Thermal barrier coatings (TBC) are used to reduce the heat flow into the metal below in order to reduce oxidation rates and to protect it from thermal softening and accelerated creep. The main application of these systems is in stationary gas and aircraft turbines. Modern TBC systems decrease the temperature load in the superalloys beneath by 200°C, or vice versa allow an increase in operating temperature in that range to improve the turbine efficiency. TBCs consist of a combination of a bond coat which can be either a MCrAlY overlay coating or a diffusion layer with a ceramic top coat. A schematic TBC system is given in Figure 12. It shows the temperature gradient and the typical configuration on a superalloy used, e.g., as a turbine blade.

**Figure 12.** Different layers of a thermal barrier system and the typical temperature gradient

All classical TBC systems, which have been developed and improved throughout the last 30 years, rely on a partially stabilized zirconia as ceramic top coat, which offers a very good combination of necessary properties [46]. Zirconia was chosen because of its low thermal conductivity in combination with a rather high thermal expansion coefficient closer to metals than that of most other ceramics [50]. In addition, it is compatible with the thermally grown alumina oxides (TGO) scales on top of the bond coat. One challenge is that ZrO is allotropic and shows three phase modifications (Figure 13).

**Figure 13.** Phase diagram of ZrO2-Y2O3 showing the allotropy of zirconia and the technically used range in which the tetragonal lattice modification remains stable

Especially the phase transformation from tetragonal to monoclinic at about 1170°C that goes along with a volume change of about 3-9% would induce detrimental cracks. This phase transformation can be suppressed by adding oxides of Yttirum, Cer, Magnesium, Niobium, or Calcium [51]. In Figure 13, the impact of yttrium addition on the phase formation is shown. In commercial technical systems, about 8 % YO1.5 is added to receive metastable partially stabilized tetragonal zirconia and suppress detrimental phase transformations. Another modification that is technically used is MgO-stabilized zirconia, which requires about 20-25 wt.% MgO. This zirconia slowly destabilizes above about 1000°C and can only be used for components of diesel engines and not in turbines. Any phase destabilization or an increased sintering behavior at higher temperatures determines the upper temperature limit of the application of zirconia, because it destroys the necessary porous structure and induces cracks. Such limitations trigger the investigation of other ceramics for even higher-temperature applications than the systems today allow. Especially several ziconates with a low thermal conductivity are looked at, of which the most promising candidate is gadolinium zirconate. Such coatings are developed as a two-layer ceramic system with classical zirconia under the novel ceramics [52]. Due to the fact that ceramics are prone to tensile strains, the microstructure has to be designed carefully in order to allow at least a certain strain tolerance. The ceramic layers today are either manufactured via atmospheric plasma spraying (APS) or electron beam physical vapor deposition (EB-PVD). In both cases, a certain strain tolerance is achieved by adjusting the microstructure [53].

combination of necessary properties [46]. Zirconia was chosen because of its low thermal conductivity in combination with a rather high thermal expansion coefficient closer to metals than that of most other ceramics [50]. In addition, it is compatible with the thermally grown alumina oxides (TGO) scales on top of the bond coat. One challenge is that ZrO is allotropic

**Figure 13.** Phase diagram of ZrO2-Y2O3 showing the allotropy of zirconia and the technically used range in which the

Especially the phase transformation from tetragonal to monoclinic at about 1170°C that goes along with a volume change of about 3-9% would induce detrimental cracks. This phase transformation can be suppressed by adding oxides of Yttirum, Cer, Magnesium, Niobium, or Calcium [51]. In Figure 13, the impact of yttrium addition on the phase formation is shown. In commercial technical systems, about 8 % YO1.5 is added to receive metastable partially stabilized tetragonal zirconia and suppress detrimental phase transformations. Another modification that is technically used is MgO-stabilized zirconia, which requires about 20-25 wt.% MgO. This zirconia slowly destabilizes above about 1000°C and can only be used for components of diesel engines and not in turbines. Any phase destabilization or an increased sintering behavior at higher temperatures determines the upper temperature limit of the

and shows three phase modifications (Figure 13).

292 Superalloys

tetragonal lattice modification remains stable

**Figure 14.** Comparison of TBC systems with APS-sprayed zirconia and EB-PVD zirconia top layers showing the differ‐ ent morphology of the ceramic coating on top of a sprayed MCrAlY bond coat on the left and a pack cementated bond coat on the right

In Figure 14, on the left the APS-sprayed microstructure is schematically shown. It possesses a pancake-like structure. The strain tolerance is created by a heavily intertwined network of fine cracks. This network separates the ceramic coating into "segmented flakes" providing a higher tolerance upon strain application through the temperature gradient or difference in thermal expansion to the material below. EB-PVD (Figure 13 on the right) coatings always exhibit the typical columnar structure. This method has the big advantage that, during the EB-PVD process, the crystals of the scales grow epitactically and perpendicular to the surface. The ceramic columns are separated from each other by small gaps, providing an exceptional tolerance to deleterious tensile strains parallel to the surface. These coatings are preferentially used for aircraft turbine blades, while for stationary turbine blades or aircraft nozzle parts often APS coatings are employed, which can be produced at lower cost. One drawback of EB-PVD zirconia top coats is that they are sensitive to calcium-magnesia-alumina silicates (CMAS) attack [54]. CMAS can derive from the use of turbines in sandy desert areas or when volcanic ash enters a turbine. The CMAS melt in the heat chamber and are deposited on the turbine blades. When they penetrate into the TBC, they cause failure and spallation. Other factors with an influence on the lifetime are hot corrosion mechanisms by sulfur, calcium, or vanadium deposits on the coatings that can reduce the lifetime [55], often by reacting with the stabilizers (e.g., yttrium), thereby destroying the resistance against phase transformation of the zirconia. When the ceramic scale remains intact, in service an alumina scale grows slowly under the zirconia ceramic. This thermally grown oxide scale (TGO) must not exceed about 3 µm in thickness to guarantee mechanical integrity and avoid spallation [56].

#### **5. Outlook**

By using diffusion coatings, overlay coatings, and ceramic top coats for high temperatures, the otherwise often very short lifetime of unprotected materials can be enhanced and makes processes and applications possible for which otherwise no material is available. At the same time, high-temperature processes have been constantly changing due to changes in fuel or operating conditions, and the thermal operation limit of superalloys has continuously increased over the years. In the future, even systems such as molybdenum-based alloys might become interesting with a thermal application potential well above the nickel- and cobaltbased superalloys of today [9]. Such developments induce also a strong driving force to further develop high-temperature coating systems in order to keep pace with such increased operating conditions, and to allow efficient and reliable operation of metallic high-temperature materials.

#### **Author details**

Mathias C. Galetz

Address all correspondence to<EMAIL_ADDRESS>
DECHEMA-Forschungsinstitut, High Temperature Materials, Frankfurt am Main, Germany

#### **References**

[1] R.C. Reed. *The Superalloys: Fundamentals and Applications*, Cambridge University Press; 2006, 283-335

often APS coatings are employed, which can be produced at lower cost. One drawback of EB-PVD zirconia top coats is that they are sensitive to calcium-magnesia-alumina silicates (CMAS) attack [54]. CMAS can derive from the use of turbines in sandy desert areas or when volcanic ash enters a turbine. The CMAS melt in the heat chamber and are deposited on the turbine blades. When they penetrate into the TBC, they cause failure and spallation. Other factors with an influence on the lifetime are hot corrosion mechanisms by sulfur, calcium, or vanadium deposits on the coatings that can reduce the lifetime [55], often by reacting with the stabilizers (e.g., yttrium), thereby destroying the resistance against phase transformation of the zirconia. When the ceramic scale remains intact, in service an alumina scale grows slowly under the zirconia ceramic. This thermally grown oxide scale (TGO) must not exceed about 3 µm in

By using diffusion coatings, overlay coatings, and ceramic top coats for high temperatures, the otherwise often very short lifetime of unprotected materials can be enhanced and makes processes and applications possible for which otherwise no material is available. At the same time, high-temperature processes have been constantly changing due to changes in fuel or operating conditions, and the thermal operation limit of superalloys has continuously increased over the years. In the future, even systems such as molybdenum-based alloys might become interesting with a thermal application potential well above the nickel- and cobaltbased superalloys of today [9]. Such developments induce also a strong driving force to further develop high-temperature coating systems in order to keep pace with such increased operating conditions, and to allow efficient and reliable operation of metallic high-temperature materials.

DECHEMA-Forschungsinstitut, High Temperature Materials, Frankfurt am Main, Germany

[1] R.C. Reed. *The Superalloys: Fundamentals and Applications*, Cambridge University

thickness to guarantee mechanical integrity and avoid spallation [56].

**5. Outlook**

294 Superalloys

**Author details**

Mathias C. Galetz

**References**

Press; 2006, 283-335

Address all correspondence to<EMAIL_ADDRESS>

[32] M.C. Galetz, X. Montero, H. Murakami. Novel processing in inert atmosphere and in air to manufacture high-activity slurry aluminide coatings modified by Pt and Pt/Ir, *Mater Corrosion*. 63 (2012) 921-928.

[16] C.E. Birchenall. Diffusion in Oxides: Assessment of Existing Data and Experimental Problems. Proceedings of the Symposium "Mass Transport in Oxides," October 1967.

[17] N. Birks, G.H. Meier, F.S. Pettit. High Temperature Corrosion. In: J.K. Tien, T. Caul‐ field (eds.). *Superalloys, Supercomposites and Superceramics*. Academic Press; 1989, p.

[18] A.S. Khanna. *Introduction to High Temperature Oxidation and Corrosion*, ASM Interna‐

[19] C. Xu, W. Gao. Pilling-Bedworth ratio for oxidation of alloys, *Mater Res Innov*. 3

[20] M. Schütze. Mechanical aspects of high-temperature oxidation, *Corr Sci*. 35 (1993)

[21] M. Schütze. Mechanical properties of oxide scales, *Oxidation Metals*. 44 (1995) 29-61.

[23] F.C. Kelley. Chromium Impregnation, *Metals Handbook*, American Society for Metals,

[24] P.A. Choquet, E.R. Naylor, R.A. Rapp. Simultaneous chromizing and aluminizing of

[25] F.D. Geib, R.A. Rapp. Simultaneous chromizing-aluminizing coating of low-alloy steels by a halide-activated, pack-cementation process, *Oxidation Metals*. 40 (1993)

[26] W. Da Costa, B. Gleeson, D.J. Young. Codeposited chromium-aluminide coatings II. Kinetics and morphology of coating growth, *J Electrochem Soc*. 141 (1994) 2690-2697.

[27] W. Da Costa, B. Gleeson, D.J. Young. Codeposited chromium-aluminide coatings I. Definition of the codeposition regimes, *J Electrochem Soc.* 141 (1994) 1464-1471.

[28] B. Gleeson, W.H. Cheung, W. Da Costa, D.J. Young. Co-deposited chromium-alumi‐ nide coatings and their high-temperature corrosion resistance. Proceedings of the 8th

[29] R. Bianco, R.A. Rapp. Pack cementation aluminide coatings on superalloys: codeposi‐

[30] Z.D. Xiang, P.K. Datta. Formation of Hf- and W-modified aluminide coatings on nickel-base superalloys by the pack cementation process, *Mater Sci Engin A*. 363

[31] B.A. Pint, J.A. Haynes, T.M. Besmann. Effect of Hf and Y alloy additions on alumi‐

Asian-Pacific Corrosion Control Conference, Bangkok. 2000, p. 43-48.

tion of Cr and reactive elements, *J Electrochem Soc*. 140 (1993) 1181-1190.

nide coating performance, *Surf Coatings Technol*. 204 (2010) 3287-3293.

[22] Allison H.B.C, L.A. Hawkins. *Gen Elect Rev*. 17 (1914) 947-951.

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#### **Chapter 13**

## **Properties of the Ultrathin Multilayer Ground State of Fe/Pd**

#### A.V. dos Santos

[46] A. Robert. Current status of thermal barrier coatings – An overview, *Surf Coatings*

[47] N. Czech, F. Schmitz, W. Stamm. Improvement of MCrAlY coatings by addition of

[48] D. Toma, W. Brandl, U. Köster. The characteristics of alumina scales formed on

[49] R.D. Jackson, M.P. Taylor, H.E. Evans, X.-H. Li. Oxidation study of an EB-PVD MCrAlY thermal barrier coating system, *Oxidation Metals*. 76 (2011) 259-271.

[50] X.Q. Cao, R. Vassen, D. Stoever. Ceramic materials for thermal barrier coatings, *J Eur*

[51] R.L. Jones. Some aspects of the hot corrosion of thermal barrier coatings, *J Therm*

[52] Y. Zhang, J. Malzbender, D.E. Mack, M.O. Jarligo, X. Cao, Q. Li, R. Vaßen, D. Stöver. Mechanical properties of zirconia composite ceramics, *Cera Int*. 39 (2013) 7595-7603.

[53] L. Singheiser, R. Steinbrech, W.J. Quadakkers, D. Clemens, B. Siebert. Thermal barri‐ er coatings for gas turbine applications – Failure mechanisms and life prediction. In: D. Coutsouradis (ed.). *Materials for Advanced Power Engineering*: Proceedings of the

6th Liege Conference, Part III. Kluwer Academic Publishers; 1998, p. 977-996.

