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17.4142 14.4142 17.75 14 17.75H12H10C9.58579 17.75 9.25 17.4142 9.25 17Z" fill="currentColor"/> </svg> Аннотация</a>Аннотация<a href="/c/dielektriki-f7886d/annotation" class="bre-article-menu__list-item tw-mx-auto tw-flex lg:tw-hidden"><svg viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"> <path fill-rule="evenodd" clip-rule="evenodd" d="M18.2363 4.12686C18.2363 3.43651 18.796 2.87686 19.4863 2.87686C20.1767 2.87686 20.7363 3.43651 20.7363 4.12686C20.7363 4.81722 20.1767 5.37686 19.4863 5.37686C18.796 5.37686 18.2363 4.81722 18.2363 4.12686ZM19.4863 1.37686C17.9675 1.37686 16.7363 2.60808 16.7363 4.12686C16.7363 4.43206 16.786 4.72564 16.8778 4.99996H7C4.79086 4.99996 3 6.79082 3 8.99996V19C3 21.2091 4.79086 23 7 23H17C19.2091 23 21 21.2091 21 19V8.99996C21 8.16642 20.745 7.39244 20.3089 6.75173C21.4258 6.40207 22.2363 5.35911 22.2363 4.12686C22.2363 2.60808 21.0051 1.37686 19.4863 1.37686ZM7 6.49996H16.6319L14.6964 8.43547C14.4035 8.72837 14.4035 9.20324 14.6964 9.49613C14.9893 9.78903 15.4641 9.78903 15.757 9.49613L18.3547 6.89846C19.0438 7.34362 19.5 8.11852 19.5 8.99996V19C19.5 20.3807 18.3807 21.5 17 21.5H7C5.61929 21.5 4.5 20.3807 4.5 19V8.99996C4.5 7.61924 5.61929 6.49996 7 6.49996ZM9.25 12C9.25 11.5857 9.58579 11.25 10 11.25H12H14C14.4142 11.25 14.75 11.5857 14.75 12C14.75 12.4142 14.4142 12.75 14 12.75H12H10C9.58579 12.75 9.25 12.4142 9.25 12ZM9.25 17C9.25 16.5857 9.58579 16.25 10 16.25H12H14C14.4142 16.25 14.75 16.5857 14.75 17C14.75 17.4142 14.4142 17.75 14 17.75H12H10C9.58579 17.75 9.25 17.4142 9.25 17Z" fill="currentColor"/> </svg> Аннотация</a></div><div class="tw-grow tw-basis-0 max-md:tw-max-w-[80px]"><a href="/c/dielektriki-f7886d/references" class="bre-article-menu__list-item"><svg viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"> <path fill-rule="evenodd" clip-rule="evenodd" d="M5 3.25C3.48122 3.25 2.25 4.48122 2.25 6V16.1667C2.25 17.6854 3.48122 18.9167 5 18.9167H9.3C9.80519 18.9167 10.2974 19.1269 10.6662 19.5139C11.0362 19.9022 11.25 20.4361 11.25 21C11.25 21.4142 11.5858 21.75 12 21.75C12.4142 21.75 12.75 21.4142 12.75 21C12.75 20.4227 12.9564 19.8833 13.3026 19.4973C13.6464 19.114 14.0941 18.9167 14.5412 18.9167H19C20.5188 18.9167 21.75 17.6855 21.75 16.1667V6C21.75 4.48122 20.5188 3.25 19 3.25H15.3882C14.2627 3.25 13.2022 3.74922 12.4341 4.60572C12.266 4.79308 12.1147 4.99431 11.9809 5.20674C11.8358 4.98777 11.6713 4.78092 11.4885 4.58908C10.6758 3.73626 9.56568 3.25 8.4 3.25H5ZM12.75 17.993C13.2735 17.6237 13.8929 17.4167 14.5412 17.4167H19C19.6904 17.4167 20.25 16.857 20.25 16.1667V6C20.25 5.30964 19.6904 4.75 19 4.75H15.3882C14.7165 4.75 14.0534 5.04681 13.5507 5.60725C13.0457 6.17037 12.75 6.95001 12.75 7.77778V17.993ZM11.25 18.0438V7.77778C11.25 6.96341 10.9414 6.18924 10.4026 5.62389C9.86506 5.05976 9.14388 4.75 8.4 4.75H5C4.30964 4.75 3.75 5.30964 3.75 6V16.1667C3.75 16.857 4.30964 17.4167 5 17.4167H9.3C10.0044 17.4167 10.6825 17.64 11.25 18.0438Z" fill="currentColor"/> </svg> Библиография</a>Библиография<a href="/c/dielektriki-f7886d/references" class="bre-article-menu__list-item tw-mx-auto tw-flex lg:tw-hidden"><svg viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"> <path fill-rule="evenodd" clip-rule="evenodd" d="M5 3.25C3.48122 3.25 2.25 4.48122 2.25 6V16.1667C2.25 17.6854 3.48122 18.9167 5 18.9167H9.3C9.80519 18.9167 10.2974 19.1269 