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Nuclear quadrupole resonance

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spectrum of a substance is specific to the substance - and NQR spectrum is a so called "chemical fingerprint." Because NQR frequencies are not chosen by the experimenter, they can be difficult to find making NQR a technically difficult technique to carry out. Since NQR is done in an environment without a static (or DC) magnetic field, it is sometimes called "
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just as the NMR experimenter is free to choose the Larmor frequency by adjusting the magnetic field. However, in solids, the strength of the EFG is many kV/m^2, making the application of EFG's for NQR in the manner that external magnetic fields are chosen for NMR impractical. Consequently, the NQR
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at which transitions occur is unique for a given substance. A particular NQR frequency in a compound or crystal is proportional to the product of the nuclear quadrupole moment, a property of the nucleus, and the EFG in the neighborhood of the nucleus. It is this product which is termed the nuclear
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Any nucleus with more than one unpaired nuclear particle (protons or neutrons) will have a charge distribution which results in an electric quadrupole moment. Allowed nuclear energy levels are shifted unequally due to the interaction of the nuclear charge with an electric field gradient supplied by
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There are several research groups around the world currently working on ways to use NQR to detect explosives. Units designed to detect landmines and explosives concealed in luggage have been tested. A detection system consists of a radio frequency (RF) power source, a coil to produce the magnetic
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the non-uniform distribution of electron density (e.g. from bonding electrons) and/or surrounding ions. As in the case of NMR, irradiation of the nucleus with a burst of RF electromagnetic radiation may result in absorption of some energy by the nucleus which can be viewed as a
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quadrupole coupling constant for a given isotope in a material and can be found in tables of known NQR transitions. In NMR, an analogous but not identical phenomenon is the coupling constant, which is also the result of an internuclear interaction between nuclei in the analyte.
1531:{\displaystyle U=-{\frac {1}{2}}\int _{\mathcal {D}}d^{3}r\rho ({\textbf {r}})\left=-{\frac {1}{2}}\int _{\mathcal {D}}d^{3}r\rho ({\textbf {r}})\left=-{\frac {1}{2}}\left({\frac {\partial E_{i}}{\partial x_{i}}}\right){\Bigg \vert }_{0}\cdot \int _{\mathcal {D}}d^{3}r\left} 87:
of the quadrupole energy level. Unlike the NMR case, NQR absorption takes place in the absence of an external magnetic field. Application of an external static field to a quadrupolar nucleus splits the quadrupole levels by the energy predicted from the
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in realtime. This particular technique allows local or remote monitoring of the extraction process, calculation of the well's remaining capacity and the water/detergents ratio the input pump must send to efficiently extract oil.
652: 479:. This potential may be produced by the electrons as stated above, whose probability distribution might be non-isotropic in general. The potential energy in this system equals to the integral over the charge distribution 221:. The nuclear quadrupole moment is associated with non-spherical nuclear charge distributions. As such it is a measure of the degree to which the nuclear charge distribution deviates from that of a sphere; that is, the 233:
created by the electronic structure of its environment. The NQR transition frequencies are proportional to the product of the electric quadrupole moment of the nucleus and a measure of the strength of the local EFG:
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claimed to exploit NQR to detect explosives but in fact could do no such thing. Nonetheless, the device was successfully sold for millions to dozens of countries, including the government of Iraq.
1029:, the first derivatives can also be neglected. One is therefore left with all nine combinations of second derivatives. However if one deals with a homogeneous oblate or prolate nucleus the matrix 149: 510: 444: 543: 477: 1538:
The remaining terms in the integral are related to the charge distribution and hence the quadrupole moment. The formula can be simplified even further by introducing the
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in solids when performed at varying temperature. Due to symmetry, the shifts become averaged to zero in the liquid phase, so NQR spectra can only be measured for solids.
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vanish. This leads to a simplification because the equation for the potential energy now contains only the second derivatives in respect to the same variable:
940: 196: 1727: 667: 108:≥ 1/2 have a magnetic dipole moment so that their energies are split by a magnetic field, allowing resonance absorption of energy related to the 1919: 1544: 240: 1897: 1798:
excitation field and a detector circuit which monitors for a RF NQR response coming from the explosive component of the object.
