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  <front>
    <journal-meta>
      <journal-id journal-id-type="issn">2411-3336</journal-id>
      <journal-id journal-id-type="eissn">2541-9404</journal-id>
      <journal-title-group>
        <journal-title xml:lang="ru">Записки Горного института</journal-title>
        <journal-title xml:lang="en">Journal of Mining Institute</journal-title>
      </journal-title-group>
      <publisher>
        <publisher-name xml:lang="ru">Санкт-Петербургский горный университет императрицы Екатерины ΙΙ</publisher-name>
        <publisher-name xml:lang="en">Empress Catherine II Saint Petersburg Mining University</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id custom-type="pmi" pub-id-type="custom">pmi-6889</article-id>
      <article-id pub-id-type="uri">https://pmi.spmi.ru/pmi/article/view/6889</article-id>
      <article-categories>
        <subj-group subj-group-type="section-heading" xml:lang="ru">
          <subject>Минералогия и петрография</subject>
        </subj-group>
        <subj-group subj-group-type="section-heading" xml:lang="en">
          <subject>Mineralogy and petrography</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title xml:lang="en">Morphometry of aggregates and modeling of phase transition kinetics under metamorphism</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Морфометрия агрегатов и моделирование кинетики фазовых превращений при метаморфизме</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name name-style="eastern">
            <surname>Gulbin</surname>
            <given-names>Yu. L.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Гульбин</surname>
              <given-names>Ю. Л.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Gulbin</surname>
              <given-names>Yu. L.</given-names>
            </name>
          </name-alternatives>
          <email>gulbin@spmi.ru</email>
          <xref ref-type="aff" rid="aff1"/>
        </contrib>
        <aff-alternatives id="aff1">
          <aff>
            <institution xml:lang="ru">Санкт-Петербургский государственный горный институт (технический университет) (Россия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Saint-Petersburg State Mining Institute (Technical University) (Russia)</institution>
          </aff>
        </aff-alternatives>
      </contrib-group>
      <pub-date pub-type="epub" iso-8601-date="2009-12-11">
        <day>11</day>
        <month>12</month>
        <year>2009</year>
      </pub-date>
      <pub-date date-type="collection">
        <year>2009</year>
      </pub-date>
      <volume>183</volume>
      <fpage>174</fpage>
      <lpage>180</lpage>
      <history>
        <date date-type="received" iso-8601-date="2008-10-17">
          <day>17</day>
          <month>10</month>
          <year>2008</year>
        </date>
        <date date-type="accepted" iso-8601-date="2008-12-07">
          <day>07</day>
          <month>12</month>
          <year>2008</year>
        </date>
        <date date-type="rev-recd" iso-8601-date="2009-12-11">
          <day>11</day>
          <month>12</month>
          <year>2009</year>
        </date>
      </history>
      <permissions>
        <copyright-statement xml:lang="ru">© 2009 Ю. Л. Гульбин</copyright-statement>
        <copyright-statement xml:lang="en">© 2009 Yu. L. Gulbin</copyright-statement>
        <copyright-year>2009</copyright-year>
        <copyright-holder xml:lang="ru">Ю. Л. Гульбин</copyright-holder>
        <copyright-holder xml:lang="en">Yu. L. Gulbin</copyright-holder>
        <license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/4.0" xml:lang="ru">
          <license-p>Эта статья доступна по лицензии Creative Commons Attribution 4.0 International (CC BY 4.0)</license-p>
        </license>
        <license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/4.0" xml:lang="en">