[54] N. Chellah, M.-H. Vidal-Sétif, C. Petitjean, P.-J. Panteix, C. Rapin, and M. Vilasi. 8th International Symposium on High-Temperature Corrosion and Protection of Materi‐

[55] B. Bordenet, W. König, G. Witz, and H.-P. Bossmann. 8th International Symposium

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on High-Temperature Corrosion and Protection of Materials, 2012.

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rhenium, *Surf Coatings Technol*. 68/69 (1994) 17-21.

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/61289

#### **Abstract**

The technological evolution in the recent years allowed us to improve computers. Consequently, the numeric calculus with computational methods had a big progress. In theoretical physics that had a benefit with this technology, we can highlight the cal‐ culation of the solids' electronic structure. Using the first principles method, LMTO (Linear Muffin-Tin Orbital) with the ASA (Atomic Sphere Approximation) approxi‐ mation, we will study the band structure in the magnetic multilayers. The choice of these methods was based on two aspects: (a) The computer available to perform the job; a CRAY super computer that belongs to the Supercomputer National Center. Be‐ cause the LTMO method presents good vectorization, it allows us to perform calcula‐ tions with many atoms in the unitary cell, which would be too difficult with a smaller computer. (b) The fact that the LMTO method already presented good results in stud‐ ies like intermetallic alloys and of iron nitride substituted.

**Keywords:** Band structure, calculation of the first principles, Ultrathin Multilayer

### **1. Introduction**

#### **1.1. Calculation of band structure: A brief history**

In this section, a brief history of the calculation of band structure is provided, invoking the main methods used in this way. This does not intend to supplement, but to give the reader a good basis, especially for those who are not experts in the area, to understand the concepts used in this chapter. The understanding of the distribution of electrons in solids gives an appreciation of some of their physical properties. The most interesting properties of the new material industry, such as magnetization, come from the distribution of electrons in a solid. Theoretically, we should treat a system of several electrons distributed randomly in the

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

material. However, we cannot follow this infinite number, and we must use the Born-Oppenheimer approximation. We treated electrons and the nuclei as if they were separate from each other. So, we will calculate the energy of the ground state, depending on the position of the atomic nuclei. This implies that the basic problem is to calculate the steady states of the interacting electrons system moving in a periodic electrostatic field originated by the fixed nuclei i.e., to obtain the electronic structure of solids and consequently the structure of the same band. The identification of the electronic structure of solids involves considering an infinite number of the interacting fermions. But what does this mean? This leads us to solve the Schrödinger equation for an electron moving in an average field of other electrons over the field of the nuclei. Therefore, the field is determined by the distribution of the electronic charge, the adjustment for correlation, and the exchange effect. And it is usually calculated selfconsistently as we shall see later on.

In the recent years and with the advent of powerful computers, which are faster and more accurate. Furthermore, the appearance of linear methods [01- 02] for calculating the structure of the ordered solid bands. We can see that some of the main calculation methods had a breakthrough. It comes from a theoretical but also a practical point of view because there was a technological breakthrough in providing fast and accurate computers. We can then identify the physical properties with greater ease and certainty of outcomes [05-06]. An important work of Hohenberg-Kohn-Sham [07-08] provides the theoretical base pair to the other methods because they teach us to work with the mean-field theory using the electron density function and the energy of the ground state.

Other methods have also emerged with the DVM [10] ("Discrete Variational Method"), SPR-LMTO [11] ("Spin Polarized Relativistic Linear Muffin-Tin Orbital"), and the FLMTO [12] (TUB Linear Muffin-Tin Orbital "). Currently, the first purest strains of methods are employed to study the defects in the crystal lattice [13].

The calculation of the first principles band structure is a very important tool in the study of thin films and multilayers. Such systems are investigated by different techniques, such as Xray and Mossbauer duration or magnetization measurements [15-19].

In the modern calculation of the first principles applied to magnetic multilayers, Jarlborg and Freeman [21, 22]did some work that can be used as a primary reference. These calculations were motivated by the comments made by TJ Taler et al. [23] Ni / Cu alloys use ferromagnetic resonance. However, it should be considered that at that time, there was a difficulty in the experimental physics to build very thin layers (of the order 5-15 angstroms), which made the comparison between the calculations and the very difficult experience.

More recent studies using the first principles methods, such as performed by Blügel et al. [24] using the FLAPW ("Full Linear Augmented Plane Waves") that presented a good agreement with the experimental work carried out by Celinski et al. [19] In the case of magnetic multi‐ layers, in the recent years, there has been a promising advance in both the theoretical and experimental study, which can be checked in fairly comprehensive references on the subject [25]. However, it is necessary to continue the theoretical investigation of the magnetic prop‐ erties and the structural ultrafine multilayer because there are still questions to be answered about the charge transfer, magnetic moments, and the "stress" in the interface region, which causes changes in the density of the states. Another problem to be studied is the multilayer stability into the very thin structures. Properties, such as the hyperfine field and isomer shift of multilayer stability, are also a point of interest. In this work, we will hold extremely thin multilayer calculations worrying about the interface region between the materials that make up the multilayer.

material. However, we cannot follow this infinite number, and we must use the Born-Oppenheimer approximation. We treated electrons and the nuclei as if they were separate from each other. So, we will calculate the energy of the ground state, depending on the position of the atomic nuclei. This implies that the basic problem is to calculate the steady states of the interacting electrons system moving in a periodic electrostatic field originated by the fixed nuclei i.e., to obtain the electronic structure of solids and consequently the structure of the same band. The identification of the electronic structure of solids involves considering an infinite number of the interacting fermions. But what does this mean? This leads us to solve the Schrödinger equation for an electron moving in an average field of other electrons over the field of the nuclei. Therefore, the field is determined by the distribution of the electronic charge, the adjustment for correlation, and the exchange effect. And it is usually calculated self-

In the recent years and with the advent of powerful computers, which are faster and more accurate. Furthermore, the appearance of linear methods [01- 02] for calculating the structure of the ordered solid bands. We can see that some of the main calculation methods had a breakthrough. It comes from a theoretical but also a practical point of view because there was a technological breakthrough in providing fast and accurate computers. We can then identify the physical properties with greater ease and certainty of outcomes [05-06]. An important work of Hohenberg-Kohn-Sham [07-08] provides the theoretical base pair to the other methods because they teach us to work with the mean-field theory using the electron density function

Other methods have also emerged with the DVM [10] ("Discrete Variational Method"), SPR-LMTO [11] ("Spin Polarized Relativistic Linear Muffin-Tin Orbital"), and the FLMTO [12] (TUB Linear Muffin-Tin Orbital "). Currently, the first purest strains of methods are employed to

The calculation of the first principles band structure is a very important tool in the study of thin films and multilayers. Such systems are investigated by different techniques, such as X-

In the modern calculation of the first principles applied to magnetic multilayers, Jarlborg and Freeman [21, 22]did some work that can be used as a primary reference. These calculations were motivated by the comments made by TJ Taler et al. [23] Ni / Cu alloys use ferromagnetic resonance. However, it should be considered that at that time, there was a difficulty in the experimental physics to build very thin layers (of the order 5-15 angstroms), which made the

More recent studies using the first principles methods, such as performed by Blügel et al. [24] using the FLAPW ("Full Linear Augmented Plane Waves") that presented a good agreement with the experimental work carried out by Celinski et al. [19] In the case of magnetic multi‐ layers, in the recent years, there has been a promising advance in both the theoretical and experimental study, which can be checked in fairly comprehensive references on the subject [25]. However, it is necessary to continue the theoretical investigation of the magnetic prop‐ erties and the structural ultrafine multilayer because there are still questions to be answered

ray and Mossbauer duration or magnetization measurements [15-19].

comparison between the calculations and the very difficult experience.

consistently as we shall see later on.

300 Superalloys

and the energy of the ground state.

study the defects in the crystal lattice [13].

### **2. Introduction to calculate the electronic structure of ultrathin multilayers**

In this chapter, we will investigate the magnetic properties of ultrathin multilayers and hyperfine Iron and Palladium (Fe / Pd). The multilayer research is done in a few different stoichiometries in order to have a better understanding of their magnetic properties and behavior in the pressure. We begin by studying the electronic structure of the ultrathin multilayers of Fe and Pd, with a composition of 50% of each element. Below, we will investigate the behavior of two different systems: the dual system ultrathin multilayers of iron and a palladium (2 Fe / Pd), and the inverse system (2 Pd / Fe). This enables a comparison between these three different systems, which will show a clear change in the band structure of the systems when we change its stoichiometric structure. The theoretical research for both Fe / Pd ultrathin multilayers, as in the case of the 2 Fe / Pd and 2 Pd / Fe systems, is made using the LMTO, method of Andersen [01-02], and approximation of the atomic spheres (ASA). To study the electronic structure of multilayer systems, in the ferromagnetic case, we performed the calculations with a spin polarization and the parameterization of von Barth and Hedin [36] for energy correlation and exchange of an electron gas. In the self-consistent calculations for the non-magnetic case, we used the Hedin-Lundqvist potential [34]. This LMTO calculation does not include the spin-orbit interaction as it is very small and put term fixes combined [01]. To solve the equation, Schrödinguer used the s atomic orbitals that present the results. We then started with the calculations of the structure of the Fe / Pd ultrathin multilayers.

#### **3. Magnetic structure and electronics of the Fe/Pd ultrathin multilayers**

Calculations were performed using a structural model in which the bilayers grow in the direction (0,0,1) with a packaging sequence ABA type with tetragonal structure. The ratio of the axes was c / a = 1.41 with the Fe atoms occupying the position (0,0,0) and Pd atoms at (0,1/2,1/2). We chose the muffin tin-spheres involving atoms with the same radius for both the Fe and the Pd atoms. We performed self-consistent calculations for various lattice parameters through which we obtained the amount of the theoretical equilibrium. Figure 1 shows the total energy as a function of lattice parameter for the ferromagnetic and nonmagnetic states. We noted that the stability of the ferromagnetic state in relation to the non-magnetic state is good because the energy difference in the volume balance between the ferromagnetic state and the non-magnetic is ΔE = -22.98mRy by atom. The lattice parameter in the balance was calculated using a third-degree polynomial, which was the best fit of the plotted points for both the ferromagnetic state and the non-magnetic state. We obtained the lattice parameters a = 7,188u.a. for the ferromagnetic state and a = 7,044u.a. for the non-magnetic state. The value found for the ferromagnetic state is greater than the one found for the ordered alloy of 50% Fe and 50% Pd on self-consistent calculations. With the growth of the interatomic distances, Fe / Pd bilayers, and the consequent reduction of metal-metal interaction, such a system shows a slightly different magnetic behavior of the pure materials.

All tables are taken from the PhD thesis in reference 41. In table 1, we have the magnetic moment on the Fe site equal to 2,870µB in the Fe/Pd ultrathin multilayers. We noted that there was an increase in the magnetic moment on the website of Fe, compared to the pure iron that is 2,217µB [41].This is in agreement with the experimental work that measured the magnetic moments in the Fe / Pd multilayer [19].Here, we noticed a strong magnetic moment featuring a super magnetic alloy. In Table 1, it is easy to see that the greatest contribution of the electrons in the Fermi level N (EF) is the electrons d-down the Fe site due to the loads transferred to this site.

**Table 1.** Parameters calculated for the spin polarization ofFe / Pd bilayers using a self-consistent potential. Here, n is electron / spin; N in states / atom spin Ry; Nc states / Ry unit cell; y in mJ / molK2; EF Ry and ΔQ into electron.

#### **4. Density states of the Fe/Pd ultrathin multilayers**

The calculation of the density of states of d in the bilayers of the Fe and Pd sites are shown in Figures 2 and 3, respectively. We noted that there is a narrowing of the bands of the ultrathin multilayers compared to a league and the ordered FePd. Therefore, the metal-metal interaction causes a small change in the spin up and down states of the Fe and Pd metals. Figure 3 noted that the Pd site spin up and spin down states are busy unlike the one found for the DOS-d Fe site, which has many empty d spin-down states above the Fermi energy. In the Fe site, there are magnetic moments as the area below the Fermi energy is different between the up and down states, which is largely featuring a high magnetic moment in this place. This is in

ferromagnetic state and the non-magnetic state. We obtained the lattice parameters a = 7,188u.a. for the ferromagnetic state and a = 7,044u.a. for the non-magnetic state. The value found for the ferromagnetic state is greater than the one found for the ordered alloy of 50% Fe and 50% Pd on self-consistent calculations. With the growth of the interatomic distances, Fe / Pd bilayers, and the consequent reduction of metal-metal interaction, such a system shows a

All tables are taken from the PhD thesis in reference 41. In table 1, we have the magnetic moment on the Fe site equal to 2,870µB in the Fe/Pd ultrathin multilayers. We noted that there was an increase in the magnetic moment on the website of Fe, compared to the pure iron that is 2,217µB [41].This is in agreement with the experimental work that measured the magnetic moments in the Fe / Pd multilayer [19].Here, we noticed a strong magnetic moment featuring a super magnetic alloy. In Table 1, it is easy to see that the greatest contribution of the electrons in the Fermi level N (EF) is the electrons d-down the Fe site due to the loads transferred to this

**Up Down Up - Down Up i Down Up-Down**

**Table 1.** Parameters calculated for the spin polarization ofFe / Pd bilayers using a self-consistent potential. Here, n is electron / spin; N in states / atom spin Ry; Nc states / Ry unit cell; y in mJ / molK2; EF Ry and ΔQ into electron.

