Photoinduced Formation of Shape-Selective Pt Nanoparticles

Photoinduced Formation of Shape-Selective Pt Nanoparticles

(Parte 1 de 2)

DOI: 10.1021/la904070n ALangmuir X, X(X), X–X ©XXXX American Chemical Society

Photoinduced Formation of Shape-Selective Pt Nanoparticles

Subrata Kundu* and Hong Liang*

Materials Science & Mechanical Engineering, Texas A&M University, College Station, Texas 77843-3123 Received October 26, 2009. Revised Manuscript Received December 10, 2009

A new synthetic route has been utilized for the formation of multiple-shaped Pt nanoparticles (NPs) under UV- photoirradiation. The one-step process exclusively generates different shapes, such as spheres, cubes, short and long wires, and flakelike nanostructures. The reduction of Pt(IV) ions was done using alkaline 2,7-DHN in CTAB micellar media under3hUV-photoirradiation. The synthesized PtNPsare stable for morethan 4months inambient conditions. Bychangingthesurfactant-to-metal ionmolarratiosandtheconcentrationofreducing agent,theparticlesize andshape can be tuned. The mechanisms of the particles formation with variable shapes and the effects of different reaction parameters are studied in detail. The present approach can be extended to a fast synthetic method for the formation of other metallic and semiconductor particles with variable shapes. The evolved Pt NPs will find promising applications in different types of organic and inorganic catalysis reactions, medicinal applications, and nanoelectronics.


In recent years,intenseresearchactivitieshave been devoted to colloidal metal nanoparticles(NPs). This is mainly due to their various potentialapplicationsin electronics,1 catalysis,2 magnetic devices,3 optics,4 biodiagnostics,5 andgassensing,6 etc.Theoptical, catalytic, electronic,and magneticpropertiesof the colloidalmaterials strongly depend on their size and shapes. For example, colloidal gold NPs having diameter less than 5 nm emit intense photoluminescence, whereas NPs with sizes greater than 5 nm exhibit good catalytic propertiesfor low-temperatureCO oxidation.7,8 NPs having very high surface-to-volumeratios show dramatic changes in their properties compared to that of their bulk element.The size and shape effects of the NPs show a directrelationshipbetweenthe catalyticactivityand particlesmorphology.2 Amongvariousmetals,noblemetalNPsareparticularlyinteresting due to their close lying conduction and valence bands in which electrons move freely. The free electrons in metal can generate surfaceplasmonresonance(SPR)bandswhichchangewithparticle size,shape,andthe correspondingmediums.Thefascinatingcolor ofnoblemetalNPsalsodependsontheirsize and shapesaswellas the refractiveindex of the surrounding medium.The synthesisof metalNPs with well-definedsizesandshapeshas been investigated but still remains a challenging task.

Among the different noble metals studied, platinum NPs have attracted much attention due to their distinctive ability in catalyzingpartialoxidation,9hydrogenation,10anddehydrogenation11 of a variety of important molecules that are essential in manyindustrial applications. Therefore,the synthesis ofbareand stable platinum NPs are particularly important in different catalytic reactions involving platinum element.

Recently, a number of chemical methods have been developed for the synthesis of platinum NPs. The first study on shapecontrolled Pt NPs using a linear polymer as stabilizing agent was reported by Ahmadi et al. in 1996.12 They selectively synthesized cubic and tetrahedral Pt NPs by changing the molar concentration of the stabilizing agent to the Pt salt precursor. Recently, various other methods have been developed for the synthesis of size- and shape-controlled Pt NPs like rods,13 wires,14 chains,15 quasi-spherical,16 tetrahedral,17 cubic,18 and polypods,19 etc. El- Sayed’s group reported earlier that the shape effect of Pt NPs can change the reaction pathway to a great extent.17,18 Colliodal Pt nanowires were synthesized by Fenske et al. using dodecylamine as ligand.20 Previously, Jana et al. synthesized quasi-spherical Pt NPs at higher yields.16 Mafune et al. developed a laser irradiation method for the synthesis of Pt NPs in an aqueous solution of sodium dodecyl sulfate (SDS).21 Kinge et al. synthesized tetrahedral Pt NPs using poly(vinylpyrrolidone) (PVP) as capping agentinthepresenceofprepreparedPtseedparticles.22Songetal. synthesized Pt nanowire networks using a soft template in the presence of sodium borohydride.23 Somorjai’s group also synthesized size- and shape-controlled Pt NPs using mesoporous silica

