Thermal expansion anisotropy as source for microstrain broadening of polycrystalline cementite, Fe₃C

Abstract

Cementite (Fe3C) powder consisting of polycrystalline particles was investigated by synchrotron X‐ray diffraction and neutron diffraction at temperatures between 10 and 973 K. The data reveal a pronouncedly anisotropic thermal expansion of the orthorhombic unit cell as well as microstrain broadening varying considerably with temperature. Using a theory for predicting thermal‐microstress‐induced microstrain already applied in previous work to ambient‐temperature sealed‐tube X‐ray powder diffraction data from the same material [Leineweber (2012). J. Appl. Cryst.45, 944–949], the temperature‐dependent extent of the measured microstrain broadening could be quantitatively related to the measured temperature‐dependent anisotropy of the thermal expansion. Thereby, the fact that the extent of the measured microstrain broadening is somewhat smaller than the predicted amount can be explained by the presence of the free surfaces of the powder particles reducing the level of microstress‐induced microstrain.

Global optimum of microstructure parameters in the CMWP line-profile-analysis method by combining Marquardt-Levenberg and Monte-Carlo procedures

“…Krivoglaz has shown that strain broadening can only be caused by one dimensional linear defects [16] which are dislocations. (An exception to this case is when line broadening is caused by pure ECSs, as discussed in references [26] and [27].) With this:…”

“…As mentioned before, compatibility strains in polycrystalline materials can either be related to (i) strain gradients built up by GNDs [22][23][24] or to (ii) pure elastic strains below the yield point of hard precipitates or inclusions [25][26][27]. For the first case it has been shown in several works that LPA catches both GNDs and SSDs together.…”

“…For example GNDs producing long-range internal stress in dislocation cell structures [28][29][30], GND type misfit dislocations at the interface between  and ' phases in Ni-base superalloys [25], or the GNDs at the interphase between martensite laths and austenite layers are always included in the total dislocation densities together with the SSDs [31,32]. In the second case non-deformable, elastically strained hard particles or phases produce peak shifts [25][26][27]. Leineweber [26,27] has shown that anisotropic thermal expansion in polycrystalline orthorhombic cementite produces temperature dependent line broadening.…”

“…Planar defects are included by calculating the profile functions for layered structures [15,17,21]. Compatibility strains are either related to (i) strain gradients produced by geometrically necessary dislocations (GNDs) [22][23][24] or to (ii) anisotropic pure elastic strains of hard inclusions [25][26][27]. The first is captured in the strain profiles delivering the total dislocation density including the dislocation density of both GNDs and statistically stored dislocations (SSDs) [28][29][30][31][32].…”

“…The first is captured in the strain profiles delivering the total dislocation density including the dislocation density of both GNDs and statistically stored dislocations (SSDs) [28][29][30][31][32]. Line broadening due to the second is caused by peak shifts of elastically anisotropic hard inclusions or phases strained below the yield point [25][26][27]. This needs additional peak profiles.…”