271:, a form of elastic scattering from the incident photons and the sample. Rayleigh scattering occurs when the induced polarization of the atoms, resulting from the incident photons, does not couple with possible vibrational modes of the atoms. The resulting emitted radiation has the same energy as the incident radiation, meaning no frequency shift is observed. This peak is generally quite intense and is not of direct interest for Brillouin spectroscopy. In an experiment, the incident light is most often a high power laser. This results in a very intense Rayleigh peak which has the ability to wash out the Brillouin peaks of interest. In order to adjust for this, most spectrum are plotted with the Rayleigh peak either filtered out or suppressed.
405:, relates stress and strain within a given material. The number of independent elastic constants found within the elastic tensor can be reduced through symmetry operations and depends on the symmetry of a given material ranging from 2 for non-crystalline substances or 3 for cubic crystals to 21 for systems with triclinic symmetry. The tensor is unique to given materials and thus must be independently determined for each material in order to understand their elastic properties. The elastic tensor is especially important to mineral physicist and seismologists looking to understand the bulk, polycrystalline, properties of deep Earth minerals. It is possible to determine elastic properties of materials such as the adiabatic bulk modulus,
98:), can be obtained through a Raman spectroscopy study shedding light on structure and chemical composition, whereas Brillouin scattering involves the scattering of photons by low frequency phonons providing information regarding elastic properties. Optical phonons and molecular vibrations measured in Raman spectroscopy typically have wavenumbers between 10 and 4000 cm, while phonons involved in Brillouin scattering are on the order of 0.1â6 cm. This roughly two order of magnitude difference becomes obvious when attempting to perform Raman spectroscopy vs. Brillouin spectroscopy experiments.
291:
regime, as a result, longitudinal waves, which are transmitted via compression parallel to the propagation direction, can transmit their energy through the material easily and thus travel quickly. The motion of transverse waves, on the other hand, is perpendicular to the propagation direction and is thus less easily propagated through the medium. As a result, longitudinal waves travel more quickly through solids than transverse waves. An example of this can be seen in
432:, without first finding the complete elastic tensor through techniques such as the determination of an equation of state through a compression study. Elastic properties found in this way, however, do not scale well to bulk systems such as those found within rock assemblages in the Earth's mantle. In order to calculate the elastic properties of bulk material with randomly oriented crystals the elastic tensor is needed.
1767:
349:
two transverse waves will be degenerate, as they will be traveling along elastically identical crystallographic planes. In non-isotropic solids the two transverse waves will be distinguishable from one another, but not distinguishable as being horizontally or vertically polarized without a deeper understanding of the material being studied. They are then generically labeled transverse 1 and transverse 2.
264:
of the absorbed photon. Anti-Stokes scattering describes the interaction scenario in which the incoming photon absorbs a phonon, phonon annihilation, and a photon with a higher energy than that of absorbed photon is emitted. The figure illustrates the differences between Raman scattering and
Brillouin scattering along with Stokes and anti-Stokes interactions as is seen in experimental data.
1779:
74:
348:
According to the equation, acoustic waves with varying speeds will appear on the
Brillouin spectra with varying wavenumbers: faster waves with higher magnitude wavenumbers and slower waves with smaller wavenumbers. Therefore, three distinct Brillouin lines will be observable. In isotropic solids, the
290:
In practice, six
Brillouin lines of interest are generally seen in a Brillouin spectrum. Acoustic waves have three polarization directions one longitudinal and two transverse directions each being orthogonal to the others. Solids can be considered nearly incompressible, within an appropriate pressure
263:
The equations describe both the constructive (Stokes) and destructive (anti-Stokes) interactions between a photon and phonon. Stokes scattering describes the interaction scenario in which the material absorbs the photon, creating a phonon, inelastically emitting a photon with a lower energy than that
295:
with an approximate acoustic longitudinal wave velocity of 5965 m/s and transverse wave velocity of 3750 m/s. Fluids cannot support transverse waves. As a result, transverse wave signals are not found in
Brillouin spectra of fluids. The equation shows the relationship between acoustic wave
274:
The second noteworthy aspect of the figure is the distinction between
Brillouin and Raman peaks. As previously mentioned, Brillouin peaks range from 0.1 cm to approximately 6 cm while Raman scattering wavenumbers ranges from 10â10000 cm. As Brillouin and Raman spectroscopy probe two
251:
The second equation describes the application of conservation of momentum to the system. The phonon, which is either generated or annihilated, has a wavevector which is a linear combination of the incident and scattered wavevectors. This orientation will become more apparent and important when the
248:
Brillouin scattering occurs. The energy imparted on an incident photon from a phonon is relatively small, generally around 5-10% that of the photon's energy. Given an approximate frequency of visible light, ~10 Hz, it is easy to see that
Brillouin scattering generally lies in the GHz regime.
