Macroscopic description of interface migration by ledge and kink motion controlled by volume diffusion View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1991-06

AUTHORS

W. W. Mullins

ABSTRACT

A macroscopic description is developed of the diffusion-limited migration of an interface on which only certain preferred interface sites(e.g., kinks or ledges) serve as diffusion sinks. The interface is assumed to be macroscopically flat and is represented by a mathematical plane, ∑. The description is developed by (1) deriving a one-dimensional diffusion equation forc, the concentration averaged over planes parallel to ∑, (2) establishing a macroscopic boundary condition relatingc to the normal gradient ofc at ∑ in terms of the interface structure(i.e., sink site distribution), and (3) evaluating the boundary condition, in the limit of very low super-saturation, for several idealized models of ledged or kinked interfaces. Two types of growth problems are then treated in the low supersaturation limit: a macrosteady-state problem, in which the interface grows into a finite slab of matrix in which the gradient of c is approximately uniform, and a time-dependent problem, in which an interface of fixed structure advances into a semi-infinite slab of uniform initial concentration. The results are compared to computer simulations and to previous work. Possible extensions of the approach to nonplanar interfaces are discussed. More... »

PAGES

1225-1233

References to SciGraph publications

  • 1982. Crystal Growth Kinetics in INTERFACIAL ASPECTS OF PHASE TRANSFORMATIONS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf02660654

    DOI

    http://dx.doi.org/10.1007/bf02660654

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1029767688


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/03", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Chemical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/09", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Engineering", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0306", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Physical Chemistry (incl. Structural)", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0912", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Materials Engineering", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0913", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mechanical Engineering", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, 15213, Pittsburgh, PA", 
              "id": "http://www.grid.ac/institutes/grid.147455.6", 
              "name": [
                "Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, 15213, Pittsburgh, PA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Mullins", 
            "givenName": "W. W.", 
            "id": "sg:person.013517176323.92", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013517176323.92"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/978-94-009-7870-6_13", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031286632", 
              "https://doi.org/10.1007/978-94-009-7870-6_13"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1991-06", 
        "datePublishedReg": "1991-06-01", 
        "description": "A macroscopic description is developed of the diffusion-limited migration of an interface on which only certain preferred interface sites(e.g., kinks or ledges) serve as diffusion sinks. The interface is assumed to be macroscopically flat and is represented by a mathematical plane, \u2211. The description is developed by (1) deriving a one-dimensional diffusion equation forc, the concentration averaged over planes parallel to \u2211, (2) establishing a macroscopic boundary condition relatingc to the normal gradient ofc at \u2211 in terms of the interface structure(i.e., sink site distribution), and (3) evaluating the boundary condition, in the limit of very low super-saturation, for several idealized models of ledged or kinked interfaces. Two types of growth problems are then treated in the low supersaturation limit: a macrosteady-state problem, in which the interface grows into a finite slab of matrix in which the gradient of c is approximately uniform, and a time-dependent problem, in which an interface of fixed structure advances into a semi-infinite slab of uniform initial concentration. The results are compared to computer simulations and to previous work. Possible extensions of the approach to nonplanar interfaces are discussed.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/bf02660654", 
        "inLanguage": "en", 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136292", 
            "issn": [
              "1073-5623", 
              "1543-1940"
            ], 
            "name": "Metallurgical and Materials Transactions A", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "6", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "22"
          }
        ], 
        "keywords": [
          "semi-infinite slab", 
          "nonplanar interface", 
          "macroscopic description", 
          "diffusion sink", 
          "boundary conditions", 
          "volume diffusion", 
          "finite slab", 
          "interface migration", 
          "kinked interface", 
          "initial concentration", 
          "interface", 
          "supersaturation limit", 
          "uniform initial concentration", 
          "idealized model", 
          "slab", 
          "mathematical plane", 
          "time-dependent problems", 
          "computer simulation", 
          "growth problems", 
          "kink motion", 
          "fixed structure", 
          "plane", 
          "simulations", 
          "diffusion", 
          "motion", 
          "sink", 
          "gradient", 
          "matrix", 
          "previous work", 
          "ledges", 
          "problem", 
          "limit", 
          "possible extensions", 
          "structure", 
          "description", 
          "conditions", 
          "concentration", 
          "work", 
          "model", 
          "FORC", 
          "results", 
          "terms", 
          "approach", 
          "types", 
          "extension", 
          "migration", 
          "OFC", 
          "diffusion-limited migration", 
          "one-dimensional diffusion equation forc", 
          "diffusion equation forc", 
          "equation forc", 
          "macroscopic boundary condition relatingc", 
          "boundary condition relatingc", 
          "condition relatingc", 
          "relatingc", 
          "normal gradient ofc", 
          "gradient ofc", 
          "low supersaturation limit", 
          "macrosteady-state problem"
        ], 
        "name": "Macroscopic description of interface migration by ledge and kink motion controlled by volume diffusion", 
        "pagination": "1225-1233", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1029767688"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/bf02660654"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/bf02660654", 
          "https://app.dimensions.ai/details/publication/pub.1029767688"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-01-01T18:06", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_254.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/bf02660654"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf02660654'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf02660654'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf02660654'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf02660654'


