Inverse Pole Figures Research Articles

Recrystallization Behavior and Texture Evolution in Low Carbon Steel during Hot Deformation in Austenite/Ferrite Region

Hot compression tests are carried out on low carbon steel with carbon content of 0.037 wt% over a temperature range of 900–700 °C. Stress–strain curves show that deformation resistance decreases from 870 to 820 °C and then increases. The temperatures of Ar3 and Ar1 are 873.8 and 796.4 °C, respectively, and the phase transformation speed reaches a maximum at 840 °C. The volume fractions of recrystallized grain, subgrain, and deformed grain are analyzed using optical microscope and electron back‐scattering diffraction. The distributions and the proportions of misorientation angles are also calculated. Textures are described using the inverse pole figure (IPF) colored orientation maps and orientation distribution functions (ODF). The results show that dynamic recrystallization (DRX) of austenite occurs to varying degrees during deformation in the austenite and double‐phase region. Dynamic recovery (DRV) of ferrite leads to the growth of ferrite grains in the double‐phase region. DRX of ferrite by the subgrain coalescence occurs at 700 °C. The main deformation textures in most of the double‐phase and single ferrite region are both cube texture. However, {112}<110> component has the highest texture intensity at 750 °C, reaching 5. The evolution mechanism of microstructure and texture is also discussed.

Mechanical behavior and microstructure evolution during deformation of AA7075-T651

In view of developing a physics-based constitutive material model for AA7075-T651, the mechanical behavior and microstructure evolution of the material has been studied through compression tests using Gleeble thermo-mechanical simulator. The tests were performed at wide range of temperatures (room temperature (RT), 100, 200, 300, 400 and 500 °C) with two constant strain rates (0.01 and 1 s-1). The true stress-strain curves depicted an increase in the flow stress with increase in the strain rate and decrease in the deformation temperature, with an exception at RT. The effects of softening mechanisms, such as adiabatic heating, dissolution of precipitates, dynamic recovery (DRV) and dynamic recrystallization (DRX), on the flow stress level, strain rate sensitivity (SRS) and temperature sensitivity over the entire range of temperatures were analyzed. Pertaining to the microstructure analysis, the intermetallic particles present in the initial as-received (AR) material were identified as (Al,Cu)6(Fe,Cu) and SiO2 with the help of back-scattered electron (BSE) imaging and energy dispersive X-ray spectroscopy (EDS). The microstructure of the material after the deformation processes were analyzed and compared with that of the AR state using inverse pole figures (IPF), grain orientation spread (GOS) and grain boundary rotation maps generated from electron back-scattered diffraction (EBSD) scans. DRV was observed for deformation at 300 °C, whereas a combination of DRV and incomplete DRX took place for 400 and 500 °C depending on the strain rate. The fraction of recrystallized grains was higher in case of deformation at higher temperature and lower strain rate. Furthermore, the difference in microstructure evolution on different surfaces of the deformed samples as well as at different locations on individual surfaces was also investigated.

Correlating Prior Austenite Grain Microstructure, Microscale Deformation and Fracture of Ultra-High Strength Martensitic Steels

Herein, we correlate the prior austenite grain (PAG) microstructure to deformation and fracture mechanisms of an ultra-high strength martensitic steel. To this end, a low-carbon martensitic steel is subjected to five heat-treatments and the PAG microstructure in the material is reconstructed from the EBSD inverse pole figure maps of the martensitic microstructure. The deformation and fracture response of all heat-treated materials are characterized by in situ tension tests of dog-bone and single-edge notch specimens that allow us to capture both the macroscopic mechanical response and the evolution of microscopic strains via microscale digital image correlation. The experimental results, together with microstructure-based finite element analysis, are then used to elucidate the effect of the PAG microstructure on the mechanical response of the material. Our results show that the interaction between the heterogeneous deformation fields induced by the notch and the bimodal PAG size distribution leads to an increase in the propensity of shear deformation and degradation in the fracture response of the material with increasing heat-treatment temperature and time. Our results also suggest that achieving a unform distribution of fine grains is an effective way to enhance both the strength and fracture properties of this class of materials.

