Influence of Temperature Dependence of Solubility on Kinetics for Reactive Diffusion in a Hypothetical Binary System

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Influence of temperature dependence of solubility for each phase on kinetics of reactive diffusion has been theoretically analyzed for a hypothetical binary system consisting of two primary solid-solution phases (α and γ) and one compound phase (β). For the analysis, we consider that the β phase is produced owing to the reactive diffusion between the α and γ phases in a semi-infinite diffusion couple and the growth of the β phase is controlled by volume diffusion. In such a case, the parabolic relationship holds good between the thickness <I>l</I> of the β phase and the annealing time <I>t</I> as follows: <I>l</I><SUP>2</SUP>=<I>Kt</I>. Here, the parabolic coefficient <I>K</I> is mathematically expressed as a function of the interdiffusion coefficients and the solubility ranges of the α, β and γ phases. The temperature dependencies of the parabolic coefficient <I>K</I>, the solubility range Δ<I>y</I><SUP>θ</SUP> and the interdiffusion coefficient <I>D</I><SUP>θ</SUP> of the θ (θ=α,β,γ) phase are described by Arrhenius equations of <I>K</I>=<I>K</I><SUB>0</SUB>exp(−<I>Q<SUB>K</SUB></I>⁄<I>RT</I>), Δ<I>y</I><SUP>θ</SUP>=Δ<I>y</I><SUB>0</SUB><SUP>θ</SUP>exp(−<I>Q</I><SUP>θ</SUP>⁄<I>RT</I>) and <I>D</I><SUP>θ</SUP>=<I>D</I><SUB>0</SUB><SUP>θ</SUP>exp(−<I>Q<SUB>D</SUB></I><SUP>θ</SUP>⁄<I>RT</I>), respectively. The analysis indicates that <I>Q<SUB>K</SUB></I> is close to <I>Q<SUB>D</SUB></I><SUP>β</SUP>+<I>Q</I><SUP>β</SUP> at <I>Q<SUB>D</SUB></I><SUP>β</SUP>≤<I>Q<SUB>D</SUB></I><SUP>α</SUP> and <I>Q<SUB>D</SUB></I><SUP>β</SUP>≤<I>Q<SUB>D</SUB></I><SUP>γ</SUP> but greater than <I>Q<SUB>D</SUB></I><SUP>β</SUP>+<I>Q</I><SUP>β</SUP> at <I>Q<SUB>D</SUB></I><SUP>β</SUP>><I>Q<SUB>D</SUB></I><SUP>α</SUP> or <I>Q<SUB>D</SUB></I><SUP>β</SUP>><I>Q<SUB>D</SUB></I><SUP>γ</SUP>. As a consequence, the temperature dependency of the parabolic coefficient is directly related with those of the interdiffusion coefficient and the solubility range of the compound phase in the former case but not in the latter case.

収録刊行物

  • Materials transactions  

    Materials transactions 49(4), 715-722, 2008-04-01 

    The Japan Institute of Metals and Materials

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各種コード

  • NII論文ID(NAID)
    10021145585
  • NII書誌ID(NCID)
    AA1151294X
  • 本文言語コード
    ENG
  • 資料種別
    ART
  • ISSN
    13459678
  • NDL 記事登録ID
    9447171
  • NDL 雑誌分類
    ZP41(科学技術--金属工学・鉱山工学)
  • NDL 請求記号
    Z53-J286
  • データ提供元
    CJP書誌  CJP引用  NDL  J-STAGE 
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