm-3m) 中氢的振动频率(2300 cm–1) [8,9]相近. 对LiYH4, Li2YH5和Li3YH6相变序列中的结构, 均进行声子谱计算, 发现除LiYH4-P21/m和Li3YH6-P21/m不具有动力学稳定性之外, 其他结构都没有虚频率的声子 (Fig.S1).

    图 15 200 GPa下　(a) P4/nmm (LiYH4), (b) I4/mmm (Li2YH5)和 (c) P4/nmm (Li3YH6)的声子色散曲线(左)和投影声子态密度(右)\r\nFig. 15. Phonon dispersion (left), projected phonon density of states (PHDOS) (right) for (a) P4/nmm (LiYH4), (b) I4/mmm (Li2YH5) and (c)P4/nmm (Li3YH6) at 200 GPa.
    图 15  200 GPa下　(a) P4/nmm (LiYH4), (b) I4/mmm (Li2YH5)和 (c) P4/nmm (Li3YH6)的声子色散曲线(左)和投影声子态密度(右)
    Fig. 15.  Phonon dispersion (left), projected phonon density of states (PHDOS) (right) for (a) P4/nmm (LiYH4), (b) I4/mmm (Li2YH5) and (c)P4/nmm (Li3YH6) at 200 GPa.
    下载: 全尺寸图片 幻灯片

    3.5   LinYHn+3 (n = 1—3)电子结构分析

    通过将LinYHn+3 (n = 1—3)在不同压力下的电子能带的导带底和价带顶的能量值作差得到带隙随着压力的变化曲线, 如图16所示, 图中小于0 eV的部分代表此时的能带没有带隙(呈金属特征), 大于0 eV的部分表明此压力下该结构是绝缘体或半导体. 分析得到, 除Li3YH6-P4/nmm结构在常压下呈现金属特征之外, LiYH4-P4/nmm, Li2YH5-I4/mmm在常压下都是绝缘体, 且随压力升高均发生金属化转变, 转变压力分别为25 GPa和8 GPa. 图17显示了这3种热力学和动力学均稳定的结构在200 GPa时的电子能带结构和态密度, 表明了3种化合物的金属性. 从图中还可以发现, 对于P4/nmm (LiYH4), I4/mmm (Li2YH5), P4/nmm (Li3YH6) 这3种结构, 处于费米能级处的总电子态密度很小, Y元素对其起到了主要贡献作用, 而H的贡献几乎为零. 随后对上述结构进行了Bader电荷分析, 如表1—3所示, Li和Y原子的部分电荷向H原子转移, 这表明Li和Y原子都是带正电的电子供体, H原子为带负电的电子受体, H与Li/Y原子间存在离子相互作用. 同时, H-H之间不形成H2单元, 而是呈现离子性.

