430:-direction expand. Eventually, the interstitial atoms move to sites along the z-axis. When the interstitial atoms move, this leads to a reduction in strain energy. In BCC metals, interstitial sites of an unstrained lattice are equally favorable. The interstitial solutes create elastic dipoles. However, once a strain is applied on the lattice, such as that formed by a dislocation, 1/3 of the sites become more favorable than the other 2/3. Solute atoms will therefore move to occupy the favorable sites, forming a short ranged order of solutes immediately within the vicinity of the dislocation. The motion of the interstitial solutes to these other sites constitutes a change in the elastic dipoles, so there is a relaxation time associated with this change which can be connected to the diffusivity and migration enthalpy of the solute atoms. In the new, relaxed solute configuration, more energy is therefore required to break a dislocation from this order.
389:
atoms at this boundary would differ from the bulk. Moving through this field of solute atoms would therefore produce a similar drag on dislocations as the
Cottrell atmosphere. Suzuki later observed such segregation in 1961. The Suzuki effect is often associated with adsorption of substitutional solute atoms to the stacking fault, but it has also been found to occur with interstitial atoms diffusing out of the stacking fault.
20:
407:
hundredths of a percent of either element within the solution, while the remainder is supersaturated. This revelation led to observed special magnetic phenomena in iron, mainly the presence of magnetism and time decrease of permeability due to small amount of carbon and nitrogen remaining in the iron. Moreover, the additional presence of magnetism leads to an elastic-after effect.
411:
mechanism for calculating the solubility of carbon and nitrogen in α-iron. A sample in a mixture of hydrogen and ammonia (or carbon monoxide) is mixed and heated until a stationary state was reached, where the mass of carbon and nitrogen taken up during the process can be found by estimating the changes in the weight of the sample.
725:
The interstitials that occupy the normal sites in an unstressed lattice will promote internal friction. Substituted solute atoms and interstitials in strain fields of a dislocation or at grain boundaries have their internal friction changed. Therefore, the Snoek effect can measure carbon and nitrogen
95:
The collection of solute atoms at the dislocation relieves the stresses associated with the dislocation, which lowers the energy of the dislocation's presence. Thus, moving the dislocation out of this
Cottrell atmosphere constitutes an increase in energy, so it is not favorable for the dislocation to
410:
By preparing samples containing a larger amount of carbon or nitrogen in solid solution, magnetic and elastic phenomena are greatly enhanced. The solubility of nitrogen is much larger than the solubility of carbon in solid solution. The study of the Snoek effect on annealed irons provides a reliable
388:
The Suzuki effect is characterized by the segregation of solutes to stacking fault defects. When dislocations in an FCC system split into two partial dislocations, a hexagonal close-packed (HCP) stacking fault is formed between the two partials. H. Suzuki predicted that the concentration of solute
433:
However, a stress applied in the direction will not lead to any changes in the locations of the interstitial atoms as the three directions of the cube will be equally stressed, and on average, equally occupied by carbon atoms. When a stress is applied along a cube edge and at an amount below the
77:
diffusing towards a dislocation, which contains a small gap at its core (as it is a more open structure), see Figure 1. Once the atom has diffused into the dislocation core the atom will stay. Typically only one interstitial atom is required per lattice plane of the dislocation. The collection of
406:
an elastic effect, called the Snoek effect. The Snoek effect was discovered by J. L. Snoek in 1941. At room temperature, the solubility of carbon and nitrogen in solid solutions is exceedingly small. By raising, the temperature beyond 400C and cooling at a moderate rate, it is easy to keep a few
392:
Once two partial dislocations have split, they cannot cross-slip around obstacles anymore. Just as the
Cottrell atmosphere provided a force against dislocation motion, the Suzuki effect in the stacking fault will lead to increased stresses for recombination of partials, leading to increased
65:
Cottrell atmospheres occur in body-centered cubic (BCC) and face-centered cubic (FCC) materials, such as iron or nickel, with small impurity atoms, such as boron, carbon, or nitrogen. As these interstitial atoms distort the lattice slightly, there will be an associated residual stress field
823:
Waseda, Osamu; Veiga, Roberto GA; Morthomas, Julien; Chantrenne, Patrice; Becquart, Charlotte S.; Ribeiro, Fabienne; Jelea, Andrei; Goldenstein, Helio; Perez, Michel (March 2017). "Formation of carbon
Cottrell atmospheres and their effect on the stress field around an edge dislocation".
