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<title>Crystallization</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Crystallization</span></span>

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</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="Crystallization_(disambiguation)" class="mw-disambig" title="Crystallization (disambiguation)">Crystallization (disambiguation)</a>.</div>

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</style><table class="infobox hlist" style="width:18em; text-align:center; font-size:95%;"><tbody><tr><th colspan="2" class="infobox-above" style="padding-bottom:0.3em; background:transparent; line-height:1.1em; font-size:125%; font-weight:bold;"></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File"></span></td></tr><tr><th colspan="2" class="infobox-header" style="background:#E7C6A5;">Fundamentals</th></tr><tr><td colspan="2" class="infobox-full-data" style="line-height:1.4em;">

<ul><li><a href="Crystal" title="Crystal">Crystal</a></li>

<li><a href="Crystal_structure" title="Crystal structure">Crystal structure</a></li>

<li><a href="Nucleation" title="Nucleation">Nucleation</a></li></ul>

</td></tr><tr><th colspan="2" class="infobox-header" style="background:#E7C6A5;">Concepts</th></tr><tr><td colspan="2" class="infobox-full-data" style="line-height:1.4em;">

<ul>

<li><a href="Crystal_growth" title="Crystal growth">Crystal growth</a></li>

<li><a href="Recrystallization_(chemistry)" title="Recrystallization (chemistry)">Recrystallization</a></li>

<li><a href="Seed_crystal" title="Seed crystal">Seed crystal</a></li>

<li><a href="Protocrystalline" title="Protocrystalline">Protocrystalline</a></li>

<li><a href="Single_crystal" title="Single crystal">Single crystal</a></li></ul>

</td></tr><tr><th colspan="2" class="infobox-header" style="background:#E7C6A5;">Methods and technology</th></tr><tr><td colspan="2" class="infobox-full-data" style="line-height:1.4em;">

<ul><li><a href="Boule_(crystal)" title="Boule (crystal)">Boules</a></li>

<li><a href="Bridgman%E2%80%93Stockbarger_method" title="Bridgman–Stockbarger method">Bridgman–Stockbarger method</a></li>

<li><a href="Van_Arkel%E2%80%93de_Boer_process" title="Van Arkel–de Boer process">Van Arkel–de Boer process</a></li>

<li><a href="Czochralski_method" title="Czochralski method">Czochralski method</a></li>

<li><a href="Epitaxy" title="Epitaxy">Epitaxy</a></li>

<li><a href="Flux_method" title="Flux method">Flux method</a></li>

<li><a href="Fractional_crystallization_(chemistry)" title="Fractional crystallization (chemistry)">Fractional crystallization</a></li>

<li><a href="Fractional_freezing" title="Fractional freezing">Fractional freezing</a></li>

<li><a href="Hydrothermal_synthesis" title="Hydrothermal synthesis">Hydrothermal synthesis</a></li>

<li><a href="Kyropoulos_method" title="Kyropoulos method">Kyropoulos method</a></li>

<li><a href="Laser-heated_pedestal_growth" title="Laser-heated pedestal growth">Laser-heated pedestal growth</a></li>

<li><a href="Lely_method" title="Lely method">Lely method</a></li>

<li><a href="Micro-pulling-down" title="Micro-pulling-down">Micro-pulling-down</a></li>

<li><a href="Shaping_processes_in_crystal_growth" title="Shaping processes in crystal growth">Shaping processes in crystal growth</a></li>

<li><a href="Skull_crucible" title="Skull crucible">Skull crucible</a></li>

<li><a href="Verneuil_method" title="Verneuil method">Verneuil method</a></li>

<li><a href="Zone_melting" title="Zone melting">Zone melting</a></li></ul>

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<p><b>Crystallization</b> is a process that leads to solids with highly organized <a href="Atom" title="Atom">atoms</a> or <a href="Molecule" title="Molecule">molecules</a>, i.e. a <a href="Crystal" title="Crystal">crystal</a>. The ordered nature of a crystalline solid can be contrasted with <a href="Amorphous_solids" class="mw-redirect" title="Amorphous solids">amorphous solids</a> in which atoms or molecules lack regular organization. Crystallization can occur by various routes including <a href="Precipitation_(chemistry)" title="Precipitation (chemistry)">precipitation</a> from solution, <a href="Freezing" title="Freezing">freezing</a> of a <a href="Liquid" title="Liquid">liquid</a>, or <a href="Deposition_(phase_transition)" title="Deposition (phase transition)">deposition</a> from a gas. Attributes of the resulting crystal can depend largely on factors such as <a href="Temperature" title="Temperature">temperature</a>, air <a href="Pressure" title="Pressure">pressure</a>, cooling rate, or <a href="Solution_(chemistry)" title="Solution (chemistry)">solute concentration</a>.

</p><p> occurs in two major steps. The first is <a href="Nucleation" title="Nucleation">nucleation</a>, the appearance of a crystalline phase from either a <a href="Supercooling" title="Supercooling">supercooled</a> liquid or a <a href="Supersaturation" title="Supersaturation">supersaturated</a> solvent. The second step is known as <a href="Crystal_growth" title="Crystal growth">crystal growth</a>, which is the increase in the size of particles and leads to a crystal state. An important feature of this step is that loose particles form layers at the crystal's surface and lodge themselves into open inconsistencies such as pores, cracks, etc.

</p><p> is also a chemical solid–liquid separation technique, in which <a href="Mass_transfer" title="Mass transfer">mass transfer</a> of a solute from the liquid solution to a pure solid crystalline phase occurs. In <a href="Chemical_engineering" title="Chemical engineering">chemical engineering</a>, crystallization occurs in a <a href="Crystallizer" class="mw-redirect" title="Crystallizer">crystallizer</a>. Crystallization is therefore related to <a href="Precipitation_(chemistry)" title="Precipitation (chemistry)">precipitation</a>, although the result is not <a href="Amorphous_solid" title="Amorphous solid">amorphous</a> or disordered, but a crystal.

</p>

<div class="mw-heading mw-heading2"><h2 id="Process">Process</h2></div>

<div role="note" class="hatnote navigation-not-searchable">See also: <a class="mw-selflink-fragment" href="#Dynamics">Crystallization § Dynamics</a></div>

<p>The crystallization process consists of two major events, <i><a href="Nucleation" title="Nucleation">nucleation</a></i> and <i><a href="Crystal_growth" title="Crystal growth">crystal growth</a></i> which are driven by thermodynamic properties as well as chemical properties.

<i>Nucleation</i> is the step where the solute molecules or atoms dispersed in the <a href="Solvent" title="Solvent">solvent</a> start to gather into clusters, on the microscopic scale (elevating solute concentration in a small region), that become stable under the current operating conditions. These stable clusters constitute the nuclei. Therefore, the clusters need to reach a critical size in order to become stable nuclei. Such critical size is dictated by many different factors (<a href="Temperature" title="Temperature">temperature</a>, <a href="Supersaturation" title="Supersaturation">supersaturation</a>, etc.). It is at the stage of nucleation that the atoms or molecules arrange in a defined and <a href="Frequency" title="Frequency">periodic</a> manner that defines the <a href="Crystal_structure" title="Crystal structure">crystal structure</a> – note that "crystal structure" is a special term that refers to the relative arrangement of the atoms or molecules, not the <a href="Macroscopic_scale" title="Macroscopic scale">macroscopic</a> properties of the crystal (size and shape), although those are a result of the internal crystal structure.