*Corresponding authors. E-mail:;;

Ph 979-862-2578; Fax 979-845-3081. (1) Kundu, S.; Liang, H. Adv. Mater. 2008, 20, 826. (2) Kundu, S.; Lau, S.; Liang, H. J. Phys. Chem. C 2009, 113, 5150. (3) Mandal,M.;Kundu,S.;Sau,T.K.; Yusuf, S.M.;Pal,T.Chem.Mater. 2003, 15, 3710. (4) Alivisatos, A. P. Science 1996, 271, 933. (5) Shim, S.-Y.; Lim, D.-K.; Nam, J.-M. Nanomedicine 2008, 3, 215. (6) Ruiz, A.; Arbiol, J.; Cirera, A.; Cornet, A.; Morante, J. R. Mater. Sci. Eng., C 2002, 19, 105. (7) Haruta, M.; Tsubota, M.; Kobayashi, T.; Kageyama, H.; Genet, M. J.;

Delmon, B. J. Catal. 1993, 144, 175. (8) Sakurai, H.; Haruta, M. Appl. Catal., A 1995, 127, 93. (9) Kim, J. H.; Woo, H. J.; Kim, C. K.; Yoon, C. S. Nanotechnology 2009, 20, 235306. (10) Cheng, H.; Xi, C.; Meng, X.; Hao, Y.; Yu, Y.; Zhao, F. J. Colliod Interface

Sci. 2009, 336, 675. (1) Xu, J.; Yu, X.; Zou, Z.; Li, Z.; Wu, Z.; Akins, D. L.; Yang, H. Chem. Commun. 2008, 4, 5740.

(12) Ahmadi, T. S.; Wang, Z. L.; Green, T. C.; Henglein, A.; El-sayed, M. A.

Science 1996, 272, 1924. (13) Chen, J.; Xiong, Y.; Yin, Y.; Xia, Y. Small 2006, 2, 1340. (14) Chen, Y.; Johnson, E.; Peng, X. J. Am. Chem. Soc. 2007, 129, 10937. (15) Ford, W. E.; Harnack, O.; Yasuda, A.; Wessels, J. M. Adv. Mater. 2001, 13, 1793. (16) Jana, N. R.; Peng, X. J. Am. Chem. Soc. 2003, 125, 14280. (17) Narayanan, R.; El-Sayed, M. A. Nano Lett. 2004, 4, 1343. (18) Petroski, J. M.; Green, T. C.; El-Sayed, M. A. J. Phys. Chem. A 2001, 105, 5542. (19) Teng, X.; Yang, H. Nano Lett. 2005, 5, 885. (20) Fenske, D.; Borchert, H.; Kehres, J.; Kr€oger, R.; Parisi, J.; Kolny-Olesiak,

J. Langmuir 2008, 24, 9011. (21) Mafun e, F.; Kohno, J.; Takeda, Y.; Kondow, T. J. Phys. Chem. B 2003, 107, 4218. (2) Kinge, S.; Bonnemann, H. Appl. Organomet. Chem. 2006, 20, 784. (23) Song, Y.; Garcia, R. M.; Dorin, R. M.; Wang, H.; Qiu, Y.; Coker, E. N.; Steen, W. A.; Miller, J. E.; Shelnutt, J. A. Nano Lett. 2007, 7, 3650.

B DOI: 10.1021/la904070n Langmuir X, X(X), X–X

Article Kundu and Liang as template.24 Herricks et al. studied the morphological change of Pt NPs with the addition of NaNO3 in a polyol process at 160 C.25 Chen et al. modified the polyol process by introduction of trace amounts of iron species to the reaction mixture and generate branched multipods.26 Recently, Lim et al. further modified the polyol process by adding iron species to produce multioctahedral Pt nanostructures.27 Tsuji et al. studied the role of poly(vinylpyrrolidone) for the formation of branched Pt nanostructuresinpolyolprocess.28Afewothermethodshavealsobeen reportedin the literature for the synthesis ofPt NPs.29-31 Most of the above conventional heating methods required either harsh reducing conditions, addition of separate seed particles, long reaction time, produce only one particle shape, or sometimes generate a mixture of multiple shaped particles with lower yields.