286:
The figure also highlights the difference between Stokes and anti-Stokes scattering. Stokes scattering, positive photon creation, is displayed as a positive shift in wavenumber. Anti-Stokes scattering, negative photon annihilation, is displayed as a negative shift in wavenumber. The locations of
247:
denote the incident and scattered waves. The first equation is the result of the application of the conservation of energy to the system of the incident photon, the scattered photon, and the interacting phonon. Applying conservation of energy also sheds light upon the frequency regime in which
358:
660:
256:
77:
An illustration of an example
Brillouin and Raman spectrum. In practice the distinction between Brillouin and Raman spectroscopy depends on which frequencies we choose to sample. Brillouin scattering generally lies within the GHz frequency
914:
275:
fundamentally different interaction regimes this is not too large of an inconvenience. The fact that
Brillouin interactions are such low frequency however creates technical challenges when performing experiments for which a
526:
1134:
Muller U. P., Sanctuary R., Seck P., Kruger J. âCh. (2005) Scanning
Brillouin microscopy: acoustic microscopy at gigahertz frequencies. Archives des Sciences Naturelles, Physiques et Mathematiques, 46, 11-25.
163:
829:
In a cubic material it is possible to determine the complete elastic tensor from pure longitudinal and pure transverse phonon velocities. In order make the above calculations the phonon wavevector,
86:
in many ways; in fact the physical scattering processes involved are identical. However, the type of information gained is significantly different. The process observed in Raman spectroscopy,
1223:
1598:
833:, must be pre-determined from the geometry of the experiment. There are three main Brillouin spectroscopy geometries: 90 degree scattering, backscattering, and platelet geometry.
826:
reduces to 3 independent components. Equation 5 shows the complete elastic tensor for a cubic material. The relations between the elastic constants and can be found in Table 1.
218:
711:
624:
594:
1271:
966:
343:
435:
Using
Equation 3, it is possible to determine the sound velocity through a material. In order to obtain the elastic tensor the Christoffel Equation needs to be applied:
65:. Brillouin spectroscopy can be used to determine the complete elastic tensor of a given material which is required in order to understand the bulk elastic properties.
824:
781:
564:
399:
1026:
939:
741:
654:
430:
1006:
986:
849:
1489:
1122:
Bass J. (1995) Elasticity of minerals, glasses, and melts. Mineral Physics and Crystallography: a Handbook of Physical Constants, AGU Reference Shelf 2, 45-63.
1422:
1367:
1336:
1331:
1704:
1522:
1384:
267:
The figure depicts three important details. The first is the Rayleigh line, the peak which has been suppressed at 0 cm. This peak is a result of
1653:
1472:
1316:
1593:
1395:
1296:
283:âbased spectrometer. In some cases a single gratingâbased spectrometer has been used to collect both Brillouin and Raman spectra from a sample.
1539:
1517:
1264:
1605:
1527:
1197:
1357:
1462:
1407:
440:
279:
are usually used in order to overcome. A Raman spectroscopy system is generally less technically complicated and can be performed with a
107:
1805:
1689:
1441:
1257:
1237:
1694:
1512:
287:
peaks are symmetric about the Rayleigh line because they correspond to the same energy level transition but of a different sign.
