WANG Xiaoxue, DING Yuqing, WANG Hui. First-Principles Study of the High-Pressure Phase Transition and Physical Properties of Rubidium Nitrate[J]. Chinese Journal of High Pressure Physics, 2024, 38(4): 040103. doi: 10.11858/gywlxb.20240776
Citation: TAN Ye, XIAO Yuanlu, XUE Tao, LI Jun, JIN Ke. Melting of MB2 Alloy under Shock Compression[J]. Chinese Journal of High Pressure Physics, 2019, 33(2): 020106. doi: 10.11858/gywlxb.20190729

Melting of MB2 Alloy under Shock Compression

doi: 10.11858/gywlxb.20190729
  • Received Date: 26 Feb 2019
  • Rev Recd Date: 14 Mar 2019
  • Issue Publish Date: 25 Jun 2019
  • Reverse impact experiments were performed at a shock pressure range from 30 GPa to 73 GPa to investigate the dynamic response of magnesium aluminum alloy. A displacement interferometer system for any reflector was employed to measure the impact velocity and sample/window interface particle velocities. The Hugoniot data obtained in this study had a good agreement with the data published before, however, the sound velocities extracted from our experiments showed a transition from longitudinal to bulk sound velocity. This discontinuity is attributed to melting transition under shock compression, and the transition pressure range is estimated from 40 GPa to 57 GPa.

     

  • 盐类矿物是指以矿石或岩石形式存在于自然界的碱金属/碱土金属的卤化物、硫酸盐、碳酸盐、硝酸盐等,被广泛应用于工业和农业领域[1]。该类矿物在高温高压下的结构相变在物理与地球科学领域备受关注,例如:2013 年理论与实验研究发现,典型离子晶体 NaCl 在高压下转变为 Na3Cl和NaCl3[2];Santos等[3]发现,作为地球深部碳循环重要载体的碳酸盐在高温高压下具有10余种结构。硝酸根离子(NO3)和碳酸根离子(CO23)具有等电子结构,形成的盐类矿物均为离子晶体。离子晶体中的离子键易受外部温度和压强调控而发生结构相变,鉴于NO3CO23在结构和电子性质上具有相似之处,高温高压下碱金属硝酸盐是否具有丰富的结构相变是值得深入探讨的问题。

    碱金属硝酸盐被广泛用于多个领域,如作为传热、储热介质等运用于工业炸药、冶金淬火硬化、太阳能和核能领域[46]。碱金属硝酸盐在较低压强下已经展现出丰富的相变行为[7],引起了许多关注。研究发现,在常压下硝酸铷(RbNO3)从熔融态退火至常温的过程中历经了4个不同的结构,即Ⅰ、Ⅱ、Ⅲ、Ⅳ相。Ⅰ相在熔点至564 K的区间内稳定,为NaCl型的立方无序结构(空间群Fm¯3m[8];Ⅱ相在564~492 K区间稳定,具有菱方结构(空间群R¯3m[7];Ⅲ相在492~437 K区间稳定,一般认为是CsCl型立方结构(空间群Pm¯3m[8];Ⅳ相在常温下稳定,为菱方结构(空间群P31[7]。2001年,Liu等[9]利用分子动力学模拟方法从理论上发现了RbNO3在Ⅳ→Ⅲ相变过程中NO3基团从定向有序变为无序。在高压实验研究方面,1984年Dean等[10]通过原位X射线衍射研究发现了RbNO3的Ⅳ→Ⅴ结构相变,其相变压强约为1.2 GPa,高压Ⅴ相为正交结构(空间群Pmmn)。

    与RbNO3的高温研究相比,RbNO3的高压研究并不丰富。本研究将基于第一性原理计算,结合CALYPSO晶体结构预测软件,系统地探索零温下RbNO3在0~100 GPa区间的结构与物理性质。

