Preparation of High Corrosion Resistance Ni-Fe-Sm Alloy Films in Reline SystemEI北大核心CSCD

针对在传统水溶液电解质中制备的 Ni-Fe 合金存在表面粗糙且耐腐蚀性能差的问题,在氯化胆碱-尿素离子液体体系 (Reline)中,加入稀土元素 Sm 对 Ni-Fe 合金进行改性,制备 Ni-Fe-Sm 三元合金膜。采用循环伏安测试、塔菲尔测试、扫描电镜、X 射线能谱仪研究金属离子在 Reline 离子液体中的电化学行为、合金膜表面形貌及其耐腐蚀性能。结果表明,Ni(Ⅱ)、 Fe(Ⅱ)为一步不可逆还原过程,Ni-Fe-Sm 合金在 Reline 体系中成核机制为三维瞬时成核。合金膜表面各金属元素分布均匀, 微观结构呈瘤状球形颗粒,合金膜表面细致,裂纹少,排布整齐。在 3.5 wt.%NaCl 和 10 wt.%HCl 溶液中,加入稀土元素 Sm, 合金膜的耐腐蚀性能显著提高,当沉积电位为?1.22 V,沉积时间为 20 min 时,自腐蚀电流密度最小,腐蚀速度最低,自腐蚀电位最正,耐腐蚀性能最高。进一步丰富了在 Reline 体系中添加稀土元素提高合金耐腐蚀性能的认识,使其在防护、存储等领域有较好的应用前景。     

Effect of Constituent Elements on the Corrosion Resistance of Single-Phase CoCrFeNi High-Entropy Alloys in NaCl SolutionEI北大核心CSCD

High entropy alloys (HEAs) origin from a new alloy design concept with multi-principal elements, which have attracted significant interests in the past decade. The high configurational entropy in HEAs results in simple solid solutions with fcc and bcc structures. Especially, the single solid solution CoCrFeNi alloy exhibits excellent properties in many aspects, such as mechanical properties, thermal stability, radiation resistance and corrosion resistance. The excellent corrosion resistance of CoCrFeNi alloy is ascribed to the single-phase structure and uniform element distribution coupled with much higher Cr content than stainless steel. The single-phase structure and uniform element distribution can prevent the occurrence of localized corrosion, and higher Cr content can protect the alloy surface better with the form of oxidation film. Moreover, the corrosion resistance of CoCrFeNi-based HEAs, such as CoCrFeNiAlx, CoCrFeNiCux, CoCrFeNiTix, have also been extensively investigated. In most CoCrFeNi-based HEAs, the elements of Co, Cr, Fe and Ni are with equal-atomic ratio. However, the equal-atomic ratio is not necessary to obtain satisfactory properties and to ensure the single fcc structure in Co-Cr-Fe-Ni system. Accordingly, it is essential to further consider the effect of alloying elements on the corrosion resistance in Co-Cr-Fe-Ni HEA. In this work, the effect of Co, Fe and Ni elements on the corrosion resistance of single fcc Co-Cr-Fe-Ni system with concentrated constitution but different atomic ratios in 3.5% NaCl solution are investigated by using LSCM and EIS. The potentiodynamic polarization results indicate that the increase of Fe and the decrease of Ni will decrease the passivation current density of the alloys when the Co and Cr contents are equal. With the increase of Co and the decrease of Ni, the alloys show smaller passivation current density and better corrosion resistance when the Fe and Cr contents are equal. With the decrease of Co and the increase of Fe and Ni, the alloys show higher corrosion potential and smaller corrosion tendency when the Cr content is constant. These results will be helpful for the design of corrosion resistant HEAs in NaCl aqueous solution.     

