Grain boundary - Knowledge

1468:

temperature or pressure. This may strongly affect the macroscopic properties of the material, for example the electrical resistance or creep rates. Grain boundaries can be analyzed using equilibrium thermodynamics but cannot be considered as phases, because they do not satisfy Gibbs' definition: they are inhomogeneous, may have a gradient of structure, composition or properties. For this reasons they are defined as complexion: an interfacial material or stata that is in thermodynamic equilibrium with its abutting phases, with a finite and stable thickness (that is typically 2–20 Å). A complexion need the abutting phase to exist and its composition and structure need to be different from the abutting phase. Contrary to bulk phases, complexions also depend on the abutting phase. For example, silica rich amorphous layer present in Si

1476:, is about 10 Å thick, but for special boundaries this equilibrium thickness is zero. Complexion can be grouped in 6 categories, according to their thickness: monolayer, bilayer, trilayer, nanolayer (with equilibrium thickness between 1 and 2 nm) and wetting. In the first cases the thickness of the layer will be constant; if extra material is present it will segregate at multiple grain junction, while in the last case there is no equilibrium thickness and this is determined by the amount of secondary phase present in the material. One example of grain boundary complexion transition is the passage from dry boundary to biltilayer in Au-doped Si, which is produced by the increase of Au. 3386: 312: 236: 1510:

the complications of how point defects behave has been manifested in the temperature dependence of the Seebeck effect. In addition the dielectric and piezoelectric response can be altered by the distribution of point defects near grain boundaries. Mechanical properties can also be significantly influenced with properties such as the bulk modulus and damping being influenced by changes to the distribution of point defects within a material. It has also been found that the Kondo effect within

1410: 3779: 690: 112: 1269:. Theoretical methods have also been developed and are in good agreement. A key observation is that there is an inverse relationship with the bulk modulus meaning that the larger the bulk modulus (the ability to compress a material) the smaller the excess volume will be, there is also direct relationship with the lattice constant, this provides methodology to find materials with a desirable excess volume for a specific application. 20: 3791: 35: 1524:

no method to control the structure and properties of most metals and alloys with atomic precision. Part of the problem is related to the fact that much of the theoretical work to understand grain boundaries is based upon construction of bicrystal (two) grains which do not represent the network of grains typically found in a real system and the use of classical force fields such as the

287:

two lattices. Thus a boundary with high Σ might be expected to have a higher energy than one with low Σ. Low-angle boundaries, where the distortion is entirely accommodated by dislocations, are Σ1. Some other low-Σ boundaries have special properties, especially when the boundary plane is one that contains a high density of coincident sites. Examples include coherent

1533:

point of view much of the research on grain boundaries has focused on bi-crystal systems, these are systems which only consider two grain boundaries. There has been recent work which has made use of novel grain evolution models which show that there are substantial differences in the material properties associated with whether curved or planar grains are present.

232:, whose misorientation is greater than about 15 degrees (the transition angle varies from 10 to 15 degrees depending on the material), are normally found to be independent of the misorientation. However, there are 'special boundaries' at particular orientations whose interfacial energies are markedly lower than those of general high-angle grain boundaries. 304:. However, it is common to describe a boundary only as the orientation relationship of the neighbouring grains. Generally, the convenience of ignoring the boundary plane orientation, which is very difficult to determine, outweighs the reduced information. The relative orientation of the two grains is described using the 275:, direct evidence of the grain structure meant the hypothesis had to be discarded. It is now accepted that a boundary consists of structural units which depend on both the misorientation of the two grains and the plane of the interface. The types of structural unit that exist can be related to the concept of the 1523:

There has been a significant amount of work experimentally to observe both the structure and measure the properties of grain boundaries but the five dimensional degrees of freedom of grain boundaries within complex polycrystalline networks has not yet been fully understood and thus there is currently

1456:

Grain boundaries are the preferential site for segregation of impurities, which may form a thin layer with a different composition from the bulk and a variety of atomic structures that are distinct from the abutting crystalline phases. For example, a thin layer of silica, which also contains impurity

286:

In this framework, it is possible to draw the lattice for the two grains and count the number of atoms that are shared (coincidence sites), and the total number of atoms on the boundary (total number of site). For example, when Σ=3 there will be one atom of each three that will be shared between the

1509:

It is known that most materials are polycrystalline and contain grain boundaries and that grain boundaries can act as sinks and transport pathways for point defects. However experimentally and theoretically determining what effect point defects have on a system is difficult. Interesting examples of

1514:

can be tuned due to a complex relationship between grain boundaries and point defects. Recent theoretical calculations have revealed that point defects can be extremely favourable near certain grain boundary types and significantly affect the electronic properties with a reduction in the band gap.

1401:

The movement of high-angle boundaries occurs by the transfer of atoms between the neighbouring grains. The ease with which this can occur will depend on the structure of the boundary, itself dependent on the crystallography of the grains involved, impurity atoms and the temperature. It is possible

270:

In comparison to low-angle grain boundaries, high-angle boundaries are considerably more disordered, with large areas of poor fit and a comparatively open structure. Indeed, they were originally thought to be some form of amorphous or even liquid layer between the grains. However, this model could

1047:

The situation in high-angle boundaries is more complex. Although theory predicts that the energy will be a minimum for ideal CSL configurations, with deviations requiring dislocations and other energetic features, empirical measurements suggest the relationship is more complicated. Some predicted

266:

If the dislocations in the boundary remain isolated and distinct, the boundary can be considered to be low-angle. If deformation continues, the density of dislocations will increase and so reduce the spacing between neighboring dislocations. Eventually, the cores of the dislocations will begin to

247:

or grain which is gradually bent by some external force. The energy associated with the elastic bending of the lattice can be reduced by inserting a dislocation, which is essentially a half-plane of atoms that act like a wedge, that creates a permanent misorientation between the two sides. As the

1532:

could be required to give realistic insights. Accurate modelling of grain boundaries both in terms of structure and atomic interactions could have the effect of improving engineering which could reduce waste and increase efficiency in terms of material usage and performance. From a computational

248:

grain is bent further, more and more dislocations must be introduced to accommodate the deformation resulting in a growing wall of dislocations – a low-angle boundary. The grain can now be considered to have split into two sub-grains of related crystallography but notably different orientations.

1467:

These grain boundary phases are thermodynamically stable and can be considered as quasi-two-dimensional phase, which may undergo to transition, similar to those of bulk phases. In this case structure and chemistry abrupt changes are possible at a critical value of a thermodynamic parameter like

1082:

The excess volume is another important property in the characterization of grain boundaries. Excess volume was first proposed by Bishop in a private communication to Aaron and Bolling in 1972. It describes how much expansion is induced by the presence of a GB and is thought that the degree and

680:

involved limits the misorientation of the boundary. A completely random polycrystal, with no texture, thus has a characteristic distribution of boundary misorientations (see figure). However, such cases are rare and most materials will deviate from this ideal to a greater or lesser degree.

1372:

The apparent activation energy (Q) may be related to the thermally activated atomistic processes that occur during boundary movement. However, there are several proposed mechanisms where the mobility will depend on the driving pressure and the assumed proportionality may break down.

466: 1292:

A boundary moves due to a pressure acting on it. It is generally assumed that the velocity is directly proportional to the pressure with the constant of proportionality being the mobility of the boundary. The mobility is strongly temperature dependent and often follows an

1397:

Since low-angle boundaries are composed of arrays of dislocations and their movement may be related to dislocation theory. The most likely mechanism, given the experimental data, is that of dislocation climb, rate limited by the diffusion of solute in the bulk.

1500:

computer simulations of grain boundaries have shown that the band gap can be reduced by up to 45%. In the case of metals grain boundaries increase the resistivity as the size of the grains relative to the mean free path of other scatters becomes significant.