          <license-p>This article is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0)</license-p>
        </license>
      </permissions>
      <self-uri xlink:type="simple" xlink:href="https://pmi.spmi.ru/pmi/article/view/6889">https://pmi.spmi.ru/pmi/article/view/6889</self-uri>
      <abstract xml:lang="ru">
        <p>Рассмотрены некоторые общие закономерности, связывающие структуру метаморфических пород и механизмы фазовых реакций. К числу подобных закономерностей следует отнести влияние кинетики нуклеации и роста кристаллических зародышей на гранулометрические характеристики агрегатов. Дан краткий обзор существующих моделей генезиса гранулометрических распределений, на примере гранатов метапелитов проанализированы кинетические зависимости и факторы метаморфической кристаллизации, включая явление лавинообразной нуклеации зародышей при конечном перегреве пород и рост порфиробластов в условиях диффузионного лимита. Продемонстрированы новые подходы к моделированию природных гранулометрических кривых.</p>
      </abstract>
      <abstract xml:lang="en">
        <p>The paper discusses some general relations between the structure of metamorphic rocks and mechanisms of phase reactions. Among these relations is the influence of nucleation and growth of kinetics on the crystal size distribution. A brief overview is made of theoretical models which have been proposed to explain granulometric properties of rocks, and kinetic laws and factors on the metamorphic crystallization are considered by the example of metapelitic garnets, including the phenomenon of avalanche nucleation at finite overheating as well as the growth of porphyroblasts under diffusion-limited conditions. As a result, a new approach to modeling of native granulometric curves is presented.</p>
      </abstract>
      <kwd-group xml:lang="ru">
        <title>Ключевые слова</title>
        <kwd>гранат</kwd>
        <kwd>гранулометрическое распределение</kwd>
        <kwd>зональность</kwd>
        <kwd>кинетика</kwd>
        <kwd>кристаллизация</kwd>
        <kwd>метаморфический агрегат</kwd>
        <kwd>моделирование</kwd>
        <kwd>морфометрия</kwd>
      </kwd-group>
      <kwd-group xml:lang="en">
        <title>Keywords</title>
        <kwd>crystallization</kwd>
        <kwd>garnet</kwd>
        <kwd>grain size distribution</kwd>
        <kwd>kinetics</kwd>
        <kwd>metamorphic aggregate</kwd>
        <kwd>modeling</kwd>
        <kwd>morphometry</kwd>
        <kwd>zoning</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body/>
  <back>
    <ref-list>
      <ref id="ref1">
        <label>1</label>
        <mixed-citation xml:lang="ru">Гульбин Ю.Л. Компьютерное моделирование и оценка точности стереологических реконструкций при гранулометрическом анализе минеральных агрегатов // Обогащение руд. 2007. N 3. C. 24-28.</mixed-citation>
        <mixed-citation xml:lang="en">Gulbin Yu.L. On estimation and hypothesis testing of the grain size distribution by the Saltykov method // Image. Anal. Stereol. 2008. V.27, pp.163-174</mixed-citation>
      </ref>
      <ref id="ref2">
        <label>2</label>
        <mixed-citation xml:lang="ru">Гульбин Ю.Л. Исследование кинетики порфиробластеза (на примере гранатов Северного Приладожья) / Ю.Л. Гульбин, Е.А. Сорокина, И.М. Гайдамако // Труды III Ферсмановской сессии (Апатиты, 27-28 апреля 2006 г.). Апатиты: Изд-во K&amp;M, 2006. С. 116-118.</mixed-citation>
        <mixed-citation xml:lang="en">Gulbin Yu.L., Sorokina E.A., Gaidamako I.M. Investigation of porphyroblast forming (on an example of garnets from </mixed-citation>
      </ref>
      <ref id="ref3">
        <label>3</label>
        <mixed-citation xml:lang="ru">Ридли Дж. Роль кинетики в развитии метаморфических моноструктур минералов / Ридли Дж., Томпсон А.Б. // Взаимодействие флюид – порода при метаморфизме / Под ред Дж.Уолтера и Б.Вуда. М.: Мир, 1989. С. 182-224.</mixed-citation>
