Comprehensive microstructural characterization and ... · Comprehensive microstructural...

Acta Materialia 51 (2003) 2457–2475www.actamat-journals.com

Comprehensive microstructural characterization andpredictive property modeling of plasma-sprayed zirconia

coatings

A. Kulkarni a,∗, Z. Wanga, T. Nakamuraa, S. Sampatha, A. Golanda,H. Hermana, J. Allenb, J. Ilavskybc, G. Longb, J. Frahmd, R.W. Steinbrechd

a State University of New York, Old Engineering, Room 314, Stony Brook, NY 11794, USAb National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

c University of Maryland, College Park, MD 20742, USAd IWV-2: Institute for Materials and Processing in Energy Systems, Forschungszentrum Julich, Germany

Received 3 September 2002; received in revised form 23 December 2002; accepted 9 January 2003

Abstract

Quantitative microstructure characterization to better understand processing-microstructure-property correlations isof considerable interest in plasma sprayed coating research. This paper quantifies, by means of small-angle neutronscattering (SANS) data, microstructure (porosity, opening dimensions, orientation and morphologies) in plasma sprayedpartially-stabilized zirconia (PSZ) coatings, primarily used as thermal barrier coatings. We report on the investigationof the influence of feedstock characteristics on microstructure and establish its influence on the resultant thermal andmechanical properties. The microstructural parameters determined by SANS studies are then assembled into a prelimi-nary model to develop a predictive capability for estimating the properties of these coatings. Thermal conductivity andelastic modulus were predicted using finite element analysis and ultimately compared to experimental values. 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Keywords: Plasma sprayed thermal barrier coatings; Small angle neutron scattering; Porosity; Thermal conductivity; Elastic modulus;Finite element model

1. Introduction

Zirconia-based ceramic coatings are widely usedfor the thermal, oxidation and hot corrosion protec-tion of high temperature components in gas tur-

∗ Corresponding author: Tel.:+1-631-6324511; fax:+1-631-6328440.

E-mail address: [email protected] (A.Kulkarni).

1359-6454/03/$30.00 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.doi:10.1016/S1359-6454(03)00030-2

bines and diesel engines[1,2]. These coatings pro-vide insulation to metallic structures, thus delayingthe thermally-induced failure mechanisms thatgovern the component durability and life[3,4]. Theminimum general requirements for an effectiveceramic thermal barrier coating (TBC) are recog-nized to be: (i) low thermal conductivity; (ii) hightemperature viability (�1000°C); (iii) phase stab-ility; (iv) resistance to thermal fatigue and thermalshock; and (v) ease of application[5]. The most

2458 A. Kulkarni et al. / Acta Materialia 51 (2003) 2457–2475

commonly employed TBC is partially-stabilizedzirconia (PSZ), where the stabilizer is generallyyttria. This class of ceramic has a very low thermalconductivity, effectively insulating the underlyingsuperalloy substrate (through an oxidation resistantbond coat) from the high temperature environment.For gas turbine applications, the thickness of theTBC is in the range of 125–300 µm.

Plasma sprayed TBCs have been readilyemployed in these applications [6,7]. The processinvolves melting of feedstock materials in a plasmaplume and rapidly transporting these molten par-ticles to the substrate, where rapid solidification ofindividual particle occurs upon impingement. Suc-cessive build-up of these “splats” results in a lay-ered arrangement in the coating, analogous to abrick-wall-like structure where the splats areentwined in complex arrays [8,9]. This splat-basedlayered microstructure leads to an intrinsic ani-sotropy of the coating in the direction perpendicu-lar to the spray direction. The splats are separatedby interlamellar pores resulting from rapid solidi-fication of the lamellae, globular pores formed byincomplete inter-splat contact or around unmeltedparticles, and intrasplat cracks due to thermalstresses and tensile quenching stress relaxation.This unique attribute of the microstructural fea-tures contributes to a further decrease in thermalconductivity. The remarkable feature of the TBCis its survivability, both in thermal shock and in thedifficult environmental conditions within the gasturbine. The tenacious characteristic of the TBCoriginates from the porosity, microcracks and theinherent toughness (R-curve behavior) of these cer-amics [10–12]. Finite element modeling to studythe effects of pore sizes, shapes and orientationson the mechanical properties of plasma sprayedcoatings has been attempted [13]. Although numer-ous studies involving modeling of the evolution ofsuch deposits have been carried out, serious ques-tions remain, which become particularly importantwhen dealing with TBC performance andreliability [14,15].

This paper will explore plasma spraying ofTBCs, with special reference to process-relatedmicrostructures and imperfections and their result-ant influence on the coating properties. Of principalinterest will be the anisotropic nature of the

deposits, that is, the layers of splats. This is alsoreflected in the anisotropic array of porosity, whichsmall-angle neutron scattering (SANS) methodshave allowed us to distinguish [16–18]. RecentSANS studies on these coatings have been usedto resolve and quantify the microstructural featureswith respect to porosity, dimensionality and orien-tation information [19]. Finally, through the appli-cation of a variety of characterization method-ologies, plasma sprayed TBCs can be reasonablywell understood, leading to the process-control ofmicrostructure.

