effect of crystal orientation on lapping and polishing processes of natural quartz

ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 47, no. 5, september 2000 1217

Effect of Crystal Orientation on Lapping andPolishing Processes of Natural Quartz

Pedro L. Guzzo and Jose Daniel B. De Mello

Abstract—Lapping and polishing processes of naturalquartz are investigated in relation to crystallographic orien-tation and applied normal stress. Weight loss measurementsand surface profilometry were carried out in X-, Y-, Z-,and AT-cut samples. The relationship found between mate-rial removal rate and stress depends on specimen orienta-tion. Based on indentation fracture mechanics, this behav-ior is discussed in relation to fracture toughness and scratchhardness anisotropy of quartz crystals. Scanning electronmicroscopy (SEM) shows that brittle microcracking is theprimary mechanism involved with material removal in thelapping process. Plastic deformation mechanisms begin tooperate on lapped and polished surfaces above a certainvalue of stress. Surface profiles and SEM micrographs showthat the roughness of lapped surfaces decreases with in-creasing normal stress, but an opposite behavior is observedin polished surfaces.

I. Introduction

Since the 1940s, α-quartz has been the material ofchoice in the majority of frequency control devices. Due

to its piezoelectric and elastic properties, quartz crystalshave been used in the production of electromechanical de-vices such as resonators, filters, and sensors [1], [2]. Virtu-ally all devices fabricated today use cultured quartz. Thesecrystals exhibit greater uniformity than natural quartz andare frequently available free from inclusions, twins, andwith low amounts of impurities. One of the remaining usesof natural electronic-grade material is in the manufactureof resonators used as pressure sensors in deep wells. Inaddition to crystal quality, the manufacturing technologyused to fabricate these units is of primary importance.The metrological accuracy required for high-Q resonatorsdepends on both surface finish and accuracy of plate ge-ometry [1]. Because quartz is a brittle material, lappingand polishing are one of the few types of manufacturingprocesses that can operate on a fine enough scale to gen-erate surfaces with required topography and plates withrequired accuracy.From the tribological point of view, lapping and polish-

ing processes are classified as three-body abrasive wear inwhich hard abrasive particles (grits) are free to roll andslide between two sliding surfaces and cause damage on at

Manuscript received July 7, 1999; accepted April 7, 2000. Thiswork was financed by CNPq (P:620136/92-8) and FAPEMIG (TEC263/92). One of the authors (P.L.G.) is grateful for financial supportprovided by CNPq and FAPEMIG.The authors are with the Universidade Federal de Uberlandia, De-

partamento de Ciencias Fısicas, Laboratorio de Tribologia e Mate-riais, Campus Santa Monica, Bloco 1R, 38400-902 Uberlandia, MG,Brazil (e-mail: [email protected]).

least one of the two surfaces [3]. With lapping, the materialremoval occurs by multiple indentations and scratches dueto the interactions between the lapping plate, the speci-men, and the abrasive particles. Polishing is regarded asa special case of lapping, which can be modified by chem-ical processes and typically produces specularly reflectingsurfaces [4]. Direct evidence currently available indicatesthat the basic mechanisms by which material is removedduring abrasive wear [3] depend on a large number of oper-ating conditions such as hardness, shape, and size of abra-sive particles, contact forces, sliding velocity, and abrasionfluid. Because the rate of material removal and the surfacefinish are affected by the nature of wear mechanisms, itappears worthwhile to better understand the fundamentalaspects of abrasion in quartz crystals.In the present work, lapping and polishing of quartz

single crystals were studied in relation to crystallographicorientation and normal stress. X-, Y-, Z-, and AT-cut sam-ples of natural quartz were lapped and polished with nor-mal stresses ranging from 3 to 97 KPa. Wear micromech-anisms and surface roughness were characterized by scan-ning electron microscopy and surface profilometry, respec-tively. Roughness and material removal rate are sensi-tive to applied normal stress and are dependent on speci-men orientation. This dependence is discussed in relationto fracture toughness and scratch hardness anisotropy ofquartz crystal and indentation fracture mechanics.

