Electrophoretic deposition of titanium/silicon-substituted hydroxyapatite composite coating and its interaction with bovine serum albumin

Silicon-substituted hydroxyapatite (Ca10(PO4)6-x(SiO4)x(OH)2-x, Si-HA) composite coatings on a bioactive titanium substrate were prepared by electrophoretic deposition technique with the addition of triethanolamine (TEA) to enhance the ionization degree of Si-HA suspension. The surface structure was characterized by XRD, SEM, XRF, EDS and FTIR. The bond strength of the coating was investigated. The results show that the depositing thickness and the images of Si-HA coating can be changed with the variation of deposition time. The XRD spectra of Ti/Si-HA coatings show the characteristic diffraction peaks of HA, and the incorporation of silicon changes the lattice parameter of the crystal. The FTIR spectra shows that the most notable effect of silicon substitution is the decrease of intensities of -OH and PO43- groups with the silicon contents increasing. XRD and EDS element analyses present that the content of silicon in the coating increases with increasing silicon concentration in the suspension. The bioactive TiO2 coating formed may improve the bond strength of the coatings. The interaction of Ti/Si-HA coating with BSA is much greater than that of Ti/HA coating, suggesting that the incorporation of silicon in HA is significant to improve the bioactive performance of HA.     

Nanostructured Si,Mg, CO<Subscript>3</Subscript><Superscript>2−</Superscript> Substituted Hydroxyapatite Coatings Deposited by Liquid Precursor Plasma Spraying: Synthesis and Characterization

In this study, a novel liquid precursor plasma spraying (LPPS) process was used to deposit Si, Mg, CO₃ ²⁻ substituted hydroxyapatite (HA) coatings (alone and cosubstituted) onto Ti-6Al-4V substrates. Salts of silicon, magnesium, and carbonate elements were directly added into the HA liquid precursor for subsequent plasma spraying. The phase composition, structure, and morphology of all HA coatings were characterized by x-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and Fourier transform infrared (FTIR) spectroscopy. The results indicated that the trace elements were successfully incorporated into the HA structure and nanostructured coatings were obtained for all doped HA formulations. The incorporation of trace elements into the HA structure reduced its crystallinity, especially when silicon, magnesium and carbonate ions entered simultaneously into the HA structure. FTIR spectra showed that the Si-HA and Mg-HA coatings had decreased intensities in both the O-H and P-O bands and that the CO₃ ²⁻-HA coating was mainly a B-type carbonate-substituted HA. The results showed that the LPPS process is an effective and simple method to synthesize trace element substituted biomimetic HA coatings with nanostructure.     

Microstructure, mechanical and wear properties of laser processed SiC particle reinforced coatings on titanium

Laser processing of Ti-SiC composite coating on titanium was carried out to improve wear resistance using Laser Engineered Net Shaping (LENS™) — a commercial rapid prototyping technology. During the coating process a Nd:YAG laser was used to create small liquid metal pool on the surface of Ti substrate in to which SiC powder was injected to create Ti-SiC metal matrix composite layer. The composite layers were characterized using X-ray diffraction, scanning and transmission electron microscopy equipped with fine probe chemical analysis. Laser parameters were found to have strong influence on the dissolution of SiC, leading to the formation of TiSi₂, Ti₅Si₃ and TiC with a large amount of SiC on the surface. Detailed matrix microstructural analysis showed the formation of non-stoichiometric compounds and TiSi₂ in the matrix due to non-equilibrium rapid solidification during laser processing. The average Young's modulus of the composite coatings was found to be in the range of 602 and 757 GPa. Under dry sliding conditions, a considerable increase in wear resistance was observed, i.e., 5.91 × 10^− 4 mm³/Nm for the SiC reinforced coatings and 1.3 × 10⁻³ mm³/Nm for the Ti substrate at identical test conditions.     