Influence of Ultrasonic Rolling on Corrosion Resistance of 7075 Aluminum AlloyEI北大核心CSCD

表面纳米化处理是一种有效改善耐腐蚀性能的手段,但受表面粗糙度和残余应力等因素的影响,其相关机制并不清晰。 运用透射电镜(TEM)和扫描电镜(SEM)研究经超声表面滚压工艺(USRP)处理后 7075 铝合金的组织和性能。结果表明： 经 1 道次和 15 道次 USRP 处理后,7075 铝合金表面粗糙度减小并且引入了残余压应力。滚压 15 个道次的试样表面能获得平均晶粒尺寸为 52 nm 的纳米晶。相较于未处理试样,经 1 道次和 15 道次 USRP 处理后试样的耐腐蚀性能均显著提高。其中, 滚压 15 个道次试样的耐腐蚀性能提升更为显著。这主要是因为纳米晶可以使材料表面形成更加致密的钝化膜,导致其耐腐蚀性能显著提高,而表面粗糙度降低和引入残余压应力是提升耐腐蚀性能的次要因素。对比分析残余应力、表面粗糙度和表面纳米晶对 7075 铝合金耐腐蚀性能的影响,揭示了 7075 铝合金经表面纳米化处理后耐腐蚀性能提升的机制。     

Corrosion Resistance of Deformed Cu-Ni Alloy in Seawater

ＣｏｒｏｓｉｏｎＲｅｓｉｓｔａｎｃｅｏｆＤｅｆｏｒｍｅｄＣｕＮｉＡｌｏｙｉｎＳｅａｗａｔｅｒＺｈｕＸｉａｏｌｏｎｇ，ＬｉｎＬｅｙｕｎ（朱小龙）（林乐耘）ＧｅｎｅｒａｌＲｅｓｅａｒｃｈＩｎｓｔｉｔｕｔｅｆｏｒＮｏｎｆｅｒｒｏｕｓＭｅｔａｌｓ，Ｂｅｉｊ...     

Effect of Pyrrole and N-Methylpyrrole Coatings on Corrosion Resistance of Mild Steel

COATING ON THE SURFACE of metals bypolymeric materials have been widely used inindustries for the protection of this materials against ofcorrosion[1-4].Electropolymerization is an effective technique forthe surface coating of various conductive materialswith wide variety of polymers with various thick nesses[5].Recently,electropolymerization of pyrrole on steelsubstrates has been investigated with the aim ofproducing uniform and strongly adherent coatings[6-9].It was found that only lim…     

Study on the Galvanic Current of Corrosion Behavior for AH32 Long-Scale Specimen in Simulated Tidal ZoneEI北大核心CSCD

The environment of the tidal zone is very complex. The interactions of dry-wet alternation and sea erosion lead to serious corrosion of steel structures, which makes it difficult to adopt protective methods. Therefore, it is of great significance to study the corrosion and protection methods of steel in tidal zone. For long-scale steel through the tidal zone and immersion zone, there is a big difference in corrosion behavior with complete immersion condition, the potential of the steel surface changes due to the influence of oxygen concentration difference and tidal fluctuations or other factors. In this study, the galvanic current and open circuit potential of the long-scale AH32 steel were monitored in simulated tidal zone. The results shows that the potential at different tide levels and different immersion depths for a long-scale AH32 specimen is not unified, with the macro cell was formed by the difference of oxygen supply, which caused internal galvanic current. The essence of the galvanic current is the net current that was generated by the sum of anode and cathode current. Galvanic current at different positions on the long-scale AH32 specimen varies with the tidal movement periodically in tidal zone. When tide is at the highest level, the galvanic current of all parts accesses a maximum value, and among these maximum values, the largest one is at the middle part of specimen, which causes the biggest anodic dissolution current density. According to the variation of the galvanic current, the time distributions of the drying, wetting and immersion states were calculated, and the results showed that the corrosion scale of the long-scale AH32 specimen at different positions depends on the time all location of wetting and immersion in tidal zone. The macro cell caused the galvanic current when all parts of the specimen were immersed. At wetting state, the solution resistance of the thin liquid film is very large, which leads to the change of the driving potential of the macro cell into the potential drop. Thus, macro cell is ineffective in the wetting state and cannot produce the galvanic current. According to the relation between wetting time and quantity of electricity at wetting state, the maximum wetting time of the long-scale AH32 specimen is shown above average mean tide level in tidal zone, which indicates that the corrosion loss of this part is maximum due to wetting state. In addition to weight loss measurements, maximum of it for long-scale AH32 specimen was obtained at the average mean tide level caused by immersion state. It can be indicated the maximum weight loss of the long-scale AH32 specimen should appear upper the average mean tide level part in tidal zone. These results were consistent with measurements of corrosion rates.     