</p><p>The <i>crystal growth</i> is the subsequent size increase of the nuclei that succeed in achieving the critical cluster size. Crystal growth is a dynamic process occurring in <a href="Equilibrium_chemistry" title="Equilibrium chemistry">equilibrium</a> where solute molecules or atoms precipitate out of solution, and dissolve back into solution. <a href="Supersaturation" title="Supersaturation">Supersaturation</a> is one of the driving forces of crystallization, as the solubility of a species is an <a href="Equilibrium_chemistry" title="Equilibrium chemistry">equilibrium</a> process quantified by K<sub>sp</sub>. Depending upon the conditions, either nucleation or growth may be predominant over the other, dictating crystal size.

</p><p>Many compounds have the ability to crystallize with some having different crystal structures, a phenomenon called <a href="Polymorphism_(materials_science)" class="mw-redirect" title="Polymorphism (materials science)">polymorphism</a>. Certain polymorphs may be <a href="Metastable" class="mw-redirect" title="Metastable">metastable</a>, meaning that although it is not in <a href="Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a>, it is kinetically stable and requires some input of energy to initiate a transformation to the equilibrium phase. Each polymorph is in fact a different thermodynamic <a href="Solid" title="Solid">solid</a> state and crystal polymorphs of the same compound exhibit different physical properties, such as dissolution rate, shape (angles between facets and facet growth rates), melting point, etc. For this reason, <a href="Polymorphism_(biology)" title="Polymorphism (biology)">polymorphism</a> is of major importance in industrial manufacture of crystalline products. Additionally, crystal phases can sometimes be interconverted by varying factors such as <a href="Temperature" title="Temperature">temperature</a>, such as in the transformation of <a href="Anatase" title="Anatase">anatase</a> to <a href="Rutile" title="Rutile">rutile</a> phases of <a href="Titanium_dioxide" title="Titanium dioxide">titanium dioxide</a>.

</p>

<div class="mw-heading mw-heading2"><h2 id="In_nature">In nature</h2></div>

<p>There are many examples of natural process that involve crystallization.

</p><p><a href="Geological_time_scale" class="mw-redirect" title="Geological time scale">Geological time scale</a> process examples include:

</p>

<ul><li>Natural (mineral) crystal formation (see also <a href="Gemstone" title="Gemstone">gemstone</a>);</li>

<li><a href="Stalactite" title="Stalactite">Stalactite</a>/<a href="Stalagmite" title="Stalagmite">stalagmite</a>, rings formation;</li></ul>

<p><a href="Human_scale" title="Human scale">Human time scale</a> process examples include:

</p>

<ul><li><a href="Snowflake" title="Snowflake">Snow flakes</a> formation;</li>

<li><a href="Honey" title="Honey">Honey</a> crystallization (nearly all types of honey crystallize).</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Methods">Methods</h2></div>

<p>Crystals can be formed by various methods, such as: cooling, evaporation, addition of a second solvent to reduce the solubility of the solute (technique known as <a href="Antisolvent" class="mw-redirect" title="Antisolvent">antisolvent</a> or drown-out), solvent layering, sublimation, changing the cation or anion, as well as other methods.

</p><p>The formation of a supersaturated solution does not guarantee crystal formation, and often a seed crystal or scratching the glass is required to form nucleation sites.

</p><p>A typical laboratory technique for crystal formation is to dissolve the solid in a solution in which it is partially soluble, usually at high temperatures to obtain supersaturation. The hot mixture is then filtered to remove any insoluble impurities. The filtrate is allowed to slowly cool. Crystals that form are then filtered and washed with a solvent in which they are not soluble, but is miscible with the <a href="Mother_liquor" title="Mother liquor">mother liquor</a>. The process is then repeated to increase the purity in a technique known as recrystallization.

</p><p>For biological molecules in which the solvent channels continue to be present to retain the three dimensional structure intact, microbatch<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> crystallization under oil and vapor diffusion<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> have been the common methods.

</p>

<div class="mw-heading mw-heading3"><h3 id="Typical_equipment">Typical equipment</h3></div>

<p>Equipment for the <a href="#Main_crystallization_processes">main industrial processes for crystallization</a>.

</p>

<ol><li><i>Tank crystallizers</i>. Tank crystallization is an old method still used in some specialized cases. Saturated solutions, in tank crystallization, are allowed to cool in open tanks. After a period of time the mother liquor is drained and the crystals removed. Nucleation and size of crystals are difficult to control.<sup id="cite_ref-TankCrystallizerJinzong_3-0" class="reference"><a href="#cite_note-TankCrystallizerJinzong-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Typically, labor costs are very high.</li>

<li><i>Mixed-Suspension, Mixed-Product-Removal (MSMPR)</i>: MSMPR is used for much larger scale inorganic crystallization. MSMPR can crystalize solutions in a continuous manner.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li></ol>

<div class="mw-heading mw-heading2"><h2 id="Thermodynamic_view">Thermodynamic view</h2></div>

<p>The crystallization process appears to violate the <a href="Second_principle_of_thermodynamics" class="mw-redirect" title="Second principle of thermodynamics">second principle of thermodynamics</a>. Whereas most processes that yield more orderly results are achieved by applying heat, crystals usually form at lower temperatures – especially by <a href="Supercooling" title="Supercooling">supercooling</a>. However, the release of the heat of fusion during crystallization causes the entropy of the universe to increase, thus this principle remains unaltered.

</p><p>The molecules within a pure, <i>perfect crystal</i>, when heated by an external source, will become liquid. This occurs at a sharply defined temperature (different for each type of crystal). As it liquifies, the complicated architecture of the crystal collapses. Melting occurs because the <a href="Entropy" title="Entropy">entropy</a> (<i>S</i>) gain in the system by spatial randomization of the molecules has overcome the <a href="Enthalpy" title="Enthalpy">enthalpy</a> (<i>H</i>) loss due to breaking the crystal packing forces:

</p>

<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T(S_{\text{liquid}}-S_{\text{solid}})>H_{\text{liquid}}-H_{\text{solid}},}">

<msub>

<mtext>liquid</mtext>

</mrow>

</msub>

<msub>

<mtext>solid</mtext>

</mrow>

</msub>

<msub>

<mtext>liquid</mtext>

</mrow>

</msub>

<msub>

<mtext>solid</mtext>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle T(S_{\text{liquid}}-S_{\text{solid}})>H_{\text{liquid}}-H_{\text{solid}},}</annotation>

</semantics>

</math></span><img src="./73b7f534dd075e3fbf152906ada7e0dad75ad5d5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:35.246ex; height:3.009ex;" alt="{\displaystyle T(S_{\text{liquid}}-S_{\text{solid}})>H_{\text{liquid}}-H_{\text{solid}},}" loading="lazy"></span></dd>

<msub>

<mtext>liquid</mtext>

</mrow>

</msub>

<msub>

<mtext>solid</mtext>

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<annotation encoding="application/x-tex">{\displaystyle G_{\text{liquid}}<G_{\text{solid}}.}</annotation>

</semantics>

</math></span><img src="./ea4d2cf805a6668e81cd4e33485a41abf97e971c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.23ex; height:2.843ex;" alt="{\displaystyle G_{\text{liquid}}<G_{\text{solid}}.}" loading="lazy"></span></dd></dl>

<p>Regarding crystals, there are no exceptions to this rule. Similarly, when the molten crystal is cooled, the molecules will return to their crystalline form once the temperature falls beyond the turning point. This is because the thermal randomization of the surroundings compensates for the loss of entropy that results from the reordering of molecules within the system. Such liquids that crystallize on cooling are the exception rather than the rule.

