Revista Latinoamericana de Metalurgia y Materiales, Vol. 21, N° 1, 2001,

MICROSTRUCTURAL TEXTURE IN MATERIALS SCIENCE:REFRACTORIES

M. Velez and M. KarakusCeramic Engineering Dept., University of Missouri-Rolla, Rolla, MO 65409-0330 USA

mvelez@umr.edu

Abstraer

This work summarizes important aspects of microstructure analysis of ceramics, emphasizing refractories. The objectiveis to use texture as a way of characterization. A comparison is made within different fields of Materials Science. The worki also part of an effort of organizing a huge database available on new and used refractories obtained from a range ofapplications. In this particular case, examples of applications in refractories for glass tank melters are presented. The finalgoal is to create a web digital library of microstructures for structural, refractory ceramic materials and related materials (i.e.,tones as defects in glasses, raw materials).

Resumen

Key words: Cathodoluminescence, Cerarnic materials, Optical microscopy, refractories

Este trabajo presenta algunos aspectos importantes en el análisis de la microest:ructura de material s cerámicos, haciendoénfasis en refractarios. El objetivo principal es la descripción de la textura como parte de la caracterización de estos materiales.Tambien se presenta una comparación en diferentes campos de la Ciencia de Materiales. El trabajo es un paso en un esfuerzode organizar la información disponible en relación a refractarios nuevos y usados (post mortem) en varias aplicaciones. Enparticular, se presentan ejemplos de refractarios empleados en la fusión y producción de materials vítreos. La meta final escrear una biblioteca digital, disponible en Internet, sobre la microestructura de materials cerámicos y ejemplos relacionados(i.e., defectos en vidrio provenientes de materiales refractarios, materias primas)

Palabras Clave: Catodoluminescencia, Cerámicas, Microscopía óptica, Refractarios

1. IntroduetionA surface property that has a direct impact on the

results of many types of analysis ofmaterials is its texture or roughness. In general, texturecan be defined as any three dimensional feature(s) foundon a very small or large surface, and these features canrange in size from the atomic level (-10 nm, as in an or-derly array of atoms) to earth-size or macro level (tens ofkm, as in satellite imagery of the earth surface). Texture issometimes referred in Materials Science by other terms,inc1uding surface appearance, surface texture, surface to-pology, surface morphology, surface topography, crystal-lographic texture (or preferred orientation of crystallites),surface roughness, rugosity, particle shape, spatial struc-ture of the surface laye r, textureof rocks (as in Geolo gy,where sedimentary rocks are described by the size and shapeofits constituents particles), mathematical morphology, andpattern spectrum. Selecting the right/correct/bést charac-terization method is critical to accurately describing theexact texture of the surface in question and its features.

Examples of applications are found in the analy-sis of very flat surfaces, such as polished silicon wafers,and also on metal s and ceramics, with roughness in the

order of micrometers. Two surface roughness terms arecommonly used: average roughness, RA, and root-mean-square, RMS. For N measurements of height z¡ and aver-age height z, the average roughness is the mean deviationof the height measurements and can be described as:

N

RA = (J/~'¡)?:z - z :I

i=1

and RMS is the standard deviation

N

RMS = [(l/N) ? :(z - z )2:112I

Several measurement techniques are in usage to-day, the optimum method depends on the type and scale ofroughness to be measured for a particular application. Sur-face roughness is commonly measured using mechanicaJand optical profilers, SEM, and atomic force and scanningtunneling microscopes. In the profilometer technique. astylus connected to an electromechanical tran du r'dragged along the surface, and the centerline average (U--\roughness is calculated from the mean amplimde of mefluctua

M. Velez and M. Karakus /Revista Latinoamericana de Metalurgia y Materiales

tionsof the amplified electrical signal.Angle-resolved scatterometers are also applied to sur-

face roughness measurement. Depth of resolution is an im-portant parameter for characterization (Table 1). Opticalscatterometry involves ilIurninating a sample with light and

measuring the angular distribution of light that is scattered.The technique is useful for characterizing the topology oftwo general categories of surfaces. First, on surfaces thatcan be defined by some surface statistics, and second, forthe shapes of structures (lines) of periodically pattemed sur-faces.

Table 1. Analytical methods for surface cheracterization (adapted from [1]).