        <mixed-citation xml:lang="en">North Ladoga region) // Proc. III Fersman session. Apatity, Russia, 27-28 April, 2006. Apatity, 2006, pp. 116-118.</mixed-citation>
      </ref>
      <ref id="ref4">
        <label>4</label>
        <mixed-citation xml:lang="ru">Carlson W.D. The significance of intergranular diffusion to the mechanisms and kinetics of porphyroblast crystallization // Contrib. Mineral. Petrol. 1989. V.103, рр. 1-24.</mixed-citation>
        <mixed-citation xml:lang="en">Ridley J., Thompson A.B. The role of mineral kinetics in the development of metamorphic microtextures / </mixed-citation>
      </ref>
      <ref id="ref5">
        <label>5</label>
        <mixed-citation xml:lang="ru">Denison C. Three-dimensional quantitative textural analysis of metamorphic rocks using high-resolution computed X-ray tomography. Part II: Application to natural samples / C.Denison, W.D.Carlson // J.Metamorph. Geol. 1997. V.15, pp. 45-57.</mixed-citation>
        <mixed-citation xml:lang="en">Fluid-rock interactions during metamorphism. WaltherJ.V., Wood B.J., Eds. (Advances in Physical Geochemistry, V.5. New York: Springer-Verlag, 1986, pp.154-193.</mixed-citation>
      </ref>
      <ref id="ref6">
        <label>6</label>
        <mixed-citation xml:lang="ru">Eberl D.D. On geological interpretation of crystal size distributions: Constant vs. proportionate growth / D.D.Eberl, D.E.Kile, V.A.Drits// Am. Miner. 2002. V.87, pp.1235-1241.</mixed-citation>
        <mixed-citation xml:lang="en">Carlson W.D. The significance of intergranular diffusion to the mechanisms and kinetics of porphyroblast crystallization // Contrib. Mineral. Petrol. 1989. V.103, pp.1-24.</mixed-citation>
      </ref>
      <ref id="ref7">
        <label>7</label>
        <mixed-citation xml:lang="ru">Finlay C.A. Evidence for differences in growth rate among garnets in pelitic schists from Northern Sutherland, Scotland / C.A.Finlay, A.Kerr // Miner. Mag. 1987. V.51, pp. 569-576.</mixed-citation>
        <mixed-citation xml:lang="en">Denison C., Carlson W.D. Three-dimensional quantitative textural analysis of metamorphic rocks using </mixed-citation>
      </ref>
      <ref id="ref8">
        <label>8</label>
        <mixed-citation xml:lang="ru">Galwey A.K. Crystal size frequency distribution of garnets in some analysed metamorphic rocks from Mallaig, Inverness, Scotland / A.K.Galwey, K.A.Jones // Geol. Mag. 1966. V.103, pp.143-152.</mixed-citation>
        <mixed-citation xml:lang="en">high-resolution computed X-ray tomography. Part II: Application to natural samples // J. Metamorph. Geol. 1997. </mixed-citation>
      </ref>
      <ref id="ref9">
        <label>9</label>
        <mixed-citation xml:lang="ru">Higgins M.D. Measurement of crystal size distributions // Am. Mineral. 2000. V.85, pp.1105-1116.</mixed-citation>
        <mixed-citation xml:lang="en">V.15, pp. 45-57.</mixed-citation>
      </ref>
      <ref id="ref10">
        <label>10</label>
        <mixed-citation xml:lang="ru">Jones K.A. A study of possible factors concerning garnet formation in rocks from Ardara, Co. Donegal, Ireland / K.A.Jones, A.K.Galwey// Geol. Mag. 1964. V.101, pp.76-93.</mixed-citation>
        <mixed-citation xml:lang="en">Eberl D.D., Kile D.E., Drits V.A. On geological interpretation of crystal size distributions: Constant vs. proportionate growth // Am. Miner. 2002. V. 87, pp.1235-1241.</mixed-citation>
      </ref>
      <ref id="ref11">
        <label>11</label>
        <mixed-citation xml:lang="ru">Kaneko Y. Crystal-size distributions of garnets in metapelites from the northeastern Bushveld contact aureole, South Africa / Y.Kaneko, T.Tsunogae, T.Miyano // Am Mineral. 2005. V.90, pp.1422-1433.</mixed-citation>
        <mixed-citation xml:lang="en">Finlay C.A., Kerr A. Evidence for differences in growth rate among garnets in pelitic schists from Northern Sutherland, Scotland // Miner. Mag. 1987. V.51, pp. 569-576.</mixed-citation>