Effect of Fe on Microstructure and Coercivity of SmCo-Based MagnetsEI北大核心CSCD

High-temperature permanent magnets have an important application in the aerospace and other high-tech fields, among which 2:17-type SmCo magnets have become the first choice for high-temperature permanent magnets due to the strong magnetic anisotropy and high Curie temperature. Although there are studies on the effect of Fe on the remanence and coercivity, the role that Fe plays on coercivity mechanism of SmCo magnets is still unclear. In this work, Sm(CobalFexCu0.08-0.10Zr0.03-0.033) z (x= 0.10-0.16, z=6.90 and 7.40) magnets are prepared and the magnetic properties under different temperatures are investigated. The magnets with an intrinsic coercivity of 603.99 kA/m and a maximum energy product of 87.30 kJ/m(3) at 500 degrees C. are obtained. It is revealed that at room temperature the coercivity of the magnets increases with increasing Fe content, however, at 500 degrees C. the coercivity shows an opposite dependency on Fe content. Moreover, the effect of Fe on coercivity is more obvious at low z value. The phase structure and composition analyses were characterized by XRD and TEM. The results show that with the increase of Fe content, the size of the 2: 17R cell phase increases, the volume ratio of cell boundary 1: 5H phase decreases, and furthermore, both Fe content in the 2: 17R phase and Cu content in the 1: 5H phase increase. The variations of Fe and Cu contents in both phases lead to the change of the domain wall energy difference. With the increase of Cu content of 1:5H phase, the domain wall energy of 1: 5H phase (gamma(1:6)) drops faster at room temperature, the coercivity is determined by gamma(2:17)-gamma(1:5), so the coercivity increases with increasing Fe content. While at 500 degrees C, due to gamma(1:6) at its Curie temperature, the coercivity is mainly determined by the domain wall energy of 2: 17R phase (gamma(1:17)), which decreases with increasing Fe content. The increase of Fe content at the low z value results in a smaller growth of cell size, which leads to a more significant change in coercivity.     

Effect of Microstructure on Corrosion Behavior of Mg–Sr Alloy in Hank's Solution

Mg–Sr alloy has been studied as a potential biodegradable material with excellent bioactivity to promote the bone formation. However, its degradation behavior needs to be well controlled to avoid the negative effect, which is important for future application. Therefore in this study, the microstructure and its effect on corrosion behavior of an Mg–1.5 Sr alloy were investigated. The microstructures of the alloy under different processing procedures were characterized by both optical and scanning electron microscopes. The corrosion performance was studied in Hank's solution using immersion,potentiodynamic polarization and electrochemical impedance spectroscopy(EIS) tests. The results showed that the grain size and the amount and distribution of b-Mg_(17)Sr_2 had obvious effects on the corrosion behavior of Mg–Sr alloy. The smaller the grain size was, the more the protective surface layer formed on Mg–Sr alloy, and the higher the corrosion resistance was. For the as-cast Mg–Sr alloy, the network-like second phases precipitated along the grain boundaries could not hinder the corrosion due to their own corrosion cracking accelerating the intergranular corrosion. However, the refinement of second phases increased the corrosion resistance of the as-extruded alloy. After solution treatment at 450 °C for 5 h, the grains in the alloy did not grow much and b-Mg_(17)Sr_2 phases homogenously distributed in the alloy, resulting in the increase in corrosion resistance. However, after aging treatment, large amount of precipitated second phases increased the galvanic corrosion of the alloy, accelerating the development of corrosion.     

The Effect of Potassium Phosphate on the Corrosion of АМг6 Alloy in Water-Acetate Solutions

Corrosion-electrochemical investigation of an 6 type alloy was carried out in aqueous solutions of potassium acetate and phosphate. The corroded surface was examined by IR spectroscopy. The alloy is shown to corrode in the passive state at a rate of no more than 0.0002 mm/year. A small addition of potassium phosphate (1%) noticeably impedes, and a large (10%)—accelerates the alloy's corrosion. An explanation of these effects was suggested.     