2. Experimental procedure

The primary aim of this investigation has beento examine the effect of material feedstock charac-teristics (such as particle density, size and shape)on the anisotropic void structure, which, in turn,affects the properties of PSZ coatings, in this casemole fraction of 7–8% yttria. Four powders, madeby four different manufacturing methods, wereinvestigated. The feedstock characteristics, theirorigin, particle size distribution and nitrogen sorp-tion (BET)-based surface areas are listed inTable 1.1

The different powder morphologies are shownin Fig. 1. The powders made by the F&C method,which involves electric melting of parent ore, sol-idifying and crushing the ingot, producesangular/polyhedral particles. The SG techniqueinvolves wet chemical synthesis, exhibitingspherical/equiaxed morphology (the particles arecomprised of sub-µm unit-particles), thus leadingto higher surface area. The A&S techniqueinvolves agglomeration of powders with bindersand subsequent high temperature treatment, pro-ducing globular/rough-textured particles. Theplasma densified HOSP process, involving spraydrying and plasma densification, produces hollowspheres, sometimes nested.

X-ray phase characterization carried of these

1 Information on commercial products is given for complete-ness and does not necessarily constitute or imply their endorse-ment by the National Institute of Standards and Technology.

2459A. Kulkarni et al. / Acta Materialia 51 (2003) 2457–2475

Table 1Feedstock characteristics

Powder type Processing Manufacturer Particle size Surface areadistribution (µm) (m2/g)

Fused and crushed (F&C) Cast material, subsequently MSM ZY7∗ 10–60 0.08crushed

Sol gel (SG) Wet precipitation chemical MEL PWA 1375 G 5–50 3.96technique

Agglomerated and sintered Spray dried and sintered Metco AE 7216 20–70 0.4(A&S)Plasma densified (HOSP) Plasma flame processed/densified Metco AE7593 20–120 0.48

Fig. 1. PSZ powder morphologies observed under SEM (50 µm scalebar).

powders is shown in Fig. 2. Since SG and F&Cmethods yield uniform chemistry, the only phasedetected in these powders is the tetragonal phase,whereas a combination of monoclinic (m) andtetragonal (t) phases, is detected for powders pro-duced by the other two methods. In all samples,the existence of the cubic phase cannot be excludeddue to scattering related limitations [20].

Coatings were deposited onto steel substrates

using a Sulzer Metco∗ 3 MB plasma torch, at 100mm standoff distance. The spray parameters arelisted in Table 2. In-flight particle diagnostics wereperformed using a Tecnar DPV system to monitorparticle temperature and velocity, the results ofwhich are shown in Table 3. To understand theeffects of process parameters on the droplet sub-strate interaction, splats were collected on polishedstainless steel substrates. Coatings of 1 mm thick-


Fig. 2. Phase characterization of powders.

Table 2Processing parameters for all powders

Parameters Value

Current (A) 650Voltage (V) 66–68Primary gas (SLM) Argon: 40Secondary gas (SLM) Hydrogen: 8Carrier gas (SCCM) Argon: 3000Feed rate (g/min) 20–40Standoff distance (mm) 100

ness were produced for microstructural characteriz-ation and property measurements, whereas 3–4 mmthick coatings were deposited for the SANS stud-ies.

Splats, collected on polished stainless steel sub-strates, were observed under a white light surfaceinterferometer (Zygo TM∗) to quantify the surface

Table 3In-flight diagnostics

Powder type Temperature (°C) Velocity (m/s)

F&C 2710 ± 300 111 ± 30SG 2670 ± 300 112 ± 30A&S 2760 ± 300 125 ± 30HOSP 2720 ± 300 90 ± 30

(Uncertainties given are standard deviations)

profile and the dimensionality of the splats. Free-standing coatings were evaluated for porosity con-tent, property (thermal conductivity and elasticmodulus) measurements and SANS studies. Infor-mation on porosity was attained using two tech-niques. Surface-connected porosity was measuredby mercury intrusion porosimetry (MIP) using aQuantachrome Autoscan 33∗ porosimeter. Thetechnique gave an uncertainty of standard devi-ation ± 3–5% based on the average of 3 measuredspecimens. The total porosity content (open andclosed porosity), used for SANS analysis, wasdetermined using the precision density method,where mass-over-volume ratios were obtained fora cut rectilinear specimen. This technique gives afractional density (or porosity) uncertainty of stan-dard deviation ± 1% based on the average of 10measured identical specimens and an assumedtheoretical density of 6 g/cm3. Thermal conduc-tivity measurements were carried out on a 12.5 mm(0.5 inch) diameter disk, coated with carbon, usinga Holometrix laser flash∗ thermal diffusivity instru-ment. The standard deviation is based on the aver-age of 3 specimens. Phase and microstructuralstudies were also carried out.