Deformation of binary and boron-doped Ni3Al alloys at high pressures studied with synchrotron x-ray diffraction

In situ x-ray synchrotron diffraction experiments were carried out on nickel-based high-strength superalloys under pressure to understand their deformation mechanism using a diamond anvil cell (DAC). Radial x-ray diffraction determines the room-temperature equations of state and yield strengths of binary Ni3Al alloy and 500 ppm boron-doped Ni3Al to pressures of 20 and 46 GPa, respectively. Crystallographic preferred orientations observed in these superalloys due to anisotropic stress field in DAC indicate the onset of plastic deformation. Inverse pole figure analysis reveals that the underlying deformation mechanisms change from an octahedral slip to a simultaneous activation of octahedral and cube slips upon doping with boron. The yield-strength values were found to increase with pressure and are comparable to those determined from axial diffraction experiments. The results indicate that the yield strength of Ni3Al:B is about 0.5 GPa higher (at pressures below 20 GPa) due to grain boundary strengthening by boron. It is shown that due to high elastic anisotropy of Ni3Al alloy, the yield-strength estimations from diffraction experiments strongly depend on the micromechanical model used to convert the measured elastic strains into stresses.

Surface machining effect on material behavior of additive manufactured SUS 316L

Abstract Microstructural change of the additive manufactured (AMed) SUS 316 L part via surface machining and its effects on mechanical properties are analyzed. The laminated surface layer is formed with higher hardness and higher strength comparing to the inside due to the distortion of grains through repeated melting and rapid solidification. Through the microstructure analysis of inverse pole figure and grain boundary information maps on the surface before and after surface machining, we found out how the surface layer affects the material behavior. The surface machined simple-stepped-model (SSM) specimen showed an increase in deformation by about 5.6–8.9% compared to as-built one. Moreover, in the case of the additive manufactured SSM specimen with a small corner radius, the amount of deformation increased after machining. Therefore, we believe that when the design of mechanical parts that are manufactured by AM process should be considered the surface machining effect studied in this work.

Effect of Aging Temperature and Time on Secondary Phase Precipitation and Texture in an Ultrafine Grained 2205 Duplex Stainless Steel after Cold Rolling

Abstract The present work evaluates the precipitation of secondary phases in a cold-rolled ultrafine-grained 2205 duplex stainless steel after aging at temperatures ranging from 600°C to 950°C for different annealing times (300–86,400 s). X-ray diffraction, scanning electron microscopy coupled with electron backscattered diffraction, and transmission electron microscopy were used for microstructural characterization. Mechanical properties were evaluated using tensile and Vickers microhardness tests. σ- (sigma), χ- (chi), and chromium carbide (M23C6) phases were identified. σ- and austenite phase volume fractions increased with aging time, whereas χ-phase and carbides remained nearly constant, and the ferritic volume fraction decreased. Inverse pole figures of σ-phase, for a specimen aged at 850°C for 24 h, showed a localized distribution of orientations, normal to the rolling direction, being centered around the [001], whereas for the other annealing conditions, a concentration between the orientations [001] and [110] was observed. Although mechanical strength was increased, the ductility was reduced as the secondary phase precipitation proceeded.

An exploration of microstructural in-homogeneity in the 6082 Al alloy processed through room temperature multi-axial forging

In the current work, open die multi-axial forging (MAF) of 6082 Al alloy was performed at room temperature. The resulting microstructure and mechanical properties were found to have a gradient from the periphery towards the center. The resulting inhomogeneity was quantified with the help of electron backscattered diffraction, X-ray diffraction analysis, hardness and tensile strength measurement. The recrystallized grains were found after the partition of inverse pole figure (IPF) maps by using the criteria (Grain orientation spread<1°& boundary misorientation angle>15°). The sub-grains were found by partition of the IPF-maps by using the criteria (Grain orientation spread>2° & 2° < Grain rotation angle<15°). The high driving force (dislocation density) available at center of the MAF sample was responsible for the increase in sub-grains size up-to micrometer regime as well as increase in the volume fraction of recrystallized grains. The presence of a strong deformation texture (Goss ({110} 〈001〉)) and the recrystallized texture (Rotated Cube texture ({001} 〈110〉)) were observed, as we proceed towards the center of the MAF sample.

