Diffusion of Helium in Calcite and Aragonite:A First-Principles Study

 引用本文:
 Citation:

## Diffusion of Helium in Calcite and Aragonite:A First-Principles Study

###### 通讯作者: LIU Hong, liuh@cea-ies.ac.cn ;
• 中图分类号: O521.2

## 氦在方解石和文石中的扩散：基于第一性原理的研究

###### Corresponding author: LIU Hong, liuh@cea-ies.ac.cn ;
• CLC number: O521.2

• 摘要: Helium diffusion in carbonate minerals is important for studying the physical and chemical properties and dynamic processes of Earth’s degassing. This paper discussed helium incorporation and diffusion mechanism in crystals of calcite and aragonite based on density functional theory calculations. The diffusion pathways, activation energies (Ea), and frequency factors (v) of helium under the surface and mantle condition were calculated. Calculations show an apperant anisotropy of helium diffusion in calcite, with more energetically favorable directions along a(b) axis. The moderate anisotropy of helium diffusion is showed in aragonite, in which the diffusion rate along c axis is slower than that along a axis. Under high pressure conditions, the activation energies of helium diffusion in aragonite increase with pressure. The closure temperature for calcite crystal varies from −54 ℃ to −25 ℃ in the direction [010], and for aragonite varies from −12 ℃ to 23 ℃ in [100]. Aragonite may be more retentive for helium than calcite under surface condition, which agrees well with previous experimental studies.
• Figure 1.  Schematic diagrams showing unit cell of calcite ((a) and (b)) and aragonite ((c) and (d)) (The two structures both show layers of Ca2+ cations and layers of planar CO3 groups stacked perpendicular to the c-axis. Green: Ca, red: O, gray: C.)

Figure 2.  Diffusion pathways of helium atom in calcite along [010] (a) and [001] via the S1′ site and reaching the S3 site (b); in aragonite along [100] (c) and [001] via the S1′ site and reaching the S1″ site (d)

Figure 3.  Energy barriers of different paths for helium diffusion in calcite: (a) ${S_1^{\rm Cal}- S_2^{\rm Cal}}$ path in the [010] direction, (b) ${S_1^{\rm Cal}- S_{1'}^{\rm Cal}-S_3^{\rm Cal}}$ path in the [001] direction; in aragonite: (c) ${S_1^{\rm Arg}- S_2^{\rm Arg}}$ path in the [100] direction, (d) ${S_1^{\rm Arg}- S_{1'}^{\rm Arg}-S_{1''}^{\rm Arg}}$ path in the [001] direction

Figure 4.  Comparisons of our Arrhenius relations for calcite (a) and aragonite (b) with the data of Cherniak et al.[4] (He diffusion in calcite displays marked anisotropy, while in aragonite shows moderate anisotropy.)

Figure 5.  Effect of pressure on helium diffusion in aragonite up to 14 GPa in the [100] (a) and [001] (b) directions (The diffusion coefficients obviously decrease with pressure increasing in both directions.)

Figure 6.  Calculated closure temperature (Tc) as a function of grain radius (a) along different directions in calcite and aragonite (Closure temperature are plotted for assuming spherical geometry (A=55) of the crystals. Helium in each carbonate composition using Dodson’s (1973) equation and a cooling rate of 10 ℃/Ma.)