87:
371:
is the solute concentration. The existence of the
Cottrell atmosphere and the effects of viscous drag have been proven to be important in high temperature deformation at intermediate stresses, as well as contributing to the power-law breakdown regime.
90:
A dislocation moving with a
Cottrell Atmosphere around it. At high stresses (top), the dislocation can "break free" of the atmosphere, while at low stresses (bottom), the dislocation must drag the solutes with it, and motion is much
698:
253:
401:
Under an applied stress, interstitial solute atoms, such as carbon and nitrogen can migrate within the α-Fe lattice, a BCC metal. These short-range migrations of carbon and nitrogen solute atoms result in an internal friction
553:
99:
Once a dislocation has become pinned, a large force is required to unpin the dislocation prior the yielding, thus at room temperature, the dislocation will not get unpinned. This produces an observed upper yield point in a
123:
and large forces for deep drawing and forming large sheets, making them a hindrance to manufacture. Some steels are designed to remove the
Cottrell atmosphere effect by removing all the interstitial atoms. Steels such as
859:
Veiga, R.G.A.; Goldenstein, H.; Perez, M.; Becquart, C.S. (1 November 2015). "Monte Carlo and molecular dynamics simulations of screw dislocation locking by
Cottrell atmospheres in low carbon Fe–C alloys".
108:
to generate new dislocations that are not pinned. These dislocations are free to move in the crystal, which results in a subsequent lower yield point, and the material will deform in a more plastic manner.
977:
151:, an effective frictional force that makes moving the dislocation more difficult (and thus slowing plastic deformation). This drag force can be expressed according to the equation:
586:
438:
before stress, showing the presence of internal friction. A torsional pendulum is typically used as a means of studying this lagging effect. The angle of lag is taken to be
309:
289:
414:
Carbon and nitrogen atoms occupy octahedral interstices at the midpoints of the cube edges and at the centers of the cube faces. If a stress is applied a long the
720:
606:
369:
349:
329:
613:
156:
451:
788:
Blavette, D.; Cadel, E.; Fraczkiewicz, A.; Menand, A. (1999). "Three-Dimensional Atomic-Scale
Imaging of Impurity Segregation to Line Defects".
1259:
380:
While the
Cottrell atmosphere is a general effect, there are additional related mechanisms that occur under more specialized circumstances.
1194:"Mobility of dislocations in the iron-based C-, N-, H-solid solutions measured using internal friction: Effect of electron structure"
1402:
1326:
116:
for a few hours, enables the carbon atoms to rediffuse back to dislocation cores, resulting in a return of the upper yield point.
393:
difficulty in bypassing obstacles (such as precipitates or particles), and therefore resulting in a stronger material.
561:
is the ratio of consecutive magnitudes of one cycle of the pendulum. When the magnitude of one cycle decreases to
734:
Materials in which dislocations described by Cottrell atmosphere include metals and semiconductor materials such
101:
1042:
Hickel, T.; Sandlöbes, S.; Marceau, R. K. W.; Dick, A.; Bleskov, I.; Neugebauer, J.; Raabe, D. (2014-08-15).
125:
446:
is considered a measure of internal friction. The internal friction is expressed according to the equation:
96:
move forward in the crystal. As a result, the dislocation is effectively pinned by the Cottrell atmosphere.
140:
105:
982:
Science Reports of the Research Institutes, Tohoku University. Ser. A, Physics, Chemistry and Metallurgy
1279:
1193:
1099:
1043:
1363:
1286:. Proceedings of the 14th International Conference on Internal Friction and Mechanical Spectroscopy.
1158:
1111:
1055:
1008:
763:
71:
564:
144:
59:
754:
Cottrell, A. H.; Bilby, B. A. (1949), "Dislocation Theory of Yielding and Strain Ageing of Iron",
1100:"Effect of small quantities of carbon and nitrogen on the elastic and plastic properties of iron"
1379:
1332:
1322:
1299:
1255:
1213:
1174:
1127:
1071:
1024:
958:
919:
877:
841:
805:
28:
294:
261:
1371:
1291:
1205:
1166:
1119:
1063:
1016:
950:
911:
869:
833:
797:
771:
113:
67:
735:
78:
solute atoms around the dislocation core due to this process is the Cottrell atmosphere.