The calculation of the density of states of d in the bilayers of the Fe and Pd sites are shown in Figures 2 and 3, respectively. We noted that there is a narrowing of the bands of the ultrathin multilayers compared to a league and the ordered FePd. Therefore, the metal-metal interaction causes a small change in the spin up and down states of the Fe and Pd metals. Figure 3 noted that the Pd site spin up and spin down states are busy unlike the one found for the DOS-d Fe site, which has many empty d spin-down states above the Fermi energy. In the Fe site, there are magnetic moments as the area below the Fermi energy is different between the up and down states, which is largely featuring a high magnetic moment in this place. This is in

N 5.4686 2.5986 2.8700 5.1563 4.7759 0.3804 ns 0.3318 0.3275 0.0043 0.2824 0.2997 -0.0173 np 0.3718 0.3707 0.0011 0.3048 0.3326 -0.0278 Nd 4.7650 1.9004 2.8646 4.5691 4.1436 0.4255

slightly different magnetic behavior of the pure materials.

**Fe Pd**

N(EF) 1.8851 13.8763 1.4616 3.5053

ΔQ 0.06744 -0.06744

**4. Density states of the Fe/Pd ultrathin multilayers**

Nt(EF) 15.7614 4.9669 NC(ef) 20.7283 v 3.5924

EF 0.6532

site.

302 Superalloys

**Figure 1.** Total energy as a function of lattice parameters, the Fe / Pd bilayer. We did not present the error because they are smaller than the points.

agreement with the results in Table 1. The Fe-Pd interaction decreases the occupation of the d-down states in the ultrathin multilayers compared to the Fe-Pd and Fe nitrides 4PdN.

**Figure 2.** Density of states designed to electrons with spin up and down for d in the Fe / Pd bilayer in the Fe site.

**Figure 3.** Density of states designed to electrons with spin up and down states for d in the Fe / Pd bilayer in the Pd site.

### **5. Pressure influence on the magnetic properties of the Fe/Pd ultrathin multilayers**

Now, we investigate the behavior of the magnetic properties against pressure. The pressure effect is simulated by reducing the spacing of the lattice. We perform these self-consistent calculations for some lattice parameters of the Fe / Pd ultrathin multilayers, but we keep the tetragonal structure unchanged. The results of these calculations are shown in Figure 4. In this figure, we seethe variation of the magnetic moment on the site of the Fe and Pd due to the lattice parameter. In the Fe site, the magnetic moment decreases until the lattice parameter which sharply drops to zero. In the Pd site, the magnetic moment remains constant until it also falls abruptly to zero in the same lattice parameter a = 6,321ua. We can associate this lattice parameter limit value at a certain critical pressure. This type of behavior also happens in other leagues, known as Invar [56,57,60,61] alloys. Similar behavior of the magnetic moment has been obtained for iron carbides in ferromagnetic calculations [61]. We have published data from experimental studies on this fact in ultrathin multilayers of intermetallic materials systems.

**Figure 4.** Magnetic moment due to the lattice parameter for the Fe / Pd, Fe, and Pd monolayers on site.

**Figure 3.** Density of states designed to electrons with spin up and down states for d in the Fe / Pd bilayer in the Pd site.

**5. Pressure influence on the magnetic properties of the Fe/Pd ultrathin**

Now, we investigate the behavior of the magnetic properties against pressure. The pressure effect is simulated by reducing the spacing of the lattice. We perform these self-consistent calculations for some lattice parameters of the Fe / Pd ultrathin multilayers, but we keep the tetragonal structure unchanged. The results of these calculations are shown in Figure 4. In this figure, we seethe variation of the magnetic moment on the site of the Fe and Pd due to the lattice parameter. In the Fe site, the magnetic moment decreases until the lattice parameter which sharply drops to zero. In the Pd site, the magnetic moment remains constant until it also falls abruptly to zero in the same lattice parameter a = 6,321ua. We can associate this lattice parameter limit value at a certain critical pressure. This type of behavior also happens in other leagues, known as Invar [56,57,60,61] alloys. Similar behavior of the magnetic moment has been obtained for iron carbides in ferromagnetic calculations [61]. We have published data from experimental studies on this fact in ultrathin multilayers of intermetallic materials

**multilayers**

304 Superalloys

systems.

**Table 2.** Parameters calculated for spin polarization potential monolayers using self-consistent calculations. Here, n is in electron / spin; N in states / atom spin Ry; Nc states / Ry unit cell, y in mJ / molK2, EF Ry and ΔQ electrons. We obtain the critical pressure Pc = 109Kbar.

This result is of the order of the critical pressure of league ordered Fe-Pd [55], and also comparable to the theoretical and experimental results for Fe4Ni [59], Fe4PdN [57], and Fe4SnN [60], which are made known to have the Invar behavior type and magnetic collapse with pressure feature. The issue of electronic redistribution due to this transition from the ferro‐ magnetic state to the non-magnetic state will be discussed. To do so, we focus our attention in table 2, which shows some parameters obtained through the self-consistent calculation of the lattice parameter of the magnetic collapse shown in Figure 4. A comparison of Tables 1 and 2 show a large increase in the charge transfer to the site Fe. This excess charge will populate the state d spin down the Fe site, and also, there is an inversion of spin up electrons in the electron spin down that will cause the magnetic collapse. The results presented in Table 2 show that for high pressures, there is a redistribution. But this is not merely an average of the spin up and down, which existed before the occupation in Table 1. This redistribution is a consequence of the strong metal-metal interactions in front of the reduction of the lattice spacing. On the other hand, Table 2 shows an increase in the specific heat coefficient y. This value corresponds to a large number of states at the Fermi energy for the non-magnetic state. This growth occurs mainly in the up states, both in the Fe and the Pd sites. 7 the critical pressure Pc = 109Kbar. This result is of the order of the critical pressure of league ordered Fe-Pd [55], and also comparable to the theoretical and experimental results for Fe4Ni [59], Fe4PdN [57], and Fe4SnN [60], which are made known to have the Invar behavior type and magnetic collapse with pressure feature. The issue of electronic redistribution due to this transition from the ferromagnetic state to the non-magnetic state will be discussed. To do so, we focus our attention in table 2, which shows some parameters obtained through the self-consistent calculation of the lattice parameter of the magnetic collapse shown in Figure 4. A comparison of Tables 1 and 2 show a large increase in the charge transfer to the site Fe. This excess charge will populate the state d spin down the Fe site, and also, there is an inversion of spin up electrons in the electron spin down that will cause the magnetic collapse. The results presented in Table 2 show that for high pressures, there is a redistribution. But this is not merely an average of the spin up and down, which existed before the occupation in Table 1. This redistribution is a consequence of the strong metal-metal interactions in front of the reduction of the lattice spacing. On the other hand, Table 2 shows an increase in the specific heat coefficient y. This value corresponds to a large number of states at the Fermi energy for the non-

magnetic state. This growth occurs mainly in the up states, both in the Fe and the Pd sites.

presented. We noted that there was a widening of the band - d of the non-magnetic state in relation to the ferromagnetic state. Also, the DOS moves as a whole to higher energies, and the Fermi energy increases. **Figure 5.** a -The DOS in the Fe site in the non-magnetic state (dotted lines) and in the ferromagnetic state (solid lines) are presented. b–The density of states designed for electrons with spin up and down states for d in the Fe / Pd bilayers: (a) at the Fe site in balance volume (solid lines), the magnetic collapse (dotted lines) and (b) Pd site in volume balance (solid lines), the magnetic collapse (dashed lines).

Figure 5a -The DOS in the Fe site in the non-magnetic state (dotted lines) and in the ferromagnetic state (solid lines) are

In Figure 5b,we see the DOS in the non-magnetic (dashed lines) and ferromagnetic (solid

line) states to the site of Pd. This site also promotes the DOS to a higher energy. Even in the magnetic collapse, some free states remain above the Fermi energy at the Fe site. Figure 5b–The density of states designed for electrons with spin up and down states for d in the Fe / Pd bilayers: (a) at We noted that there was a widening of the band - d of the non-magnetic state in relation to the ferromagnetic state. Also, the DOS moves as a whole to higher energies, and the Fermi energy increases.

In Figure 5b,we see the DOS in the non-magnetic (dashed lines) and ferromagnetic (solid line) states to the site of Pd. This site also promotes the DOS to a higher energy. Even in the magnetic collapse, some free states remain above the Fermi energy at the Fe site. 8

Figure 6 -The unit cell of 2Fe / 2 Pd and Pd / Fe ultrathin multilayers. **Figure 6.** The unit cell of 2Fe / 2 Pd and Pd / Fe ultrathin multilayers.

This result is of the order of the critical pressure of league ordered Fe-Pd [55], and also comparable to the theoretical and experimental results for Fe4Ni [59], Fe4PdN [57], and Fe4SnN [60], which are made known to have the Invar behavior type and magnetic collapse with pressure feature. The issue of electronic redistribution due to this transition from the ferro‐ magnetic state to the non-magnetic state will be discussed. To do so, we focus our attention in table 2, which shows some parameters obtained through the self-consistent calculation of the lattice parameter of the magnetic collapse shown in Figure 4. A comparison of Tables 1 and 2 show a large increase in the charge transfer to the site Fe. This excess charge will populate the state d spin down the Fe site, and also, there is an inversion of spin up electrons in the electron spin down that will cause the magnetic collapse. The results presented in Table 2 show that for high pressures, there is a redistribution. But this is not merely an average of the spin up and down, which existed before the occupation in Table 1. This redistribution is a consequence of the strong metal-metal interactions in front of the reduction of the lattice spacing. On the other hand, Table 2 shows an increase in the specific heat coefficient y. This value corresponds to a large number of states at the Fermi energy for the non-magnetic state. This growth occurs

This result is of the order of the critical pressure of league ordered Fe-Pd [55], and also comparable to the theoretical and experimental results for Fe4Ni [59], Fe4PdN [57], and Fe4SnN [60], which are made known to have the Invar behavior type and magnetic collapse with pressure feature. The issue of electronic redistribution due to this transition from the ferromagnetic state to the non-magnetic state will be discussed. To do so, we focus our attention in table 2, which shows some parameters obtained through the self-consistent calculation of the lattice parameter of the magnetic collapse shown in Figure 4. A comparison of Tables 1 and 2 show a large increase in the charge transfer to the site Fe. This excess charge will populate the state d spin down the Fe site, and also, there is an inversion of spin up electrons in the electron spin down that will cause the magnetic collapse. The results presented in Table 2 show that for high pressures, there is a redistribution. But this is not merely an average of the spin up and down, which existed before the occupation in Table 1. This redistribution is a consequence of the strong metal-metal interactions in front of the reduction of the lattice spacing. On the other hand, Table 2 shows an increase in the specific heat coefficient y. This value corresponds to a large number of states at the Fermi energy for the nonmagnetic state. This growth occurs mainly in the up states, both in the Fe and the Pd sites.

 (a) (b) Figure 5a -The DOS in the Fe site in the non-magnetic state (dotted lines) and in the ferromagnetic state (solid lines) are

**Figure 5.** a -The DOS in the Fe site in the non-magnetic state (dotted lines) and in the ferromagnetic state (solid lines) are presented. b–The density of states designed for electrons with spin up and down states for d in the Fe / Pd bilayers: (a) at the Fe site in balance volume (solid lines), the magnetic collapse (dotted lines) and (b) Pd site in volume balance

We noted that there was a widening of the band - d of the non-magnetic state in relation to the ferromagnetic state. Also, the DOS moves as a whole to higher energies, and the Fermi energy

magnetic collapse, some free states remain above the Fermi energy at the Fe site.

We noted that there was a widening of the band - d of the non-magnetic state in relation to the ferromagnetic state. Also, the DOS moves as a whole to higher energies, and the Fermi energy

In Figure 5b,we see the DOS in the non-magnetic (dashed lines) and ferromagnetic (solid line) states to the site of Pd. This site also promotes the DOS to a higher energy. Even in the

Figure 5b–The density of states designed for electrons with spin up and down states for d in the Fe / Pd bilayers: (a) at

7

mainly in the up states, both in the Fe and the Pd sites.

the critical pressure Pc = 109Kbar.

306 Superalloys

presented.

increases.

increases.

(solid lines), the magnetic collapse (dashed lines).