1072:

It is concluded that no general and useful criterion for low energy can be enshrined in a simple geometric framework. Any understanding of the variations of interfacial energy must take account of the atomic structure and the details of the bonding at the

262:

These concepts of tilt and twist boundaries represent somewhat idealized cases. The majority of boundaries are of a mixed type, containing dislocations of different types and Burgers vectors, in order to create the best fit between the neighboring grains.

1083:

susceptibility of segregation is directly proportional to this. Despite the name the excess volume is actually a change in length, this is because of the 2D nature of GBs the length of interest is the expansion normal to the GB plane. The excess volume (

1190: 1262:. Although a rough linear relationship between GB energy and excess volume exists the orientations where this relationship is violated can behave significantly differently affecting mechanical and electrical properties. 1039:

is the radius of the dislocation core. It can be seen that as the energy of the boundary increases the energy per dislocation decreases. Thus there is a driving force to produce fewer, more misoriented boundaries (i.e.,

291:

boundaries (e.g., Σ3) and high-mobility boundaries in FCC materials (e.g., Σ7). Deviations from the ideal CSL orientation may be accommodated by local atomic relaxation or the inclusion of dislocations at the boundary.

2807:

Doherty, R.D.; Hughes, D.A.; Humphreys, F.J.; Jonas, J.J.; Jensen, D.Juul; Kassner, M.E.; King, W.E.; McNelley, T.R.; McQueen, H.J.; Rollett, A.D. (November 1997). "Current issues in recrystallization: a review".

267:

overlap and the ordered nature of the boundary will begin to break down. At this point the boundary can be considered to be high-angle and the original grain to have separated into two entirely separate grains.

780: 322: 1367: 547: 2775:

Forrest, Robert M.; Lazar, Emanuel A.; Goel, Saurav; Bean, Jonathan J. (5 December 2022). "Quantifying the differences in properties between polycrystals containing planar and curved grain boundaries".

279:, in which repeated units are formed from points where the two misoriented \ In coincident site lattice (CSL) theory, the degree of fit (Σ) between the structures of the two grains is described by the 259:

of the dislocations are orthogonal, then the dislocations do not strongly interact and form a square network. In other cases, the dislocations may interact to form a more complex hexagonal structure.

2500:

Bassiri-Gharb, Nazanin; Fujii, Ichiro; Hong, Eunki; Trolier-Mckinstry, Susan; Taylor, David V.; Damjanovic, Dragan (2007). "Domain wall contributions to the properties of piezoelectric thin films".

1376:

It is generally accepted that the mobility of low-angle boundaries is much lower than that of high-angle boundaries. The following observations appear to hold true over a range of conditions:

889: 3395: 2115:

Ma, Shuailei; Meshinchi Asl, Kaveh; Tansarawiput, Chookiat; Cantwell, Patrick R.; Qi, Minghao; Harmer, Martin P.; Luo, Jian (March 2012). "A grain boundary phase transition in Si–Au".

1048:

troughs in energy are found as expected while others missing or substantially reduced. Surveys of the available experimental data have indicated that simple relationships such as low

959: 300:

A boundary can be described by the orientation of the boundary to the two grains and the 3-D rotation required to bring the grains into coincidence. Thus a boundary has 5 macroscopic

3656: 697:

The energy of a low-angle boundary is dependent on the degree of misorientation between the neighbouring grains up to the transition to high-angle status. In the case of simple

3651: 243:

The simplest boundary is that of a tilt boundary where the rotation axis is parallel to the boundary plane. This boundary can be conceived as forming from a single, contiguous

822: 251:

An alternative is a twist boundary where the misorientation occurs around an axis that is perpendicular to the boundary plane. This type of boundary incorporates two sets of

3191: 2461:

Kishimoto, Kengo; Tsukamoto, Masayoshi; Koyanagi, Tsuyoshi (November 2002). "Temperature dependence of the Seebeck coefficient and the potential barrier scattering of

1104: 1567:

Lehockey, E.M.; Palumbo, G.; Lin, P.; Brennenstuhl, A.M. (May 1997). "On the relationship between grain boundary character distribution and intergranular corrosion".

1066: 3707: 1839:

Oberdorfer, Bernd; Setman, Daria; Steyskal, Eva-Maria; Hohenwarter, Anton; Sprengel, Wolfgang; Zehetbauer, Michael; Pippan, Reinhard; Würschum, Roland (April 2014).

1260: 1037: 1006: 671: 2264:

Mayadas, A. F.; Shatzkes, M. (15 February 1970). "Electrical-Resistivity Model for Polycrystalline Films: the Case of Arbitrary Reflection at External Surfaces".

1233: 1213: 982: 2342:

Meyer, René; Waser, Rainer; Helmbold, Julia; Borchardt, Günter (2003). "Observation of Vacancy Defect Migration in the Cation Sublattice of Complex Oxides by

1265:

Experimental techniques have been developed which directly probe the excess volume and have been used to explore the properties of nanocrystalline copper and

2935: 1112: 1406:) may operate in certain conditions. Some defects in the boundary, such as steps and ledges, may also offer alternative mechanisms for atomic transfer. 1488:) but they also can detrimentally affect the electronic properties. In metal oxides it has been shown theoretically that at the grain boundaries in Al 2207:

Bean, Jonathan J.; Saito, Mitsuhiro; Fukami, Shunsuke; Sato, Hideo; Ikeda, Shoji; Ohno, Hideo; Ikuhara, Yuichi; McKenna, Keith P. (4 April 2017).

2073:

Cantwell, Patrick R.; Tang, Ming; Dillon, Shen J.; Luo, Jian; Rohrer, Gregory S.; Harmer, Martin P. (January 2014). "Grain boundary complexions".

2730:"Comparing Five and Lower-Dimensional Grain Boundary Character and Energy Distributions in Copper: Experiment and Molecular Statics Simulation" 2625:

Chen, Jian-Hao; Li, Liang; Cullen, William G.; Williams, Ellen D.; Fuhrer, Michael S. (2011). "Tunable Kondo effect in graphene with defects".

1433:

that will retard its movement. Only at higher velocities will the boundary be able to break free of its atmosphere and resume normal motion.

3525: 315:

The characteristic distribution of boundary misorientations in a completely randomly oriented set of grains for cubic symmetry materials.

461:{\displaystyle R={\begin{bmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{bmatrix}}} 3712: 3437: 1790:

Steyskal, Eva-Maria; Oberdorfer, Bernd; Sprengel, Wolfgang; Zehetbauer, Michael; Pippan, Reinhard; Würschum, Roland (31 January 2012).

719: 301: 3603: 2895: 1896:

Bean, Jonathan J.; McKenna, Keith P. (May 2016). "Origin of differences in the excess volume of copper and nickel grain boundaries".

1662:

Grimmer, H.; Bollmann, W.; Warrington, D. H. (March 1974). "Coincidence-site lattices and complete pattern-shift in cubic crystals".

1303: 477: 2535:

Dang, Khanh Q.; Spearot, Douglas E. (2014). "Effect of point and grain boundary defects on the mechanical behavior of monolayer

3702: 3694: 3755: 3733: 2864: 2057: 2016: 1948: 1646: 1485: 176: 3748: 3598: 3264: 3129: 2978: 148: 3738: 3636: 3332: 2985: 830: 155: 3817: 3760: 3618: 3588: 3517: 195: 94:

through a material, so reducing crystallite size is a common way to improve mechanical strength, as described by the

3795: 3470: 2142:

Guhl, Hannes; Lee, Hak-Sung; Tangney, Paul; Foulkes, W.M.C.; Heuer, Arthur H.; Nakagawa, Tsubasa; Ikuhara, Yuichi;

1964:

Tang, Ming; Carter, W. Craig; Cannon, Rowland M. (14 August 2006). "Grain Boundary Transitions in Binary Alloys".

3743: 3666: 3540: 3139: 1697:

Sutton, A.P; Balluffi, R.W (September 1987). "Overview no. 61 On geometric criteria for low interfacial energy".