In the present research, we have developed a process to synthesize shape-controlled Pt NPs in the presence of a cationic surfactant,cetyltrimethylammoniumbromide(CTAB),under3h of UV-photoirradiation. The method exclusively generates different shapes, such as spherical particles with different sizes, nanocubes, short or long nanowires, and nanoflakes within a very short time. The reduction of the Pt(IV) ions was done with alkaline 2,7-dihydroxynaphthalene (2,7-DHN) under 3 h UV- photoirradiation in the presence of CTAB. The particles’ size and shape can be controlled just by changing the molar ratios of the surfactant-to-metal ion and the concentration of the 2,7-DHN. To the best of our knowledge, shape-controlled synthesis of Pt NPs using a simple photochemical method has not been previously explored. The present process generates high yields of all different shapes. The synthesized particles are stable for more than 4 months under ambient conditions, and the process is simple, straightforward, reproducible, and cost-effective.

Experimental Section

Reagents. Cetyltrimethylammonium bromide (CTAB, 9%), platinum chloride (PtCl4), and sodium hydroxide (NaOH) were purchased from Sigma-Aldrich and used as received. The 2,7- dihydroxynaphthalene (2,7-DHN), 1,2-dihydroxynaphthalene (1,2-DHN), and 2-naphthol (2-N) were also obtained from the samesourceand recrystallizedinhot water. Deionized (DI) water was used for the entire synthesis.

Instruments. The UV-vis absorption spectra were recorded in a Hitachi (model U-4100) UV-vis-NIR spectrophotometer equipped with a 1 cm quartz cuvette holder for liquid samples. A high-resolution transmission electron microscope (HR-TEM) (JEOL JEM 2010) was used at an accelerating voltage of 200 kV. The energy dispersive X-ray spectrum (EDS) was recorded withanOxfordInstrumentsINCA energysystemconnected with the TEM. The XRD analysis was done with a scanning rate of 0.020 s-1 in the 2θ range 25 -80 using a Brukar-AXS D8 Advanced Bragg-Brentano X-ray powder diffractometer with Cu KR radiation (λ = 0.154178 nm). The X-ray photoelectron spectroscopy (XPS) analysis was carried out using a Kratos Axis UltraImagingX-rayphotoelectronspectrometerwithmonochromatic Al KR line (1486.7 eV). The instrument integrates a magnetic immersion lens and charge neutralization system with a spherical mirror analyzer, which provides real-time chemical state and elemental imaging using a full range of pass energies. The emitted photoelectrons were detected by the analyzer at a passing energy of 20 eV with energy resolution of 0.1 eV. The incident X-ray beam is normal to the sample surface and the detectoris45 awayfromthe incidentdirection.The analysisspot onthesampleis0.4mmby0.7mm.AxenonlampfromNewport Corp. ata wavelength of260 nm onthe sample was used for UV- photoirradiation. The approximate intensity was 20 μW, and the bandwidth of irradiation was 260 ( 8n m. Thed istance of the sample from the light source was 18 cm. The sample was placed over a wooden box with a stand to make the light shine on it directly.

Photochemical Synthesis of Shape-Controlled Pt NPs.

Shape selective Pt NPs were synthesized by varying the concentrations of CTAB, Pt(IV) ions, and 2,7-DHN under UV-photoirradiation. In a typical synthesis process, 30 mL of CTAB (0.1M) was mixed with 4 mL of 10-2 M Pt(IV) solution. Then 6 mL of 2,7-DHN (10-2 M) and 500 μL of 1 M NaOH were added. The solution mixture was stirred for 1-2 min using a magnetic stirrer. Then the mixed solution was placed under UV-photoirradiation continuously for 3 h with stirring. This processsubsequentlyproduceslongPtnanowires.Forthesynthesis of other shaped Pt NPs like Pt nanospheres, short nanowires, nanocubes, and nanoflakes, we varied the molar concentration ratios of Pt(IV) ion relative to CTAB. The final concentration of allthereactants,irradiationtime,shapeoftheparticles,andshape distribution are given in Table 1. The mixed solution was initially reddish-orange in color (after 10-15 min UV-irradiation) and turnedyellowish-greenafter30minandfinallybecamedeepgreen to blackish after 3 h of UV-photoirradiation. The solution mixture was centrifuged at 6000 rpm for 20 min and again at 4000 rpm for 10 min to remove extra surfactants and other chemicals from the Pt NP solution. The precipitated Pt NPs are light blackish in color and found to be stable for more than 4 months in ambient conditions at room temperature (25 C).