</p><p>The nature of the crystallization process is governed by both thermodynamic and kinetic factors, which can make it highly variable and difficult to control. Factors such as impurity level, mixing regime, vessel design, and cooling profile can have a major impact on the size, number, and shape of crystals produced.

</p>

<div class="mw-heading mw-heading2"><h2 id="Dynamics">Dynamics</h2></div>

<p>As mentioned above, a crystal is formed following a well-defined pattern, or structure, dictated by forces acting at the molecular level. As a consequence, during its formation process the <a href="Crystal" title="Crystal">crystal</a> is in an environment where the solute <a href="Concentration" title="Concentration">concentration</a> reaches a certain critical value, before changing status. Solid formation, impossible below the <a href="Solubility" title="Solubility">solubility</a> threshold at the given <a href="Temperature" title="Temperature">temperature</a> and <a href="Pressure" title="Pressure">pressure</a> conditions, may then take place at a concentration higher than the theoretical solubility level. The difference between the actual value of the solute concentration at the crystallization limit and the theoretical (static) solubility threshold is called <a href="Supersaturation" title="Supersaturation">supersaturation</a> and is a fundamental factor in crystallization.

</p>

<div class="mw-heading mw-heading3"><h3 id="Nucleation">Nucleation</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Nucleation" title="Nucleation">Nucleation</a></div>

<p>Nucleation is the initiation of a phase change in a small region, such as the formation of a solid crystal from a liquid solution. It is a consequence of rapid local fluctuations on a molecular scale in a homogeneous phase that is in a state of metastable equilibrium. Total nucleation is the sum effect of two categories of nucleation – primary and secondary.

</p>

<div class="mw-heading mw-heading4"><h4 id="Primary_nucleation">Primary nucleation</h4></div>

<p>Primary nucleation is the initial formation of a crystal where there are no other crystals present or where, if there are crystals present in the system, they do not have any influence on the process. This can occur in two conditions. The first is homogeneous nucleation, which is nucleation that is not influenced in any way by solids. These solids include the walls of the crystallizer vessel and particles of any foreign substance. The second category, then, is heterogeneous nucleation. This occurs when solid particles of foreign substances cause an increase in the rate of nucleation that would otherwise not be seen without the existence of these foreign particles. Homogeneous nucleation rarely occurs in practice due to the high energy necessary to begin nucleation without a solid surface to catalyze the nucleation.

</p><p>Primary nucleation (both homogeneous and heterogeneous) has been modeled as follows:<sup id="cite_ref-Tavare_5-0" class="reference"><a href="#cite_note-Tavare-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>

</p>

<mfrac>

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<mrow>

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<annotation encoding="application/x-tex">{\displaystyle B={\dfrac {dN}{dt}}=k_{n}(c-c^{*})^{n},}</annotation>

</semantics>

</math></span><img src="./1da5b482f8ae0b303091cf874fb2b142764bdb53.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:24.089ex; height:5.509ex;" alt="{\displaystyle B={\dfrac {dN}{dt}}=k_{n}(c-c^{*})^{n},}" loading="lazy"></span></dd></dl>

<p>where

</p>

<dl><dd><i>B</i> is the number of nuclei formed per unit volume per unit time,</dd>

<dd><i>N</i> is the number of nuclei per unit volume,</dd>

<dd><i>k<sub>n</sub></i> is a rate constant,</dd>

<dd><i>c</i> is the instantaneous solute concentration,</dd>

<dd><i>c</i><sup>*</sup> is the solute concentration at saturation,</dd>

<dd>(<i>c</i> − <i>c</i><sup>*</sup>) is also known as supersaturation,</dd>

<dd><i>n</i> is an empirical exponent that can be as large as 10, but generally ranges between 3 and 4.</dd></dl>

<div class="mw-heading mw-heading4"><h4 id="Secondary_nucleation">Secondary nucleation</h4></div>

<p>Secondary nucleation is the formation of nuclei attributable to the influence of the existing microscopic crystals in the magma.<sup id="cite_ref-McCabeSmith_6-0" class="reference"><a href="#cite_note-McCabeSmith-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> More simply put, secondary nucleation is when crystal growth is initiated with contact of other existing crystals or "seeds".<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The first type of known secondary crystallization is attributable to fluid shear, the other due to collisions between already existing crystals with either a solid surface of the crystallizer or with other crystals themselves. Fluid-shear nucleation occurs when liquid travels across a crystal at a high speed, sweeping away nuclei that would otherwise be incorporated into a crystal, causing the swept-away nuclei to become new crystals. Contact nucleation has been found to be the most effective and common method for nucleation. The benefits include the following:<sup id="cite_ref-McCabeSmith_6-1" class="reference"><a href="#cite_note-McCabeSmith-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>

</p>

<ul><li>Low kinetic order and rate-proportional to supersaturation, allowing easy control without unstable operation.</li>

<li>Occurs at low supersaturation, where growth rate is optimal for good quality.</li>

<li>Low necessary energy at which crystals strike avoids the breaking of existing crystals into new crystals.</li>

<li>The quantitative fundamentals have already been isolated and are being incorporated into practice.</li></ul>

<p>The following model, although somewhat simplified, is often used to model secondary nucleation:<sup id="cite_ref-Tavare_5-1" class="reference"><a href="#cite_note-Tavare-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>

</p>

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<msup>

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<annotation encoding="application/x-tex">{\displaystyle B={\dfrac {dN}{dt}}=k_{1}M_{T}^{j}(c-c^{*})^{b},}</annotation>

</semantics>

</math></span><img src="./b57b9e7b4631a99304dc0980299bd378f20c0b45.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:27.287ex; height:5.509ex;" alt="{\displaystyle B={\dfrac {dN}{dt}}=k_{1}M_{T}^{j}(c-c^{*})^{b},}" loading="lazy"></span></dd></dl>

<p>where

</p>

<dl><dd><i>k</i><sub>1</sub> is a rate constant,</dd>

<dd><i>M<sub>T</sub></i> is the suspension density,</dd>

<dd><i>j</i> is an empirical exponent that can range up to 1.5, but is generally 1,</dd>

<dd><i>b</i> is an empirical exponent that can range up to 5, but is generally 2.</dd></dl>

<div class="mw-heading mw-heading3"><h3 id="Growth">Growth</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Crystal_growth" title="Crystal growth">Crystal growth</a></div>

<p>Once the first small crystal, the nucleus, forms it acts as a convergence point (if unstable due to supersaturation) for <a href="Molecules" class="mw-redirect" title="Molecules">molecules</a> of solute touching – or adjacent to – the crystal so that it increases its own dimension in successive layers. The pattern of growth resembles the rings of an onion, as shown in the picture, where each colour indicates the same mass of solute; this mass creates increasingly thin layers due to the increasing surface area of the growing crystal. The supersaturated solute mass the original nucleus may <i>capture</i> in a time unit is called the <i>growth rate</i> expressed in kg/(m<sup>2</sup>*h), and is a constant specific to the process. Growth rate is influenced by several physical factors, such as <a href="Surface_tension" title="Surface tension">surface tension</a> of solution, <a href="Pressure" title="Pressure">pressure</a>, <a href="Temperature" title="Temperature">temperature</a>, relative crystal <a href="Velocity" title="Velocity">velocity</a> in the solution, <a href="Reynolds_number" title="Reynolds number">Reynolds number</a>, and so forth.