129: 224:

are those with a misorientation less than about 15 degrees. Generally speaking they are composed of an array of

162: 3578: 3500: 1278: 897: 133: 3593: 3583: 2888: 693:

The energy of a tilt boundary and the energy per dislocation as the misorientation of the boundary increases

3837: 3717: 3365: 2990: 2968: 2582:

Zhang, J.; Perez, R. J.; Lavernia, E. J. (1993). "Dislocation-induced damping in metal matrix composites".

2209:"Atomic structure and electronic properties of MgO grain boundaries in tunnelling magnetoresistive devices" 144: 3269: 3023: 2918: 1440:

effect. This effect is often exploited in commercial alloys to minimise or prevent recrystallization or

3832: 3626: 2923: 2406:"The relationship between grain boundary structure, defect mobility and grain boundary sink efficiency" 1421:

Since a high-angle boundary is imperfectly packed compared to the normal lattice it has some amount of

228:

and their properties and structure are a function of the misorientation. In contrast the properties of

3641: 3570: 3028: 3018: 1529: 1497: 791: 239:

Schematic representations of a tilt boundary (top) and a twist boundary between two idealised grains.

79: 3827: 3783: 3507: 3403: 3276: 3239: 3154: 3033: 3013: 2881: 2680:"Stability of point defects near MgO grain boundaries in FeCoB/MgO/FeCoB magnetic tunnel junctions" 1547: 3631: 3475: 3420: 3169: 3134: 1484:

Grain boundaries can cause failure mechanically by embrittlement through solute segregation (see

122: 67: 59: 1436:

Both low- and high-angle boundaries are retarded by the presence of particles via the so-called

1429:

where solute atoms may possess a lower energy. As a result, a boundary may be associated with a

3385: 3327: 3144: 1445: 1402:

that some form of diffusionless mechanism (akin to diffusionless phase transformations such as

280: 1086: 3684: 3480: 3442: 3249: 3201: 1724:

Aaron, H. B.; Bolling, G. F. (1972). "Free volume as a criterion for grain boundary models".

1542: 1286: 1051: 169: 3408: 3281: 3117: 3008: 2741: 2694: 2644: 2591: 2556: 2474: 2417: 2362: 2308: 2273: 2220: 2163: 2082: 1973: 1905: 1852: 1803: 1733: 1671: 1603: 1525: 1238: 1015: 71: 991: 558: 8: 3822: 3425: 3413: 3288: 3254: 3234: 1841:"Grain boundary excess volume and defect annealing of copper after high-pressure torsion" 272: 87: 2745: 2698: 2648: 2595: 2560: 2478: 2421: 2366: 2312: 2277: 2224: 2167: 2086: 1977: 1909: 1856: 1807: 1737: 1675: 1607: 3674: 3485: 3430: 2973: 2835: 2757: 2710: 2660: 2634: 2607: 2517: 2438: 2405: 2386: 2324: 2241: 2208: 2189: 1940: 1873: 1840: 1594:

Raj, R.; Ashby, M. F. (April 1971). "On grain boundary sliding and diffusional creep".

1384: 1294: 1218: 1198: 1009: 967: 311: 2821: 2706: 1580: 3608: 3447: 3375: 3355: 3075: 2945: 2860: 2761: 2714: 2664: 2611: 2521: 2443: 2378: 2328: 2246: 2128: 2098: 2053: 2022: 2012: 1989: 1944: 1878: 1821: 1776: 1745: 1710: 1642: 63: 47: 2839: 2404:

Uberuaga, Blas Pedro; Vernon, Louis J.; Martinez, Enrique; Voter, Arthur F. (2015).

2390: 2193: 1761:"Correlation between energy and volume expansion for grain boundaries in FCC metals" 3646: 3452: 3370: 3360: 3159: 3092: 3063: 3056: 2852: 2825: 2817: 2785: 2749: 2702: 2679: 2652: 2599: 2564: 2509: 2482: 2433: 2425: 2370: 2316: 2281: 2236: 2228: 2179: 2171: 2124: 2090: 2045: 1981: 1936: 1913: 1868: 1860: 1816: 1811: 1791: 1772: 1741: 1706: 1679: 1634: 1611: 1576: 1185:{\displaystyle \delta V=\left({\frac {\partial V}{\partial A}}\right)_{T,p,n_{i}},} 288: 2374: 2175: 2094: 1985: 1917: 1864: 1380:

The mobility of low-angle boundaries is proportional to the pressure acting on it.

271:

not explain the observed strength of grain boundaries and, after the invention of

3535: 3530: 3495: 3315: 3214: 3149: 3112: 3107: 2958: 2904: 1461: 677: 305: 2101: 2049: 235: 3345: 3310: 3298: 3293: 3259: 3229: 3219: 3122: 3046: 3000: 2753: 2143: 256: 209: 95: 83: 2513: 1683: 1638: 3811: 3490: 3303: 3102: 2789: 1792:"Direct Experimental Determination of Grain Boundary Excess Volume in Metals" 1460:

Grain boundary complexions were introduced by Ming Tang, Rowland Cannon, and

1437: 1414: 985: 2285: 2146:(2015). "Structural and electronic properties of Σ7 grain boundaries in α-Al 2026: 74:

of the material. Most grain boundaries are preferred sites for the onset of

3196: 3186: 3080: 2963: 2447: 2382: 2250: 2184: 1993: 1882: 1825: 1441: 1282: 1041: 208:

It is convenient to categorize grain boundaries according to the extent of

2856: 2729: 1409: 3679: 3350: 3224: 3051: 1496:

and MgO the insulating properties can be significantly diminished. Using

252: 244: 225: 91: 55: 39: 27: 2465:-type PbTe films prepared on heated glass substrates by rf sputtering". 3244: 2930: 2830: 2603: 2499: 1615: 1403: 136: in this section. Unsourced material may be challenged and removed. 23: 2656: 2568: 2486: 2429: 2320: 2232: 689: 58:, in a polycrystalline material. Grain boundaries are two-dimensional 2953: 1388: 701:

the energy of a boundary made up of dislocations with Burgers vector

86:

from the solid. They are also important to many of the mechanisms of

75: 1789: 1760: 111: 3550: 3320: 3068: 2114: 1838: 1511: 2873: 2639: 3560: 775:{\displaystyle \gamma _{s}=\gamma _{0}\theta (A-\ln \theta )\,\!} 2040:

Hart, Edward W. (1972). "Grain Boundary Phase Transformations".

1528:

often do not describe the physics near the grains correctly and

283:

of the ratio of coincidence sites to the total number of sites.

1266: 19: 1566: 34: 3555: 1518: 1504: 1362:{\displaystyle M=M_{0}\exp \left(-{\frac {Q}{RT}}\right)\,\!} 1277:

The movement of grain boundaries (HAGB) has implications for

1413:

Grain growth can be inhibited by second phase particles via

1285:

while subgrain boundary (LAGB) movement strongly influences

542:{\displaystyle 2\cos \;\theta \;+1=a_{11}+a_{22}+a_{33}\,\!} 90:. On the other hand, grain boundaries disrupt the motion of 16:

Interface between crystallites in a polycrystalline material

2806: 2403: 2341: 2460: 2299:

McCluskey, M. D.; Jokela, S. J. (2009). "Defects in ZnO".

3657:

Zeitschrift für Kristallographie – New Crystal Structures

1661: 3652:

Zeitschrift für Kristallographie – Crystalline Materials

3545: 337: 2846: 2141: 2072: 1479: 1306: 1241: 1221: 1201: 1115: 1089: 1054: 1018: 994: 970: 900: 833: 794: 722: 561: 480: 325: 2774: 2624: 1393:

The boundary mobility increases with misorientation.

