On the Existence of Layered Polymeric Nitrogen
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摘要: 在高温高压的极端条件下,分子晶体氮会打破传统三键机制向单键聚合态转变。氮在高压下的独特解离机制使聚合氮的研究意义超越了含能材料范畴,在基础物理学领域亦有深刻的科学意义。继立方偏转聚合氮cg-N(空间群I213)之后,第2个在实验上被发现的层状结构聚合氮LP-N(空间群Pba2)一直存在争议。主要的问题在于,LP-N的结构除了没有被高压X射线衍射实验验证之外,还与随后被发现的黑磷结构聚合氮BP-N(空间群Cmca)具有相近的合成温压条件和合成路径以及几乎相同的拉曼光谱特征。LP-N的合成很可能具有独特的相变动力学势垒。为此,选择独辟蹊径,从低温固态分子氮λ-N2出发,利用双面激光加热金刚石压砧技术,结合高压同步辐射X射线衍射和高压拉曼光谱分析方法,在约140 GPa、2600 K的条件下观察到了具有Pba2结构的聚合氮LP-N。结合第一性原理计算,分析了它的原子体积随压力的变化关系(p-V曲线),并探讨了LP-N高温高压合成动力学因素。研究结果不仅使我们更全面地认识LP-N,还进一步揭示了聚合氮的高压路径依赖特性。Abstract: Under the extreme conditions of high temperature and high pressure, molecular crystal nitrogen breaks the traditional three-bond mechanism and transforms into a single-bond polymerization state. The unique dissociation mechanism of nitrogen under high pressure makes the research significance of polymeric nitrogen beyond the scope of energetic materials, and also has profound scientific significance in the field of fundamental physics. Following the cubic gauche polymeric nitrogen cg-N (space group I213), the second experimentally discovered layered structure polymeric nitrogen LP-N (space group Pba2) has been controversial. The main problem is that, in addition to not being verified by other high-pressure X-ray diffraction experiments, LP-N structure has the similar synthesis temperature and pressure conditions and synthesis pathways, as well as almost the same Raman spectral characteristics as the subsequently discovered black phosphorus structure polymeric nitrogen BP-N (space group Cmca). The high-temperature and high-pressure synthesis of LP-N is likely to have a unique phase transition kinetic barrier. In this work, we started from the low-temperature solid-state molecular nitrogen λ-N2, used double-sided laser-heated diamond anvil cell (LHDAC) technology, combined with high-pressure X-ray diffraction based on the synchrotron radiation and high-pressure Raman scattering spectroscopy, supplemented by first-principles calculations, and observed the Pba2 structure of polymeric nitrogen LP-N at the conditions of about 141 GPa and about 2600 K. Combined with first-principles calculations, we compared and analyzed its pressure-dependent evolution of the volume per atom (p-V curve) and discussed the kinetic factors of LP-N synthesis at high temperature and high pressure. In addition to a more comprehensive understanding of LP-N, this paper further reveals the high-pressure path-dependent characteristics of polymeric nitrogen.