    在0 K和0、20、40、60、80和100 GPa的压强条件下,使用CALYPSO软件[1112]进行RbNO3的结构搜索。结构预测过程中演化代数为20,模拟采用2倍胞和4倍胞,每个分子式的体积在32~70 Å3区间,体积随压强的升高而减小。基于第一性原理计算,交换关联泛函采用广义梯度近似(generalized gradient approximation,GGA)[13]的Perdew-Burke-Ernzerhof(PBE)泛函[13]、Original vdW-DF泛函[14]、Revised PBE for solids(PBEsol)泛函[15]以及Revised PBE Hammer et al.(RPBE)泛函[16],数值模拟在VASP[17]软件包中实现,采用投影缀加波(projected augmented wave,PAW)[18]方法,Rb、N、O的价电子分别选为4s24p65s1、2s22p3和2s22p4,平面波截断能取520 eV,对于R3mPnmaPmmn相,布里渊区采样的网格尺寸分别为10×10×10、6×8×6和10×8×10,总能量收敛至小于1×10−5 eV/atom。采用有限位移法结合PHONOPY软件[19]计算声子谱,扩胞数分别为3×3×2、2×3×2和3×3×3。弹性模量计算采用Voigt-Reuss-Hill(VRH)平均法[2021],晶体结构和声子模式的原子位移可视化通过VESTA软件[22]和V_Sim软件[23]实现。

    RbNO3的常温常压结构为RbNO3-Ⅳ相,空间群为P31。采用4种不同交换关联泛函优化0 GPa下RbNO3-Ⅳ相的平衡体积与晶胞参数,结果列于表1。对比实验结果可以发现,4种交换关联泛函的准确性从低到高依次为RPBE、vdW-DF、 PBE、 PBEsol。因此,后续研究将主要基于PBE和PBEsol泛函展开。

    表  1  RbNO3-Ⅳ相的晶格常数的理论值与实验值的比较
    Table  1.  Comparison between experimental and calculated lattice parameters of RbNO3-Ⅳ phase
    Method Condition a c Volume/Å3
    Simulation PBE 10.68(+1.62%) 7.60(+1.88%) 867.56(+5.29%)
    vdW-DF 10.72(+2.00%) 7.62(+2.14%) 876.29(+6.35%)
    PBEsol 10.39(−1.14%) 7.39(−0.94%) 797.69(−3.19%)
    RPBE 11.14(+5.99%) 7.91(+6.03%) 982.63(+19.26%)
    Experiment T=296 K[24] 10.47 7.44 815.58
    T=298 K[25] 10.55 7.47 831.43
    Average 10.51 7.46 823.96
    下载: 导出CSV 
    | 显示表格

    采用PBE和PBEsol泛函在0~100 GPa压强范围内对能量较低的备选结构进行精细优化后发现,R3mPnmaP31Pmmn相在不同的压强区间内具有热力学稳定性,其焓差随压强变化曲线如图1所示。在0 GPa下,2种泛函的预测结果均表明R3m相的能量最稳定;随压强的升高,R3m相均转变为Pnma相。继续加压,PBE泛函与PBEsol泛函预测的相变序列不同:PBE泛函预测结果表明,Pnma相先相变至Ⅳ相(即P31结构),再相变至Ⅴ相(即Pmmn结构);PBEsol泛函预测结果表明,Pnma相直接转变为Ⅴ相。压强-体积关系如图2所示,其中,ΔV/V为体积坍塌率。除PBE泛函预测的Pnma→Ⅳ相变中不能看到明显的体积坍缩以外,PBE泛函所预测的其余2个相变和PBEsol预测的2个相变均存在明显的体积坍塌,这种体积不连续表明它们均为一级相变。

    图  1  R3mP31Pmmn相相对于Pnma相的热力学焓差曲线
    Figure  1.  Calculated enthalpy difference of R3m, P31 and Pmmn phases relative to Pnma as a function of pressure
    图  2  R3mPnmaP31Pmmn相的体积随压强的变化
    Figure  2.  Calculated volume of R3m, Pnma, P31 and Pmmn phases as a function of pressure