2206: 2847:Gottstein, Gunter; Shvindlerman, Lasar S. (2009). 2581: 1361: 1254: 1227: 1207: 1184: 1098: 1060: 1031: 1000: 976: 953: 883: 816: 774: 665: 541: 460: 30:metal; grain boundaries evidenced by acid etching. 1933:Recrystallization and Related Annealing Phenomena 1930: 1358: 950: 880: 813: 771: 662: 538: 3809: 1963: 884:{\displaystyle \gamma _{0}=Gb/4\pi (1-\nu )\,\!} 101: 2298: 2263: 2006: 1696: 1457:cations, is often present in silicon nitride. 552:while the direction of the rotation axis is: 2889: 2678:Bean, Jonathan J.; McKenna, Keith P. (2018). 1723: 3726: 2727: 2677: 2534: 2042:The Nature and Behavior of Grain Boundaries 2007:Sutton, Adrian P.; Balluffi, R. W. (1995). 1895: 471:Using this system the rotation angle θ is: 2896: 2882: 2547:under tension via atomistic simulations". 1519:Relationship between theory and experiment 1505:Defect concentration near grain boundaries 491: 487: 2829: 2638: 2437: 2240: 2183: 1872: 1815: 1631:Physical Foundations of Materials Science 1628: 1357: 1289:and the nucleation of recrystallization. 954:{\displaystyle A=1+\ln(b/2\pi r_{0})\,\!} 949: 879: 812: 770: 661: 537: 196:Learn how and when to remove this message 1593: 1408: 688: 310: 295: 234: 54:is the interface between two grains, or 33: 18: 3810: 2999: 1931:Humphreys, F.J.; Hatherly, M. (2004). 2877: 1486:Hinkley Point A nuclear power station 1272: 3790: 3130:Phase transformation crystallography 2810:Materials Science and Engineering: A 2728:Korolev, V. V.; Bean, J. J. (2022). 2039: 1758: 1387:controlling process is that of bulk 134:adding citations to reliable sources 105: 3637:Journal of Chemical Crystallography 2903: 2009:Interfaces in Crystalline Materials 1106:) is defined in the following way, 13: 2849:Grain Boundary Migration in Metals 2800: 1941:10.1016/B978-0-08-044164-1.X5000-2 1480:Effect to the electronic structure 1141: 1133: 1055: 684: 14: 3849: 2707:10.1103/PhysRevMaterials.2.125002 3789: 3778: 3777: 3384: 2129:10.1016/j.scriptamat.2011.10.011 1664:Acta Crystallographica Section A 1077: 110: 2768: 2721: 2671: 2618: 2575: 2528: 2493: 2454: 2397: 2335: 2292: 2257: 2200: 2135: 2108: 2066: 2033: 2000: 1957: 1924: 1889: 817:{\displaystyle \theta =b/h\,\!} 121:needs additional citations for 3579:Bilbao Crystallographic Server 1832: 1817:10.1103/PhysRevLett.108.055504 1783: 1752: 1717: 1690: 1655: 1622: 1587: 1560: 946: 919: 876: 864: 767: 749: 658: 655: 629: 623: 597: 591: 565: 562: 1: 2822:10.1016/S0921-5093(97)00424-3 2375:10.1103/PhysRevLett.90.105901 2176:10.1016/j.actamat.2015.07.042 2095:10.1016/j.actamat.2013.07.037 1986:10.1103/PhysRevLett.97.075502 1918:10.1016/j.actamat.2016.02.040 1865:10.1016/j.actamat.2013.12.036 1581:10.1016/S1359-6462(97)00018-3 1553: 1451: 102:High and low angle boundaries 42:in a polycrystalline material 2584:Journal of Materials Science 1777:10.1016/0036-9748(89)90482-1 1746:10.1016/0039-6028(72)90252-X 1711:10.1016/0001-6160(87)90067-8 7: 3627:Crystal Growth & Design 2919:Timeline of crystallography 2050:10.1007/978-1-4757-0181-4_6 1536: 1295:Arrhenius type relationship 230:high-angle grain boundaries 66:, and tend to decrease the 10: 3854: 3438:Nuclear magnetic resonance 2754:10.1007/s11661-021-06500-5 2549:Journal of Applied Physics 2502:Journal of Electroceramics 2467:Journal of Applied Physics 2301:Journal of Applied Physics 1629:Gottstein, Günter (2004). 1596:Metallurgical Transactions 214:Low-angle grain boundaries 3773: 3693: 3665: 3642:Journal of Crystal Growth 3617: 3569: 3516: 3463: 3394: 3382: 3177: 3168: 3091: 2944: 2911: 2687:Physical Review Materials 2514:10.1007/s10832-007-9001-1 1684:10.1107/S056773947400043X 1639:10.1007/978-3-662-09291-0 1530:density functional theory 1498:density functional theory 3818:Crystallographic defects 3508:Single particle analysis 3366:Hermann–Mauguin notation 2790:10.37819/nanofab.007.250 1548:Segregation in materials 1195:at constant temperature 1099:{\displaystyle \delta V} 277:coincidence site lattice 212:between the two grains. 3632:Crystallography Reviews 3476:Isomorphous replacement 3270:Lomer–Cottrell junction 2355:Physical Review Letters 2307:(7): 071101–071101–13. 2286:10.1103/physrevb.1.1382 1966:Physical Review Letters 1796:Physical Review Letters 1061:{\displaystyle \Sigma } 3145:Spinodal decomposition 2162:. Elsevier BV: 16–28. 1418: 1363: 1256: 1229: 1209: 1186: 1100: 1075: 1062: 1033: 1002: 978: 955: 885: 818: 776: 711:Read–Shockley equation 694: 667: 543: 462: 316: 240: 43: 31: 3685:Gregori Aminoff Prize 3481:Molecular replacement 2857:10.1201/9781420054361 2353:Tracer Experiments". 1543:Abnormal grain growth 1412: 1364: 1257: 1255:{\displaystyle n_{i}} 1230: 1210: 1187: 1101: 1070: 1063: 1034: 1032:{\displaystyle r_{0}} 1003: 979: 956: 886: 819: 777: 692: 668: 544: 463: 314: 296:Describing a boundary 238: 38:Differently-oriented 37: 22: 2991:Structure prediction 2734:Metall Mater Trans A 2044:. pp. 155–170. 1765:Scripta Metallurgica 1526:embedded atom method 1304: 1239: 1235:and number of atoms 1219: 1199: 1113: 1087: 1052: 1016: 1001:{\displaystyle \nu } 992: 968: 898: 831: 792: 720: 709:is predicted by the 666:{\displaystyle \,\!