{"id":22876,"date":"2024-07-17T15:47:43","date_gmt":"2024-07-17T13:47:43","guid":{"rendered":"https:\/\/www.linseis.com\/determination-of-the-cte-density\/"},"modified":"2025-02-14T17:44:06","modified_gmt":"2025-02-14T16:44:06","slug":"determination-of-the-cte-density","status":"publish","type":"post","link":"https:\/\/www.linseis.com\/en\/wiki\/determination-of-the-cte-density\/","title":{"rendered":"Determination of the CTE density"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"22876\" class=\"elementor elementor-22876 elementor-9942\" data-elementor-post-type=\"post\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9eb8745 e-flex e-con-boxed e-con e-parent\" data-id=\"9eb8745\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-fb52706 elementor-toc--minimized-on-tablet elementor-widget elementor-widget-table-of-contents\" data-id=\"fb52706\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;headings_by_tags&quot;:[&quot;h2&quot;],&quot;exclude_headings_by_selector&quot;:[],&quot;marker_view&quot;:&quot;numbers&quot;,&quot;no_headings_message&quot;:&quot;No headings were found on this page.&quot;,&quot;minimize_box&quot;:&quot;yes&quot;,&quot;minimized_on&quot;:&quot;tablet&quot;,&quot;hierarchical_view&quot;:&quot;yes&quot;,&quot;min_height&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]},&quot;min_height_tablet&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]},&quot;min_height_mobile&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]}}\" data-widget_type=\"table-of-contents.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-toc__header\">\n\t\t\t\t\t\t<h4 class=\"elementor-toc__header-title\">\n\t\t\t\tTable of Contents\t\t\t<\/h4>\n\t\t\t\t\t\t\t\t\t\t<div class=\"elementor-toc__toggle-button elementor-toc__toggle-button--expand\" role=\"button\" tabindex=\"0\" aria-controls=\"elementor-toc__fb52706\" aria-expanded=\"true\" aria-label=\"Open table of contents\"><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-chevron-down\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M207.029 381.476L12.686 187.132c-9.373-9.373-9.373-24.569 0-33.941l22.667-22.667c9.357-9.357 24.522-9.375 33.901-.04L224 284.505l154.745-154.021c9.379-9.335 24.544-9.317 33.901.04l22.667 22.667c9.373 9.373 9.373 24.569 0 33.941L240.971 381.476c-9.373 9.372-24.569 9.372-33.942 0z\"><\/path><\/svg><\/div>\n\t\t\t\t<div class=\"elementor-toc__toggle-button elementor-toc__toggle-button--collapse\" role=\"button\" tabindex=\"0\" aria-controls=\"elementor-toc__fb52706\" aria-expanded=\"true\" aria-label=\"Close table of contents\"><svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-chevron-up\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M240.971 130.524l194.343 194.343c9.373 9.373 9.373 24.569 0 33.941l-22.667 22.667c-9.357 9.357-24.522 9.375-33.901.04L224 227.495 69.255 381.516c-9.379 9.335-24.544 9.317-33.901-.04l-22.667-22.667c-9.373-9.373-9.373-24.569 0-33.941L207.03 130.525c9.372-9.373 24.568-9.373 33.941-.001z\"><\/path><\/svg><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<div id=\"elementor-toc__fb52706\" class=\"elementor-toc__body\">\n\t\t\t<div class=\"elementor-toc__spinner-container\">\n\t\t\t\t<svg class=\"elementor-toc__spinner eicon-animation-spin e-font-icon-svg e-eicon-loading\" aria-hidden=\"true\" viewBox=\"0 0 1000 1000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M500 975V858C696 858 858 696 858 500S696 142 500 142 142 304 142 500H25C25 237 238 25 500 25S975 237 975 500 763 975 500 975Z\"><\/path><\/svg>\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8a9139e elementor-widget elementor-widget-heading\" data-id=\"8a9139e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Thermal expansion and density<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-cbf12b4 e-con-full e-flex e-con e-child\" data-id=\"cbf12b4\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-a5b4d15 e-con-full e-flex e-con e-child\" data-id=\"a5b4d15\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-6605541 elementor-widget elementor-widget-text-editor\" data-id=\"6605541\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The thermal expansion of materials can lead to great commercial damage. In construction, for example, expansion joints must be provided in order to compensate for changes in length in the event of\u00a0<strong>temperature fluctuations.<\/strong>\u00a0Furthermore, the\u00a0<strong>coefficients of expansion<\/strong>\u00a0of materials in contact must be matched to one another. If the coefficients of expansion of a ceramic body and a glazing differ too much, so-called\u00a0<strong>\u201cspiderweb cracks\u201d<\/strong>\u00a0are formed, which can often be observed on old porcelain plates.