#### In the rest of this chapter, we will study the 2 Fe/Pd and 2 Pd/Fe ultrathin multilayers. To accomplish the calculation of the band structure of the ultrathin multilayers of Fe-Pd, we introduced some modifications to **6. The electronic structure of 2Fe/Pd and 2Pd/Fe ultrathin multilayers**

(0, 0, 0), (0, 1/2, 1/2) to the Fe atoms as bilayers in Figure 6. The structure used herein is a tetragonal structure of c / a = 2.23. With this structure, we note that all Fe atoms have the same vicinity in the 2 Fe / Pd system. The above two systems used 1500 points in the power window and 1330 points k in the reciprocal space (we changed the number of points because we changed the crystal lattice). In the rest of this chapter, we will present the results of the calculations of the electronic structure and some comparisons between the systems. In the magnetic properties of the multilayer 2 Fe / Pd and 2 Pd / Fe, we performed the calculations of the total energy for some lattice parameters. With these calculations, we obtained the volume In the rest of this chapter, we will study the 2 Fe/Pd and 2 Pd/Fe ultrathin multilayers. To accomplish the calculation of the band structure of the ultrathin multilayers of Fe-Pd, we introduced some modifications to the unit cell structure so we can have a better description of the actual physical system (1/2, 1/2, 0) for Pd and (0, 0, 0), (0, 1/2, 1/2) to the Fe atoms as bilayers in Figure 6. The structure used herein is a tetragonal structure of c / a = 2.23.

**6 THE ELECTRONIC STRUCTURE OF 2 FE / PD AND 2 PD / FE ULTRATHIN MULTILAYERS**

the unit cell structure so we can have a better description of the actual physical system (1/2, 1/2, 0) for Pd and

of theoretical equilibrium for both systems. Figure 7a shows the total energy states for the non-magnetic (NM) and ferromagnetic (FM) states of 2 Pd / Fe, depending on the lattice parameters. We used a threedegree polynomial to get the best fit curve. Figure 7b has the total energy as a function of the lattice parameter for the non-magnetic states (NM) and ferromagnetic (FM) states for the 2 Fe / Pd system. We have noted that in both systems, there is a good stability of the ferromagnetic state in relation to the non-magnetic state. The energy of the difference in the volume balance between the ferromagnetic and non-magnetic state is ΔE = -13mRy by atom for the 2 Fe / Pd system. While in the 2 Pd / Fe system, the difference is even greater: ΔE = -20,7mRy by atom. Compared with the With this structure, we note that all Fe atoms have the same vicinity in the 2 Fe / Pd system. The above two systems used 1500 points in the power window and 1330 points k in the reciprocal space (we changed the number of points because we changed the crystal lattice). In the rest of this chapter, we will present the results of the calculations of the electronic structure and some comparisons between the systems. In the magnetic properties of the multilayer 2 Fe / Pd and 2 Pd / Fe, we performed the calculations of the total energy for some lattice parameters. With these calculations, we obtained the volume of theoretical equilibrium for both systems. Figure 7a shows the total energy states for the non-magnetic (NM) and ferro‐ magnetic (FM) states of 2 Pd / Fe, depending on the lattice parameters. We used a three-degree polynomial to get the best fit curve. Figure 7b has the total energy as a function of the lattice parameter for the non-magnetic states (NM) and ferromagnetic (FM) states for the 2 Fe / Pd system.

We have noted that in both systems, there is a good stability of the ferromagnetic state in relation to the non-magnetic state. The energy of the difference in the volume balance between the ferromagnetic and non-magnetic state is ΔE = -13mRy by atom for the 2 Fe / Pd system. While in the 2 Pd / Fe system, the difference is even greater: ΔE = -20,7mRy by atom. Compared with the bilayer of Fe / Pd, we noted that they are more stable, since ΔE is even higher than the two systems: 2Fe / 2 Pd and Pd / Fe. These differences will be further explored when we discuss the influence of pressure on the magnetic properties.

The minimum total energy shows that the lattice parameter in the balance is 7,069ua for the ferromagnetic state and 6,890u.a for the non-magnetic state in the 2 Fe / Pd system. The lattice parameter for the ferromagnetic state was equal to 7,297uaand 7,209ua for the non-magnetic state. Thus, it is evident that if we put more layers of Pd, there will be an expansion of the Fe-Pd system, since the Pd atom is larger than the Fe atom. The magnetic moment calculated for the Fe site for both systems is high. We noted that the three systems studied in this chapter have magnetic moments on the site Fe, greater than the pure Fe, which is 2,217 µB. This is already known in the literature. Furthermore, this result agrees with the experimental [19] and theoretical studies performed by Richter et al. [29] to calculate the magnetic moment of Fe in place relative to the thickness of the multilayer. This suggests that increasing the number of Pd layers in the system increases the magnetic moment on the site Fe. Now, if we compare the magnetic moment on the Fe site with certain ordered alloys, we can note that it is larger and even greater than in nitrides [34,35,36,38,41]. In the Pd site, the magnetic moment has a different behavior from that found on the website of Fe, and the largest magnetic moment is in the 2 Fe / Pd system.

**Table 3.** Parameters calculated for the spin polarization in ultrathin multilayers volume balance of 2 Pd / Fe (in parentheses) and 2 Fe / Pd (outside the parentheses) using a self-consistent potential. Here, n is electron / spin; N in states / atom spin Ry; Nc states / Ry unit cell; y in mJ / molK2; EF Ry and ΔQ into electrons.

9

We have noted that in both systems, there is a good stability of the ferromagnetic state in relation to the non-magnetic state. The energy of the difference in the volume balance between the ferromagnetic and non-magnetic state is ΔE = -13mRy by atom for the 2 Fe / Pd system. While in the 2 Pd / Fe system, the difference is even greater: ΔE = -20,7mRy by atom. Compared with the bilayer of Fe / Pd, we noted that they are more stable, since ΔE is even higher than the two systems: 2Fe / 2 Pd and Pd / Fe. These differences will be further explored when we

The minimum total energy shows that the lattice parameter in the balance is 7,069ua for the ferromagnetic state and 6,890u.a for the non-magnetic state in the 2 Fe / Pd system. The lattice parameter for the ferromagnetic state was equal to 7,297uaand 7,209ua for the non-magnetic state. Thus, it is evident that if we put more layers of Pd, there will be an expansion of the Fe-Pd system, since the Pd atom is larger than the Fe atom. The magnetic moment calculated for the Fe site for both systems is high. We noted that the three systems studied in this chapter have magnetic moments on the site Fe, greater than the pure Fe, which is 2,217 µB. This is already known in the literature. Furthermore, this result agrees with the experimental [19] and theoretical studies performed by Richter et al. [29] to calculate the magnetic moment of Fe in place relative to the thickness of the multilayer. This suggests that increasing the number of Pd layers in the system increases the magnetic moment on the site Fe. Now, if we compare the magnetic moment on the Fe site with certain ordered alloys, we can note that it is larger and even greater than in nitrides [34,35,36,38,41]. In the Pd site, the magnetic moment has a different behavior from that found on the website of Fe, and the largest magnetic moment is in the 2

**Up Down Up-Down Up Down i Up-Down**

O.OI21)

n 5.3700(5.5074) 2.6704(2.5247) 2.7096(2.9697) 5.1263(5.1523) 4.7863(4.8312) 0.3400(0.3211) ns 0.3268(0.3327) 0.3279(0.3327) -0.00 11 (-.0043) 0.2834(0.2828) 0.2991(0.2949) -O.OI57(-

np 0.3668(0.3676) 0.3756(0.3676) -0.0088(-.0022) 0.3097(0.2995) 0.3291(0.2995) -0.0194(-0.0091) Nd 4.6864(4.8071) 1.9669(1.8309) 2.7195(2.9762) 4.5332(4.5700) 4.1581(1.5197) 0.3751(0.3423)

**Table 3.** Parameters calculated for the spin polarization in ultrathin multilayers volume balance of 2 Pd / Fe (in parentheses) and 2 Fe / Pd (outside the parentheses) using a self-consistent potential. Here, n is electron / spin; N in

N(EF) 1.7855(1.2308) 12.6785(18.5056) 4.5332(4.9316) 1.9580(1.5197)

states / atom spin Ry; Nc states / Ry unit cell; y in mJ / molK2; EF Ry and ΔQ into electrons.

discuss the influence of pressure on the magnetic properties.

**Fe Pd**

NT(EF) 14.4640(19.7364) 6.4913(6.4513) Nr(EF) 45.9223(27.3666) Y 7.9587(4.7428) EF 0.6789(0.6109) ΔQ 0.0453(0.0351) -0.0892(-0.0161)

Fe / Pd system.

308 Superalloys

Figure 7 - Total energy as a function of lattice parameters, the Fe / Pd bilayer. We did not present the error because they are smaller than the points. **Figure 7.** Total energy as a function of lattice parameters, the Fe / Pd bilayer. We did not present the error because they are smaller than the points. According to the energy parameter of the lattice ultrathin multilayers: (a) 2 Fe / Pd and (b) 2 Pd / Fe.

Table 3 -The specific heat coefficient, which is proportional to the total density of states and the Fermi level of the unit cell. We note that the 2Fe /Pd systems and 2 Pd / Fe is greater than that of the Fe / Pd bilayer where we now have a larger number of sites in the unit cell. The 2 Fe / Pd system is greater than 2 Pd / Fe, because the density of the states at the Fermi level is higher at the site of Fe in the Pd site. The Fermi energy is higher in the 2 Fe / Pd system. This shows that there is an increase in the Fermi energy when we increase the number of layers of Fe.

### **7. State density of the 2Fe/Pd and 2Pd/Fe ultrathin multilayers**

The density of states for the electrons Fe and Pd multilayers are shown in Figures 8a, 8b, 9a, and 10b. Figures 8a and 8b show the DOS to the 2Fe / Pd system to the site of Fe (8a) and the site of Pd (8b) that spin in both directions, which is the balancing lattice parameter. In these figures, we noted initially that the Pd site states are all busy for both spin directions, but there are many empty down spin states in the Fe site. It is found in Figures 9a and 9b that DOS-d spin both directions of the equilibrium lattice parameter of the 2 Pd / Fe. In this system, we also found that for the Pd site, there are virtually no empty states above the Fermi energy, but in the Fe site, there are still several unoccupied states above the Fermi energy, as in the 2 Fe / Pd system.

Here, we find a change in the DOS form of a system to another. In the Pd site, there is a reversal peak height of up states in the 2 Pd/ Fe system with the next largest peaks at the Fermi energy. Also, a peak appears on the Pd site in the spin down states in the 2 Fe / Pd system where the area of energy is between 0,4Ry and 0,6Ry. This reflects the interaction with the states of Fe d down because if we look at the DOS on the Fe site in Figure 5.8a, we see that there is a peak in this energy range. Furthermore, this shows the influence of the two Fe sites on Pd since this interaction does not happen in the 2 Pd / Fe system.

#### **8. Hyperfine parameters**

It is evident that the Mossbauer Effect is an effective ferment when dealing with the magnetic structure of the nuclei and their interaction with the neighborhood. The hyperfine property related only to the site of the iron atom, the hyperfine field (in kg), and isomer shift (in mm / s) will be theoretically discussed. Initially, we propose that the magnetic field in the core is given by H = Hext + HFC + Horb + Hdip.

So, we understand that: Hext is the external applied magnetic field at the nucleus; and HFC is the hyperfine interaction (or Fermi contact term), which comes from an unbalanced spin density of the s-electrons can see these settings in references 30 and 31 with details.

To find the Fermi contact term we must use the following equation: gN is the nuclear gyro‐ magnetic ratio and y- (0) is the wave function at the nucleus for the spin-up and spin-down selectrons.

Properties of the Ultrathin Multilayer Ground State of Fe/Pd http://dx.doi.org/10.5772/61289 311

Table 3 -The specific heat coefficient, which is proportional to the total density of states and the Fermi level of the unit cell. We note that the 2Fe /Pd systems and 2 Pd / Fe is greater than that of the Fe / Pd bilayer where we now have a larger number of sites in the unit cell. The 2 Fe / Pd system is greater than 2 Pd / Fe, because the density of the states at the Fermi level is higher at the site of Fe in the Pd site. The Fermi energy is higher in the 2 Fe / Pd system. This shows that there is an increase in the Fermi energy when we

The density of states for the electrons Fe and Pd multilayers are shown in Figures 8a, 8b, 9a, and 10b. Figures 8a and 8b show the DOS to the 2Fe / Pd system to the site of Fe (8a) and the site of Pd (8b) that spin in both directions, which is the balancing lattice parameter. In these figures, we noted initially that the Pd site states are all busy for both spin directions, but there are many empty down spin states in the Fe site. It is found in Figures 9a and 9b that DOS-d spin both directions of the equilibrium lattice parameter of the 2 Pd / Fe. In this system, we also found that for the Pd site, there are virtually no empty states above the Fermi energy, but in the Fe site, there are still several unoccupied states above the Fermi energy, as in the 2 Fe /

Here, we find a change in the DOS form of a system to another. In the Pd site, there is a reversal peak height of up states in the 2 Pd/ Fe system with the next largest peaks at the Fermi energy. Also, a peak appears on the Pd site in the spin down states in the 2 Fe / Pd system where the area of energy is between 0,4Ry and 0,6Ry. This reflects the interaction with the states of Fe d down because if we look at the DOS on the Fe site in Figure 5.8a, we see that there is a peak in this energy range. Furthermore, this shows the influence of the two Fe sites on Pd since this

It is evident that the Mossbauer Effect is an effective ferment when dealing with the magnetic structure of the nuclei and their interaction with the neighborhood. The hyperfine property related only to the site of the iron atom, the hyperfine field (in kg), and isomer shift (in mm / s) will be theoretically discussed. Initially, we propose that the magnetic field in the core is

So, we understand that: Hext is the external applied magnetic field at the nucleus; and HFC is the hyperfine interaction (or Fermi contact term), which comes from an unbalanced spin

To find the Fermi contact term we must use the following equation: gN is the nuclear gyro‐ magnetic ratio and y- (0) is the wave function at the nucleus for the spin-up and spin-down s-

density of the s-electrons can see these settings in references 30 and 31 with details.