Preparation of Pt NPs Samples for TEM, EDS, XRD, and XPS Analyses. The CTAB-stabilized Pt NPs were characterizedusingTEM,EDS,XRD,andXPSanalyses.Thesample for TEM analysis was prepared by placing a drop of the corresponding Pt NP solution onto a carbon-coated Cu TEM grid

Table 1. Final Concentrations of All the Reaction Parameters, Time of UV-Photoirradiation, and Particle Shape Distribution for the Formation of Pt NPs set no. final concn of CTAB (M) final concn of

Pt(IV) solution (M) final concn of 2,7-DHN (M) final concn of NaOH (M) time of UV irradiation (h) shape of the particles particles shape distribution

(24) Konya, Z.; Puntes, V. F.; Kiricsi, I.; Zhu, J.; Alivisatos, P.; Somorjai, G. A.

Catal. Lett. 2002, 81, 137. (25) Herricks, T.; Chen, J.; Xia, Y. Nano Lett. 2004, 4, 2367. (26) Chen, J.; Herricks, T.; Xia, Y. Angew. Chem., Int. Ed. 2005, 4, 2589. (27) Lim, B.; Lu, X.; Jiang, M.; Camargo, P. H. C.; Cho, E. C.; Lee, E. P.; Xia,

Y. Nano Lett. 2008, 8, 4043. (28) Tsuji,M.;Jiang,P.;Hikino, S.;Lim,S.;Yano,R.; Jang,S.-M.; Yoon,S.-H.;

Ishigami, N.; Tang, X.; Kamurudin, K. S. N. Colloids Surf., A 2008, 317, 23. (29) Ahmadi, T. S.; Wang, Z. L.; Henglein, A.; El-Sayed, M. A. Chem. Mater. 1996, 8, 1161. (30) Lee, H.; Habas, S. E.; Kweskin, S.; Butcher, D.; Somorjai, G. A.; Yang,

P. D. Angew. Chem., Int. Ed. 2006, 45, 7824. (31) Kijima, T.; Yoshimura, T.; Uota, M.; Ikeda, T.; Fujikawa, D.; Mouri, S.; Uoyama, S. Angew. Chem., Int. Ed. 2004, 43, 228.

DOI: 10.1021/la904070n CLangmuir X, X(X), X–X

Kundu and Liang Article followed by slow evaporation of the solvent at ambient conditions. The EDS analysis was done from the same samples during the TEM measurement.The samples for XRDand XPS analyses were prepared on a glass substrate for making thin films. Before theNPsdeposition,thewaferswerecleanedthoroughlyinacetone and sonicated forabout 30min.Thenthesubstrate was dried and used for Pt NP deposition. After deposition the sample was dried in a vacuum chamber. Final samples were prepared with 8-10 depositions, dried, and then analyzed using XRD and XPS techniques.

Results and Discussion

Transmission Electron Microscopy (TEM) Analysis.