1709:
1679:
1610:
1544:
1638:
1429:
1326:
231:
are the angular frequency and wavevector of the photon, respectively. While the phonon angular frequency and wavevector are
663:
Relationships between elastic constants and X for cubic systems depending upon the direction of propagation of the phonon,
1436:
1341:
1570:
1417:
1306:
1726:
1565:
1534:
1467:
94:
modes. Information relating to modes of vibration, such as the six normal modes of vibration of the carbonate ion, (CO
1716:
1658:
1507:
1379:
276:
101:
In Brillouin scattering, and similarly Raman scattering, both energy and momentum are conserved in the relations:
1742:
1721:
1484:
1362:
626:, whose eigenvalues are equal to ÏV2, where Ï is density and V is acoustic velocity. The polarization matrix,
1783:
1615:
1311:
1229:
1402:
1148:
Mazzacurati, V; Benassi, P; Ruocco, G (1988). "A new class of multiple dispersion grating spectrometers".
1771:
1643:
1374:
1288:
790:, and acoustic wave velocities, ÏV2, have been determined and tabulated. For example, in a cubic system
35:
1080:
1037:
171:
39:
31:
27:
1699:
1412:
1321:
686:
599:
569:
280:
268:
91:
43:
1113:
Buzgar N., Apopei A., (2009) The Raman study of certain carbonates. Geologie. Tomul LV, 2, 97-112.
944:
1747:
1684:
1663:
1479:
1457:
1390:
1301:
1042:
314:
83:
530:
The Christoffel Equation is essentially an eigenvalue problem which relates the elastic tensor,
1648:
1575:
1549:
1233:
1193:
1165:
1096:
793:
786:
For specific symmetries the relationship between a specific combination of elastic constants,
750:
533:
368:
1011:
924:
1157:
1088:
716:
629:
87:
62:
26:
technique which allows the determination of elastic moduli of materials. The technique uses
408:
909:{\displaystyle \Delta \omega =v_{\text{s}}{\frac {2n\omega }{c}}\sin {\frac {\theta }{2}}}
357:
58:
30:
scattering of light when it encounters acoustic phonons in a crystal, a process known as
1084:
841:
The frequency shift of the incident laser light due to Brillouin scattering is given by
659:
991:
971:
402:
365:
Brillouin spectroscopy is a valuable tool for determining the complete elastic tensor,
1799:
1161:
57:
This technique is commonly used to determine the elastic properties of materials in
1280:
259:
Geometric relationships between longitudinal, L, and transverse, T, acoustic waves.
23:
1187:
401:, of solids. The elastic tensor is an 81 component 3x3x3x3 matrix which, through
255:
1169:
1100:
1071:
Polian, Alain (2003). "Brillouin scattering at high pressure: an overview".
20:
1136:
73:
566:, to the crystal orientation and the orientation of the incident light,
747:
is determined from the Brillouin spectra, it is possible to determine
1092:
656:, contains the corresponding polarizations of the propagating waves.
521:{\displaystyle c_{ijkl}\Lambda _{kl}=\lambda _{kl}\delta _{kl}p_{kl}}
292:
51:
47:
968:
is the velocity of acoustic waves (speed of sound in the medium),
158:{\displaystyle \hbar \Omega =\pm \hbar (\omega _{i}-\omega _{s})}
1253:
1249:
1014:
994:
974:
947:
927:
852:
796:
753:
719:
689:
632:
602:
572:
536:
443:
411:
371:
317:
174:
110:
252:
orientation of the experimental setup is discussed.
1735:
1672:
1631:
1624:
1586:
1558:
1500:
1450:
1350:
1287:
1020:
1000:
980:
960:
933:
908:
818:
775:
735:
705:
648:
618:
588:
558:
520:
424:
393:
337:
212:
157:
1186:William Hayes; Rodney Loudon (13 December 2012).