Corrosion inhibition of gatifloxacin on mild steel in 3% HCL solution北大核心CSCD

The inhibition effect of gatifloxacin on the corrosion of mild steel in 3%HCl solution was investigated by means of mass loss measurements and electrochemical measurements. The surface morphology of the steel after corrosion was studied by scanning electron microscope (SEM). The results demonstrated that the highest inhibition efficiency of gatifloxacin reached 95.6% for a dose of gatifloxacin 700 mg/L. Gatifloxacin acted as a mixed-type inhibitor, the cathodic and anodic processes of corrosion were suppressed. Thermodynamic parameters were acquired from data of weight loss at different experimental temperatures, which suggested that the adsorption of gatifloxacin on metal surface obeyed Langmuir adsorption isotherm model. The adsorption processes were exothermic, and belong to chemisorption and physisorption. The entropy of adsorption processes increased. © 2016, Corrosion Science and Protection Technology. All rights reserved.     

Progress and Application of Microstructure Simulation of Alloy SolidificationEI北大核心CSCD

Solidification structures are the interaction links between the alloy components and their mechanical properties. Scientifically comprehending about the formation mechanisms, dominant factors and control methods in alloy solidification has a significant effect on the structure control and optimization. Dendritic structure is the most frequently observed solidification microstructure of alloys and controlled by heat, solute, melt flow, capillary and many other factors. Modelling and simulating can accurately quantify various phenomena and evolution rules in the process of solidification, thus play an increasingly important role in the design, preparation, processing and performance optimization of alloy materials. Over the past two decades, remarkable progress has been made and various models have been proposed in microstructure simulation during alloy solidification process, such as deterministic method, phase field (PF), Monte Carlo (MC) and cellular automaton (CA). With the advantages of clear physical meaning, easily programming and high calculation efficiency, CA method has been widely applied in the study of solidification structure simulation and exhibits great advantages. Considering the current development level of computer hardware, numerical model and calculation method, microstructure simulation of large components mainly adopts macro-microscopic coupling calculation method, such as CA-FD/FE model. The heat transfer and other multi-physical fields are calculated at the level of coarse mesh, where-as nucleation and dendritic growth are simulated at a much finer grid level. This paper reviews the main models and development of CA method used for nucleation simulation. The key aspects in the simulation of dendritic growth including mean solid-interface interface curvature, growth kinetics and the algorithm for eliminating "pseudo anisotropy" are discussed. Based on this, the development and application status of macro-micro coupling model during casting, directional solidification and other manufacturing fields are summarized. Finally, the existing problems and future tendency for simulation of solidification structures are analyzed.     

Corrosion Behavior of GH4169 Alloy in NaCl Solution Spray Environment at 600°CEI北大核心CSCD

The corrosion behavior of engine materials of airplanes working in marine environments is accelerated by the synergistic effects of NaCl particles and water vapor at high temperatures. This work examined the corrosion behavior of GH4169 alloy with a NaCl solution spraying at 600 degrees C using an oxidation kinetics test and micro characterization technology in the aspects of corrosion kinetics, corrosion layer phase composition, and microstructure. The weight gain of the GH4169 alloy corroded in the NaCl solution spraying environment was much lower than that in solid NaCl + wet O-2 after 20 h corrosion at 600 degrees C. The corrosion products of the GH4169 alloy in the NaCl solution spray environment were less complex than those in the solid NaCl + wet O-2 environment, but they were denser. In addition, Cl was concentrated in the inner layer of the corrosion products and accelerated the corrosion of GH4169 alloy via an active oxidation mechanism at the initial stage. When NaCl deposition was increased, the corrosion mechanism of GH4169 alloy changed gradually to Cl-induced active oxidation. The sensitivity of GH4169 alloy in the NaCl solution spray environment at 600 degrees C was analyzed. Overall, the sensitivity of elements in GH4169 alloy to chlorine activated corrosion was Ti > Al > Nb, Cr > Fe > Mo, Ni, whereas the sensitivity of the oxides was TiO2 > MoO2 > Cr2O3(Nb2O5) > Fe2O3 > Al2O3 > NiO.     