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-7396df6 e-con-full e-flex e-con e-child\" data-id=\"7396df6\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-fa6511d elementor-widget elementor-widget-image\" data-id=\"fa6511d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"800\" height=\"534\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/iStock-873866046-min-2048x1367-2-1024x684.jpg\" class=\"attachment-large size-large wp-image-14547\" alt=\"\" srcset=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/iStock-873866046-min-2048x1367-2-1024x684.jpg 1024w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/iStock-873866046-min-2048x1367-2-300x200.jpg 300w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/iStock-873866046-min-2048x1367-2-768x513.jpg 768w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/iStock-873866046-min-2048x1367-2-1536x1025.jpg 1536w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/iStock-873866046-min-2048x1367-2.jpg 2048w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-59f6594 elementor-widget elementor-widget-spacer\" data-id=\"59f6594\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8b852c8 elementor-widget elementor-widget-text-editor\" data-id=\"8b852c8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The expansion takes place in all spatial directions, so that the density changes, since the mass remains constant. In the case of\u00a0<strong>anisotropic materials, the expansion is direction-dependent<\/strong>, so that the direction of the expansion must be specified. Consequently, all spatial directions must be taken into account to determine the density or the\u00a0<strong>volume expansion coefficient.<\/strong><\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-72ccd75 elementor-widget elementor-widget-heading\" data-id=\"72ccd75\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Definition of thermal expansion<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-40545f1 elementor-widget elementor-widget-text-editor\" data-id=\"40545f1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The <a href=\"https:\/\/www.linseis.com\/en\/wiki\/determination-of-the-cte-density\/\"><strong>coefficient of thermal expansion (CTE)<\/strong><\/a> is defined as the relative change in length on a temperature change of one Kelvin:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5ba0d8c elementor-widget__width-initial elementor-widget elementor-widget-text-editor\" data-id=\"5ba0d8c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>\u03b1= \u2206L\/(L0 *\u2206T)<br \/>\nmit:<br \/>\n\u2206L: Length change [m]<br \/>\nL0: Output length [m]<br \/>\n\u2206T: Temperature change [K]<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f333ecd elementor-widget elementor-widget-text-editor\" data-id=\"f333ecd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<section class=\"container\">\n<div class=\"row\">\n<div class=\"spb_content_element col-sm-12 spb_text_column\">\n<div class=\"spb_wrapper clearfix\">\n<p>giving results in \u03b1 units of K-1 (\u201cper Kelvin\u201d). It is temperature-dependent and therefore changes but often only to a small extent, depending on the temperature range under consideration. Its magnitude is typically 10-6 K-1 and is therefore often given in \u201cppm K-1\u201d.<\/p>\n<p>Materials with<strong>\u00a0low expansion coefficients<\/strong>\u00a0are, for example, quartz glass and the metal INVAR, which have an expansion coefficient of less than 1 ppm K-1. The largest coefficients of expansion have polymers (up to about 200 ppm K-1). Some materials have\u00a0<strong>negative expansions, depending on the temperature range.<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-77b5557 elementor-widget elementor-widget-heading\" data-id=\"77b5557\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Phase transformations<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a02ac69 elementor-widget elementor-widget-text-editor\" data-id=\"a02ac69\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Coefficients of expansion of different phases of the same material differ. For example, the coefficients of expansion of polymers above the <strong>glass<\/strong> <strong>transition<\/strong> temperature are greater than those below.<\/p>\n<p>Another known example is the phase <strong>transformations<\/strong> <strong>of<\/strong> <strong>elemental<\/strong> <strong>iron<\/strong>: up to 90\u00b0C, the cubic-space-centered crystal structure is stable (<strong>\u03b1<\/strong>-iron), from 906\u00b0C to 1401\u00b0C, it has the most cubic density (<strong>\u03b2<\/strong>-iron), and above 1539\u00b0C again it returns to the cubic-space-centered crystal structure (<strong>\u03b4<\/strong>-iron). Since the space filling of the most cubic-density packing (74%) is greater than that of the cubic-centered packing (68%), there are jumps in density and thus also in length in the phase transformations. These are used to detect phase transitions in iron alloys:<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-50997b7 elementor-widget__width-initial elementor-widget elementor-widget-image\" data-id=\"50997b7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"515\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Applikation-CTE-Dichte-2048x1317-1-1024x659.jpg\" class=\"attachment-large size-large wp-image-9979\" alt=\"\" srcset=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Applikation-CTE-Dichte-2048x1317-1-1024x659.jpg 1024w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Applikation-CTE-Dichte-2048x1317-1-300x193.jpg 