Introduction

Despite the widespread use of noble gases as tracers of mantle processes and as geological chronometers, many fundamental aspects on their geochemical behavior remain poorly understood. Noble gas diffusion in mantle minerals is generally considered very fast based on their chemical inertness and incompatibility to mantle minerals as the basic assumption in previous studies. Diffusive concentration of impurities to grain boundaries has been well documented not only in synthetic materials and ceramics but also in geological materials more recently. Because the intergranular transport medium within a rock is of paramount importance for the transport and/or storage of elements which are incompatible to the rock-forming minerals. But no studies have evaluated the behavior of the large, uncharged, noble gas in this regard. Here, we address an important characteristic of noble gas geochemistry about which no data and little understanding exist: to what extent do grain boundaries diffusion of noble gases involved. The phenomenon has not commonly been considered, yet if significant, it would have important implications for several fields in geochemistry, including studies on evolution of chemical/isotopic heterogeneity in the Earth's mantle and noble gas geochronology.

Synthesis of highly dense and fine-grained aggregates of mantle composites by vacuum sintering of nano-sized mineral powders

Synthesized mineral powders with particle size of < 100 nm are vacuum sintered to obtain highly dense and fine-grained polycrystalline mantle composites: single phase aggregates of forsterite (Mg2SiO4), olivine (Mg1.8Fe0.2SiO4), diopside (CaMgSi2O6), and enstatite (MgSiO3); two phase composites of forsterite + spinel (MgAl2O4) and forsterite + periclase (MgO); and, three phase composites of forsterite + enstatite + diopside. Nano-sized powders of colloidal SiO2 (Fig.1A) and highly dispersed Mg(OH)2 with particle size of ≦ 50 nm are used as chemical sources for MgO and SiO2, which are common components for all of the aggregates. These powders are mixed with powders of CaCO3, MgAl2O4, and Fe(CO2CH3) to introduce mineral phases of diopside, spinel, and olivine to the aggregates, respectively. To synthesize highly dense composites through pressureless sintering, we find that calcined powders should be composed of particles that have: (i) fully reacted to the desired minerals, (ii) a size of < 100 nm, and (iii) less propensity to coalesce. Such calcined powders are compressed by using cold isostatic pressing and then vacuum sintered. The temperature and duration of the sintering process are tuned to achieve a balance between high density and fine grain size. Highly dense (i.e. porosity ≦ 1 vol%) polycrystalline mantle mineral composites with grain size of 0.3-1.1 μm are successfully synthesized with this method.

In such materials, the volume fraction of the grain boundaries is 10-2~10-3 (Fig. 2B) which is desirable, particularly for experimental studies of diffusion. The apparent diffusion coefficient in polycrystalline body is described as a sum of the diffusion coefficient of grain boundary and crystal lattice (Fig. 2A). (Di bulk =s Dil+(1-s)D igb ), where , δ is grain boundary width (ca. 1×10-9 m, Hiraga et al., 2004), d is grain size) Thus, I expect to detect chemical components from grain boundaries using conventional whole rock chemical analysis.

Diffusion of argon into forsterite

Argon diffusion experiments were performed on the gem quality clear forsterite sample (Myanmar) and synthetic polycrystalline forsterite with grain size of 500 nm and porosity≦ 0.06 vol%. The samples were placed on a platinum plate, and then put in an electric tube furnace. Samples surface were directly exposed to the Ar gas pressure of 0.15 MPa at 1280 °C for 10, 100 and 133 hours. Argon atoms are expected to diffuse into the crystals from their surface resulting in formation of concentration gradients at near-surface. Total amounts of diffused Ar were determined by in-vacuo heating extraction and noble gas mass spectrometry (Fig. 3). Depth concentration profiles of 40Ar started from the near-surface were calculated to reproduce the total amounts of Ar incorporated into the synthetic polycrystalline forsterite with several uptake durations (Fig. 4). The calculated diffusion distance by follow equation was < 100 nm even after diffusion anneal of 133 hours, indicating very slow Ar diffusion with a diffusion coefficient (D) of 1.44×10-21 m2/s at 1280・C. Amount of Ar released from the single natural forsterite crystal was several orders of magnitude lower than those from the synthetic polycrystalline forsterite, indicating a significant uptake of Ar at grain boundaries. This result is consistent with the result by Thomas et al. (2008).