    图 16 LinYHn+3 (n = 1−3)体系的带隙随压力的变化关系\r\nFig. 16. Change curves of the electron band gap with pressure for LinYHn+3 (n = 1−3).
    图 16  LinYHn+3 (n = 1−3)体系的带隙随压力的变化关系
    Fig. 16.  Change curves of the electron band gap with pressure for LinYHn+3 (n = 1−3).
    下载: 全尺寸图片 幻灯片
    图 17 (a) LiYH4-P4/nmm, (b) Li2YH5-I4/mmm和 (c) Li3YH6-P4/nmm相结构在200 GPa下的电子能带结构和局域态密度; 水平虚线表示费米能级\r\nFig. 17. Electronic band structures and local density of states for (a) P4/nmm LiYH4, (b) I4/mmm Li2YH5 and (c) P4/nmm Li3YH6, calculated at 200 GPa. The horizontal dotted line indicates the Fermi energy levels.
    图 17  (a) LiYH4-P4/nmm, (b) Li2YH5-I4/mmm和 (c) Li3YH6-P4/nmm相结构在200 GPa下的电子能带结构和局域态密度; 水平虚线表示费米能级
    Fig. 17.  Electronic band structures and local density of states for (a) P4/nmm LiYH4, (b) I4/mmm Li2YH5 and (c) P4/nmm Li3YH6, calculated at 200 GPa. The horizontal dotted line indicates the Fermi energy levels.
    下载: 全尺寸图片 幻灯片
    表 1  通过Bader电荷分析得到的P4/nmm (LiYH4) 在200 GPa的压力下, Li, Y和H原子剩余的价电子数量; σ(e)代表得失价电子数目(正值表示失去电子, 负值表示得到电子)
    Table 1.  Number of remaining valence electrons in Li, Y and H atoms of P4/nmm (LiYH4) obtained by bader charge analysis under the pressure of 200 GPa; σ(e) represents the number of valence electrons gained and lost (positive means lost electrons, negative means gained electrons).
    原子剩余价电子数目得失电子情况 σ(e)
    Li10.2998040.700196
    Li20.3000350.699965
    Y19.6880361.311964
    Y29.6880361.311964
    H11.538704–0.538704
    H21.508556–0.508556
    H31.495277–0.495277
    H41.469508–0.469508
    H51.538704–0.538704
    H61.469508–0.469508
    H71.508556–0.508556
    H81.495277–0.495277
    下载: 导出CSV 
    | 显示表格
    表 3  通过Bader电荷分析得到的P4/nmm (Li3YH6) 在200 GPa的压力下, Li, Y和H原子剩余的价电子数量; σ(e)代表得失价电子数目(正值表示失去电子, 负值表示得到电子)
    Table 3.  Number of remaining valence electrons in Li, Y and H atoms of P4/nmm (Li3YH6) obtained by bader charge analysis under the pressure of 200 GPa; σ(e) represents the number of valence electrons gained and lost (positive means lost electrons, negative means gained electrons).
    原子剩余价电子数目得失电子情况σ(e)
    Li10.3057130.694287
    Li20.3092840.690716
    Li30.3137980.686202
    Li40.3091650.690835
    Li50.3137980.686202
    Li60.3057130.694287
    Y19.7611391.238861
    Y29.7611391.238861
    H11.548839–0.548839
    H21.548839–0.548839
    H31.674347–0.674347
    H41.528941–0.528941
    H51.475093–0.475093
    H61.556821–0.556821
    H71.556821–0.556821
    H81.548839–0.548839
    H91.475093–0.475093
    H101.528941–0.528941
    H111.548839–0.548839
    H121.628839–0.628839
    下载: 导出CSV 
    | 显示表格

    假设P4/nmm (LiYH4), I4/mmm (Li2YH5), P4/nmm (Li3YH6) 这3种结构中存在H2单元, 那么在200 GPa时, 平均每个H2单元接受的电子数分别为1.006e, 1.049e, 1.103e, 比300 GPa下P-3m1 (Li2MgH16) 结构中每个H2单元接收的额外电子数目 (0.39e[15]) 多得多. 同时, 如前所述, 这3个结构中最近邻的H原子之间的距离分别为1.89 Å, 1.48 Å, 1.50 Å, 均远大于常温常压下H2分子中H—H键长(0.74 Å), 同时也比500 GPa下“金属”氢中的H—H间距(0.98 Å)[32]大得多. 根据之前的文献报道, 如果每个H2单元接受的电子数达到0.6e左右, H—H键长增大到约1 Å时, H2分子就会解离; 一旦H2分子的数量和它们接受的电子之间达到了最佳的妥协, 一种替代的低能量结构(如笼形结构)就出现了[8,15]. 计算的结果与这一规律相符, 进一步说明了3个结构中没有H2单元. 由于H的比例不够高, 没有足够的H2单元去接收Li和Y提供的电子, 使得没有足够多的H为费米能级做贡献. 初步探索了P4/nmm (LiYH4), I4/mmm (Li2YH5), >P4/nmm (Li3YH6) 相的超导电性, 计算了它们的电声耦合常数λ, 均在0—0.2之间, 和UH6体系的电声耦合参数接近(λ = 0.38, Tc = 1.32 K)[16], 远远小于其他已报道的高温超导体的电子-声子耦合参数(H3S(λ = 2.30, Tc = 200 K)[16], YH6 (λ = 3.00, Tc = 165 K)[16], MgH16 (P-1, λ = 0.83, Tc = 48—73 K)[15], LiMgH16(P1, λ = 1.63, Tc = 160—178 K)[15], Li2MgH16 (P-3m1, λ = 1.25, Tc = 180—201 K)[15], Li3MgH16 (C2, λ = 2.78, Tc = 197—212 K)[15], Li2MgH16 (Fd-3m, λ = 3.35, Tc = 430—473 K)[15], Li2YH17 (Fd-3m, λ = 1.00, Tc = 112 K)[15]); 后续拟考虑开展更高氢含量的Li-Y-H三元体系研究, 为发现并合成新型高温超导提供理论支撑.

