The superplastic behavior has been found in Fe 3Al and FeAl alloys with grain sizes of 100～600 μm. The large grained Fe 3Al and FeAl alloys exhibit all deformation characteristics of conventional fine grain size sup...The superplastic behavior has been found in Fe 3Al and FeAl alloys with grain sizes of 100～600 μm. The large grained Fe 3Al and FeAl alloys exhibit all deformation characteristics of conventional fine grain size superplastic alloys. However, superplastic behavior was found in large grained iron aluminides without the usual prerequisites for the superplasticity of a fine grain size and grain boundary sliding. The metallographic examinations have shown that average grain size of large grained iron aluminides decreased during superplastic deformation. Transmission electron microscopy (TEM) observations have shown that there were a great number of subgrain boundaries which formed a network and among which the proportion of low and high angle boundaries increased with the increase of strain. The observed superplastic phenomenon is explained by continuous recovery and recrystallization. During superplastic deformation, an unstable subgrain network forms and these subboundaries absorb gliding dislocations and transform into low and high angle grain boundaries. A dislocation gliding and climb process accommodated by subboundary sliding, migration and rotation, allows the superplastic flow to proceed.展开更多
This work addresses the alloying of titanium aluminides used in aircraft engine applications and automobiles. The oxidation resistance behavior of two titanium aluminides of α2 ＋ γ （Ti3Al ＋ TiAl） and orthorhombi...This work addresses the alloying of titanium aluminides used in aircraft engine applications and automobiles. The oxidation resistance behavior of two titanium aluminides of α2 ＋ γ （Ti3Al ＋ TiAl） and orthorhombic Ti2NbAl, recognized as candidates for high-temperature applications, was investigated by exposure of the alloys for 100 h in air. Thus, oxidation resistance was expressed as the mass gain rate, whereas surface aspects were analyzed using scanning electron microscopy in conjunction with energy-dispersive X-ray spectroscopy, and the type of oxidation products was analyzed by X-ray diffraction and Raman spectroscopy. The orthorhombic Ti2NbAl alloy was embrittled, and pores and microcracks were formed as a result of oxygen diffusion through the external oxide layer formed during thermal oxidation for 100 h.展开更多
The effects of microstructure on the deformation and fracture behaviour of two-phase TiAl alloys were investjgated under monotonic and cyclical loading conditions, over a range of temperatu res.The tensile behaviour i...The effects of microstructure on the deformation and fracture behaviour of two-phase TiAl alloys were investjgated under monotonic and cyclical loading conditions, over a range of temperatu res.The tensile behaviour is analyzed for deformation temperatures between RT and 950℃, Fracture resistance behaviour and toughening mechanisms at RT and 800℃ are analyzed. and the inverse relationship botween ductility and toughness is explained using the crack initiation toughness. The preliminary results of load-controlled fatigue behaviour at 800℃ are interpreted using the tensile behaviour because deformation structure and fracture modes are similar under these two loading conditions展开更多
This paper reviews recent research on embrittlement of iron aluminides brought about by exposure to moisture or hydrogen. The tensile and fatigue crack growth behavior of several Fe-Al alloys, ranging in aluminum cont...This paper reviews recent research on embrittlement of iron aluminides brought about by exposure to moisture or hydrogen. The tensile and fatigue crack growth behavior of several Fe-Al alloys, ranging in aluminum content from 16 to 35a%, is described. It will be shown that tensile ductility and fatigue crack growth behavior are dependent on type and degree of long range order, grain structure, temperature and environment. Environments studied include vacuum,oxygen, hydrogen gas, electrolytically charged hydrogen and moist air. All cases of embrittlement are ultimately traceable to the interaction of hydrogen with the lattice.展开更多