II. Experimental Procedure

A left-hand natural quartz block was oriented using po-larized light, etching, and X-ray diffraction techniques [5].X-, Y-, Z-, and AT-cut plates free from inclusions andcracks were cut up on a diamond saw to within ± 1◦ of therequired crystallographic plane. Following the IRE stan-dard [6], X-, Y-, and Z- cuts were identified by {11 2 0},{10 1 0}, and {0001}, respectively. The AT-cut is turnedof 3.5◦ in relation to the minor rhombohedral plane {01 11}. The plates were lapped with a coarse alumina (Al2O3)abrasive to eliminate surface flaws induced by sawing andto improve the parallelism between faces. Cylindrical sam-ples with 14.25 mm in diameter were then obtained by us-ing ultrasonic machining. These samples were etched in asolution of HF (40%) during 15 minutes in order to observethe presence of twins; they then were lapped to match thethickness of 5.5 mm.Lapping and polishing experiments were carried out in

a Logithec PM4 precision lapping machine in which it was

0885–3010/$10.00 c© 2000 IEEE

1218 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 47, no. 5, september 2000

possible to monitor the rotation of the lapping plate, thetime of abrasive machining, the slurry flow rate, and thenormal force applied on the sample. The lapping was madeon a cast iron plate with radial grooves, and the abrasiveused was alumina with mean grain sizes of 3 and 15 µm.The polishing was made with alumina of 0.05 µm on a platerecovered with expanded polyurethane. In both cases, theconcentration of the slurry was 85 g/l of distilled water.The abrasive slurry was continuously supplied during theexperiments. The normal force varied between 0.5 and 15.5N, and the sliding speed was fixed on 75 mm/s. Three ex-periments of 20 minutes were performed for each tribolog-ical condition. The material removal rate was determinedby weight loss, using a MC210P Sartorius balance withprecision of 10−5 g. The roughness profiles were obtainedat the end with a Rank Taylor Robson profilometer, typeSurtronic 3+, using a cut-off value of 0.8 mm. Seven pro-files were obtained in random directions on the specimensurface. The center-line average (Ra) and the average ofthe peak-to-valley heights (Rz) were chosen to character-ize the surface roughness. By using a Carl Zeiss DSM 94Amicroscope, scanning electron microscopy (SEM) was usedto characterize the wear micromechanisms responsible formaterial removal and surface finish related to lapping andpolishing processes.

III. Results

Prior to testing and recording of actual rates of materialremoval, the circumstances under which weight loss varieswith the time of lapping were investigated. Fig. 1 shows theevolution of material removal rate (MRR) as a function oftime measured at tribological conditions that exhibit theessential features of lapping and polishing processes usedin this study. The MRR varies over a wide range whenlapping is carried out with a grit size of 15 µm and normalstress (Pn) equal to 96.9 KPa. When lapping is performedwith 15 µm grits and Pn = 3.1 KPa, the variability of theMRR observed above 10 minutes are under statistical fluc-tuations usually found in abrasive wear processes of brittlesolids. For abrasive particles with 1 µm, MRR seems to beindependent of lapping time. Based on these observations,the time of lapping and polishing experiments was set at20 minutes.Fig. 2 shows the MRR as a function of Pn used to lap

X-, Y-, Z-, and AT-cut samples of natural quartz. For bothsizes of abrasive particles, MRR increases with Pn up tonear 50 KPa. Above this value, MRR is not significantlyaffected by Pn. In the range of stress investigated here, weobserved that the MRR resulting from lapping with 15 µmgrits was roughly twice the respective rates obtained withgrits of 3 µm. Fig. 2 also shows that the relationship be-tween MRR and Pn is dependent on specimen orientation.AT-cut exhibits the highest material removal rate, whichdecreases in the sequence, AT > Y ∼= X > Z. The weightloss measured after the polishing process is near zero forall specimen orientations.