In-plane and out-of-plane elastic modulii weremeasured for coatings bonded to the substrate.Depth-sensitive indentation measurements werecarried out with a Fischerscope 100 C microhard-ness tester∗ using a Vickers-type indenter at roomtemperature (with a maximum load Fmax = 1 N).An example of a force penetration curve, showingloading (Curve 1) and unloading (Curve 2), isdepicted in Fig. 3. The elastic modulus wasdetermined from the elastic recovery part of theforce-penetration curve (Curve 3). Curve 3 is a rep-


Fig. 3. Force-penetration curve during depth-sensitivemicrohardness testing. The quantities shown are the depth ofindentation at maximum load, hmax, the final depth ofimpression after unloading, hp, and the intercept of the linearfit, hr.

resentation of a linear fit to the unloading curve atFmax using the equation [DIN ISO 14577].

dFdh

�2

�pEr�Ar, (1)

where Er is the reduced elastic modulus

Er � �1�ni

Ei

�1�n

E ��1

, (2)

with the suffix i on the Poisson’s ratio n and Ereferring to the indenter diamond. Note that thePoisson’s ratio of the TBC was assumed to be n= 0.25. The contact area Ar is related to theimpression depth hr (intercept of the unloading tan-gent with the abscissa in Fig. 3) by

Ar � 26x43xh2r , (3)

To examine the anisotropy of the various micro-structures, measurements were carried out bothparallel and perpendicular to the spray direction.

Small-angle neutron scattering studies were car-ried out on the 8 m SANS instrument at the ColdNeutron Research Facility at the National Instituteof Standards and Technology, Gaithersburg, MD[21,22]. In this experiment, a monochromatic beamof thermalized neutrons passes through the speci-men in transmission geometry and the scattered

neutrons are recorded on a two-dimensional detec-tor; Fig. 4(a). The details of the experiment aredescribed elsewhere [16,19]. The scattering occursat the void-grain interface due to differences inscattering length density between the material andthe pores. The experiment involved two types ofmeasurements, the first being anisotropic Porodscattering. Orientational averaging of the Porodscattering from the sample enables one to obtainthe total void surface area per unit sample volume,independent of the precise void morphology. Thefine features in the microstructure are major con-tributors to this deduced surface area. The secondtype of measurement is anisotropic multiple SANS(MSANS), which involves a measurement of thebeam-broadening due to anisotropic multiple scat-tering by long wavelength neutrons. The multiplescattering usually arises from the coarse features inthe microstructure. The MSANS beam-broadeningversus wavelength for two sample orientations,with the incident beam out-of-plane (in the spraydirection) and in-plane (i.e., in the substrate plane),yields information on microstructural anisotropy.The sector-averaged anisotropic MSANS data alsoprovide microstructural orientation information, asdiscussed in detail elsewhere [19,23–26].

In Porod scattering, the scattering intensity, I(Q),is a function of the magnitude and direction of thescattering vector, Q, and its orientational average,�I(Q)� is given by:

�I(Q)��2p��r�2ST

Q4 , (4)

where, |Q| = [4p /l]sinq, 2q is the scattering angle,l is the wavelength, ST is the total surface area perunit volume and |�r|2 is the scattering contrastbetween voids and solid matrix; Fig. 4(b). Pre-viously [16–19], it has been shown how the aniso-tropic Porod scattering can be divided into twoanisotropic contributions, one from interlamellarpores that are predominantly parallel to the sub-strate, the other from intrasplat cracks that are pre-dominantly perpendicular to the substrate. Afurther isotropic component can be attributed tolarge globular pores and randomly-oriented irregu-lar voids. However, this Porod scattering contri-bution is generally too small to be distinguished byanisotropic Porod scattering measurements, alone.


Fig. 4. Experimental setup and scattering intensity curve [16] along with model coating microstructure.

More complete microstructural information wasobtained by combining MSANS measurements fordifferent sample orientations, anisotropic Porodsurface area distributions, and the total porositydetermined from precision density measurements.The MSANS beam-broadening shows muchgreater sensitivity to the coarse globular andirregular porosity than does the Porod scatteringanalysis. For interpretation of the anisotropicMSANS beam-broadening data, the interlamellarpores and intrasplat cracks are considered to com-prise two space-filling networks of oblate sphe-roids, each with a fixed aspect ratio, b and theglobular pores are considered spheres; Fig. 4(c).

While the oblate disc radii of the individual sphe-roidal elements are almost arbitrary and can bedefined for mathematical convenience, the meanopening dimensions, �O.D.�, for the two popu-lations, together with the associated volume frac-tions and orientation distributions, and the volumefraction and mean radius of the globular pores,determine the MSANS broadening and anisotropyactually observed. Since the cracks are generallyfiner than the interlamellar pores, the aspect ratiofor the cracks is set to a smaller value (moreoblate) than for the interlamellar pores. To acquirea quantitative delineation of the three void compo-nents (interlamellar pores, intrasplat cracks and


globular pores) in terms of their porosity contri-bution, dimensionality and orientation distribution,the following four constraints have to be fulfilledin the MSANS analysis: [19]

1. The component porosities are consistent withthe total porosity obtained using precision den-sity measurements.

2. The component surface areas are consistent withthe total surface area obtained from anisotropicPorod scattering experiments.

