We report on the Raman spectra of Ti3SiC2 (312), M2AlC(211) (M=Ti, V, Cr, and Nb) and Ti4AlN3 (413), as representative compounds from the family of Mn+1AXn phases. Intense and narrow first-order Raman peaks are observed, and we present an analysis of the spectra based on symmetry considerations and from results of first-principles calculations of phonon frequencies. The agreement between experimental and calculated mode energies is excellent. The identification of the modes enables application of Raman scattering as a diagnostic tool for the detailed study of the structural and physical properties of this family of compounds and their engineered solid solutions

Amer, Maher S.

Barsoum, Michel W.

Gupta, Surojit

Spanier, Jonathan E.

English

CORE

Wright State University CORE Scholar Mechanical and Materials Engineering Faculty Publications Mechanical and Materials Engineering 1-2005 Vibrational Behavior of the Mn+1AXn Phases from First-Order Raman Scattering (M=Ti,V,Cr, A=Si, X=C,N) Jonathan E. Spanier Surojit Gupta Maher S. Amer Wright State University - Main Campus, maher.amer@wright.edu Michel W. Barsoum Follow this and additional works at: https://corescholar.libraries.wright.edu/mme  Part of the Materials Science and Engineering Commons, and the Mechanical Engineering Commons Repository Citation Spanier, J. E., Gupta, S., Amer, M. S., & Barsoum, M. W. (2005). Vibrational Behavior of the Mn+1AXn Phases from First-Order Raman Scattering (M=Ti,V,Cr, A=Si, X=C,N). Physical Review B: Condensed Matter and Materials Physics, 71 (1), 012103. https://corescholar.libraries.wright.edu/mme/280 This Article is brought to you for free and open access by the Mechanical and Materials Engineering at CORE Scholar. It has been accepted for inclusion in Mechanical and Materials Engineering Faculty Publications by an authorized administrator of CORE Scholar. For more information, please contact library-corescholar@wright.edu. Vibrational behavior of the Mn+1AXn phases from first-order Raman scattering„M =Ti,V,Cr, A=Si, X=C,N)Jonathan E. Spanier,* Surojit Gupta, Maher Amer,† and Michel W. BarsoumDepartment of Materials Science and Engineering, Drexel University, Philadelphia, Pennsylvania 19104, USAsReceived 24 June 2004; revised manuscript received 3 September 2004; published 21 January 2005dWe report on the Raman spectra of Ti3SiC2 s312d, M2AlC s211d sM =Ti, V, Cr, and Nbd and Ti4AlN 3 s413d,as representative compounds from the family ofMn+1AXn phases. Intense and narrow first-order Raman peaksare observed, and we present an analysis of the spectra based on symmetry considerations and from results offirst-principles calculations of phonon frequencies. The agreement between experimental and calculated modeenergies is excellent. The identification of the modes enables application of Raman scattering as a diagnostictool for the detailed study of the structural and physical properties of this family of compounds and theirengineered solid solutions.DOI: 10.1103/PhysRevB.71.012103 PACS numberssd: 78.30.2j, 63.20.Dj, 71.15.MbRecently, seemingly unrelated layered solids such asgraphite, ternary carbides and nitridesssee belowd, hexago-nal BN, ice, and most importantly, mica—and thus much ofgeology—were all classified as kinking nonlinear elasticsKNEd solids.1 These solids all deform by the formation ofdislocation-based incipient kink bandssIKB’s d, that are fullyreversible, that give way to mobile dislocation walls, whichin turn collapse into kink boundaries.2 Furthermore, it wasshown that the hysteretic mesoscopic units—invoked to ex-plain the behavior of nonlinear mesoscopic elasticsolids3,4—are nothing but IKB’s. Understanding the behaviorof KNE solids is thus important in geology, the behavior ofgraphite, as well as a new class of layered ternary carbidesand nitrides, viz., theMAX phases.The so-calledMAX phasesfMn+1AXn, wherenù1, M isan early transition metal,A is anA-groupsmostly IIIA, IVAdelement, andX is C or Ng have recently attracted consider-able attention due to their unusual physical, mechanical, andthermal properties.5,6 In all these compounds, near-close-packed transition metal carbide and/or nitride layers are in-terleaved with layers of pureA-group element. When=1,e.g., Ti2AlN shereafter referred to as 211d, every third layeris an A-group element layersFig. 