Fig. 1. Evolution of material removal rate (MRR) with lapping timefor alumina grits of 1 µm and 15 µm.

The relationships between the center-line averageroughness (Ra) and Pn are shown in Fig. 3. In Fig. 3(a) weobserved that Ra measured on surfaces lapped with gritsof 15 µm decreased with increasing Pn up to near 40 KPa.Above this value, Ra decreased for AT-cut and remainedunchanged for the other specimen orientations. Fig. 3(a)also shows that Y- and AT-cut exhibit larger values of Rathan X- and Z-cut samples. In lapping with 3 µm grits, Fig.3(b) shows that Ra continuously decreases as Pn increases.Also, the roughness of Z-cut is lower compared with thoseof X-, Y-, and AT-cut samples. However, Fig. 3(c) showsthat the polishing wear performed with high stresses in-creases the roughness independently of specimen orienta-tion. Compared with Y-, Z-, and AT-cut surfaces, Fig. 3(c)also shows that the roughness of X-cut is more affected byPn.

guzzo and de mello: lapping and polishing of natural quartz 1219

Fig. 2. Relationships between the rate of material removal (MRR)and the normal stress (Pn) of natural quartz samples lapped withalumina grits.

The dependences of MRR and Ra with Pn resultingfrom the lapping process can be adjusted by a power rela-tion of the form:

MRR = a(Pn)p (1)

and

Ra = b(Pn)q (2)

where a and b are proportional constants and p and qare exponents. Considering each lapping condition sepa-rately, Table I shows the values of a, b, p, and q obtainedby least square linear regression. From the fitting factorvalues shown in Table I, one observes that MRR and Raare satisfactorily correlated with Pn by (1) and (2), re-spectively.The micrographs in Figs. 4 and 5 represent the surface

patterns resulting from lapping and polishing processes.Fig. 4 shows that the nature of wear micromechanismsand the size of individual events (such as cracks, indenta-tions, and scratches) are readily affected by both normalstress and abrasive grit size. Figs. 4(a), 4(c), and 5 showthat brittle microcracking controls the material removalin lapping processes performed with low stresses. A com-plex wear situation is observed when lapping is carried outwith normal stress higher than 40 KPa. Besides brittle mi-crocracking, Figs. 4(b) and 4(d) show the existence of flatzones, which probably were generated by plastic deforma-tion mechanisms. The presence of flat zones on lapped sur-faces explains the decrease in roughness in Figs. 3(a) and3(b). Fig. 5 shows that the size of events related to brittlemicrocracking is dependent on specimen orientation.

IV. Discussion

A. Wear Micromechanisms

Brittle microcracking may occur when highly concen-trated stresses are imposed by abrasive particles, partic-ularly in the surface of brittle solids. In this case, largeamounts of material are detached from the surface dueto crack formation and crack propagation [3]. From in-dentation fracture mechanics [7], [8], surface loading bya sharp indenter can result in radial, median, half-pennyand lateral vents under the point of indentation. As abra-sive grits can be simulated by the translation of sharp in-denters across the surface [9], the effectiveness of brittlemicrocracking in abrasive wear will depend on the lengthof cracks through the media. According to Lawn andFuller [10], the length of median vents induced by pyra-midal indenters increases with increasing normal stressand indenter sharpness. The extension of radial and lateralvents are related to extension of median vents and residualstresses associated with the zone of inelastic deformationabout the singular point [7]. In lapping with loads lowerthan 50 KPa (where brittle microcraking appears to bethe primary wear mechanism), crack length increases withincreasing normal stress due to severe interaction between


TABLE IProportional Constants and Exponents of Material Removal Rate (MRR) and Surface Roughness (Ra)

Dependences on Normal Stress (Pn) Related to Lapping Process of Natural Quartz.

