晶體生長(zhǎng)理論概述以過飽和度為推動(dòng)力，在過飽和溶液中存在晶體或者在介穩(wěn)區(qū)內(nèi)加入晶種，晶體開始生長(zhǎng)。晶體生長(zhǎng)一直是研究領(lǐng)域的熱點(diǎn)，在工業(yè)結(jié)晶中，有很多模型解釋晶體的生長(zhǎng)，常見的有統(tǒng)計(jì)表面能模型、形態(tài)學(xué)模型、二維成核模型和連續(xù)階模型等ADDINEN.CITE<EndNote><Cite><Author>Bennema</Author><Year>1976</Year><RecNum>50</RecNum><DisplayText><styleface="superscript">[89]</style></DisplayText><record><rec-number>50</rec-number><foreign-keys><keyapp="EN"db-id="wdpx5dzxppfdfpe9f2nppsp599xp9p2fdx9a"timestamp="1612352257">50</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Bennema,P.</author></authors></contributors><titles><title>TheoryandExperimentforCrystalGrowthfromSolution:ImplicationsforIndustrialCrystallization</title></titles><dates><year>1976</year></dates><urls></urls></record></Cite></EndNote>[89]。1.1晶體擴(kuò)散學(xué)說工業(yè)結(jié)晶常用擴(kuò)散學(xué)說解釋晶體生長(zhǎng)機(jī)理ADDINEN.CITE<EndNote><Cite><Author>丁緒淮</Author><Year>1985</Year><RecNum>19</RecNum><DisplayText><styleface="superscript">[66,90]</style></DisplayText><record><rec-number>19</rec-number><foreign-keys><keyapp="EN"db-id="wdpx5dzxppfdfpe9f2nppsp599xp9p2fdx9a"timestamp="1611496514">19</key></foreign-keys><ref-typename="Book">6</ref-type><contributors><authors><author>丁緒淮</author><author>談遒</author></authors></contributors><titles><title>工業(yè)結(jié)晶</title></titles><dates><year>1985</year></dates><publisher>化學(xué)工業(yè)出版社</publisher><urls></urls></record></Cite><Cite><Author>Myerson</Author><Year>2002</Year><RecNum>51</RecNum><record><rec-number>51</rec-number><foreign-keys><keyapp="EN"db-id="wdpx5dzxppfdfpe9f2nppsp599xp9p2fdx9a"timestamp="1612352522">51</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Myerson</author><author>Allan,S.</author></authors></contributors><titles><title>HandbookOfIndustrialCrystallization,2NdEdition</title></titles><pages>xi</pages><dates><year>2002</year></dates><urls></urls></record></Cite></EndNote>[66,90]。晶體生長(zhǎng)擴(kuò)散原理圖見圖2.3。（1）溶質(zhì)擴(kuò)散：將結(jié)晶的溶質(zhì)分子通過擴(kuò)散作用穿過晶核表面邊界層，由液相中轉(zhuǎn)移至晶體表面；（2）表面反應(yīng)：到達(dá)晶核表面的溶質(zhì)分子嵌入晶面，晶體長(zhǎng)大。結(jié)晶環(huán)境決定晶體的生長(zhǎng)過程的控制步驟是擴(kuò)散反應(yīng)還是表面反應(yīng)過程。圖2-3晶體生長(zhǎng)的擴(kuò)散原理示意圖Figure2-3Schematicdiagramofthediffusionprincipleofcrystalgrowth1.2晶體表面生長(zhǎng)機(jī)理表面熵因子ADDINEN.CITE<EndNote><Cite><Author>Barata</Author><Year>1996</Year><RecNum>52</RecNum><DisplayText><styleface="superscript">[91]</style></DisplayText><record><rec-number>52</rec-number><foreign-keys><keyapp="EN"db-id="wdpx5dzxppfdfpe9f2nppsp599xp9p2fdx9a"timestamp="1612355512">52</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Barata,PauloA.</author><author>Serrano,MariaL.