1181:
1179:
1212:Cummins & Schoen, 1972, Laser Handbook vol 2
361:Cubic elastic tensor after symmetry reduction.
1265:
38:of a material. The scattering occurs when an
34:, to determine phonon energies and therefore
8:
1337:Vibrational spectroscopy of linear molecules
1150:Journal of Physics E: Scientific Instruments
1066:
1064:
1062:
1060:
1058:
1628:
1332:Nuclear resonance vibrational spectroscopy
1272:
1258:
1250:
743:are known from the experimental setup and
1705:Inelastic electron tunneling spectroscopy
1385:Resonance-enhanced multiphoton ionization
1028:is the angle of incidence of the light.
1013:
993:
973:
952:
946:
926:
896:
872:
866:
851:
801:
795:
758:
752:
724:
718:
694:
688:
637:
631:
607:
601:
577:
571:
541:
535:
509:
496:
483:
467:
448:
442:
416:
410:
376:
370:
327:
316:
201:
188:
173:
146:
133:
109:
1473:Extended X-ray absorption fine structure
1130:
1128:
658:
356:
254:
72:
1137:http://orbilu.uni.lu/handle/10993/13482
1054:
941:is the angular frequency of the light,
123:
111:
783:, given the density of the material.
667:, and the eigenvector of the phonon,
82:Brillouin spectroscopy is similar to
7:
1778:
90:, primarily involves high frequency
1008:is the vacuum speed of light, and
853:
691:
574:
464:
324:
114:
69:Comparison with Raman spectroscopy
14:
1690:Deep-level transient spectroscopy
1442:Saturated absorption spectroscopy
1777:
1766:
1765:
1695:Dual-polarization interferometry
1710:Scanning tunneling spectroscopy
1685:Circular dichroism spectroscopy
1680:Acoustic resonance spectroscopy
1189:Scattering of Light by Crystals
213:{\displaystyle q=(k_{t}-k_{s})}
1639:Fourier-transform spectroscopy
1327:Vibrational circular dichroism
207:
181:
152:
126:
1:
1437:Cavity ring-down spectroscopy
1342:Thermal infrared spectroscopy
1073:Journal of Raman Spectroscopy
706:{\displaystyle \Lambda _{kl}}
619:{\displaystyle \lambda _{kl}}
589:{\displaystyle \Lambda _{kl}}
1571:Inelastic neutron scattering
1225:Optical Properties of Solids
988:is the index of refraction,
961:{\displaystyle v_{\text{s}}}
679:= transverse acoustic waves.
1632:Data collection, processing
1508:Photoelectron/photoemission
338:{\displaystyle V=\Omega /q}
1822:
1717:Photoacoustic spectroscopy
1659:Time-resolved spectroscopy
1162:10.1088/0022-3735/21/8/012
683:Using the equation, where
277:Fabry-Perot interferometer
1761:
1743:Astronomical spectroscopy
1722:Photothermal spectroscopy
304:, and phonon wavenumber,
1806:Vibrational spectroscopy
819:{\displaystyle c_{ijkl}}
776:{\displaystyle c_{ijkl}}
559:{\displaystyle c_{ijkl}}
394:{\displaystyle c_{ijkl}}
1727:Pumpâprobe spectroscopy
1616:Ferromagnetic resonance
1408:Laser-induced breakdown
1230:Oxford University Press
1192:. Courier Corporation.
1021:{\displaystyle \theta }
934:{\displaystyle \omega }
1423:Glow-discharge optical
1403:Raman optical activity
1317:Rotationalâvibrational
1022:
1002:
982:
962:
935:
910:
820:
777:
737:
736:{\displaystyle p_{ij}}
707:
680:
650:
649:{\displaystyle p_{kl}}
620:
590:
560:
522:
426:
395:
362:
339:
260:
214:
159:
79:
36:interatomic potentials
17:Brillouin spectroscopy
1644:Hyperspectral imaging
1023:
1003:
983:
963:
936:
911:
821:
778:
738:
708:
662:
651:
621:
591:
561:
523:
427:
425:{\displaystyle K_{s}}
396:
360:
340:
258:
215:
160:
92:molecular vibrational
76:
1396:Coherent anti-Stokes
1351:UVâVisâNIR "Optical"
1232:. pp. 289â290.