MRR vs. Pn Ra vs. Pn

Abrasive grit size Crystal plane a p R1 b q R1

15 µm X 14.57 0.22 0.98 0.31 -0.05 0.99Y 19.32 0.16 0.92 0.41 -0.08 0.92Z 13.44 0.17 0.95 0.27 -0.03 0.95AT 24.12 0.14 0.97 0.34 -0.05 0.94

3 µm X 4.18 0.35 0.96 0.13 -0.05 0.99Y 7.03 0.21 0.99 0.12 -0.05 0.81Z 6.21 0.17 0.99 0.12 -0.07 0.99AT 13.25 0.15 0.96 0.12 -0.04 0.96

1Fitting factor R is defined by R = r2, r is the correlation coefficient.

the specimen surface and the points of the abrasive parti-cles. An increase in the size of abrasive particles also con-tributes to an increase on crack length. In the three-bodyabrasive wear, the surface density of abrasive particles (i.e.,the number of abrasive particles per unit of specimen area)decreases with increasing grit size [11]. Consequently, theeffective stress due to each particle acting on the speci-men surface increases with increasing the size of abrasivegrits. Thus, the effectiveness of brittle microcracking byincreasing grit size and normal stress explains the rates ofmaterial removal shown in Fig. 2 up to near Pn = 50 KPa.

Above a certain value of stress, plastic flow zones similarto those in Figs. 4(b) and 4(d) begin to appear on quartzlapped surfaces. The coexistence of plastic and brittle wearmechanisms has been observed in studies on several engi-neering ceramics [12] and ionic single crystals [13], [14]. Ithas been reported that plastic deformation is favored whenthe load on the abrasive particle is small, i.e., for small gritsizes or low applied stresses. In the present work however,plastic processes were observed at stress levels much higherthan those required to crack propagation. The plastic de-formation observed on lapped surfaces of quartz crystalsis attributed to the inhibition of fracture by the hydro-static pressure associated with indentation [7], [15] and tothe considerable reduction of yield stress resulting froma large increase in temperature of the contact area [16],[17]. At the interface between abrasive grits and the slidingsurface, it is assumed that temperature and compressivecomponents of the stress field increase with increasing Pn.Under these contact conditions, plastic flow may developon the free surface of quartz crystals, which are partiallydetached from the media due to brittle microcracking.

Fig. 6 associates the occurrence of wear micromech-anisms with MRR vs. Pn and Ra vs. Pn dependences.The power curves in Fig. 6 were fitted to experimentalpoints and summarize the tribological conditions investi-gated here. From Ra vs. Pn curve, it is assumed that plas-tic deformation begin to operate at stress levels as smallas 20 KPa. However, plastic deformation affects MRR vs.Pn dependence at stress levels higher than 50 KPa. Itis well known that the rate of material removal and the

roughness of surfaces worn by plastic deformation mech-anisms are lower than those resulting from brittle micro-cracking [3]. Therefore, by increasing the normal stress, theaction of plastic deformation mechanisms together withbrittle microcracking contributes to keep the MRR in astable level and to decrease the surface roughness of quartzcrystals. Further experimental work is required to investi-gate whether or not the increase of normal stress inducesdamage on abrasive particles. Similar to plastic flow, se-vere blunting of abrasive particles also may contribute todecreasing the effectiveness of brittle microcracking [12].