</p><p>The main values to control are therefore:

</p>

<ul><li>Supersaturation value, as an index of the quantity of solute available for the growth of the crystal;</li>

<li>Total crystal surface in unit fluid mass, as an index of the capability of the solute to fix onto the crystal;</li>

<li>Retention time, as an index of the probability of a molecule of solute to come into contact with an existing crystal;</li>

<li>Flow pattern, again as an index of the probability of a molecule of solute to come into contact with an existing crystal (higher in <a href="Laminar_flow" title="Laminar flow">laminar flow</a>, lower in <a href="Turbulent_flow" class="mw-redirect" title="Turbulent flow">turbulent flow</a>, but the reverse applies to the probability of contact).</li></ul>

<p>The first value is a consequence of the physical characteristics of the solution, while the others define a difference between a well- and poorly designed crystallizer.

</p>

<div class="mw-heading mw-heading3"><h3 id="Size_distribution">Size distribution</h3></div>

<p>The appearance and size range of a crystalline product is extremely important in crystallization. If further processing of the crystals is desired, large crystals with uniform size are important for washing, filtering, transportation, and storage, because large crystals are easier to filter out of a solution than small crystals.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Also, larger crystals have a smaller surface area to volume ratio, leading to a higher purity. This higher purity is due to less retention of <a href="Mother_liquor" title="Mother liquor">mother liquor</a> which contains impurities, and a smaller loss of yield when the crystals are washed to remove the mother liquor. In special cases, for example during drug manufacturing in the pharmaceutical industry, small crystal sizes are often desired to improve drug dissolution rate and bio-availability. The theoretical crystal size distribution can be estimated as a function of operating conditions with a fairly complicated mathematical process called population balance theory (using <a href="Population_balance_equation" title="Population balance equation">population balance equations</a>).<sup id="cite_ref-CrystalSizeBeck_9-0" class="reference"><a href="#cite_note-CrystalSizeBeck-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Main_crystallization_processes">Main crystallization processes</h2></div>

<p>Some of the important factors influencing solubility are:

</p>

<ul><li>Concentration</li>

<li>Temperature</li>

<li>Solvent mixture composition</li>

<li>Polarity</li>

<li>Ionic strength</li></ul>

<p>So one may identify two main families of crystallization processes:

</p>

<ul><li>Cooling crystallization</li>

<li>Evaporative crystallization</li></ul>

<p>This division is not really clear-cut, since hybrid systems exist, where cooling is performed through <a href="Evaporation" title="Evaporation">evaporation</a>, thus obtaining at the same time a concentration of the solution.

</p><p>A crystallization process often referred to in <a href="Chemical_engineering" title="Chemical engineering">chemical engineering</a> is the <a href="Fractional_crystallization_(chemistry)" title="Fractional crystallization (chemistry)">fractional crystallization</a>. This is not a different process, rather a special application of one (or both) of the above.

</p>

<div class="mw-heading mw-heading3"><h3 id="Cooling_crystallization">Cooling crystallization</h3></div>

<div class="mw-heading mw-heading4"><h4 id="Application">Application</h4></div>

<p>Most <a href="Chemical_compound" title="Chemical compound">chemical compounds</a>, dissolved in most solvents, show the so-called <i>direct</i> solubility that is, the solubility threshold increases with temperature.

</p>

<p>So, whenever the conditions are favorable, crystal formation results from simply cooling the solution. Here <i>cooling</i> is a relative term: <a href="Austenite" title="Austenite">austenite</a> crystals in a steel form well above 1000 °C. An example of this crystallization process is the production of <a href="Glauber's_salt" class="mw-redirect" title="Glauber's salt">Glauber's salt</a>, a crystalline form of <a href="Sodium_sulfate" title="Sodium sulfate">sodium sulfate</a>. In the diagram, where equilibrium temperature is on the <a href="Cartesian_coordinates" class="mw-redirect" title="Cartesian coordinates">x-axis</a> and equilibrium concentration (as mass percent of solute in saturated solution) in <a href="Cartesian_coordinates" class="mw-redirect" title="Cartesian coordinates">y-axis</a>, it is clear that sulfate solubility quickly decreases below 32.5 °C. Assuming a saturated solution at 30 °C, by cooling it to 0 °C (note that this is possible thanks to the <a href="Freezing-point_depression" title="Freezing-point depression">freezing-point depression</a>), the precipitation of a mass of sulfate occurs corresponding to the change in solubility from 29% (equilibrium value at 30 °C) to approximately 4.5% (at 0 °C) – actually a larger crystal mass is precipitated, since sulfate entrains <a href="Mineral_hydration" title="Mineral hydration">hydration</a> water, and this has the side effect of increasing the final concentration.

</p><p>There are limitations in the use of cooling crystallization:

</p>

<ul><li>Many solutes precipitate in hydrate form at low temperatures: in the previous example this is acceptable, and even useful, but it may be detrimental when, for example, the mass of water of hydration to reach a stable hydrate crystallization form is more than the available water: a single block of hydrate solute will be formed – this occurs in the case of <a href="Calcium_chloride" title="Calcium chloride">calcium chloride</a>);</li>

<li>Maximum supersaturation will take place in the coldest points. These may be the heat exchanger tubes which are sensitive to scaling, and <a href="Heat_transfer" title="Heat transfer">heat exchange</a> may be greatly reduced or discontinued;</li>

<li>A decrease in temperature usually implies an increase of the <a href="Viscosity" title="Viscosity">viscosity</a> of a solution. Too high a viscosity may give hydraulic problems, and the <a href="Laminar_flow" title="Laminar flow">laminar flow</a> thus created may affect the crystallization dynamics.</li>

<li>It is not applicable to compounds having <i>reverse</i> solubility, a term to indicate that solubility increases with temperature decrease (an example occurs with sodium sulfate where solubility is reversed above 32.5 °C).</li></ul>

<div class="mw-heading mw-heading4"><h4 id="Cooling_crystallizers">Cooling crystallizers</h4></div>

<p>The simplest cooling crystallizers are tanks provided with a <a href="Industrial_mixer" class="mw-redirect" title="Industrial mixer">mixer</a> for internal circulation, where temperature decrease is obtained by heat exchange with an intermediate fluid circulating in a jacket. These simple machines are used in batch processes, as in processing of <a href="Pharmaceuticals" class="mw-redirect" title="Pharmaceuticals">pharmaceuticals</a> and are prone to scaling. Batch processes normally provide a relatively variable quality of the product along with the batch.

</p><p>The <i>Swenson-Walker</i> crystallizer is a model, specifically conceived by Swenson Co. around 1920, having a semicylindric horizontal hollow trough in which a hollow <a href="Screw" title="Screw">screw</a> conveyor or some hollow discs, in which a refrigerating fluid is circulated, plunge during rotation on a longitudinal axis. The refrigerating fluid is sometimes also circulated in a jacket around the trough. Crystals precipitate on the cold surfaces of the screw/discs, from which they are removed by scrapers and settle on the bottom of the trough. The screw, if provided, pushes the slurry towards a discharge port.