10.6662 19.5139C11.0362 19.9022 11.25 20.4361 11.25 21C11.25 21.4142 11.5858 21.75 12 21.75C12.4142 21.75 12.75 21.4142 12.75 21C12.75 20.4227 12.9564 19.8833 13.3026 19.4973C13.6464 19.114 14.0941 18.9167 14.5412 18.9167H19C20.5188 18.9167 21.75 17.6855 21.75 16.1667V6C21.75 4.48122 20.5188 3.25 19 3.25H15.3882C14.2627 3.25 13.2022 3.74922 12.4341 4.60572C12.266 4.79308 12.1147 4.99431 11.9809 5.20674C11.8358 4.98777 11.6713 4.78092 11.4885 4.58908C10.6758 3.73626 9.56568 3.25 8.4 3.25H5ZM12.75 17.993C13.2735 17.6237 13.8929 17.4167 14.5412 17.4167H19C19.6904 17.4167 20.25 16.857 20.25 16.1667V6C20.25 5.30964 19.6904 4.75 19 4.75H15.3882C14.7165 4.75 14.0534 5.04681 13.5507 5.60725C13.0457 6.17037 12.75 6.95001 12.75 7.77778V17.993ZM11.25 18.0438V7.77778C11.25 6.96341 10.9414 6.18924 10.4026 5.62389C9.86506 5.05976 9.14388 4.75 8.4 4.75H5C4.30964 4.75 3.75 5.30964 3.75 6V16.1667C3.75 16.857 4.30964 17.4167 5 17.4167H9.3C10.0044 17.4167 10.6825 17.64 11.25 18.0438Z" fill="currentColor"/> </svg> Библиография</a></div><div class="tw-grow tw-basis-0 max-md:tw-max-w-[80px]"><a href="/c/dielektriki-f7886d/versions" class="bre-article-menu__list-item"><svg viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"> <path fill-rule="evenodd" clip-rule="evenodd" d="M10.9565 3.85864H7.51619C7.8045 3.2057 8.4577 2.75 9.21734 2.75H13.5652H14.7687C15.4365 2.75 16.0697 3.0466 16.4972 3.55959L19.2502 6.86313C19.5871 7.26748 19.7717 7.77718 19.7717 8.30354V10.6957V16.7826C19.7717 17.5422 19.316 18.1954 18.663 18.4838V13.3043V10.9122C18.663 10.0349 18.3555 9.18542 17.7939 8.51149L15.0409 5.20795C14.3284 4.35298 13.273 3.85864 12.1601 3.85864H10.9565ZM14.913 22.7499C16.6051 22.7499 18.0354 21.6293 18.5022 20.0898C20.0762 19.8113 21.2717 18.4365 21.2717 16.7826V10.6957V8.30354C21.2717 7.42628 20.9641 6.57678 20.4025 5.90285L17.6496 2.59931C16.9371 1.74434 15.8817 1.25 14.7687 1.25H13.5652H9.21734C7.56341 1.25 6.18869 2.44548 5.91016 4.01947C4.37062 4.48633 3.25 5.91662 3.25 7.60864V18.9999C3.25 21.071 4.92893 22.7499 7 22.7499H14.913ZM7 5.35864C5.75736 5.35864 4.75 6.366 4.75 7.60864V18.9999C4.75 20.2426 5.75736 21.2499 7 21.2499H14.913C16.1557 21.2499 17.163 20.2426 17.163 18.9999V13.3043V10.9122C17.163 10.7991 17.1545 10.6867 17.1378 10.5761H15.3043C13.9296 10.5761 12.8152 9.46164 12.8152 8.08694V5.45611C12.6051 5.39215 12.3845 5.35864 12.1601 5.35864H10.9565H7ZM14.3152 6.68014V8.08694C14.3152 8.63322 14.758 9.07607 15.3043 9.07607H16.3118L14.3152 6.68014ZM6.72827 13.3043C6.72827 12.8901 7.06406 12.5543 7.47827 12.5543H14.4348C14.849 12.5543 15.1848 12.8901 15.1848 13.3043C15.1848 13.7185 14.849 14.0543 14.4348 14.0543H7.47827C7.06406 14.0543 6.72827 13.7185 6.72827 13.3043ZM7.47827 16.9022C7.06406 16.9022 6.72827 17.238 6.72827 17.6522C6.72827 18.0664 7.06406 18.4022 7.47827 18.4022H10.9565C11.3707 18.4022 11.7065 18.0664 11.7065 17.6522C11.7065 17.238 11.3707 16.9022 10.9565 16.9022H7.47827Z" fill="currentColor"/> </svg> Версии</a>Версии<a href="/c/dielektriki-f7886d/versions" class="bre-article-menu__list-item tw-mx-auto tw-flex lg:tw-hidden"><svg viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"> <path fill-rule="evenodd" clip-rule="evenodd" d="M10.9565 3.85864H7.51619C7.8045 3.2057 8.4577 2.75 9.21734 2.75H13.5652H14.7687C15.4365 2.75 16.0697 3.0466 16.4972 3.55959L19.2502 6.86313C19.5871 7.26748 19.7717 7.77718 19.7717 8.30354V10.6957V16.7826C19.7717 