The smooth pattern shown in Fig. 4(e) corresponds toa specular reflecting surface obtained by polishing withPn = 3.1 KPa. Smooth surfaces and insignificant mate-rial removal suggest that mild wear mechanisms are con-trolling the quartz polishing process. Little information isavailable on the subject of the wear micromechanisms in-volved in polishing processes of brittle solids. Samuels [4]suggested that microchipping is the dominant material re-moval mechanism in almost all polishing situations, evenfor many materials that are brittle in bulk form. This sug-gestion is based on the assumption that the depth of pene-tration of an individual particle is less than a critical value.The critical depth is related to a critical effective stressabove which brittle microcracking occurs [7]. As the num-ber of contact particles interacting with the polishing sur-face is high, we expect that the stress operating on quartzsurfaces by each particle is under the critical value. Fig.4(e) also shows residual material such as clusters attachedon the polished surface. These clusters, probably a mix-ture of quartz and alumina, suggest that polishing is con-trolled by both mechanical and chemical mechanisms [4].Using water as a polishing fluid, the chemical interactionbetween H2O and quartz surface would play a substantialrole in abrasive processes due to the hydrolysis of SI-Obonds by OH-related species [18], [19]. The effect of Pn onthe surface pattern resulting from the polishing wear is ob-served by comparing Figs. 4(e) and (f). Rough and diffusereflecting surfaces are produced when quartz specimenswere polished with Pn ≥ 30 KPa. Fig. 4(f) suggests thatplastic deformation mechanisms begin to operate when the


Fig. 3. Relationships between the center-line average roughness (Ra) and the normal stress (Pn) of natural quartz samples lapped (a) and(b) and polished (c) with alumina grits.

surface of quartz specimens is exposed to intense mechan-ical action by the polishing medium. Contrary to lapping,the roughness of polished surfaces increases with increasingPn because here the severity of abrasive wear is increasedby plastic flow processes.

B. Crystallographic Orientation

Indentation fracture analysis in brittle solids made clearthat lateral crack extension provides a basis for estimat-ing material removal rates for several practical situations.Evans and Wilshaw [20] consider that material removal bylateral fracture is assumed to occur when the lateral vents

from adjacent scratches intersect. For a three-body abra-sive wear configuration, these authors predict that thereis an upper limit for the volume removed by N abrasiveparticles:

V ∝ P5/4

K3/4IC H

1/2Nl (3)

where V is the volume wear per unit area (m3/m2), P isthe nominal load (N/m2), and l is the mean path length(m) of abrasive grits. KIC and H are the fracture tough-ness (N/m3/2) and the static hardness (N/m2) of the spec-imen, respectively.


Fig. 4. SEM micrographs of Y-cut surfaces of natural quartz lapped (a)-(d) and polished (e), (f) with alumina grits.


Fig. 5. SEM micrographs of Z- and AT-cut surfaces of natural quartz lapped with alumina grits and Pn = 3.1 KPa.

More recently, Buijs and Korpel-van Houten [21] de-rived a model for material removal that was experimentallyverified by lapping of glass. According to these authors,material removal mainly occurs by rolling particles thatindent the specimen surface with its sharp corners. Ma-terial is removed when the normal stress per load-bearingparticle is high enough for chipping or when unchipped lat-eral cracks are surrounded by other lateral cracks. Whenthe density of lateral cracks is so high that every new crackleads to chipping, the total material removal is given by:

Z = ανF

3/4i FlRA

E5/4

KICH2 (4)

where Z is the thickness loss rate (m/s), α is a material-

independent constant that depends on the particle shape,ν is the relative velocity between specimen and lappingplate (m/s), Fi is the normal force per particle (N), Ft isthe nominal force (N), R is the mean radius of the abrasiveparticles (m), A is the specimen area (m2), and E is theYoung’s modulus (N/m2).

In order to analyze the MRR measured from quartzlapping in relation to the above mentioned models, Ta-ble II shows values of E, Hs (scratch hardness), and KIC

for low-indice planes of natural quartz. Young’s moduliwere derived from the elastic compliance coefficients mea-sured by Bechmann [22]. Although (3) and (4) deal withH, in the present study we used the scratch hardness be-cause consistent values of H measured as a function of


TABLE IIYoung’s Modulus (E), Scratch Hardness (HS), and Fracture

Toughness (KIC) Measured on X-, Y-, Z-,

and AT-Cut Planes of Natural Quartz.