     

    This table displays all metadata directly associated to this object as RDF triples.

    133 TRIPLES      22 PREDICATES      89 URIs      77 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf02660654 schema:about anzsrc-for:03
    2 anzsrc-for:0306
    3 anzsrc-for:09
    4 anzsrc-for:0912
    5 anzsrc-for:0913
    6 schema:author N90c373ad2e73487f962c088c86b499c3
    7 schema:citation sg:pub.10.1007/978-94-009-7870-6_13
    8 schema:datePublished 1991-06
    9 schema:datePublishedReg 1991-06-01
    10 schema:description A macroscopic description is developed of the diffusion-limited migration of an interface on which only certain preferred interface sites(e.g., kinks or ledges) serve as diffusion sinks. The interface is assumed to be macroscopically flat and is represented by a mathematical plane, ∑. The description is developed by (1) deriving a one-dimensional diffusion equation forc, the concentration averaged over planes parallel to ∑, (2) establishing a macroscopic boundary condition relatingc to the normal gradient ofc at ∑ in terms of the interface structure(i.e., sink site distribution), and (3) evaluating the boundary condition, in the limit of very low super-saturation, for several idealized models of ledged or kinked interfaces. Two types of growth problems are then treated in the low supersaturation limit: a macrosteady-state problem, in which the interface grows into a finite slab of matrix in which the gradient of c is approximately uniform, and a time-dependent problem, in which an interface of fixed structure advances into a semi-infinite slab of uniform initial concentration. The results are compared to computer simulations and to previous work. Possible extensions of the approach to nonplanar interfaces are discussed.
    11 schema:genre article
    12 schema:inLanguage en
    13 schema:isAccessibleForFree false
    14 schema:isPartOf Neeb56000279e4e8fb2c42f1a3e247086
    15 Nf62eb321cd214ac79c7ee362ce6b0fdf
    16 sg:journal.1136292
    17 schema:keywords FORC
    18 OFC
    19 approach
    20 boundary condition relatingc
    21 boundary conditions
    22 computer simulation
    23 concentration
    24 condition relatingc
    25 conditions
    26 description
    27 diffusion
    28 diffusion equation forc
    29 diffusion sink
    30 diffusion-limited migration
    31 equation forc
    32 extension
    33 finite slab
    34 fixed structure
    35 gradient
    36 gradient ofc
    37 growth problems
    38 idealized model
    39 initial concentration
    40 interface
    41 interface migration
    42 kink motion
    43 kinked interface
    44 ledges
    45 limit
    46 low supersaturation limit
    47 macroscopic boundary condition relatingc
    48 macroscopic description
    49 macrosteady-state problem
    50 mathematical plane
    51 matrix
    52 migration
    53 model
    54 motion
    55 nonplanar interface
    56 normal gradient ofc
    57 one-dimensional diffusion equation forc
    58 plane
    59 possible extensions
    60 previous work
    61 problem
    62 relatingc
    63 results
    64 semi-infinite slab
    65 simulations
    66 sink
    67 slab
    68 structure
    69 supersaturation limit