3. The circularly-averaged MSANS beam broad-ening versus wavelength model predictions areconsistent with the experimental data for bothorientations: out-of-plane (spray direction) andin-plane (orthogonal direction).

4. The predicted MSANS anisotropy(perpendicular to the substrate) is consistentwith that observed experimentally.

With these constraints, it has been possible todetermine the volume-weighted mean-openingdimensions of the intrasplat cracks and interlamel-lar pores, their orientation distributions withrespect to the spray direction, and the diameters ofthe globular pores. Porosity and surface area con-tributions may also be distinguished.

3. Results and discussions

The experimental SANS results are presentedwith phase and microstructural characterizations inorder to determine the porosity-property relation-ships. An x-ray phase analysis carried out on thecoatings is shown in Fig. 5. All of the coatingsshow a predominant, non-transformable, tetragonalphase structure as a result of rapid solidification.Again, the results do not exclude the possibility ofcubic phase. Fig. 5 also shows that there is a smallamount of monoclinic content retained for the coat-ing produced from the HOSP and A&S powders.

SEM microstructures are shown in Fig. 6. Sig-nificant differences are observed for each case.While well-adhered splats are observed for thedeposit from F&C feedstock, combinations ofinterlamellar pores, cracks and globular pores areobserved for the other coatings. The microstruc-

Fig. 5. Phase characterization of coatings.

tures also show the columnar structure within theindividual splats, which arises from directionalheat extraction through the substrate and also fromthe solidification direction. Interlamellar pores arealso visible. These result from poor adhesionbetween the splats as they accumulate to form thecoating. Macroscopically, the coating from the SGfeedstock has numerous interlamellar pores com-pared with the others. The HOSP coating showslarger numbers of unmelted particles owing to thebroad powder particle size distribution.

The measured coating properties, i.e., theporosity from MIP and precision density, the ther-mal conductivity and the elastic modulus, are listedin Table 4. MIP indicates that there is a consider-able variation in the surface-connected porosity forthe four cases. The total porosity measured usingprecision density also shows a wide variation. Theporosity for the coating deposited from F&C feed-stock is the least porous owing to the splats beingwell-adhered to one another. This is also consistentwith the high thermal conductivity and elasticmodulus values for this coating. The coating madefrom HOSP feedstock shows a significantly lowerthermal conductivity and elastic modulus than dothe other coatings. This is likely due to its hollowspherical morphology and a broad particle size dis-tribution. There also exists a slight anomalybetween results for coatings made from the SG andA&S feedstocks. The SG coating shows lower


Fig. 6. SEM secondary electron images of fracture cross-sections of the coatings (10 µm scale-bar shown), I – interlamellar pores,P – Globular pores.

Table 4Coating property measurements

Feedstock MIP porosity (%) PD porosity (%) Th. conductivity (W/m K) Elastic modulus (GPa)

F&C 7.3 ± 0.4 7.6 ± 0.1 0.95 ± 0.02 76 ± 14SG 12.5 ± 0.6 13.5 ± 0.2 0.85 ± 0.01 69 ± 17A&S 14.5 ± 0.7 15 ± 0.2 0.89 ± 0.02 72 ± 20HOSP 10 ± 0.5 12.2 ± 0.2 0.64 ± 0.01 48 ± 11

thermal conductivity and elastic modulus despitehaving a lower porosity. Large numbers of interla-mellar pores are observed in the SG microstructure,which might explain this anomaly, although furtherinvestigation is needed.

For a quantitative evaluation of the microstruc-tures, and a better insight into the property anomal-ies, SANS measurements were carried out, and theresults are given below.

3.1. SANS results

SANS results along with the MSANS model fitsare presented in this section. These results include[19] the component porosities of the interlamellarpores and intrasplat cracks, together with theirmean opening dimensions and approximate orien-tation distributions, as well as the porosity of theglobular pores and their mean diameter. To model


the intrasplat cracks and interlamellar pores, theseare assumed (as in earlier studies [19]) to compriseseparate networks of oblate spheroidal elementswith aspect ratio values of 1/10 for the intrasplatcracks and 1/5 for the interlamellar pores. Totalporosities, measured using the precision densitymethod, and total void surface areas, obtained froma solid-angle averaging of the anisotropic Porodscattering intensity versus Q (Fig. 4(b)), were alsoused as input for the MSANS model. Fig. 7 showsthe MSANS broadening data (rc in the units of Q)with model-fits (lines) for the coating made fromF&C feedstock. The circularly-averaged MSANSbroadening, rc, versus l for both the sample orien-tations is shown in Fig. 7(a); Fig. 7(b) shows theanisotropic angular variation of MSANS rc at dif-ferent wavelengths in the plane of the spray direc-tion.