**7. State density of the 2Fe/Pd and 2Pd/Fe ultrathin multilayers**

increase the number of layers of Fe.

interaction does not happen in the 2 Pd / Fe system.

**8. Hyperfine parameters**

given by H = Hext + HFC + Horb + Hdip.

Pd system.

310 Superalloys

electrons.

**Figure 8.** Density of states designed with spin up and down, to the states in d 2FePd / Pd ultrathin monolayers: (a) at the site of Fe and (b) the Pd site.

Another property to be calculated is the isomer shift of a given Beheerder atom comparing the nucleus electronic density ρ (0) with a reference nuclei: α-Fe (BCC). In this case, Fe BCC with lattice parameters of a = 2865A °. Thus, the isomer shift is calculated by the Equation 6: where ρa = Density of electrons in the nuclei; ρs = Density of electrons in the reference nuclei; and α = constant of proportionality.

To understand the electron density in the nucleus, the isomer shift of a given atom is calculated comparing the nucleus electronic density *ρ* (0) with reference nuclei: α-Fe (BCC) in this case. The Fe BCC with lattice parameters of *a*=2865A°.Thus, the isomer shift is calculated by the Eq. 6: *IS* = *ρ<sup>a</sup>* (0)−*ρ<sup>s</sup>* (0) *α*, where: ρ<sup>a</sup> = Density of electrons in the nuclei; ρ<sup>s</sup> = Density of electrons in the reference nuclei; andα = constant of proportionality.

In Table 4, we have the values of the HFC and IS systems for 2 Fe / Pd and 2 Pd / Fe. In this table, it is clear that if we change the neighborhood Fe site, there is a major change in the Fermi contact field. When we have2 Fe / Pd multilayer, we have the lowest Fermi contact term of the three systems, 210 kOe, which is less than the experimental value 330kOe of pure Fe. In the Fe bilayer / Pd multilayer and 2 Pd / Fe, we found the value higher than the experimental pure Fe. In the 2 Fe / Pd system, the site Fe receives loads of the Pd site, which will narrow the gap between the s electrons up and down causing a reduction in the Fermi contact field that is 210

**Figure 9.** States density designed to electrons with spin up and down states for d in the 2 Pd / Fe multilayer: (a) the site Fe and (b) the Pd site.

kOe. When we have two layers of Pd, the charge transfer to the s states increases the difference between the electrons up and down, increasing the Fermi contact field (see table 4). This behavior of the Fermi contact field is consistent with the magnetic moment of the behavior on the site Fe, which confirms the empirical relationship of the magnetic moment that is propor‐ tional to the hyperfine field. Table 4 also shows the values calculated for the IS, which is greater for the bilayer Fe / Pd. The above results can be used for comparison with the experimental results of M. Li et al. [68,69], which show that when a Pd layer is placed in the 8Angstron, the Fermi contact field increased from 330 kOe to 335 kOe, which agrees qualitatively with our calculations. The differences are due to the calculations simulated at zero Kelvin temperature.

**Table 4.** Hyperfine parameters calculated for 2 Pd / Fe and 2 Fe / Pd using spin polarization. Fermi contact term (HPC) in kOe, isomeric deviation (S) in mm / s.

### **9. Influence of pressure on the magnetic properties and structure of the 2Fe/ Pd and 2Pd / feelectronic ultrathin multilayers**

In this section, we analyze the behavior of the magnetic properties and electronic structure of the 2 Fe / Pd and 2 Pd / Fe multilayer with pressure. We do this by varying the lattice parameter, which simulates a variation in pressure. Every self-consistent calculation submitted, the lattice parameter shows a variation of 2%. In Figures 10a and 10b, the magnetization shows as a function of the lattice parameter. Figure 10a shows the magnetization in the Fe site for both systems. We have noted that there is a different behavior between the two systems against the pressure. For the 2Fe / Pd system, there is an abrupt decrease in the magnetic moment of Fe, leading to the collapse of the magnetic moment. This transition from a ferromagnetic state to the non-magnetic state was obtained for the Fe / Pd bilayers [42].This behavior is observed experimentally in nitride [33] and in accordance with the calculations performed by bands [46]. In the case of 2 Pd / Fe, the pressure is not enough for a drop to zero in the magnetic moment. This behavior was observed in the alloys ordered Fe-Pd, depending on the Pd concentration in the league [34]. Figure 10b shows a similar behavior in the Pd site. However, in the 2 Fe / Pd system, there is a small increase of pressure in the magnetic moment in the Pd sites, but this is not very big. The 2 Pd / Fe system shows a different behavior: the magnetic moment does not drop to zero with increasing pressure and leaves a significant magnetization, as Fe-Pd alloys with the same proportions of Fe and Pd [32].

In figures 7a and 7b, we see the graph of the total energy as a function of the lattice parameter for the ferromagnetic and nonmagnetic states. From these data, we obtain the critical pressure of 92 kbar for the 2Fe / Pt system and 277 kbar for 2 Pd / Fe. Earlier in this chapter, we obtained a PC bilayer Fe / Pd with 109 kbar. It is clear that if we put more layers of Pd with respect to Fe, the PC system increases. These results are in the order of magnitude of ordered alloys Fe3Pd [34] and results to carbides Fe4C [42] and certain iron nitrides replaced [34,35,36,37,39]. In this situation, we noted that the multilayer has a similar behavior league that ordered the invar type.

kOe. When we have two layers of Pd, the charge transfer to the s states increases the difference between the electrons up and down, increasing the Fermi contact field (see table 4). This behavior of the Fermi contact field is consistent with the magnetic moment of the behavior on the site Fe, which confirms the empirical relationship of the magnetic moment that is propor‐ tional to the hyperfine field. Table 4 also shows the values calculated for the IS, which is greater for the bilayer Fe / Pd. The above results can be used for comparison with the experimental results of M. Li et al. [68,69], which show that when a Pd layer is placed in the 8Angstron, the Fermi contact field increased from 330 kOe to 335 kOe, which agrees qualitatively with our calculations. The differences are due to the calculations simulated at zero Kelvin temperature.

**Figure 9.** States density designed to electrons with spin up and down states for d in the 2 Pd / Fe multilayer: (a) the site

210 388

**Table 4.** Hyperfine parameters calculated for 2 Pd / Fe and 2 Fe / Pd using spin polarization. Fermi contact term (HPC)

2Fe/Pd 2Pd/Fe Fel

Fe and (b) the Pd site.

312 Superalloys

Fe

in kOe, isomeric deviation (S) in mm / s.

**HFC(kOe) IS(mm/s)**

0.316 0.456 Analyzing the decrease of the magnetic moment with increasing pressure, we studied the electron redistribution that occurred in the multilayer systems. Table 5 has some parameters obtained through self-consistent calculations for the spin polarization of the 2Fe / Pd systems (outside the parentheses) and 2 Pd / Fe (in the parentheses). Comparing Table 5 with Table 1, we noticed that there was an increase in the load transfer to the Fe site for both systems. This is due to the decrease of interatomic distances and the interpenetration of the electronic clouds. There was also a considerable increase in the density of states at the Fermi level for both compounds, which causes an increase in the specific heat coefficient y. The more general point is that there was an electronic redistribution in both systems. In the 2 Fe / Pd system, the transferred load Pd site to the Fe site population almost exclusively, the states d-down, together with a reversal of spin up electrons down, makes the non-magnetic system. Therefore, despite the pressure, the 2 Pd / Fe ferromagnetic state remains.

13

**Figure 10.** Magnetic moment due to the lattice parameter for ultrathin multilayers: (a) at the site of Fe and (b) Pd site.

Table 5 shows high pressure and low volume. And there is an electronics redistribution of the s electrons and this redistribution is not purely an average spin-up and down. Analyzing the decrease of the magnetic moment with increasing pressure, we studied the electron redistribution that occurred in the multilayer systems. Table 5 has some parameters obtained

Figure 10 - Magnetic moment due to the lattice parameter for ultrathin multilayers: (a) at the site of Fe and (b) Pd site.

exclusively, the states d-down, together with a reversal of spin up electrons down, makes the non-

systems. In water, 6.5120 parameters with dotted lines for the2Fe / Pd system are shown, and full lines are seen for the 2 Pd / Fe system. We also noted that the d-DOS, as a whole, is

Table 5 shows high pressure and low volume. And there is an electronics redistribution of the s

Figures 11a-d present the DOS for the spin-up and spin-down of the Fe site for both

magnetic system. Therefore, despite the pressure, the 2 Pd / Fe ferromagnetic state remains.

electrons and this redistribution is not purely an average spin-up and down.

Figures 11a-d present the DOS for the spin-up and spin-down of the Fe site for both systems. In water, 6.5120 parameters with dotted lines for the2Fe / Pd system are shown, and full lines are seen for the 2 Pd / Fe system. We also noted that the d-DOS, as a whole, is moved to higher energies for both systems, but the 2 Pd / Fe d-DOS system is still taken to higher energies. There is also an increase in the Fermi energy of the system. It is clear that the 2 Fe / Pd system undergoes a transformation from the ferromagnetic phase to the non-magnetic phase, as in through self-consistent calculations for the spin polarization of the 2Fe / Pd systems (outside the parentheses) and 2 Pd / Fe (in the parentheses). Comparing Table 5 with Table 1, we noticed that there was an increase in the load transfer to the Fe site for both systems. This is due to the decrease of interatomic distances and the interpenetration of the electronic clouds. There was also a considerable increase in the density of states at the Fermi level for both compounds, which causes an increase in the specific heat coefficient y. The more general point is that there was an electronic redistribution in both systems. In the 2 Fe / Pd system, the transferred load Pd site to the Fe site population almost this system, there is practically no more difference between the area below the Fermi energy of up situations for the down states. In the Fe site of the 2 Pd/ Fe system, there is a difference between these areas that features a magnetic moment in this site.

13

The results shown in Figures 12 and 13 show a strong dependence of the HFC and IS with the spacing of the lattice, which is also checked for nitrides experimentally [33]. In all cases, the absolute value of the pressure decreases with HFC. This may be associated with the reduction in the contribution of the s electrons to the spin density at the core of Fe. We noted that for the 2Fe / Pd system in low volume. In the 2 Pd / Fe system with pressure, there was a decrease to zero for the HFC, and the same happens with the magnetic moment of the Fe site in this system (Figure 10). This confirms the proportionality between the HFC and magnetic moment. The IS behavior on the Fe sites due to the reduction in lattice spacing is quite similar for both the 2 Pd / Fe as well as for the 2Fe / Pd system. These results suggest that the difference between the hyperfine parameters can be related to the expansion of the lattice due to the larger radius of the atomic Pd atoms. In fact, the reduction in HFC when a Pd atom is replaced by the Fe atoms (2 Pd / Fe and 2 Fe / Pd) can be viewed as a simulation of applying pressure in the 2 Pd / Fe system (Figure 12). <sup>14</sup>

Table 5 shows high pressure and low volume. And there is an electronics redistribution of the

**Figure 10.** Magnetic moment due to the lattice parameter for ultrathin multilayers: (a) at the site of Fe and (b) Pd site.

Figure 10 - Magnetic moment due to the lattice parameter for ultrathin multilayers: (a) at the site of Fe and (b) Pd site.

magnetic system. Therefore, despite the pressure, the 2 Pd / Fe ferromagnetic state remains.

electrons and this redistribution is not purely an average spin-up and down.

Analyzing the decrease of the magnetic moment with increasing pressure, we studied the

Table 5 shows high pressure and low volume. And there is an electronics redistribution of the s

Figures 11a-d present the DOS for the spin-up and spin-down of the Fe site for both

systems. In water, 6.5120 parameters with dotted lines for the2Fe / Pd system are shown, and full lines are seen for the 2 Pd / Fe system. We also noted that the d-DOS, as a whole, is

electron redistribution that occurred in the multilayer systems. Table 5 has some parameters obtained through self-consistent calculations for the spin polarization of the 2Fe / Pd systems (outside the parentheses) and 2 Pd / Fe (in the parentheses). Comparing Table 5 with Table 1, we noticed that there was an increase in the load transfer to the Fe site for both systems. This is due to the decrease of interatomic distances and the interpenetration of the electronic clouds. There was also a considerable increase in the density of states at the Fermi level for both compounds, which causes an increase in the specific heat coefficient y. The more general point is that there was an electronic redistribution in both systems. In the 2 Fe / Pd system, the transferred load Pd site to the Fe site population almost exclusively, the states d-down, together with a reversal of spin up electrons down, makes the non-

Figures 11a-d present the DOS for the spin-up and spin-down of the Fe site for both systems. In water, 6.5120 parameters with dotted lines for the2Fe / Pd system are shown, and full lines are seen for the 2 Pd / Fe system. We also noted that the d-DOS, as a whole, is moved to higher energies for both systems, but the 2 Pd / Fe d-DOS system is still taken to higher energies. There is also an increase in the Fermi energy of the system. It is clear that the 2 Fe / Pd system undergoes a transformation from the ferromagnetic phase to the non-magnetic phase, as in

s electrons and this redistribution is not purely an average spin-up and down.