Tribological properties of titanium aluminides coatings produced on pure Ti by laser surface alloying

Titanium aluminides coatings were in-situ synthesized on a pure Ti substrate with a preplaced Al powder layer by laser surface alloying. The friction and wear properties of the titanium aluminides coatings at different normal loads and sliding speeds were investigated. It was found that the hardness of the titanium aluminides coatings was in the following order: Ti₃Al coating > TiAl coating > TiAl₃ coating. Friction and wear tests revealed that, at a given sliding speed of 0.10 m/s, the wear volume of pure Ti and the titanium aluminum coatings all increased with increasing normal load. At a given normal load of 2 N, for pure Ti, its wear volume increased with increasing sliding speed; for the titanium aluminides coatings, the wear volume of Ti₃Al coating and TiAl coating first increased and then decreased, while the wear volume of TiAl₃ coating first decreased and then increased with increasing sliding speed. In addition, the friction coefficients of pure Ti and the titanium aluminides coating decreased drastically with increasing sliding speed. Under the same dry sliding test conditions, the wear resistance of the titanium aluminium coatings was in the following order: Ti₃Al coating > TiAl coating > TiAl₃ coating.     

Hydroxyapatite coating on titanium substrate by electrophoretic deposition method: Effects of titanium dioxide inner layer on adhesion strength and hydroxyapatite decomposition

Nanosized hydroxyapatite (HA) powders were prepared by a chemical precipitation method and electrophoretically deposited on Ti6Al4V substrates. The powders were calcined before the deposition process in order to obtain crack-free coating surfaces. As an inner layer between Ti6Al4V substrate and HA coating, nanosized titanium dioxide (TiO₂) powders were deposited, using different coating voltages, in order to connect substrate and HA tightly. Moreover, this layer is considered to be acting as a diffusion barrier, reducing the HA decomposition due to ion migration from the metal substrate into the HA. After the sintering stage, adhesion strengths of coatings were measured by shear testing, phase changes were studied by X-ray diffraction, and coating morphology was analyzed through scanning electron microscopy observations. Results showed that usage of the TiO₂ inner layer prevented HA decomposition. Furthermore, decreasing the voltage used in TiO₂ deposition resulted in crack-free surfaces and increased adhesion strength of the overall coating.     

Durability of Titanium/Dicalcium Silicate Composite Coatings in Simulated Body Fluid

Titanium/dicalcium silicate composite coatings with different ratios (weight ratios as Ca₂SiO₄: Ti = 3:7, 5:5, 7:3) were prepared by plasma spraying. Effects of titanium addition on coating properties, such as bonding strength, flexural modulus, and dissolution in simulated physiological environment, were studied. Results showed that the bonding strength between coating and Ti-6Al-4V substrate increased with increase of titanium content in the composite coatings. It was explained by the narrowed dissimilarity of thermal expansion coefficients between the coatings and substrates. Degradation of mechanical properties after immersion in simulated body fluid was also studied. The dissolution of dicalcium silicate in the composite coatings resulted in the decrease of flexural strength and flexural modulus of the coatings in the simulated physiological environment. The higher titanium content in the composite coatings, the stabler are the composite coatings in the physiological environment.     

Adhesion of a chemically deposited monetite coating to a Ti substrate

Monetite is a promising biomaterial for restoring the function of the compromised skeletal structures due to its superior osteoconductive and resorption properties. However, its potential as a coating for orthopaedic implants in load bearing applications has not yet been investigated. The aim of this study was to prepare monetite coating on Ti substrate in mild conditions, which may allow incorporation of protein-based drugs during the coating deposition. Coatings were prepared using chemical deposition of monetite on Ti substrate in acidic conditions at 75 °C for 24 h. Coatings were characterised by scanning electron microscope (SEM), energy-dispersive X-ray spectroscopy (EDS), X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR). Adhesion of the coatings to Ti substrate was measured using tensile tests. EDS confirmed the calcium phosphate nature of the coating and XRD and FTIR confirmed the monetite phase of the coatings. SEM revealed that the coatings were formed of densely packed plate-like monetite crystals, with the crystal size approximately 20 × 10 × 5 μm. Adhesion tests showed cohesive failure of the monetite coatings and the tensile strength of the coating was in the range of 15.43 ± 0.20 MPa. Mechanical tests showed that monetite coatings were stable and could be considered for use with Ti orthopaedic implants.     