972: 1691: 1867: 92:. The technique is very sensitive to the nature and symmetry of the bonding around the nucleus. It can characterize 1816:
Due to the strong temperature dependence of the NQR frequency, it can be used as a precise temperature sensor with
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shape of the nucleus. NQR is a direct observation of the interaction of the quadrupole moment with the local
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zero). Because the EFG at the location of a nucleus in a given substance is determined primarily by the
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in cartesian coordinates (note that the equations below use the Einstein sum-convention):
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where q is related to the largest principal component of the EFG tensor at the nucleus.
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In principle, the NQR experimenter could apply a specified EFG in order to influence
89: 30: 647:{\displaystyle U=-\int _{\mathcal {D}}d^{3}r\rho ({\textbf {r}})V({\textbf {r}})} 1838: 942:
will not be relevant and can therefore be omitted. Since nuclei do not have an
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Another practical use for NQR is measuring the water/gas/oil coming out of an
218: 41:). Unlike NMR, NQR transitions of nuclei can be detected in the absence of a 206: 70: 1809: 226: 222: 210: 202: 658:
at the center of the considered nucleus. This method corresponds to the
1802: 1622:, choosing the z-axis as the one with the maximal principal component 1854: 370:". Many NQR transition frequencies depend strongly upon temperature. 214: 1783:{\displaystyle \nu ={\frac {1}{2}}\left({\frac {e^{2}qQ}{h}}\right)} 1615:{\textstyle V_{ii}={\frac {\partial ^{2}V}{\partial x_{i}^{2}}}=eq} 904:{\displaystyle V({\textbf {r}})=V(0)+\left+{\frac {1}{2}}\left+...} 198:
is the (normally applied) magnetic field external to the nucleus.
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involved in the particular bond with other nearby nuclei, the NQR
298:{\displaystyle \omega _{Q}\sim {\frac {e^{2}Qq}{\hbar }}=C_{q}} 1465: 1265: 1119: 593: 554: 1022:{\textstyle {\textbf {E}}=-\mathrm {grad} V({\textbf {r}})} 49:". The NQR resonance is mediated by the interaction of the 45:, and for this reason NQR spectroscopy is referred to as " 1699: 1662: 1628: 1547: 1065: 1035: 975: 951: 919: 551: 518: 485: 452: 419: 395: 1730: 1093: 670: 577: 389:
Consider a nucleus with a non-zero quadrupole moment
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to obtain the proportionality written above. For an
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is referred to as the quadrupole coupling constant.