This paper describes a new process for producing titanium aluminides, in particular TiAl, from TiO2 raw material. On the basis of obtained results, the non-completed reaction of TiO2 with Al and Ca in a special reacti...This paper describes a new process for producing titanium aluminides, in particular TiAl, from TiO2 raw material. On the basis of obtained results, the non-completed reaction of TiO2 with Al and Ca in a special reaction vessel results in the production of granulates of titanium aluminides especially Ti3Al and other Ti- Al phases as the metallic product and Ca12Al14O33 as the non-metallic product. By adding KClO4 in the mixture, a nearly completed reaction can be carried out. The products of this reaction are titanium aluminide particularly TiAl as the metallic part and CaAl4O7 （grossite） as the non-metallic slag part. Both product and slag are produced in a separated form. This process, called KRH-method is described in this article. The scanning electron microscopic microstructure of metallic part of the product shows different phases： the matrix phase is TiAI, where the needle form precipitation is TiAl2 and the plate form precipitation includes TiAI and Ti3Al phases. The microstructure of the remelted metallic part indicates dendritic phase with a lamellar structure comprising of TiAl and Ti3Al phases. The interdendritic phase of TiAI is also seen.展开更多
The iron aluminides show anomalous stress peaks at temperatures of the order of 400～600 ℃, irrespective of whether the crystal structure is B2 type or DO 3 type. Such features will be examined on the basis of therma...The iron aluminides show anomalous stress peaks at temperatures of the order of 400～600 ℃, irrespective of whether the crystal structure is B2 type or DO 3 type. Such features will be examined on the basis of thermally activated dislocation processes, considering the influence of test parameters such as temperature and strain rate, and material parameters such as crystal composition and orientation. Detailed analyses of deformation modes by slip step studies, transmission electron microscopy examinations of dislocation structures, and texture studies will also be considered. Observations of dislocation structures are clearly of great interest for suggesting the possible models of deformation, but suffer from two major weaknesses: the post mortem structures in samples deformed at high temperature may not be the same as those producing plasticity; almost all possible hypotheses for strengthening can find support from such observations, since almost all imaginable dislocation configurations can be found with sufficient diligence by the researcher. Strengthening at intermediate temperatures in DO 3 and B2 ordered iron aluminides will be analysed here, making combined use of observations of deformation structures and examinations of the influence of varying the deformation parameters.展开更多
Nanocrystal ODS （oxide dispersion strengthening） aluminide coatings were produced on a stainless steel and nickel-based superalloy by the pock aluminizing process assisted by ball peening, Pure Al powders and 1% of ...Nanocrystal ODS （oxide dispersion strengthening） aluminide coatings were produced on a stainless steel and nickel-based superalloy by the pock aluminizing process assisted by ball peening, Pure Al powders and 1% of ultra-fine Y2O3 powders were mixed by ball milling. The ultra-fine Y2O3 powders were dispersed in Al particles. Ball peening welded the Al particles onto the substrate and accelerated the formation of aluminide coating. Nanocrystal ODS aluminide coatings were produced by the outward growth at a much low temperature （below 600℃） in a short treatment time. The effects of the operation temperature and treatment time on the formation of the coatings were analyzed. SEM （scanning electron microscope）, AFM （atomic force microscope）, EDS （energy dispersive X-ray spectroscopy）, XRF （X-ray fluorescence spectrometer） and XRD （X-ray diffraction） methods were applied to investigate the microstructure of the coatings. High-temperature oxidation tests were carried out to evaluate the oxidation resistance of the ODS aluminide coatings.展开更多
A numerical method has been developed to extract the composition-dependent interdiffusivity from the concentration profiles in the aluminide coating prepared by pack cementation. The procedure is based on the classic ...A numerical method has been developed to extract the composition-dependent interdiffusivity from the concentration profiles in the aluminide coating prepared by pack cementation. The procedure is based on the classic finite difference method (FDM). In order to simplify the model, effect of some alloying elements on interdiffusivity can be negligible. Calculated results indicate the interdiffusivity in aluminide coating strongly depends on the composition and give the formulas used to calculate interdiffusivity at 850, 950 and 1050癈. The effect on interdiffusivity is briefly discussed.展开更多