17.5422 19.316 18.1954 18.663 18.4838V13.3043V10.9122C18.663 10.0349 18.3555 9.18542 17.7939 8.51149L15.0409 5.20795C14.3284 4.35298 13.273 3.85864 12.1601 3.85864H10.9565ZM14.913 22.7499C16.6051 22.7499 18.0354 21.6293 18.5022 20.0898C20.0762 19.8113 21.2717 18.4365 21.2717 16.7826V10.6957V8.30354C21.2717 7.42628 20.9641 6.57678 20.4025 5.90285L17.6496 2.59931C16.9371 1.74434 15.8817 1.25 14.7687 1.25H13.5652H9.21734C7.56341 1.25 6.18869 2.44548 5.91016 4.01947C4.37062 4.48633 3.25 5.91662 3.25 7.60864V18.9999C3.25 21.071 4.92893 22.7499 7 22.7499H14.913ZM7 5.35864C5.75736 5.35864 4.75 6.366 4.75 7.60864V18.9999C4.75 20.2426 5.75736 21.2499 7 21.2499H14.913C16.1557 21.2499 17.163 20.2426 17.163 18.9999V13.3043V10.9122C17.163 10.7991 17.1545 10.6867 17.1378 10.5761H15.3043C13.9296 10.5761 12.8152 9.46164 12.8152 8.08694V5.45611C12.6051 5.39215 12.3845 5.35864 12.1601 5.35864H10.9565H7ZM14.3152 6.68014V8.08694C14.3152 8.63322 14.758 9.07607 15.3043 9.07607H16.3118L14.3152 6.68014ZM6.72827 13.3043C6.72827 12.8901 7.06406 12.5543 7.47827 12.5543H14.4348C14.849 12.5543 15.1848 12.8901 15.1848 13.3043C15.1848 13.7185 14.849 14.0543 14.4348 14.0543H7.47827C7.06406 14.0543 6.72827 13.7185 6.72827 13.3043ZM7.47827 16.9022C7.06406 16.9022 6.72827 17.238 6.72827 17.6522C6.72827 18.0664 7.06406 18.4022 7.47827 18.4022H10.9565C11.3707 18.4022 11.7065 18.0664 11.7065 17.6522C11.7065 17.238 11.3707 16.9022 10.9565 16.9022H7.47827Z" fill="currentColor"/> </svg> Версии</a></div></div></div></nav><div><meta itemprop="image primaryImageOfPage" content="https://i.bigenc.ru/resizer/resize?sign=7JK17_fgqWlQEFIk2cRkfA&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=120"><article itemscope itemprop="mainEntity" itemtype="https://schema.org/Article"><div itemprop="publisher" itemscope itemtype="https://schema.org/Organization"><meta itemprop="name" content="Автономная некоммерческая организация «Национальный научно-образовательный центр «Большая российская энциклопедия»"><meta itemprop="address" content="Покровский бульвар, д. 8, стр. 1А, Москва, 109028"><meta itemprop="telephone" content="+7 (495) 781-15-95"><meta 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Научно-образовательный портал «Большая российская энциклопедия»"><img src="https://i.bigenc.ru/resizer/resize?sign=7JK17_fgqWlQEFIk2cRkfA&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=120" onerror="this.setAttribute('data-error', 1)" alt="Физика" data-nuxt-img sizes="320px" srcset="https://i.bigenc.ru/resizer/resize?sign=7JK17_fgqWlQEFIk2cRkfA&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=120 120w,https://i.bigenc.ru/resizer/resize?sign=Jf8Ovt6NK1CJRMEXmLmu9w&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=320 320w,https://i.bigenc.ru/resizer/resize?sign=9FmjZNIS1_JG-eBy3nkCow&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=480 480w,https://i.bigenc.ru/resizer/resize?sign=W0YAxakNej-ihBYTmKOUhA&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=640 640w,https://i.bigenc.ru/resizer/resize?sign=bU5vxPnJKBxMhvgLEjl-uA&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=768 768w,https://i.bigenc.ru/resizer/resize?sign=CO7eqX0CglCAJmsuCYDJxQ&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=1024 1024w,https://i.bigenc.ru/resizer/resize?sign=SNrDJXfJeDUaOjs9TGABPA&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=1280 