Electrodeposition of hydroxyapatite coating on CoNiCrMo substrate in dilute solution

In the present work, calcium phosphate coatings on CoNiCrMo substrate were prepared by electrodeposition at different voltages (− 1.4,−1.6,−1.8,−2.0 and − 2.2 V versus Ag/AgCl) in the mixed solution of 0.6 mM Ca(NO₃)₂·4H₂O and 0.36 mM NH₄H₂PO₄ at 80 °C. The electrocrystallization process of the moderate potential (− 1.8 V) was addressed. To investigate the role of pH on HA formation during electrodeposition, different kinds of uncharged substrates (including CoNiCrMo, non-conducting polyethylene, Ti substrate and glass) were placed close to the cathode separately in some of the electrodeposition experiments at − 1.8 V. Moreover, the effect of pH on saturation indexes with respect to hydroxyapatite, octacalcium phosphate and dicalcium dihydrogen phosphate of this dilute solution were calculated by a computer program PHREEQC. The results showed the moderate potential sample (− 1.8 V) exhibited a uniform coating consisted of fine crystallized hydroxyapatite with hexagonal prism shape. It was also found the local pH value plays a crucial role in the formation of HA during the electrodeposition.     

钛合金表面GO/HA/MAO复合膜层的制备及其性能

为了改善钛合金种植体在体液中的腐蚀及摩擦腐蚀行为,延长其在人体环境中的服役时间,在微弧氧化 (MAO)膜层上采用溶胶凝胶(Sol-gel)法于羟基磷灰石(HA)和氧化石墨烯(GO)的混合溶胶中浸渍提拉成膜,从而在 Ti6Al4V 合金表面成功地制备了 GO/ HA/ MAO 复合膜层。 结果表明,MAO 膜层表面的微孔及微球被 GO/ HA 薄膜有效的覆盖且较为致密;膜层的物相组成主要为金红石相及锐钛矿相的 TiO₂、HA、SiO₂ 和GO;根据电化学腐蚀和摩擦腐蚀结果分析知,GO/ HA/ MAO 复合膜层在模拟体液(SBF)中的耐蚀性及耐摩擦腐蚀性相比于 MAO 膜层和 Ti6Al4V 基体均得到了显著提高。     

Surface modification of magnetron-sputtered hydroxyapatite thin films via silicon substitution for orthopaedic and dental applications

There have been a significant advances made in the field of bioceramics, particularly hydroxyapatite (HA) during the past 10 years. Emphasis has now shifted towards designing HA with enhanced bioactivity for bone tissue repair. The aim of this study was to assess whether surface wettability can be correlated with cellular interactions with silicon-substituted hydroxyapatite (SiHA)-coated titanium (Ti) substrates. SiHA thin coatings of varying Si compositions were deposited on Ti substrates via a magnetron co-sputtering technique. These coatings were then subjected to an in vitro study using primary human ostoeblast (HOB) cells, to evaluate their biological property. HOB cells showed initial poor adhesion and spreading on hydrophobic Ti surface. The application of HA or SiHA thin coatings on Ti substrates by magnetron co-sputtering technique renders the surface more hydrophilic, with water contact angles between 30 and 40°. HOB cells attached, spread and proliferated well on these coatings. Enhanced calcification (formation of calcium phosphate nodules across the collagenous matrices) was observed on SiHA coatings with increasing Si content. This interdisciplinary paper highlighted that enhanced bioactivity was associated with surface wettability. Producing a nanostructured HA coating on a Ti substrate by magnetron sputtering resulted in the promotion of cell proliferation and calcification, and the latter was further enhanced with Si substitution. Hence, SiHA thin coating holds great potential as an alternative dental material.     

Structure and oxidation behavior of Si-Y co-deposition coatings on an Nb silicide based ultrahigh temperature alloy prepared by pack cementation technique