Interdiffusion coefficients at 950℃ and 1050℃ are calculated by Wagner analysis method as a function of composition of β-NiAI phase. The β-NiAI phase is formed by pack cementation on surface of superalloy. Results...Interdiffusion coefficients at 950℃ and 1050℃ are calculated by Wagner analysis method as a function of composition of β-NiAI phase. The β-NiAI phase is formed by pack cementation on surface of superalloy. Results of the calculation show that interdiffusion coefficients in β-NiAI phase strongly depend on the compositions and vary over several orders of magnitude. Compared with the interdiffusion coefficients in the stoichiometric β-NiAI phase, the interdiffusion coefficients in β-NiAI phase formed on superalloy is obviously small, probably due to the composition, complicated microstructure and precipitates. However, it could be seen clearly that the shapes of the diffusivity curves are very similar to each other. The similarity of the diffusion curves and the difference between interdiffusion coefficients imply that the compositions, microstructures and precipitates of superalloy have a distinctly adverse effect on the interdiffusion of Ni and Al atoms during aluminization, but do not change the essential characteristics of β-NiAI phase.展开更多
Two low alloy steels 0.5Cr-0.5Mo-0.25V and H85 were pack-aluminized at 900°for 4 h by using Fe-Al powder mixture containing 48% Fe, 20.6% Al- 29.4% Al2O3 and 2% NH4Cl by weight. The microhardness and oxidation re...Two low alloy steels 0.5Cr-0.5Mo-0.25V and H85 were pack-aluminized at 900°for 4 h by using Fe-Al powder mixture containing 48% Fe, 20.6% Al- 29.4% Al2O3 and 2% NH4Cl by weight. The microhardness and oxidation resistance at 900℃ of the aluminide coatings were studied. It was found that pack-aluminizing improves the microhardness of the 0.5Cro.5Mo-0.25V steel while it reduces the microhardness of the H85 steel. Pack aluminizing highly improves the oxidation resistance after 20h exposure at 900℃ in air for the investigated steels.展开更多
Gam matitanium aluminide ( γ TiAl) alloys are emerging as a revolutionary engineeringmaterialsfor hightemperaturestructuralapplications. Onthebasisoftheinformation avail ablein the public domain, this paper discuss...Gam matitanium aluminide ( γ TiAl) alloys are emerging as a revolutionary engineeringmaterialsfor hightemperaturestructuralapplications. Onthebasisoftheinformation avail ablein the public domain, this paper discussesthe historical background,status and future prospect of gam maalloytechnologyintheareasofalloy development/ design,processdevelop ment, and applications.展开更多
The Editor-in-Chief has retracted this article [1] because Figures 11 and 12 appear to be identical with Figures 3 and 4respectively from a previously published article [2].Sehrish MUKHTAR,Waqas ASGHAR,Zubair BUTT,Zah...The Editor-in-Chief has retracted this article [1] because Figures 11 and 12 appear to be identical with Figures 3 and 4respectively from a previously published article [2].Sehrish MUKHTAR,Waqas ASGHAR,Zubair BUTT,Zaheer ABBAS,Mudaser ULLAH and Rana ATTA-UR-REHMAN did not respond to correspondence about this retraction.展开更多
A method was presented to prepare aluminide coatings on metals by combining the pack aluminizing with the ball impact process. This technique applied mechanical vibration to a retort, which was loaded with pack-alumin...A method was presented to prepare aluminide coatings on metals by combining the pack aluminizing with the ball impact process. This technique applied mechanical vibration to a retort, which was loaded with pack-aluminizing powder, specimens and alloy balls. Pack aluminizing was carried out with repeated ball impact, which accelerated chemical reactions and atomic diffusion. Aluminide coatings were formed at a relatively lower temperature (below 600 ℃) and in a shorter treatment time, compared with the conventional pack aluminizing. The effects of the operation temperature and the treatment time on the formation of the coatings were analysed. The SEM, EDS and XRD analysis results show that the aluminide coatings appear to be homogeneous, with a high density and free of porosity, and have excellent adherence to the substrate. The coatings mainly consist of Al-rich phases such as η-Fe2Al5, θ-FeAl3 and ?CrAl5. Oxidation resistance was studied by high-temperature tests. The formation mechanism of the Al-coatings was also investigated. This technique provides a new approach for industrial diffusion coatings with great energy and time savings.展开更多
An experimental study has been carried out to investigate the effect of microstructure on sliding wear behavior of Fe-Al coatings and Fe-Al/WC composite coatings produced by high velocity arc spraying (HVAS) and cored...An experimental study has been carried out to investigate the effect of microstructure on sliding wear behavior of Fe-Al coatings and Fe-Al/WC composite coatings produced by high velocity arc spraying (HVAS) and cored wires. After heat treatment at 300°C, 450°C, 550°C, 650°C and 800°C, the microstructure of the coatings will be changed. The changes of microstructure have obvious effects on the microhardness of the coatings, which may be the most important factor influencing the coatings sliding wear behavior. After heat treated at 450°C-650°C, increasing of the amounts of iron aluminides (including Fe3Al and FeAl ) and dispersion strengthening of Fe2\V2C and Fe6W6C will lead to a rise of microhardness of the coatings. Increasing the microhardness through heat treatment would improve the sliding wear resistance of the iron aluminide based coatings coatings.展开更多