1038:Brillouin scattering
1012:
992:
972:
945:
925:
850:
794:
751:
717:
687:
630:
600:
570:
534:
441:
409:
369:
315:
300:, angular frequency
172:
108:
40:electromagnetic wave
32:Brillouin scattering
1700:Hadron spectroscopy
1490:Conversion electron
1451:X-ray and Gamma ray
1358:Ultravioletâvisible
1085:2003JRSp...34..633P
675:= longitudinal and
281:diffraction grating
269:Rayleigh scattering
1748:Force spectroscopy
1673:Measured phenomena
1664:Video spectroscopy
1368:Cold vapour atomic
1222:Fox, Mark (2010).
1043:Raman spectroscopy
1018:
998:
978:
958:
931:
906:
816:
773:
733:
703:
681:
646:
616:
586:
556:
518:
422:
391:
363:
335:
261:
210:
155:
84:Raman spectroscopy
80:
1793:
1792:
1757:
1756:
1649:Spectrophotometry
1576:Neutron spin echo
1550:Beta spectroscopy
1463:Energy-dispersive
1199:978-0-486-16147-1
1001:{\displaystyle c}
981:{\displaystyle n}
955:
904:
888:
869:
239:. The subscripts
42:interacts with a
1813:
1781:
1780:
1769:
1768:
1629:
1540:phenomenological
1289:Vibrational (IR)
1274:
1267:
1260:
1251:
1244:
1243:
1219:
1213:
1210:
1204:
1203:
1183:
1174:
1173:
1145:
1139:
1132:
1123:
1120:
1114:
1111:
1105:
1104:
1093:10.1002/jrs.1031
1079:(7â8): 633â637.
1068:
1027:
1025:
1024:
1019:
1007:
1005:
1004:
999:
987:
985:
984:
979:
967:
965:
964:
959:
957:
956:
953:
940:
938:
937:
932:
915:
913:
912:
907:
905:
897:
889:
884:
873:
871:
870:
867:
832:
825:
823:
822:
817:
815:
814:
789:
782:
780:
779:
774:
772:
771:
746:
742:
740:
739:
734:
732:
731:
712:
710:
709:
704:
702:
701:
678:
674:
670:
666:
655:
653:
652:
647:
645:
644:
625:
623:
622:
617:
615:
614:
595:
593:
592:
587:
585:
584:
565:
563:
562:
557:
555:
554:
527:
525:
524:
519:
517:
516:
504:
503:
491:
490:
475:
474:
462:
461:
431:
429:
428:
423:
421:
420:
400:
398:
397:
392:
390:
389:
344:
342:
341:
336:
331:
307:
303:
299:
246:
242:
238:
234:
230:
226:
219:
217:
216:
211:
206:
205:
193:
192:
164:
162:
161:
156:
151:
150:
138:
137:
88:Raman scattering
63:material science
1821:
1820:
1816:
1815:
1814:
1812:
1811:
1810:
1796:
1795:
1794:
1789:
1753:
1731:
1668:
1620:
1582:
1554:
1496:
1446:
1346:
1307:Resonance Raman
1283:
1278:
1248:
1247:
1240:
1221:
1220:
1216:
1211:
1207:
1200:
1185:
1184:
1177:
1147:
1146:
1142:
1133:
1126:
1121:
1117:
1112:
1108:
1070:
1069:
1056:
1051:
1034:
1010:
1009:
990:
989:
970:
969:
948:
943:
942:
923:
922:
874:
862:
848:
847:
839:
837:Frequency shift
830:
797:
792:
791:
787:
754:
749:
748:
744:
720:
715:
714:
690:
685:
684:
676:
672:
668:
664:
633:
628:
627:
603:
598:
597:
596:, to a matrix,
573:
568:
567:
537:
532:
531:
505:
492:
479:
463:
444:
439:
438:
412:
407:
406:
372:
367:
366:
355:
313:
312:
305:
301:
297:
244:
240:
236:
232:
228:
224:
197:
184:
170:
169:
142:
129:
106:
105:
97:
71:
59:mineral physics
12:
11:
5:
1819:
1817:
1809:
1808:
1798:
1797:
1791:
1790:
1788:
1787:
1775:
1762:
1759:
1758:
1755:
1754:
1752:
1751:
1745:
1739:
1737:
1733:
1732:
1730:
1729:
1724:
1719:
1714:
1713:
1712:
1702:
1697:
1692:
1687:
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1670:
1669:
1667:
1666:
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1656:
1651:
1646:
1641:
1635:
1633:
1626:
1622:
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1618:
1613:
1608:
1603:
1602:
1601:
1590:
1588:
1584:
1583:
1581:
1580:
1579:
1578:
1568:
1562:
1560:
1556:
1555:
1553:
1552:
1547:
1542:
1537:
1532:
1531:
1530:
1525:
1523:Angle-resolved
1520:
1515:
1504:
1502:
1498:
1497:
1495:
1494:
1493:
1492:
1482:
1477:
1476:
1475:
1470:
1465:
1454:
1452:
1448:
1447:
1445:
1444:
1439:
1434:
1433:
1432:
1427:
1426:
1425:
1410:
1405:
1400:
1399:
1398:
1388:
1382:
1377:
1372:
1371:
1370:
1360:
1354:
1352:
1348:
1347:
1345:
1344:
1339:
1334:
1329:
1324:
1319:
1314:
1309:
1304:
1299:
1293:
1291:
1285:
1284:
1279:
1277:
1276:
1269:
1262:
1254:
1246:
1245:
1238:
1228:(2 ed.).
1214:
1205:
1198:
1175:
1156:(8): 798â804.
1140:
1124:
1115:
1106:
1053:
1052:
1050:
1047:
1046:
1045:
1040:
1033:
1030:
1017:
997:
977:
951:
930:
919:
918:
917:
916:
903:
900:
895:
892:
887:
883:
880:
877:
865:
861:
858:
855:
838:
835:
813:
810:
807:
804:
800:
770:
767:
764:
761:
757:
730:
727:
723:
700:
697:
693:
643:
640:
636:
613:
610:
606:
583:
580:
576:
553:
550:
547:
544:
540:
515:
512:
508:
502:
499:
495:
489:
486:
482:
478:
473:
470:
466:
460:
457:
454:
451:
447:
419:
415:
388:
385:
382:
379:
375:
354:
351:
346:
345:
334:
330:
326:
323:
320:
221:
220:
209:
204:
200:
196:
191:
187:
183:
180:
177:
166:
165:
154:
149:
145:
141:
136:
132:
128:
125:
122:
119:
116:
113:
95:
70:
67:
13:
10:
9:
6:
4:
3:
2:
1818:
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1801:
1786:
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1764:
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1749:
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1406:
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1401:
1397:
1394:
1393:
1392:
1389:
1386:
1383:
1381:
1380:Near-infrared
1378:
1376:
1373:
1369:
1366:
1365:
1364:
1361:
1359:
1356:
1355:
1353:
1349:
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1239:9780199573363
1235:
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1195:
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1190:
1182:
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1129:
1125:
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1107:
1102:
1098:
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1090:
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1078:
1074:
1067:
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1063:
1061:
1059:
1055:
1048:
1044:
1041:
1039:
1036:
1035:
1031:
1029:
1015:
995:
975:
949:
928:
901:
898:
893:
890:
885:
881:
878:
875:
863:
859:
856:
846:
845:
844:
843:
842:
836:
834:
827:
811:
808:
805:
802:
798:
784:
768:
765:
762:
759:
755:
728:
725:
721:
698:
695:
661:
657:
641:
638:
634:
611:
608:
604:
581:
578:
551:
548:
545:
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538:
528:
513:
510:
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500:
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487:
484:
480:
476:
471:
468:
458:
455:
452:
449:
445:
436:
433:
417:
413:
404:
386:
383:
380:
377:
373:
359:
352:
350:
332:
328:
321:
318:
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309:
294:
288:
284:
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278:
272:
270:
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257:
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202:
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178:
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143:
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134:
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117:
104:
103:
102:
99:
93:
89:
85:
75:
68:
66:
64:
60:
55:
54:scattering.