Technique Oepth res o lut ion Lateral resolution Observations

Light rniaoscopy 0,2 wrn \¡\Atll whte light MorpholOJY, opticalprope tíes

Optica I m icroscopy \J\A tll 10 nrn to seve· al urn,Qualitative and

~lwrn quantitative analysis ofcatllodolurninescerce [2] dependirQ on Electron defe:ts, and tllEir

bea m ene gy di str ibuti on

Mematical proftle- [3] 0,5 nrn 0.1-25 wrnMeasU'es surfaceroughness

Optical seatterornete- 0.1 nrnLase wavElerQtll used Topographl"

to illurninate the sarnple characte- izatíon

Optical profiler 0.1 nrn 0,35-9 um suface rOJghness

SBvl From nm to urn, 1-50 nrn in secondary(images can be

dependi rQ on lile enhancEd by usingaccElerati rQ voltage Electron m ode staeo pa ir5 )

SLM" [4]Topography data ofsurface textLre

STMjSFMO STM, 0,1 nrn; STM, atomi c; Real-spaoe 3D irnagirQ,SFM, atornic to 1 nrn high resolution

SFr-'l, 1 nm proft Iornetr y

TEM None 0.2 nrn or better Atorni e structir e andmicrostructural analysis

EOSc 0,02 to wmOS 1 wm fa bulk IrnagirQjmapping of

samoles: ",1 nrn fa tllin cherni cal Elernentsseeti ons in STBvld

STBvld NoneIrnagirQ, 0.2-10 nrn; Mieros tructur al,

EB..S", 0,5-10 nrn; crvs tal!ogr aphi e ardEOS~ 3-30 nrn eornpositi onal ana Iysis

E~Ar leo nrn to 5 pm leo nm to 5 wm Quanti tativ e analysis ofmajor, rrínor, and traceconsti tuents

LEE09 0.42 nm 0,1 rnrn to ",10 tmSU'faee erystal!ogr aphyand rnicrostr uctur e

RHEED~ n.z-mrm 2eo wrn x 4 mmsuface structure ofcrys tal s, distinguis hesbetween d) and 3Ddefe:ts

E9:A' AES, 5-10 nrn; AES, 30 nm; su face cornpositionAESi ISS, ruterrnost atorni c ISS, 150 wrn; characte-izationISS~ layer; SIMS,down to 100 wrn

SIMS1 SIMS, 1 or 2 mondava s

aConfocal Scanning Laser MicroscopybScanning Tunneling Microscopy and Scanning ForceMicroscopyCEnergy-Dispersive X-Ray SpectroscopydScanning Transmission Electron Microscopy

eElectron Energy-Loss Spectrometry

'Electron Probe X-Rey Microanalysis

9Low-Energy Electron DiffractionhReflection High-Energy Electron Diffraction

iElectron Spectroscopy for Chemical AnalysisiAuger Spectroscopy'Ton Scattering Spectroscopy

'Secondarv Ion Mass spectrometry

Revista Latinoamericana de Metalurgia y Materiales, Vol. 21, N° 1, 2001.

. Surface damage in terms of craters, cracks, voids, androughness has been reported inrelation to machining brittle materials,· such as ceramics.Except perhaps for the intent of quantitatively describingirregular fracture surfaces withfraetal geometry [5], mostof this work is based on descriptive observations from mi-crographs (optical or electron microscopy) with little quan-tifying of the damage. Surface damage will effect deterio-ration of the mechanical properties, such as strength. Inorder tocharacterize the surface integrity of machined surfaces ofceramics, the flexural strength can be used as measurementsince it is dependent on poth its inherent resistance to frac-ture and the presence of defects [6]. Applications are found,for instance, in thecharacterization of limestone caIcined under different con-ditions [7].

The surfaces of most particles are rough on a micro-scopic scale, and the contact occurs athigh points, which are called asperites [8]. Layer silicateminerals and pristine amorphous solids have relativelysmooth surfaces with irregularities finer than 100 nm.Crushed mineral s have surfaces with step-like featurescoarser than a few rnicrons, and aggregates have very roughsurfaces with irregularities approaching the crystallite size.Interparticle friction and sliding is resisted by chemicaladhesion anJ¡ physical resistance produced by the micro-scopic steps and asperites on the particle surfaces.

