Diffusion - Kakusan (English spelling) diffusion

Japanese: 拡散 - かくさん（英語表記）diffusion

Inside the mineral crystals that make up rocks, each atom vibrates due to external conditions such as temperature, and there is always a chance that it will move a small distance. Atoms become more likely to move when external forces such as concentration gradients of chemical components, stress and strain, and other factors such as rising temperature and lattice defects are added. When the concentration in a stationary mixed fluid at a uniform temperature is not uniform, changes occur that bring the concentration closer to a uniform distribution. Furthermore, when the temperature distribution is not uniform, thermal diffusion occurs. In general, the driving force for the movement of a substance is the gradient of the chemical potential of the component at each location, and the phenomenon in which a substance moves as a result of this is called diffusion. Diffusion is the movement of groups of atoms, ions, and molecules in a gas, liquid, or solid medium, and is the permeation of one substance by another substance, which can cause the movement of gas through gas, the movement of liquid through liquid, or the movement of solids through solids. Diffusion can be in a steady state where the change in component concentration is not time-dependent, or in an unsteady state where the concentration changes with time, and both examples are seen in petrology. Steady-state diffusion is described by Fick's first law, which in the one-dimensional case is
J = - D ∂ C / ∂ x
Here, D is the diffusion constant. In the case of a non-steady state, the change in concentration over time is proportional to the change in gradient and is expressed by Fick's second law. In the one-dimensional case, ∂ C /∂ t = - D (∂ ² C /∂ x ² )
In this formula, when the diffusion coefficient is not related to the concentration, it can be expressed as follows:
D = D ₀・exp {─ Q / ( RT )}
Here, R is the gas constant, T is the absolute temperature, and Q is the activation energy. _The constant D0 does not depend on temperature. The diffusion rate depends exponentially on temperature, and increases as the temperature increases. The difference in diffusion rate between low and high temperatures is significant. When rocks are formed, substances move and are affected by diffusion phenomena, so in petrology, the temperature at the time of formation is very important, and the results are thought to be reflected in the composition and structure of the rock [Suzuki: 1994]. Diffusion is the process of change in concentration distribution that occurs when a mixture of different types of particles approaches a state of thermal equilibrium. In rocks, the phenomenon of the components moving without the medium moving can be ignored when the medium is solid or fluid. When a rock contains a fluid, if the speed of movement of the fluid itself is expected to be relatively fast compared to the movement of the components within the fluid, the movement of the components within the fluid can be ignored. However, when the medium is solid, diffusion plays a major role as components move within the solid medium [Suzuki: 1994, Liesegang: 1913, Ostrand & Dewey: 1915].
When diffusion occurs within a polycrystalline aggregate such as a rock, the results of the movement of components vary considerably depending on the location in the crystal where the diffusion occurs. Generally, lattice diffusion takes place inside crystals, in which atoms move while replacing the crystal lattice. Lattice diffusion can also be faster if there are defects in the crystal. On the other hand, at the surface of a crystal, substances move more easily due to surface energy, so surface diffusion takes place. Also, at the interfaces between crystal grains, grain boundary diffusion, which is different from surface diffusion, takes place.
In general, the activation energy for surface diffusion is smaller than that for grain boundary diffusion and lattice diffusion, and the activation energy for lattice diffusion is usually the largest. Although there are voids in rocks, there are not many free surfaces, so the contribution of surface diffusion is unlikely to be very large. However, since there is generally some fluid in underground spaces, a comparison with the movement of materials through fluids must be considered.
Grain boundary diffusion is diffusion that moves along polycrystalline grain boundaries, a phenomenon that occurs because the atomic arrangement of polycrystalline grain boundaries is more disordered than in single crystals. Grain boundaries are the two-dimensional spread of crystal lattice disorder, and grain boundary diffusion in polycrystals is generally more severe than lattice diffusion within the crystal. In polycrystalline materials, diffusion proceeds quickly along the grain boundaries, followed by internal diffusion into the crystal lattice. In aggregates of mineral grains such as rocks, grain boundary diffusion is thought to make the largest contribution of all solid-state diffusion [Suzuki: 1994].

