_:Nc78e66157d2543f189a066656af30b3b _:N51038cf212004d1aa3e623f080b8562b .
_:N7fc6cdb2fa92483099f25779c71e6182 .
"intermediate veloicities" .
"relevant microstruetural length scale" .
.
_:Nb89119ae56e44c878d13c9664ace82bf _:Nc78e66157d2543f189a066656af30b3b .
"interface" .
"Materials Engineering" .
"diffusion coefficient" .
_:N2aa5b11eb8744a4dbe56ef21e0ea819c "P. R." .
"undercooled melt" .
"zone boundary" .
"1986" .
_:Na3d8dae2a64b4b3fb724e392c70662db "pub.1001658689" .
_:N7975ce5f246d42ef83e79af90ceddf7d .
_:N51038cf212004d1aa3e623f080b8562b .
"solidification rate" .
_:N21b27c530ca94ff4b0f403f407a45235 "Springer Nature" .
"https://doi.org/10.1007/978-94-009-4456-5_5" .
_:N7975ce5f246d42ef83e79af90ceddf7d "Jones" .
_:Na3d8dae2a64b4b3fb724e392c70662db .
"important consequences" .
"liquid diffusion coefficient" .
"solidification theory" .
.
_:Nb89119ae56e44c878d13c9664ace82bf _:N2aa5b11eb8744a4dbe56ef21e0ea819c .
"chapters" .
_:N89b5513d89b34afbb6637659ee7c251c "10.1007/978-94-009-4456-5_5" .
_:N89b5513d89b34afbb6637659ee7c251c "doi" .
"solidification" .
"en" .
"Engineering" .
_:N59d6507e56674f7abf99c4111e3f6278 .
_:N51038cf212004d1aa3e623f080b8562b _:N7fc6cdb2fa92483099f25779c71e6182 .
"non-equilibrium occurs" .
"V1/2D" .
_:N89b5513d89b34afbb6637659ee7c251c .
"occurs" .
"Boettinger" .
"boundaries" .
_:N4802fb53d4e746be8732da3df52a3e16 "978-94-010-8483-3" .
_:N89b5513d89b34afbb6637659ee7c251c .
_:N4802fb53d4e746be8732da3df52a3e16 .
_:Na3d8dae2a64b4b3fb724e392c70662db "dimensions_id" .
"Coriell" .
_:Nbcb24e5ec0374670ac7c81d04ba59a8a "Springer Nature - SN SciGraph project" .
_:N2aa5b11eb8744a4dbe56ef21e0ea819c "Sahm" .
"initial undercooling" .
"alloy" .
"S. R." .
"model" .
"microstructure formation" .
.
"temperature" .
.
_:Nbcb24e5ec0374670ac7c81d04ba59a8a .
"composition" .
_:N59d6507e56674f7abf99c4111e3f6278 _:N0787480d66c449a4b5d09af45bfa651f .
"equilibrium" .
"microstruetural length scale" .
"parameter v" .
"rate" .
"function" .
"chapter" .
"liquid solid interface" .
"https://scigraph.springernature.com/explorer/license/" .
.
"W. J." .
"solute redistribution" .
"dendritic growth" .
_:N4802fb53d4e746be8732da3df52a3e16 "Science and Technology of the Undercooled Melt" .
"alloy dendritic growth theory" .
_:N7975ce5f246d42ef83e79af90ceddf7d "H." .
"redistribution" .
"interfacial equilibrium" .
.
"consequences" .
"scale" .
.
_:N59d6507e56674f7abf99c4111e3f6278 .
"range" .
"local interfacial equilibrium" .
"81-109" .
_:N0787480d66c449a4b5d09af45bfa651f .
"number" .
_:N0787480d66c449a4b5d09af45bfa651f .
_:N21b27c530ca94ff4b0f403f407a45235 .
"undercooling" .
"non-equilibrium interface conditions" .
_:N4802fb53d4e746be8732da3df52a3e16 .
"growth" .
"growth theory" .
"microstructure" .
.
"Peclet number" .
"degree" .
_:Na3d8dae2a64b4b3fb724e392c70662db .
"assumption" .
_:N2aa5b11eb8744a4dbe56ef21e0ea819c .
.
_:N4802fb53d4e746be8732da3df52a3e16 "978-94-009-4456-5" .
"freezing range" .
"expression" .
"veloicities" .
"different degrees" .
"topic" .
"modification" .
"dendritic growth theories" .
.
"theory" .
_:Nc78e66157d2543f189a066656af30b3b _:N7975ce5f246d42ef83e79af90ceddf7d .
_:N21b27c530ca94ff4b0f403f407a45235 .
.
"In order to apply solidification theory to the interpretation of micro- structures produced by rapid solidification, several modifications are required. Different degrees of non-equilibrium occur during solidification and constitute a hierarchy which is followed with increasing solidification rate. Analytical expressions are given for a model of non-equilibrium interface conditions which describe the temperatures and compositions at the liquid solid interface as a function of solidification velocity. For solidification at intermediate veloicities (\u224310 cm/s) the assumption of local interfacial equilibrium remains valid but microstructures are often produced under conditions where the solute Peclet number Pc= V1/2D, is greater than one. The parameters V, 1 and D are the solidification velocity, relevant microstruetural length scale and liquid diffusion coefficient respectively. This fact requires that several topics in solidification theory be modified. Such a modification is presented for alloy dendritic growth theory. For alloys solidifying dendritically into undercooled melts, solute redistribution dominates the relatinship between growth rate and initial undercooling when the initial undercooling is smaller than the alloy freezing range (difference between liquidus and solidus temperatures). This fact has several important consequences for the eutectic coupled zone boundaries and for arrayed dendritic growth." .
"order" .
"analytical expressions" .
"velocity" .
.
.
"solute Peclet number" .
"melt" .
.
"formation" .
_:N7fc6cdb2fa92483099f25779c71e6182 "C. M." .
.
_:N7fc6cdb2fa92483099f25779c71e6182 "Adam" .
.
"solidification velocity" .
"conditions" .
_:Nbcb24e5ec0374670ac7c81d04ba59a8a .