1367:
1162:
1115:
1059:
1012:
767:
705:
693:{\displaystyle \tan(\delta )=Q^{-1}={\frac {\ln {\frac {1}{n}}}{\pi \times v\times t}}}
591:
354:
334:
314:
248:{\displaystyle F_{drag}={\frac {kT\Omega }{vD_{sol}}}\int {\frac {J\centerdot J}{c}}dA}
120:
86:
1123:
938:
899:
139:
The Cottrell atmosphere also has important consequences for material behavior at high
1396:
954:
915:
873:
837:
775:
129:
36:
148:
147:
conditions. Moving a dislocation with an associated Cottrell atmosphere introduces
44:
1209:
1067:
801:
19:
548:{\displaystyle \tan(\delta )=\left({\frac {\log(decrement)}{\pi }}\right)=Q^{-1}}
40:
1295:
999:
Suzuki, Hideji (1962-02-15). "Segregation of Solute Atoms to Stacking Faults".
1375:
1170:
1044:"Impact of nanodiffusion on the stacking fault energy in high-strength steels"
1383:
1303:
1217:
1178:
1131:
1075:
1028:
962:
923:
881:
845:
1351:
1336:
1146:
809:
726:
concentration in BCC alpha-Fe and other solutes present in ternary alloys.
133:
56:
1020:
104:
graph. Beyond the upper yield point, the pinned dislocation will act as
23:
A carbon atom below a dislocation in iron, forming a Cottrell atmosphere
52:
900:"Steady-state creep of alloys due to viscous motion of dislocations"
1280:"The Snoek relaxation in bcc metals—From steel wire to meteorites"
85:
48:
18:
608:, then the internal fraction behaves according to the equation:
74:
426:
axes will contract, while the octahedral interstices along the
1192:
Gavriljuk, V. G.; Shyvaniuk, V. N.; Teus, S. M. (2021-12-15).
291:
is the diffusivity of the solute atom in the host material,
978:"Chemical Interaction of Solute Atoms with Dislocations"
434:
yield stress, the interstitial atom will lead to strain
418:, or direction, the octahedral interstices along the
1352:"Theory of the snoek effect in ternary b.c.c. alloys"
1147:"Theory of the snoek effect in ternary b.c.c. alloys"
708:
616:
594:
567:
454:
357:
337:
317:
297:
264:
159:
714:
692:
600:
580:
547:
363:
343:
323:
303:
283:
247:
1254:. Cambridge, UK: Cambridge. pp. 569–570.
722:is the vibrational frequency of the pendulum.
8:
112:Leaving the sample to age, by holding it at
119:Cottrell atmospheres lead to formation of
1321:. Cambridge: Cambridge University Press.
939:"Creep behavior of solid solution alloys"
898:Takeuchi, S.; Argon, A. S. (1976-10-01).
707:
660:
651:
639:
615:
593:
568:
566:
536:
477:
453:
356:
336:
316:
296:
269:
263:
221:
203:
182:
164:
158:
143:, i.e. when the material is experiencing
1001:Journal of the Physical Society of Japan
746:
227:
1273:
1271:
1245:
1243:
1241:
1239:
1237:
1235:
1233:
1231:
1229:
1227:
1093:
1091:
1089:
1087:
1085:
7:
1284:Materials Science and Engineering: A
1250:Marc Meyers, Krishan Chawla (2009).
937:Mohamed, Farghalli A. (1979-04-01).
893:
891:
331:is the velocity of the dislocation,
756:Proceedings of the Physical Society
351:is the diffusion flux density, and
66:surrounding the interstitial. This
298:
191:
14:
943:Materials Science and Engineering
1319:Mechanical behavior of materials
1252:Mechanical Behavior of Materials
874:10.1016/j.scriptamat.2015.06.012
838:10.1016/j.scriptamat.2016.09.032
82:Influence on Mechanical Behavior
1198:Journal of Alloys and Compounds
629:
623:
588:of its original value in time
581:{\displaystyle {\frac {1}{n}}}
516:
486:
467:
461:
136:are added to remove nitrogen.
1:
1210:10.1016/j.jallcom.2021.161260
1124:10.1016/S0031-8914(41)90517-7
1068:10.1016/j.actamat.2014.04.062
976:Suzuki, Hideji (1952-01-01).
802:10.1126/science.286.5448.2317
47:are pinned in some metals by
1317:Hosford, William F. (2005).
955:10.1016/0025-5416(79)90034-X
916:10.1016/0001-6160(76)90036-5
70:field can be relaxed by the
16:Concept in materials science
1098:Snoek, J. L. (1941-07-01).