    表 2  通过Bader电荷分析得到的I4/mmm (Li2YH5)在200 GPa的压力下, Li, Y和H原子剩余的价电子数量; σ(e)代表得失价电子数目(正值表示失去电子, 负值表示得到电子)
    Table 2.  Number of remaining valence electrons in Li, Y and H atoms of I4/mmm (Li2YH5) obtained by bader charge analysis under the pressure of 200 GPa; σ(e) represents the number of valence electrons gained and lost (positive means lost electrons, negative means gained electrons).
    原子剩余价电子数目得失电子情况σ(e)
    Li10.3095830.690417
    Li20.3098310.690169
    Li30.3095830.690417
    Li40.3095830.690417
    Y19.7580491.241951
    Y29.7580491.241951
    H11.548559–0.548559
    H21.518422–0.518422
    H31.518422–0.518422
    H41.548559–0.548559
    H51.488825–0.488825
    H61.548435–0.548435
    H71.518422–0.518422
    H81.518422–0.518422
    H91.548435–0.548435
    H101.488825–0.488825
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    利用基于粒子群优化算法的结构预测方法结合第一性原理计算对三元氢化物LinYHn+3 (n = 1—3) 高压下的晶体结构进行了研究. 结果表明LiYH4-P4/nmm, Li2YH5-I4/mmm和Li3YH6-P4/nmm结构可分别在169—221 GPa, 141—300 GPa和166—300 GPa压力范围内由LiH和YH3按一定配比加压合成. 在LinYHn+3 (n = 1—3) 体系中虽未发现笼合物结构, 但LiYH4-P4/nmm, Li2YH5-I4/mmm和Li3YH6-P4/nmm结构中Li原子均被9个H原子围绕, Y原子均被12个氢原子围绕, 并具有金属化特征. 与LiYH4和Li3YH6相比, Li2YH5稳定结构的稳定压力范围更广, 且最低稳定压力更小, 在实验上更容易通过LiH和YH3加压合成. 稳定结构的电荷转移分析结果表明: 由于LinYHn+3 (n = 1—3) 的H含量较低, 接收电子的H2单元数量和Li, Y可提供的电子数量没有达成一定的比例, 使得H在费米能级附近的贡献有限; 又因为富氢化合物的高温超导性主要来源于化合物中H2单元解离后的单H对费米能级附近的贡献, 以至于LinYHn+3 (n = 1—3)的金属性不强, 未呈现出很好的超导电性; 后续可向LinYHn+3 (n = 1—3)体系中加氢, 以期发现新的超导体系. 本文的结论为三元富氢化合物的实验合成提供了有益的指导, 对新型三元高温超导体的理论设计具有一定的参考意义.

