Beke Dezső L, Azim Asmaa A
Department of Solid State Physics, Doctoral School of Physics, University of Debrecen, P.O. Box 2, H-4010 Debrecen, Hungary.
Physics Department, Faculty of Science Ain Shams University, Abbassia, Cairo 11566, Egypt.
Materials (Basel). 2024 Aug 20;17(16):4116. doi: 10.3390/ma17164116.
General derivation of the well-known Ren-Otsuka relationship, 1αdTodx=-αβ (where To, , α and β(>0) are the transformation temperature and composition, as well as the composition and temperature coefficient of the critical shear constant, ', respectively) for shape memory alloys, SMAs, is provided based on the similarity of interatomic potentials in the framework of dimensional analysis. A new dimensionless variable, tox=ToxTmx, describing the phonon softening (where is the melting point) is introduced. The dimensionless values of the heat of transformation, Δ, and entropy, Δ, as well as the elastic constants ', , and A=c44c' are universal functions of () and have the values at (0) within sub-classes of host SMAs having the same type of crystal symmetry change during martensitic transformation. The ratio of dtodx and has the same constant value for all members of a given sub-class, and relative increase in ' with increasing composition should be compensated by the same decrease in . In the generalized Ren-Otsuka relationship, the anisotropy factor appears instead of ', and α as well as β are the differences between the corresponding coefficients for the and ' elastic constants. The obtained linear relationship between h and rationalizes the observed empirical linear relationships between the heat of transformation measured by differential scanning calorimetry (DSC) () and the martensite start temperature, .
基于尺寸分析框架内原子间势的相似性，给出了形状记忆合金（SMA）中著名的任 - 大冢关系（1αdTodx = -αβ，其中To、α和β(>0)分别为转变温度、成分以及临界剪切常数'的成分和温度系数）的一般推导。引入了一个新的无量纲变量tox = ToxTmx来描述声子软化（其中 是熔点）。转变热Δ和熵Δ的无量纲值，以及弹性常数'、 和A = c44c'是()的通用函数，并且在马氏体转变期间具有相同类型晶体对称性变化的主体SMA子类中，在(0)处具有 值。对于给定子类的所有成员，dtodx与 的比值具有相同的常数值，并且随着成分增加'的相对增加应由 的相同减少来补偿。在广义任 - 大冢关系中，出现的是各向异性因子 而不是'，并且α以及β是 和'弹性常数的相应系数之间的差异。所得到的h与 之间的线性关系使通过差示扫描量热法（DSC）测量的转变热()与马氏体起始温度 之间观察到的经验线性关系合理化。