Effect of Gravity on Directionally Solidified Structure of SuperalloysEI北大核心CSCD

分别利用常规下抽拉法与新型上提拉法进行不同方向的高温合金定向凝固实验,对比研究重力对单晶铸件凝固组织的影响。结果表明,在常规下抽拉法实验的向上凝固过程中,容易出现雀斑、γ/γ’共晶上聚和籽晶回熔紊乱等问题。原因是糊状区内液体由于元素偏析引起密度减小,在重力作用下形成了上重下轻的失稳状态并引起对流。而通过新型上提拉法实现的顺重力凝固过程中,密度减小的液体处于糊状区上端,形成上轻下重的稳定状态,使重力的作用由失稳因素转化为维持稳定的因素,抑制了液体对流的产生与发展。采用新型上提拉法制备的单晶铸件中彻底消除了雀斑缺陷,抑制了γ/γ’共晶组织的向上聚集,也保证了低密度籽晶稳定的回熔和外延生长。顺重力定向凝固技术从根本上消除了重力对高温合金定向凝固的不良影响,有希望发展成为新一代的先进单晶叶片成型技术。     

Preparation of the Thermal-assisted Self-healing Bionic Super Slippery Surface on Aluminum Alloy Substrate and the Effect of Lubricant on Its PerformanceEI北大核心CSCD

仿猪笼草超滑表面具有疏液性和防污性等优异性能。然而仿生超滑表面的润滑油膜受损后,其超滑性能会被破坏, 因此制备具有自修复性能的仿生超滑表面对于解决其耐久性差的问题至关重要。首先采用阳极氧化法在铝合金基体表面制备锥形微结构,然后经过全氟硅烷进行低能修饰,最后往微结构间隙中注入全氟聚醚、低黏度硅油和高黏度硅油三种不同的润滑油,得到三种仿生超滑表面。水滴在三种仿生超滑表面的接触角分别为~116°、~105°、~103°,滑动角分别为~10°、~10°、~9°。试验结果表明,全氟聚醚和低黏度硅油的仿生超滑表面比高黏度硅油的仿生超滑表面具有更优的自清洁性和防污性,可以有效地预防污染物堆积造成的疏液性失效。此外,全氟聚醚与低黏度硅油的仿生超滑表面呈现较好的热辅助自修复性,修复后的疏水性与新制备样品基本一致;高黏度硅油仿生超滑表面只表现出一定的自修复能力,修复后与新制备样品的疏水性存在差异。所制备出的具有热辅助自修复功能的铝合金基底仿生超滑涂层,在海洋生物污损防护方面具有潜在的应用前景,并为克服传统仿生超滑表面使用耐久性差的问题提供了解决思路。     

The Effect of Homogenization on the Corrosion Behavior of Al–Mg Alloy

The effect of homogenization on the corrosion behavior of 5083-O aluminum alloy is presented in this paper. The intergranular corrosion and exfoliation corrosion were used to characterize the discussed corrosion behavior of 5083-O aluminum alloy. The variations in the morphology, the kind and distribution of the precipitates, and the dislocation configurations in the samples after the homogenization were evaluated using optical microscopy (OM), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The effects of the highly active grain boundary character distribution and the types of constituent particles on the corrosion are discussed on the basis of experimental observations. The results indicated that the corrosion behavior of 5083-O alloy was closely related to the microstructure obtained by the heat treatment. Homogenization carried out after casting had the optimal effect on the overall corrosion resistance of the material. Nevertheless, all samples could satisfy the requirements of corrosion resistance in marine applications.     

Chemical Units in Solid Solutions and Alloy Composition DesignEI北大核心CSCD

Industrial alloys all have specific chemical compositions as standardized in specifications. Understanding the structural origin of special compositions for these solid-solution alloys is significant to shortening the development of new industrial alloys. It is well accepted that all alloys are based on solid solutions characterized by chemical short-range ordering. Previously it was only possible to describe the deviation of solute distribution from average mode in a statistical manner. The lack of an accurate structural tool to address the characteristic short-range-order structures constitutes the major obstacle in establishing an effective structural model that allows precise composition design for alloys. Since alloys with good comprehensive performance do have specific chemical compositions, their compositions should correspond to molecule-like specific structural units. After a long effort of more than a decade, we have developed a new structural tool, so-called the cluster-plus-glue-atom model, to address any short-range-ordered structures. In particular, solid solutions can be understood as being constructed from the packing of special chemical units covering only the nearest-neighbor cluster and a few glue atoms located at the next outer shell, expressed in molecule-like cluster formula [cluster] (glue atoms). Such units represent the smallest particles that are representative of the whole structures, just like molecules do for chemical substances. After introducing Friedel oscillation, the cluster-plus-glue-atom model is turned into the cluster-resonance model that provides also the inter-cluster packing modes. Ideal atomic density is hence obtained which is only proportional to the number of atoms in the unit and the cube of the cluster radius. The calculation of chemical unit is then possible and is conducted in typical binary Cu-based industrial alloys. The calculated formulas give chemical composition that highly agree with the most popular alloy specifications. The work demonstrates its high potential for developing chemically complex alloys.     