The overall MSANS model results for porositycontributions and mean opening dimensions aresummarized in Table 5. Estimated standard uncer-tainties are given in parentheses. The anisotropicorientation distributions of the intrasplat cracks andinterlamellar pores (not shown here) are alsoimportant in meeting the MSANS model con-straints described earlier. The orientation distri-butions for the interlamellar-pore (b = 1/5) sphe-roidal elements and the intrasplat-crack (b = 1/10)elements are separately parameterized in terms ofthe relative probabilities of finding the normal tothese elements within the range 0–30° from thespray direction, 30–60° from the spray directionand 60–90° from the spray direction. To obtainMSANS model fits that satisfy all of the con-straints, intrasplat cracks are found to be predomi-nantly perpendicular to the substrate (spheroidal-elements normals 60–90° from the spray direction),and the interlamellar pores are found to be pre-dominantly parallel to the substrate (spheroidal-elements normals 0–30° from the spray direction).While the aspect ratios of the spheroidal elementsare much milder than the true aspect ratios of theinterlamellar pores and intrasplat cracks, the valuesabove suffice for the respective populations ofspheroidal voids assumed to form a space-fillingnetwork throughout each void system. Indeed, therelatively small area of each spheroidal elementpermits undulations in the true interlamellar pores

and intrasplat cracks to be followed. Furthermore,it is the mean opening dimension, �O.D.� = 4R/3, rather than the oblate disc diameter, 2 R, thatis the physical dimension of interest. (In contrast,for the globular voids, the diameter fitted is asso-ciated with the actual mean globular porediameter.) Thus, the �O.D.� values of the aniso-tropic void systems are reported in Table 5, sinceit is these dimensions that should pertain to actualcracks and pores (of extreme aspect ratios) withinthe coating microstructure. The results explain theanomaly between the coatings made from the SGand A&S feedstocks. The reduced thermal conduc-tivity and elastic modulus in the SG case can beattributed to a larger amount of interlamellarporosity, despite this system having a lower totalporosity. The quantitative separation of the coatingmicrostructure into its components, obtained fromthe MSANS model results, is shown in Fig. 8.

Table 5 does not reveal why the coating madefrom HOSP feedstock has such different thermo-mechanical properties from the other coatings(Table 4). To investigate this and other issues (e.g.,the increased number of globular pores for the A&S case) in more detail, the dimensionality of thecollected splats was examined for all of the coat-ings. The splat morphologies are shown in Fig. 9.The disk-shaped splat morphology of the F&Cfeedstock suggests complete particle melting,resulting in well-adhered splats and consequentlya decreased porosity and the higher thermal con-ductivity and elastic modulus that is observed.While the splats are fragmented in all of the coat-ings, one reason for the high percentage of globularpores in the coating prepared with A&S feedstockcould be the missing cores observed in almostevery splat. This could be a result of higher particlevelocity during spraying, therefore, less residencetime in the plasma and a lower degree of melting.Further investigation is being carried out to deter-mine the extent of melting.

To understand better the correlation between theanisotropy of the microstructure and that of theproperties, Table 6 shows the measured elasticmodulus both in-plane (parallel to the substrateplane) and out-of-plane (perpendicular to the sub-strate plane). Given that planar voids perpendicularto the displacement direction depress the elastic


Fig. 7. MSANS broadening experimental data (symbols) with model-fits (lines) for the coating made from F&C feedstock case: (a)MSANS rc vs l for both the sample orientations; (b) anisotropic angular MSANS, rc, at different wavelengths

modulus, the results are consistent with the aniso-tropies derived from MSANS. Except for theHOSP material, all TBCs show an anisotropyeffect. The MSANS results also show a similarproportion of interlamellar pores and intrasplatcracks in the system. The extent of the anisotropyis greatest for the A&S case, consistent with theSANS studies. In the case of anisotropy, the elastic

modulus measured perpendicular to the spraydirection is 15–20% higher.

Figs 10 and 11 show the porosity–thermal con-ductivity and the porosity–elastic modulus relation-ships for the four sprayed materials. Inverse lineardependence of the experimental results of thermalconductivity and elastic modulus are observed withrespect to the amount of interlamellar pores,


Table 5Quantitative MSANS model results

Material PD porosity (%) Component porosities (%) Mean opening Globular poredimensions (µm) diameter (µm)

Interlamellar pores Intrasplat cracks Globular pores

F&C 7.6 ± 0.1 2.1 (2) 2.1 (2) 3.4 (3) 0.053 0.34 (6)SG 13.5 ± 0.2 4.1 (6) 3.4 (5) 6.0 (6) 0.105 0.68 (6)A&S 15 ± 0.2 3.8 (5) 2.3 (4) 8.9 (7) 0.108 0.70 (2)HOSP 12.2 ± 0.2 3.6 (5) 3.4 (5) 5.2 (3) 0.107 0.69 (5)

Fig. 8. Quantitative delineation of the coating microstructural features.

obtained from SANS measurements. This suggeststhat not only do the interlamellar pores play a rolein impeding the heat flow in the system, they alsoprovide a cushioning effect for the splats, thusaffecting the modulus in a similar way. The resultsshow consistency along these lines for three of thefour feedstocks.