1419:
1356:The Philosophical Magazine
1296:10.1016/j.msea.2006.02.232
1151:The Philosophical Magazine
776:10.1088/0370-1298/62/1/308
1376:10.1080/14786437108217028
1278:Weller, M. (2006-12-20).
1171:10.1080/14786437108217028
1403:Crystallographic defects
1350:Koiwa, M. (1971-09-01).
1145:Koiwa, M. (1971-09-01).
132:and small quantities of
304:{\displaystyle \Omega }
284:{\displaystyle D_{sol}}
141:homologous temperatures
126:interstitial free steel
43:in 1949 to explain how
716:
694:
602:
582:
549:
365:
345:
325:
311:is the atomic volume,
305:
285:
249:
92:
24:
717:
695:
603:
583:
559:logarithmic decrement
550:
366:
346:
326:
306:
286:
250:
89:
31:, the concept of the
22:
706:
614:
592:
565:
452:
355:
335:
315:
295:
262:
157:
1368:1971PMag...24..539K
1163:1971PMag...24..539K
1116:1941Phy.....8..711S
1060:2014AcMat..75..147H
1021:10.1143/JPSJ.17.322
1013:1962JPSJ...17..322S
796:(5448): 2317–2319.
768:1949PPSA...62...49C
33:Cottrell atmosphere
862:Scripta Materialia
826:Scripta Materialia
712:
690:
598:
578:
545:
361:
341:
321:
301:
281:
245:
93:
35:was introduced by
25:
1261:978-0-511-45557-5
904:Acta Metallurgica
715:{\displaystyle v}
688:
668:
601:{\displaystyle t}
576:
523:
376:Similar phenomena
364:{\displaystyle c}
344:{\displaystyle J}
324:{\displaystyle v}
237:
216:
106:Frank–Read source
29:materials science
1410:
1388:
1387:
1362:(189): 539–554.
1347:
1341:
1340:
1314:
1308:
1307:
1275:
1266:
1265:
1247:
1222:
1221:
1189:
1183:
1182:
1157:(189): 539–554.
1142:
1136:
1135:
1095:
1080:
1079:
1039:
1033:
1032:
996:
990:
989:
973:
967:
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934:
928:
927:
895:
886:
885:
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849:
820:
814:
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779:
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751:
736:silicon crystals
721:
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114:room temperature
1418:
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1248:
1225:
1191:
1190:
1186:
1144:
1143:
1139:
1097:
1096:
1083:
1048:Acta Materialia
1041:
1040:
1036:
998:
997:
993:
984:(in Japanese).
975:
974:
970:
936:
935:
931:
910:(10): 883–889.
897:
896:
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853:
822:
821:
817:
787:
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782:
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748:
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84:
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5:
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1390:
1389:
1342:
1327:
1309:
1267:
1260:
1223:
1184:
1137:
1110:(7): 711–733.
1081:
1034:
1007:(2): 322–325.
991:
968:
929:
887:
851:
815:
780:
745:
743:
740:
731:
728:
711:
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37:A. H. Cottrell
15:
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384:Suzuki effect
383:
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318:
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102:stress–strain
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88:
81:
79:
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69:
63:
61:
60:interstitials
58:
54:
50:
46:
42:
38:
34:
30:
21:
1359:
1355:
1345:
1318:
1312:
1290:(1): 21–30.
1287:
1283:
1251:
1201:
1197:
1187:
1154:
1150:
1140:
1107:
1103:
1051:
1047:
1037:
1004:
1000:
994:
985:
981:
971:
949:(1): 73–80.
946:
942:
932:
907:
903:
865:
861:
854:
829:
825:
818:
793:
789:
783:
762:(1): 49–62,
759:
755:
749:
733:
724:
701:
610:
558:
556:
448:
443:
439:
435:
432:
427:
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419:
415:
413:
409:
403:
400:
397:Snoek effect
391:
387:
379:
257:
153:
149:viscous drag
138:
130:decarburized
121:LĂĽders bands
118:
111:
98:
94:
72:interstitial
64:
45:dislocations
32:
26:
1054:: 147–155.
41:B. A. Bilby
1204:: 161260.
988:: 455–463.
742:References
557:Where the
1384:0031-8086
1304:0921-5093
1218:0925-8388
1179:0031-8086
1132:0031-8914
1076:1359-6454
1029:0031-9015
963:0025-5416
924:0001-6160
882:1359-6462
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228:⋅
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1364:Bibcode
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1104:Physica
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790:Science
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436:lagging
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