Pattern Recognition Theory has been introduced to per-form surface textures classification [9], and in general todescribe better the texture of engineering surfaces usingcomputer and mathematical tools. For instance, usingAtomic Force Microscopy (AFM) image representing thesurface textures of various material s formed by various pro-cesses and treated by mathematical transformations. TheresuIts are linked to properties of surface materials and theprocess of growth and crystallization on the interface ofdifferent materials. Other advanced techniques are repre-sented by the attainment of fraetal dimensions from SEMimages [10], the use of Scanning Tunneling Microscopy(STM) to characterize mathematically surface texture pa-rameters [11], the analysis of fiber optic transducer andconventional profilometer data by use of statistical func-tions [3], and by using Fourier analysis of AFM images[12]. Another emerging techniques include Gaussian Tex-ture Analysis of SEM rnicrographs, as in this case, of or-ganic materials, carried by the Center of Imaging Science[13]. In particular, the work at the Center of Imaging Sci-ence at Rochester University on morphological texture clas-sification indicates that gray-scale granulometrie classifi-ers can discriminate between textures that have rather simi-lar visual characteristics [14].

This work exemplifies different microstructure texturesencountered in Cerarnics, with special emphasis in refrac-

5

tories using optical and electron microscopy. Several ex-amples are typified and some problems are presented.2. Texture in Materials

2.1. Ceramics

Orienting or aligning a second phase such as fibers,whiskers, and platelets during green body or powder con-solidation processing can achieve textured ceramics. Tex-tured cerarnics show improved 01' unique properties (elec-trical, magnetic, and mechanical, forinstance) and have been obtained by applying field gradi-ents during fabrication. Texture can be developed in ce-ramics, which lack plasticity as compared to metals, bygrain rotation or oriented anisotropic grain growth [15].Common processing methods include hot-forging, hot-pressing, tape casting, extrusion, and slip casting. As anexample, high-textured mullite has been obtained by en-hancing the anisotropic grain growth by Ti02-doping andby templating grain growth on oriented acicular mulliteseed particles in a mullite precursor [16]. The in situ graingrowth and alignment wasdeveloped by tape casting in mullite-whisker-seeded andtitania-doped diphasic mullite gels.

Processing also has effect on the crystallographic tex-ture domain, as on the successive thermomechanical treat-ment ofBi-based (2223) superconductor Ag-sheated tapes,by pressing and rolling results indicate a large increase inthe crystalline density and preferred orientation in the ini-tial steps, and saturation after the third cycle of treatment[17]. Another applications are found on eteroepitaxialdiamond film growth [18], hurnidity-sensing behavior ofsulfated zirconia [19], surface texture of multicrystallinesilicon solar cells [20], and the fabrication and evaluationof composite ionic conductors [21].

2.2 Comparison lo Metals

Local variations in chernical composition and micro-structure arise during manufacture and processing of met-als. Furthermore, the rnicrostructure rnight be anisotro-pie, and variations rnight exist, for example, between thetransverse and the longitudinal directionof rolled metal bars or textures may occur. Textured SUf-

faces can be used to impart a number of desirable proper-ties 01' characteristics on finished metal products [22]. Thetypes of textures that are often rolled onto the sheets usedfor refrigerator panelsserve to conceal dirt, for instance. Embossed or coinedprotrusions can enhance the grip of metal stair treads andwalkways. Corrugations provide enhanced strength andrigidity. Still other textures can be used to modify theoptical or acoustical characteristic of a material.

6 M. Velez and M. Karakus /Revista Latinoamericana de Metalurgia y Materiales

Crystallographic Texture develops in metals duringplastic deformation by slip plane rotation. Preferredorientation in polycrystalline materials can be detectedwith a Debye-Seherrer eamera and diffraetometer withtexture attaehment [23].The use of eleetron backseattering diffraetion patterns(EBSPs) in eonjunetion with SEM allows the determina-tion of preferred orientation, or crystallographic texture,in combination with microstructural data [24]. Ex-amples are found in textures induced by extrusion ofaluminum alloys [25,26], processing of zincelectrogalvanized coatings [27], electrodeposition ofpolycrystalline Ni [28], processing of ferritic alloys [29]and steels [30].