In order to improve the oxidation resistance of silicide coatings on Nb silicide based alloys, Y-modified silicide coatings were prepared by co-depositing Si and Y at 1050, 1150 and 1250 °C for 5-20 h, respectively. It has been found that the coatings prepared by co-depositing Si and Y at 1050 and 1150 °C for 5-20 h as well as at 1250 °C for 5 h were composed of a thick (Nb,X)Si₂ (X represents Ti, Cr and Hf elements) outer layer and a thin (Nb,X)₅Si₃ inner layer, while the coatings prepared by co-depositing Si and Y at 1250 °C for 10-20 h possessed a thin outer layer composed of (Ti,Nb)₅Si₃ and Ti-based solid solution, a thick (Nb,X)Si₂ intermediate layer and a thin (Nb,X)₅Si₃ inner layer. EDS analyses revealed that the content of Y in the (Nb,X)Si₂ layers of all the coatings was about 0.34-0.58 at.% while that in the outer layers of the coatings prepared by co-depositing Si and Y at 1250 °C for 10-20 h was about 1.39-1.88 at.%. The specimens treated by co-depositing Si and Y at 1250 °C for 10 h were selected for oxidation test. The oxidation behavior of the coating specimens at 1250 °C indicated that the Si-Y co-deposition coating had better oxidation resistance than the simple siliconized coating because the oxidation rate constant of the Si-Y co-deposition coating was lower than that of the simple siliconized coating by about 31%. The scale developing on the Si-Y co-deposition coating consisted of a thicker outer layer composed of SiO₂ and TiO₂ and a thinner SiO₂ inner layer.     

Pulsed microwave plasma polymerization of silicon oxide ?lms: Application of efficient permeation barriers on polyethylene terephthalate

A microwave driven low pressure plasma reactor is developed based on a modi?ed Plasmaline antenna for plasma processing of polyethylene terephthalate (PET) foils and bottles. It allows for the treatment of thermolabile packaging materials, e.g. plasma sterilization and permeation barrier coating. Silicon oxide ?lms are deposited on PET foils as a permeation barrier coating. A pulsed hexamethyldisiloxane:oxygen plasma is ignited under various conditions and the oxygen permeation is investigated. A criterion for the homogeneous deposition of SiO_x coatings is described depending on the residence time of process gases. Additionally, the composition of the coatings is analyzed by means of Fourier transform infrared spectroscopy regarding carbon and hydrogen content. A strong relation between barrier properties and ?lm composition is found: good oxygen barriers are observed as carbon content is reduced and ?lms become inorganic, quartz-like. A residual permeation as low as J = 1.0 ± 0.3 cm³ m^− 2 day^− 1bar^− 1 for SiO_x coated PET foils is achieved. The dependencies of important plasma parameters, such as gas mixture, process pressure, power and pulse conditions on oxygen permeation through packaging foil are shown to optimize the coating process.     

Mechanical and tribological properties of multi-element (AlCrTaTiZr)N coatings

Multi-element (AlCrTaTiZr)N coatings are deposited onto Si and cemented carbide substrates by reactive RF magnetron sputtering in an Ar + N₂ mixture. The influence of substrate bias voltage, ranging from 0 to − 200 V, on the microstructural, mechanical and tribological properties of these nitride coatings is studied. A reduction in concentration of N and Al is observed with increasing substrate biases. The (AlCrTaTiZr)N coatings show the face-centered-cubic crystal structure (B1-NaCl type). The use of substrate bias changes the microstructure of the (AlCrTaTiZr)N coating from the columns with microvoids in boundaries to the dense and less identified columns. The compressive macrostress increases from − 0.9 GPa to − 3.6 GPa with an increase of substrate bias. The hardness and adhesion increase to peak values of 36.9 GPa and 60.7 N at the bias voltage of − 150 V, respectively. The tribological properties of the (AlCrTaTiZr)N coatings against 100Cr6 steel balls are evaluated by a ball-on-disc tribometer with a 10 N applied load. With an increase of substrate bias, the wear rate reduces while the friction coefficient almost keeps constant at 0.75. The lowest wear rate of 3.65 × 10^− 6 mm³/Nm is obtained for the (AlCrTaTiZr)N coating deposited at the bias voltage of − 150 V.     

TC4钛合金表面激光熔覆WC增强镍基复合涂层的组织及耐磨性

为提高TC4钛合金的耐磨性,利用激光熔覆技术(laser cladding,LC)在TC4钛合金表面制备Ni60+50%WC(体积分数)和deloro22(d22)粉末打底+(Ni60+50%WC)2种耐磨复合涂层。采用扫描电子显微镜(SEM)、能谱仪(EDS)以及X射线衍射仪(XRD)来表征涂层的微观结构和物相组成;使用HV-1000显微维氏硬度计、HRS-2M型高速往复摩擦磨损试验机和WDW-100D电子万能试验机来分析涂层的性能。结果表明:2种涂层均由W₂C、TiC、Ni₁₇W₃、Ni₃Ti和Ti_xW_1-x相组成,2种涂层不仅与基体呈现出优异的冶金结合,而且组织均匀致密,没有裂纹瑕疵;由于涂层中存在着原位合成的硬质相和细晶强化共同作用使得涂层硬度显著提高,约为TC4基体的2.82倍;2种涂层的摩擦系数(COF)和磨损量都远低于TC4钛合金基体;Ni60+50%WC复合涂层和d22粉末打底+(Ni60+50%WC)复合涂层的抗剪切结合强度分别为188....     