</p><p>A common practice is to cool the solutions by flash evaporation: when a liquid at a given T<sub>0</sub> temperature is transferred in a chamber at a pressure P<sub>1</sub> such that the liquid saturation temperature T<sub>1</sub> at P<sub>1</sub> is lower than T<sub>0</sub>, the liquid will release <a href="Heat" title="Heat">heat</a> according to the temperature difference and a quantity of solvent, whose total <a href="Latent_heat" title="Latent heat">latent heat</a> of vaporization equals the difference in <a href="Enthalpy" title="Enthalpy">enthalpy</a>. In simple words, the liquid is cooled by evaporating a part of it.

</p><p>In the sugar industry, vertical cooling crystallizers are used to exhaust the <a href="Molasses" title="Molasses">molasses</a> in the last crystallization stage downstream of vacuum pans, prior to centrifugation. The massecuite enters the crystallizers at the top, and cooling water is pumped through pipes in counterflow.

</p>

<div class="mw-heading mw-heading3"><h3 id="Evaporative_crystallization">Evaporative crystallization</h3></div>

<p>Another option is to obtain, at an approximately constant temperature, the precipitation of the crystals by increasing the solute concentration above the solubility threshold. To obtain this, the solute/solvent mass ratio is increased using the technique of <a href="Evaporation" title="Evaporation">evaporation</a>. This process is insensitive to change in temperature (as long as hydration state remains unchanged).

</p><p>All considerations on control of crystallization parameters are the same as for the cooling models.

</p>

<div class="mw-heading mw-heading4"><h4 id="Evaporative_crystallizers">Evaporative crystallizers</h4></div>

<p>Most industrial crystallizers are of the evaporative type, such as the very large <a href="Sodium_chloride" title="Sodium chloride">sodium chloride</a> and <a href="Sucrose" title="Sucrose">sucrose</a> units, whose production accounts for more than 50% of the total world production of crystals. The most common type is the <i>forced circulation</i> (FC) model (see <a href="Evaporator" title="Evaporator">evaporator</a>). A pumping device (a <a href="Pump" title="Pump">pump</a> or an axial flow <a href="Axial_flow_pump" class="mw-redirect" title="Axial flow pump">mixer</a>) keeps the crystal <a href="Slurry" title="Slurry">slurry</a> in homogeneous <a href="Suspension_(chemistry)" title="Suspension (chemistry)">suspension</a> throughout the tank, including the exchange surfaces; by controlling pump <a href="Fluid_dynamics" title="Fluid dynamics">flow</a>, control of the contact time of the crystal mass with the supersaturated solution is achieved, together with reasonable velocities at the exchange surfaces. The Oslo, mentioned above, is a refining of the evaporative forced circulation crystallizer, now equipped with a large crystals settling zone to increase the retention time (usually low in the FC) and to roughly separate heavy slurry zones from clear liquid. Evaporative crystallizers tend to yield larger average crystal size and narrows the crystal size distribution curve.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="DTB_crystallizer">DTB crystallizer</h3></div>

<p>Whichever the form of the crystallizer, to achieve an effective <a href="Process_control" class="mw-redirect" title="Process control">process control</a> it is important to control the retention time and the crystal mass, to obtain the optimum conditions in terms of crystal specific surface and the fastest possible growth.<sup id="cite_ref-Seepmaetal2025_11-0" class="reference"><a href="#cite_note-Seepmaetal2025-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> This can be achieved by a separation – to put it simply – of the crystals from the liquid mass, in order to manage the two flows in a different way. The practical way is to perform a gravity <a href="Settling" title="Settling">settling</a> to be able to extract (and possibly recycle separately) the (almost) clear liquid, while managing the mass flow around the crystallizer to obtain a precise slurry density elsewhere. A typical example is the DTB (<i>Draft Tube and Baffle</i>) crystallizer, an idea of Richard Chisum Bennett (a Swenson engineer and later President of Swenson) at the end of the 1950s. The DTB crystallizer (see images) has an internal circulator, typically an axial flow mixer – yellow – pushing upwards in a draft tube while outside the crystallizer there is a settling area in an annulus; in it the exhaust solution moves upwards at a very low velocity, so that large crystals settle – and return to the main circulation – while only the fines, below a given grain size are extracted and eventually destroyed by increasing or decreasing temperature, thus creating additional supersaturation. A quasi-perfect control of all parameters is achieved as DTF crystallizers offer superior control over crystal size and characteristics.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> This crystallizer, and the derivative models (Krystal, CSC, etc.) could be the ultimate solution if not for a major limitation in the evaporative capacity, due to the limited diameter of the vapor head and the relatively low external circulation not allowing large amounts of energy to be supplied to the system.

</p>

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<ul><li><a href="Abnormal_grain_growth" title="Abnormal grain growth">Abnormal grain growth</a></li>

<li><a href="Chiral_resolution#Resolution_by_crystallization" title="Chiral resolution">Chiral resolution by crystallization</a></li>

<li><a href="Crystal_habit" title="Crystal habit">Crystal habit</a></li>

<li><a href="Crystal_structure" title="Crystal structure">Crystal structure</a></li>

<li><a href="Crystallite" title="Crystallite">Crystallite</a></li>

<li><a href="Fractional_crystallization_(chemistry)" title="Fractional crystallization (chemistry)">Fractional crystallization (chemistry)</a></li>

<li><a href="Igneous_differentiation" title="Igneous differentiation">Igneous differentiation</a></li>

<li><a href="Laser_heated_pedestal_growth" class="mw-redirect" title="Laser heated pedestal growth">Laser heated pedestal growth</a></li>

<li><a href="Micro-pulling-down" title="Micro-pulling-down">Micro-pulling-down</a></li>

<li><a href="Protein_crystallization" title="Protein crystallization">Protein crystallization</a></li>

<li><a href="Pumpable_ice_technology" title="Pumpable ice technology">Pumpable ice technology</a></li>

<li><a href="Quasicrystal" title="Quasicrystal">Quasicrystal</a></li>

<li><a href="Recrystallization_(chemistry)" title="Recrystallization (chemistry)">Recrystallization (chemistry)</a></li>

<li><a href="Recrystallization_(metallurgy)" title="Recrystallization (metallurgy)">Recrystallization (metallurgy)</a></li>

<li><a href="Seed_crystal" title="Seed crystal">Seed crystal</a></li>

<li><a href="Single_crystal" title="Single crystal">Single crystal</a></li>

<li><a href="Symplectite" title="Symplectite">Symplectite</a></li>

<li><a href="Vitrification" title="Vitrification">Vitrification</a></li>

<li><a href="X-ray_crystallography" title="X-ray crystallography">X-ray crystallography</a></li></ul>

</div>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFChayen1992" class="citation journal cs1">Chayen, Blow (1992). "Microbatch crystallization under oil – a new technique allowing many small-volume crystallization trials". <i>Journal of Crystal Growth</i>. <b>122</b> (<span class="nowrap">1–</span>4): <span class="nowrap">176–</span>180. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1992JCrGr.122..176C">1992JCrGr.122..176C</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0022-0248%2892%2990241-A">10.1016/0022-0248(92)90241-A</a>.</cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFBenvenuti2007" class="citation journal cs1">Benvenuti, Mangani (2007). <a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fnprot.2007.198">"Crystallization of soluble proteins in vapor diffusion for x-ray crystallography"</a>. <i>Nature Protocols</i>. <b>2</b> (7): <span class="nowrap">1633–</span>1651. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fnprot.2007.198">10.1038/nprot.2007.198</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17641629">17641629</a>.</cite></span>