300w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Applikation-CTE-Dichte-2048x1317-1-768x494.jpg 768w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Applikation-CTE-Dichte-2048x1317-1-1536x988.jpg 1536w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Applikation-CTE-Dichte-2048x1317-1.jpg 2048w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9b6a47e elementor-widget elementor-widget-heading\" data-id=\"9b6a47e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Measurement of the expansion coefficient<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f3a894e elementor-widget elementor-widget-text-editor\" data-id=\"f3a894e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The measuring method to be selected depends on the state of aggregation of the sample, the size of the coefficient of expansion of the sample to be measured and the temperature range to be considered. The mechanical properties of the sample must also be taken into account in the production of suitable samples and thus in the selection of the measurement method.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c9c0525 elementor-widget elementor-widget-heading\" data-id=\"c9c0525\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Liquids<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-07f3c6a elementor-widget elementor-widget-text-editor\" data-id=\"07f3c6a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The expansion or density of liquids is generally determined by pycnometers. In this case, a constant volume of the sample is temperature-controlled and the mass is determined. Fluids usually expand with increasing temperature. <strong>A well-known exception is water which has its density maximum at 4 \u00b0C (\u201canomaly of water\u201d).<\/strong><\/p><p>Furthermore, the so-called <strong>bending<\/strong> <strong>oscillation<\/strong> <strong>method<\/strong> is used. In this case, the density is calculated from the measurement of the natural frequency of a bending oscillator filled with the liquid to be investigated.<\/p><p>Liquids can also be measured using suitable liquid containers on a <a href=\"https:\/\/www.linseis.com\/en\/instruments\/dilatometer\/\"><strong>push rod dilatometer<\/strong><\/a>. In this case, make sure that no gases escape from the liquid or escaping gases also leave the container, whereby, however, the liquid sample must not escape.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6132160 elementor-widget elementor-widget-heading\" data-id=\"6132160\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Solid body<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bca70af elementor-widget elementor-widget-text-editor\" data-id=\"bca70af\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Solids are usually measured using (push rod) dilatometers or <a href=\"https:\/\/www.linseis.com\/en\/service-support\/methods-of-thermal-analysis\/thermomechanical-analysis\/\"><strong>thermo-mechanical analyzers (TMA)<\/strong><\/a>. In this case, the sample is introduced into an oven, and contact is made with it using a push rod. The change in length of the sample is transmitted by the push rod to a sensor. Depending on the oven used, a <strong>temperature<\/strong> <strong>range<\/strong> <strong>of -263 to +2800\u00b0C<\/strong> can be covered. Depending on the temperature range, push rods made of quartz glass, aluminum oxide or graphite are used. <strong>Differential<\/strong> <strong>transformers<\/strong> <strong>(LVDT \u2013 linear variable differential transformers)<\/strong> and recently also optical encoders are mostly used as sensors.<\/p><p>If the samples are difficult to process, fragile or easily deformable due to their properties, so that they do not withstand the force of the contacting push rod, <a href=\"https:\/\/www.linseis.com\/en\/instruments\/dilatometer\/dil-l74-optical-dilatometer\/\"><strong>optical dilatometers<\/strong><\/a>, also called <a href=\"https:\/\/www.linseis.com\/en\/instruments\/additional-devices-support\/relative-humidity-l40-rh\/\"><strong>heating microscopes<\/strong><\/a>, are used. Here, as in the case of the push rod dilatometer, the sample is placed in a furnace. The sample is observed using a camera whose images are measured. Through image analysis, not only the expansion (here even in 2 dimensions) but also changes in shape and melting can be observed and <a href=\"https:\/\/www.linseis.com\/en\/properties\/contact-angle\/\"><strong>contact angles<\/strong><\/a> calculated.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-80d22bb elementor-widget__width-initial elementor-widget elementor-widget-image\" data-id=\"80d22bb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"691\" height=\"303\" src=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Contact-angle.jpg\" class=\"attachment-large size-large wp-image-9999\" alt=\"\" srcset=\"https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Contact-angle.jpg 691w, https:\/\/www.linseis.com\/wp-content\/uploads\/2024\/07\/Contact-angle-300x132.jpg 300w\" sizes=\"(max-width: 691px) 100vw, 691px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3112811 elementor-widget elementor-widget-text-editor\" data-id=\"3112811\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Powdered samples are measured in special adapters. In this case, make sure that the enclosed air but not the sample, can escape<strong> (analogous to the measurement of liquids)<\/strong>. The degree of compaction (bulk density, vibration density and tapped density) of the sample must also be observed: it must not be changed by the measurement conditions.