Anisotropy of Segregation at Grain Boundaries and Surfaces
- PDF / 187,257 Bytes
- 2 Pages / 594 x 792 pts Page_size
- 46 Downloads / 249 Views
DOI: 10.1007/s11661-006-9039-8 Ó The Minerals, Metals & Materials Society and ASM International 2007
ERRATUM TO: METALLURGICAL AND MATERIALS TRANSACTIONS A DOI MTA/123238/ETP06139A
CORRECTION to Metall. Mater. Trans. A, September 2006, vol. 37A, pp. 2595–2620 Due to author error, the following term was omitted in Eq. [32]: N n X 2 i¼N J
max þ2
Jmax X j¼N þ2i
" z
j
i iþj xi xiþj eBB þnxi ð1 xiþj ÞeAB þ ð1 xi Þxiþj eAB þ ð1 o x Þð1 x ÞeAA 2 2 ð xÞ eBB þ 2xð1 xÞeAB þ ð1 xÞ eAA
#
The corrected Eq. [32] for the internal energy of a grain boundary (GB), should thus read: es ¼
þ1 nzi NX i i ½ðxi Þ2 eBB þ 2xi ð1 xi ÞeAB þ ð1 xi Þ2 eAA DEel x 2 i¼1
þ
+
Jmax X i1 nX zj ½xi xij eBB þ xi ð1 xij ÞeAB þ ð1 xi Þxij eAB þ ð1 xi Þð1 xij ÞeAA 2 i¼2 j¼1 Jmax X Jmax nP X zj ½xi x0 eBB þ xi ð1 x0 ÞeAB þ ð1 xi Þx0 eAB þ ð1 xi Þð1 x0 ÞeAA 2 i¼1 j¼i
Jmax X Jmax nX zj ½xi xiþj eBB þ xi ð1 xiþj ÞeAB þ ð1 xi Þxiþj eAB þ ð1 xi Þð1 xiþj ÞeAA 2 i¼1 j¼1 " i ij # Jmax þ1 X x x eBB þ xi ð1 xij ÞeAB þ ð1 xi Þxij eAB þ ð1 xi Þð1 xij ÞeAA n NX + zj 2 i¼J þ1 j¼1 þxi xiþj eBB þ xi ð1 xiþj ÞeAB þ ð1 xi Þxiþj eAB þ ð1 xi Þð1 xiþj ÞeAA
+
max
nzðN þ 1Þ ½ðxÞ2 eBB þ 2xð1 xÞeAB þ ð1 xÞ2 eAA 2 " i iþj # Jmax N x x eBB þ xi ð1 xiþj ÞeAB þ ð1 xi Þxiþj eAB þ ð1 xi Þð1 xiþj ÞeAA X n X j n o þ z 2 i¼N J þ2 j¼N þ2i ð xÞ2 eBB þ 2xð1 xÞeAB þ ð1 xÞ2 eAA max
PAUL WYNBLATT, Professor Emeritus, is with the Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA. Contact e-mail: [email protected]. edu DOMINIQUE CHATAIN, Directeur de Recherches is with the CRMCN-CNRS, Campus de Luminy, 13288 Marseille Cedex 9, France. The online version of the original article can be found at http:// www.dx.doi.org/MTA/123238/ETP06139A 438—VOLUME 38A, FEBRUARY 2007
The omitted term reflects internal energy contributions arising in the region of the GB composition profile, where the composition excursion associated with GB segregation connects to the bulk composition of the crystal. When N, the total number of atom planes that have a composition different from the bulk, is chosen to be large enough (refer to the article), the omitted term METALLURGICAL AND MATERIALS TRANSACTIONS A
makes a negligible contribution to the total internal energy of the boundary. As a result, all of the energies reported in the article are correct within a small fraction of a mJ/m2. However, a note of caution should be sounded. If the equilibrium GB composition profile is determined by seeking the atom plane compositions that minimize the expression for the total GB energy, without including the
METALLURGICAL AND MATERIALS TRANSACTIONS A
preceding correction term, then errors could ensue in the computed composition profile. Such errors would occur in the vicinity of the connection between the segregation profile and the bulk. This possible problem did not arise in the published article, as a different approach was used to evaluate the equilibrium compos
Data Loading...
