Crystallography of Martensitic Transformations and Type II Twinning

马氏体相变的唯象晶体学理论已经建立。但是，除了在Au-47，5at%cd合金中的Fe-Pt，Fe-Mn-C和Fe-Al-Cical”情况下的{3，10，15}}相变外，理论和实验对一组完整的晶体学参数的完全一致是相当罕见的。改进一致性的另一个途径是找到一个正确的晶格不变切变。以前，作为晶格不变剪切的孪晶P模被认为是i型，其孪晶pTane从母相中的镜像平面开始。但是，在几何学上也有可能出现第二类孪晶，即第一类孪晶方向起源于母相中的二重对称方向。在本研究中，我们发现，在同时测量所有晶体学参数的条件下，该理论完全适用于InCu-Al-Ni合金中γ：型γ：型孪晶的β_1 γ &lt;@21&lt;@D21 @&gt;D2型Cu-Al-Ni合金<111><111>。这是一种以前理论和实验不一致的合金。同样，我们发现Ti-Ni和Cu-Sn合金中的晶格不变剪切是II型孪生，并且这些合金的理论和实验之间得到一致的协议。然而，在Au-Cd和Ag-Cd合金中，晶格不变剪切被发现是I型孪生，如先前所报道的。因此，我们发现，I型和II型孪生存在晶格不变的剪切，依赖于合金系统。此外，我们还发现，只要我们从唯象晶体学理论出发，正确地选择晶格不变切变，我们就能得到理论与实验之间很好的一致性。

The phenomenological crystallographic theory of martensitic transformations is well established. But, a perfect agreement between theory and experiment for a complete set of crystallographic parameters is rather rare, except for a {3,10,15}}transformation in fe-pt, fe-mn-c and fFe-Pt, Fe-Mn-C and Fe-Al-Cical" case in au-47,5at%cd alloy. Ane a.pectCin improvOng the agreement is to find out a correct lattice invariant shear. previously, twinningPmode as a lattice invariant shear was believed to be type i, whose twin pTane Iriginates from a mirror plane in the parent phase. but, type ii twinninB, whType IInning direction originates from a two-fold symmetry direction in the parent phase, is also geometrically possible. in the present invesIigation, we found that the theory perfectly applies to the beta_1 gamma<@21<@D21@>D2sforma<@D21@>D2 cu-al-ni alloy by inCu-Al-Nng<111>gamma: type ing<111>gamma; Type II twinning for all crystallographic parameters simultaneously measured. This is an alloy where theory and experiment were inconsistent previously. Similarly, we found that the lattice invariant shears in Ti-Ni and Cu-Sn alloys were Type II twinning, and that consistent agreements were obtained between theory and experiment for these alloys. However, in Au-Cd and Ag-Cd alloys, the lattice invariant shear were found to be type I twinning as previously reported. Thus, we found that both Type I and Type II twinning are present as lattice invariant shears, dependent upon alloy systems. Further-more, we found that we can get a good agreement between theory and experiment, if we choose a lattice invariant shear correctly from the phenomenological crystallographic theory.