<\/p><p>Materials with particularly low expansion coefficients are measured using <strong>interferometric<\/strong> <strong>methods<\/strong>. In this case, monochromatic light is reflected from the sample and brought to interference with a second beam<strong> (principle of the Michelson interferometer)<\/strong>. The change in length results from the wavelength of the light used and the number of interferences. Such measuring devices are also called <a href=\"https:\/\/www.linseis.com\/en\/news\/the-new-linseis-l75-hp-high-pressure-dilatometer\/\"><strong>laser dilatometers<\/strong><\/a>.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fc98544 elementor-widget elementor-widget-heading\" data-id=\"fc98544\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Laser Dilatometer \u2013 Performing a measurement<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-95c1b4b elementor-widget__width-initial elementor-widget elementor-widget-video\" data-id=\"95c1b4b\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/3ON3jPSY9yE&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a85613a elementor-widget elementor-widget-spacer\" data-id=\"a85613a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-8d043c4 e-flex e-con-boxed e-con e-parent\" data-id=\"8d043c4\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d2ad453 elementor-widget elementor-widget-html\" data-id=\"d2ad453\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"FAQPage\",\r\n  \"mainEntity\": [{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"What is the coefficient of thermal expansion (CTE)?\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The coefficient of linear expansion \u03b1, also called CTE (\\\"coefficient of thermal expansion\\\"), is defined as the relative change in length with a temperature change of one Kelvin:\r\n\r\n\u03b1 = \u2206L \/ (L\u2080 * \u2206T)\r\n\r\nWhere:\r\n\r\n\u2206L: Change in length [m]\r\nL\u2080: Initial length [m]\r\n\u2206T: Temperature change [K]\r\nThis gives \u03b1 the unit K\u207b\u00b9 (\u201cper Kelvin\u201d). It is temperature-dependent and changes, often only slightly, depending on the temperature range under consideration. Its typical magnitude is 10\u207b\u2076 K\u207b\u00b9 and is therefore often expressed in \\\"ppm K\u207b\u00b9.\\\"\"\r\n    }\r\n  },{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"How does thermal expansion affect the density of a material?\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"Expansion occurs in all spatial directions, leading to a change in density since the mass remains constant. The expansion is direction-dependent in anisotropic materials, so the direction of expansion must be specified.\r\nTo determine density or the volumetric expansion coefficient, all spatial directions must be considered.\"\r\n    }\r\n  },{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"What methods are used to measure the expansion coefficient of solids?\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"Solids are usually measured using (push rod) dilatometers or thermomechanical analyzers (TMA). The sample is placed in a furnace and contacted with a push rod. The length change of the sample is transmitted to a sensor via the push rod.\r\nDepending on the furnace used, a temperature range from -263 to +2800 \u00b0C can be covered. Depending on the temperature range, push rods made of quartz glass, aluminum oxide, or graphite are used.\r\nSensors typically used include linear variable differential transformers (LVDT) and, more recently, optical encoders.\"\r\n    }\r\n  }]\r\n}\r\n<\/script>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The thermal expansion of materials can lead to major economic damage. In the construction industry, for example, expansion joints must be provided to compensate for changes in length due to temperature fluctuations.<\/p>\n","protected":false},"author":3,"featured_media":9948,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[106],"tags":[],"class_list":["post-22876","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-wiki"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/posts\/22876","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/comments?post=22876"}],"version-history":[{"count":0,"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/posts\/22876\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/media\/9948"}],"wp:attachment":[{"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/media?parent=22876"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/categories?post=22876"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/tags?post=22876"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}