314 Superalloys

**Figure 11.** States that the density is designed to the electrons with spin up and down states for d, the multilayer 2 Fe / Pd, and 2 Pd / Fe. The volume of the magnetic breakdown are as follows: (a) the Fe site (solid lines 2 Pd / Fe), (dotted lines 2 Fe / Pd).

follows: (a) the Fe site (solid lines 2 Pd / Fe), (dotted lines 2 Fe / Pd).

Figure 11 states that the density is designed to the electrons with spin up and down states for d, the multilayer 2 Fe / Pd, and 2 Pd / Fe. The volume of the magnetic breakdown are as

**Figure 12.** Hyperfine fields due to the lattice parameter.

#### **10. Conclusion**

In this paper, we used the LMTO method to the nearest ASA to investigate the electronic structure of ultrathin alloys, and the electronic structure of multilayer was analyzed.

The self-consistent calculations performed for the Fe / Pd ultrathin multilayers show a difference in the electronic structure when the stoichiometry of the multilayer systems is changed. As we increase the number of Pd layers relative to Fe, there is an increase in the magnetic moment on the website of Fe as well as an increase in the volume of the unit cell. Comparing the magnetic moment on the Fe site in the multilayer Fe / Pd alloys with certain ordered FePd and nitrides [32,33,39,40], we noticed a considerable increase. The hyperfine properties calculated for the multilayer Fe / Pd compared with the experimental results of M. Li et al. [42,43] have reasonable results from a qualitative point of view. The differences are due to the structure of the experimental multilayer, which is not ideal.

When subjected to pressure, the 2 Fe / Pd systems (2 Pd/ Fe and Fe / Pd) presented different behaviors among themselves. The 2Fe / Pd and Fe / Pd systems exhibited a magnetic collapse with an increasing pressure, while the 2 Pd / Fe magnetic moment were maintained in both the Fe and Pd sites. The hyperfine properties also changed with pressure.

#### **Author details**

A.V. dos Santos

Address all correspondence to<EMAIL_ADDRESS>
Universidade Regional Integrada do Alto Uruguai e das Missões – URI, Campus Santo Ângelo, Santo Ângelo, RS, Brazil

#### **References**

**Figure 12.** Hyperfine fields due to the lattice parameter.

In this paper, we used the LMTO method to the nearest ASA to investigate the electronic

The self-consistent calculations performed for the Fe / Pd ultrathin multilayers show a difference in the electronic structure when the stoichiometry of the multilayer systems is changed. As we increase the number of Pd layers relative to Fe, there is an increase in the magnetic moment on the website of Fe as well as an increase in the volume of the unit cell. Comparing the magnetic moment on the Fe site in the multilayer Fe / Pd alloys with certain ordered FePd and nitrides [32,33,39,40], we noticed a considerable increase. The hyperfine properties calculated for the multilayer Fe / Pd compared with the experimental results of M. Li et al. [42,43] have reasonable results from a qualitative point of view. The differences are

When subjected to pressure, the 2 Fe / Pd systems (2 Pd/ Fe and Fe / Pd) presented different behaviors among themselves. The 2Fe / Pd and Fe / Pd systems exhibited a magnetic collapse with an increasing pressure, while the 2 Pd / Fe magnetic moment were maintained in both

structure of ultrathin alloys, and the electronic structure of multilayer was analyzed.

due to the structure of the experimental multilayer, which is not ideal.

the Fe and Pd sites. The hyperfine properties also changed with pressure.

**10. Conclusion**

316 Superalloys

[17] Broeder, F. J. A. den., Kniper, D., Donkersloot, H. C., Horing, *W.^ppl.* Phys. Lati., 49,

S., Kirschner, J., Phys

507, 1989.

318 Superalloys

tifc, 1994.

France 1993.

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[20] Néel, M. L., J. PhysRad, 15, 225, 1954.

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[22] Jarlborg, T., Freeman, A. J. Appl. Phys., 53, 8041, 1982.

[26] Hedin, L., Lundquist, B. L., J. Phys. C, 4, 3065, 1965.

[27] Barth, V. von, Hedin, L., J. Phys. C, 5, 1629, 1972.

[31] Gumbsch, P., Daw, M. S., Phys Rev 44, 3934, 1991.

[34] Kuhnen C. A., Silva E. Z., da., PhysRev.B 46, 8915, 1992.

[38] Bohland, J., Kuhnen, C. A., BrazilianJ. Phys 23, 288, 1993.

[36] Kuhnen, C. A. Santos A. V. dos., J. Magn. Magn. Mat. 130, 353, 1994.

[39] Willams, A. R., Kubler, J., Gellat Jr. D., Phys Rev. B, 19, 6094 1979.

[37] Cord1er-Robert, C., Foct, J., Eur J. Solid State Inorg. Chem. 29, 39. 1992.

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[19] Celinski, Z., Heinrich, B., Cochran, J. F., Muir, W. B., Arrot,a

[23] Taler, T. J., Ketterson, J. B., Hiliard, J. E., Phys Rev. Lett., 41, 336, 1978.

[24] Blügel, S., Drittler, B., Zeller, R., Dederichs, P. H.,. Appl. Phys., 49, 547, 1989.

[28] Kittel, C., Introduction to Solid State Physics. New York, John Wiley, 1971.

[29] Richter, R., Gay, J. G., Smith, J. R., Phys Rev Lett, 54, 2704, 1990.

[30] Piecuch, M., Nevot, L., Matential Science Fórum, 59/60 1989.

[25] Bennett, L. H., Watson, R. E., (Eds.) Magnetic Multílayers, Singapore: World Scien‐

[32] Dffiny, B., Speriosu, V. S., Metin, S., Parkin, S. P., Gurney, B., Baumgart, \* P., Wilhoit,

[33] Yang, C. L. Abd-Elmequid, M. M., Micklitz, H., Otto, J. W., Jong, Y., Xue, D. S., LI, F.

[35] George, J. M., tese Université Paris sub-Laboratori de Physique dês Solides Orsay

#### Superalloys

#### **Chapter 14**

## **Mechanical Properties of the Thermal Barrier Coatings Made of Cobalt Alloy MAR-M509**

Zenon Aleksander Opiekun

320 Superalloys

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/61100

#### **Abstract**

This manuscript presents the microstructure, geometrical product specification, and results of scratch tests performed on the interlayer of thermal barrier coating (TBC) with Rockwell's intender. The TBC was provided by depositing two layers, metallic interlayer and external ceramic layer, onto a plate coating made of cobalt alloy MAR-M509 in plasma spraying process.

Based on measurements of microhardness made with Berkovitz's indenter using Nano Scratch-Tester (CSM Instruments), it was stated that elastic (Ee) to total energy (Ec) parameters (MIT = Ee/Ec), γ phase matrix of alloy MAR-M509 (MITγ), metallic interlayer (45% Ni–22% Co–17% Cr–16% Al–0.3% Y) (MITM), and ceramic layer (MITZrO2), are proportion, that is, 0.29:0.22:0.50. The surface of the casting was sandblasted with Al2O3 powder in an air stream before the TBC was introduced. Scratches were made along the cross section from a mould material (MAR-M509) through metallic interlayer and external ceramic layer in the TBC. Friction force, friction factor, and acoustic emission were recorded during the test. It has been proven that metallic interlayer in the TBC of ca. 200 µm thickness forms tough coating without pores with good cohesion values and very good adhesion values to the mould.

**Keywords:** Cobalt alloy MAR-M509, geometrical product specification (GPS), ther‐ mal barrier coating (TBC), microstructure, microhardness, interlayer cohesion, ad‐ hesion, nanoscratch test

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### **1. Introduction**

Thermal barrier coatings (TBCs) are applied via plasma spraying technology (air plasma system [APS]) and build up usually with two layers: metallic interlayer and external ceramic layer [1–3]. For special purposes, when a high density of coating together with its good bonding with the mould is demanded, the TBC is applied in vacuum plasma spraying process (vacuum plasma spray [VPS]) or low-pressure plasma spraying technique (low-pressure plasma spray [LPPS]) [4]. The TBC has an excellent heat resistance and a small thermal conductivity. They are characterized by an erosion and abrasion resistance and resistance to aggressive chemicals [5]. Therefore, TBCs are becoming more commonly used as coatings of jet-propelled parts of aircraft engines (combustor, blade outer air seal [BOAS], and blades of turbine), valves, and parts in chemical reactors [6–7].

Materials with MeCrAlY group single oxides that belong to ceramic materials are usually applied on metallic interlayers. These are most often used on the external layer in the TBC: Al2O3, ZrO2, ThO2, BeO, MgO, CeO2, Cr2O3i Y2O3 [5,6]. Thermal barrier coatings are the layers that separate the surface of metallic material from the stream of hot gases. Simultaneously, they reduce the temperature of metallic items [8]. In the end, such an influence of the TBC causes an improvement of performance characteristic of jet turbine engine, a reduction of fuel consumption, an increase of inlet gas temperature (ca. 100–170°C) (Fig. 1) [9], and a decrease of toxic substance emission from outlet gases because of better fuel consumption [7].

ZrO2 oxide stabilized by Y2O3 is most often used for the external layer in the TBC [10–15]. Functional properties, adhesion, cohesion, and crack resistance depend on the phase compo‐ sition of this oxide. Solid solutions prepared on the basis of regular ZrO2 (C) have low resistant to changeable heat load. A considerable improvement of the crack resistance of these solutions is noticed during the presence of tetragonal phase of ZrO2 (T) in the TBC. Factors that favor the tetragonal phase in the TBC after cooling down to the room temperature from the tem‐ perature of plasma spraying are small ZrO2–8% Y2O3 irregular grain sizes, with the introduc‐ tion of about 8 wt% of Y2O3 to the solid solution of ZrO2–Y2O3(Fig. 2) [16].

The aim of this article was to describing the cohesion and adhesion of the metallic interlayer made of 45% Ni–22% Co–17% Cr–16% Al–0.3% Y alloy and to present the geometrical product specification of the ceramic external layer made of ZrO2 oxides deposited on the casting of plate made of MAR-M509 cobalt alloy.

The main criterion to accommodate metallic interlayer is to compensate stress between the substrate and the external ceramic layer. TBC with plastic interlayer decreases its own stress and enhances connection between harder substrate and fragile hard external ceramic layer [17– 19].

The mechanical properties of TBC layers defined were by microhardness made with Berko‐ vitz's indenter when Nano Scratch-Tester (CSM Instruments) was used. The coating was obtained by single-spraying metallic powder made of 45% Ni–22% Co–17% Cr–16% Al–0.3%

coatings made of cobalt alloy MAR-M509. Archives of Foundry Engineering, 14 (1/2014), **Figures** Mechanical Properties of the Thermal Barrier Coatings Made of Cobalt Alloy MAR-M509 http://dx.doi.org/10.5772/61100 323

[29] Opiekun Z.A., Trytek A.: Cohesion and adhesion interlayer of the thermal barrier

159–164.

**1. Introduction**

322 Superalloys

parts in chemical reactors [6–7].

plate made of MAR-M509 cobalt alloy.

Thermal barrier coatings (TBCs) are applied via plasma spraying technology (air plasma system [APS]) and build up usually with two layers: metallic interlayer and external ceramic layer [1–3]. For special purposes, when a high density of coating together with its good bonding with the mould is demanded, the TBC is applied in vacuum plasma spraying process (vacuum plasma spray [VPS]) or low-pressure plasma spraying technique (low-pressure plasma spray [LPPS]) [4]. The TBC has an excellent heat resistance and a small thermal conductivity. They are characterized by an erosion and abrasion resistance and resistance to aggressive chemicals [5]. Therefore, TBCs are becoming more commonly used as coatings of jet-propelled parts of aircraft engines (combustor, blade outer air seal [BOAS], and blades of turbine), valves, and

Materials with MeCrAlY group single oxides that belong to ceramic materials are usually applied on metallic interlayers. These are most often used on the external layer in the TBC: Al2O3, ZrO2, ThO2, BeO, MgO, CeO2, Cr2O3i Y2O3 [5,6]. Thermal barrier coatings are the layers that separate the surface of metallic material from the stream of hot gases. Simultaneously, they reduce the temperature of metallic items [8]. In the end, such an influence of the TBC causes an improvement of performance characteristic of jet turbine engine, a reduction of fuel consumption, an increase of inlet gas temperature (ca. 100–170°C) (Fig. 1) [9], and a decrease

of toxic substance emission from outlet gases because of better fuel consumption [7].

tion of about 8 wt% of Y2O3 to the solid solution of ZrO2–Y2O3(Fig. 2) [16].

tion) depend on fat of layers and their spraying thermal parameters [20–23].