53:
49:
45:
41:
37:
33:
29:
25:
22:
18:
1782:
1770:
1750:(a misnomer)
1736:Applications
1654:Time-stretch
1545:paramagnetic
1363:Fluorescence
1281:Spectroscopy
1224:
1217:
1208:
1188:
1153:
1149:
1143:
1118:
1109:
1076:
1072:
920:
840:
828:
785:
682:
529:
437:
434:
364:
353:Applications
347:
289:
285:
273:
266:
262:
250:
222:
100:
81:
56:
44:density wave
24:spectroscopy
16:
15:
1322:Vibrational
403:Hooke's Law
1528:Two-photon
1430:absorption
1312:Rotational
1049:References
296:velocity,
1606:Terahertz
1587:Radiowave
1485:Mössbauer
1170:0022-3735
1101:0377-0486
1016:θ
929:ω
899:θ
894:
882:ω
857:ω
854:Δ
692:Λ
605:λ
575:Λ
494:δ
481:λ
465:Λ
325:Ω
195:−
144:ω
140:−
131:ω
124:ℏ
121:±
115:Ω
112:ℏ
28:inelastic
21:empirical
1800:Category
1772:Category
1501:Electron
1468:Emission
1418:emission
1375:Vibronic
1032:See also
671:, where
1784:Commons
1611:ESR/EPR
1559:Nucleon
1387:(REMPI)
1081:Bibcode
78:regime.
1625:Others
1413:Atomic
1236:
1196:
1168:
1099:
921:where
293:quartz
223:Where
52:phonon
48:photon
19:is an
1566:Alpha
1535:Auger
1513:X-ray
1480:Gamma
1458:X-ray
1391:Raman
1302:Raman
1297:FT-IR
1234:ISBN
1194:ISBN
1166:ISSN
1097:ISSN
713:and
243:and
235:and
227:and
61:and
1594:NMR
1158:doi
1089:doi
891:sin
1802::
1599:2D
1518:UV
1178:^
1164:.
1154:21
1152:.
1127:^
1095:.
1087:.
1077:34
1075:.
1057:^
308:.
46:,
1273:e
1266:t
1259:v
1242:.
1202:.
1172:.
1160::
1103:.
1091::
1083::
996:c
976:n
954:s
950:v
902:2
886:c
879:n
876:2
868:s
864:v
860:=
831:q
812:l
809:k
806:j
803:i
799:c
788:X
769:l
766:k
763:j
760:i
756:c
745:V
729:j
726:i
722:p
699:l
696:k
677:T
673:L
669:U
665:q
642:l
639:k
635:p
612:l
609:k
582:l
579:k
552:l
549:k
546:j
543:i
539:c
514:l
511:k
507:p
501:l
498:k
488:l
485:k
477:=
472:l
469:k
459:l
456:k
453:j
450:i
446:c
418:s
414:K
387:l
384:k
381:j
378:i
374:c
333:q
329:/
322:=
319:V
306:q
302:Ω
298:V
245:s
241:i
237:q
233:Ω
229:k
225:Ï
208:)
203:s
199:k
190:t
186:k
182:(
179:=
176:q
153:)
148:s
135:i
127:(
118:=
96:3
50:-
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