Diffusion of neutron induced 4He, 21Ne and 37Ar in forsterite

In order to introduce controlled amounts of the noble gases homogeneously into natural single forsterite crystals and synthesized polycrystalline forsterite, they were irradiated by neutrons in a nuclear reactor. The key reaction we exploit is 40Ca(n,α)37Ar, whereby 37Ar is in situ produced in the forsterite (Mg2SiO4) doped with minor amount (~3wt%) of diopside (CaMgSi2O6). 38Ar was produced by 37Cl(n,γ)38Cl(β-)38Ar from trace amount of Cl involved as impurity in the sample. Nuclear reaction of major elements associated with α-emission produces 4He. Neon isotopes are produced by (n,α) reactions of Mg. Temperature dependent diffusive release of the in-situ produced noble gas nuclides were then determined simultaneously by high precision stepped heating in vacuum and noble gas mass spectrometry. In stepwise heating, the sample to be analyzed was dropped into the crucible and then heated at a given temperature (400 °C to 1900 °C) for a given time (15 to 60 minute), and after extracted gases were measured, the same sample was heated again at a higher temperature to release gases from higher retentive sites of the sample. Because the noble gas components even in the same sample shows different origins (e.g. crystal lattice, grain boundary, inclusion and crystal surface), they will have different release patterns during stepwise heating. The determined diffusivities exhibit the Arrhenius behavior at a temperature range from 900 to 1300・C. Although D(4He) is about one order of magnitude higher than D(21Ne), D(37Ar) and D(38Ar), activation energies (Ea) fall in a range from 30 to 130 kJ/mol for all noble gas isotopes. No systematic difference in diffusivities for single crystal- and polycrystalline-forsterite was observed. This suggests that a role of grain boundaries for transporting the gases is negligible when noble gases are already incorporated in mineral lattice and then they diffuse out from the samples.

Implications for noble gas behavior in the Earth

In this study we performed two different diffusion experiments. The result from diffusive uptake of Ar shows between 10-9 and 10-11 times lower diffusivity than diffusion of neutron induced of 4He, 21Ne and 37Ar. The geological phenomenon is more like the diffusion of neutron induced of 4He, 21Ne and 37Ar experiment. Assuming time scale for diffusion from the values of D obtained in this study, which is the order of a few cm year-1. Result from the Arrhenius plot shows the grain boundary in forsterite is no effective pathway for diffusion of noble gases. The values of noble gases diffusion coefficient are a 109 times higher than that of Mg2+ of forsterite. Rather those values were closer to the value of interstitial diffusion pathway. These suggest that noble gases were not use neighbor vacancy like the atoms sited in between normal lattice sites. Due to its inert nature, the diffusion of noble gases maybe a special case in which its intralattice migration is effectively controlled by distortion of crystal lattice to allow passage of the noble gas atoms into a new site.

It is well known that grain boundary act as an effective pathway for diffusion of elements those are incompatible to rock-forming minerals (i.e., Dgb>>Dl). Although noble gases are highly incompatible to forsterite, a major constituent of the Earth's mantle, the observation that their Dgb is negligible implies that mechanism in grain boundary diffusion for noble gases are quite different. The results of this study suggest that behavior of radiogenic noble gas isotopes, such as 4He, 21Ne and 40Ar, in the mantle decouple from their parent element such as U, Th and K. This will give a new constraint for the evolution of noble gas isotope ratios of radiogenic / primordial noble gas isotope ratio (4He/3He, 21Ne/22Ne, and 40Ar/36Ar) over geologic timescales and scale length of several domains in the convecting mantle.

Fig.1 (A) SEM images of the Nano-sized powders of colloidal SiO2. (B) SEM images of forsterite (Fo100) aggregate, sintered at constant conditions of 1310 ・C for 3 h. (C) Comparisons of light transparency of the aggregates of a forsterite, b enstatite, c diopside, d olivine, e forsterite + periclase, f forsterite + spinel and g forsterite + enstatite + diopside. All sample thicknesseswerefixed at 0.5mm.

Fig.2 (A) Schematic drawing the apparent diffusion coefficient (Dibulk, red arrow) in polycrystalline body. The apparent diffusion coefficientred is the sum of the diffusion coefficient of grain boundary (Digb, blue arrow) and that of crystal lattice (Dil, green arrow). (B) contribution to Dgb of Dbulk with respect to grain size, d.

Fig. 3 The amount of released Ar in isothermal experiments of single crystal and synthetic polycrystalline forsterite. The diffusion experiment were performed at 1280・C.

Fig. 4 Diffusion profiles for Ar diffusion in forsterite (Mg2SiO4). Diffusion profiles were determined by high precision stepped heating and noble gas mass spectrometry. Measured concentration gradients were fitted with complementary error-function curves.

Fig.5Arrheniusplotforapparent(a).4He(b).21Neand(c).37Arand38Ardiffusivityinnaturalandsyntheticforsterite(Mg2SiO4),calculatedforplaneslabgeometry.BlacksolidanddottedlinesindicatepreviousmeasurementsinolivinebyTrullandKurz(1993)andHart(1984)respectively.