    70 terms
    71 time-dependent problems
    72 types
    73 uniform initial concentration
    74 volume diffusion
    75 work
    76 schema:name Macroscopic description of interface migration by ledge and kink motion controlled by volume diffusion
    77 schema:pagination 1225-1233
    78 schema:productId Nabe14a11d7e742008db0c98296f37b2e
    79 Nfe4dcf20e84a4d1491e50c60c185c307
    80 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029767688
    81 https://doi.org/10.1007/bf02660654
    82 schema:sdDatePublished 2022-01-01T18:06
    83 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    84 schema:sdPublisher N5597f6f3965b41adad6b4d77c0dc4a6a
    85 schema:url https://doi.org/10.1007/bf02660654
    86 sgo:license sg:explorer/license/
    87 sgo:sdDataset articles
    88 rdf:type schema:ScholarlyArticle
    89 N5597f6f3965b41adad6b4d77c0dc4a6a schema:name Springer Nature - SN SciGraph project
    90 rdf:type schema:Organization
    91 N90c373ad2e73487f962c088c86b499c3 rdf:first sg:person.013517176323.92
    92 rdf:rest rdf:nil
    93 Nabe14a11d7e742008db0c98296f37b2e schema:name dimensions_id
    94 schema:value pub.1029767688
    95 rdf:type schema:PropertyValue
    96 Neeb56000279e4e8fb2c42f1a3e247086 schema:issueNumber 6
    97 rdf:type schema:PublicationIssue
    98 Nf62eb321cd214ac79c7ee362ce6b0fdf schema:volumeNumber 22
    99 rdf:type schema:PublicationVolume
    100 Nfe4dcf20e84a4d1491e50c60c185c307 schema:name doi
    101 schema:value 10.1007/bf02660654
    102 rdf:type schema:PropertyValue
    103 anzsrc-for:03 schema:inDefinedTermSet anzsrc-for:
    104 schema:name Chemical Sciences
    105 rdf:type schema:DefinedTerm
    106 anzsrc-for:0306 schema:inDefinedTermSet anzsrc-for:
    107 schema:name Physical Chemistry (incl. Structural)
    108 rdf:type schema:DefinedTerm
    109 anzsrc-for:09 schema:inDefinedTermSet anzsrc-for:
    110 schema:name Engineering
    111 rdf:type schema:DefinedTerm
    112 anzsrc-for:0912 schema:inDefinedTermSet anzsrc-for:
    113 schema:name Materials Engineering
    114 rdf:type schema:DefinedTerm
    115 anzsrc-for:0913 schema:inDefinedTermSet anzsrc-for:
    116 schema:name Mechanical Engineering
    117 rdf:type schema:DefinedTerm
    118 sg:journal.1136292 schema:issn 1073-5623
    119 1543-1940
    120 schema:name Metallurgical and Materials Transactions A
    121 schema:publisher Springer Nature
    122 rdf:type schema:Periodical
    123 sg:person.013517176323.92 schema:affiliation grid-institutes:grid.147455.6
    124 schema:familyName Mullins
    125 schema:givenName W. W.
    126 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013517176323.92
    127 rdf:type schema:Person
    128 sg:pub.10.1007/978-94-009-7870-6_13 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031286632
    129 https://doi.org/10.1007/978-94-009-7870-6_13
    130 rdf:type schema:CreativeWork
    131 grid-institutes:grid.147455.6 schema:alternateName Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, 15213, Pittsburgh, PA
    132 schema:name Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, 15213, Pittsburgh, PA
    133 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...