    考虑到PBEsol泛函对实验Ⅳ相的平衡体积与晶胞参数的描述更为准确,后续研究将主要采用PBEsol泛函预测零温下RbNO3的相变序列(R3mPnmaPmmn)。该序列所对应的2个相变点的压强分别为1.7和8.2 GPa,相应的体积坍塌率分别为3.73%和2.54%。由于碳酸钙的结构与碱金属硝酸盐的结构相似,两者具有等电子结构,因此,对比了它们的高压相变序列。碳酸钙的相变序列为:R¯3cPnmaPmmnP21/c,相变压强分别为1、40和67 GPa[26]。可以发现,RbNO3PnmaPmmn的相变压强远低于CaCO3发生相同相变时的压强,其可能的原因如下:一方面,Rb+NO3之间的离子相互作用比Ca2+CO23之间的离子作用更弱;另一方面,Rb+的半径大于Ca2+的半径,Rb+产生的“化学预压缩”更强。上述零温理论预测出了能量比常温常压下的Ⅳ相更小的2个低压新相(R3m相和Pnma相),表明低压下RbNO3可能存在不同于实验给出的常温常压下Ⅳ相的低温新相。

    预测获得的0 GPa下的R3m相、4 GPa下的Pnma相和12 GPa下的Pmmn相的平衡态晶格常数、原子位置列于表2,相应的晶体结构见图3。3个结构存在明显差异,三方相的单胞包含3个RbNO3分子式,而正交相的单胞则分别包含4和2个RbNO3分子式。3个相在0、4、12 GPa压强下的弹性常数列于表3,可以发现,三方相和正交相分别有7和9个独立的弹性常数。在R3m相中,C44随压强的升高先减小后增大,其余的弹性常数均与压强呈正相关。3个相的弹性模量,即体积模量B、剪切模量G以及杨氏模量E也列于表3中,分别表示抵抗脆性变形、抵抗塑性变形和抵抗张力的能力。同一压强下Pmmn相的弹性模量最大,表明Pmmn相的抗变形能力比另2个相更强。此外,根据“伯恩-黄昆”弹性稳定性判据[2728]分析3个相的机械稳定性,判别条件见式(1)和式(2)。力稳定性分析显示:12 GPa时,Pnma相的C55 < 0,不满足弹性稳定性判据,因而Pnma相不是弹性稳定结构;除此之外,各相在相应压强下的弹性常数均满足弹性稳定判据。

    表  2  高压下R3mPnmaPmmn相的晶格参数和原子位置
    Table  2.  Lattice parameters and atomic coordinates of R3m, Pnma and Pmmn phases at different pressures
    Phase Pressure/GPa Lattice parameters Wyckoff positions
    R3m 0 a=b=5.64 Å, c=9.48 Å,
    α=β=90°, γ=120°
    Rb1: 3a(0.3333, 0.6667, 0.1699)
    N1: 3a(0.3333, 0.6667, 0.7275)
    O1: 9b(0.5373, 0.0746, 0.3953)
    Pnma 4 a=7.18 Å, b=5.61 Å, c=6.77 Å,
    α=β=γ=90°
    Rb1: 4c(0.483, 0.250, 0.686)
    N1: 4c(0.350, 0.250, 0.122)
    O1: 4c(0.448, 0.250, 0.275)
    O5: 8d(0.302, 0.444, 0.043)
    Pmmn 12 a=4.67 Å, b=5.34 Å, c=4.63 Å,
    α=β=γ=90°
    Rb1: 2b(0.500, 0, 0.400)
    N1: 2a(0, 0, 0.992)
    O1: 2a(0, 0, 0.721)
    O3: 4e(0, 0.204, 0.128)
    下载: 导出CSV 
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    图  3  R3mPnmaPmmn相的晶体结构
    Figure  3.  Crystal structures of R3m, Pnma, and Pmmn phase
    表  3  高压下R3mPnmaPmmn相的弹性常数和弹性模量
    Table  3.  Elastic constant and elastic moduli of R3m, Pnma and Pmmn phase at high pressure GPa
    Phase Pressure C11 C12 C13 C14 C22 C23 C33 C44 C55 C66 B G E
    R3m 0 37 14 11 −4 13 7 12 15 7 19
    4 75 28 21 −8 39 6 23 35 11 29
    12 124 46 42 −15 94 12 39 66 19 52
    Pnma 0 22 7 9 41 9 32 7 10 9 16 10 24
    4 50 19 30 73 19 69 12 17 19 36 17 44
    12 96 43 59 129 35 119 19 −5 34 69 −57 −236
    Pmmn 0 26 9 9 50 16 54 15 5 5 21 10 26
    4 60 16 25 84 32 83 33 20 9 40 21 53
    12 113 25 53 143 59 129 60 37 16 72 35 91
    下载: 导出CSV 
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    C11>|C12|,C44>0,C213<12C33(C11+C12),C214<12C44(C11C12)
    (1)
    C11>0,C11C22>C212,C11C22C33+2C12C13C23C11C223C22C213C33C212>0C44>0,C55>0,C66>0
    (2)