1782: 1714: 1682: 1644: 1614: 1530: 1077: 1051: 1021: 961: 934: 903: 646: 561: 537: 504: 471: 438: 405: 357: 327: 297: 201:In the case of NQR, nuclei with spin ≥ 1, such as 190: 166: 143: 1445: 1350: 1209: 850: 748: 37:technique related to nuclear magnetic resonance ( 969:, which would interact with the electric field 8: 1892:. London: Peter Peregrinus Ltd. p. 48. 1874:. In Jacqueline MacDonald, J. R. Lockwood: 1839:"Nuclear Quadrupole Resonance Spectroscopy" 1878:. Report MR-1608, Rand Corporation, 2003. 1758: 1751: 1737: 1729: 1698: 1672: 1661: 1633: 1627: 1594: 1589: 1571: 1564: 1552: 1546: 1517: 1512: 1496: 1495: 1475: 1464: 1463: 1450: 1444: 1443: 1429: 1414: 1404: 1390: 1373: 1368: 1355: 1349: 1348: 1334: 1319: 1309: 1291: 1290: 1275: 1264: 1263: 1249: 1232: 1227: 1214: 1208: 1207: 1193: 1188: 1170: 1163: 1145: 1144: 1129: 1118: 1117: 1103: 1092: 1064: 1040: 1034: 1010: 1009: 989: 977: 976: 974: 953: 952: 950: 918: 878: 868: 855: 849: 848: 834: 824: 806: 799: 780: 766: 753: 747: 746: 732: 714: 678: 677: 669: 635: 634: 619: 618: 603: 592: 591: 576: 553: 552: 550: 526: 525: 517: 493: 492: 484: 460: 459: 451: 427: 426: 418: 397: 396: 394: 349: 343: 319: 313: 289: 264: 257: 248: 242: 183: 159: 126: 120: 1868:Appendix K: Nuclear quadrupole resonance 1829: 277: 1890:Temperature measurement & control 446:, which is surrounded by a potential 7: 144:{\displaystyle \omega _{L}=\gamma B} 1876:Alternatives for Landmine Detection 1497: 1292: 1146: 1059:will be diagonal and elements with 1011: 978: 954: 679: 636: 620: 527: 494: 461: 428: 398: 1582: 1568: 1422: 1407: 1327: 1312: 1181: 1167: 999: 996: 993: 990: 817: 803: 725: 717: 25: 654:One can write the potential as a 505:{\textstyle \rho ({\textbf {r}})} 439:{\textstyle \rho ({\textbf {r}})} 374:Derivation of resonance frequency 1837:Smith, J. A. S. (January 1971). 1803:fake device known as the ADE 651 104:In the case of NMR, nuclei with 1502: 1492: 1297: 1287: 1151: 1141: 1016: 1006: 929: 923: 699: 693: 684: 674: 641: 631: 625: 615: 532: 522: 499: 489: 466: 456: 433: 423: 1: 1843:Journal of Chemical Education 1690:nucleus one obtains with the 538:{\textstyle V({\textbf {r}})} 472:{\textstyle V({\textbf {r}})} 231:electric field gradient (EFG) 28:Nuclear quadrupole resonance 562:{\textstyle {\mathcal {D}}} 358:{\displaystyle \omega _{Q}} 1936: 1920:Nuclear magnetic resonance 962:{\textstyle {\textbf {p}}} 406:{\textstyle {\textbf {Q}}} 219:electric quadrupole moment 1872:Naval Research Laboratory 1692:frequency-energy relation 913:The first term involving 18:Nuclear quadrupole moment 1888:Leigh, James R. (1988). 1870:, by Allen N. Garroway, 53:gradient (EFG) with the 1820:on the order of 10 °C. 1540:electric field gradient 167:{\displaystyle \gamma } 1784: 1716: 1684: 1646: 1616: 1532: 1079: 1053: 1023: 963: 944:electric dipole moment 936: 905: 648: 563: 539: 506: 473: 440: 407: 359: 329: 299: 192: 168: 145: 1785: 1717: 1685: 1647: 1617: 1533: 1080: 1054: 1024: 964: 937: 906: 649: 564: 540: 507: 474: 441: 408: 360: 330: 328:{\displaystyle C_{q}} 300: 193: 169: 146: 1728: 1715:{\textstyle E=h\nu } 1697: 1660: 1626: 1545: 1091: 1078:{\textstyle i\neq j} 1063: 1033: 973: 949: 917: 668: 575: 549: 516: 483: 450: 417: 393: 342: 312: 241: 182: 158: 119: 1645:{\textstyle Q_{zz}} 1599: 1522: 1378: 1237: 1198: 1052:{\textstyle Q_{ij}} 660:multipole expansion 413:and charge density 59:charge