The analysis of microstructural images (QuantitativeMetallography) ean be consideredas an abstraet problem of 2D or 3D geometry without anyaccount of the actual phase compositions. This branch istermed Mathematical Morphology (MM) and it is gener-ally valid for all microstructures [31]. The methods ofMM are designed to quantify geometric structures; a po-rous medium, for instance, is made of two complimentarysets, grains and pores. Quantifying any structure thencomes down to measuring sets, obtained by successivetransformations, which from the initial image will pro-gressively reveal the set to be measured. These transfor-mations are cornbinations of elementary morphologicaltransformations [32].

Quantitative metallography refers to the accumulationof data necessary to describe a 3Dmicrostructure, tbat is, its 3D dimensional geometry, usu-ally to correlate microstructure to manufacturing or per-formance history. The geometrie parameters are describedbased on the standard morphological, such as maximumparticle diameter or mean intereeptlength. The following possibilities for quantifying the mi-erostructure are available [31]:1. Description of basic 2D parameters such as area frae-ti on , and planar size distribution;2. Complex 2D description including shape and arrange-ment of mathematical morphology;

3. 3D deseription by stereological parameters such asvolume fraction, spatial size distribution, specifie surfaeearea, derived from 2D measurements; and4. Direct evaluation of 3D geometry by sectioning or ste-reometric measurements.

2.3 Catalysts and Ceramic Membranes

Textural properties of catalysts are an important area ofcharacterization of catalytic materials. It comprises sur-face area, total pore volume, and mean pore radius [i.e.,33,34] and texture. Surface area, pore size and pore vol-ume are among the most fundamental and important prop-

erties in catalysis because the active sites are present or dis-persed throughout the internal surface through the reac-tants and products are transported. The size and number ofpores determine the internal surface area. It is usually ad-vantageous to have high surface area (high density of smallpores) to maximize the dispersion of catalytic components;however, large molecules might be excluded from passingthrough the small pores, which might have an importanteffect in given process. The pore structure and surface areamust be optimized to provide maximum utilization of ac-tive catalytic sites for a given feedstock [35]. A pure metalcatalyst will change in surface roughness or crystal struc-ture during use.

Promoters in catalysis can be classified as either texturalpromoters or structural promoters. A textural promoter isan inert substance, which inhibits the sintering of microc-rystals of the active catalyst, by being present in tbe form ofvery fine partic1es (physical effect), while structural pro-moters act by a chemical effect. As example of application,chromia/zirconia catalysts have been tailored in texture frommicro porous to mesoporous and macroporous material s[36].

Crystallographic texture is also of interest in the devel-opment of special functions in membranes, for instance,special boehmite gel membranes exhibit (020) texture, andthe (020) surface of gamma-AIOOH(boehmite) grains are parallel to the top surface of the mem-brane [37].

2.4 Cement Pastes and Concrete

The morphological characteristics of coarse aggregatescan be measured by standard methods such as the test metbodfor index and particle shape and texture (ASTM D- 3398);the test method for uncompacted void content of coarse ag-gregate as influenced by particle shape, surface texture,and grading (ASTM C-1252); and the test method for unitweight and voids in aggregate test (ASTM C-29). DigitalImage-analysis has also been used to characterize coarseaggregates, by using improved techniques as in evaluatingasphalt-concrete mixtures [38].

The particle shape and surface texture of normal Port-land cement and supplementary materials has been observedby using AFM where neither profilometer [39] nor SEM[40] ean provide detailed images of the fine materials. Jthas been shown for example, that siliea fume is composedof two complimentary parts (hemispheres or eylinders),nano-size particles are found in all materials, and a rela-tively smooth surface was ob erved in tbe hydrated cementpaste [41]. Fine texture is referred as a general indicationof grain ize. as in the measurement of alite grains usingpoli hed crosssections in t clinker [42], measured by opti-cal microsctlpYCc:1W;;Z;;~a::::!h~i2IrlIODcement-based materials, directly••...••""-4.. •••••;;::::rosm!C(]rre development, is a current area of

Cezecr-oesed materials are considered random com-;' length scales and understanding of the

Revista Latinoamericana de Metalurgia y Materiales, Vol. 21, N° 1, 2001.

macro- and microstructure would lead to the understand-ing ofthe microstructure-property relationships [43]. Forinstance, one current approach at the National Institute ofStandard Materials (NIST) is to characterize the micro-structure of concretes using optical and electro n micros-copy and digitizing the information (color, texture, andgeometrical parameters). The digital data is then analyzedand used to simulate hydration reactions, percolation prob-lems, and microstructure development.