</author></authors></contributors><titles><title>Salting-outprecipitationofpotassiumdihydrogenphosphate(KDP).I.Precipitationmechanism</title><secondary-title>JournalofCrystalGrowth</secondary-title></titles><periodical><full-title>JournalofCrystalGrowth</full-title></periodical><pages>361-369</pages><volume>160</volume><number>3-4</number><dates><year>1996</year></dates><urls></urls></record></Cite></EndNote>[91]常用來表示晶體表面或界面的生長(zhǎng)情況。f（a）當(dāng)f<3（b）當(dāng)3<f（c）當(dāng)f>5由此可知，表面熵因子越大，晶體表面生長(zhǎng)速率越慢，表面越光滑，晶體呈螺旋位錯(cuò)模式生長(zhǎng)；表面熵因子越小，表面越粗糙，晶體呈連續(xù)模式生長(zhǎng)。1.2晶體生長(zhǎng)動(dòng)力學(xué)模型根據(jù)大量的實(shí)驗(yàn)結(jié)果，結(jié)晶過程中的操作條件影響晶體動(dòng)力學(xué)生長(zhǎng)，包括過飽和度、溫度和攪拌等因素。根據(jù)晶體生長(zhǎng)速率與晶體粒度之間的關(guān)系，可將晶體生長(zhǎng)分為粒度無關(guān)生長(zhǎng)、粒度相關(guān)生長(zhǎng)及生長(zhǎng)分散三種類型。粒度無關(guān)生長(zhǎng)晶體的生長(zhǎng)速率與晶體的粒度無關(guān)，結(jié)晶過程中所有晶體以相同速率生長(zhǎng)，符合?L定律。G在實(shí)際應(yīng)用中通常采用如下的經(jīng)驗(yàn)關(guān)聯(lián)式：G=式中，G為生長(zhǎng)速率，Ea為生長(zhǎng)活化能，k粒度相關(guān)生長(zhǎng)晶體的生長(zhǎng)與晶體的粒徑有關(guān)，不同大小的結(jié)晶顆粒對(duì)晶體的生長(zhǎng)有影響，國(guó)內(nèi)外學(xué)者提出了各種經(jīng)驗(yàn)?zāi)Ｐ?，如下表所示。?-1粒度相關(guān)生長(zhǎng)模型ADDINEN.CITE<EndNote><Cite><Author>Mullin</Author><Year>2001</Year><RecNum>53</RecNum><DisplayText><styleface="superscript">[92]</style></DisplayText><record><rec-number>53</rec-number><foreign-keys><keyapp="EN"db-id="wdpx5dzxppfdfpe9f2nppsp599xp9p2fdx9a"timestamp="1612849110">53</key></foreign-keys><ref-typename="Book">6</ref-type><contributors><authors><author>Mullin</author><author>JW</author></authors></contributors><titles><title>Crystallization(FourthEdition)</title></titles><dates><year>2001</year></dates><urls></urls></record></Cite></EndNote>[92]Table2-1Granularityrelatedgrowthmodel模型名稱模型形式模型參數(shù)Bransom模型G=G0Canning模型G=G0，a1，aASL模型G=GMJ模型G={1?exp?[?a(L+C)]}aMJ2模型G=GStrong模型G=ε(3)生長(zhǎng)分散即相同粒度的晶體在相同的生長(zhǎng)條件下以不同的生長(zhǎng)速率生長(zhǎng)。通常用以下方程式描述生長(zhǎng)速率與分散系數(shù)的關(guān)系A(chǔ)DDINEN.CITE<EndNote><Cite><Author>Bourne</Author><Year>1978</Year><RecNum>54</RecNum><DisplayText><styleface="superscript">[93]</style></DisplayText><record><rec-number>54</rec-number><foreign-keys><keyapp="EN"db-id="wdpx5dzxppfdfpe9f2nppsp599xp9p2fdx9a"timestamp="1612851110">54</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Bourne,J.R.</author><author>Davey,R.J.</author><author>Mcculloch,J.</author></authors></contributors><titles><title>Thegrowthkineticsofhexamethylenetetraminecrystalsfromawater/acetonesolution</title><secondary-title>ChemicalEngineeringScience</secondary-title></titles><periodical><full-title>ChemicalEngineeringScience</full-title></periodical><pages>199-204</pages><volume>33</volume><number>2</number><dates><year>1978</year></dates><urls></urls></record></Cite></EndNote>[93]：D其中，Dg1.3晶體生長(zhǎng)動(dòng)力學(xué)在結(jié)晶過程中，晶體的成核與生長(zhǎng)是同時(shí)發(fā)生的，且互相爭(zhēng)奪溶液中的溶質(zhì)分子，分別測(cè)定各自速率十分困難。1971年，Randolph和Larson提出粒度衡算方程ADDINEN.CI