本論文は6章からなる。第1章はイントロダクションであり、地球での希ガス元素及びその同位体比の分布の総括から始まり、希ガス元素の挙動を理解するためには、固体地球内での希ガス元素の分配や拡散の知識が欠かせないが、分配や溶解度のデータに比べて拡散係数のデータは少なく、単結晶を用いた研究しかないことを強調している。固体地球は多結晶質の岩石から構成されており、結晶内拡散と粒界拡散の2種類の拡散が起きているので、本研究の目的は希ガス元素について両者の拡散過程を評価し、地球規模の現象の理解を深めることであると述べている。

第2章では、これまで測定されていなかった希ガス元素の粒界拡散係数を求めるために使う高密度・極細粒フォルステライト多結晶体の合成について述べている。フォルステライト(Mg2SiO4)はマントル中に多く存在する鉱物であるカンラン石の端成分で、固体地球物質の代表として実験に使用した。原料であるナノサイズのSiO2粒子とMg(OH)2粒子の粉末を混合し、仮焼き,加圧成形,焼結する方法でフォルステライト多結晶体の合成を行った。仮焼温度や焼結温度の最適化に工夫を凝らした結果、これまでで最高の品質である粒径0.4 μm、空孔率0.06%以下の高密度、極細粒多結晶体の合成に成功した。

第3章では、拡散実験の解析方法について、基礎的な原理の説明から始めて、多結晶体の場合の結晶内拡散と粒界拡散の関係の定式化,さらには実際の段階加熱実験から拡散係数を求めるデータ解析方法と、順を追って述べている。

第4章では、天然単結晶と合成多結晶のフォルステライトをArの入った電気炉の中で加熱し、結晶表面から拡散して取り込まれる量を測定して拡散係数を求めた実験が述べられている。しかし、この方法では試料を133時間1280℃のAr中に置いても拡散距離は50nm程度であり、拡散係数を測るには適していないことが示された。

第5章では、試料内部に均一に希ガス元素を分布させ、段階加熱で抽出して拡散定数を測定する実験が述べられている。この方法は希ガス元素の拡散定数を求める方法としては過去に例のない斬新な実験方法であり、高い評価に値する。希ガス元素が均一に分布している鉱物試料は、試料を原子炉内で中性子照射し、そこで起きる核反応で希ガス元素の同位体が生成することで実現した。わずかなCaやClが均質に分布しているフォルステライト試料を中性子で照射すると、24Mg(n,α)21Ne、40Ca(n,α)37Ar、37Cl(n,γ)38Cl(β-)38Arなどの核反応が起き、試料内部に均一にNeやArの同位体が生成する。これらの核反応ではα粒子も放出されるので、4Heも試料内に均一に分布する。これらの希ガス元素同位体は400℃から1900℃まで段階加熱法により温度成分ごとに抽出され、質量分析装置で定量し、拡散定数を求めた。その結果,900-1300℃では4He、21Ne、37Arともおおむねアレニウスの関係が成り立ち,この温度範囲の拡散定数と活性化エネルギー値を求めることが出来た。カンラン石中のHeの拡散定数を測定した例が過去に2例あるが、本研究の測定値はその2例の中間的な値であった。カンラン石中のNe、Arの拡散係数は本研究で始めて測定され、Heより1~2桁低い値であった。本研究の結果で特筆すべきは、測定誤差を考慮すると天然単結晶のフォルステライトと合成多結晶のフォルステライトとでは4He、21Ne、37Arとも拡散定数に系統的な差が見られないことであり、希ガス元素については粒界拡散の寄与が無視できると結論づけた。

第6章では第5章の実験結果をもとに希ガス元素の地球化学への展開が述べられており、これまでの研究で粒界拡散の寄与が大きいことが示されている金属元素とは異なり、希ガス元素ではマントル鉱物中での粒界拡散の寄与が無視できることを強調している。このように、本研究では、斬新な実験方法によって希ガス元素の拡散定数を求め、マントル内の物質循環の議論に制約を与えるデータを提供することが出来、地球化学に大きな貢献をすることができた。

なお、本論文の第2章の主要部分は平賀岳彦、橘ちひろ,田阪美樹、宮崎智詞、小林民夫、賞雅朝子、大橋直樹、佐野聡との、第4章と第5章の主要部分は角野浩史、平賀岳彦、長尾敬介,野津憲治との共同研究であるが、論文提出者が主体となって分析及び検証を行ったもので、論文提出者の寄与が十分であると判断する。

したがって、博士(理学)の学位を授与できると認める。