    为了确定RbNO3的3个相的动力学稳定性,采用有限位移法计算了它们的声子谱。若声子谱具有负频率,则意味着动力学不稳定[29]。在简谐近似下,分别计算了R3mPnmaPmmn相在不同压强下的声子色散曲线以及声子分波态密度(phonon density of states, PHDOS),结果如图4所示。可以看出,声子谱均未出现负频率,表明3个相在相应压强下均具有动力学稳定性。

    图  4  R3mPnmaPmmn相的声子色散曲线以及声子态密度
    Figure  4.  Phonon-dispersion curves and the PHDOS of R3m, Pnma and Pmmn phase

    声子态密度分析研究表明,RbNO3的3个相的声子态密度分布趋势皆与常压下的CaCO3[30]十分相似,例如:当RbNO3(CaCO3)的振动频率低于10 THz(12 THz)时,声子态密度的贡献主要来自于O原子与金属阳离子Rb+(Ca2+);在振动频率32 THz附近,声子态密度的贡献主要来自于O原子;在振动频率大于40 THz的高频区,声子态密度的贡献来自于N―O键或者C―O键。采用V_Sim软件对Γ点处声子的振动模式进行可视化分析,结果表明:当频率小于10 THz时,N原子与O原子之间的距离不变,Rb和NO3协同振动;在32 THz附近,R3mPnma相的N―O振动和C―O振动均为对称伸缩振动,与方解石和文石的特性类似;在21 THz附近,N―O振动和C―O振动均为平面内弯曲振动;在RbNO3(CaCO3)的振动频率约为24 THz(25 THz)时,N―O振动(C―O振动)均为平面外弯曲振动;在大于40 THz的范围内,N―O振动和C―O振动均为反对称弯曲振动。相对于0 GPa的R3m相和4 GPa的Pnma相而言,12 GPa的Pmmn相的声子振动频率整体升高,但不同模式的频率分布范围大致相同。

    为了研究R3mPnmaPmmn相中原子间的成键行为,计算了0 GPa的R3m相、4 GPa的Pnma相和12 GPa的Pmmn相的电子局域函数(electron localization functionm, ELF),计算结果如图5所示。三维ELF图中等值面的取值为0.8,二维ELF图的晶格切面分别为(1.000 14.005 31.363)、(20.145 2.048 −1.000)和(4.542 1.000 −1.516)。可以看出,N原子与O原子间的ELE值趋近于1,表明N―O之间存在强共价键。

    图  5  R3mPnmaPmmn相的电子局域函数
    Figure  5.  Electron localization function of R3m, Pnma and Pmmn phase