</li>

<li id="cite_note-TankCrystallizerJinzong-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-TankCrystallizerJinzong_3-0">^</a></b></span> <span class="reference-text">Jinzong Machinery, “Tank crystallizer is an old method still used in some specialized cases. Saturated solutions, in tank crystallization, are allowed to cool in open tanks. After a period of time the mother liquor is drained and the crystals removed.”</span>

</li>

<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.stevenabbott.co.uk/practical-solubility/MSMPR.php">"MSMPR Crystallizer | Practical Solubility Science | Prof Steven Abbott"</a>. <i>www.stevenabbott.co.uk</i><span class="reference-accessdate">. Retrieved <span class="nowrap">May 25,</span> 2024</span>.</cite></span>

</li>

<li id="cite_note-Tavare-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-Tavare_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Tavare_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Tavare, N. S. (1995). <i>Industrial Crystallization</i>. Plenum Press, New York.</span>

</li>

<li id="cite_note-McCabeSmith-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-McCabeSmith_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-McCabeSmith_6-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">McCabe & Smith (2000). <i>Unit Operations of Chemical Engineering</i>. McGraw-Hill, New York.</span>

</li>

<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.reciprocalnet.org/edumodules/crystallization/">"Crystallization"</a>. <i>www.reciprocalnet.org</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20161127173509/http://www.reciprocalnet.org/edumodules/crystallization/">Archived</a> from the original on November 27, 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">January 3,</span> 2017</span>.</cite></span>

</li>

<li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><cite id="CITEREFBeckHäkkinenMalthe-SørenssenAndreassen2009" class="citation journal cs1">Beck, Ralf; Häkkinen, Antti; Malthe-Sørenssen, Didrik; Andreassen, Jens-Petter (May 7, 2009). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/S1383586609000355">"The effect of crystallization conditions, crystal morphology and size on pressure filtration of l-glutamic acid and an aromatic amine"</a></span>. <i>Separation and Purification Technology</i>. <b>66</b> (3): <span class="nowrap">549–</span>558. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.seppur.2009.01.018">10.1016/j.seppur.2009.01.018</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1383-5866">1383-5866</a>.</cite></span>

</li>

<li id="cite_note-CrystalSizeBeck-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-CrystalSizeBeck_9-0">^</a></b></span> <span class="reference-text">Ralf Beck et al., “The effect of crystallization conditions, crystal morphology and size on pressure filtration…”, *Separation and Purification Technology* 2009.</span>

</li>

<li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="http://thermalkinetics.net/evaporation-equipment/submerge-circulating-crystallizer">"Submerge Circulating Crystallizers"</a>. <i>Thermal Kinetics Engineering, PLLC</i><span class="reference-accessdate">. Retrieved <span class="nowrap">January 3,</span> 2017</span>.</cite></span>

</li>

<li id="cite_note-Seepmaetal2025-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-Seepmaetal2025_11-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFSeepmaKoskampColinChiou2025" class="citation journal cs1">Seepma, Sergěj Y.M.H.; Koskamp, Janou A.; Colin, Michel G.; Chiou, Eleftheria; Sobhan, Rubayat; Bögels, Tim F.J.; Bastiaan, Tom; Zamanian, Hadi; Baars, Eric T.; de Moel, Peter J.; Wolthers, Mariëtte; Kramer, Onno J.I. (2025). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.watres.2024.122781">"Mechanistic model advancements for optimal calcium removal in water treatment: Integral operation improvements and reactor design strategies"</a>. <i>Water Research</i>. <b>268</b> (Pt. B): 122781. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2025WatRe.26822781S">2025WatRe.26822781S</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.watres.2024.122781">10.1016/j.watres.2024.122781</a></span>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0043-1354">0043-1354</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/39550848">39550848</a>.</cite></span>

</li>

<li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://swensontechnology.com/draft-tube-baffle-crystallizers/">"Draft Tube Baffle (DTB) Crystallizer"</a>. <i>Swenson Technology</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160925070515/http://www.swensontechnology.com/equipment/draft-tube-baffle-dtb-crystallizer/">Archived</a> from the original on September 25, 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">November 15,</span> 2023</span>.</cite></span>

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160303181456/http://acaschool.iit.edu/lectures04/JLiangXtal.pdf">"Small Molecule Crystallization"</a> (<a href="PDF" title="PDF">PDF</a>) at <a href="Illinois_Institute_of_Technology" title="Illinois Institute of Technology">Illinois Institute of Technology</a> website</li>

<li>Arkenbout-de Vroome, Tine (1995). <i>Melt Crystallization Technology</i> CRC <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>1-56676-181-6</bdi></li>

<li>Geankoplis, C.J. (2003) "Transport Processes and Separation Process Principles". 4th Ed. Prentice-Hall Inc.</li>

<li>Glynn P.D. and Reardon E.J. (1990) "Solid-solution aqueous-solution equilibria: thermodynamic theory and representation". Amer. J. Sci. 290, 164–201.</li>

<li>Jancic, S. J.; Grootscholten, P.A.M.: “Industrial Crystallization”, Textbook, Delft University Press and Reidel Publishing Company, Delft, The Netherlands, 1984.</li>

<li>Mersmann, A. (2001) <i>Crystallization Technology Handbook</i> CRC; 2nd ed. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-8247-0528-9</bdi></li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070521072608/http://www.ashemorris.com/crystallisation.aspx">Batch Crystallization</a></li>

<li><a rel="nofollow" class="external text" href="http://www.cheresources.com/cryst.shtml">Industrial Crystallization</a></li></ul>

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</style></div><div role="navigation" class="navbox" aria-labelledby="Concepts_in_enantioselective_synthesis111" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Concepts_in_enantioselective_synthesis111" style="font-size:114%;margin:0 4em">Concepts in <a href="Enantioselective_synthesis" title="Enantioselective synthesis">enantioselective synthesis</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Chirality types</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Chirality_(chemistry)" title="Chirality (chemistry)">Chirality</a></li>

<li><a href="Stereocenter" title="Stereocenter">Stereocenter</a></li>

<li><a href="Planar_chirality" title="Planar chirality">Planar chirality</a></li>

<li><a href="C2-Symmetric_ligands" title="C2-Symmetric ligands"><i>C</i><sub>2</sub>-symmetric ligands</a></li>

<li><a href="Axial_chirality" title="Axial chirality">Axial chirality</a></li>

<li><a href="Supramolecular_chirality" title="Supramolecular chirality">Supramolecular chirality</a></li>

<li><a href="Inherent_chirality" title="Inherent chirality">Inherent chirality</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Chiral molecules</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Stereoisomerism" title="Stereoisomerism">Stereoisomer</a></li>

<li><a href="Enantiomer" title="Enantiomer">Enantiomer</a></li>

<li><a href="Diastereomer" title="Diastereomer">Diastereomer</a></li>

<li><a href="Meso_compound" title="Meso compound">Meso compound</a></li>

<li><a href="Racemic_mixture" title="Racemic mixture">Racemic mixture</a></li>

<li><a href="Enantiomeric_excess" title="Enantiomeric excess">Enantiomeric excess</a> (ee)</li>

<li><a href="Diastereomeric_excess" class="mw-redirect" title="Diastereomeric excess">Diastereomeric excess</a> (de)</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Analysis</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Optical_rotation" title="Optical rotation">Optical rotation</a></li>

<li><a href="Chiral_derivatizing_agent" title="Chiral derivatizing agent">Chiral derivatizing agents</a></li>

