88:
Since both different pressures and exposure times can give the same langmuir (see
Definition) it can be difficult to convert Langmuir (L) to exposure pressure × time (Torr·s) and vice versa. The following equation can be used to easily convert between the two:
267:
is an integer allowing different magnitudes of pressure or exposure time to be used in conversion. The units are represented in the . Using the prior example, for a dose of 100 L a pressure of 2.5 × 10 Torr can be applied for 40 seconds, thus,
80:. For example, exposing a surface to a gas pressure of 10 Torr for 100 seconds corresponds to 1 L. Similarly, keeping the pressure of oxygen gas at 2.5·10 Torr for 40 seconds will give a dose of 100 L.
878:
779:
205:
713:
600:
533:
979:
974:
640:
538:
The number flux for an ideal gas, that is the number of gas molecules passing through (in a single direction) a surface of unit area in unit time, can be derived from
451:
396:
292:
318:
422:
370:
344:
265:
245:
225:
1047:
899:. Gas adsorption experiments typically operate around ambient temperature with light gases, and so the langmuir remains useful as a practical unit.
794:
1076:
92:
1108:
988:
927:
of the surface and the molecules, so that the langmuir gives a lower limit of the time it needs to completely cover a surface.
724:
884:
664:
548:
486:
647:
646:
the root-mean-square speed, although the two are related). The number density of an ideal gas depends on the
1072:
1051:
539:
924:
1013:
920:
912:
53:
992:
939:
931:
942:
on sample surfaces is in the range of one to several hours. In order to keep the surface free of
616:
1029:
1004:
Alpert, D. (1953). "New
Developments in the Production and Measurement of Ultra High Vacuum".
984:
37:
1021:
887:
between number flux and pressure is only strictly valid for a given temperature and a given
427:
375:
271:
297:
57:
41:
25:
401:
349:
323:
1017:
1103:
888:
610:
250:
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210:
72:
of the gas by the time of exposure. One langmuir corresponds to an exposure of 10
1097:
943:
935:
346:. However, this dosage could also be gained with 8 × 10 Torr for 1250 seconds, here
946:, the pressure of the residual gas in a UHV chamber should be below 10 Torr.
873:{\displaystyle J_{N}={\frac {C{\bar {u}}}{4}}=p{\sqrt {\frac {1}{2\pi kTm}}}.}
45:
1033:
718:
The mean speed of the gas molecules can also be derived from kinetic theory:
916:
56:, and so is used only in this field. It is named after American physicist
908:
891:
of adsorbing gas. However, the dependence is only on the square roots of
69:
930:
This also illustrates why ultra-high vacuum (UHV) must be used to study
462:
33:
1073:"Velocity Probability Distribution Functions in Three Dimensions, Etc"
1025:
247:
are any two numbers whose product equals the desired
Langmuir value,
77:
915:
is 1), one langmuir (1 L) leads to a coverage of about one
73:
919:
of the adsorbed gas molecules on the surface. In general, the
49:
774:{\displaystyle {\bar {u}}={\sqrt {\frac {8kT}{\pi m}}},}
200:{\displaystyle xy=x\times 10^{-n}\cdot y\times 10^{n-6}}
938:
or even single molecules. The typical time to perform
461:
Exposure of a surface in surface physics is a type of
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551:
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430:
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980:
Quantities, Units and
Symbols in Physical Chemistry
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259:
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199:
975:International Union of Pure and Applied Chemistry
708:{\displaystyle C={\frac {N}{V}}={\frac {p}{kT}}.}
911:hitting the surface sticks to it (that is, the
595:{\displaystyle J_{N}={\frac {C{\bar {u}}}{4}},}
528:{\displaystyle \Phi =\int {J_{N}}\,{\rm {d}}t.}
476:) to give a number of particles per unit area (
8:
68:The langmuir is defined by multiplying the
983:, 2nd edition, Oxford: Blackwell Science.
958:Surfaces and Interfaces of Solid Materials
841:
818:
817:
811:
802:
796:
743:
729:
728:
726:
687:
674:
666:
621:
620:
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572:
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351:
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273:
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188:
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128:
106:
105:
94:
24:) is a unit of exposure (or dosage) to a
967:
465:, that is the integral of number flux (
788:is the mass of a gas molecule. Hence
52:. It is a practical unit, and is not
7:
642:is the mean speed of the molecules (
514:
490:
189:
151:
148:
145:
142:
107:
14:
472:) with respect to exposed time (
1079:from the original on 2009-02-08
1012:(7). AIP Publishing: 860–876.
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734:
626:
577:
194:
184:
156:
137:
112:
102:
1:
1109:Units of amount of substance
1048:"Collisions with a Surface"
1125:
1006:Journal of Applied Physics
635:{\displaystyle {\bar {u}}}
648:thermodynamic temperature
54:dimensionally homogeneous
960:(3rd ed.), Springer
923:varies depending on the
907:Assuming that every gas
874:
775:
709:
636:
596:
529:
447:
446:{\displaystyle xy=100}
418:
392:
391:{\displaystyle y=12.5}
366:
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261:
241:
221:
201:
875:
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530:
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419:
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367:
341:
315:
289:
287:{\displaystyle x=2.5}
262:
242:
222:
202:
940:physical experiments
921:sticking coefficient
913:sticking coefficient
795:
725:
665:
654:) and the pressure (
617:
549:
487:
428:
424:. In both scenarios
402:
376:
350:
324:
313:{\displaystyle y=40}
298:
272:
251:
231:
211:
93:
1018:1953JAP....24..860A
993:Electronic version.