Shape selective Pt NPs were synthesized by reduction of Pt(IV) ions in the presence of alkaline 2,7-DHN in a CTAB micellar mediaunder3hofUV-photoirradiation.Figures1A-Lshowthe transmission electron microscopy (TEM) images of the shape controlled Pt NPs at various reaction conditions as given in Table 1. Figure 1A is the TEM image of small sized spherical Pt NPs at lower magnification (corresponding curve A, Figure 3). Figure 1B shows very high magnification images of the spheres. The average diameter of the spheres is ∼30 ( 5n m. All the particles are monodisperse and were formed after 3 h of UV- photoirradiation. Figures 1C,D show the TEM images of the larger sized spherical NPs at lower and higher magnification (corresponding to curve B, Figure 3). The average diameter of thoseparticlesis∼330(50nm.Figure1EistheTEMimageofPt nanocubesatlowermagnification,andFigure1FisaTEMimage of the Pt nanocubes at higher magnification from another part of the samples (corresponding to curve C, Figure 3). The average side lengths of the cubes are ∼28 ( 5 nm. The yields of the cubes are more than 90%, and the rest are other different shapes like triangular and hexagonal prisms. The insets of Figure 1F show two images. One is the corner of a high magnified image of single cube showing different crystal planes, and the lowest spacing between two planes is 0.228 nm. The growth of (1) lattice direction is indicated by a white line. Another inset shows the corresponding SAED pattern and signifies that the cubes are single crystalline in nature. Figure 1G shows a TEM images of the “bacteria”-shaped small Pt nanowires. The inset shows the corresponding higher magnification images. Figure 1H shows the higher magnification images of the short Pt nanowires (corresponding to curve D, Figure 3). The average length of the wires ranges from 215 to 310 nm and their average diameter from ∼50 ( 5 nm. From the image it is clearly visible that the Pt nanowireshavingdifferentcrystalplanesgrowalongthelengthof the wires, and the lattice spacing is 0.23 nm, which corresponds to growth along Æ111æ direction. Figure 1I is the TEM images of the longer Pt nanowires at lower magnification (corresponding curve E, Figure 3). Figure 1J is the TEM image of Pt nanowires at a higher magnification, and the inset is the image of a single wire. Theaveragelengthanddiameterofthewiresare1-3μmand∼40 ( 3 nm, respectively. Parts K and L of Figure 1 are the low- and high-magnification TEM images of the Pt nanoflakes (corresponding to curve F, Figure 3). All particles are formed with flakelike morphology. The red arrows show that the surfactant CTAB molecule capped the particles. From the above TEM analysis we can clearly observe different shaped Pt NPs that are formed with high yields.

UV-vis Spectroscopy Study. Figure 2 shows the UV-vis absorption spectra of the reaction mixture at different stages of the synthesis process. Curve A in Figure 2 shows the absorption spectra of aqueous CTAB solution, which has no specific band in the UV-vis region. A colorless solution of aqueous 2,7-DHN in watershowstwodistinctabsorptionbandspeakingat282and322 nm (curve B, Figure 2) due to the presence of aromatic moiety in 2,7-DHN. The reddish-orange color aqueous Pt(IV) chloride solution forms a small hump ranging from ∼235 to 265 nm due to ligand-to-metal charge transfer (LMCT) spectra (curve C, Figure2).32WiththeadditionofCTABtothePt(IV)solution,the peak for Pt(IV) shifted a little, and a new hump appeared ranging from ∼250 to 280 nm (curve D, Figure 2), which might be due to the formation of an adduct or complex of CTAB with Pt(IV).3 After the addition ofalkaline 2,7-DHN with the mixture containing CTAB and Pt(IV) solution, the original peaks of 2,7-DHN and Pt(IV) disappeared, and two new peaks at 248 and 342 nm appeared (Figure 2, curve E). This might be due to interaction of 2,7-DHN with the adduct or interaction of Pt(IV) ions with 2,7- DHN. UV-irradiation of a mixture of CTAB, 2,7-DHN, and NaOH yields initially light greenish color. This greenish color turns to deep greenish and finally blackish with increasing irradiation time might be due to formation of hydroxyl or quinone derivatives of 2,7-DHN. Now after UV-irradiation of the solution mixture containing CTAB, Pt(IV), 2,7-DHN, and NaOH, the solution changed color from reddish-orange to yellowish-green to dark green and finally blackish in color after 3 h of UV-photoirradiation. After one time centrifugation, this blackish solution containing Pt NPs shows two small intense bands at 248 and 330 nm. This might be due to the presence of excess surfactant or excess 2,7-DHN in the solution (curve F, Figure 2). After centrifugation 2-3 times and redispersion in water, the aqueous solution shows an optical absorption band (curve G, Figure 2) having no specific peaks due to formation of Pt NPs. Curve G is the broad absorption band of the purified Pt NPsolutionthatdoesnotshowanypeaksprovingthepresenceof excess surfactant or other chemicals in curve F. This optical absorption band is due to the formation of Pt NPs having similarities with other previous reports.21,34-36 The absence of any specific peaks of Pt NPs is due to the very small imaginary parts of their dielectric constants. The synthesized Pt NPs solutions are stable at room temperature and in ambient conditions. The inset of Figure 2 shows the light blackish color Pt NPs solution indicated with “P” after redispersion in aqueous solution. In Figure 3, curves A-F are the different optical absorption bandsofdifferentshapedPtNPsolutions.CurvesAandBarethe absorption bands for spherical Pt NPs. Curve C is the absorption bands for Pt nanocubes, whereas curves D and E are the absorption band for Pt nanowires of different lengths. Curve F istheabsorptionbandforPtnanoflakes.Theabsorptionbandfor longerPtnanowiresshowstwosmallintensebandsat250and343 nm. All other curves have no specific bands as observed in Figure 3.