      </ref>
      <ref id="ref12">
        <label>12</label>
        <mixed-citation xml:lang="ru">Kile D.E. On the origin of size-dependent and size-independent crystal growth: Influence of advection and diffusion / D.E.Kile, D.D.Eberl // Am. Miner. 2003. V.88, pp.1514-1521.</mixed-citation>
        <mixed-citation xml:lang="en">Galwey A.K., Jones K.A. Crystal size frequency distribution of garnets in some analysed metamorphic rocks from Mallaig, Inverness, Scotland. Geol. Mag. 1966. V.103, pp.143-152.</mixed-citation>
      </ref>
      <ref id="ref13">
        <label>13</label>
        <mixed-citation xml:lang="ru">Kretz R. Grain-size distribution for certain metamorphic minerals in relation to nucleation and growth // J. Geol. 1966. V.74, pp.147-173.</mixed-citation>
        <mixed-citation xml:lang="en">Higgins M.D. Measurement of crystal size distributions // Am. Mineral. 2000. V.85. pp.1105-1116.</mixed-citation>
      </ref>
      <ref id="ref14">
        <label>14</label>
        <mixed-citation xml:lang="ru">Kretz R. Kinetics of the crystallization of garnet at two localities near Yellowknife // Can. Mineral. 1973. V.12, pp. 1-20.</mixed-citation>
        <mixed-citation xml:lang="en">Jones K.A., Galwey A.K. A study of possible factors concerning garnet formation in rocks from Ardara, Co. Donegal, Ireland // Geol. Mag. 1964. V.101, pp.76-93.</mixed-citation>
      </ref>
      <ref id="ref15">
        <label>15</label>
        <mixed-citation xml:lang="ru">Kretz R. Some models for the rate of crystallization of garnet in metamorphic rocks // Lithos. 1974. V.7, pp. 123-131.</mixed-citation>
        <mixed-citation xml:lang="en">Kaneko Y., Tsunogae T., Miyano T. Crystal-size distributions of garnets in metapelites from the northeastern Bushveld contact aureole, South Africa // Am Mineral. 2005. V.90, pp.1422-1433.</mixed-citation>
      </ref>
      <ref id="ref16">
        <label>16</label>
        <mixed-citation xml:lang="ru">Marsh B.D. Crystal size distribution (CSD) in rocks and kinetics and dynamics of crystallization. I. Theory // Contrib. Mineral. Petrol. 1988. V.99, pp.277-291.</mixed-citation>
        <mixed-citation xml:lang="en">Kile D.E., Eberl D.D. On the origin of sizedependent and size-independent crystal growth: Influence of advection and diffusion // Am. Miner. 2003. V.88, pp.1514-1521.</mixed-citation>
      </ref>
      <ref id="ref17">
        <label>17</label>
        <mixed-citation xml:lang="ru">Marsh B.D. On the interpretation of crystal size distributions in magmatic systems // J.Petrol. 1998. V.39, pp. 553-599.</mixed-citation>
        <mixed-citation xml:lang="en">Kretz R. Grain-size distribution for certain metamorphic minerals in relation to nucleation and growth // J. Geol. 1966. V.74, pp. 147-173.</mixed-citation>
      </ref>
      <ref id="ref18">
        <label>18</label>
        <mixed-citation xml:lang="ru">Sahagian D.L. 3D particle size distributions from 2D observations: stereology for natural applications / D.L.Sahagian, A.A.Proussevitch // J. Volcanol. Geotherm. Res. 1998. V.84, pp.173–196.</mixed-citation>
        <mixed-citation xml:lang="en">Kretz R. Kinetics of the crystallization of garnet at two localities near Yellowknife // Can. Mineral. 1973. V.12, pp.1-20.</mixed-citation>
      </ref>
      <ref id="ref19">
        <label>19</label>
        <mixed-citation xml:lang="ru">Zeh A. Crystal size distribution (CSD) and textural evolution of accessory apatite, titanite and allanite during four stages of metamorphism: an example from the Moine Supergroup, Scotland // J. Petrol. 2004. V.45, pp. 2101-2132.</mixed-citation>
        <mixed-citation xml:lang="en">Kretz R. Some models for the rate of crystallization of garnet in metamorphic rocks // Lithos. 1974. V.7, pp. </mixed-citation>
      </ref>
    </ref-list>
  </back>
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