    此外,计算了0 GPa的R3m相、4 GPa的Pnma相和12 GPa的Pmmn相的晶体轨道哈密顿布居(crystal orbital Hamiton population, COHP),计算结果如图6所示。COHP为负表示成键态。相对于O―O键和N―O键而言,Rb―O键对COHP的贡献非常小,几乎可以忽略不计,符合Rb+NO3之间为离子相互作用的事实。在−1.5~0 eV范围内,O―O键的COHP为正值,表明其主要来源为反键轨道,包含NO3从Rb+处获取的1个价电子的贡献。在0 eV以下,N―O键的COHP几乎全部为负值,表明NO3中的N―O键是极为稳定的强共价键,与ELF的分析结果一致。在0 GPa的R3m相、4 GPa的Pnma相和12 GPa的Pmmn相中,N原子与O原子的键长分别为1.26、1.25和1.26 Å。计算Bader电荷转移以确定Rb原子、N原子和O原子之间的电子转移情况,计算结果如表4所示。这3个结构中,硝酸根离子分别从Rb+获得了0.90e、0.87e和0.86e的电荷,表明压强抑制Rb+的电荷向NO3离子转移。

    图  6  R3mPnmaPmmn相的COHP
    Figure  6.  Crystal orbital Hamilton populations of R3m, Pnma and Pmmn phase
    表  4  高压下R3mPnmaPmmn相的元胞内的Bader电荷转移
    Table  4.  Calculated Bader charges within R3m, Pnma and Pmmn phases primitive cells at different pressures
    Phase Pressure/GPa Atoms Number Charge/e Charge transfer/e
    R3m 0 Rb 1 8.10 0.90
    N 1 4.16 0.84
    O 3 6.58 −0.58
    Pnma 4 Rb 4 8.13 0.87
    N 4 4.13 0.87
    O1 4 6.57 −0.57
    O2 4 6.58 −0.58
    O3 4 6.59 −0.59
    Pmmn 12 Rb 2 8.14 0.86
    N 2 4.07 0.93
    O1 2 6.58 −0.58
    O2 2 6.59 −0.59
    O3 2 6.62 −0.62
    下载: 导出CSV 
    | 显示表格

    图7给出了0 GPa的R3m相、4 GPa的Pnma相和12 GPa的Pmmn相的电子能带结构和电子态密度( density of states, DOS)。电子态密度结果表明,价带主要来自O的p轨道,导带主要来自N-p与O-p的杂化。3个结构在相应压强下的带隙分别为3.06、3.40和3.10 eV。带隙的存在说明它们均为半导体材料,然而3个结构的带隙类型不同,其中,R3m结构具有直接带隙,PnmaPmmn结构具有间接带隙。此外,还可以发现,在结构相变过程中,带隙随压强的增加呈现非单调变化的规律,即第1次相变带隙增大,而第2次相变带隙减小。

    图  7  R3mPnmaPmmn相的能带结构和电子态密度
    Figure  7.  Band structures and partial densities of states of R3m, Pnma and Pmmn phases

    采用第一性原理计算与CALYPSO结构预测相结合的方法系统地研究了RbNO3在0~100 GPa压强范围内的高压结构与物理性质。以RbNO3常温常压结构的实验数据为参照,测试了PBE、vdW-DF、RPBE、PBEsol泛函对结构描述的准确性,发现PBEsol泛函给出的结果最准确。基于PBEsol泛函预测出零温下RbNO3的高压相变序列为R3mPnmaPmmn,相变压强分别约为1.7 和8.2 GPa;2次相变均为一级结构相变,相应的体积坍塌率分别为3.73%和2.54%。预测零温下RbNO3存在2个低压新相,即R3m相和Pnma相,它们在能量上均优于早期实验在常温常压下给出的P31结构,表明降温可能会诱导RbNO3发生结构相变。0 GPa的R3m相、4 GPa的Pnma相和12 GPa的Pmmn相均具有力学稳定性和动力学稳定性,其带隙分别为3.06、3.40和3.10 eV,对比分析发现,压强会抑制Rb+的电荷向NO3转移。本研究获得的硝酸铷结构与电子性质随压强的变化规律可以为其他碱金属硝酸盐的理论与实验研究提供参考。

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