{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T23:10:05Z","timestamp":1787008205666,"version":"build-2736575974"},"reference-count":21,"publisher":"IOP Publishing","issue":"3","license":[{"start":{"date-parts":[[2017,7,24]],"date-time":"2017-07-24T00:00:00Z","timestamp":1500854400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2017,7,24]],"date-time":"2017-07-24T00:00:00Z","timestamp":1500854400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Balsells foundation"},{"DOI":"10.13039\/501100006188","name":"Einstein Foundation Berlin","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100006188","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000001","name":"US National Science Foundation","doi-asserted-by":"crossref","award":["CMMI-1311721"],"award-info":[{"award-number":["CMMI-1311721"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["2D Mater."],"published-print":{"date-parts":[[2017,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Experiments on graphene growth through chemical vapor deposition (CVD) involving methane (CH\n                    <jats:sub>4<\/jats:sub>\n                    ) and hydrogen (H\n                    <jats:sub>2<\/jats:sub>\n                    ) gases reveal a complex shape evolution and a non-monotonic dependence on the partial pressure of H\n                    <jats:sub>2<\/jats:sub>\n                    (\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mstyle displaystyle=\"false\">\n                          <mml:mstyle displaystyle=\"false\">\n                            <mml:msub>\n                              <mml:mrow>\n                                <mml:mi>p<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mrow>\n                                <mml:mstyle displaystyle=\"false\">\n                                  <mml:msub>\n                                    <mml:mrow>\n                                      <mml:mi mathvariant=\"normal\">H<\/mml:mi>\n                                    <\/mml:mrow>\n                                    <mml:mn>2<\/mml:mn>\n                                  <\/mml:msub>\n                                <\/mml:mstyle>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                          <\/mml:mstyle>\n                        <\/mml:mstyle>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    ). To explain these intriguing observations, we develop a microkinetic model for the stepwise decomposition of CH\n                    <jats:sub>4<\/jats:sub>\n                    into mobile radicals and consider two possible mechanisms of attachment to graphene crystals: CH radicals to hydrogen-decorated edges of the crystals and C radicals to bare crystal edges. We derive an effective mass flux and an effective kinetic coefficient, both of which depend on\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mstyle displaystyle=\"false\">\n                          <mml:mstyle displaystyle=\"false\">\n                            <mml:msub>\n                              <mml:mrow>\n                                <mml:mi>p<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mrow>\n                                <mml:mstyle displaystyle=\"false\">\n                                  <mml:msub>\n                                    <mml:mrow>\n                                      <mml:mi mathvariant=\"normal\">H<\/mml:mi>\n                                    <\/mml:mrow>\n                                    <mml:mn>2<\/mml:mn>\n                                  <\/mml:msub>\n                                <\/mml:mstyle>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                          <\/mml:mstyle>\n                        <\/mml:mstyle>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    , and incorporate these into a phase field model. The model reproduces both the non-monotonic dependence on\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mstyle displaystyle=\"false\">\n                          <mml:mstyle displaystyle=\"false\">\n                            <mml:msub>\n                              <mml:mrow>\n                                <mml:mi>p<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mrow>\n                                <mml:mstyle displaystyle=\"false\">\n                                  <mml:msub>\n                                    <mml:mrow>\n                                      <mml:mi mathvariant=\"normal\">H<\/mml:mi>\n                                    <\/mml:mrow>\n                                    <mml:mn>2<\/mml:mn>\n                                  <\/mml:msub>\n                                <\/mml:mstyle>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                          <\/mml:mstyle>\n                        <\/mml:mstyle>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    and the characteristic shapes of graphene crystals observed in experiments. At small\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mstyle displaystyle=\"false\">\n                          <mml:mstyle displaystyle=\"false\">\n                            <mml:msub>\n                              <mml:mrow>\n                                <mml:mi>p<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mrow>\n                                <mml:mstyle displaystyle=\"false\">\n                                  <mml:msub>\n                                    <mml:mrow>\n                                      <mml:mi mathvariant=\"normal\">H<\/mml:mi>\n                                    <\/mml:mrow>\n                                    <mml:mn>2<\/mml:mn>\n                                  <\/mml:msub>\n                                <\/mml:mstyle>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                          <\/mml:mstyle>\n                        <\/mml:mstyle>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    , growth is limited by the kinetics of attachment while at large\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mstyle displaystyle=\"false\">\n                          <mml:mstyle displaystyle=\"false\">\n                            <mml:msub>\n                              <mml:mrow>\n                                <mml:mi>p<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mrow>\n                                <mml:mstyle displaystyle=\"false\">\n                                  <mml:msub>\n                                    <mml:mrow>\n                                      <mml:mi mathvariant=\"normal\">H<\/mml:mi>\n                                    <\/mml:mrow>\n                                    <mml:mn>2<\/mml:mn>\n                                  <\/mml:msub>\n                                <\/mml:mstyle>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                          <\/mml:mstyle>\n                        <\/mml:mstyle>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    growth is limited because the effective mass flux is small. We also derive a simple analytical model that captures the non-monotone behavior, enables the two mechanisms of attachment to be distinguished and provides guidelines for CVD growth of defect-free 2D crystals.\n                  <\/jats:p>","DOI":"10.1088\/2053-1583\/aa74f1","type":"journal-article","created":{"date-parts":[[2017,5,25]],"date-time":"2017-05-25T07:15:39Z","timestamp":1495696539000},"page":"031010","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["H\n                    <sub>2<\/sub>\n                    -dependent attachment kinetics and shape evolution in chemical vapor deposition graphene growth"],"prefix":"10.1088","volume":"4","author":[{"given":"Esteban","family":"Meca","sequence":"first","affiliation":[{"name":"University of California"},{"name":"Weierstrass Institute"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vivek B","family":"Shenoy","sequence":"additional","affiliation":[{"name":"University of Pennsylvania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John","family":"Lowengrub","sequence":"additional","affiliation":[{"name":"University of California"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2017,7,24]]},"reference":[{"key":"tdmaa74f1bib001","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1039\/C2NR32629A","type":"journal-article","volume":"5","author":"Edwards","year":"2013","journal-title":"Nanoscale"},{"key":"tdmaa74f1bib002","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1038\/nature12385","type":"journal-article","volume":"499","author":"Geim","year":"2013","journal-title":"Nature"},{"key":"tdmaa74f1bib003","doi-asserted-by":"publisher","first-page":"2898","DOI":"10.1021\/nn400280c","type":"journal-article","volume":"7","author":"Butler","year":"2013","journal-title":"ACS Nano"},{"key":"tdmaa74f1bib004","doi-asserted-by":"publisher","first-page":"768","DOI":"10.1038\/nnano.2014.207","type":"journal-article","volume":"9","author":"Fiori","year":"2014","journal-title":"Nat. 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All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2016-12-21","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2017-05-22","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2017-07-24","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}