168:
generated. The first derivatives of the field, or the second derivatives of the potential, is the electric field gradient. The nine components of the EFG are thus defined as the second partial derivatives of the electrostatic potential, evaluated at the position of a nucleus:
596:
253:
370:
513:
265:
are combined as a symmetric 3 × 3 matrix. Under the assumption that the charge distribution generating the electrostatic potential is external to the nucleus, the matrix is
664:
696:
521:
175:
287:
821:
281:) = 0, holds. Relaxing this assumption, a more general form of the EFG tensor which retains the symmetry and traceless character is
113:
is the distance from a nucleus. This sensitivity has been used to study effects on charge distribution resulting from substitution,
701:
Electric field gradient as well as the asymmetry parameter can be evaluated numerically for large electric systems as shown in.
444:
423:. Given the traceless character, only two of the principal components are independent. Typically these are described by
75:
87:
601:
79:
816:
669:
67:
137:
to calculate EFGs and provide a deeper understanding of specific EFGs in crystals from measurements.
130:
125:
can be investigated with above methods using the EFG's sensitivity to local changes, like defects or
83:
811:
806:
154:
71:
270:
777:
741:
134:
8:
59:
51:
28:
781:
745:
731:
102:
98:
94:
and therefore generate an inhomogeneous electric field at the position of the nucleus.
765:
55:
24:
719:
785:
126:
114:
122:
62:
greater than one-half) to generate an effect which can be measured using several
591:{\displaystyle \vert V_{zz}\vert \geq \vert V_{yy}\vert \geq \vert V_{xx}\vert }
420:
165:
91:
90:(PAC). The EFG is non-zero only if the charges surrounding the nucleus violate
44:
40:
20:
789:
768:; Reiner J. Vianden (1979). "The electric field gradient in noncubic metals".
248:{\displaystyle V_{ij}={\frac {\partial ^{2}V}{\partial x_{i}\partial x_{j}}}.}
800:
63:
365:{\displaystyle \varphi _{ij}=V_{ij}-{\frac {1}{3}}\delta _{ij}\nabla ^{2}V,}
720:"Algorithm to compute the electric field gradient tensor in ionic crystals"
395:
266:
48:
736:
118:
101:
in the immediate vicinity of a nucleus. This is because the EFG
54:
and the other nuclei. The EFG couples with the nuclear electric
718:
Hernandez-Gomez, J J; Marquina, V; Gomez, R W (25 July 2013).
717:
164:). The derivative of this potential is the negative of the
764:
16:
Rate of change of the electric field at an atomic nucleus
508:{\displaystyle \eta ={\frac {V_{xx}-V_{yy}}{V_{zz}}}.}
398:. The principal tensor components are usually denoted
672:
604:
524:
447:
290:
178:
145:
A given charge distribution of electrons and nuclei,
690:
658:
590:
507:
364:
247:
798:
129:. In crystals the EFG is in the order of 10V/m.
585:
569:
563:
547:
541:
525:
133:has become an important tool for methods of
735:
822:Electric and magnetic fields in matter
799:
659:{\displaystyle V_{zz}+V_{yy}+V_{xx}=0}
117:, and charge transfer. Especially in
39:) measures the rate of change of the
383:) is evaluated at a given nucleus.
13:
347:
226:
213:
199:
58:of quadrupolar nuclei (those with
14:
833:
691:{\displaystyle 0\leq \eta \leq 1}
258:For each nucleus, the components
97:EFGs are highly sensitive to the
76:electron paramagnetic resonance
711:
1:
704:
140:
88:perturbed angular correlation
80:nuclear quadrupole resonance
7:
10:
838:
68:nuclear magnetic resonance
790:10.1103/RevModPhys.51.161
770:Reviews of Modern Physics
394:) is symmetric it can be
131:Density functional theory
269:, for in that situation
419:in order of decreasing
155:electrostatic potential
33:electric field gradient
692:
660:
592:
509:
366:
249:
84:Mössbauer spectroscopy
72:microwave spectroscopy
693:
661:
593:
510:
367:
250:
670:
602:
522:
445:
288:
176:
135:nuclear spectroscopy
782:1979RvMP...51..161K
746:2011arXiv1107.0059H
432:asymmetry parameter
60:spin quantum number
52:charge distribution
29:solid-state physics
688:
656:
588:
505:
362:
271:Laplace's equation
245:
99:electronic density
817:Quantum chemistry
766:Kaufmann, Elton N
500:
331:
240:
115:weak interactions
66:methods, such as
56:quadrupole moment
47:generated by the
829:
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153:), generates an
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123:local structure
17:
12:
11:
5:
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812:Atomic physics
809:
807:Electrostatics
795:
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776:(1): 161â214.
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166:electric field
142:
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92:cubic symmetry
45:atomic nucleus
41:electric field
15:
9:
6:
4:
3:
2:
834:
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724:Rev. Mex. FĂs
721:
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451:
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439:
438:, defined as
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138:
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127:phase changes
124:
120:
116:
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100:
95:
93:
89:
85:
81:
77:
73:
69:
65:
64:spectroscopic
61:
57:
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50:
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42:
38:
34:
30:
26:
22:
773:
769:
749:. Retrieved
730:(1): 13â18.
727:
723:
713:
700:
517:
435:
431:
424:
413:
406:
399:
396:diagonalized
391:
387:
385:
380:
376:
374:
278:
274:
259:
257:
161:
157:
150:
146:
144:
110:
106:
96:
78:(EPR, ESR),
36:
32:
18:
801:Categories
705:References
141:Definition
105:scales as
49:electronic
737:1107.0059
683:≤
680:η
677:≤
567:≥
545:≥
471:−
449:η
348:∇
335:δ
321:−
293:φ
267:traceless
227:∂
214:∂
200:∂
25:molecular
751:23 April
430:and the
119:crystals
109:, where
103:operator
778:Bibcode
742:Bibcode
666:, thus
421:modulus
375:where â
82:(NQR),
70:(NMR),
121:, the
43:at an
31:, the
27:, and
21:atomic
732:arXiv
518:with
390:(and
753:2016
598:and
412:and
786:doi
386:As
273:, â
86:or
37:EFG
19:In
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784:.
774:51
772:.
740:.
728:58
726:.
722:.
698:.
434:,
427:zz
416:xx
409:yy
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402:zz
262:ij
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792:.
788::
780::
755:.
744::
734::
686:1
674:0
654:0
651:=
646:x
643:x
639:V
635:+
630:y
627:y
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619:+
614:z
611:z
607:V
586:|
581:x
578:x
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570:|
564:|
559:y
556:y
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537:z
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530:V
526:|
503:.
496:z
493:z
489:V
482:y
479:y
475:V
466:x
463:x
459:V
452:=
436:η
425:V
414:V
407:V
400:V
392:Ï
388:V
381:r
379:(
377:V
360:,
357:V
352:2
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300:j
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