    References

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    Ashcroft N W 2004 Phys. Rev. Lett. 92 187002Google Scholar

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    Shamp A, Zurek E 2017 Nov. Supercond. Mater. 3 14Google Scholar

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    Eremets M I, Trojan I A, Medvedev S A, Tse J S, Yao Y 2008 Science 319 1509Google Scholar

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    Zurek E, Hoffmann R, Ashcroft N W, Oganov A R, Lyakhov A O 2009 Proc. Natl. Acad. Sci. U S A. 106 17640Google Scholar

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    孙莹, 刘寒雨, 马琰铭 2021 物理学报 70 017407Google Scholar

    Sun Y, Liu H Y, Ma Y M 2021 Acta Phys. Sin. 70 017407Google Scholar

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    Bi T, Zarifi N, Terpstra T, Zurek E 2019 Reference Module in Chemistry, Molecular Science and Chemical Engineering
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    Drozdov A P, Eremets M I, Troyan I A, Ksenofontov V, Shylin S I 2015 Nature 525 73Google Scholar

    [8]

    Peng F, Sun Y, Pickard C J, Needs R J, Wu Q, Ma Y M 2017 Phys. Rev. Lett. 119 107001Google Scholar

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    Liu H Y, Naumov I I, Hoffmann R, Ashcroft N W, Hemley R J 2017 Proc Natl Acad Sci U S A. 114 6990Google Scholar

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    Somayazulu M, Ahart M, Mishra A K, Geballe Z M, Baldini M, Meng Y, Struzhkin V V, Hemley R J 2019 Phys. Rev. Lett. 122 027001Google Scholar

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    Wang C Z, Yi S, Cho J H 2019 Phys. Rev. B 100 060502Google Scholar

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    Kong P P, Minkov V S, Kuzovnikov M A, Besedin S P, Drozdov A P, Mozaffari S, Balicas L, Balakirev F F, Prakapenka V B, Greenberg E, Knyazev D A, Eremets M I 2019 arXiv: 1909.10482
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    Sun Y 2020 Ph. D. Dissertation (Jilin: Jilin University) (in Chinese)
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    Grishakov K S, Degtyarenko N N, Mazur E A 2019 J. Exp. Theor. Phys. 128 105Google Scholar

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    Li Y W, Hao J, Liu H Y, Tse J S, Wang Y C, Ma Y M 2015 Sci. Rep. 5 9948Google Scholar

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    Wang Y C, Lv J, Zhu L, Ma Y M 2012 Comput. Phys. Commun. 183 2063Google Scholar

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    Wang Y C, Lv J, Zhu L, Ma Y M 2010 Phys. Rev. B 82 094116Google Scholar

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    Gao B, Gao P Y, Lu S H, Lv J, Wang Y C, Ma Y M 2019 Sci. Bull. 064 301Google Scholar

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    Kresse G G, Furthmuller J 1996 Phys. Rev. B 54 11169Google Scholar

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    Perdew J P, Wang Y 1992 Phys. Rev. B 46 12947Google Scholar

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    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

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    Cited By

    期刊类型引用(1)

    1. 王庆相，李少强，赖运金，常涛，李安. 第一性原理计算在超导材料中的应用. 粉末冶金工业. 2024(03): 1-7 . 百度学术

    其他类型引用(0)

  • 图 1  LiYH4每分子式的基态静态焓随压力的变化关系, 以具有P4/nmm空间群的LiYH4结构为基准; 插图为300—330 GPa压力范围内的局部放大图

    Figure 1.  Ground-state static enthalpy curves per formula unit as a function of pressure (with respect to the P4/nmm structure) for static LiYH4. The inset is a partial enlargement of the pressure range 300−330 GPa.

    DownLoad: Full-Size Img PowerPoint

    图 2  LiYH4的晶体结构. 绿色、紫色、粉色小球分别代表Li, Y, H原子(Li-H, Y-H和H-H距离分别小于2.20 Å, 2.47 Å和2.00 Å)(a) 101.325 kPa时的P21/m; (b) 压力为150 GPa时的P4/nmm; (c) 压力为300 GPa时的Cmmm

    Figure 2.  Crystal structures of (a) P21/m LiYH4 at 1 atm, (b) P4/nmm LiYH4 at 150 GPa and (c) Cmmm LiYH4 at 300 GPa. The green, purple and pink spheres represent Li, Y and H atoms, respectively. Lines are drawn for Li-H, Y-H and H-H separations shorter than 2.20 Å, 2.47 Å and 2.00 Å, respectively.