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磁驱动固体套筒内爆是指电流通过金属套筒表面时,在洛仑兹力的作用下金属套筒径向向内箍缩内爆的物理过程。1973年,Turchi等[1]首次提出磁驱动固体套筒内爆的概念。自20世纪90年代以来,磁驱动固体套筒实验被广泛应用于高压状态方程[2]、材料本构[3]、层裂损伤[4]、磁瑞利-泰勒(Magneto-Rayleigh-Taylor,MRT)不稳定性发展[5–6]、Richtmyer-Meshkov(RM)不稳定性发展[7]等研究。
磁驱动固体套筒实验涉及热扩散、磁扩散、焦耳加热、弹塑性、断裂、层裂等物理过程,并伴有大变形、界面不稳定性等现象。磁驱动固体套筒理论有薄壳模型[8–10]、不可压缩模型[11–13]、电作用量-速度模型[14–15]、全电路模型[15]和磁流体力学模型[16–17]等。这些理论模型已被用于脉冲功率装置、磁驱动固体套筒实验的模拟、设计和研究[7–17]。阚明先等[17]采用二维磁流体力学程序MDSC2模拟回流罩结构磁驱动固体套筒实验时发现,根据回流罩结构磁驱动固体套筒实验测量的电流或回路电流不能直接模拟磁驱动固体套筒,模拟的套筒速度总是比测量速度大,即回路电流并不完全从固体套筒表面流过。回路电流与固体套筒上通过的电流之间存在一个电流系数。由于MDSC2程序[17]以外的理论计算或数值模拟都未提到电流系数,因此,本研究采用其他理论模型对磁驱动固体套筒实验进行模拟,分析回路电流与通过固体套筒的电流之间的关系,通过模拟分析不同回流罩结构固体套筒实验,进一步探讨磁驱动固体套筒实验中电流系数的影响因素和变化规律。
1. 负载结构
大电流脉冲装置上的固体套筒实验通常采用回流罩结构[15, 17–18]。回流罩结构固体套筒实验的初始结构的rz剖面如图1所示,其中,虚线为对称轴。回流罩结构固体套筒实验装置从外到内依次为金属回流罩、绝缘材料和金属套筒,套筒两端为金属电极,上端为阳极,下端为阴极。回路电流从回流罩金属流入,绕过绝缘材料,经过套筒的外表面从阴极流出。电流加载后,电极外面的固体套筒被切割成与阴阳极之间的间隙等高的套筒,在洛仑兹力作用下沿径向向内箍缩。表1为FP-2装置[19]中回流罩结构磁驱动固体套筒实验的套筒参数。图2显示了FP-2装置上不同实验测得的电流变化曲线,电流的上升时间约为
5500 ns,电流峰值为9~11 MA。表 1 磁驱动固体套筒实验的套筒参数Table 1. Liner parameters of the magnetically driven solid liner experimentsExp. No. Liner material Liner’s inner radius/mm Liner’s thickness/mm 1 Al 45 0.6 2 Al 30 0.6 3 Al 45 1.6 4 Al 30 1.9 2. 电流系数的不可压缩模型验证
在薄壳模型、不可压缩模型、电作用量-速度模型、全电路模型、磁流体力学模型等[8–16]适用于磁驱动固体套筒的理论模型中,固体套筒边界的磁感应强度(B)为
B(t)=μ0Iexp(t)2πro (1) 式中:μ0为真空磁导率,Iexp(t)为磁驱动实验测量电流,ro为固体套筒的外半径。
二维磁驱动数值模拟程序MDSC2是由中国工程物理研究院流体物理研究所开发的二维磁流体力学程序[20–21]。该程序已被广泛应用于磁驱动飞片发射、超薄飞片、磁驱动准等熵压缩、磁驱动样品等实验的模拟研究[22–25]。最近,研究人员发现,采用MDSC2程序模拟FP-2装置上的磁驱动固体套筒实验时,基于实验测量的电流或回路电流并不能正确模拟套筒的动力学过程,模拟的套筒速度总是比实验测量值大。为正确模拟FP-2装置上的磁驱动固体套筒实验,需将边界磁感应强度公式[17]修正为
B(t)=μ0fcIexp(t)2πro (2) 式中:fc为回流罩结构rz柱面套筒的电流系数,fc<1。由于文献[17]之外的理论计算或数值模拟中均未提到电流系数fc,因此,需要确定fc是回流罩固体套筒实验固有的,还是MDSC2程序造成的。下面采用固体套筒的不可压缩模型理论确认电流系数是否存在。
在磁驱动固体套筒的不可压缩模型[11–13]中,不考虑套筒的磁扩散,假设磁压只作用于套筒的外表面,且磁压做功全部转化为套筒动能,套筒不可压缩,只作径向运动。设ρ为套筒密度,h为套筒高度,vo为套筒外界面速度,ri、vi分别为套筒内半径和内界面速度,r、v为套筒内某点的径向位置(ri≤r≤ro)和速度,由不可压缩假设,有