The distinctive hollow morphology and broadparticle size distribution of the HOSP feedstockpowder may be the underlying reason for this coat-ing’s lower thermal conductivity and elastic modu-lus. The dimensions of the splats were measured inan attempt to explain this anomaly of low thermalconductivity and elastic modulus for the HOSPfeedstock. Fig. 12 shows splat morphologies fortwo cases: F&C and HOSP. The table within thefigure shows the splat thickness measured in eachcase. The thickness of the splats is the lowest forthe HOSP case, thus resulting in a large number

of splat interfaces and leading to a reduction in thethermal conductivity and elastic modulus. Itremains unclear as to why this high frequency ofsplat interface does not manifest itself in either theinterlamellar porosity or the surface area of thecoating made from the HOSP feedstock.

3.2. SANS-based models

Due to their unique morphology, the thermal andmechanical properties of plasma-sprayed coatingsare very different from the properties of the corre-sponding bulk materials. The existence of pore dis-tributions and splat boundaries significantlyreduces the thermal conductivity and elastic modu-lus of plasma-sprayed PSZ coatings. To estimatethe effective properties numerically, two require-ments must be satisfied. First, the model samplevolume must be large enough to include a rep-


Fig. 9. Single splat morphologies (50 µm scale-bar shown).

Table 6Values of E-Modulii for in-plane and out-of-plane directions

F&C SG A&S HOSP

E. Modulus [GPa] E. Modulus [GPa] E. Modulus [GPa] E. Modulus [GPa]

Perpendicular Parallel Perpendicular Parallel Perpendicular Parallel Perpendicular Parallel

Average 89 76 80 69 89 72 47 48Variation 13 14 20 17 21 20 10 11

resentative thermal or mechanical response. If themodeling volume is too small, the numericalresults may not be representative due to the stoch-astic nature of the plasma-spray microstructure,and also because of numerical artifacts introducedat the boundaries. Second, microstructural featuresmust be included in sufficient detail in the model

to reflect the real microstructure of the coatings.Various approaches have been taken, such as theObject Oriented Finite Element (OOF) modeling[27], which can be used to quantify real micro-structures from images produced by SEM oroptical microscopy. In the OOF method, consider-able detail, such as voids and impurities, can be


Fig. 10. Porosity–Thermal Conductivity relationships show-ing the close connection with interlamellar porosity. Verticalbars indicate the statistical standard deviation in the measuredthermal conductivity.

Fig. 11. Porosity–Elastic modulus relationships showing theclose connection with interlamellar porosity. Vertical bars indi-cate the statistical standard deviation in the measured elasticmodulus.

included as long as it is clearly visible in the inputimage. The method has considerable predictivecapability based on the empirical 2D representationof real microstructures over a limited sampledomain (typically a SEM field-of-view). However,a compromise must usually be made between thesmallest sizes resolved and the sample domain size(as controlled by the microscope magnification).Also, problems can arise in interpreting fine aniso-tropic features that are partly out of the plane ofview, particularly if the cracks or planar pores aredifficult to detect because of resolution limits.Thus, there is a need for more analytical micro-structure models such as that of Kachanov et al.[15]. However such models must include all of theessential microstructure components over the full

resolution range of significance, and must beapplied over a sufficiently large macroscopicdomain to accommodate the stochastic spatial vari-ations in the microstructure present in the actualcoating. To address these issues, we have con-structed a finite element model, which has both asufficient resolution and scale of domain, butincludes only the most important collective micro-structure components, such as total porosity, poremorphology and orientation, etc. To realize thismodel, volumetrically-averaged MSANS modelresults were graphically represented in a matrix. Afinite element simulation procedure was then usedto estimate the effective properties of these coat-ing microstructures.

Following along the lines of the MSANS analy-sis, we divide the internal voids into three compo-nents: interlamellar pores (“Pores” ), intrasplatcracks (“Cracks” ) and globular or irregular pores(“Voids” ). These three components differ in meansize, size distributions, orientation distribution andmorphology. However, for the model, all of thepore shapes are idealized to be hexagonal. Weassume that the aspect ratio b/a = 1/10 (a and bare major and minor axes, respectively) for Cracks,b/a = 1/5 for Pores, and b/a = 0.87 for Voids,which are here approximated as regular hexagons.Through MSANS analysis, the volume fractions,mean pore dimensions and orientations of thePores, Voids and Cracks can be determined, aswell as the total porosity. These mean openingdimensions closely correspond to the dimensionsof the microstructural features in the SEM imagesof the PSZ coatings. The procedures to build a 2Drepresentation of a 3D axially-symmetric porousmodel are shown below using the example of thecoating produced from the F&C feedstock powder.