    DownLoad: Full-Size Img PowerPoint

    图 3  考虑零点能(ZPE) 修正后不同LiYH4结构的焓值在　(a) 0−35 GPa范围内和 (b) 290−325 GPa范围内随压力的变化关系

    Figure 3.  Change of enthalpy of different LiYH4 structures with pressure in the range of (a) 0−35 GPa and (b) 290−325 GPa after the correction of zero point energy (ZPE) was considered.

    DownLoad: Full-Size Img PowerPoint

    图 4  不同LiYH4结构　(a) P21/m (1 atm), (b) P4/nmm (150 GPa)和 (c) Cmmm (300 GPa)的等值面值为0.5的三维电子局域函数(ELF)

    Figure 4.  Three-dimensional electron local function (ELF) with anisosurface value of 0.5 for different LiYH4 phase structures (a) P21/m (101.325 kPa), (b) P4/nmm (150 GPa) and (c) Cmmm (300 GPa).

    DownLoad: Full-Size Img PowerPoint

    图 5  Li2YH5的晶体结构. 绿色、紫色、粉色小球分别代表Li, Y, H原子(Li-H, Y-H和H-H距离分别小于2.20 Å, 2.47 Å和2.00 Å)(a) 101.325 kPa下的Cmc21; (b) 101.325 kPa下的Pmn21; (c) 101.325 kPa下的Pmmn; (d) 300 GPa下的I4/mmm

    Figure 5.  The crystal structures of (a) Cmc21 Li2YH5 at 101.325 kPa, (b) Pmn21 Li2YH5 at 101.325 kPa, (c) Pmmn Li2YH5 at 1 101.325 kPa and (d) I4/mmm Li2YH5at 300 GPa. The green, purple and pink spheres represent Li, Y and H atoms, respectively. Lines are drawn for Li-H, Y-H and H-H separations shorter than 2.20 Å, 2.47 Å and 2.00 Å, respectively.

    DownLoad: Full-Size Img PowerPoint

    图 6  Li2YH5每分子式的基态静态焓随压力的变化关系, 以具有I4/mmm空间群的Li2YH5结构为基准; 插图为考虑零点能 (ZPE) 修正后焓随压力的变化

    Figure 6.  Ground-state static enthalpy curves per formula unit as a function of pressure (with respect to the I4/mmm structure) for static Li2YH5. The inset shows a modified enthalpy curve considering zero point energy (ZPE).

    DownLoad: Full-Size Img PowerPoint

    图 7  不同Li2YH5结构　(a) Cmc21 (101.325 kPa), (b) Pmmn (101.325 kPa)和 (c) I4/mmm (300 GPa)的等值面值为0.5的三维电子局域函数(ELF)

    Figure 7.  Three-dimensional electron local function (ELF) with anisosurface value of 0.5 for different Li2YH5 phase structures (a) Cmc21 (101.325 kPa), (b) Pmmn (101.325 kPa) and (c) I4/mmm (300 GPa).

    DownLoad: Full-Size Img PowerPoint

    图 8  Li3YH6的晶体结构. 绿色、紫色、粉色小球分别代表Li, Y, H原子(Li-H, Y-H和H-H距离分别小于2.20 Å, 2.47 Å和2.00 Å)(a) P21/m (101.325 kPa); (b) Cmcm (100 GPa); (c) P4/nmm (300 GPa)

    Figure 8.  Crystal structures of (a) P21/m Li3YH6 at 101.325 kPa, (b) CmcmLi3YH6 at 100 GPa and (c) P4/nmn Li3YH6 at 300 GPa. The green, purple and pink spheres represent Li, Y and H atoms, respectively.Lines are drawn for Li-H, Y-H and H-H separations shorter than 2.30 Å, 2.47 Å and 2.00 Å, respectively.

    DownLoad: Full-Size Img PowerPoint

    图 9  Li3YH6的每个公式单位的焓值随压力的变化关系, 以P4/nmm结构的焓值为基准(考虑ZPEs的影响)

    Figure 9.  Eenthalpy curves per formula unit as a function of pressure with respect to the predicted P4/nmm structure for static Li3YH6, ZPEs included.