rivi=rovo (3) rv=rovo (4) 则套筒总动能Ek为
Ek=∫roriρπrhv2dr=πρhr2ov2olnrori (5) 由于磁压只作用于套筒的外表面,且磁压做功全部转化为套筒动能,则
dEkdt=2πμ0rohvoB2 (6) 将式(5)代入式(6)并积分,可得
dvodt=−v2oro−1ln(ro/ri)[B22μ0ρro+v2o2ro(1−r2or2i)] (7) dvidt=−v2iri−1ln(ro/ri)[B22μ0ρri+v2o2ri(1−r2ir2o)] (8) 采用上述不可压缩模型,对固体套筒实验4进行不可压缩模型模拟验证。图3给出了采用不可压缩模型模拟得到的套筒内界面速度。显然,采用回路电流或测量电流直接模拟的套筒速度明显比实验测量速度大,后者是前者的0.82倍,即计算不可压缩模型的边界磁感应强度时不能用式(1),而是用式(2)。不可压缩模型的模拟结果表明,对于回流罩固体套筒实验,回路电流或测量电流与固体套筒上通过的电流之间的电流系数不是MDSC2程序造成的,而是回流罩固体套筒实验固有的。
3. 电流系数规律
从第2节的模拟可知,磁驱动固体套筒理论的边界磁感应强度公式中包含电流系数,它反映了有多少回路电流从套筒实际流过。在磁驱动实验中,实验测量的电流是流入回流罩之前的电流,即回路电流,而不是从套筒直接流过的电流。从套筒流过的电流很难被直接测量,因此,电流系数难以预知。回流罩的结构比较复杂,阴阳电极之间连有金属套筒、绝缘材料,金属套筒与绝缘材料之间是真空,回流罩结构的分流机制包括阴阳极间的并联电路分流、漏磁、真空击穿等。事实上,电流系数是通过数值模拟发现的,由磁流体力学程序模拟速度与磁驱动套筒实验测量速度的对比确定。当前的固体套筒实验的模拟都是后验的,无法直接正确预测,因此,研究电流系数的变化规律非常重要,是正确设计和预测固体套筒实验的基础。
由于磁流体力学模型[21, 26]是包含固体弹塑性、热扩散、磁扩散等物理过程的可压缩模型,能够比不可压缩模型更加准确地描述磁驱动固体套筒实验,因此,下面将采用MDSC2程序对FP-2装置上开展的磁驱动固体套筒实验的电流系数变化规律进行研究。
图4给出了实验1~实验4的套筒内界面模拟速度。可以看出,应用式(2)的磁流体力学模型能正确描述磁驱动固体套筒实验。然而,不同的磁驱动固体套筒实验对应的电流系数是不同的。回流罩结构磁驱动固体套筒实验的电流系数和套筒的初始尺寸列于表2。
表 2 磁驱动固体套筒实验的电流系数Table 2. Current coefficients of the magnetically driven solid liner experimentsExp. No. Liner’s inner radius/mm Liner’s thickness/mm fc 1 45 0.6 0.87 2 30 0.6 0.90 3 45 1.6 0.85 4 30 1.9 0.88 由表2可知:电流系数是常数,不随时间的发展而变化,即电流系数与实验过程无关;对于不同的套筒,电流系数有所不同,说明电流系数与套筒的初始结构有关。由实验1和实验2可知,当套筒厚度相同时,若套筒内半径不同,则电流系数不同,且内半径越大,电流系数越小。对比实验1和实验3,或者实验2和实验4可知,当套筒内半径相同时,若套筒厚度不同,则电流系数不同,且套筒厚度越大,电流系数越小。
4. 结 论
采用不可压缩模型验证了回流罩结构磁驱动固体套筒实验中电流系数的存在,即回流罩结构磁驱动固体套筒实验的实验电流/回路电流并不完全从负载套筒的表面通过,实验电流/回路电流与套筒表面流过的电流之间存在一个电流系数。采用包含固体弹塑性、热扩散、磁扩散的磁流体力学模型,对回流罩结构磁驱动固体套筒实验的电流系数进行了确定和分析,结果显示,磁流体力学模型和有电流系数的边界磁感应强度公式能正确模拟回流罩结构磁驱动固体套筒实验。电流系数与套筒结构的关系为:
(1) 不同套筒对应的电流系数不同;
(2) 电流系数与实验过程无关,由套筒初始结构决定;
(3) 套筒厚度相同时,电流系数由套筒内半径决定,套筒内半径越大,电流系数越小;
(4) 套筒内半径相同时,电流系数由套筒厚度决定,套筒厚度越大,电流系数越小。
正确认识磁驱动固体套筒实验的电流系数变化规律,使磁驱动固体套筒实验的磁流体模拟从后验模拟发展成先验的准确设计和预测,有助于降低实验成本,加快柱面相关的实验研究。