1d; for n=2s312d, everyfourth layer sFig. 2d; for n=3s413d, everyfifth layer. Thereare over fifty 211 compounds, at least three 312 compounds,and one 413, namely, Ti4AlN 3.5,6Though the Raman spectrum of Ti3S C2 has been reportedpreviously,7 tentative assignments of atoms involved with afew of the observed modes were made therein on the basis ofcomparison with TiC0.67. The purpose of this paper is topresent the 300 K Raman spectra ofMAX phase compoundsselected to represent each of the three stoichiometries, alongwith ab initio calculations and symmetry analysis for thesesolids, thus permitting the definitive identification of the ob-served Raman peaks. The understanding of these modes, es-pecially the shear modes, should lead to a much better un-derstanding of IKB’s and in turn the deformation of KNE’s.Fully dense, predominantly single phase samples ofCr2AlC sRef. 8d, Ti2AlC sRef. 9d, V2AlC sRef. 10d, Ti4AlN 3sRef. 11d, and Nb2AlC sRef. 12d were made byreactively hot isostatic pressing the appropriate stoichio-metric mixtures of powders of the constituent elementsand/or appropriate carbides. The V2AlC samples containedsome relatively large platelike grains. The samples were frac-tured to expose<232 mm2 basal planes that were studied.FIG. 1. sColor onlined Raman spectrum collected within a singlegrain of V2AlC. The measured, Lorentzian-fitted energies are ap-proximately sad 158, sbd 239, scd 258, andsdd 360 cm−1. Shownabove the plot are schematics of the corresponding atomic displace-ments for the Raman-active phonons in the 211 unit cell for V2AlC.The C atoms are denoted by black spheres; the V atoms are en-circled and blueslight grayd and occupy sites in every other elemen-tal atomic plane. The Al atoms are denoted in yellowsoff-whited,and occupy sites in every third plane.PHYSICAL REVIEW B 71, 012103s2005d1098-0121/2005/71s d/012103s4d/$23.00 ©2005 The American Physical Society012103-1The Ti3SiC2 samples were made using a sinter forgingtechnique.13 The resulting samples also had large platelikegrains with diameters of 1 to 2 mm and thicknesses of theorder of 200mm.Unpolarized Raman scattering was collected at 300 Kfrom within single grains of V2AlC and Ti3SiC2 and frompolycrystalline samples of the other 211 phases and Ti4AlN 3.HeNe laser excitations543.5 nmd was focused to a spot sizeof ,4 mm with an incident power of,12 mW. The spectrawere collected in the backscattering configurationzsx,x+ydz̄ sx is arbitrary with respect to the axes in the basalplane,zi c-axisd; using a Renishaw 2000 spectrometer withan air-cooled CCD array detector. All experimental peak en-ergies and linewidths reported were obtained from multiple-peak Lorentzian fitting, and the experimental resolution ofthe peak positions is within 1–2 cm−1.Phonon energies were calculated based on first-principlescalculations of total energy, Hellman-Feynman forces, andthe dynamical matrix usingVASP sRef. 14d andPHONONsRef.15d as implemented within MedeA.16 Here the Kohn-Shamequation is solved using projector augmented wave17,18sPAWd potentials and the generalized gradientapproximation19 sGGAd. The summation is constrained to a33333 k-point mesh. The structures were optimized whilemaintaining the constraints imposed by the space-group sym-metry elements using calculated lattice parameters reportedpreviously ssee Table Id.20–22 For the phonon calculations,nonequivalent atoms positions for each of the structures wereused to generate rhombohedral supercells