} 559: 478: 323: 130:improve this article 72:thermal conductivity 3838:Mineralogy concepts 3255:Cottrell atmosphere 3235:Partial dislocation 2979:Restriction theorem 2746:2022MMTA...53..449K 2699:2018PhRvM...2l5002B 2649:2011NatPh...7..535C 2596:1993JMatS..28..835Z 2561:2014JAP...116a3508D 2479:2002JAP....92.5331K 2422:2015NatSR...5E9095U 2367:2003PhRvL..90j5901M 2313:2009JAP...106g1101M 2278:1970PhRvB...1.1382M 2225:2017NatSR...745594B 2168:2015AcMat..99...16G 2087:2014AcMat..62....1C 2011:. Clarendon Press. 1978:2006PhRvL..97g5502T 1910:2016AcMat.110..246B 1857:2014AcMat..68..189O 1808:2012PhRvL.108e5504S 1738:1972SurSc..31...27A 1676:1974AcCrA..30..197G 1608:1971MT......2.1113R 273:electron microscopy 222:subgrain boundaries 3675:Carl Hermann Medal 3486:Molecular dynamics 3333:Defects in diamond 3328:Stone–Wales defect 2974:Reciprocal lattice 2936:Biocrystallography 2604:10.1007/BF01151266 2410:Scientific Reports 2213:Scientific Reports 2144:Finnis, Michael W. 2117:Scripta Materialia 1616:10.1007/BF02664244 1569:Scripta Materialia 1419: 1359: 1273:Boundary migration 1252: 1225: 1205: 1182: 1096: 1058: 1029: 998: 974: 951: 881: 814: 772: 695: 676:The nature of the 663: 539: 458: 452: 317: 302:degrees of freedom 253:screw dislocations 241: 44: 32: 3833:Materials science 3805: 3804: 3769: 3768: 3376:Thermal ellipsoid 3341: 3340: 3250:Frank–Read source 3210: 3209: 3076:Aperiodic crystal 3042: 3041: 2924:Crystallographers 2866:978-0-429-14738-8 2657:10.1038/nphys1962 2569:10.1063/1.4886183 2487:10.1063/1.1512964 2430:10.1038/srep09095 2321:10.1063/1.3216464 2266:Physical Review B 2233:10.1038/srep45594 2059:978-1-4757-0183-8 2018:978-0-19-851385-8 1950:978-0-08-044164-1 1771:(11): 1913–1918. 1759:Wolf, D. (1989). 1699:Acta Metallurgica 1648:978-3-642-07271-0 1575:(10): 1211–1218. 1431:solute atmosphere 1350: 1279:recrystallization 1228:{\displaystyle p} 1208:{\displaystyle T} 1148: 977:{\displaystyle G} 206: 205: 198: 180: 64:crystal structure 48:materials science 3845: 3793: 3792: 3781: 3780: 3724: 3723: 3647:Kristallografija 3501:Gerchberg–Saxton 3396:Characterisation 3388: 3371:Structure factor 3175: 3174: 3160:Ostwald ripening 2997: 2996: 2942: 2941: 2898: 2891: 2884: 2875: 2874: 2870: 2843: 2833: 2794: 2793: 2772: 2766: 2765: 2725: 2719: 2718: 2684: 2675: 2669: 2668: 2642: 2622: 2616: 2615: 2579: 2573: 2572: 2546: 2545: 2544: 2532: 2526: 2525: 2497: 2491: 2490: 2473:(9): 5331–5339. 2458: 2452: 2451: 2441: 2401: 2395: 2394: 2352: 2350: 2349: 2339: 2333: 2332: 2296: 2290: 2289: 2272:(4): 1382–1389. 2261: 2255: 2254: 2244: 2204: 2198: 2197: 2187: 2139: 2133: 2132: 2112: 2106: 2105: 2070: 2064: 2063: 2037: 2031: 2030: 2004: 1998: 1997: 1961: 1955: 1954: 1928: 1922: 1921: 1893: 1887: 1886: 1876: 1851:(100): 189–195. 1836: 1830: 1829: 1819: 1787: 1781: 1780: 1756: 1750: 1749: 1721: 1715: 1714: 1705:(9): 2177–2201. 1694: 1688: 1687: 1659: 1653: 1652: 1626: 1620: 1619: 1602:(4): 1113–1127. 1591: 1585: 1584: 1564: 1368: 1366: 1365: 1360: 1356: 1352: 1351: 1349: 1338: 1322: 1321: 1261: 1259: 1258: 1253: 1251: 1250: 1234: 1232: 1231: 1226: 1214: 1212: 1211: 1206: 1191: 1189: 1188: 1183: 1178: 1177: 1176: 1175: 1153: 1149: 1147: 1139: 1131: 1105: 1103: 1102: 1097: 1068:are misleading: 1067: 1065: 1064: 1059: 1038: 1036: 1035: 1030: 1028: 1027: 1007: 1005: 1004: 999: 983: 981: 980: 975: 960: 958: 957: 952: 945: 944: 929: 890: 888: 887: 882: 857: 843: 842: 823: 821: 820: 815: 808: 781: 779: 778: 773: 745: 744: 732: 731: 672: 670: 669: 664: 654: 653: 641: 640: 622: 621: 609: 608: 590: 589: 577: 576: 548: 546: 545: 540: 536: 535: 523: 522: 510: 509: 467: 465: 464: 459: 457: 456: 449: 448: 437: 436: 425: 424: 411: 410: 399: 398: 387: 386: 373: 372: 361: 360: 349: 348: 201: 194: 190: 187: 181: 179: 145:"Grain boundary" 138: 114: 106: 3853: 3852: 3848: 3847: 3846: 3844: 3843: 3842: 3828:Crystallography 3808: 3807: 3806: 3801: 3765: 3722: 3689: 3661: 3613: 3565: 3536:CrystalExplorer 3512: 3496:Phase retrieval 3459: 3390: 3389: 3380: 3337: 3316:Schottky defect 3215:Perfect crystal 3206: 3202:Abnormal growth 3164: 3150:Supersaturation 3113:Miscibility gap 3094: 3087: 3038: 2995: 2959:Bravais lattice 2940: 2907: 2905:Crystallography 2902: 2867: 2803: 2801:Further reading 2798: 2797: 2778:Nanofabrication 2773: 2769: 2726: 2722: 2682: 2676: 2672: 2623: 2619: 2580: 2576: 2543: 2540: 2539: 2538: 2536: 2533: 2529: 2498: 2494: 2459: 2455: 2402: 2398: 2348: 2346: 2345: 2344: 2343: 2340: 2336: 2297: 2293: 2262: 2258: 2205: 2201: 2156:Acta Materialia 2153: 2149: 2140: 2136: 2113: 2109: 2075:Acta Materialia 2071: 2067: 2060: 2038: 2034: 2019: 2005: 2001: 1962: 1958: 1951: 1929: 1925: 1898:Acta Materialia 1894: 1890: 1845:Acta Materialia 1837: 1833: 1788: 1784: 1757: 1753: 1726:Surface Science 1722: 1718: 1695: 1691: 1660: 1656: 1649: 1627: 1623: 1592: 1588: 1565: 1561: 1556: 1539: 1521: 1507: 1495: 1491: 1482: 1475: 1471: 1462:W. Craig Carter 1454: 1342: 1337: 1333: 1329: 1317: 1313: 1305: 1302: 1301: 1275: 1246: 1242: 1240: 1237: 1236: 1220: 1217: 1216: 1200: 1197: 1196: 1171: 1167: 1154: 1140: 1132: 1130: 1126: 1125: 1114: 1111: 1110: 1088: 1085: 1084: 1080: 1053: 1050: 1049: 1023: 1019: 1017: 1014: 1013: 1010:Poisson's ratio 993: 990: 989: 969: 966: 965: 940: 936: 925: 899: 896: 895: 853: 838: 834: 832: 829: 828: 804: 793: 790: 789: 740: 736: 727: 723: 721: 718: 717: 699:tilt boundaries 687: 685:Boundary energy 678:crystallography 649: 645: 636: 632: 617: 613: 604: 600: 585: 581: 572: 