Crystal E1 H2s K2

IC K3IC

plane (GPa) (GPa) (MPa m1/2) (MPa m1/2)

X {1120} 78.3 20 0.70 0.85±0.02Y {1010} 78.3 15 0.80 0.97±0.02Z {0001} 104.2 45 1.40 1.15±0.03AT ∼ {0111} 127.6 – – 0.86±0.03

1Bechmann [22].2Nogueira and De Mello [23].3Iwasa and Bradt [24].–Not determined.

Fig. 6. MRR and Ra dependences on Pn adjusted to experimentalpoints obtained from lapping X-cut samples with alumina grits of 15µm (BM: brittle microcracking; PD: plastic deformation).

crystallographic orientation were not found in the litera-ture. The reported values of KIC were determined by us-ing single-point scratch tests [23] and the controlled sur-face flaw method [24]. Both measurements show that theZ-cut is more resistant to crack propagation than the X-,Y-, and AT-cut planes. In addition, experimental values ofHs show that Z-cut is harder than X- and Y-cut planes.Thus, the volume wear predicted by (3) and (4) should belower when lapping is carried out on surfaces parallel tothe Z-cut plane. This prediction is in agreement with theexperimental measurements of MRR in Fig. 2.The MRR resulting from lapping with Pn = 3.1 KPa

and Pn = 96.9 KPa are plotted in Fig. 7 in relation to1/(K3/4

IC H1/2s ) and E5/4/(KICH

2s ). For this, we adopted

KIC as those values determined by [23]. The AT-cut pointsare not plotted because a consistent value for Hs was not

available. In both models, the origin of the diagram con-stitutes a data point because infinite values of KIC andHs would yield infinite wear resistance. However, becausewe are dealing with values of KIC and Hs varying over anarrow range, we did not include the origin in our plots.Thus, Fig. 7 suggests that MRR increases with increas-ing 1/(K3/4

IC H1/2s ) and E5/4/(KICH

2s ) ratios. Experimen-

tal points are better fitted by the model from Buijs andKorpel-van Houten [21] because differences found in MRRof X- and Y-cut are only noticed by the combination ofmechanical properties proposed by these authors. Addi-tionally, SEM micrographs shown in Figs. 4 and 5 showthat abrasive particles interact with quartz surface muchmore by indenting than by scratching events. This obser-vation is in agreement with (4) that is based on singleindentations produced by rolling particles. Both modelsverify that lapped surfaces parallel to the Z-cut plane ex-hibit the lowest values for MRR.Experimental MRR dependences on Pn shown in Ta-

ble I have exponents ranging from 0.14 to 0.35. This rangedoes not include the exponents predicted by (3) and (4),which are about five times higher. This discrepancy maybe explained by the nature of wear micromechanisms as-sociated with lapping of quartz crystals. The (3) and (4)are based on the assumption that material is exclusivelyremoved by brittle microcracking. It does not take intoaccount the occurrence of plastic flow above certain stresslevels. As has been shown, the simultaneous action of plas-tic deformation together with brittle microcracking de-creases the severity of abrasive wear. Because plastic de-formation is favored when Pn increases, the amount of ma-terial removal given by (3) and (4) are overestimated in re-lation to experimental measurements. In order to attempta broad interpretation of MRR dependence on Pn, we sug-gest that basic concepts of plastic deformation should beincorporated into indentation fracture analysis related toabrasive wear of brittle solids.Based on the depth of lateral fractures induced by an

indenting particle, Buijs and Korpel-van Houten [21] sug-gested that the roughness of lapped surfaces is associatedwith mechanical properties as follows:

Rz = α1E

1/2

HF

1/2i (5)

where α1 is a constant depending on particle shape. Therelationships shown in Fig. 8 suggest that the roughnessof quartz lapped surfaces increases with increasingE

1/2/Hs ratios. The Z-cut exhibits the lowest values ofRa and Rz because it is more resistant to abrasive wearthan X-, Y-, and AT-cut planes. The relationships shownin Figs. 7 and 8 made clear that the rate of material re-moval and the surface roughness resulting from the lap-ping process of quartz single crystals are connected to eachother and can be predicted by suitable combinations ofmechanical properties based on indentation fracture me-chanics.