Nanoindentation and electron backscatter diffraction mapping in laser powder bed fusion of stainless steel 316L

This study on laser powder bed fusion (L-PBF) of AISI 316 L addresses the anisotropy in microstructure and micro-mechanical properties, from the observation of electron backscatter diffraction (EBSD) and nanoindentation maps in parts made with different volumetric energy densities (VED) and in grains at different crystallographic orientations. Similar experimentation was done with conventionally made AISI 316 L, with the aim of comparing anisotropy and micro-mechanical response. It was observed that the variations of VED, calculated from different process parameters combinations, have an influence on crystallographic oriented grain growth evolution affecting the nanoindentation performance. This progression was responsible of the variation in grain size and average misorientation angles and played important role in determining the micro-mechanical behavior. The highest nanoindentation response was obtained at a VED = 56.67 J/mm3, with an average indentation modulus of 196.77 GPa and hardness of 3.68 GPa. From Texture Pole Figures (PFs) and Inverse Pole Figures (IPFs) of EBSD maps, it was revealed that the highest texture strength of 〈101〉 oriented grains along with the evolution and domain of 〈111〉 oriented grains enhanced the micro-mechanical properties at that VED value. The other causes of this behavior are the relatively lower grain size (11.62 μm) and a higher average misorientation angle (11.74°), when comparing it with rest of the L-PBF AISI 316 L parts. The additional but undesirable strong 〈001〉 texture somehow contributed to the slight mitigation on the micro-mechanical properties in conventional AISI 316 L stainless steels and these parts were found to be comparatively less anisotropic than the parts obtained from L-PBF process.

Microstructure and mechanical properties of the AA7075 tube fabricated using shear assisted processing and extrusion (ShAPE)

Shear-assisted processing and extrusion (ShAPE) experimental setup and tooling were adopted for extruding thin-walled AA7075 aluminum tube from as-cast non-homogenized billet material in a single run. The mechanical and microstructural characterizations were performed on the as-extruded tube through tensile, hardness, electron backscatter diffraction (EBSD), and energy dispersive spectroscopy (EDS) tests. The results showed that the ShAPE process developed a significantly refined microstructure with uniform and almost equiaxed grain structure on both hoop and axial cross-sections of the extrudate as well as through the thickness of the material. The pole figures and inverse pole figures of the EBSD data showed a strong shear texture development, and it was found out that axial shear is the dominant deformation mechanism in the regions near the inner surface of the tube, while combined axial and torsional shears are the two dominant modes of deformation near the outer surface of the extrudate. As for the mechanical properties, there was an increase of 150 and 73% in the yield and ultimate strengths of the tube produced using ShAPE process, respectively, and an 18% decrease in maximum uniform plastic elongation compared to the conventionally extruded AA7075-O tube.

Texture evolution in nanocrystalline Ta under shock compression

We present systematic investigation on texture evolution in nanocrystalline Ta under planar shock wave loading at different impact velocities. Seven representative initial textures and two loading directions are studied via large-scale molecular dynamics simulations. Orientation mapping and texture analysis, including orientation distribution functions, pole figures, and inverse pole figures, are performed. Shock compression induces a ⟨221⟩ texture in nanocrystalline Ta initially with no texture, ⟨100⟩ fiber texture, {100}⟨100⟩ texture, and θ+γ rolling texture via twinning, which can be traced back to grains initially with ⟨100⟩. A ⟨100⟩ texture is induced via twinning for nanocrystalline Ta initially with no texture, ⟨110⟩ fiber texture, and α+γ rolling texture and can be traced back to ⟨110⟩. Dislocation slip and grain boundary sliding lead to the movement of ⟨110⟩ toward ⟨111⟩, and the strengthening of ⟨100⟩ and ⟨111⟩ orientation densities. The generation of new textures is observed for most cases. However, no new texture is found in the ⟨111⟩ fiber texture case for shock loading parallel to the fiber, and a much slower elastic–plastic transition occurs due to the lack of deformation twinning.

Grain-size gradient structure by abnormal grain growth

We report a novel method to synthesize bulk grain-size gradient polycrystalline Ni by AGG. By periodical sintering in the large volume press (LVP), AGG repeatedly occurs, resulting in exceptionally large grains on the sample surface, but the inner grains are still small. The formation of grain-size gradient profile is attributed to the uneven plastic deformation caused by compression in the LVP. Besides, the gradient structure can be achievable with uniformity by employing tungsten with a high shear modulus into the sample assembly. This work would guide us to design bulk heterogeneous gradient nanostructured materials with both excellent strength and ductility. The uniform grained gradient structure obtained with the improved LVP assembly. (a) The improved LVP assembly with W tablet used between Ni sample and outer Mo-capsule; (b) Inverse pole figure mapping characterization of uniform grain-size gradient structure comprised of smaller grains.

