Mesoscale strain measurement in deformed crystals: A comparison of X-ray microdiffraction with electron backscatter diffraction

Mapping of residual stresses at the mesoscale is increasingly practical thanks to technological developments in electron backscatter diffraction (EBSD) and X-ray microdiffraction using high brilliance synchrotron sources. An analysis is presented of a Cu single crystal deformed in compression to about 10% macroscopic strain. Local orientation measurements were made on sectioned and polished specimens using EBSD and X-ray microdiffraction. In broad strokes, the results are similar to each other with orientations being observed that are on the order of 5° misoriented from that of the original crystallite. At the fine scale it is apparent that the X-ray technique can distinguish features in the structure that are much finer in detail than those observed using EBSD even though the spatial resolution of EBSD is superior to that of X-ray diffraction by approximately two orders of magnitude. The results are explained by the sensitivity of the EBSD technique to the specimen surface condition. Dislocation dynamics simulations show that there is a relaxation of the dislocation structure near the free surface of the specimen that extends approximately 650 Å into the specimen. The high spatial resolution of the EBSD technique is detrimental in this respect as the information volume extends only 200 Å or so into the specimen. The X-rays probe a volume on the order of 2 µm in diameter, thus measuring the structure that is relatively unaffected by the near-surface relaxation.     

Layer-stacking irregularities in C36-type Nb–Cr and Ti–Cr Laves phases and their relation with polytypic phase transformations

Specific layer-stacking irregularities have been identified in C36 (4H) Nb–Cr and Ti–Cr Laves phases on the basis of X-ray diffraction line-profile analysis and high-resolution transmission electron microscopy. Domain boundaries and transformation errors within domains could be distinguished. The layer-stacking irregularities in both C36-NbCr₂ and C36-TiCr₂ can be associated with a preceding C14 (2H) → C36 (4H) phase transformation carried out by glide of mobile synchro-Shockley partial dislocation dipoles in an ordered fashion. The stacking irregularities observed can be interpreted as deviations from such perfect “ordered glide”. The interpretation is supported by the observation that, in the case of C36-NbCo₂, where no preceding C14 → C36 transformation occurs, different layer-stacking irregularities are observed.     

Elastic and plastic deformation of NaCl and Ni3Al polycrystals during compression in a multi-anvil apparatus

Abstract

The compression behaviour in a multi-anvil apparatus of pure NaCl and of a foil of Ni₃Al embedded in a pressure medium of NaCl has been studied by energy-dispersive X-ray diffraction. At ambient temperature, the pressure and stresses, determined from line positions of NaCl, were constant throughout the sample chamber. Line positions and line widths of NaCl reflections were reversible on pressure release. A saturation of microstrains observed in NaCl at 2 GPa is thus attributed to brittle fracture setting in at uniaxial stresses of around 0.3 GPa. Ni₃Al polycrystals, in contrast, undergo extensive (ductile) plastic deformation above 4 GPa. The compression behaviour of both Ni₃Al and NaCl is identical to that previously determined in a diamond anvil cell. While a multi-anvil device thus has the advantage, compared with a diamond anvil cell, of constant pressure and stress throughout the sample chamber, microstrains in poly-crystalline samples arise in both devices. Samples in a multi-anvil apparatus thus need to be mixed with a pressure medium and to consist of essentially single crystals just as in a diamond anvil cell. Annealing experiments at high pressures confirm that the release of the uniaxial stress component in the pressure medium does not cause a release of microstrains in the embedded sample if the latter has been plastically deformed. Annealing for the purpose of attaining hydrostatic conditions in compression studies thus has to be carried out with care.     