    DownLoad: Full-Size Img PowerPoint

    图 10  不同Li3YH6结构　(a) P21/m(101.325 kPa), (b) Cmcm (100 GPa)和 (c) P4/nmm (300 GPa)的等值面值为0.5的三维局域函数 (ELF)

    Figure 10.  Three-dimensional electron local function (ELF) with an isosurface value of 0.5 for different Li3YH6 phase structures (a) P21/m (1 101.325 kPa), (b) Cmcm (100 GPa) and (c) P4/nmm (300 GPa).

    DownLoad: Full-Size Img PowerPoint

    图 11  LiYH4的不同结构(P21/m, P4/nmm和Cmmm)相对于LiH + YH3的焓随压力的变化曲线(包含ZPEs的影响)

    Figure 11.  Enthalpy curves of various structures (P21/m, P4/nmm and Cmmm) of LiYH4 relative to the products LiH + YH3 as functions of pressure, ZPEs included.

    DownLoad: Full-Size Img PowerPoint

    图 12  Li2YH5的不同结构(Cmc21, Pmmn和I4/mmm)相对于2 LiH + YH3的焓随压力的变化曲线(包含ZPEs的影响)

    Figure 12.  Enthalpy curves of various structures (Cmc21, Pmmn and I4/mmm) of Li2YH5 relative to the products 2 LiH + YH3 as functions of pressure, ZPEs included.

    DownLoad: Full-Size Img PowerPoint

    图 13  Li3YH6的不同结构(P21/m, Cmcm和P4/nmm)相对于3 LiH + YH3的焓随压力的变化曲线(包含ZPEs的影响)

    Figure 13.  Enthalpy curves of various structures (P21/m, Cmcm and P4/nmm) of Li3YH6 relative to the products 3 LiH + YH3 as functions of pressure, ZPEs included.

    DownLoad: Full-Size Img PowerPoint

    图 14  LinYHn+3 (n = 1—3) 在不同压力下相对于LiH和YH3的形成焓. 实心的标志表明氢化物在对应的压力下稳定, 而空心的标志表明是亚稳或者不稳定

    Figure 14.  Enthalpy of formation of LinYHn+3 (n = 1−3) with respect to LiH and YH3 at different pressures. The solid mark indicates that the hydride is stable at the corresponding pressure, while the hollow mark indicates that it is metastable or unstable.

    DownLoad: Full-Size Img PowerPoint

    图 15  200 GPa下　(a) P4/nmm (LiYH4), (b) I4/mmm (Li2YH5)和 (c) P4/nmm (Li3YH6)的声子色散曲线(左)和投影声子态密度(右)

    Figure 15.  Phonon dispersion (left), projected phonon density of states (PHDOS) (right) for (a) P4/nmm (LiYH4), (b) I4/mmm (Li2YH5) and (c)P4/nmm (Li3YH6) at 200 GPa.

    DownLoad: Full-Size Img PowerPoint

    图 16  LinYHn+3 (n = 1−3)体系的带隙随压力的变化关系

    Figure 16.  Change curves of the electron band gap with pressure for LinYHn+3 (n = 1−3).

    DownLoad: Full-Size Img PowerPoint

    图 17  (a) LiYH4-P4/nmm, (b) Li2YH5-I4/mmm和 (c) Li3YH6-P4/nmm相结构在200 GPa下的电子能带结构和局域态密度; 水平虚线表示费米能级

    Figure 17.  Electronic band structures and local density of states for (a) P4/nmm LiYH4, (b) I4/mmm Li2YH5 and (c) P4/nmm Li3YH6, calculated at 200 GPa. The horizontal dotted line indicates the Fermi energy levels.