Elastic Properties of Alloy ZE10 Sheets Evaluation by Kerns Texture Parameters

The ZE10 magnesium alloy with the rare-earth metal additives, which contribute to a better forming of the alloy, was used as studied material. The ZE10 magnesium alloy with the rare-earth metal additives, which contribute to a better forming of the alloy, was used as studied material. Sheet material is usually straightened on roller levelers to relieve residual stresses and improve flatness. The metal is subjected to alternating deformation by bending when straightening. The changes in the structure, crystallographic texture and, as a result, physical and mechanical properties occur in the metal are often not taken into account in the future. The elastic modulus is an important parameter, for example, in the production of products using bending. In this work, the elastic modulus of sheets of magnesium alloy ZE10 was estimated in three main directions. A starting sheet was obtained by extruding an ingot, then rolling in the longitudinal direction and then rolling with a change in direction by 90° after each pass in combination with heating to 350°C. The original sheets were subsequently subjected to alternate folding. Evaluations were made of the elastic modulus of the original sheet, as well as the sheets after 0.5, 1.0, 3.0 and 5.0 alternating bending cycles. To estimate the elastic modulus, we used the Kearns texture parameters , which we calculated from the inverse pole figures, as well as the elastic constants of the single crystal of the ZE10 alloy found by us. The maximum deviation of the calculated and experimental values of the elastic modulus did not exceed 5.2%. Strong correlations and quadratic regression equations have been established between the values of the elastic modulus, mechanical characteristics (tensile strength, yield stress, elongation), on the one hand, and the above-mentioned parameters of the Kerns texture, on the other hand. The approximation reliability coefficients are 0.76 - 0.99.

Surface Purity Effect on Irregularities of Changes in Deformation Texture of Zr-2.5% Nb Alloy

This work is a continuation of a series of works on the study of regularities and structural mechanisms of changes in characteristics of crystallographic texture during cold deformation of plates made of Zr2.5%Nb alloy. Effects of influence of surface cleanliness of the plates on the textural regularities during their rolling were investigated. For this, longitudinal fragments of the tube Æ15.0´1.5 mm² were used, flattened, annealed at 580°C in a vacuum of 1.5...3.0 Pa and rolled along the axis of the original tube with various degrees deformation up to 56%, which is likened to longitudinal rolling of plates. Techniques of maximally uniform straightening of tube fragments were used. An analysis of the results of studies of textural changes during cross rolling of plates, straightened from rings of the same tube and pretreated under similar conditions, is also carried out. To analyze the results, the method of inverse pole figures was used, which, in these studies, is distinguished by the possibility of achieving satisfactory accuracy in calculating the integral characteristics of texture. On this basis, the Kearns textural coefficient was calculated along the normal to the plates’ plane. Corrections were introduced for texture dissimilarity along the thickness of the plates, which is caused by the unbending of the preliminary blanks. Additionally, the analysis of texture distributions was carried out using original techniques. According to the results obtained – as a result of X-ray measuring from the plates’ surface – oscillations of the course of changes in the texture coefficient were revealed. This is associated with an alternating process of relaxation of residual stresses during deformation. It has been established that this effect is initiated from the near-surface regions, is associated with a near-surface impurity, and in some cases can penetrate to a considerable depth of the plates. The twinning nature of such regularities is confirmed and active systems of twins are noted.

Effect of β Phase Decomposition on Recrystallization in α-Zr Region in Zr-2.5%Nb Pressure Tube Material