568: 560: 557: 556: 531: 527: 518: 514: 505: 501: 479: 476: 475: 451: 450: 444: 440: 438: 432: 428: 426: 420: 416: 413: 412: 406: 402: 400: 394: 390: 388: 382: 378: 375: 374: 368: 364: 362: 356: 352: 350: 344: 340: 333: 332: 324: 321: 320: 306:rotation matrix 298: 257:Burgers vectors 202: 191: 185: 182: 139: 137: 127: 115: 104: 28:polycrystalline 17: 12: 11: 5: 3851: 3841: 3840: 3835: 3830: 3825: 3820: 3803: 3802: 3800: 3799: 3787: 3774: 3771: 3770: 3767: 3766: 3764: 3763: 3758: 3753: 3752: 3751: 3746: 3741: 3730: 3728: 3721: 3720: 3715: 3710: 3705: 3699: 3697: 3691: 3690: 3688: 3687: 3682: 3677: 3671: 3669: 3663: 3662: 3660: 3659: 3654: 3649: 3644: 3639: 3634: 3629: 3623: 3621: 3615: 3614: 3612: 3611: 3606: 3601: 3596: 3591: 3586: 3581: 3575: 3573: 3567: 3566: 3564: 3563: 3558: 3553: 3548: 3543: 3538: 3533: 3528: 3522: 3520: 3514: 3513: 3511: 3510: 3505: 3504: 3503: 3493: 3488: 3483: 3478: 3473: 3471:Direct methods 3467: 3465: 3461: 3460: 3458: 3457: 3456: 3455: 3450: 3440: 3435: 3434: 3433: 3428: 3418: 3417: 3416: 3411: 3400: 3398: 3392: 3391: 3383: 3381: 3379: 3378: 3373: 3368: 3363: 3358: 3356:Ewald's sphere 3353: 3348: 3342: 3339: 3338: 3336: 3335: 3330: 3325: 3324: 3323: 3318: 3308: 3307: 3306: 3301: 3299:Frenkel defect 3296: 3294:Bjerrum defect 3286: 3285: 3284: 3274: 3273: 3272: 3267: 3262: 3260:Peierls stress 3257: 3252: 3247: 3242: 3237: 3232: 3230:Burgers vector 3222: 3220:Stacking fault 3217: 3211: 3208: 3207: 3205: 3204: 3199: 3194: 3189: 3183: 3181: 3179:Grain boundary 3172: 3166: 3165: 3163: 3162: 3157: 3152: 3147: 3142: 3137: 3132: 3127: 3126: 3125: 3123:Liquid crystal 3120: 3115: 3110: 3099: 3097: 3089: 3088: 3086: 3085: 3084: 3083: 3073: 3072: 3071: 3061: 3060: 3059: 3054: 3043: 3040: 3039: 3037: 3036: 3031: 3026: 3021: 3016: 3011: 3005: 3003: 2994: 2993: 2988: 2986:Periodic table 2983: 2982: 2981: 2976: 2971: 2966: 2961: 2950: 2948: 2939: 2938: 2933: 2928: 2927: 2926: 2915: 2913: 2909: 2908: 2901: 2900: 2893: 2886: 2878: 2872: 2871: 2865: 2844: 2816:(2): 219–274. 2802: 2799: 2796: 2795: 2767: 2740:(2): 449–459. 2720: 2693:(12): 125002. 2670: 2633:(7): 535–538. 2627:Nature Physics 2617: 2590:(3): 835–846. 2574: 2541: 2527: 2492: 2453: 2396: 2361:(10): 105901. 2347: 2334: 2291: 2256: 2199: 2151: 2147: 2134: 2123:(5): 203–206. 2107: 2065: 2058: 2032: 2017: 1999: 1956: 1949: 1923: 1888: 1831: 1782: 1751: 1716: 1689: 1670:(2): 197–207. 1654: 1647: 1621: 1586: 1558: 1557: 1555: 1552: 1551: 1550: 1545: 1538: 1535: 1520: 1517: 1506: 1503: 1493: 1489: 1481: 1478: 1473: 1469: 1453: 1450: 1446:heat-treatment 1395: 1394: 1391: 1381: 1370: 1369: 1355: 1348: 1345: 1341: 1336: 1332: 1328: 1325: 1320: 1316: 1312: 1309: 1274: 1271: 1249: 1245: 1224: 1204: 1193: 1192: 1181: 1174: 1170: 1166: 1163: 1160: 1157: 1152: 1146: 1143: 1138: 1135: 1129: 1124: 1121: 1118: 1095: 1092: 1079: 1076: 1057: 1026: 1022: 997: 973: 962: 961: 948: 943: 939: 935: 932: 928: 924: 921: 918: 915: 912: 909: 906: 903: 892: 891: 878: 875: 872: 869: 866: 863: 860: 856: 852: 849: 846: 841: 837: 825: 824: 811: 807: 803: 800: 797: 783: 782: 769: 766: 763: 760: 757: 754: 751: 748: 743: 739: 735: 730: 726: 686: 683: 674: 673: 660: 657: 652: 648: 644: 639: 635: 631: 628: 625: 620: 616: 612: 607: 603: 599: 596: 593: 588: 584: 580: 575: 571: 567: 564: 550: 549: 534: 530: 526: 521: 517: 513: 508: 504: 500: 497: 494: 490: 486: 483: 469: 468: 455: 447: 443: 439: 435: 431: 427: 423: 419: 415: 414: 409: 405: 401: 397: 393: 389: 385: 381: 377: 376: 371: 367: 363: 359: 355: 351: 347: 343: 339: 338: 336: 331: 328: 297: 294: 210:misorientation 204: 203: 118: 116: 109: 103: 100: 98:relationship. 52:grain boundary 15: 9: 6: 4: 3: 2: 3850: 3839: 3836: 3834: 3831: 3829: 3826: 3824: 3821: 3819: 3816: 3815: 3813: 3798: 3797: 3788: 3786: 3785: 3776: 3775: 3772: 3762: 3759: 3757: 3754: 3750: 3747: 3745: 3742: 3740: 3737: 3736: 3735: 3732: 3731: 3729: 3725: 3719: 3716: 3714: 3711: 3709: 3706: 3704: 3701: 3700: 3698: 3696: 3692: 3686: 3683: 3681: 3678: 3676: 3673: 3672: 3670: 3668: 3664: 3658: 3655: 3653: 3650: 3648: 3645: 3643: 3640: 3638: 3635: 3633: 3630: 3628: 3625: 3624: 3622: 3620: 3616: 3610: 3607: 3605: 3602: 3600: 3597: 3595: 3592: 3590: 3587: 3585: 3582: 3580: 3577: 3576: 3574: 3572: 3568: 3562: 3559: 3557: 3554: 3552: 3549: 3547: 3544: 3542: 3539: 3537: 3534: 3532: 3529: 3527: 3524: 3523: 3521: 3519: 3515: 3509: 3506: 3502: 3499: 3498: 3497: 3494: 3492: 3491:Patterson map 3489: 3487: 3484: 3482: 3479: 3477: 3474: 3472: 3469: 3468: 3466: 3462: 3454: 3451: 3449: 3446: 3445: 3444: 3441: 3439: 3436: 3432: 3429: 3427: 3424: 3423: 3422: 3419: 3415: 3412: 3410: 3407: 3406: 3405: 3402: 3401: 3399: 3397: 3393: 3387: 3377: 3374: 3372: 3369: 3367: 3364: 3362: 3361:Friedel's law 3359: 3357: 3354: 3352: 3349: 3347: 3344: 3343: 3334: 3331: 3329: 3326: 3322: 3319: 3317: 3314: 3313: 3312: 3309: 3305: 3304:Wigner effect 3302: 3300: 3297: 3295: 3292: 3291: 3290: 3289:Interstitials 3287: 3283: 3280: 3279: 3278: 3275: 3271: 3268: 3266: 3263: 3261: 3258: 3256: 3253: 3251: 3248: 3246: 3243: 3241: 3238: 3236: 3233: 3231: 3228: 3227: 3226: 3223: 3221: 3218: 3216: 3213: 3212: 3203: 3200: 3198: 3195: 3193: 3190: 3188: 3185: 3184: 3182: 3180: 3176: 3173: 3171: 3167: 3161: 3158: 3156: 3153: 3151: 3148: 3146: 3143: 3141: 3138: 3136: 3135:Precipitation 3133: 3131: 3128: 