Source: Asakura Publishing Dictionary of Petrology Information

Japanese:

岩石を構成する鉱物結晶の内部では，各原子は温度などの外的条件によって振動しており，常に微小な距離を移動する確率をもっている．外部から化学成分の濃度勾配や応力歪などの力が加わり，さらに温度の上昇や格子欠陥などの要因が加わると原子は移動しやすくなる．一様な温度の静止混合流体中の濃度が均一でないときには，濃度を一様分布に近づける変化が起こる．また温度の分布が一様でなければ熱拡散（thermal diffusion）が起こる．一般に物質が移動する場合の駆動力は，各場所における成分の化学ポテンシャルの勾配で，この結果物質が移動する現象が拡散（diffusion）である．拡散現象は気体，液体または固体の媒質の中で，原子，イオン，分子の群が移動することで，一つの物質の他の物質による透過作用で，気体を通じた気体の移動，液体を通じた液体の移動，固体を通じた固体の移動などが起こる．拡散現象には成分濃度の変化が時間によらない定常状態の場合と，濃度が時間と共に変化する非定常状態の場合があり，岩石学ではどちらの例も認められる．定常状態の拡散はフィック（Fick）の第一法則で表され，一次元の場合には，
　J＝-D・∂C/∂x
として表される．ここでDは拡散係数（diffusion constant）である．非定常状態の場合は濃度の時間的変化が勾配の場所による変化に比例してフィックの第二法則で表される．一次元の場合は
　∂C/∂t＝-D（∂²C/∂x²）
として表される．この式で拡散係数が濃度に関係しない場合には次のように表される．
　D＝D₀・exp｛─Q/（RT）｝
ここで，R：気体定数，T：絶対温度，Q：活性化エネルギーである．定数D₀は温度に依存しない．拡散速度は温度に指数関数的に依存し，温度が高くなると大きくなる．低温の場合と高温の場合の拡散速度の差は著しい．岩石が形成される際には物質が移動し拡散現象に影響を受けるので，岩石学では形成の際の温度が非常に関係し，その結果が岩石の組成や構造に表れていると考えられる［鈴木 : 1994］．拡散は異種の粒子の混合系が熱平衡状態に近づく際におこる濃度分布の変化の過程である．岩石では，媒体が移動せずにその中の成分が移動する現象には，媒体が固体の場合と流体の場合がある．岩石が流体を含む場合には，流体内部の成分の移動に比べて流体自体の移動速度が相対的に速いことが予想される場合は，流体内部での成分の移動は無視できる．しかし媒体が固体の場合には，成分が固体媒体の内部を移動するため拡散現象が主要な役割を果たすことになる［鈴木 : 1994，Liesegang : 1913, Ostrand & Dewey : 1915］．
岩石のような多結晶の集合体の中で拡散が行われる場合には，拡散の行われる結晶の場所によって成分の移動結果はかなり異なる．一般に結晶内部では結晶格子を置換しながら原子が移動する格子拡散（lattice diffusion）が行われる．格子拡散でも結晶中に欠陥が存在すると速くなる．一方結晶表面では表面エネルギーのために物質は移動しやすく表面拡散（surface diffusion）が行われる．また結晶粒の間の界面では表面とは異なる粒界拡散（grain boundary diffusion）が行われる．
一般に表面拡散の活性化エネルギーは粒界拡散や格子拡散に比べて小さく，格子拡散の活性化エネルギーが最も大きいのが普通である．岩石の中では空隙はあるものの自由な表面はあまり存在しないので表面拡散の寄与はあまり大きくないであろう．しかし地下の空間には一般に多少の流体が存在するので，流体を媒体とした物質の移動との比較を考えなければならない．
粒界拡散は多結晶粒界を移動する拡散で，単結晶に比して多結晶粒界の原子配列の乱れが著しいために起こる現象である．結晶格子の乱れの二次元的広がりが粒界であり，多結晶の粒界拡散は一般に結晶内部の格子拡散よりも著しい．多結晶体では拡散は粒界に沿って速やかに進行し，次いで結晶格子内への内部拡散が起こる．岩石のような鉱物粒の集合体では，粒界拡散の寄与が固体拡散の中で最も大きいものと考えられる［鈴木 : 1994］．

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