First, a domain of 500 × 300 pixels is consideredas shown in Fig. 13(a), which also shows the spraydirection. The total porosity in the system andquantitative classification of void components byMSANS, coupled with SEM images of individualfeatures, allows the number of Cracks, Pores andVoids to be calculated, to the (convenient) totalof 600 features. Incorporating this volumetrically-averaged information defines a domain largeenough to predict stable results with a standarddeviation � 5% [13]. As an example, an illus-


Fig. 12. Figure shows the surface profile of single splat, the dimensions of which are quantified in the table.

tration of such a calculation for the coating fromF&C feedstock is presented. In this system with atotal porosity of 7.8%, calculations show 375Cracks, 190 Pores and 35 Voids to be present. Thesecond step is to generate the geometric model, asshown in Fig. 13 A. Given the dimensions of thesevoid systems, the resolution on the model is zoo-med to present the actual components, in this case0.01 µm/pixel. Feature locations are chosen ran-domly, while the orientation distributions of Poresand Cracks are each defined by the orientationalprobabilities obtained from the MSANS analysisof the real microstructure as shown in Table 7.Estimated uncertainties are given in parentheses. Inthis case, 289 Cracks are placed with the normal tothe crack between 60–90° from the spray direction(normal to the coating), 85 Cracks have their nor-mal between 30–60° from the spray direction, andso on. The exact value of the orientation (f) is stillrandomly determined within the specific ranges.Finally, a random finite element mesh is generated,as shown in Fig. 13(b). 11500 4-noded elementsare used in this model. Similarly, computationalmodels of the other three coating systems are con-structed. Although these 2D models do not directlyreflect the exact microstructure of the coatings,they do include the averaged geometric features ofthe porous structures.

Steady state heat transfer analyses were carried

out to calculate the effective thermal conductivityfor both the spray direction and the transversedirection of the four coating systems. For theanalysis of the vertical direction (i.e. the spraydirection), a fixed temperature is prescribed forboth the top and the bottom boundaries, and theother two boundaries are considered as isolatedboundaries, as shown in Fig. 14. An effective ther-mal conductivity in the spray direction can bedetermined from the following equation,

Keff �QL

W�T, (5)

where Keff is the effective thermal conductivity, Qis the total heat flux in the spray direction acrossa transverse model cross-section, W and L are thewidth and height of the domain, and �T is the tem-perature difference between the top and bottomboundaries. Note that Q is constant for any trans-verse cross-section in a steady state analysis. Theeffective thermal conductivity in the transversedirection can be calculated in a similar fashion.Table 8 shows the calculated results for the foursystems.

Fig. 14 shows the calculated heat flux in thespray direction for the coatings prepared from theF&C feedstock powder. It is clearly seen that thereare concentrations of heat flux between neighbor-ing pores. Thus, the presence of pores narrows the


Fig. 13. Computational model of the F&C coating system, with a domain size of 500 × 300 pixels. (a) Randomly distributed pores,grouped into three types: Cracks, Pores and Voids, with fixed temperatures T1 and T2 along the top and bottom boundaries The heatflux q = 0 indicates no heat loss across boundaries. (b) Finite element mesh, 11500 elements are used.

Table 7Distributions and morphologies of pores in F&C PSZ coating

Number of features b/a a (µm) b (µm)

0°� f � 30° 30°� f � 90° 60° � f � 90° Total

Crack 1 85 289 375 1/10 0.26(6) 0.02(7)Pore 168 13 9 190 1/5 0.26(6) 0.05(3)Void 35 1/1.15 0.34(7) 0.30(2)

(total porosity is 7.88%)


Fig. 14. Contour of heat flux in the spray direction for the coating made from F&C feedstock. Darker areas have higher heat flux.

Table 8Effective thermal conductivities of the four systems (Km = 2 W/mK)

F&C SG A&S HOSP

KL (W/mK) 1.62 1.37 1.35 1.42KT (W/mK) 1.55 1.31 1.35 1.34

path of heat transfer and this reduces the effectivethermal conductivity.

Fig. 15 shows the effective thermal conduc-tivities for the four systems, each normalized to thebulk thermal conductivity, Km. Here, KL and KT

are the thermal conductivity in the spray directionand in the transverse direction, respectively. Asshown, both KL and KT decrease with increased

Fig. 15. Comparison of calculated and experimental results ofeffective thermal conductivity for the four coating systems.

total porosity. The ratio of the effective conduc-tivity to the bulk conductivity (2 W/m K) rangesfrom 66–80%. The PSZ coating prepared from F&C feedstock has the lowest porosity in the four sys-tems, and the highest effective conductivity. Thecoatings from SG and A&S feedstocks have lowerconductivities due to higher porosities. The resultsshow that the effective thermal conductivities areslightly higher in the spray direction than in thetransverse direction, except for the A&S case. Thistrend can probably be explained by the orientationdistributions of the Cracks. Most Cracks tend to beoriented close to the vertical direction (i.e., cracknormals are nearly in the substrate plane). Thiscauses a higher thermal resistance to the heat fluxin the horizontal direction. Although the orien-tation distribution of the interlamellar pores is thereverse from that for Cracks, the total number ofCracks is much higher than that of Pores, exceptfor the A&S case. This results in a higher overallresistance of heat flux in the transverse direction.However, the difference in the effective thermalconductivities in the two directions is actually quitesmall. The largest difference is about 6%, whichis found in the model of the coating prepared fromHOSP feedstock.