417:{\displaystyle n=8}
365:{\displaystyle x=8}
339:{\displaystyle n=6}
956:Lueth, H. (1997),
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260:{\displaystyle n}
240:{\displaystyle y}
220:{\displaystyle x}
38:ultra-high vacuum
36:) and is used in
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1088:
1087:
1085:
1084:
1069:
1063:
1062:
1060:
1059:
1050:. Archived from
1044:
1038:
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995:
972:
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711:
706:
701:
699:
688:
683:
675:
641:
639:
638:
633:
631:
630:
622:
613:of the gas, and
601:
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1046:
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1002:
998:
973:
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885:proportionality
847:
813:
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746:
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567:
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168:
124:
91:
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66:
58:Irving Langmuir
42:surface physics
12:
11:
5:
1122:
1120:
1112:
1111:
1106:
1096:
1095:
1090:
1089:
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1039:
996:
991:. p. 65.
966:
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951:
948:
944:contaminations
936:nanostructures
904:
901:
889:molecular mass
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628:
625:
611:number density
603:
602:
591:
586:
579:
576:
570:
564:
559:
555:
540:kinetic theory
536:
535:
524:
521:
516:
507:
503:
498:
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492:
468:
458:
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439:
436:
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361:
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65:
62:
13:
10:
9:
6:
4:
3:
2:
1121:
1110:
1107:
1105:
1102:
1101:
1099:
1078:
1074:
1068:
1065:
1054:on 2008-05-28
1053:
1049:
1043:
1040:
1035:
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1015:
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1007:
1000:
997:
994:
990:
989:0-632-03583-8
986:
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926:
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918:
914:
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900:
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894:
890:
886:
867:
860:
857:
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851:
848:
844:
838:
835:
830:
820:
814:
808:
803:
799:
791:
790:
789:
787:
768:
761:
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750:
747:
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731:
721:
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719:
702:
696:
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689:
684:
679:
676:
671:
668:
661:
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659:
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653:
649:
645:
623:
612:
608:
589:
584:
574:
568:
562:
557:
553:
545:
544:
543:
541:
522:
519:
505:
501:
496:
493:
483:
482:
481:
479:
475:
471:
464:
456:
454:
440:
437:
434:
431:
411:
408:
405:
385:
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359:
356:
353:
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327:
307:
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179:
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121:
118:
115:
99:
96:
83:
81:
79:
75:
71:
63:
61:
59:
55:
51:
47:
44:to study the
43:
39:
35:
31:
27:
23:
19:
1081:. Retrieved
1067:
1056:. Retrieved
1052:the original
1042:
1009:
1005:
999:
978:
970:
957:
929:
906:
896:
892:
882:
785:
783:
717:
655:
651:
643:
606:
604:
537:
477:
473:
466:
460:
87:
67:
29:
21:
17:
15:
932:solid-state
76:during one
1098:Categories
1083:2009-05-10
1058:2009-05-10
950:References
934:surfaces,
925:reactivity
457:Derivation
84:Conversion
64:Definition
46:adsorption
1034:0021-8979
917:monolayer
852:π
824:¯
759:π
735:¯
627:¯
578:¯
497:∫
491:Φ
177:−
166:×
160:⋅
130:−
122:×
20:(symbol:
1077:Archived
977:(1993).
909:molecule
70:pressure
18:langmuir
1014:Bibcode
609:is the
463:fluence
34:crystal
26:surface
1032:
987:
784:where
605:where
207:Here,
78:second
40:(UHV)
1104:Gases
903:Usage
50:gases
32:of a
1030:ISSN
985:ISBN
895:and
883:The
386:12.5
320:and
227:and
74:Torr
30:e.g.
16:The
1022:doi
658:):
644:not
480:):
441:100
282:2.5
48:of
1100::
1075:.
1028:.
1020:.
1010:24
1008:.
542::
453:.
398:,
372:,
308:40
294:,
170:10
126:10
60:.
1086:.
1061:.
1036:.
1024::
1016::
962:.
897:T
893:m
868:.
861:m
858:T
855:k
849:2
845:1
839:p
836:=
831:4
821:u
815:C
809:=
804:N
800:J
786:m
769:,
762:m
754:T
751:k
748:8
741:=
732:u
703:.
697:T
694:k
690:p
685:=
680:V
677:N
672:=
669:C
656:p
652:T
650:(
624:u
607:C
590:,
585:4
575:u
569:C
563:=
558:N
554:J
523:.
520:t
515:d
506:N
502:J
494:=
478:Φ
474:t
469:N
467:J
438:=
435:y
432:x
412:8
409:=
406:n
383:=
380:y
360:8
357:=
354:x
334:6
331:=
328:n
305:=
302:y
279:=
276:x
255:n
235:y
215:x
195:]
190:s
185:[
180:6
174:n
163:y
157:]
152:r
149:r
146:o
143:T
138:[
133:n
119:x
116:=
113:]
108:L
103:[
100:y
97:x
28:(
22:L
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