ZrO2 oxide stabilized by Y2O3 is most often used for the external layer in the TBC [10–15]. Functional properties, adhesion, cohesion, and crack resistance depend on the phase compo‐ sition of this oxide. Solid solutions prepared on the basis of regular ZrO2 (C) have low resistant to changeable heat load. A considerable improvement of the crack resistance of these solutions is noticed during the presence of tetragonal phase of ZrO2 (T) in the TBC. Factors that favor the tetragonal phase in the TBC after cooling down to the room temperature from the tem‐ perature of plasma spraying are small ZrO2–8% Y2O3 irregular grain sizes, with the introduc‐

The aim of this article was to describing the cohesion and adhesion of the metallic interlayer made of 45% Ni–22% Co–17% Cr–16% Al–0.3% Y alloy and to present the geometrical product specification of the ceramic external layer made of ZrO2 oxides deposited on the casting of

The main criterion to accommodate metallic interlayer is to compensate stress between the substrate and the external ceramic layer. TBC with plastic interlayer decreases its own stress and enhances connection between harder substrate and fragile hard external ceramic layer [17– 19]. Useful properties of TBC (erosion invulnerability, thermal fatigue, scale off, and mastica‐

The mechanical properties of TBC layers defined were by microhardness made with Berko‐ vitz's indenter when Nano Scratch-Tester (CSM Instruments) was used. The coating was obtained by single-spraying metallic powder made of 45% Ni–22% Co–17% Cr–16% Al–0.3%

**Figure 1.** Effect of TBC on reducing temperature of turbine blade [9] (a), and BOAS made of MAR-M509 alloy (b) (schemes).

Y alloy and triple-spraying ceramic powder made of ZrO2–8% Y2O3 oxides onto the surface of the casting with a MultiCoat Plasma Coating System (SulzerMetco).

**Figure 2.** Phase equilibrium system ZrO2–Y2O3.

#### **2. Materials and methods of testing**

Plate castings made of cobalt alloy MAR-M509 with a dimension of 4 × 20 × 90 mm were used for tests. The composition of plates was as follows: 0.60% C, 28.83% Cr, 10.0% Ni, 7.12% W, 3.77% Ta, 0.36% Zr, 0.18% Ti, 0.007% B, 0.43% Fe, 0.02% Mn, 0.03% Si, 0.002% S, and the rest is Co. The plates were casted in the multilayer ceramic mould (MCM) at initial temperature ca. 1000°C. The liquid alloy MAR-M509 at temperature ca. 1495 ± 5°C [24,25] was poured over MCM in a medium-frequency induction vacuum furnace. The surface of plate castings was at first sandblasted with Al2O3 powder of 200 ÷ 250 µm grain diameter in an air stream of pressure of ca. 0.35 MPa for a few seconds. After a single layer of 45% Ni–22% Co–17% Cr–16% Al–0.3% Y powder alloy was covered, triple layers of ZrO2–8% Y2O3 powder oxides in an argonhydrogen plasma beam were applied. The plates were heated at a temperature of about 120°C before the layers were covered.

Two spray powders were used in the experiment: one 45% Ni–22% Co–17% Cr–16% Al–0.3% Y powder alloy, which shows fine spherical morphology with particle granulation, ca.75 ± 15 µm, and ZrO2–Y2O3 oxide powder, which shows irregular morphology with particle granula‐ tion, ca.53 ± 15 µm.

A deposition of all layers in the TBC was done using the following: primary plasma gas, Ar (40 l/ min); secondary plasma gas, H2 (10 l/min); electric current, about 600 A; powder feet rate (40 g/min); and spray distance, about 130 mm. The traverse speed of a spraying gun was constant at 2 mm/min, and the speed of rotating holder was also constant (60 rot/min) (Fig. 3).

**2. Materials and methods of testing**

**Figure 2.** Phase equilibrium system ZrO2–Y2O3.

324 Superalloys

before the layers were covered.

tion, ca.53 ± 15 µm.

Plate castings made of cobalt alloy MAR-M509 with a dimension of 4 × 20 × 90 mm were used for tests. The composition of plates was as follows: 0.60% C, 28.83% Cr, 10.0% Ni, 7.12% W, 3.77% Ta, 0.36% Zr, 0.18% Ti, 0.007% B, 0.43% Fe, 0.02% Mn, 0.03% Si, 0.002% S, and the rest is Co. The plates were casted in the multilayer ceramic mould (MCM) at initial temperature ca. 1000°C. The liquid alloy MAR-M509 at temperature ca. 1495 ± 5°C [24,25] was poured over MCM in a medium-frequency induction vacuum furnace. The surface of plate castings was at first sandblasted with Al2O3 powder of 200 ÷ 250 µm grain diameter in an air stream of pressure of ca. 0.35 MPa for a few seconds. After a single layer of 45% Ni–22% Co–17% Cr–16% Al–0.3% Y powder alloy was covered, triple layers of ZrO2–8% Y2O3 powder oxides in an argonhydrogen plasma beam were applied. The plates were heated at a temperature of about 120°C

Two spray powders were used in the experiment: one 45% Ni–22% Co–17% Cr–16% Al–0.3% Y powder alloy, which shows fine spherical morphology with particle granulation, ca.75 ± 15 µm, and ZrO2–Y2O3 oxide powder, which shows irregular morphology with particle granula‐

A deposition of all layers in the TBC was done using the following: primary plasma gas, Ar (40 l/ min); secondary plasma gas, H2 (10 l/min); electric current, about 600 A; powder feet rate

**Figure 3.** Multicoat plasma coating system. View of system (a), spraying gun F4 MB-HBS type (b), scheme of spraying (c). **Figure 3.** Multicoat plasma coating system. View of system (a), spraying gun F4 MB-HBS type (b), scheme of spraying (c).

The state of surface of plate castings was assessed with the Talyscan 150 (Taylor-Hobson) tool working with the Mountains Map Universal program before and after the ceramic layers was deposited. Six amplitude parameters of geometrical product specification (GPS) were ana‐ lyzed: Sa (arithmetic mean), Sz (mean of the 5 highest peaks and the 5 lowest points), St (total height), Sq (quadratic mean), Sp (highest peak over the mean), and Sv (lowest valley under the mean).

X-ray examination surface of the TBC was performed with the Siemens Kristalloflex D500 Xray diffractometer.

The testing of microstructure layers in the TBC was conducted with a Berkovitz's indenter and Nano Scratch-Tester (CSM Instruments).

The examination of cohesion and adhesion of the TBC was carried out with the Revetest Scratch Tester CSM Instruments tool. The surface of sample with the TBC was scratched with the diamond Rockwell's intender of a 200-µm top radius. During the test, six different forces were applied: 2, 4, 8, 16, 32, and 40 N onto the surface of a cross section (MAR-M509 mould and TBC). It has been assumed that each scratch is 0.5 mm long. In the interlayer of the TBC and in the MAR-M509 mould, scratches were made at a 5-N intender load along 0.5 mm. All scratches were made at a rate of 1 mm/min—the speed of the intender. The Revetest Scratch Tester tool was calibrated according to reference sample covered with TiN coating. Friction force, friction factor, and acoustic emission were recorded during the test; 100% of acoustic emission scale equals 65-dB value.

### **3. Results**

#### **3.1. Geometrical structure of a surface**

The geometrical product specification (GPS) and the surface load–capacity curve of external ceramic layer in the TBC are presented in Figure 4.

#### **3.2. Microstructure and X-ray diffraction pattern**

The microstructure of the plate casting made of alloy MAR-M509 with the TBC at the cross section is presented in Figures 5 and 6. The X-ray diffraction patterns of the external ceramic layer in the TBC surface are shown in Figure 7.

#### **3.3. Measurements of microhardness**

Nano Scratch Tester (CSM Instruments) equipped with a Berkovitz's indenter (a pyramid with equilateral triangle as the base area) is to measure microhardness and to determine other mechanical properties of single grains, thin layer, and phase boundaries when loading spreads from 0 to 500 mN [26].

A ratio of elastic strain energy (Ee) to total energy (Ec) when forcing the indenter of the hardness tester is a very important feature of the tested materials.

Figure 8 shows example courses of changes of energy plastic deformation (Ep) and energy of elastic deformation (Ee), which describe the forcing of Berkovitz's indenter into a γ phase, into the metallic interlayer (45% Ni–22% Co–17% Cr–16% Al–0.3% Y), and into the external ceramic layer (ZrO2) [27]. Table 1 shows values of energy of plastic deformation (Ep), energy of elastic deformation (Ee), total energy (Ec), ratio Ee/Ec, longitudinal modulus of elasticity (Young's modulus E), and microhardness HV0.05 for γ phase, metallic interlayer, and external ceramic layer (the average value from five measurements).

**Figure 4.** Surface topography of the external ceramic layer in the TBC. 3D view (a), plate surface with amplitude pa‐ rameters (b), coating map (c), load-capacity curve of GPS and its parameters (d), surface profile (e), and geometrical parameters Sk, Spk, Svk, Sr1, Sr2.

#### **3.4. Cohesion and adhesion**

The testing of microstructure layers in the TBC was conducted with a Berkovitz's indenter and

The examination of cohesion and adhesion of the TBC was carried out with the Revetest Scratch Tester CSM Instruments tool. The surface of sample with the TBC was scratched with the diamond Rockwell's intender of a 200-µm top radius. During the test, six different forces were applied: 2, 4, 8, 16, 32, and 40 N onto the surface of a cross section (MAR-M509 mould and TBC). It has been assumed that each scratch is 0.5 mm long. In the interlayer of the TBC and in the MAR-M509 mould, scratches were made at a 5-N intender load along 0.5 mm. All scratches were made at a rate of 1 mm/min—the speed of the intender. The Revetest Scratch Tester tool was calibrated according to reference sample covered with TiN coating. Friction force, friction factor, and acoustic emission were recorded during the test; 100% of acoustic

The geometrical product specification (GPS) and the surface load–capacity curve of external

The microstructure of the plate casting made of alloy MAR-M509 with the TBC at the cross section is presented in Figures 5 and 6. The X-ray diffraction patterns of the external ceramic

Nano Scratch Tester (CSM Instruments) equipped with a Berkovitz's indenter (a pyramid with equilateral triangle as the base area) is to measure microhardness and to determine other mechanical properties of single grains, thin layer, and phase boundaries when loading spreads

A ratio of elastic strain energy (Ee) to total energy (Ec) when forcing the indenter of the

Figure 8 shows example courses of changes of energy plastic deformation (Ep) and energy of elastic deformation (Ee), which describe the forcing of Berkovitz's indenter into a γ phase, into the metallic interlayer (45% Ni–22% Co–17% Cr–16% Al–0.3% Y), and into the external ceramic layer (ZrO2) [27]. Table 1 shows values of energy of plastic deformation (Ep), energy of elastic deformation (Ee), total energy (Ec), ratio Ee/Ec, longitudinal modulus of elasticity (Young's modulus E), and microhardness HV0.05 for γ phase, metallic interlayer, and external ceramic

hardness tester is a very important feature of the tested materials.

Nano Scratch-Tester (CSM Instruments).

emission scale equals 65-dB value.

**3.1. Geometrical structure of a surface**

ceramic layer in the TBC are presented in Figure 4.

**3.2. Microstructure and X-ray diffraction pattern**

layer in the TBC surface are shown in Figure 7.

layer (the average value from five measurements).

**3.3. Measurements of microhardness**

from 0 to 500 mN [26].

**3. Results**

326 Superalloys

The control was scratched with the diamond Rockwell's indenter on the surface of a crosssectional MAR-M509 mould and TBC (Fig. 9).

**Figure 5.** Microstructure at the cross section: mould (MAR-M509) coating (TBC) (a, b), external ceramic layer (ZrO2) (d), metallic interlayer (45% Ni–22% Co–17% Cr–16% Al–0.3% Y) (c), and SEM micrograph.

Figure 10 shows the surface scratches at the cross section: mould (MAR-M509)–metallic interlayer 45% Ni–22% Co–17% Cr–16% Al–0.3% Y in the TBC together with diagrams of friction force, friction factor, and acoustic emission changes.

The scratches of samples in the direction from the mould (MAR-M509 cobalt alloy) through the metallic interlayer in the TBC at the cross section, which is made at constant intender loads, reveal the presence of typical plastic strain cones (Fig. 10b), crack cones in the coating (Fig. 10a), and "pushes-P" of mould material into this interlayer. The surfaces of longitudinal sections of Aca cones, which characterize the cohesion of the interlayer, are described by a

Mechanical Properties of the Thermal Barrier Coatings Made of Cobalt Alloy MAR-M509 http://dx.doi.org/10.5772/61100 329

**Figure 6.** Microstructure of TBC (a), graph of roentgen dispersion radiation from 1 area (b), share of elements in 1 area (c), chemical composition in microareas (1–4) of TBC (table).

product lx ly (Fig. 10e) [28] and are plotted as a function of loading force (Fig. 11). The "pushes" of mould material into a metallic interlayer and the lack of cracks at a boundary–mould interlayer (Fig. 11) indicate a very good interlayer adhesion to the mould.