Effect of silicate anion distribution in sodium silicate solution on silicate conversion coatings of hot-dip galvanized steels

Silicate conversion coatings are prepared by immersing hot-dip galvanized (HDG) steel sheets in sodium silicate solutions with 5 wt.% SiO₂ and SiO₂:Na₂O molar ratio in the range of 1.00 to 4.00. The coating with better corrosion resistance is usually obtained in silicate solution with higher molar ratio (3.00-4.00). In this article, the distribution of types of silicate anion in solutions is investigated by transmission infrared spectroscopy (FT-IR) and nuclear magnetic resonance spectroscopy (²⁹Si NMR), and the surface of the silicate coating is analyzed using reflection infrared spectroscopy (RA-IR). Results indicate that the anion distribution is mainly monomer, linear and less cyclic anions at low molar ratios in very alkaline solutions. With increase in the molar ratio, small anions decrease, two- and three-dimensional anions increase. Accordingly, the silicate coating prepared in the solution with high molar ratio (≥ 3.00) contains a higher number of large silicate anions, and Si-O-Zn and Si-O-Si bonds of the coating increase, leading to the formation of more dense silicate coating and better corrosion resistance of the coating. Based on the above results and the potential-pH diagram of zinc, probable causes for differences in structure and compactness of silicate coatings, prepared by immersing HDG steels in sodium silicate solutions with different SiO₂:Na₂O molar ratio, are discussed.     

High-velocity oxyfuel thermal spray coatings for biomedical applications

Plasma spraying is used to produce most commercially available bioceramic coatings for dental implants; however, these coatings still contain some inadequacies. Two types of coatings produced by the high- velocity oxyfuel (HVOF) combustion spray process using commercially available hydroxyapatite (HA) and fluorapatite (FA) powders sprayed onto titanium were characterized to determine whether this relatively new coating process can be applied to bioceramic coatings. Diffuse reflectance Fourier transform infrared (FTIR) spectroscopy, x- ray diffraction (XRD), and scanning electron microscopy (SEM) were used to characterize the composition, microstructure, and morphology of the coatings. The XRD and FTIR techniques revealed an apatitic structure for both HA and FA coatings. However, XRD patterns indicated some loss in crystallinity of the coatings due to the spraying process. Results from FTIR showed a loss in the intensity of the OH^∼ and F^∼ groups due to HVOF spraying; the phosphate groups, however, were still present. Analysis by SEM showed a coating morphology similar to that obtained with plasma spraying, with complete coverage of the titanium substrate. Interfacial SEM studies revealed an excellent coating-to-substrate apposition. These results indicate that with further optimization the HVOF thermal spray process may offer another method for producing bioceramic coatings.     

钛基材上电化学沉积羟基磷灰石

通过电沉积法在经过阳极氧化的钛基材表面沉积磷酸钙盐涂层,再经碱热处理使磷酸钙涂层转变为羟基磷灰石涂层。扫描电镜(SEM)观察了阳极氧化后生成的TiO2纳米管的微观结构,以及生成的羟基磷灰石的形貌。X射线衍射仪(XRD)分析了涂层的相组成,同时测定了涂层与基体的结合强度。试验结果表明:电沉积涂层CaHPO4·2H2O经碱处理后转变为羟基磷灰石;电沉积添加双氧水与钛基材经过阳极氧化后使得涂层与基体结合强度有所提高。模拟体液浸泡试验表明涂层具有良好的生物活性。     

Structure and properties of selected (Cr–Al–N,TiC–C,Cr–B–N) nanostructured tribological coatings