2.5 Refractories

The phase composition, porosity, and texture of refrac-tories are deterrnined experimentally, routinely using at leastoptical and electron microscopy of polished samples. Thestarting compositions, and particle sizings, and processingtechniques together with firing schedule, affect the results.Thus, crystallite size and aggregate size are a measure oftexture in refractories, defects such as microcracks can alsobe imaged and measured. In many refractory bricks, pre-existing cracks are in the millimeter range, even up to thearder of 10 rnrn. An increasing extent of microcrackingmust accompany increasingly coarse-crystalline rnicrostruc-tures and the use of stil! coarser-sized premanufacturedgrain or aggregate is cornrnon [44]. Accordingly, depend-ing on the coarseness o/ their texture, refractories can beexpected to have a markedly below-cerarnic Young's modu-tus values. A further consequence of micro cracking withopen porosity, which also sets refractories apart from fine-grained ceramics, is a sharp reduction of the elastic limit.Texture and coarseness also have influence on corrosionbehavior of refractories. Since the surface:volume ratio ofthe grain particles increases as their size decreases, thesmaller particles are successively more vulnerable to cor-rosive-liquid attack. Thus, compromising the corrosionresistance of the grain somewhat by the use of graded siz-ing improves the resistance of the grain-matrix-pore sys-tem as a whole.

Physical characterization of refractory aggregates rou-tinely include visual analysis (macro- and microscopic),particle size distribution, packing density, aggregate shape,surface texture, and particle density - where surface tex-ture indicates the 2D rendering of the surface, or perhapsthe 3D detailing of the physical surface; i.e., surface mor-phology. Microcracking and presence of inclusions can alsobe noted by visual analysis and description of the surfacetexture.

Most monolithic refractories contain alumina aggre-gatesof various types including fusedaluminas, tabular alumina, and calcined bauxite. Thesurface morphology is enhanced by using specialtechniques, such as optical microscopy assistedwith cathodoluminescence (CLM) of polished sections. Theanalysis of different refractories using CLM has beenpresented earlier [45-48]. Thermal annealing of high-

alumina ceramics coupled with scanning electronmicroscopy is another cornrnonly employed method.

2.6 Post-mortem Study of Glass Melting Furnaee Refrac-tories

The Refractories Research Center in University of Mis-souri-Rolla initiated the research program "Post-mortemcharacterization of glass plant refractories", in 1996, in or-der to understand refractory corrosion mechanisms and todevelop refractories for the glass making industry. The pro-gram involves collection of a large group of post-mortemglass plant refractories and their characterization as well aslaboratory corros ion test simulation. CathodoluminescenceMicroscopy (CLM) technique is the primary characteriza-tion technique. The description and advantages of the tech-nique and the preliminary study of the post-mortem glassplant refractories have already been summarized [49].

Figures 1 and 2 show the corrosion texture of silica re-fractories [50] under optical and electron microscopy. Re-flected light (Fig. la) shows the typical "fish scale" mor-phology of cristobalite, however, CLM shows the dendriticmorphology that indicates a liquid phase (about 250 Imthick) during refractory service. It also shows cristobaliteat deeper locations, as well as prismatic tridymite, and wol-lastonite green fibers.

Fig. 1. Optical microscopy (reflected light andcathodoluminescence) of a silica crown brick exposed to oxyfuelconditions. Dendrite crystals of cristobalite (blue CL) and amor-phous Na.Osrich Ca-silicate glass matrix are shown at the hot face(left side).

8M. Velez and M. Karakus /Revista Latinoamericana de Metalurgia y Materiales

A similar information is obtained using SEM (Fig. 2),however, this technique is more expensive than CLM. Bothtechniques are complementary and for complete analysischemical analysis (wet method of core sections), SEM probeanalysis, and XRD is routinely made. Corrosion of AZSchecker bricks by alkalis and alkali sulfates has also beenstudied and described earlier [51].

Another application is the study of microstructures ofregenerator bricks in glass tank melters. Figure 3 illus-trates the microstructure of a periclase checker brick con-taining 95-98 % MgO. The material had a visual shatteredor burst appearance. The interior of the brick was pink incolor while the outer surface was green in color. Under theoptical microscope, periclase grains exhibited red CL color.Also, silicate phases forsterite and monticellite were iden-tified. Grain growth of periclase in the outer burst surfacewas also noted. Thermal f1uctuation, volume reduction,grain growth, and silicate phase formation are the causesfor the failure (bursting) of these checker bricks.