    DownLoad: Full-Size Img PowerPoint

    表 1  通过Bader电荷分析得到的P4/nmm (LiYH4) 在200 GPa的压力下, Li, Y和H原子剩余的价电子数量; σ(e)代表得失价电子数目(正值表示失去电子, 负值表示得到电子)

    Table 1.  Number of remaining valence electrons in Li, Y and H atoms of P4/nmm (LiYH4) obtained by bader charge analysis under the pressure of 200 GPa; σ(e) represents the number of valence electrons gained and lost (positive means lost electrons, negative means gained electrons).

    原子剩余价电子数目得失电子情况 σ(e)
    Li10.2998040.700196
    Li20.3000350.699965
    Y19.6880361.311964
    Y29.6880361.311964
    H11.538704–0.538704
    H21.508556–0.508556
    H31.495277–0.495277
    H41.469508–0.469508
    H51.538704–0.538704
    H61.469508–0.469508
    H71.508556–0.508556
    H81.495277–0.495277
    DownLoad: CSV

    表 3  通过Bader电荷分析得到的P4/nmm (Li3YH6) 在200 GPa的压力下, Li, Y和H原子剩余的价电子数量; σ(e)代表得失价电子数目(正值表示失去电子, 负值表示得到电子)

    Table 3.  Number of remaining valence electrons in Li, Y and H atoms of P4/nmm (Li3YH6) obtained by bader charge analysis under the pressure of 200 GPa; σ(e) represents the number of valence electrons gained and lost (positive means lost electrons, negative means gained electrons).

    原子剩余价电子数目得失电子情况σ(e)
    Li10.3057130.694287
    Li20.3092840.690716
    Li30.3137980.686202
    Li40.3091650.690835
    Li50.3137980.686202
    Li60.3057130.694287
    Y19.7611391.238861
    Y29.7611391.238861
    H11.548839–0.548839
    H21.548839–0.548839
    H31.674347–0.674347
    H41.528941–0.528941
    H51.475093–0.475093
    H61.556821–0.556821
    H71.556821–0.556821
    H81.548839–0.548839
    H91.475093–0.475093
    H101.528941–0.528941
    H111.548839–0.548839
    H121.628839–0.628839
    DownLoad: CSV

    表 2  通过Bader电荷分析得到的I4/mmm (Li2YH5)在200 GPa的压力下, Li, Y和H原子剩余的价电子数量; σ(e)代表得失价电子数目(正值表示失去电子, 负值表示得到电子)

    Table 2.  Number of remaining valence electrons in Li, Y and H atoms of I4/mmm (Li2YH5) obtained by bader charge analysis under the pressure of 200 GPa; σ(e) represents the number of valence electrons gained and lost (positive means lost electrons, negative means gained electrons).

    原子剩余价电子数目得失电子情况σ(e)
    Li10.3095830.690417
    Li20.3098310.690169
    Li30.3095830.690417
    Li40.3095830.690417
    Y19.7580491.241951
    Y29.7580491.241951
    H11.548559–0.548559
    H21.518422–0.518422
    H31.518422–0.518422
    H41.548559–0.548559
    H51.488825–0.488825
    H61.548435–0.548435
    H71.518422–0.518422
    H81.518422–0.518422
    H91.548435–0.548435
    H101.488825–0.488825
    DownLoad: CSV
  • [1]

    Ashcroft N W 2004 Phys. Rev. Lett. 92 187002Google Scholar

    [2]

    Shamp A, Zurek E 2017 Nov. Supercond. Mater. 3 14Google Scholar

    [3]

    Eremets M I, Trojan I A, Medvedev S A, Tse J S, Yao Y 2008 Science 319 1509Google Scholar

    [4]

    Zurek E, Hoffmann R, Ashcroft N W, Oganov A R, Lyakhov A O 2009 Proc. Natl. Acad. Sci. U S A. 106 17640Google Scholar

    [5]

    孙莹, 刘寒雨, 马琰铭 2021 物理学报 70 017407Google Scholar

    Sun Y, Liu H Y, Ma Y M 2021 Acta Phys. Sin. 70 017407Google Scholar

    [6]

    Bi T, Zarifi N, Terpstra T, Zurek E 2019 Reference Module in Chemistry, Molecular Science and Chemical Engineering
    [7]