consisting of 24,36, and 48 atoms for the 211, 312, and 413 structures, re-spectively. In these supercells, the internal degrees of free-dom were relaxed while the lattice parameters were fixed.The MAX phases are a member of the space groupD6h4sP36/mmcd. For the 211 structures, there are a total of 24modes. In addition to the three acoustic modessA2u+Eud,there are four Raman-active optical modes, three of whichare Raman-activesAg+2E2gd and one which is both Raman-active and infrared-activesEgd. For Ti3SiC2, there are sevens2Ag+2Eg+3E2gd Raman-active modes of the 33 total opti-cal modes, two of which are also infrared-active. Finally, forTi4AlN 3 there are a total of 10 modess3Ag+3Eg+4E2gd,three of which are also infrared-active.The 300-K Raman spectra of a single grain of V2AlC andTi3SiC2 are shown in Figs. 1 and 2 respectively. The spec-trum of a polycrystalline sample of Ti4AlN 3 is shown in Fig.3. For V2AlC, four distinct sharp peaks are observed atTABLE I. Lattice and structural parameterssRef. 20–22d used incalculations of phonon energies. The values listed are the result ofcalculations of energy-minimized structures usingVASP sRef. 14d.zM denotes theM-element atomic positions normalized to each lat-tice parameterc. Following the Wyckoff notation, these atoms oc-cupy the 4f sites for the 211 and 312 structures; in the 413 structure,the TiI, TiII , and NII occupy the 4f, 4e, and 4f sites, respectively.V2AlCa Ti2AlCa Cr2AlCa Nb2AlCa Ti3SiC2b Ti4AlN 3ca sÅd 2.950 3.060 2.850 3.100 3.0575 2.988c sÅd 13.290 13.670 12.720 13.800 17.6235 23.372zM 0.0840 0.0837 0.0847 0.0830 0.0727 0.0542sTiId0.1547sTiIId0.1050sNIIdaReference 20bReference 21.cReference 22.FIG. 2. sColor onlined Raman spectrum collected within a singlegrain of Ti3SiC2. The measured, Lorentzian-fitted energies are ap-proximately sad 159, sbd 226, scd 279, sdd 301, sed 625, andsfd673 cm−1. Shown above the plot are schematics of the correspond-ing atomic displacements for the Raman-active phonons in theTi3SiC2 unit cell. The C atoms are denoted by black spheres; the Tiatoms are bluesgrayd with light blue slight grayd arrows, and oc-cupy sites in every other elemental atomic plane. The Si atomsappear as yellowsoff-whited spheres with dark yellowsdark graydarrows, and occupy sites in every fourth plane.FIG. 3. Raman spectrum of Ti4AlN 3. The measured, Lorentzian-fitted energies are approximatelysad 132, sbd 181, scd 208, sdd 235,sed 386, sfd 539, sgd 563, andshd 592 cm−1.BRIEF REPORTS PHYSICAL REVIEW B71, 012103s2005d012103-2approximately 158, 240, 257, and 361 cm−1, and weakerpeaks near 413, 509, and 693 cm−1. The calculated phononenergies for the four first-order Raman active modes inV2AlC Raman-active are listed in Table II. The lattice dis-tortions associated with each of these observed Raman-activemodes are shown schematically above the plot in Fig. 1. Theresults for fitted peak positions, linewidths, and calculatedenergies for three other 211 phases are listed in Table IIalong with those for V2AlC. We note that in V2AlC thecalculated mode energy for displacements shown in Fig. 1scdis slightly higher than that for Fig. 1sbd. However, for each ofthe three other 211 structures, the calculated mode energyassociated with the atomic displacements shown in 1scd isactually lowers,5–10 %d than that of 1sbd.For Ti3SiC2, the measured spectrumsFig. 