•  [1] CHERNIAK D J, WATSON E B, THOMAS J B. Diffusion of helium in zircon and apatite [J]. Chemical Geology, 2009, 268(1): 155–166. [2] REICH M, EWING R C, EHLERS T A, et al. Low-temperature anisotropic diffusion of helium in zircon: implications for zircon (U–Th)/He thermochronometry [J]. Geochimica et Cosmochimica Acta, 2007, 71(12): 3119–3130. doi: 10.1016/j.gca.2007.03.033 [3] REINERS P W. Zircon (U-Th)/He thermochronometry [J]. Reviews in Mineralogy Geochemistry, 2005, 58(1): 151–179. doi: 10.2138/rmg.2005.58.6 [4] CHERNIAK D J, AMIDON W, HOBBS D, et al. Diffusion of helium in carbonates: effects of mineral structure and composition [J]. Geochimica et Cosmochimica Acta, 2015, 165: 449–465. doi: 10.1016/j.gca.2015.06.033 [5] COPELAND P, WATSON E B, URIZAR S C, et al. Alpha thermochronology of carbonates [J]. Geochimica et Cosmochimica Acta, 2007, 71(18): 4488–4511. doi: 10.1016/j.gca.2007.07.004 [6] COPELAND P, COX K, WATSON E B. The potential of crinoids as (U+Th+Sm) /He thermochronometers [J]. Earth and Planetary Science Letters, 2015, 42: 1–10. [7] CROS A, GAUTHERON C, PAGEL M, et al. 4He behavior in calcite filling viewed by (U-Th)/He dating, 4He diffusion and crystallographic studies [J]. Geochimica et Cosmochimica Acta, 2014, 125: 414–432. doi: 10.1016/j.gca.2013.09.038 [8] AMIDON W H, HOBBS D, HYNEK S A, et al. Retention of cosmogenic 3He in calcite [J]. Quaternary Geochronology, 2015, 27: 172–184. doi: 10.1016/j.quageo.2015.03.004 [9] BENGTSON A, EWING R C, BECKER U. He diffusion and closure temperatures in apatite and zircon: a density functional theory investigation [J]. Geochimica et Cosmochimica Acta, 2012, 86: 228–238. doi: 10.1016/j.gca.2012.03.004 [10] WANG K, BRODHOLT J, LU X. Helium diffusion in olivine based on first principles calculations [J]. Geochimica et Cosmochimica Acta, 2015, 156: 145–153. doi: 10.1016/j.gca.2015.01.023 [11] BALOUT H, ROQUES J, GAUTHERON C, et al. Helium diffusion in pure hematite (α-Fe3O3) for thermochronometric applications: a theoretical multi-scale study [J]. Computational and Theoretical Chemistry, 2017, 1099: 21–28. doi: 10.1016/j.comptc.2016.11.001 [12] SONG Z, WU H, SHU S, et al. A first-principles and experimental study of helium diffusion in periclase MgO [J]. Physics and Chemistry of Minerals, 2018, 45(7): 641–654. doi: 10.1007/s00269-018-0949-y [13] DODSON M H. Closure temperatures in cooling geological and petrological systems [J]. Contributions to Mineralogy Petrology, 1973, 40(3): 259–274. doi: 10.1007/BF00373790 [14] HOHENBERG P, KOHN W. Inhomogenous electron gas [J]. Physical Review, 1964, 136: 864–871. doi: 10.1103/PhysRev.136.B864 [15] KOHN W, SHAM L J. Quantum density oscillations in an inhomogeneous electron gas [J]. Physical Review, 1965, 137: 1697–1705. doi: 10.1103/PhysRev.137.A1697 [16] KRESSE G, FURTHMULLER J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set [J]. Computational Materials Science, 1996, 6(1): 15–50. doi: 10.1016/0927-0256(96)00008-0 [17] KRESSE G, HAFNER J. Ab initio molecular dynamics for liquid-metals [J]. Physical Review B, 1993, 47(1): 558–561. doi: 10.1103/PhysRevB.47.558 [18] BLÖCHL P E. Projected augmented-wave method [J]. Physical Review B, 1996, 50(24): 17953–17979. [19] KRESSE G, JOUBERT D. From ultrasoft pseudopotentials to the projector augmented-wave method [J]. Physical Review B, 1999, 59(3): 1758–1775. doi: 10.1103/PhysRevB.59.1758 [20] PERDEW J P, BURKE K, ERNZERHOF