    Drozdov A P, Eremets M I, Troyan I A, Ksenofontov V, Shylin S I 2015 Nature 525 73Google Scholar

    [8]

    Peng F, Sun Y, Pickard C J, Needs R J, Wu Q, Ma Y M 2017 Phys. Rev. Lett. 119 107001Google Scholar

    [9]

    Liu H Y, Naumov I I, Hoffmann R, Ashcroft N W, Hemley R J 2017 Proc Natl Acad Sci U S A. 114 6990Google Scholar

    [10]

    Somayazulu M, Ahart M, Mishra A K, Geballe Z M, Baldini M, Meng Y, Struzhkin V V, Hemley R J 2019 Phys. Rev. Lett. 122 027001Google Scholar

    [11]

    Wang C Z, Yi S, Cho J H 2019 Phys. Rev. B 100 060502Google Scholar

    [12]

    Kong P P, Minkov V S, Kuzovnikov M A, Besedin S P, Drozdov A P, Mozaffari S, Balicas L, Balakirev F F, Prakapenka V B, Greenberg E, Knyazev D A, Eremets M I 2019 arXiv: 1909.10482
    [13]

    Snider E, Dasenbrock-Gammon N, McBride R, Wang X Y, Meyers N, Lawler K V, Zurek E, Salamat A, Dias R P 2021 Phys. Rev. Lett. 126 117003Google Scholar

    [14]

    Sun Y, Lv J, Xie Y, Liu H Y, Ma Y M 2019 Phys. Rev. Lett. 123 097001Google Scholar

    [15]

    孙莹 2020 博士学位论文 (吉林: 吉林大学)

    Sun Y 2020 Ph. D. Dissertation (Jilin: Jilin University) (in Chinese)
    [16]

    Grishakov K S, Degtyarenko N N, Mazur E A 2019 J. Exp. Theor. Phys. 128 105Google Scholar

    [17]

    Li Y W, Hao J, Liu H Y, Tse J S, Wang Y C, Ma Y M 2015 Sci. Rep. 5 9948Google Scholar

    [18]

    Wang Y C, Lv J, Zhu L, Ma Y M 2012 Comput. Phys. Commun. 183 2063Google Scholar

    [19]

    Wang Y C, Lv J, Zhu L, Ma Y M 2010 Phys. Rev. B 82 094116Google Scholar

    [20]

    Gao B, Gao P Y, Lu S H, Lv J, Wang Y C, Ma Y M 2019 Sci. Bull. 064 301Google Scholar

    [21]

    Kresse G G, Furthmuller J 1996 Phys. Rev. B 54 11169Google Scholar

    [22]

    Perdew J P, Wang Y 1992 Phys. Rev. B 46 12947Google Scholar

    [23]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [24]

    Becke A D, Edgecombe K E 1990 J. Chem. Phys. 92 5397Google Scholar

    [25]

    Tang W, Sanville E, Henkelman G 2009 J. Phys.: Condens. Matter 21 084204Google Scholar

    [26]

    Bader R F W 1985 Acc. Chem. Res. 18 9Google Scholar

    [27]

    Henkelman G, Arnaldsson A, Jonsson H 2006 Comput. Mater. Sci. 36 354Google Scholar

    [28]

    Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106Google Scholar

    [29]

    Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti G L, Cococcioni M, Dabo I 2009 J. Phys.: Condens. Matter. 21 395502Google Scholar

    [30]

    Liu L L, Sun H J, Wang C Z, Lu W C 2017 J. Phys.: Condens. Matter 29 325401Google Scholar

    [31]

    Dias R P, Silvera I F 2017 Science 355 715Google Scholar

    [32]

    Mcmahon J M, Ceperley D M 2011 Phys. Rev. Lett. 106 165302Google Scholar

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  • Abstract views:  7817
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  • Cited By: 1
Publishing process
  • Received Date:  30 April 2021
  • Accepted Date:  07 September 2021
  • Available Online:  23 December 2021
  • Published Online:  05 January 2022

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