International Standards in Corrosion of Metals and Alloys. The Activities of ISO/TC 156 “Corrosion of Metals and Alloys”

We continue to inform readers about the activities of the Technical Committee Corrosion of metals and alloys of the International Organization for Standardization (ISO/TC 156). The work program of the Committee for 2000 is given. The scheme of the participation of specialists in corrosion in the activity of the Committee, as well as the procedure of submitting draft standards for the development as International standards, is shown.     

Corrosion behavior of high Al- and Fe-bronze Cu-15Al-xFe in NaCl solution北大核心CSCD

Sub-rapidly solidified Cu-15Al-xFe (x=10, 12, 15) alloy bars were prepared by copper mould casting. The corrosion behavior of the bronzes in 3.5%NaCl solution was investigated by means of potential dynamic polarization measurement and static immersing corrosion test. The microstructure of the bronzes before and after corrosion test was characterized with scanning electron microscope (SEM) and energy dispersive spectrometer (EDS), and then the relevant corrosion mechanism and the effect of Fe content on the corrosion resistance were discussed in detail. The results showed that the corrosion resistance of Cu-15Al-12Fe alloy is the best in 3.5%NaCl solution. The three bronzes Cu-15Al-xFe (x=10, 12, 15) all suffered from selective corrosion, which was resulted from the dealuminization and deferrization of the phase reach in Fe and Al. © 2016, Corrosion Science and Protection Technology. All rights reserved.     

The Effect of Texture on the Corrosion Behavior of AZ31?Mg Alloy

Magnesium (Mg) grains show anisotropic corrosion behavior, which implies that the single-phase, hot-rolled Mg alloy AZ31 sheet, if highly textured, will have different corrosion performance depending on its crystallographic orientation of the grains. Its rolling surface, dominated by (0001) basal crystallographic planes, is more corrosion resistant than its cross-section surface, which is mainly composed of $ \{ 10\overline{1} 0\} $ and $ \{ 11\overline{2} 0\} $ prismatic crystallographic planes. Furthermore, grain refinement by hot rolling is beneficial to the overall corrosion resistance of AZ31 because of the dissolution of AlMn(Fe) intermetallic precipitates in the alloy. Surface compressive deformation machining can lead to refined grains and an expected preferred grain orientation, thus improving the corrosion resistance of AZ31 alloy.     

Effect of High-Energy and Instantaneous Electropulsing Treatment on Microstructure and Properties of 42CrMo SteelEI北大核心CSCD

42CrMo steel was widely used in many industry fields for its excellent hardenability and high temperature strength. Many transmission mechanisms and fasteners, such as roller and heat-resistant gear, are made of this steel. However, the ductility of 42CrMo steel is relatively low after quenching and tempering. During high tempering Mo riched carbides at grain boundary and undecomposable martensite at low tempering are the main reasons for poor ductility of 42CrMo steel. Grain refinement can enhance both strength and ductility significantly, but traditional refinement technology will cause intergranular oxidation so that strengthening effect was weak. Although thermomechanical treatment can achieve dynamic recrystallization, its refinement effect is unstable. Elecropulsing treatment, which makes significant change in microstructure and properties of metals, has been applied in many fields such as, modification of solidified microstructure of liquid metal, healing of fatigue crack, nanocrystallization of amorphous materials and so on. Moreover, this process can produce superior mechanical properties in metals. In order to improve the mechanical properties of 42CrMo steel better, high-energy and instantaneous electropulsing treatment was applied. In this contribution, 42CrMo steel was subjected to traditional and electropulsing treatment individually. It was found that EPQ treatment (480 ms electropulsing treatment, water cooled) results in finer grain, promoting the formation of retained austenite and twin martensite; EPT treatment (180 ms electropulsing treatment, air cooled) can stabilize retained austenite in EPQ specimen and induce multiphase structure. Mechanical properties results indicate that strength-ductility balance of EPQ and EPQ+EPT specimen are 32% and 13.9% higher than that of TQ (traditional quenched) and EPQ+TT (traditional tempered) specimen respectively.