The computed effective thermal conductivities(Table 8) are higher than those measured exper-imentally. One reason for this difference may bethe effect of the splat boundaries, which areexpected to have a considerable effect on the heattransfer, and are neglected in our models. Infor-mation about the properties of these splat bound-aries is being investigated using TEM. On the otherhand, mean opening dimensions and fixed aspectratios are used for each group of pores. In the com-putational results, the thermal conductivity in thespray direction KL is slightly higher than that inthe perpendicular direction, KT (except for A&SPSZ), while in experimental results, KT is higherthan KL. This difference also reveals the importantrole of splat boundaries and pore size informationin the thermal transport and modulus properties.Most splat boundaries and interlamellar pores areperpendicular to the spray direction, therefore, theyshould cause a greater decrease in KL than in KT.

The effective elastic modulii of the four systemswere also calculated using the same model. Theresults are shown in Table 9 and Fig. 16. It is seenthat the effective modulus also decreases for bothdirections when the total porosity increases. Theratio of effective modulus to the bulk modulus,which is around 200 GPa, ranges from 50–70%.The calculated results are higher than the experi-mental results for all the systems. Again, the mainreason is that the splat boundaries and the pore sizedistribution are both neglected. These have animportant influence on the overall modulus of coat-ings. Also, for the same reason, the calculatedmodulus in the spray direction EL is higher thanthat in the transverse direction ET.

The results show the effectiveness of a SANS-based computational approach for estimation of theeffective materials properties of thermally sprayedPSZ coatings. This method can deal with the largemodel domain needed to obtain consistent proper-

Table 9Effective elastic modulus of the four systems (Em = 200GPa)

F&C SG A&S HOSP

EL (GPa) 145.8 112.8 111.0 119.2ET (GPa) 134.6 104.2 111.4 107.4

Fig. 16. Comparison of calculated and experimental results ofeffective elastic modulus for the PSZ coatings.

ties, and the major microstructural features can beincorporated into the model. In SANS-basedmodeling, there are also some limitations, such asthe absence of splat boundary information and neg-lect of the pore size distribution. Differencesbetween calculated and experimental results arecaused by these model limitations. Future effortsare underway to minimize these differences bymodifying our models.

4. Conclusions

A quantitative characterization of the micro-structural features has been demonstrated success-fully in the case of plasma sprayed PSZ coatings,using a combination of anisotropic Porod scat-tering and MSANS scattering techniques. The rep-resentation of these microstructural features withrespect to their absolute porosities, mean openingdimensions and orientation distributions in a large


domain permits the development of a predictivecapability in estimating the properties of thesecoatings. A finite element based model has beensuccessfully developed to realize these volu-metrically averaged SANS results.

In this paper, the influence of feedstock charac-teristics (particle density, size and shape) on theanisotropic void structure has been quantified toestablish the processing-microstructure-propertyrelationships. These results are correlated withthermal conductivity and elastic modulus measure-ments, the properties most sensitive to these micro-structural features. Of the four feedstocks studied,the FC feedstock has the highest density of all thepowders, thus the highest thermal conductivity andelastic modulus. It is observed that despite higherporosity, the coating made from the A&S feed-stock shows higher thermal conductivity and elas-tic modulus than the SG feedstock. This isexplained through quantitative separation of voidcomponents from the SANS results where the A&S coating has globular porosity as major constitu-ent to porosity. Thus correlation with percent inter-lamellar porosity content explains the anomaly inthe two systems. Another important result isderived for the case of technologically relevantHOSP feedstock. This feedstock, in spite ofsuperior melting in the plasma (low porosity),exhibits low thermal conductivity and elasticmodulus. While the SANS results present someinsight to explain this behavior, the single splatstudies lead to the existence of a large number ofsplat interfaces in this coating. This may be attri-buted to the distinctive hollow particle morphologyresulting in thin splats. TEM studies to supportthese results are underway. Thus, the SANSresults, together with the corresponding single splatstudies, explain coating properties and some anom-alies in the porosity-thermal conductivity andporosity-elastic modulus results.

A finite element based simulation procedure,developed from the volumetrically averaged infor-mation of the representative microstructural fea-tures (in particular, the porosities, mean openingdimensions and orientation distributions) ispresented. The preliminary results of estimatedthermal conductivity and elastic modulus show theeffectiveness of this SANS based computational

approach. The calculated results differ from theexperimental results due to lack of information onthe splat boundaries and pore size distribution.Transmission electron microscopy studies areunderway to investigate further the details of thesplat boundaries. Thus, the SANS-based modeloffers a means for correlating processing with andmicrostructure properties, a key to predicting, aswell as increasing, TBC durability.

Acknowledgements

This research was supported by the NationalScience Foundation MRSEC program at the SUNYStony Brook under the Grant No. DMR-0080021.The authors also wish to thank J. Barker and C. J.Glinka of the NIST Center for Neutron Researchfor scientific and technical support.

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