The effects of β phase decomposition on recrystallization and texture variation in Zr-2.5% Nb alloy pressure tube material were investigated. Isothermal annealing was conducted at 350 to 550 &lt;sup&gt;o&lt;/sup&gt;C for 240 hours, and isothermal annealing was performed at 500 &lt;sup&gt;o&lt;/sup&gt;C for 240 to 3,000 hours. The recrystallization and texture variation were analyzed by inverse pole figure variation using the XRD and EBSD methods. Annealing in α-Zr region at below 610 &lt;sup&gt;o&lt;/sup&gt;C induced recrystallization and texture variation in the α-Zr. These results differ from those from a previous annealing study of the α+β region at 750-830 &lt;sup&gt;o&lt;/sup&gt;C. Annealing above 400 &lt;sup&gt;o&lt;/sup&gt;C for 240 hours caused β-Zr decomposition into β-Nb. The decomposition of the β-phase by annealing above 475 &lt;sup&gt;o&lt;/sup&gt;C caused a contraction of 7.5% in the d(110) spacing in the β-phase, and a reduction in the volume fraction of the β phase by about 80%. It seems that the stress internally formed by the lattice contraction of the β-phase provides the driving force for recrystallization. In addition, it suggests that the newly formed α-Zr produced by β phase decomposition provides new nucleation sites for recrystallization and causes texture variation in the α-Zr. The reason why the recrystallization and the texture variation occurs only in the α-Zr stable region at below 610 &lt;sup&gt;o&lt;/sup&gt;C is discussed.

Influence of Texture on Deformation Mechanism of Hot Extruded Oxide Dispersion Strengthened 18Cr Ferritic Steel

This paper focuses on studying the influence of texture on the deformation mechanism of oxide dispersion strengthened (ODS) 18Cr ferritic steel subjected to high-temperature tensile testing after consolidation by hot extrusion. The initial microstructure of the hot extruded steel showed preferential (1 1 0) planes alignment in perpendicular and parallel direction to extruded (ED) and transverse (TD), respectively. Two types of anisotropy have been highlighted: (1) A strong anisotropy of elongation properties with a transverse ductility is lower as compared to the axial ductility; (2) yield stress anisotropy (mechanical strength anisotropy) which is found to be temperature dependent. The material flow in 〈1 1 1〉 direction is observed during the application of load along extruded direction during the tensile test; however, (1 1 0) slip plane normal is parallel to the direction of loading for transverse direction and brings the Schmid factor to a lower level which makes slip activation unlikely. Deformation band is found to be aligned with the loading direction in the ED specimen and covering across a number of neighboring ferrite grains could be noticed irrespective of material flow. However, the areas near the grain boundaries in the microstructure are found to be the strain gradient regions. Further, it shows a preferential accommodation of strain in proximity to the boundary network for TD specimen. High temperature (973 K) tensile test in ED is found to promote grain-subdivision of elongated bands by dynamic recrystallization, and inverse pole figure distribution reveals a preferential increase in the intensity of clustering toward (1 1 1) plane parallel to the loading direction.

Study on the microstructural and texture evolution of Hot Rolled Al7075/ graphene/ carbon nanotubes reinforced composites

Hot rolling (95% reduction in thickness) was applied on the Stir Cast and Hot Rolled Al7075 matrix composites reinforced with graphene nanoplates (GNPs) and carbon nanotubes (CNTs). The effects of reinforcements on the microstructural and texture evolution of hot rolled composites were studied. Scanning electron microscope (SEM) revealed that reinforcements were elongated parallel to the rolling direction. Energy dispersive X-ray spectroscopy (EDS) from the black elongated phases shows a high fraction of carbon and it confirms that they are clusters of GNPs and CNTs (depends on the sample) and second phase precipitates are AlXFe (X: 3, 6). Electron backscatter diffraction (EBSD) was employed for microstructure characterization and texture evolution of composites. According to inverse pole figure (IPF) maps, in all composites the majority of grains were elongated parallel to roll direction. According to grain orientation spread (GOS<2°) maps, addition of GNPs and % CNTs lead to stimulate the occurrence of recrystallization in the matrix. The grain orientation spread (GOS<2°) maps near the clusters of reinforcements revealed that particle stimulate nucleation (PSN) occurred in the interface of matrix/reinforcements. By presence of GNPs and CNTs in the Al7075 matrix a different texture evolution during hot rolling of prepared composites were observed.