M. Generalized gradient approximation made simple [J]. Physical Review Letters, 1996, 77(18): 3865–3868. doi: 10.1103/PhysRevLett.77.3865 [21] CHADI D J. Special points for Brillouin-zone integrations [J]. Physical Review B, 1977, 16(4): 1746–1747. doi: 10.1103/PhysRevB.16.1746 [22] BRIK M G. First-principles calculations of structural, electronic, optical and elastic properties of magnesite MgCO3 and calcite CaCO3 [J]. Physica B: Condensed Matter, 2011, 406(4): 1004–1012. doi: 10.1016/j.physb.2010.12.049 [23] MALSEN E N, STRELTSOV V A, STRELTSOVA N R, et al. X-ray study of the electron density in calcite, CaCO3 [J]. Acta Crystallographica Section B: Structural Science, 1993, 49(4): 636–641. doi: 10.1107/S0108768193002575 [24] OGANOV A R, GLASS C W, ONO S. High-pressure phases of CaCO3: crystal structure prediction and experiment [J]. Earth and Planetary Science Letters, 2006, 241(1): 95–103. [25] DICKENS B, BOWEN J S. Refinement of the crystal of the aragonite phase of CaCO3 [J]. Physics and Chemistry A, 1971, 75(1): 27–32. [26] HENKELMAN G. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points [J]. Journal of Chemical Physics, 2000, 113(22): 9978–9985. doi: 10.1063/1.1323224 [27] VINEYARD G H. Frequency factors and isotope effects in solid state rate processes [J]. Journal of Physics and Chemistry of Solids, 1957, 3(1/2): 121–127. [28] BENDER M L. Helium-uranium dating of corals [J]. Geochimica et Cosmochimica Acta, 1973, 37(5): 1229–1247. doi: 10.1016/0016-7037(73)90058-6
•  [1] 赵金 , 郑海飞 . 0.1~800 MPa压力下方解石拉曼光谱的实验研究. 高压物理学报, 2003, 17(3): 226-229 . doi: 10.11858/gywlxb.2003.03.012 [2] 蓝蔚青 , 王蒙 , 车旭 , 孙晓红 , 陈扬易 , 谢晶 . Effect of High Pressure Processing with Different Holding Time on the Quality of Pomfret (Pampus argenteus) Fillets. 高压物理学报, 2018, 32(6): 065301-1-065301-11. doi: 10.11858/gywlxb.20180549 [3] 赵永年 , 张志林 , 崔启良 , 刘振先 , 邹广田 . 石墨Raman活性模E2g的压缩行为及CC键力常数的压力效应. 高压物理学报, 1992, 6(1): 48-53 . doi: 10.11858/gywlxb.1992.01.007 [4] 陈桂玉 , 殷岫君 , 张云 , 刘志毅 , 沈中毅 . Zr70Cu30非晶合金退火时结构弛豫过程的压力效应. 高压物理学报, 1989, 3(1): 18-24 . doi: 10.11858/gywlxb.1989.01.003 [5] 刘志明 , 崔田 , 何文炯 , 邹广田 , 韦孟伏 , 陈长安 . 压力对金属铌中氦原子凝聚的影响. 高压物理学报, 2008, 22(3): 225-231 . doi: 10.11858/gywlxb.2008.03.001 [6] 李圣爱 , 王玮 , 刘甦 , 万贤纲 . 钙钛矿结构材料Sr8CaRe3Cu4O24压力效应的研究. 高压物理学报, 2009, 23(1): 31-36 . doi: 10.11858/gywlxb.2009.01.005 [7] 刘志明 , 崔田 , 何文炯 , 邹广田 , 韦孟伏 , 陈长安 . 压力下替位氢对金属锂能带结构的影响. 高压物理学报, 2005, 19(1): 5-9 . doi: 10.11858/gywlxb.2005.01.002 [8] 刘振兴 , 孟宪仁 , 沈德元 , 林明柱 , 涂清云 , 林振金 , 桑丽华 , 彭志强 . T1系单相超导材料的高氧压合成及压力对超导性的影响. 高压物理学报, 1995, 9(1): 29-33 . doi: 10.11858/gywlxb.1995.01.005 [9] JIANG Shuqing , YANG Xue , WANG Yu , ZHANG Xiao , CHENG Peng . Symmetrization and Chemical Precompression Effect of Hydrogen-Bonds in H2-H2O System. 高压物理学报, 2019, 33(2): 020102-1-020102-8. doi: 10.11858/gywlxb.20190730 [10] SHANG Bing , WANG Tong-Tong . Numerical Study of Inertial Effects of Concrete-Like Materials in Split Hopkinson Pressure Bar Tests. 高压物理学报, 2017, 31(2): 114-124. doi: 10.11858/gywlxb.2017.02.003 [11] 李晓阳 , 陆阳 , 晏浩 . Electrical Transport Properties of Hexagonal TaSi2 Crystals Based on Structural Stability under High Pressure. 高压物理学报, 2018, 32(2): 021102-1-021102-7. doi: 10.11858/gywlxb.20170571 [12] 古可民 , 晏浩 , 柯峰 , 邓文 , 许家宁 , 陈斌 . Pressure-Induced Electrical Transport Anomaly, Structure Evolution and Vibration Change in Layered Material 1T-TiTe2. 高压物理学报, 2018, 32(6): 061101-1-061101-8. doi: 10.11858/gywlxb.20180568