2d shows fivedistinct peaks at approximately 159, 226, 279, 625, and673 cm−1, along with two weak peaks at approximately 260and 301 cm−1. The corresponding lattice distortions areshown in Figs. 2sad–2sfd. The calculated mode energies com-pare quite well with measured peak energies as shown inTable III. The measured peaks near 159 and 226 cm−1 areshear and longitudinal vibrations involving the Si and Tiatomic planes, respectively. The mode near 279 cm−1 in-volves shear vibrations of the Si atomic planes with antipar-allel shear of the adjacent Ti atomic planes. The mode near301 cm−1 involves longitudinal vibrations of the Si atomicplanes with antiparallel dilatation of the adjacent Ti atomicplanes. Modes at 625 and 673 cm−1 are ofE2g andAg sym-metries, respectively, and are transverse and longitudinalmodes involving adjacent C atomic planes. The mode pre-dicted at 590 cm−1 sEgd is not observed in our experiments.We note that the peak energies for our spectrum is in reason-able agreement with Ref. 7.The 300-K Raman spectrum of Ti4AlN 3 sFig. 3d exhibitseight distinct peaks of the ten expected for this structure.Experimentally fitted and calculated peak energies are com-pared in Table IV and show excellent agreement, though cal-culated modes at 248 and 255 cm−1 are not observed in ourspectrum.Common to these phases is a lower energys,135 cm−1,v, ,160 cm−1d shear mode principally involving theAplanes. Each of these structures also exhibits one or moreshear modes in the range of,180 cm−1,v, ,280 cm−1involving both theM andA atomic planes. In structures withmultiple X-group element layers, viz., Ti3SiC2 and Ti4AlN 3,higher energy Raman-active modes are observed.We remark that the intensities of the Raman peaks aresomewhat surprising considering the absorption depth ofthese materials at the laser excitation wavelength is on theorder of 10 nm.23 The relatively long phonon lifetimes sug-gest that theMAX phases may be highly ordered and/or rela-tively defect free. Significantly, the narrow linewidths alsosuggest that the anharmonicity in these phases is relativelysmall as compared with other intermetallic systems; this isTABLE II. Measured Lorentzian-fitted Raman peak energiesvexpt and full-width half-maximum linewidthsG in cm−1, and correspondingcalculated peak energies and symmetries for selected 211 aluminum carbides. In the table, the asterisk refers to a mode that could not beclearly discerned in the experimental spectrum.modeV2AlC Nb2AlC Ti2AlC Cr2AlCIrrep.vexpt G vcalc vexpt G vcalc vexpt G vcalc vexpt G vcalcsad 157.5 4.9 145 149.4 15 148 149.9 12.9 149 150.9 19.9 156 E2gsbd 239.7 4.0 244 ,211 24 197.7 268.1 9.5 262 246.3 7.3 247 Egscd 257.2 5.3 248 ,190 29 181.5 262.1 5.8 248 * - 237 E2gsdd 361.2 4.4 361 262.8 15 268.3 365.1 12.4 387 339.2 7.6 345 AgTABLE III. Measured Lorentzian-fitted Raman peak energiesvexpt and full-width half-maximum linewidthsG in cm−1, corre-sponding calculated peak energies, and symmetries for the assignedmodes in Ti3SiC2. Here, the asterisk refers to a mode for which theexperimental peak width could not be determined.Mode vexpt G vcalc Irrep.sad 159 10.5 145 E2gsbd 226 5.0 217 E2gscd 279 5.6 253 Egsdd 301 * 301 Ag- - 590 Egsed 625 5.5 622 E2gsfd 673 4.7 657 AgTABLE IV. Measured Lorentzian-fitted Raman peak energiesvexpt and full-width half-maximum linewidthsG in cm−1, corre-sponding calculated peak energies, and symmetries for the assignedmodes in Ti4AlN 3.Mode vexpt G vcalc Irrep.sad 132 9.7 135 E2gsbd 181 7.6 172 E2gscd 208 5.5 196 Egsdd 235 9.4 226 Eg- - 248 Eg- - 255 Agsed 386 11.2 374 Agsfd 539 9.3 584 E2gsgd 563 7.9 587 Agshd 592 10.6 600 E2gBRIEF REPORTS PHYSICAL REVIEW B71, 012103s2005d012103-3consistent, for example, with earlier reports of low coeffi-cients of thermal expansion and high Debye temperatures.5In general the identification of Raman modes with atomvibration is frequently used for identification of compounds,the measurement of residual stresses and the identification ofdefects. In theMAX phases, because of their layered nature,we believe identification of the modes and correlating themwith the database of physical and mechanical properties willbe of vital and crucial importance for the rapid developmentof solid solution alloys. As noted above there are over fifty211 phases and hence a correspondingly very large numberof solid solution compositions indeed. By visualizing themodes, we can now correlate changes in the Raman frequen-cies