The paper will present the state-of-art in the process, structure and properties of nanostructured multifunctional tribological coatings used in different industrial applications that require high hardness, toughness, wear resistance and thermal stability. The optimization of these coating systems by means of tailoring the structure (graded, superlattice and nanocomposite systems), composition optimization, and energetic ion bombardment from substrate bias voltage control to provide improved mechanical and tribological properties will be assessed for a range of coating systems, including nanocrystalline graded Cr_1−xAl_xN coatings, superlattice CrN/AlN coatings and nanocomposite Cr–B–N and TiC/a-C coatings. The results showed that the superlattice CrN/AlN coating exhibited a super hardness of 45 GPa when the bilayer period Λ was about 3.0 nm. Improved toughness and wear resistance have been achieved in the CrN/AlN multilayer and graded CrAlN coatings as compared to the homogeneous CrAlN coating. For the TiC/a-C coatings, increasing the substrate bias increased the hardness of TiC/a-C coatings up to 34 GPa (at −150 V) but also led to a decrease in the coating toughness and wear resistance. The TiC/a-C coating deposited at a −50 V bias voltage exhibited an optimized high hardness of 28 GPa, a low coefficient of friction of 0.19 and a wear rate of 2.37 × 10⁻⁷ mm³ N⁻¹ m⁻¹. The Cr–B–N coating system consists of nanocrystalline CrB₂ embedded in an amorphous BN phase when the N content is low. With an increase in the N content, a decrease in the CrB₂ phase and an increase in the amorphous BN phase were identified. The resulting structure changes led to both decreases in the hardness and wear resistance of Cr–B–N coatings.     

Protective Al-rich mullite coatings on Si- based ceramics against hot corrosion at 1200 °C

The hot-corrosion behavior of uncoated SiC, bulk mullite and CVD grown mullite coatings in contact with Na₂SO₄ were investigated at 1200 °C. The range of thermodynamic activity of Na₂O (10^− 4 to 10^− 6) simulated in this study makes the oxide very basic leading to high reaction rates with SiO_2. Uncoated SiC corroded severely, forming various Na₂O·SiO₂ compounds with a significant weight gain. Even though the thermodynamic activity of silica is reduced in mullite, several compounds in Na₂O·SiO₂·Al₂O₃ system were formed in case of bulk mullite. CVD based mullite coatings with high alumina content at the top surface of the coating, and therefore reduced SiO₂ activity, offered protection to the underlying SiC in corrosive environments. As predicted correctly by thermodynamic calculations, the trend in weight gain with the coated SiC samples followed the theoretically calculated SiO₂ activity in Al-rich mullite.     

Pulsed laser deposition of antifriction thin-film MoSex coatings at the different vacuum conditions

MoSe_x coatings were obtained by pulsed laser deposition in vacuum at the pressure of background Ar gas up to 10 Pa. The deposition temperature was 200 °С. The films were studied by means of X-ray diffraction, scanning and transmission electron spectroscopy, X-ray photoelectron spectroscopy, and Rutherford backscattering spectroscopy of helium ions. The tribological properties of thin-film coatings were investigated by pin-on-disk testing in air with 50% relative humidity. In addition, wear tracks were studied by micro-Raman spectroscopy. Chemical composition, structure, and tribological properties of the coatings were found to be sensitive to the presence of the inert gas. Thus, increasing the gas pressure from 10^− 4 to 10 Pa changes the chemical composition, so that the ratio of the atomic concentrations of Se and Mo (x = Se/Mo) increases from 1.5 to 2.4 in the principal deposition zone. The changing of the structure concerns the accumulation of distortions in the lattice of MoSe_x nano-crystals as increasing the distance between the basal planes and intensive formation of nano-sized inclusions of the amorphous phase and Mo nano-crystals in the volume of the coatings. At the optimal gas pressure (∼ 2 Pa), the composition of the coating was close to the stoichiometric one, and the layer adjacent to the substrate consisted of MoSe_x nano-crystals with the basal planes parallel to the substrate surface or oriented at small angles to the surface. The thickness of the oriented layer in such coatings was greater than the thickness of the similar layer in the coatings deposited in vacuum (10^− 4 Pa). The tribological properties of MoSe_x coatings deposited on substrates of stainless steel type 95 × 18 (18 at.% Cr) depend on the gas pressure. The friction coefficient in air decreases from 0.08 for deposition at the background pressure of 10^− 4 Pa to 0.04 for deposition at the optimal pressure. This change in the deposition conditions has only a marginal effect on the coating durability. Means to increase the durability are also considered.