##### 计量
• 文章访问数:  594
• 阅读全文浏览量:  558
• PDF下载量:  8
##### 出版历程
• 收稿日期:  2018-12-12
• 录用日期:  2019-01-03
• 网络出版日期:  2019-09-10
• 刊出日期:  2019-10-01

## Diffusion of Helium in Calcite and Aragonite:A First-Principles Study

###### 通讯作者: LIU Hong, liuh@cea-ies.ac.cn;
• 1. Institute of Earthquake Forecasting,China Earthquake Administration (CEA), Beijing 100036, China
• 2. Dalian University of Technology, Dalian 116024, China
• 3. Taiyuan University of Technology, Taiyuan 030024, China

### English Abstract

• Helium gas in minerals may provide plenty of useful information on Earth’s mantle evolution and geodynamic processes. There are many accessory minerals with high concentration of U and Th, such as apatite and zircon, have been widely used in (U-Th)/He dating method[1-3]. However, calcite, quartz, olivine, and other common minerals are less involved in this method. The application of carbonate (U-Th)/He method in thermo-chronometry has attracted more and more attention due to its ubiquity, large grain size, and extremely low closure temperature on the Earth[4-7]. 3He is attributed to the presence of primordial helium leaking from the mantle and 4He is produced by the decay of radioactive isotopes. High 3He/4He ratios are characteristic of samples of mantle origin. To understand dating and cooling histories of rocks, the diffusion mechanism of helium in carbonate minerals should be studied.

Recently, the experimental approaches to determining He diffusivities in carbonates have obtained some new achievements[4-8]. Copeland et al.[5] undertook a series of bulk step-heating experiments on calcite. They suggested that the diffusion of helium in calcite has no connection with the origin of minerals or the source of helium. The potentiality of calcite (U-Th)/He dating was also investigated by Cros et al.[7] Later, Amidon et al.[8] explored the production and retention of helium in calcite samples at several different locations. Step-degassing experiments were also used to investigate the diffusion of He in calcite. All the above experiments indicate that helium diffusion in calcite is influenced by multiple diffusion domains (MDD). This factor has been attributed to the loss of He from small domains with a faster diffusion rate, making it difficult to speculate bulk He retention in natural samples[8]. To avoid these limitations of bulk degassing experiments, Cherniak et al.[4] performed ion implantation experiments and NRA (nuclear reaction analysis) measurements to study helium diffusion in calcite, dolomite, magnesite, and aragonite. This approach can be used to study the anisotropy of helium diffusion. They found that the diffusion is anisotropic in calcite, dolomite and magnesite, and is slowest along the [001] direction. They found that magnesite and calcite are unlikely to be retentive of He on the Earth’s surface conditions, while dolomite and aragonite can be retentive under cooler conditions[4].

To better understand the diffusion mechanism and rate of helium in carbonates, we undertake a series of theoretical computations. The density functional theory (DFT) and climbing image nudged elastic band (CI-NEB) method are powerful for exploring the microscopic mechanism of He diffusion in minerals and have been applied to investigate the diffusion mechanism of helium in a few important minerals, such as zircon and apatite[9], olivine[10], hematite[11], preclase[12]. This method, using the microscopic atomic-scale calculations to elucidate He diffusion in perfect crystals without impurities, defects, or radiation damage, provides the basis for comparison of diffusion rate among different minerals. In this paper, the electronic nature, diffusion pathways, activation energies, and frequency factors of He diffusion in calcite and aragonite under ambient and high pressure conditions were investigated based on the DFT and CI-NEB method. After calculating the diffusion data, we discussed the anisotropy of helium diffusion in the two mineral phases. The closure temperature were also calculated using Dodson’s equation[13].

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