Effect of strain rate on tensile mechanical properties of high-purity niobium single crystals for SRF applications

An investigation of the mechanical properties of high-purity niobium single crystals is presented. Specimens were cut with different crystallographic orientations from a large grain niobium disk and uniaxial tensile tests were conducted at strain rates between 10-4 and 103 s-1. The logarithmic strain rate sensitivity for crystals oriented close to the center of a tensile axis inverse pole figure (IPF) is ~0.14 for all strain rates. The strain at failure (ranging from 0.4 to 0.9) is very sensitive to crystal orientation and maximal at ~10-2 s-1 for crystals oriented close to the center of an IPF. The high anisotropy observed at quasi-static strain rates decreased with increasing strain rate. The activation of multiple slip systems in the dynamic tests could account for this reduction in anisotropy. A transition from strain hardening to softening in the plastic domain was observed at strain rates greater than approximately 6 × 10-2 s-1 for crystals oriented close to the center of a tensile axis IPF. Shear bands were observed in specimens with orientations having similarly high Schmid factors on both {110}and {112}slip families, and they are correlated with reduced ductility. Crystal rotations at fracture are compared for the different orientations using scanning electron microscopy images and EBSD orientation maps. A rotation toward the terminal stable [101] orientation was measured for the majority of specimens (with tensile axes more than ~17° from the [001] direction) at strain rates between 1.28 × 10-2 and 1000 s-1.

Texture mapping in electron beam welded dissimilar copper-stainless steel joints by neutron diffraction

In this study, the crystallographic texture variation of electron beam welded dissimilar copper to 304L stainless-steel joints was investigated using Time-of-flight neutron diffraction measurements. The effect of beam oscillation by changing its oscillation diameter on texture orientation variation was evaluated. Neutron diffraction measurements were performed using General Materials Diffractometer beamline at Rutherford Appleton Laboratory neutron radiation source. Phase fractions and variations of crystallographic texture in terms of pole figures and inverse pole figures were obtained. The stronger texture we found in all regions of the joints i.e. heat-affected zone and fusion zone for oscillating beam compared to its non-oscillating counterparts. Also, by increasing the oscillation diameter, from its optimum value, a weaker texture was found, which had a detrimental effect on mechanical properties. Electron-backscatter diffraction texture measurements were also performed to compare and complement the results obtained from neutron texture.

Effect of initial microstructure on the deformation heterogeneities of 316L stainless steels fabricated by selective laser melting processing

The selective laser melting (SLM) is a popular additive manufacturing (AM) technique used for the fabrication of metal parts. In the present study, two 316L stainless steel specimens (SLM-I and SLM-II) with different microstructures were fabricated with different levels of energy density by changing the laser power and scanning speed, which are the main SLM process conditions. The deformation and fracture behavior of miniature SLM specimens under uniaxial tension were experimentally measured via optical microscopy (OM), field emission scanning microscopy (FE-SEM), and an electron back-scattered diffraction (EBSD) technique. In order to analyze the deformation heterogeneities under uniaxial tension, the inverse pole figure (IPF) map, kernel average misorientation (KAM) map, Taylor factor (TF) map, grain boundaries (GBs), Σ3 twin boundaries (TBs), and melt pool boundaries (MPBs) developed in deformed SLM specimens were analyzed at different strain levels. The effect of microstructural factors on the deformation heterogeneities of SLM specimens was explained by the evolution of KAM, GBs, MPBs, and Σ3 TBs. The initial microstructures of the SLM specimens significantly influenced the generation and propagation of cracks under uniaxial tension.

Defining the hematite topotaxial crystal growth in magnetite–hematite phase transformation

Magnetite and hematite iron oxides are minerals of great economic and scientific importance. The oxidation of magnetite to hematite is characterized as a topotaxial reaction in which the crystallographic orientations of the hematite crystals are determined by the orientation of the magnetite crystals. Thus, the transformation between these minerals is described by specific orientation relationships, called topotaxial relationships. This study presents electron-backscatter diffraction analyses conducted on natural octahedral crystals of magnetite partially transformed into hematite. Inverse pole figure maps and pole figures were used to establish the topotaxial relationships between these phases. Transformation matrices were also applied to Euler angles to assess the diffraction patterns obtained and confirm the identified relationships. A new orientation condition resulting from the magnetite–hematite transformation was characterized, defined by the parallelism between the octahedral planes {111} of magnetite and rhombohedral planes \{10\bar {1}1\} of hematite. Moreover, there was a coincidence between one of the octahedral planes of magnetite and the basal {0001} plane of hematite, and between dodecahedral planes {110} of magnetite and prismatic planes \{11\bar {2}0\} of hematite. All these three orientation conditions are necessary and define a growth model for hematite crystals from a magnetite crystal. A new topotaxial relationship is also proposed: (111)Mag || (0001)Hem and (\bar {1}\bar {1}1)_{\rm Mag} || (10\bar {1}1)_{\rm Hem}.