<li><a href="Nuclear_magnetic_resonance_spectroscopy_of_stereoisomers" title="Nuclear magnetic resonance spectroscopy of stereoisomers">NMR spectroscopy of stereoisomers</a></li>

<li><a href="Ultraviolet%E2%80%93visible_spectroscopy_of_stereoisomers" title="Ultraviolet–visible spectroscopy of stereoisomers">Ultraviolet–visible spectroscopy of stereoisomers</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Chiral_resolution" title="Chiral resolution">Chiral resolution</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Recrystallization_(chemistry)" title="Recrystallization (chemistry)">Recrystallization</a></li>

<li><a href="Kinetic_resolution" title="Kinetic resolution">Kinetic resolution</a></li>

<li><a href="Chiral_column_chromatography" title="Chiral column chromatography">Chiral column chromatography</a></li>

<li><a href="Diastereomeric_recrystallization" title="Diastereomeric recrystallization">Diastereomeric recrystallization</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Reactions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Asymmetric_induction" title="Asymmetric induction">Asymmetric induction</a></li>

<li><a href="Chiral_pool_synthesis" class="mw-redirect" title="Chiral pool synthesis">Chiral pool synthesis</a></li>

<li><a href="Chiral_auxiliary" title="Chiral auxiliary">Chiral auxiliaries</a></li>

<li><a href="Asymmetric_catalysis" class="mw-redirect" title="Asymmetric catalysis">Asymmetric catalysis</a></li>

<li><a href="Organocatalysis" title="Organocatalysis">Organocatalysis</a></li>

<li><a href="Biocatalysis" title="Biocatalysis">Biocatalysis</a></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Separation_processes90" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><div id="Separation_processes90" style="font-size:114%;margin:0 4em"><a href="Separation_process" title="Separation process">Separation processes</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Processes</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Sorption" title="Sorption">Absorption</a></li>

<li><a href="Acid%E2%80%93base_extraction" title="Acid–base extraction">Acid–base extraction</a></li>

<li><a href="Adsorption" title="Adsorption">Adsorption</a></li>

<li><a href="Chromatography" title="Chromatography">Chromatography</a></li>

<li><a href="Cross-flow_filtration" title="Cross-flow filtration">Cross-flow filtration</a></li>

<li><a href="Cyclonic_separation" title="Cyclonic separation">Cyclonic separation</a></li>

<li><a href="Decantation" title="Decantation">Decantation</a></li>

<li><a href="Dialysis_(chemistry)" title="Dialysis (chemistry)">Dialysis</a></li>

<li><a href="Dissolved_air_flotation" title="Dissolved air flotation">Dissolved air flotation</a></li>

<li><a href="Distillation" title="Distillation">Distillation</a></li>

<li><a href="Drying" title="Drying">Drying</a></li>

<li><a href="Electrochromatography" title="Electrochromatography">Electrochromatography</a></li>

<li><a href="Electrofiltration" title="Electrofiltration">Electrofiltration</a></li>

<li><a href="Extraction_(chemistry)" title="Extraction (chemistry)">Extraction</a></li>

<li><a href="Filtration" title="Filtration">Filtration</a></li>

<li><a href="Flocculation" title="Flocculation">Flocculation</a></li>

<li><a href="Froth_flotation" title="Froth flotation">Froth flotation</a></li>

<li><a href="Gravity_separation" title="Gravity separation">Gravity separation</a></li>

<li><a href="Leaching_(chemistry)" title="Leaching (chemistry)">Leaching</a></li>

<li><a href="Liquid%E2%80%93liquid_extraction" title="Liquid–liquid extraction">Liquid–liquid extraction</a></li>

<li><a href="Electroextraction" title="Electroextraction">Electroextraction</a></li>

<li><a href="Microfiltration" title="Microfiltration">Microfiltration</a></li>

<li><a href="Osmosis" title="Osmosis">Osmosis</a></li>

<li><a href="Precipitation_(chemistry)" title="Precipitation (chemistry)">Precipitation</a></li>

<li><a href="Recrystallization_(chemistry)" title="Recrystallization (chemistry)">Recrystallization</a></li>

<li><a href="Reverse_osmosis" title="Reverse osmosis">Reverse osmosis</a></li>

<li><a href="Sedimentation_(water_treatment)" title="Sedimentation (water treatment)">Sedimentation</a></li>

<li><a href="Solid-phase_extraction" title="Solid-phase extraction">Solid-phase extraction</a></li>

<li><a href="Sublimation_(phase_transition)" title="Sublimation (phase transition)">Sublimation</a></li>

<li><a href="Ultrafiltration" title="Ultrafiltration">Ultrafiltration</a></li></ul>

</div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Devices</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="API_oil%E2%80%93water_separator" title="API oil–water separator">API oil–water separator</a></li>

<li><a href="Belt_filter" title="Belt filter">Belt filter</a></li>

<li><a href="Centrifuge" title="Centrifuge">Centrifuge</a></li>

<li><a href="Depth_filter" title="Depth filter">Depth filter</a></li>

<li><a href="Electrostatic_precipitator" title="Electrostatic precipitator">Electrostatic precipitator</a></li>

<li><a href="Evaporator" title="Evaporator">Evaporator</a></li>

<li><a href="Filter_press" title="Filter press">Filter press</a></li>

<li><a href="Fractionating_column" title="Fractionating column">Fractionating column</a></li>

<li><a href="Leachate" title="Leachate">Leachate</a></li>

<li><a href="Mixer-settler" title="Mixer-settler">Mixer-settler</a></li>

<li><a href="Protein_skimmer" title="Protein skimmer">Protein skimmer</a></li>

<li><a href="Rapid_sand_filter" title="Rapid sand filter">Rapid sand filter</a></li>

<li><a href="Rotary_vacuum-drum_filter" title="Rotary vacuum-drum filter">Rotary vacuum-drum filter</a></li>

<li><a href="Scrubber" title="Scrubber">Scrubber</a></li>

<li><a href="Spinning_cone" title="Spinning cone">Spinning cone</a></li>

<li><a href="Still" title="Still">Still</a></li>

<li><a href="Sublimation_apparatus" class="mw-redirect" title="Sublimation apparatus">Sublimation apparatus</a></li>

<li><a href="Vacuum_ceramic_filter" title="Vacuum ceramic filter">Vacuum ceramic filter</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Multiphase<br> systems</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Aqueous_two-phase_system" title="Aqueous two-phase system">Aqueous two-phase system</a></li>

<li><a href="Azeotrope" title="Azeotrope">Azeotrope</a></li>

<li><a href="Eutectic_system" title="Eutectic system">Eutectic</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Unit_operation" title="Unit operation">Unit operation</a></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Biotechnology389" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><div id="Biotechnology389" style="font-size:114%;margin:0 4em"><a href="Biotechnology" title="Biotechnology">Biotechnology</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">History</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="History_of_biotechnology" title="History of biotechnology">History of biotechnology</a></li>

<li><a href="Timeline_of_biotechnology" title="Timeline of biotechnology">Timeline of biotechnology</a></li>

<li><a href="Competitions_and_prizes_in_biotechnology" title="Competitions and prizes in biotechnology">Competitions and prizes in biotechnology</a></li></ul>

</div></td><td class="noviewer navbox-image" rowspan="8" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Branches</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Colors_of_biotechnology" class="mw-redirect" title="Colors of biotechnology">Colors of biotechnology</a></li>