Fig. 2. SEM micrograph of a commercial silica crown brick ex-posed to oxyfuel conditions (1500°C, 200-300 ppm NaOH, 10days). Hot face is at left side, a few closed pares remain usually

larger than 400-500 microns.

Fig. 3. RL and CL micrographs of 98 % periclase checker brick from top course showing grain growth of periclase. Many pares areentrapped and enclosed within the periclase grains which are visible in the CL micragraph. Monticellite (yellow CL) is observed at the

grain boundaries of periclase

Fig. 4. RL and CL micrographs of direct bonded Mag-Chrome checker bri k. showing a silicate impurity phase, primarilymonticellite (yellow CL al grain boundaries.

Revista Latinoamericana de Metalurgia y Materiales, Vol. 21, N° 1, 2001.

Figure 4 illustrates the microstructure of direct-bonded Mag-Chrome regenerator crown bricks. The surface of thesebricks was damaged and extremely crumbly. In this zone,high porosity, silicate impurities as well as sulfate phaseswere observed. Although these bricks were direct-bonded,they still contain significant amounts of silicate phases.

The last example (Fig. 5) illustrates the microstructuresof chrome-free, fused cast, cruciform AZS block. Thissample was 2 inches thick and was coated with a yellowishfoam-like glassy material. It had a crumbly appearanceand broke in a columnar habit. The original material wasknown to be a fused cast, chrome free, AZS checker brickwith a chemistry of 50.6 % AIP3' 32.5 % Zr02, 15.6 %Si02, and 1.3 % Na.O. The foam-like coating on the sur-face contained Na-Ca-sulfate, Na2Ca(S04\' Na-Ca-Mg-AI-silicate phase, spinel, zircon and other dust partic1es. It is

very c1ear that the checker bricks were subjected to a verycorrosive gaseous and dust environment. The originalmaterial did not contain any CaO, MgO, and S. The alka-line sulfates and dusts from the batch carry over react withthe checker brick resulting in foamy surface texture due tothe glass formation and volume changes.

An ultirnate goal of the characterization prograrn at UMRis the creation of a digitallibrary for refractories, includingrefractories for glass manufacturing, defects in glasses andraw materials. Several independent techniques can be sum-marized into a large database that can provide easy accessand full documentation to users (students, field engineers,technicians, researchers). This could result in a unifiedsource of information for ceramic microstructures, regard-ing definitions, norms, and specific terminology.

Fig. 5. RL and CL micrograph of fused-cast, chrorne-free cruciform AZS checker brick showing corrosion and peeling-off AZS materialby alkalis and alkaline earth sulfates. Spinel (green CL), NaFa(S04)2' as well as Na-Ca-Mg-Al-silicate phases were forrned as results

of reaction between alkaline sulfates and AZS checker brick.

3. Conclusions

This work summarizes important aspects of microstruc-ture analysis of ceramics, emphasizing refractories. Theobjective is to use texture as a way of characterization. Acomparison is made within different fields of MaterialsScience. Characterization of material s is important to de-cide on the performance under different conditions (micro-structure-properties relationship and prediction of proper-ties, failure analysis, product development) and dependson the use of several techniques. The identification rou-tine1y consists on the confocal use of various methods:chemical analysis, X-ray diffraction, physical and chemi-cal properties determination, etc., with the use of agreednorms and regulations (i.e., ASTM standards, DIN, etc.).One cornmon technique of identification is the use of opti-

cal and electron microscopy. Such work describes the mor-phology of the materials at different resolution levels.Cathodoluminescence microscopy (CLM) examples arepresented here as an alternative for a supplemental tech-nique to aid in the identification and characterization ofrefractories. The technique is suitable for most caseswhereas most powerful techniques, such as SEM, may addvery little in some cases and/or are more expensive. CLM(color images), and all microscopy in general, present theinformation in image data formo This makes mandatorythe use of an electronic version for the digital display of theinformation. The final objective of the program at UMR isto create a digital library of ceramic microstructures(DLCM) for structural, refractory materials and relatedcases.

10 M. Velez and M. Karakus /Revista Latinoamericana de Metalurgia y Materiales

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