Fig. 7. Relationships between the rate of material removal (MRR) with the ratios 1/(K3/4IC H

1/2s ) and E5/4/(KICH2

s ).


Fig. 8. Relationships between the average peak-to-valley roughness (Rz) with the ratio E1/2/Hs.

V. Conclusions

The results of the present work can be summarized asfollows:• The rate of material removal related to the lappingprocess of natural quartz increases with increasing thenormal stress and is primarily controlled by brittle mi-crocracking up to near 50 KPa. At higher stress levels,plastic deformation mechanisms are operating simul-taneously with brittle microcracking. The superposi-tion of these wear mechanisms contributes to stabiliz-ing the rate of material removal and to decreasing theroughness of lapped surfaces.• The polishing process of natural quartz does not pro-duce significant weight loss even at high stress levels.However, the roughness of polished surfaces is read-ily affected by the normal stress. The degradation ofpolished surfaces with increasing stress suggests thatplastic deformation mechanisms also play an impor-tant role in quartz polishing.• The material removal rate and the roughness of lappedsurfaces depend on the anisotropy of quartz mechani-cal properties. The Z-cut exhibits the lowest rate ofmaterial removal and the lowest roughness becauseits fracture toughness and scratch hardness are higherthan those of X-, Y-, and AT-cut planes. Both modelsused to correlate lapping data with crystal anisotropydo not explain definitely the behavior of material re-moval and surface roughness in relation to applied nor-mal stress and quartz mechanical properties.

Acknowledgments

The undergraduate students, Israel C. Nunes and Ro-drigo P. Almeida, assisted with preparation of specimensand with lapping and polishing tests. The invaluable dis-cussions with M.Sc. Sonia A. Santana also is acknowl-edged.

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Pedro L. Guzzo was born in Birigui, Brazil,on January 25, 1965. He received the B.S. de-gree in mechanical engineering from the Fed-eral University of Uberlandia in 1988 and theM.S. degree in materials engineering from theState University of Campinas in 1992. Duringstudies for his M.S. degree, he was engaged inthe characterization of impurity-related pointdefects in natural quartz crystals. In 1996, hereceived the Ph.D. degree in physics engineer-ing from the University of Franche-Comte, Be-sancon, France. The subject of his dissertation

was connected to the study of ferrobielastic twinning in quartz singlecrystals.

Since 1997 he has been with the Physical Sciences Departementof Federal University of Uberlandia as a researcher and assistantlecturer fellow. His research interests include mechanical properties,abrasive machining, and lattice defects characterization of quartzcrystals and their isomorphs. He has published 6 papers in journalsand 15 papers in symposiums.

Jose Daniel Biasoli De Mello was born in Tambau, Brazil, onNovember 3, 1952. He received the B.S. degree in mechanical engi-neering from the Federal University of Uberlandia in 1975 and theM.S. degree in manufacturing and materials engineering from theState University of Campinas in 1978. In 1983, he received his Doc.Ing. degree in metallurgy from the Institut National Polytechniquede Grenoble, France.

Since 1983 he has been working as a group leader in the Depart-ment of Physical Sciences of Federal University of Uberlandia, wherehe is a professor and head of the Tribology and Materials Laboratory.He is also a senior researcher of National Research Council (CNPq),Brazil. In 1990, he acted as Professeur Associe in the Ecole NationaleSuperieure de Mecanique et Microtecniques, Besancon, France. Pro-fessor De Mello has published more than 80 full papers presentedand included in proceedings of conferences, congress, and journals.He is the winner of four national awards. His main research interestsare abrasive wear, wear-resistant materials, and abrasive machining.Currently, he is on a sabbatical leave working at the Department ofMaterials Science and Metallurgy, University of Cambridge, UK.

effect of crystal orientation on lapping and polishing processes of natural quartz

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