Energy Dispersive X-ray Spectroscopy (EDS) Analysis.

Figure 4 shows the results obtained from the energy dispersive X- ray spectroscopic (EDS) analysis. The EDS analysis was conducted for determination of elements present in the reaction product. As shown in the figure, the EDS spectrum consisted of different peaks for Pt, Cl, C, Cu, Cr, and Br. The large intense Pt peak came from the Pt NPs. The small Cl peak came from the chlorinated salt of Pt used for the synthesis. The C and Cu peak

(32) Hoggard, P. E.; Bridgeman, A. J.; Kunkely, H.; Vogler, A. Inorg. Chim.

Acta 2004, 357, 639. (3) Krishnaswamy, R.;Remita,H.;Imp eror-Clerc,M.;Even,C.;Davidson, P.;

Pansu, B. Chem. Phys. Chem. 2006, 7, 1510. (34) Devi, G. A.; Rao, V. J. Chem. Lett. 2000, 23, 467. (35) Yang, W.; Yang, C.; Sun, M.; Yang, F.; Ma, Y.; Zhang, Z.; Yang, X.

D DOI: 10.1021/la904070n Langmuir X, X(X), X–X

Article Kundu and Liang camefrom the Cu gridusedfor TEM analysis.The Cr peakcame from the sample holder used during the TEM analysis. A small Br peak also appeared as we used CTAB during the synthesis of Pt NPs.

X-ray Diffraction (XRD) Analysis. The X-ray diffraction

(XRD)patternofshapeselectivePtNPsexhibitsdiffractioninthe 2θ range 25 -80 and corresponds to diffraction from the (1) and (200) lattice planes as shown in Figure 5. As the intensity of the reflection is directly proportional to the X-ray coherence length of the crystal, the relative intensities of these reflection also varies with NP shape. The X-ray diffraction pattern confirmed the formation of face-centered-cubic (fcc) Pt having space group Fm3m (225) with lattice constants a = 0.3923 nm( JCPDSc ard no. 04-0802). All the peaks are well matched with the previous

Figure 1. Transmission electron microscopy (TEM) images of different shaped Pt NPs. (A) and (B) are the images of small size spherical Pt NPsatlowerandhighermagnificationhavingaveragediameter∼30(5nm.(C)and(D)arethelargersizesphericalNPsatlowerandhigher magnification. The average diameter of the particles is ∼330 ( 50 nm. (E) and (F) are images of Pt nanocubes at lower and higher magnification. The average side length of the cubes is ∼28 ( 5 nm. Inset of (F) shows the high magnified image of single cube and the corresponding SAEDpattern.(G) and (H) are imagesofthe “bacteria”-shaped smaller Ptnanowiresinlower and highermagnification.The average length of the wires is 215-310 nm, and the average diameter is 50 ( 5 nm. Inset of (G) shows the corresponding higher magnified image.(I)and(J)areimagesofthelongerPtnanowiresatlowerandhighermagnification.Theaveragelengthofthewiresare1-3μm,andthe averagediameterofthewiresis∼40(3 nm.Insetof(J)showsthehighermagnifiedimage ofasinglewire.(K) and(L) arethelow- andhighmagnification images of the Pt nanoflakes. The red arrows show the surfactant CTAB molecule capping the particles.

DOI: 10.1021/la904070n ELangmuir X, X(X), X–X

Kundu and Liang Article theoretical andexperimental XRD analysisbyBeraetal.for their study on Pt NPs.37 A small peak at a 2θ value 53.7 is also observed and matched with the report by Somorjai’s group for their synthesis of Pt NPs on mesoporous silica.24 Another two high-intensity peaks at low 2θ value (28 and 31.5 ) are also observed and matched with the literature report on Pt NPs.37 In our synthesis, we used CTAB as stabilizing agent. The selective interactionofCTABwithdifferentcrystalplanesofPtmightalter the growth rates and intensity of different crystal planes.

(Parte 1 de 2)