3124: 3121: 3119: 3116: 3114: 3111: 3109: 3106: 3105: 3104: 3103:Phase diagram 3101: 3100: 3098: 3096: 3090: 3082: 3079: 3078: 3077: 3074: 3070: 3067: 3066: 3065: 3062: 3058: 3055: 3053: 3050: 3049: 3048: 3045: 3044: 3035: 3032: 3030: 3027: 3025: 3022: 3020: 3017: 3015: 3012: 3010: 3007: 3006: 3004: 3002: 2998: 2992: 2989: 2987: 2984: 2980: 2977: 2975: 2972: 2970: 2967: 2965: 2962: 2960: 2957: 2956: 2955: 2952: 2951: 2949: 2947: 2943: 2937: 2934: 2932: 2929: 2925: 2922: 2921: 2920: 2917: 2916: 2914: 2910: 2906: 2899: 2894: 2892: 2887: 2885: 2880: 2879: 2876: 2868: 2862: 2858: 2854: 2850: 2845: 2841: 2837: 2832: 2827: 2823: 2819: 2815: 2811: 2805: 2804: 2791: 2787: 2783: 2779: 2771: 2763: 2759: 2755: 2751: 2747: 2743: 2739: 2735: 2731: 2724: 2716: 2712: 2708: 2704: 2700: 2696: 2692: 2688: 2681: 2674: 2666: 2662: 2658: 2654: 2650: 2646: 2641: 2636: 2632: 2628: 2621: 2613: 2609: 2605: 2601: 2597: 2593: 2589: 2585: 2578: 2570: 2566: 2562: 2558: 2555:(1): 013508. 2554: 2550: 2531: 2523: 2519: 2515: 2511: 2507: 2503: 2496: 2488: 2484: 2480: 2476: 2472: 2468: 2464: 2457: 2449: 2445: 2440: 2435: 2431: 2427: 2423: 2419: 2415: 2411: 2407: 2400: 2392: 2388: 2384: 2380: 2376: 2372: 2368: 2364: 2360: 2356: 2338: 2330: 2326: 2322: 2318: 2314: 2310: 2306: 2302: 2295: 2287: 2283: 2279: 2275: 2271: 2267: 2260: 2252: 2248: 2243: 2238: 2234: 2230: 2226: 2222: 2218: 2214: 2210: 2203: 2195: 2191: 2186: 2185:10044/1/25490 2181: 2177: 2173: 2169: 2165: 2161: 2157: 2145: 2138: 2130: 2126: 2122: 2118: 2111: 2103: 2100: 2096: 2092: 2088: 2084: 2080: 2076: 2069: 2061: 2055: 2051: 2047: 2043: 2036: 2028: 2024: 2020: 2014: 2010: 2003: 1995: 1991: 1987: 1983: 1979: 1975: 1972:(7): 075502. 1971: 1967: 1960: 1952: 1946: 1942: 1938: 1934: 1927: 1919: 1915: 1911: 1907: 1903: 1899: 1892: 1884: 1880: 1875: 1870: 1866: 1862: 1858: 1854: 1850: 1846: 1842: 1835: 1827: 1823: 1818: 1813: 1809: 1805: 1802:(5): 055504. 1801: 1797: 1793: 1786: 1778: 1774: 1770: 1766: 1762: 1755: 1747: 1743: 1739: 1735: 1731: 1727: 1720: 1712: 1708: 1704: 1700: 1693: 1685: 1681: 1677: 1673: 1669: 1665: 1658: 1650: 1644: 1640: 1636: 1632: 1625: 1617: 1613: 1609: 1605: 1601: 1597: 1590: 1582: 1578: 1574: 1570: 1563: 1559: 1549: 1546: 1544: 1541: 1540: 1534: 1531: 1527: 1516: 1513: 1502: 1499: 1487: 1477: 1465: 1463: 1458: 1449: 1447: 1443: 1439: 1438:Zener pinning 1434: 1432: 1428: 1424: 1416: 1415:Zener pinning 1411: 1407: 1405: 1399: 1392: 1390: 1386: 1382: 1379: 1378: 1377: 1374: 1353: 1346: 1343: 1339: 1334: 1330: 1326: 1323: 1318: 1314: 1310: 1307: 1300: 1299: 1298: 1296: 1290: 1288: 1284: 1280: 1270: 1268: 1263: 1247: 1243: 1222: 1202: 1179: 1172: 1168: 1164: 1161: 1158: 1155: 1150: 1144: 1136: 1127: 1122: 1119: 1116: 1109: 1108: 1107: 1093: 1090: 1078:Excess volume 1074: 1069: 1045: 1043: 1024: 1020: 1011: 995: 987: 986:shear modulus 971: 941: 937: 933: 930: 926: 922: 916: 913: 910: 907: 904: 901: 894: 893: 873: 870: 867: 861: 858: 854: 850: 847: 844: 839: 835: 827: 826: 809: 805: 801: 798: 795: 788: 787: 786: 764: 761: 758: 755: 752: 746: 741: 737: 733: 728: 724: 716: 715: 714: 712: 708: 704: 700: 691: 682: 679: 650: 646: 642: 637: 633: 626: 618: 614: 610: 605: 601: 594: 586: 582: 578: 573: 569: 555: 554: 553: 532: 528: 524: 519: 515: 511: 506: 502: 498: 495: 492: 488: 484: 481: 474: 473: 472: 453: 445: 441: 433: 429: 421: 417: 407: 403: 395: 391: 383: 379: 369: 365: 357: 353: 345: 341: 334: 329: 326: 319: 318: 313: 309: 307: 303: 293: 290: 284: 282: 278: 274: 268: 264: 260: 258: 254: 249: 246: 237: 233: 231: 227: 223: 219: 215: 211: 200: 197: 189: 178: 175: 171: 168: 164: 161: 157: 154: 150: 147: – 146: 142: 141:Find sources: 135: 131: 125: 124: 119:This section 117: 113: 108: 107: 99: 97: 93: 89: 85: 81: 80:precipitation 77: 73: 69: 65: 61: 57: 53: 49: 41: 36: 29: 25: 21: 3794: 3782: 3727:Associations 3695:Organisation 3187:Disclination 3178: 3118:Polymorphism 3081:Quasicrystal 3024:Orthorhombic 2964:Miller index 2912:Key concepts 2848: 2813: 2809: 2781: 2777: 2770: 2737: 2733: 2723: 2690: 2686: 2673: 2630: 2626: 2620: 2587: 2583: 2577: 2552: 2548: 2530: 2505: 2501: 2495: 2470: 2466: 2462: 2456: 2413: 2409: 2399: 2358: 2354: 2337: 2304: 2300: 2294: 2269: 2265: 2259: 2219:(1): 45594. 2216: 2212: 2202: 2159: 2155: 2137: 2120: 2116: 2110: 2078: 2074: 2068: 2041: 2035: 2008: 2002: 1969: 1965: 1959: 1932: 1926: 1901: 1897: 1891: 1848: 1844: 1834: 1799: 1795: 1785: 1768: 1764: 1754: 1732:(C): 27–49. 1729: 1725: 1719: 1702: 1698: 1692: 1667: 1663: 1657: 1630: 1624: 1599: 1595: 1589: 1572: 1568: 1562: 1522: 1508: 1483: 1466: 1459: 1455: 1442:grain growth 1435: 1430: 1426: 1422: 1420: 1400: 1396: 1375: 1371: 1291: 1283:grain growth 1276: 1264: 1194: 1081: 1071: 1046: 1042:grain growth 963: 784: 710: 706: 705:and spacing 702: 698: 696: 675: 551: 470: 299: 285: 276: 269: 265: 261: 250: 242: 229: 226:dislocations 221: 217: 213: 207: 192: 183: 173: 166: 159: 152: 140: 128:Please help 123:verification 120: 92:dislocations 78:and for the 56:crystallites 51: 45: 40:crystallites 3680:Ewald Prize 3448:Diffraction 3426:Diffraction 3409:Diffraction 3351:Bragg plane 3346:Bragg's law 3225:Dislocation 3140:Segregation 3052:Crystallite 2969:Point group 2831:10945/40175 1904:: 246–257. 