Ultrahigh pressure equation of state of CaS to 1.5 Mbar

Abstract

Energy Dispersive X-ray Diffraction (EDXD) was performed at room temperature to gather structural data on CaS between approximately 1.7 GPa to nearly 150GPa. In these experiments, CaS retained the B1 structure up to approximately 40 GPa above which it began to transform to the B2 structure. The B2 structure remained stable to the highest pressure reached, 149 GPa, where the relative volume V/V₀ was 0.490. Previous studies on CaS extended only up to 52 GPa, which is barely 10 GPa after the B1 phase changes to the B2 structure. Thus it was not possible to accurately extrapolate the equation of state (EOS) for the B2 phase region to significantly higher pressures. In the present study EOS data for CaS was collected to 150 GPa and no other structural change was observed. EOS parameters for the B1 and B2 phase regions agree well with values reported in the literature.     

The use of electron microscopy for the study of phase transitions

Two examples of the study of phase transitions by means of electron diffraction and electron microscopy are discussed.     

Phase transitions in LiKSO4: Low-temperature neutron diffraction results

Results of a detailed crystallographic study of the structural phase transitions in LiKSO₄, carried out using single crystal neutron diffraction at ambient and below-ambient temperatures (300–100 K), are presented. The study indicates two clear phase transitions at 205 K (from space group P6₃ to space group P31c), at 189 K (to space group Cc) and a third transition at about 130 K in the cooling cycle. The corresponding temperatures are 250 K, 200 K and 138 K in the heating cycle. The existence of twins, mixed phases, and extremely sluggish kinetics for the various phase transitions, as well as the structural details of the various phases in this mixed salt, can explain the apparent inconsistencies in the results of several experimental investigations reported in the literature.     

Investigation of the phase transitions of ferroelectric KIO3 and KNbO3 crystals by optical diffraction

Optical diffraction is reviewed as a technique for investigation of the phase transitions in crystals with a multidomain structure. It has been used to study the phase transitions in KIO₃ and KNbO₃ single crystals. Strong optical diffraction bands resulted from electric domains in KNbO₃ crystals and their change with temperature were observed when a laser beam passed through the crystals. The diffraction patterns observed changed abruptly at 427°C, 223°C, and -50°C respectively, at which KNbO₃ crystals undergo structural phase transitions. It is considered that the change of the diffraction patterns with temperature is due to change of the electric domains in the crystals.     

Phase transformations and structural characteristics of AL–Cu–Co(–Si) decagonal phase

The phase transformations and structural characteristics of the Al-Cu-Co-Si alloy have been studied by neutron diffraction and high-resolution electron microscopy. The Al₆₅Cu_17.5Co_17.5 decagonal phase is stable in the temperature range between 973 K and 1350 K. At the low-temperature end, it relaxes to a microcrystalline approximant structure. At the high-temperature end, it melts directly into liquid. Two distinct orthorhombic phases are identified in the Al₆₃Cu_17.5Co_17.5Si₂ microcrystalline structure. They are composed of several structure units that can also construct the Penrose tiling. Because of lack of units, a single orthorhombic phase cannot undergo the transformation towards the high-temperature decagonal phase. An analysis of the orientation relationships between the CsCl and orthorhombic phases leads to the definition of Penrose tiling-like subnetworks inside the orthorhombic unit cells so that these orthorhombic phases can be regarded as the periodic patchworks of quasiperiodic subnetworks.     

Approximant crystals of icosahedral Mg–(Ga,Al)–Zn alloys

The zero field cooled (ZFC) and field cooled (FC) low-field magnetic moment m of a dense frozen ferrofluid containing Fe₅₅Co₄₅ particles of size 4.6nm in hexane exhibits irreversibility at temperatures T?T _b≈ 30?K. FC in μ ₀ H ≤ 1?T gives rise to shifted minor hysteresis loops below T _b. At T _c≈ 10?K, sharp peaks of m ^ZFC and of the ac susceptibility χ ′, a kink of the thermoremanent magnetic moment m ^TRM, a sizeable reduction of the coercive field H _c, and the appearance of a spontaneous moment m ^SFM indicate a phase transition with near mean-field critical behaviour of both m ^SFM and χ ′ . These features are explained within a core-shell model of nanoparticles, whose strongly disordered shells gradually become blocked below T _b, while their soft ferromagnetic cores couple dipolarly and become superferromagnetic (SFM) below T _c.