地核內部的量子力學

原文網址：https://www.uni-wuerzburg.de/en/sonstiges/meldungen/detail/artikel/quantenmechanik-im-erdkern-1/

地核內部的量子力學

符茲堡大學的物理學家發現了鎳擁有的奇特性質，或許有助於解釋一些關於地球磁場的謎團。

如果沒有磁場，地球上的生物會過得相當難受：從太空來的各種粒子會大量穿越大氣層而造成所有活體身上的細胞受損。人類的科技系統也會時常故障，在某些情況其中的電子元件還會被完全摧毀。

儘管磁場對於地球上的生命來說十分重要，我們卻還尚未完全明瞭地球磁場的成因。關於地磁的起源有許多理論，但是許多專家認為它們並不完整或含有瑕疵。近日由符茲堡大學的科學家做出的新發現或許提供了一個全新角度來解釋地磁起源。他們的發現刊登於當期的《自然通訊》(Nature Communications)。根據這篇文章，此效應的關鍵潛藏於元素鎳的特殊結構之中。

理論與真實的矛盾

這篇近日刊出的國際研究負責人，符茲堡大學理論物理和天文物理研究所的教授Giorgio Sangiovanni表示：「用來解釋地球磁場的標準模型中，對地核內部金屬的導電度和導熱性採用的數值跟現實並不相符。」參與研究的人員包括同單位的博士生Andreas Hausoel和博士後研究員Michael Karolak；以及跟Giorgio Sangiovanni長期合作，維也納大學的Alessandro Toschi和Karsten Held；最後還有來自德國漢堡、(薩勒河畔)哈雷和俄羅斯葉卡捷琳堡的科學家。

地球的中心大約位在6400公里深的地方，此處溫度為6300℃，壓力則為350百萬巴左右。地核最主要的金屬――鐵和鎳於此環境下形成的實心球體構成了地球的內核。在內核之外則包裹著一層液態的外核，組成同樣是以鐵和鎳為主。外核的液態金屬流動可以加強電流而形成地球磁場――至少常見的地球發電機(geodynamo)理論是如此述說的。「但是該理論具有某些矛盾之處。」Giorgio Sangiovanni表示。

由能帶構造引起的關聯效應

Sangiovanni說明：「這是因為在室溫下鐵具有強烈的有效電子―電子關聯作用，使得它跟銅或金之類的一般金屬有很大的差異。鐵的電子系統具有很強的關聯性。」但此電子關聯效應在地核普遍的超高溫狀態下會大幅減弱，使得傳統理論也能適用在鐵身上。然而這些理論接著對鐵的導電度預測結果卻太高而跟地球發電機理論有所衝突。

鎳的出現會讓情形截然不同。「我們發現在相當高的溫度下，鎳會展現出一種獨特的異常性質。」這位物理學家如此解釋，「鎳也是強關聯金屬。不同於鐵，鎳的強關聯性主要是由其特殊能帶結構所造成，而非單獨源自電子―電子關聯作用。我們將此效應命名為『能帶結構誘發關聯性』(band-structure induced correlation)。」固體的能帶結構只取決於晶格中原子的幾何排列方式以及原子的種類。

地核中的鐵和鎳

Andreas Hausoel接著解釋：「在室溫下，鐵的原子排列方式就像是一個假想立方體中，有一顆原子位於中心位置，周圍的原子則位在角落上，形成的晶格結構我們稱為體心立方堆積(bcc)。」但隨著溫度和壓力增加，此結構會產生變化：鐵原子會靠得更緊而形成一種六方晶格，物理學家稱為六方最密堆積(hcp)晶格。結果使鐵喪失了它大部分的關聯性。

但這種情形不會發生在鎳身上，Hausoel解釋：「在此金屬中，平常狀態下原子就已經盡可能地堆積成最緊密的立方結構。即使溫度和壓力變得相當高，他們仍能維持同樣的排列方式。」唯有這種幾何穩定性產生的交互作用以及源自此幾何排列的電子關聯性，才能解釋鎳在極端環境下擁有的特殊物理行為。雖然一直以來科學家都忽視了鎳的存在，現在看來在地球磁場中鎳具有相當重要的地位。

從地球物理得到的關鍵啟發

實際上，符茲堡大學固態理論物理部門的研究重點並不是地球核心發生的事物。Sangiovanni、 Hausoel和他們的同事的研究重心為低溫下強關聯電子的性質。他們探討量子效應和所謂的多粒子效應這些下一世代的資料處理器和能量儲存裝置感興趣的現象。在此篇論文中，超導體和量子電腦也被列為關鍵字。

實驗得到的數據並未用在這類研究當中。Hausoel表示：「我們將原子的已知性質，包括從量子力學得到的觀點輸入電腦，試圖以此計算一大群原子聚集在一起時呈現的行為。」由於這類計算的過程十分複雜，科學家必須仰賴其他機構的幫助，像是德國加興萊布尼茲超級電腦中心的超級電腦SUPERMUC。

那地核跟他們的研究有何關係？Hausoel表示：「我們想要知道鎳新發現的磁力性質穩定性有多高，結果發現在相當高的溫度下鎳依然保有這些性質。」他們跟地球物理學家討論並對鎳鐵合金進行更加深入的研究之後，顯示此發現可能跟地核正在進行的活動有所關連。

Quantum mechanics inside Earth's core

Physicists from the University of Würzburg have discovered surprising properties of nickel. They could help unravel some mysteries about Earth's magnetic field.