distribution 1780: 1712: 1683:{\textstyle I=3/2} 1680: 1642: 1612: 1585: 1528: 1508: 1364: 1223: 1184: 1075: 1049: 1019: 959: 932: 901: 644: 559: 535: 512:and the potential 502: 469: 436: 403: 355: 325: 295: 188: 176:gyromagnetic ratio 164: 141: 90:Zeeman interaction 1774: 1745: 1601: 1499: 1436: 1398: 1341: 1294: 1257: 1200: 1148: 1111: 1013: 980: 956: 935:{\textstyle V(0)} 841: 788: 739: 681: 638: 622: 529: 496: 463: 430: 400: 280: 191:{\displaystyle B} 94:phase transitions 67:valence electrons 55:quadrupole moment 35:chemical analysis 16:(Redirected from 1927: 1904: 1903: 1885: 1879: 1865: 1859: 1858: 1855:10.1021/ed048p39 1834: 1789: 1787: 1786: 1781: 1779: 1775: 1770: 1763: 1762: 1752: 1746: 1738: 1721: 1719: 1718: 1713: 1689: 1687: 1686: 1681: 1676: 1654:Laplace equation 1651: 1649: 1648: 1643: 1641: 1640: 1621: 1619: 1618: 1613: 1602: 1600: 1598: 1593: 1580: 1576: 1575: 1565: 1560: 1559: 1537: 1535: 1534: 1529: 1527: 1523: 1521: 1516: 1501: 1500: 1480: 1479: 1470: 1469: 1468: 1455: 1454: 1449: 1448: 1441: 1437: 1435: 1434: 1433: 1420: 1419: 1418: 1405: 1399: 1391: 1383: 1379: 1377: 1372: 1360: 1359: 1354: 1353: 1346: 1342: 1340: 1339: 1338: 1325: 1324: 1323: 1310: 1296: 1295: 1280: 1279: 1270: 1269: 1268: 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171: 170: 165: 150: 148: 147: 142: 131: 130: 110:Larmor frequency 100:Analogy with NMR 21: 1935: 1934: 1930: 1929: 1928: 1926: 1925: 1924: 1910: 1909: 1908: 1907: 1900: 1887: 1886: 1882: 1866: 1862: 1836: 1835: 1831: 1826: 1795: 1754: 1753: 1747: 1726: 1725: 1695: 1694: 1658: 1657: 1629: 1624: 1623: 1581: 1567: 1566: 1548: 1543: 1542: 1488: 1484: 1471: 1459: 1442: 1425: 1421: 1410: 1406: 1400: 1347: 1330: 1326: 1315: 1311: 1305: 1304: 1300: 1271: 1259: 1206: 1180: 1166: 1165: 1159: 1158: 1154: 1125: 1113: 1089: 1088: 1061: 1060: 1036: 1031: 1030: 971: 970: 947: 946: 915: 914: 874: 864: 847: 830: 820: 816: 802: 801: 795: 794: 790: 762: 745: 728: 724: 716: 710: 709: 705: 666: 665: 599: 587: 573: 572: 547: 546: 514: 513: 481: 480: 448: 447: 415: 414: 391: 390: 387: 383: 379: 377: 376: 345: 340: 339: 315: 310: 309: 306: 285: 260: 259: 244: 239: 238: 217:, also have an 180: 179: 156: 155: 152: 122: 117: 116: 102: 80: 57:of the nuclear 23: 22: 15: 12: 11: 5: 1933: 1931: 1923: 1922: 1912: 1911: 1906: 1905: 1898: 1880: 1860: 1828: 1827: 1825: 1822: 1794: 1791: 1778: 1773: 1769: 1766: 1761: 1757: 1750: 1744: 1741: 1736: 1733: 1711: 1708: 1705: 1702: 1679: 1675: 1671: 1668: 1665: 1652:and using the 1639: 1636: 1632: 1611: 1608: 1605: 1597: 1592: 1588: 1584: 1579: 1574: 1570: 1563: 1558: 1555: 1551: 1526: 1520: 1515: 1511: 1507: 1504: 1494: 1491: 1487: 1483: 1478: 1474: 1467: 1462: 1458: 1453: 1447: 1440: 1432: 1428: 1424: 1417: 1413: 1409: 1403: 1397: 1394: 1389: 1386: 1382: 1376: 1371: 1367: 1363: 1358: 1352: 1345: 1337: 1333: 1329: 1322: 1318: 1314: 1308: 1303: 1299: 1289: 1286: 1283: 1278: 1274: 1267: 1262: 1256: 1253: 1248: 1245: 1241: 1235: 1230: 1226: 1222: 1217: 1211: 1204: 1196: 1191: 1187: 1183: 1178: 1173: 1169: 1162: 1157: 1153: 1143: 1140: 1137: 1132: 