<li><a href="Industrial_biotechnology" class="mw-redirect" title="Industrial biotechnology">Industrial biotechnology</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Biological concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Allele" title="Allele">Allele</a></li>

<li><a href="Fermentation" title="Fermentation">Fermentation</a></li>

<li><a href="Plasmid" title="Plasmid">Plasmid</a></li>

<li><a href="Protein" title="Protein">Protein</a></li>

<li><a href="Selective_breeding" title="Selective breeding">Selective breeding</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">General concepts</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Biotechnology_industrial_park" class="mw-redirect" title="Biotechnology industrial park">Biotechnology industrial park</a></li>

<li><a href="Biotechnology_products" class="mw-redirect" title="Biotechnology products">Biotechnology products</a></li>

<li><a href="Biotechnology_law" class="mw-redirect" title="Biotechnology law">Biotechnology law</a></li>

<li><a href="Green_Revolution" title="Green Revolution">Green Revolution</a></li>

<li><a href="Human_Genome_Project" title="Human Genome Project">Human Genome Project</a></li>

<li><a href="Pharmaceutical_company" class="mw-redirect" title="Pharmaceutical company">Pharmaceutical company</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Basic techniques<br> and tools</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Biology field</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Bioreactor" title="Bioreactor">Bioreactor</a></li>

<li><a href="Cell_culture" title="Cell culture">Cell culture</a></li>

<li><a href="Cultured_meat" title="Cultured meat">Cultured meat</a></li>

<li><a href="Flow_cytometry" title="Flow cytometry">Flow cytometry</a></li>

<li><a href="Hybridoma_technology" title="Hybridoma technology">Hybridoma technology</a></li>

<li><a href="Spectroscopy" title="Spectroscopy">Spectroscopy</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Chemical field</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Centrifugation" title="Centrifugation">Centrifugation</a></li>

<li><a href="Chromatography" title="Chromatography">Chromatography</a></li>

<li><a href="Kidney_dialysis" title="Kidney dialysis">Kidney dialysis</a></li>

<li><a href="Electrophoresis" title="Electrophoresis">Electrophoresis</a></li>

<li><a href="Extraction_(chemistry)" title="Extraction (chemistry)">Extraction</a></li>

<li><a href="Fed-batch_culture" title="Fed-batch culture">Fed Batch</a></li>

<li><a href="Filtration" title="Filtration">Filtration</a></li>

<li><a href="Sedimentation" title="Sedimentation">Sedimentation</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Applications</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Animal_cell_culture" class="mw-redirect" title="Animal cell culture">Animal cell culture</a></li>

<li><a href="Biofabrication" title="Biofabrication">Biofabrication</a></li>

<li><a href="Bioinformatics" title="Bioinformatics">Bioinformatics</a></li>

<li><a href="Biosynthesis" title="Biosynthesis">Biosynthesis</a></li>

<li><a href="Bionic_architecture" title="Bionic architecture">Bionic architecture</a></li>

<li><a href="Cell_immunity" class="mw-redirect" title="Cell immunity">Cell immunity</a></li>

<li><a href="Cloning" title="Cloning">Cloning</a>

<ul><li><a href="Reproductive_cloning" class="mw-redirect" title="Reproductive cloning">Reproductive cloning</a></li>

<li><a href="Therapeutic_cloning" class="mw-redirect" title="Therapeutic cloning">Therapeutic cloning</a></li></ul></li>

<li><a href="Embryology" title="Embryology">Embryology</a></li>

<li><a href="Environmental_biotechnology" title="Environmental biotechnology">Environmental biotechnology</a></li>

<li><a href="Genetic_engineering" title="Genetic engineering">Genetic engineering</a>

<ul><li><a href="Genetically_modified_organism" title="Genetically modified organism">Genetically modified organism</a></li>

<li><a href="Molecular_genetics" title="Molecular genetics">Molecular genetics</a></li></ul></li>

<li><a href="Gene_therapy" title="Gene therapy">Gene therapy</a></li>

<li><a href="Microbial_biodegradation" title="Microbial biodegradation">Microbial biodegradation</a></li>

<li><a href="Omics" title="Omics">Omics</a></li>

<li><a href="Pharmacogenomics" title="Pharmacogenomics">Pharmacogenomics</a></li>

<li><a href="Stem_cells" class="mw-redirect" title="Stem cells">Stem cells</a></li>

<li><a href="Telomere" title="Telomere">Telomere</a></li>

<li><a href="Tissue_culture" title="Tissue culture">Tissue culture</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Interdisciplinary <br>fields</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Biobased_economy" class="mw-redirect" title="Biobased economy">Bioeconomy</a></li>

<li><a href="Bioelectronics" title="Bioelectronics">Bioelectronics</a></li>

<li><a href="Biological_engineering" title="Biological engineering">Bioengineering</a></li>

<li><a href="Biology" title="Biology">Biology</a></li>

<li><a href="Biopharmaceutical" title="Biopharmaceutical">Biopharmacology</a></li>

<li><a href="Biomedical_engineering" title="Biomedical engineering">Biomedical engineering</a></li>

<li><a href="Biomedicine" title="Biomedicine">Biomedicine</a></li>

<li><a href="Biomimetics" title="Biomimetics">Biomimetics</a></li>

<li><a href="Biochemistry" title="Biochemistry">Biochemicals</a></li>

<li><a href="Biorobotics" title="Biorobotics">Biorobotics</a></li>

<li><a href="Chemical_engineering" title="Chemical engineering">Chemical engineering</a></li>

<li><a href="Microbiology" title="Microbiology">Microbiology</a></li>

<li><a href="Mining" title="Mining">Mining</a></li>

<li><a href="Molecular_biology" title="Molecular biology">Molecular biology</a></li>

<li><a href="Nanobiotechnology" title="Nanobiotechnology">Nanobiotechnology</a></li>

<li><a href="Virology" title="Virology">Virology</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Lists</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Index_of_biotechnology_articles" title="Index of biotechnology articles">Index of biotechnology articles</a></li>

<li><a href="List_of_biotechnology_articles" class="mw-redirect" title="List of biotechnology articles">List of biotechnology articles</a></li>

<li><a href="List_of_largest_biomedical_companies_by_market_capitalization" title="List of largest biomedical companies by market capitalization">List of largest biomedical companies by market capitalization</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div>

<ul><li><span class="noviewer" typeof="mw:File"><span title="Category"></span></span> <b>Category</b></li>

<li><span class="noviewer" typeof="mw:File"><span title="Commons page"></span></span> <b><a href="https://commons.wikimedia.org/wiki/Category:Biotechnology" class="extiw external" title="commons:Category:Biotechnology">Commons</a></b></li></ul>

</div></td></tr></tbody></table></div>

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</style></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q284256#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1758" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q284256#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1758" style="font-size:114%;margin:0 4em">Authority control databases </div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4033215-9">Germany</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Crystallization"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85034495">United States</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Cristallisation"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb119788740">France</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Cristallisation"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb119788740">BnF data</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="krystalizace"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph138259&CON_LNG=ENG">Czech Republic</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://kopkatalogs.lv/F?func=direct&local_base=lnc10&doc_number=000154805&P_CON_LNG=ENG">Latvia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007536083105171">Israel</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://lux.collections.yale.edu/view/concept/11d8f9d4-b9df-449f-adcf-7b68393bebf4">Yale LUX</a></span></li></ul></div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-06-26" href="https://en.wikipedia.org/wiki/?title=Crystallization&oldid=1297470958">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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