Without a magnetic field life on Earth would be rather uncomfortable: Cosmic particles would pass through our atmosphere in large quantities and damage the cells of all living beings. Technical systems would malfunction frequently and electronic components could be destroyed completely in some cases.

Despite its huge significance for life on our planet, it is still not fully known what creates the Earth's magnetic field. There are various theories regarding its origin, but a lot of experts consider them to be insufficient or flawed. A discovery made by scientists from Würzburg might provide a new explanatory angle. Their findings were published in the current issue of the journal Nature Communications. Accordingly, the key to the effect could be hidden in the special structure of the element nickel.

Contradiction between theory and reality

"The standard models for Earth's magnetic field use values for the electric and thermal conductivity of the metals inside our planet's core that cannot square with reality," Giorgio Sangiovanni says; he is a professor at the Institute for Theoretical Physics and Astrophysics at the University of Würzburg. Together with PhD student Andreas Hausoel and postdoc Michael Karolak, he is in charge of the international collaboration that was published recently. Among the participants are Alessandro Toschi and Karsten Held of TU Wien, who are long-term cooperation partners of Giorgio Sangiovanni, and scientists from Hamburg, Halle (Saale) and Yekaterinburg in Russia.

At Earth's centre at a depth of about 6,400 km, there is a temperature of 6,300 degrees Celsius and a pressure of about 3.5 million bars. The predominant elements, iron and nickel, form a solid metal ball under these conditions which makes up the inner core of the Earth. This inner core is surrounded by the outer core, a fluid layer composed mostly of iron and nickel. Flowing of liquid metal in the outer core can intensify electric currents and create Earth's magnetic field – at least according to the common geodynamo theory. "But the theory is somewhat contradictory," Giorgio Sangiovanni says.

Band-structure induced correlation effects

"This is because at room temperature iron differs significantly from common metals such as copper or gold due to its strong effective electron-electron interaction. It is strongly correlated," he declares. But the effects of electron correlation are attenuated considerably at the extreme temperatures prevailing in Earth's core so that conventional theories are applicable. These theories then predict a much too high thermal conductivity for iron which is at odds with the geodynamo theory.

With nickel things are different. "We found nickel to exhibit a distinct anomaly at very high temperatures," the physicist explains. "Nickel is also a strongly correlated metal. Unlike iron, this is not due to the electron-electron interaction alone, but is mainly caused by the special band structure of nickel. We baptised the effect 'band-structure induced correlation'." The band structure of a solid is only determined by the geometric layout of the atoms in the lattice and by the atom type.

Iron and nickel in Earth's core

"At room temperature, iron atoms will arrange in a way that the corresponding atoms are located at the corners of an imaginary cube with one central atom at the centre of the cube, forming a so-called bcc lattice structure," Andreas Hausoel adds. But as temperature and pressure increase, this structure changes: The atoms move together more closely and form a hexagonal lattice, which physicists refer to as an hcp lattice. As a result, iron looses most of its correlated properties.

But not so with nickel: "In this metal, the atoms are as densely packed as possible in the cube structure already in the normal state. They keep this layout even when temperature and pressure become very large," Hausoel explains. The unusual physical behaviour of nickel under extreme conditions can only be explained by the interaction of this geometric stability and the electron correlations originating from this geometry. Despite the fact that scientists have neglected nickel so far, it seems to play a major role in Earth's magnetic field.

Decisive hint from geophysics

The goings-on inside Earth's core are not the actual focus of research at the Departments of Theoretical Solid-state Physics of the University of Würzburg. Rather Sangiovanni, Hausoel and their colleagues concentrate on the properties of strongly correlated electrons at low temperatures. They study quantum effects and so-called multi-particle effects which are interesting for the next generation of data processing and energy storage devices. Superconductors and quantum computers are the keywords in this context.

Data from experiments are not used in this kind of research. "We take the known properties of atoms as input, include the insights from quantum mechanics and try to calculate the behaviour of large clusters of atoms with this," Hausoel says. Because such calculations are highly complex, the scientists have to rely on external support such as the SUPERMUC supercomputer at the Leibniz Supercomputing Centre (LRZ) in Garching.

And what's the Earth's core got to do with this? "We wanted to see how stable the novel magnetic properties of nickel are and found them to survive even very high temperatures," Hausoel says. Discussions with geophysicists and further studies of iron-nickel alloys have shown that these discoveries could be relevant for what is happening inside Earth's core.

原始論文：A. Hausoel, M. Karolak, E. Şaşɩoğlu, A. Lichtenstein, K. Held, A. Katanin, A. Toschi, G. Sangiovanni. Local magnetic moments in iron and nickel at ambient and Earth’s core conditions. Nature Communications, 2017; 8: 16062 DOI: 10.1038/ncomms16062

引用自：University of Würzburg. "Quantum mechanics inside Earth's core."