The halide activated pack cementation method is utilized to deposit aluminide and chromium modified aluminide coatings on TiAl alloys. Emphasis is placed on the effect of alloying elements on the aluminizing kinetic...The halide activated pack cementation method is utilized to deposit aluminide and chromium modified aluminide coatings on TiAl alloys. Emphasis is placed on the effect of alloying elements on the aluminizing kinetics as well as on the study of formation of chromium modified aluminide coating. The addition of a small amount of Nb and Cr in the TiAl improves significantly the aluminizing kinetics of TiAl alloys by increasing the reaction rate of active Al atoms with substrate through grain refinement as well as by increasing the solid state diffusion of Al through the formation of stable TiAl 3 layer. Cr and Al are simultaneously co deposited by diffusion into K 5 alloy, by a single step, pack cementation process. The morphologies of the coating formed on K 5 substrate, i.e., an external layer with L1 2 structure and an underlying interdiffusion zone, are presented. The mechanism for the formation of Cr modified aluminide coating is discussed.展开更多
文摘The superplastic behavior has been found in Fe 3Al and FeAl alloys with grain sizes of 100～600 μm. The large grained Fe 3Al and FeAl alloys exhibit all deformation characteristics of conventional fine grain size superplastic alloys. However, superplastic behavior was found in large grained iron aluminides without the usual prerequisites for the superplasticity of a fine grain size and grain boundary sliding. The metallographic examinations have shown that average grain size of large grained iron aluminides decreased during superplastic deformation. Transmission electron microscopy (TEM) observations have shown that there were a great number of subgrain boundaries which formed a network and among which the proportion of low and high angle boundaries increased with the increase of strain. The observed superplastic phenomenon is explained by continuous recovery and recrystallization. During superplastic deformation, an unstable subgrain network forms and these subboundaries absorb gliding dislocations and transform into low and high angle grain boundaries. A dislocation gliding and climb process accommodated by subboundary sliding, migration and rotation, allows the superplastic flow to proceed.
基金funded by National Project PCCA contract No.65/2012POS-CCE O 2.2.1 project INFRANANOCHEM-No 19/January 3,2009 of the EU(ERDF)and Romanian Government
文摘This work addresses the alloying of titanium aluminides used in aircraft engine applications and automobiles. The oxidation resistance behavior of two titanium aluminides of α2 ＋ γ （Ti3Al ＋ TiAl） and orthorhombic Ti2NbAl, recognized as candidates for high-temperature applications, was investigated by exposure of the alloys for 100 h in air. Thus, oxidation resistance was expressed as the mass gain rate, whereas surface aspects were analyzed using scanning electron microscopy in conjunction with energy-dispersive X-ray spectroscopy, and the type of oxidation products was analyzed by X-ray diffraction and Raman spectroscopy. The orthorhombic Ti2NbAl alloy was embrittled, and pores and microcracks were formed as a result of oxygen diffusion through the external oxide layer formed during thermal oxidation for 100 h.
文摘The effects of microstructure on the deformation and fracture behaviour of two-phase TiAl alloys were investjgated under monotonic and cyclical loading conditions, over a range of temperatu res.The tensile behaviour is analyzed for deformation temperatures between RT and 950℃, Fracture resistance behaviour and toughening mechanisms at RT and 800℃ are analyzed. and the inverse relationship botween ductility and toughness is explained using the crack initiation toughness. The preliminary results of load-controlled fatigue behaviour at 800℃ are interpreted using the tensile behaviour because deformation structure and fracture modes are similar under these two loading conditions
文摘This paper reviews recent research on embrittlement of iron aluminides brought about by exposure to moisture or hydrogen. The tensile and fatigue crack growth behavior of several Fe-Al alloys, ranging in aluminum content from 16 to 35a%, is described. It will be shown that tensile ductility and fatigue crack growth behavior are dependent on type and degree of long range order, grain structure, temperature and environment. Environments studied include vacuum,oxygen, hydrogen gas, electrolytically charged hydrogen and moist air. All cases of embrittlement are ultimately traceable to the interaction of hydrogen with the lattice.