1128: 1121: 1116: 1110: 1107: 1102: 1099: 1096: 1074: 1071: 1068: 1046: 1043: 1039: 1018: 1008: 1005: 1001: 998: 995: 992: 988: 985: 931: 928: 925: 922: 900: 897: 894: 891: 887: 881: 877: 871: 867: 863: 858: 852: 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99: 97: 95: 91: 86: 77: 75: 72: 68: 64: 60: 56: 52: 48: 44: 40: 36: 32: 29: 19: 1889: 1883: 1863: 1846: 1842: 1832: 1815: 1807: 1800: 1796: 1793:Applications 1724: 1087: 912: 664: 571: 388: 337: 307: 237: 200: 153: 115: 103: 85:perturbation 81: 33:or NQR is a 31:spectroscopy 27: 26: 1824:References 1818:resolution 1849:: 39–41. 1732:ν 1710:ν 1583:∂ 1569:∂ 1506:⋅ 1490:ρ 1461:∫ 1457:⋅ 1423:∂ 1408:∂ 1388:− 1362:⋅ 1328:∂ 1313:∂ 1285:ρ 1261:∫ 1247:− 1221:⋅ 1182:∂ 1168:∂ 1139:ρ 1115:∫ 1101:− 1070:≠ 987:− 862:⋅ 818:∂ 804:∂ 760:⋅ 726:∂ 718:∂ 613:ρ 589:∫ 585:− 487:ρ 421:ρ 347:ω 278:ℏ 255:∼ 246:ω 162:γ 136:γ 124:ω 78:Principle 71:frequency 1914:Category 1810:oil well 223:prolate 174:is the 1896:  378:": --> 227:oblate 154:where 63:trace 1894:ISBN 380:edit 213:and 178:and 106:spin 1851:doi 225:or 39:NMR 1916:: 1847:48 1845:. 1841:. 1801:A 1722:: 569:: 215:Cu 211:Cl 209:, 205:, 112:: 1902:. 1857:. 1853:: 1777:) 1772:h 1768:Q 1765:q 1760:2 1756:e 1749:( 1743:2 1740:1 1735:= 1707:h 1704:= 1701:E 1678:2 1674:/ 1670:3 1667:= 1664:I 1638:z 1635:z 1631:Q 1610:q 1607:e 1604:= 1596:2 1591:i 1587:x 1578:V 1573:2 1562:= 1557:i 1554:i 1550:V 1525:] 1519:2 1514:i 1510:x 1503:) 1498:r 1493:( 1486:[ 1482:r 1477:3 1473:d 1466:D 1452:0 1446:| 1439:) 1431:i 1427:x 1416:i 1412:E 1402:( 1396:2 1393:1 1385:= 1381:] 1375:2 1370:i 1366:x 1357:0 1351:| 1344:) 1336:i 1332:x 1321:i 1317:E 1307:( 1302:[ 1298:) 1293:r 1288:( 1282:r 1277:3 1273:d 1266:D 1255:2 1252:1 1244:= 1240:] 1234:2 1229:i 1225:x 1216:0 1210:| 1203:) 1195:2 1190:i 1186:x 1177:V 1172:2 1161:( 1156:[ 1152:) 1147:r 1142:( 1136:r 1131:3 1127:d 1120:D 1109:2 1106:1 1098:= 1095:U 1073:j 1067:i 1045:j 1042:i 1038:Q 1017:) 1012:r 1007:( 1004:V 1000:d 997:a 994:r 991:g 984:= 979:E 955:p 930:) 927:0 924:( 921:V 899:. 896:. 893:. 890:+ 886:] 880:j 876:x 870:i 866:x 857:0 851:| 844:) 836:j 832:x 826:i 822:x 813:V 808:2 797:( 792:[ 786:2 783:1 778:+ 774:] 768:i 764:x 755:0 749:| 742:) 734:i 730:x 721:V 712:( 707:[ 703:+ 700:) 697:0 694:( 691:V 688:= 685:) 680:r 675:( 672:V 642:) 637:r 632:( 629:V 626:) 621:r 616:( 610:r 605:3 601:d 594:D 582:= 579:U 555:D 533:) 528:r 523:( 520:V 500:) 495:r 490:( 467:) 462:r 457:( 454:V 434:) 429:r 424:( 399:Q 384:] 351:Q 321:q 317:C 291:q 287:C 283:= 274:q 271:Q 266:2 262:e 250:Q 207:O 203:N 186:B 139:B 133:= 128:L 20:)

Index

Nuclear quadrupole moment
spectroscopy
chemical analysis
NMR
magnetic field
zero Field NMR
electric field
quadrupole moment
charge distribution
trace
valence electrons
frequency
perturbation
Zeeman interaction
phase transitions
spin
Larmor frequency
gyromagnetic ratio
N
O
Cl
Cu
electric quadrupole moment
prolate
oblate
electric field gradient (EFG)
zero field NMR
Taylor-expansion
multipole expansion
electric dipole moment

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