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图 1 (a) 氮的p-T相图与聚合氮的合成条件(相图的部分数据来自文献[13–14, 16–17, 34, 37–39]),(b)~(c) 双面LHDAC实验示意图,(d)~(e) 激光加热过程中的光学照片,(f) 黑体辐射法测定温度的拟合曲线
Figure 1. (a) p-T phase diagram of nitrogen and the synthesis conditions of polymeric nitrogen (Part of the phase diagram is obtained from Refs. [13–14, 16–17, 34, 37–39].); (b)−(c) schematic diagram of double-sided LHDAC experiments; (d)−(e) optical photos during laser heating; (f) fitting curve of temperature determined by black body radiation method
图 2 (a) 激光加热前样品在55、115和140 GPa压力下的拉曼光谱,(b) 激光加热后样品在141 GPa压力下的拉曼光谱(插图为对应压力下样品腔的光学图像)
Figure 2. (a) Raman spectra of sample at 55, 115 and 140 GPa before laser heating, (b) Raman spectra of sample at 141 GPa after laser heating (Inset: optical images of sample chamber at corresponding pressure respectively.)
图 3 (a) 激光加热后样品在卸压过程中的高压XRD谱,(b) 样品卸压至123 GPa时的XRD精修谱,(c) BP-N和LP-N在123 GPa压力下的计算XRD谱与对应的晶体结构(插图为二维XRD图)
Figure 3. (a) High-pressure XRD spectra of the sample after laser heating on decompression, (b) XRD refined spectrum of the sample decompressed to 123 GPa, (c) calculated XRD spectra of BP-N and LP-N at 123 GPa and the corresponding crystal structure (Inset: two dimension XRD diagram)
图 4 聚合氮cg-N、LP-N、HLP-N和BP-N的原子体积随压力的变化关系(插图为聚合氮cg-N、BP-N和LP-N的相对计算焓值(ΔH),以LP-N(HPba2)的焓值[30]为基准)
Figure 4. (a) Volume per atom dependence of pressure on polymeric nitrogen cg-N, LP-N, HLP-N and BP-N (Inset: the relative calculated enthalpy value (ΔH) of polymeric nitrogen cg-N, BP-N and LP-N based on LP-N (HPba2) [30])
表 1 由XRD谱精修得到的晶格参数
Table 1. Lattice parameters obtained from Rietveld refinement
Material Space group a/Å b/Å c/Å α/(°) β/(°) γ/(°) V/Å3 LP-N Pba2 4.2403(2) 4.3840(7) 4.4600(7) 90 90 90 82.93(5) cg-N I213 3.1501(3) 3.1501(3) 3.1501(3) 90 90 90 31.25(9) Re P63/mmc 2.8391(3) 2.8391(3) 3.8520(4) 90 90 120 26.89(2) -
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