文摘This paper describes a new process for producing titanium aluminides, in particular TiAl, from TiO2 raw material. On the basis of obtained results, the non-completed reaction of TiO2 with Al and Ca in a special reaction vessel results in the production of granulates of titanium aluminides especially Ti3Al and other Ti- Al phases as the metallic product and Ca12Al14O33 as the non-metallic product. By adding KClO4 in the mixture, a nearly completed reaction can be carried out. The products of this reaction are titanium aluminide particularly TiAl as the metallic part and CaAl4O7 （grossite） as the non-metallic slag part. Both product and slag are produced in a separated form. This process, called KRH-method is described in this article. The scanning electron microscopic microstructure of metallic part of the product shows different phases： the matrix phase is TiAI, where the needle form precipitation is TiAl2 and the plate form precipitation includes TiAI and Ti3Al phases. The microstructure of the remelted metallic part indicates dendritic phase with a lamellar structure comprising of TiAl and Ti3Al phases. The interdendritic phase of TiAI is also seen.
文摘The iron aluminides show anomalous stress peaks at temperatures of the order of 400～600 ℃, irrespective of whether the crystal structure is B2 type or DO 3 type. Such features will be examined on the basis of thermally activated dislocation processes, considering the influence of test parameters such as temperature and strain rate, and material parameters such as crystal composition and orientation. Detailed analyses of deformation modes by slip step studies, transmission electron microscopy examinations of dislocation structures, and texture studies will also be considered. Observations of dislocation structures are clearly of great interest for suggesting the possible models of deformation, but suffer from two major weaknesses: the post mortem structures in samples deformed at high temperature may not be the same as those producing plasticity; almost all possible hypotheses for strengthening can find support from such observations, since almost all imaginable dislocation configurations can be found with sufficient diligence by the researcher. Strengthening at intermediate temperatures in DO 3 and B2 ordered iron aluminides will be analysed here, making combined use of observations of deformation structures and examinations of the influence of varying the deformation parameters.
基金the National Natural Science Foundation of China （No. 50271010）.
文摘Nanocrystal ODS （oxide dispersion strengthening） aluminide coatings were produced on a stainless steel and nickel-based superalloy by the pock aluminizing process assisted by ball peening, Pure Al powders and 1% of ultra-fine Y2O3 powders were mixed by ball milling. The ultra-fine Y2O3 powders were dispersed in Al particles. Ball peening welded the Al particles onto the substrate and accelerated the formation of aluminide coating. Nanocrystal ODS aluminide coatings were produced by the outward growth at a much low temperature （below 600℃） in a short treatment time. The effects of the operation temperature and treatment time on the formation of the coatings were analyzed. SEM （scanning electron microscope）, AFM （atomic force microscope）, EDS （energy dispersive X-ray spectroscopy）, XRF （X-ray fluorescence spectrometer） and XRD （X-ray diffraction） methods were applied to investigate the microstructure of the coatings. High-temperature oxidation tests were carried out to evaluate the oxidation resistance of the ODS aluminide coatings.
文摘A numerical method has been developed to extract the composition-dependent interdiffusivity from the concentration profiles in the aluminide coating prepared by pack cementation. The procedure is based on the classic finite difference method (FDM). In order to simplify the model, effect of some alloying elements on interdiffusivity can be negligible. Calculated results indicate the interdiffusivity in aluminide coating strongly depends on the composition and give the formulas used to calculate interdiffusivity at 850, 950 and 1050癈. The effect on interdiffusivity is briefly discussed.
文摘Interdiffusion coefficients at 950℃ and 1050℃ are calculated by Wagner analysis method as a function of composition of β-NiAI phase. The β-NiAI phase is formed by pack cementation on surface of superalloy. Results of the calculation show that interdiffusion coefficients in β-NiAI phase strongly depend on the compositions and vary over several orders of magnitude. Compared with the interdiffusion coefficients in the stoichiometric β-NiAI phase, the interdiffusion coefficients in β-NiAI phase formed on superalloy is obviously small, probably due to the composition, complicated microstructure and precipitates. However, it could be seen clearly that the shapes of the diffusivity curves are very similar to each other. The similarity of the diffusion curves and the difference between interdiffusion coefficients imply that the compositions, microstructures and precipitates of superalloy have a distinctly adverse effect on the interdiffusion of Ni and Al atoms during aluminization, but do not change the essential characteristics of β-NiAI phase.