#### **4. Summary**

Figure 10 shows the surface scratches at the cross section: mould (MAR-M509)–metallic interlayer 45% Ni–22% Co–17% Cr–16% Al–0.3% Y in the TBC together with diagrams of

**Figure 5.** Microstructure at the cross section: mould (MAR-M509) coating (TBC) (a, b), external ceramic layer (ZrO2)

The scratches of samples in the direction from the mould (MAR-M509 cobalt alloy) through the metallic interlayer in the TBC at the cross section, which is made at constant intender loads, reveal the presence of typical plastic strain cones (Fig. 10b), crack cones in the coating (Fig. 10a), and "pushes-P" of mould material into this interlayer. The surfaces of longitudinal sections of Aca cones, which characterize the cohesion of the interlayer, are described by a

friction force, friction factor, and acoustic emission changes.

328 Superalloys

(d), metallic interlayer (45% Ni–22% Co–17% Cr–16% Al–0.3% Y) (c), and SEM micrograph.

A TBC with ca. 920 µm thickness was obtained as a result of spraying melted powder with particle granulation ca. 75 ± 15 µm made of 45% Ni–22% Co–17% Cr–16% Al–0.3% Y alloy and ceramic powder made of ZrO2–8% Y2O3 oxides with particle irregular granulation ca. 53 ± 15 µm. The surface of a plate casting was made of the MAR-M509 cobalt alloy in a plasma beam (Figs. 5 and 6). Such a coating consists of two layers of fine grain metallic interlayer 45% Ni–

**Figure 7.** Diffraction patterns of the external ceramic layer in the TBC surface obtained for a grazing incident geometry *α* = 2°, 5°, and 9° and in the Bragg–Brentano geometry (BB). ZrO2 (C)—regular, ZrO2 (T)—tetragonal.

**Table 1.** The values of energy of plastic deformation (Ep), energy of elastic deformation (Ee), total energy (Ec), ratio Ee/Ec, Young's modulus E, and microhardness HV0.05. The average value from five measurements.

22% Co–17% Cr–16% Al–0.3% Y (ca. 200 µm thickness) and external ceramic layer as a mixture of two phases, regular ZrO2 (C) and tetragonal ZrO2 (T) (Fig. 7). The microstructure of the metallic interlayer in the TBC is tough, homogeneous, and deprived of porosity (total porosity less than 2%) (Fig. 5c). The thin layer of the γ phase (about 0.015 µm thick), which adheres to the metallic interlayer, is characterized by similar values of microhardness as the metallic interlayer, ca. 520 HV0.05. This is an effect of hardening of the γ phase with secondary carbides of M23C6 [27].

Mechanical Properties of the Thermal Barrier Coatings Made of Cobalt Alloy MAR-M509 http://dx.doi.org/10.5772/61100 331

**Figure 8.** The influence of loading on depth of forcing in the Berkovitz's indenter and energy change for γ phase (a), metallic interlayer (45% Ni–22% Co–17% Cr–16% Al–0.3% Y) (b), and external ceramic layer (ZrO2) (c).

**Figure 9.** Macrostructure with the picture of surface scratches (a), example of the scratch Rockwell's indenter for the a loading force 8 N of a cross section; MAR-M509 mould, metallic interlayer (45% Ni–22% Co–17% Cr–16% Al–0.3% Y) and external ceramic layer (ZrO2–8% Y2O3) (b), SEM micrograph.

22% Co–17% Cr–16% Al–0.3% Y (ca. 200 µm thickness) and external ceramic layer as a mixture of two phases, regular ZrO2 (C) and tetragonal ZrO2 (T) (Fig. 7). The microstructure of the metallic interlayer in the TBC is tough, homogeneous, and deprived of porosity (total porosity less than 2%) (Fig. 5c). The thin layer of the γ phase (about 0.015 µm thick), which adheres to the metallic interlayer, is characterized by similar values of microhardness as the metallic interlayer, ca. 520 HV0.05. This is an effect of hardening of the γ phase with secondary carbides

**Table 1.** The values of energy of plastic deformation (Ep), energy of elastic deformation (Ee), total energy (Ec), ratio

Ee/Ec, Young's modulus E, and microhardness HV0.05. The average value from five measurements.

**Figure 7.** Diffraction patterns of the external ceramic layer in the TBC surface obtained for a grazing incident geometry

**Phase Ep, pJ Ee, pJ Ec, pJ MIT = Ee/Ec E, GPa HV0.05** γ 226739 ± 3% 94733 ± 3% 321458 ± 3% 0.29 ± 0.1 122 ± 5 425 ± 5

257307 ± 5% 72309 ± 3% 333381 ± 5% 0.22 ± 0.1 103 ± 7 540 ± 8

16187 ± 5% 16124 ± 5% 32311 ± 5% 0.5 ± 0.1 125 ± 16 1220 ± 45

*α* = 2°, 5°, and 9° and in the Bragg–Brentano geometry (BB). ZrO2 (C)—regular, ZrO2 (T)—tetragonal.

of M23C6 [27].

Metallic interlayer (45% Ni–22% Co–17% Cr–16% Al–0.3% Y)

330 Superalloys

Ceramic external layer (ZrO2)

> A gradient of elastic strain energy to total energy (MIT = Ee/Ec) when forcing the Berkovitz's indenter is a very good parameter that describes elastic–plastic properties of materials (Fig. 8, Table 1). The MIT parameter equals 0.29 for the γ phase (MITγ), 0.22 for the metallic interlayer (MITM) 45% Ni–22% Co–17% Cr–16% Al–0.3% Y, and 0.50 for the external ceramic layer (MITZrO2) (Fig. 12). The metallic interlayer, which has better plastic than the substratum γ phase, was deposited on the plate surface, which was activated by sandblasting with Al2O3 particles and by heating at about 120°C. The geometrical product specification (GPS) of the sandblasted plate is isotropic. Its amplitude parameters Sa, Sq, Sp, Sv, St , and Sz are 3.1 µm, 3.9 µm, 16.2 µm,

**Figure 10.** Examples of scratches along the cross section: mould (MAR-M509) interlayer (45% Ni–22% Co–17% Cr–16% Al–0.3% Y) in the TBC, together with diagrams of friction force, friction coefficient, and acoustic emission changes for a loading force2 N (a), 4 N (b), 8 N (c), 16 N (d), 32 N (e), and 40 N (f).

18.3 µm, 34.5 µm, and 31.4 µm, respectively, and functional parameters Sk, Spk, Svk, Sr1, and Sr2 are 10 µm, 4.0 µm, 3.5 µm, 9.6%, and 91.4%, respectively. The GPS of the external ceramic layer in the TBC is also isotropic, but it is rougher than the mould. The total height St of the layer has increased by ca. 50%, and the arithmetic mean Sa increased by ca. 60% in comparison to St and Sa for the sandblasted surface of the mould. The roughness of the core (Sk) has increased by ca. 35%. The only functional parameter of GPS of ceramic layer, which is lower by ca. 100% in comparison to the mould, is the roughness of peaks (Spk) (Fig. 4).

The scratches of samples along the cross section from the mould (MAR-M509 cobalt alloy) through the metallic interlayer and external ceramic layer (Fig. 9a,b) in the TBC, which were made with Rockwell's cone at different intender loads (Fig. 10a,f), reveal the presence of typical strain and crack cones in the interlayer and "pushes-P" of mould material (γ phase) into the interlayer. A linear surface increase of longitudinal sections of these cones indicates good cohesion of the metallic interlayer (Fig. 11).

**Figure 11.** Surfaces of longitudinal sections of Aca cones plotted as a function of loading force in the metallic interlayer 45% Ni–22% Co–17% Cr–16% Al–0.3Y.

A load increase of the Rockwell's intender from 2 N to 40 N (Fig. 10a–f) causes an increase of friction force from ca. 0.3 N to 10 N, together with a minor increase of friction coefficient from ca. 0.1 to 0.2. For all scratches, no increase of acoustic emission effect is observed at boundary mould coating. The constant value of acoustic emission at 3% level (ca. 2 dB) shows that strains at boundary MAR-M509 cobalt alloy–metallic interlayer in the TBC are plastic and do not appear in this crack area (Fig. 10 a–c). The shape of "pushes" of the γ phase is similar to the

**Figure 10.** Examples of scratches along the cross section: mould (MAR-M509) interlayer (45% Ni–22% Co–17% Cr–16% Al–0.3% Y) in the TBC, together with diagrams of friction force, friction coefficient, and acoustic emission changes for a

loading force2 N (a), 4 N (b), 8 N (c), 16 N (d), 32 N (e), and 40 N (f).

332 Superalloys

cones, and its depth increases linearly together with the increase of intender loading force from ca. 3 µm for 2 N force to ca. 53 µm for 40 N force (Fig. 11). Such a course of changes happening at boundary mould (MAR-M509 cobalt alloy), that is, the metallic interlayer in the TBC during an attempt at scratching, proves a very good adhesion for this interlayer made of 45% Ni–22% Co–17% Cr–16% Al–0.3% Y alloy [29].

**Figure 12.** Macrostructure at the cross section: mould (MAR-M509) coating (TBC) with MIT parameters.

Cracks in "cohesion cones" of the metallic interlayer in the TBC are noticed when the loading force of the intender exceeds 16 N (Fig. 10d). Huge differences (even 6.5 dB) between values of acoustic emission are the effect of the interlayer cracking [29] (Fig. 10e,f).

#### **Author details**

Zenon Aleksander Opiekun

Address all correspondence to<EMAIL_ADDRESS>
Department of Casting and Welding, Rzeszów University of Technology, Rzeszów, Poland

#### **References**

[1] Pint B.A., Wright J.G., Bridlley W.J.: Evaluation of TBC systems on novel substrates. Journal of Thermal Spray Technology, 9 (6) (2000), 198–203.

[2] Parks W.P. Jr, Hoffman E.E., Lee W.Y. Wright J.G.: Thermal barrier coatings issue in advanced land-based turbines. Journal of Thermal Spray Technology, 6 (2) (1997), 187–192.

cones, and its depth increases linearly together with the increase of intender loading force from ca. 3 µm for 2 N force to ca. 53 µm for 40 N force (Fig. 11). Such a course of changes happening at boundary mould (MAR-M509 cobalt alloy), that is, the metallic interlayer in the TBC during an attempt at scratching, proves a very good adhesion for this interlayer made of 45% Ni–22%

**Figure 12.** Macrostructure at the cross section: mould (MAR-M509) coating (TBC) with MIT parameters.

of acoustic emission are the effect of the interlayer cracking [29] (Fig. 10e,f).

Journal of Thermal Spray Technology, 9 (6) (2000), 198–203.

Cracks in "cohesion cones" of the metallic interlayer in the TBC are noticed when the loading force of the intender exceeds 16 N (Fig. 10d). Huge differences (even 6.5 dB) between values

Department of Casting and Welding, Rzeszów University of Technology, Rzeszów, Poland

[1] Pint B.A., Wright J.G., Bridlley W.J.: Evaluation of TBC systems on novel substrates.

Co–17% Cr–16% Al–0.3% Y alloy [29].

334 Superalloys

**Author details**

**References**

Zenon Aleksander Opiekun

Address all correspondence to<EMAIL_ADDRESS>

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[21] Ahmet P., Ozkan S., Erdal C.: Effects of porosity on thermal loadings of functionally graded Y2O3-Zr2O/NiCoCrAlY coatings. Materials and Design, 23 (2002), 641–644. [22] Traeger F., Ahrens M., Vaßen R., Stöver D.: A life time model for ceramic thermal barrier coatings. Materials Science and Engineering, A358 (2003), 255–265.

[23] Mesratia N., Saif Q., Treheuxb D., Moughilc A., Fantozzic G., Vincent A.: Characteri‐ zation of thermal fatigue damage of thermal barrier produced by atmospheric plas‐

[24] Opiekun Z.: Analysis of process-related factors that determine structure and proper‐ ties of cobalt casting alloy intended of aircraft part. Monograph, Poznań, 2007. [25] Opiekun Z.: Temperature influence of ceramic form on the structure of cobalt alloy MAR-M509 castings. Acta Metallurgica Sinica (English Letters), 24 (1) (2011), 23–33.

[26] ISO 14577 Metallic Materials—Instrumented Indentation Test for Hardness and Ma‐

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[28] CSM Instruments, Application Bulletin: Characterization of Thermal Spray Instru‐

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336 Superalloys

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## *Edited by Mahmood Aliofkhazraei*

Superalloy, or high-performance alloy, is an alloy that exhibits several key characteristics: excellent mechanical strength, resistance to thermal creep deformation, good surface stability, and resistance to corrosion or oxidation. The crystal structure is typically face-centered cubic austenitic. Superalloy development has relied heavily on both chemical and process innovations. Superalloys develop high temperature strength through solid solution strengthening. An important strengthening mechanism is precipitation strengthening which forms secondary phase precipitates such as gamma prime and carbides. Oxidation or corrosion resistance is provided by elements such as aluminium and chromium. This book collects new developments about superalloys.

Superalloys

Superalloys

*Edited by Mahmood Aliofkhazraei*

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