directly with changes in bond energies between the vari-ous atoms and more importantly here between the layers.24As shown in Fig. 4, the agreement between measured andcalculated Raman mode energies for all the structures re-ported here is excellent; a least mean squared linear fit ofpoints shown in Fig. 4 yields a slope of 0.992±0.005. Thisconfirms the predictive capability of theab initio methodemployed for the study of the lattice dynamics of these ter-nary carbides and nitrides.We gratefully acknowledge Alexander Mavromaras andPaul Saxe from Materials Design for helpful discussions.This work was partially funded by the Division of MaterialsResearch of the National Science FoundationsDMR-0072067d and ONR sN00421-03-0085d. J.S. acknowledgespartial support by AROsYIP-W911NF-04-1-0308d.*Author to whom correspondence should be addressed. Email ad-dress: spanier@drexel.edu†Present address: Department of Mechanical and Materials Engi-neering, Wright State University, Dayton OH 45435.1M. W. Barsoum, A. Murugaiah, S. R. Kalidindi, and T. Zhen,Phys. Rev. Lett.92, 255508s2004d.2M. W. Barsoum, T. Zhen, S. R. Kalidindi, M. Radovic, and A.Murugaiah, Nat. Mater.2, 107–111s2003d.3R. A. Guyer and P. A. Johnson, Phys. Today52 s4d, 30 s1999d.4R. A. Guyer, K. R. McCall, and G. N. Boitnott, Phys. Rev. Lett.74, 3491s1995d.5M. W. Barsoum, Prog. Solid State Chem.28, 201 s2000d.6M. W. Barsoum and T. El-Raghy, Am. Sci.89, 336 s2000d.7M. Amer et al., J. Appl. Phys.84, 5817s1998d.8S. Gupta and M. W. Barsoumsunpublished.9M. W. Barsoum, M. Ali, and T. El-Raghy, Metall. Mater. Trans. A31A, 1857s2000d.10S. Gupta and M. W. Barsoum, J. Electrochem. Soc.151, D24s2004d.11A. T. Procopio, T. El-Raghy, and M. W. Barsoum, Metall. Mater.Trans. A 31A, 373 s2000d.12I. Salama, T. El-Raghy, and M. W. Barsoum, J. Alloys Compd.347, 271 s2002d.13M. W. Barsoum and T. El-Raghy, Metall. Mater. Trans. A30A,363 s1999d.14G. Kresse and J. Furthmuller, Phys. Rev. B54, 11 169s1996d.15K. Parlinski, Z. Q. Li, and Y. Kawazoe, Phys. Rev. Lett.78, 4063s1997d.16Materials Design, Angel Fire, NM.17G. Kresse and D. Joubert, Phys. Rev. B59, 1758s1999d.18P. E. Blöchl, Phys. Rev. B50, 17 953s1994d.19J. P. Perdew, K. Burke, and Y. Wang, Phys. Rev. B54, 16 533s1996d.20Z. Sun, R. Ahuja, S. Li, and J. M. Schneiger, Appl. Phys. Lett.83, 899 s2003d.21E. H. Kisi, J. A. A. Crossley, S. Myhra, and M. W. Barsoum, J.Phys. Chem. Solids59, 1437s1998d.22C. J. Rawnet al., Mater. Res. Bull.35, 1785s2000d.23S. Li H. Pettersson, C. G. Ribbing, B. Johansson, M. W. Bar-soum, and R. Ahuja, Appl. Phys. Lett.s o be published.24See EPAPS Document No. E-PRBMD0-70-109445 for anima-tions of lattice displacements. A direct link to this document maybe found in the online article’s HTML reference section. Thedocument may also be reached via the EPAPS homepageshttp://www.aip.org/pubservs/epaps.htmld or from ftp.aip.org in the di-rectory /epaps/. See the EPAPS homepage for more information.FIG. 4. sColor onlined Correspondence of experimental and cal-culated energies for selectedMAX phases. Ti3SiC2 is denoted byblue sgrayd diamonds, Ti2AlC by greensgrayd squares, V2AlC byred sgrayd solid circles, Cr2AlC by upright black triangles, Nb2AlCby inverted magentasgrayd triangles.BRIEF REPORTS PHYSICAL REVIEW B71, 012103s2005d012103-4

Vibrational Behavior of the M\u3csub\u3en+1\u3c/sub\u3e\u3cem\u3eAX\u3csub\u3en\u3c/sub\u3e\u3c/em\u3e Phases from First-Order Raman Scattering (\u3cem\u3eM\u3c/em\u3e=Ti,V,Cr, \u3cem\u3eA\u3c/em\u3e=Si, \u3cem\u3eX\u3c/em\u3e=C,N)

https://corescholar.libraries.wright.edu/cgi/viewcontent.cgi?article=1282&amp;context=mme

Vibrational Behavior of the M\u3csub\u3en+1\u3c/sub\u3e\u3cem\u3eAX\u3csub\u3en\u3c/sub\u3e\u3c/em\u3e Phases from First-Order Raman Scattering (\u3cem\u3eM\u3c/em\u3e=Ti,V,Cr, \u3cem\u3eA\u3c/em\u3e=Si, \u3cem\u3eX\u3c/em\u3e=C,N)

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