文摘Two low alloy steels 0.5Cr-0.5Mo-0.25V and H85 were pack-aluminized at 900°for 4 h by using Fe-Al powder mixture containing 48% Fe, 20.6% Al- 29.4% Al2O3 and 2% NH4Cl by weight. The microhardness and oxidation resistance at 900℃ of the aluminide coatings were studied. It was found that pack-aluminizing improves the microhardness of the 0.5Cro.5Mo-0.25V steel while it reduces the microhardness of the H85 steel. Pack aluminizing highly improves the oxidation resistance after 20h exposure at 900℃ in air for the investigated steels.
文摘Gam matitanium aluminide ( γ TiAl) alloys are emerging as a revolutionary engineeringmaterialsfor hightemperaturestructuralapplications. Onthebasisoftheinformation avail ablein the public domain, this paper discussesthe historical background,status and future prospect of gam maalloytechnologyintheareasofalloy development/ design,processdevelop ment, and applications.
文摘The Editor-in-Chief has retracted this article [1] because Figures 11 and 12 appear to be identical with Figures 3 and 4respectively from a previously published article [2].Sehrish MUKHTAR,Waqas ASGHAR,Zubair BUTT,Zaheer ABBAS,Mudaser ULLAH and Rana ATTA-UR-REHMAN did not respond to correspondence about this retraction.
基金Project(50271010) supported by the National Natural Science Foundation of China
文摘A method was presented to prepare aluminide coatings on metals by combining the pack aluminizing with the ball impact process. This technique applied mechanical vibration to a retort, which was loaded with pack-aluminizing powder, specimens and alloy balls. Pack aluminizing was carried out with repeated ball impact, which accelerated chemical reactions and atomic diffusion. Aluminide coatings were formed at a relatively lower temperature (below 600 ℃) and in a shorter treatment time, compared with the conventional pack aluminizing. The effects of the operation temperature and the treatment time on the formation of the coatings were analysed. The SEM, EDS and XRD analysis results show that the aluminide coatings appear to be homogeneous, with a high density and free of porosity, and have excellent adherence to the substrate. The coatings mainly consist of Al-rich phases such as η-Fe2Al5, θ-FeAl3 and ?CrAl5. Oxidation resistance was studied by high-temperature tests. The formation mechanism of the Al-coatings was also investigated. This technique provides a new approach for industrial diffusion coatings with great energy and time savings.
基金the National Nature Science Foundation of China(No.50235030 and No.50005024)for the financial support to this research.
文摘An experimental study has been carried out to investigate the effect of microstructure on sliding wear behavior of Fe-Al coatings and Fe-Al/WC composite coatings produced by high velocity arc spraying (HVAS) and cored wires. After heat treatment at 300°C, 450°C, 550°C, 650°C and 800°C, the microstructure of the coatings will be changed. The changes of microstructure have obvious effects on the microhardness of the coatings, which may be the most important factor influencing the coatings sliding wear behavior. After heat treated at 450°C-650°C, increasing of the amounts of iron aluminides (including Fe3Al and FeAl ) and dispersion strengthening of Fe2\V2C and Fe6W6C will lead to a rise of microhardness of the coatings. Increasing the microhardness through heat treatment would improve the sliding wear resistance of the iron aluminide based coatings coatings.
文摘The halide activated pack cementation method is utilized to deposit aluminide and chromium modified aluminide coatings on TiAl alloys. Emphasis is placed on the effect of alloying elements on the aluminizing kinetics as well as on the study of formation of chromium modified aluminide coating. The addition of a small amount of Nb and Cr in the TiAl improves significantly the aluminizing kinetics of TiAl alloys by increasing the reaction rate of active Al atoms with substrate through grain refinement as well as by increasing the solid state diffusion of Al through the formation of stable TiAl 3 layer. Cr and Al are simultaneously co deposited by diffusion into K 5 alloy, by a single step, pack cementation process. The morphologies of the coating formed on K 5 substrate, i.e., an external layer with L1 2 structure and an underlying interdiffusion zone, are presented. The mechanism for the formation of Cr modified aluminide coating is discussed.