1427:free volume 1215:, pressure 245:crystallite 186:August 2018 3823:Metallurgy 3812:Categories 3464:Algorithms 3453:Scattering 3431:Scattering 3414:Scattering 3282:Slip bands 3245:Cross slip 3095:transition 3029:Tetragonal 3019:Monoclinic 2931:Metallurgy 1554:References 1452:Complexion 1423:free space 1404:martensite 1073:interface. 281:reciprocal 156:newspapers 96:Hall–Petch 68:electrical 24:Micrograph 3571:Databases 3034:Triclinic 3014:Hexagonal 2954:Unit cell 2946:Structure 2762:245636012 2715:197631853 2665:119210230 2640:1004.3373 2612:137660500 2522:137189236 2508:: 49–67. 2329:122634653 2102:ADA601364 1464:in 2006. 1389:diffusion 1335:− 1327:⁡ 1142:∂ 1134:∂ 1117:δ 1091:δ 1056:Σ 996:ν 934:π 917:⁡ 874:ν 871:− 862:π 836:γ 796:θ 765:θ 762:⁡ 756:− 747:θ 738:γ 725:γ 643:− 611:− 579:− 489:θ 255:. If the 76:corrosion 3784:Category 3619:Journals 3551:OctaDist 3546:JANA2020 3518:Software 3404:Electron 3321:F-center 3108:Eutectic 3069:Fiveling 3064:Twinning 3057:Equiaxed 2840:17885466 2448:25766999 2416:: 9095. 2391:11680149 2383:12689009 2251:28374755 2194:94617212 2081:: 1–48. 2027:31166519 1994:17026243 1883:24748848 1826:22400941 1537:See also 1512:graphene 1287:recovery 3796:Commons 3744:Germany 3421:Neutron 3311:Vacancy 3170:Defects 3155:GP-zone 3001:Systems 2742:Bibcode 2695:Bibcode 2645:Bibcode 2592:Bibcode 2557:Bibcode 2475:Bibcode 2439:4357896 2418:Bibcode 2363:Bibcode 2309:Bibcode 2274:Bibcode 2242:5379487 2221:Bibcode 2164:Bibcode 2083:Bibcode 1974:Bibcode 1906:Bibcode 1874:3990421 1853:Bibcode 1804:Bibcode 1734:Bibcode 1672:Bibcode 1604:Bibcode 1444:during 984:is the 785:where: 170:scholar 82:of new 62:in the 60:defects 3739:France 3734:Europe 3667:Awards 3197:Growth 3047:Growth 2863: 2838: 2760: 2713: 2663: 2610: 2520: 2446: 2436: 2389: 2381: 2327: 2249: 2239: 2192: 2056: 2025: 2015: 1992: 1947: 1881: 1871: 1824: 1645: 1267:nickel 1012:, and 172: 165: 158: 151: 143: 84:phases 3761:Japan 3708:IOBCr 3561:SHELX 3556:Olex2 3443:X-ray 3093:Phase 3009:Cubic 2836:S2CID 2758:S2CID 2711:S2CID 2683:(PDF) 2661:S2CID 2635:arXiv 2608:S2CID 2518:S2CID 2387:S2CID 2325:S2CID 2190:S2CID 964:with 220:) or 177:JSTOR 163:books 88:creep 26:of a 3703:IUCr 3604:ICDD 3599:ICSD 3584:CCDC 3531:Coot 3526:CCP4 3277:Slip 3240:Kink 2861:ISBN 2444:PMID 2379:PMID 2247:PMID 2099:DTIC 2054:ISBN 2023:OCLC 2013:ISBN 1990:PMID 1945:ISBN 1879:PMID 1822:PMID 1643:ISBN 1385:rate 1383:The 1281:and 289:twin 218:LAGB 149:news 70:and 50:, a 3718:DMG 3713:RAS 3609:PDB 3594:COD 3589:CIF 3541:DSR 3265:GND 3192:CSL 2853:doi 2826:hdl 2818:doi 2814:238 2786:doi 2750:doi 2703:doi 2653:doi 2600:doi 2565:doi 2553:116 2537:MoS 2510:doi 2483:doi 2434:PMC 2426:doi 2371:doi 2317:doi 2305:106 2282:doi 2237:PMC 2229:doi 2180:hdl 2172:doi 2154:". 2125:doi 2091:doi 2046:doi 1982:doi 1937:doi 1914:doi 1902:110 1869:PMC 1861:doi 1812:doi 1800:108 1773:doi 1742:doi 1707:doi 1680:doi 1635:doi 1612:doi 1577:doi 1425:or 1324:exp 1044:). 1008:is 485:cos 132:by 46:In 3814:: 3756:US 3749:UK 2859:. 2851:. 2834:. 2824:. 2812:. 2784:. 2780:. 2756:. 2748:. 2738:54 2736:. 2732:. 2709:. 2701:. 2689:. 2685:. 2659:. 2651:. 2643:. 2629:. 2606:. 2598:. 2588:28 2586:. 2563:. 2551:. 2516:. 2506:19 2504:. 2481:. 2471:92 2469:. 2442:. 2432:. 2424:. 2412:. 2408:. 2385:. 2377:. 2369:. 2359:90 2357:. 2323:. 2315:. 2303:. 2280:. 2268:. 2245:. 2235:. 2227:. 2215:. 2211:. 2188:. 2178:. 2170:. 2160:99 2158:. 2121:66 2119:. 2097:. 2089:. 2079:62 2077:. 2052:. 2021:. 1988:. 1980:. 1970:97 1968:. 1943:. 1935:. 1912:. 1900:. 1877:. 1867:. 1859:. 1849:68 1847:. 1843:. 1820:. 1810:. 1798:. 1794:. 1769:23 1767:. 1763:. 1740:. 1730:31 1728:. 1703:35 1701:. 1678:. 1668:30 1666:. 1641:. 1633:. 1610:. 1598:. 1573:36 1571:. 1448:. 1297:: 988:, 914:ln 759:ln 713:: 651:12 638:21 619:31 606:13 587:23 574:32 533:33 520:22 507:11 446:33 434:32 422:31 408:23 396:22 384:21 370:13 358:12 346:11 308:: 2897:e 2890:t 2883:v 2869:. 2855:: 2842:. 2828:: 2820:: 2792:. 2788:: 2782:7 2764:. 2752:: 2744:: 2717:. 2705:: 2697:: 2691:2 2667:. 2655:: 2647:: 2637:: 2631:7 2614:. 2602:: 2594:: 2571:. 2567:: 2559:: 2542:2 2524:. 2512:: 2489:. 2485:: 2477:: 2463:n 2450:. 2428:: 2420:: 2414:5 2393:. 2373:: 2365:: 2351:O 2331:. 2319:: 2311:: 2288:. 2284:: 2276:: 2270:1 2253:. 2231:: 2223:: 2217:7 2196:. 2182:: 2174:: 2166:: 2152:3 2150:O 2148:2 2131:. 2127:: 2104:. 2093:: 2085:: 2062:. 2048:: 2029:. 1996:. 1984:: 1976:: 1953:. 1939:: 1920:. 1916:: 1908:: 1885:. 1863:: 1855:: 1828:. 1814:: 1806:: 1779:. 1775:: 1748:. 1744:: 1736:: 1713:. 1709:: 1686:. 1682:: 1674:: 1651:. 1637:: 1618:. 1614:: 1606:: 1600:2 1583:. 1579:: 1494:3 1492:O 1490:2 1474:3 1472:N 1470:3 1417:. 1354:) 1347:T 1344:R 1340:Q 1331:( 1319:0 1315:M 1311:= 1308:M 1248:i 1244:n 1223:p 1203:T 1180:, 1173:i 1169:n 1165:, 1162:p 1159:, 1156:T 1151:) 1145:A 1137:V 1128:( 1123:= 1120:V 1094:V 1025:0 1021:r 972:G 947:) 942:0 938:r 931:2 927:/ 923:b 920:( 911:+ 908:1 905:= 902:A 877:) 868:1 865:( 859:4 855:/ 851:b 848:G 845:= 840:0 810:h 806:/ 802:b 799:= 768:) 753:A 750:( 742:0 734:= 729:s 707:h 703:b 659:] 656:) 647:a 634:a 630:( 627:, 624:) 615:a 602:a 598:( 595:, 592:) 583:a 570:a 566:( 563:[ 529:a 525:+ 516:a 512:+ 503:a 499:= 496:1 493:+ 482:2 454:] 442:a 430:a 418:a 404:a 392:a 380:a 366:a 354:a 342:a 335:[ 330:= 327:R 216:( 199:) 193:( 188:) 184:( 174:· 167:· 160:· 153:· 126:.

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

Index