1280w,https://i.bigenc.ru/resizer/resize?sign=A65s2m2zZF6hgTDDppMoDA&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=1920 1920w" title="Физика" class="" itemprop="contentUrl"><div class="article-sidebar-meta"><dl class="tw-mt-0"><dt>Области знаний:</dt><dd>Диэлектрики и их свойства</dd></dl></div></div></div><div class="bre-article-page__container"><div class="bre-article-page__content bre-article-content"><header class="bre-article-header -show-on-tablet"><div class="bre-label__wrap"><a href="/t/chemicals" class="bre-label _link">Химические вещества</a>Химические вещества</div><h1 class="bre-article-header-title">Диэлектрики</h1></header><section class="tw-flex"><div class="-show-on-tablet tw-h-14 md:tw-h-20"><div><div><div itemprop="interactionStatistic" itemscope itemtype="https://schema.org/InteractionCounter"><meta itemprop="interactionType" content="https://schema.org/ViewAction"><meta itemprop="userInteractionCount" content=""></div><div itemprop="interactionStatistic" itemscope itemtype="https://schema.org/InteractionCounter"><meta itemprop="interactionType" content="https://schema.org/ShareAction"><meta itemprop="userInteractionCount" content=""></div><div itemprop="interactionStatistic" itemscope itemtype="https://schema.org/InteractionCounter"><meta itemprop="interactionType" content="https://schema.org/LikeAction"><meta itemprop="userInteractionCount" content=""></div></div></div></div></section><div class="js-preview-link-root"><div itemprop="articleBody" class="bre-article-body"><section><section>Диэле́ктрики, вещества, плохо проводящие <a href="/c/elektricheskii-tok-1ceecb" class="bre-preview-link" itemprop="url" data-external="false">электрический ток</a>. Термин «диэлектрики» введён <a href="/c/faradei-maikl-2bd1d1" class="bre-preview-link" itemprop="url" data-external="false">М. Фарадеем</a> для обозначения веществ, в которые проникает <a href="/c/elektrostatika-d0f99c" class="bre-preview-link" itemprop="url" data-external="false">электростатическое поле</a>. При помещении в <a href="/c/elektricheskoe-pole-21b68c" class="bre-preview-link" itemprop="url" data-external="false">электрическое</a> поле любого вещества <a href="/c/elektron-provodimosti-ca8846" class="bre-preview-link" itemprop="url" data-external="false">электроны</a> и атомные ядра испытывают силы со стороны этого поля. В результате часть зарядов направленно перемещается, создавая электрический ток. Остальные же заряды перераспределяются так, что «центры тяжести» положительных и отрицательных зарядов смещаются относительно друг друга. В последнем случае говорят о <a href="/c/poliarizatsiia-dielektrikov-7914b3" class="bre-preview-link" itemprop="url" data-external="false">поляризации</a> вещества. В зависимости от того, какой из этих двух процессов (поляризация или <a href="/c/elektricheskaia-provodimost-032955" class="bre-preview-link" itemprop="url" data-external="false">электрическая проводимость</a>) преобладает, вещества делят на диэлектрики (все неионизованные газы, некоторые жидкости и твёрдые тела) и проводники (металлы, <a href="/c/elektrolity-db9e74" class="bre-preview-link" itemprop="url" data-external="false">электролиты</a>, <a href="/c/plazma-0c9643" class="bre-preview-link" itemprop="url" data-external="false">плазма</a>). Электрическая проводимость диэлектриков по сравнению с металлами очень мала. Удельное <a href="/c/elektricheskoe-soprotivlenie-32aba1" class="bre-preview-link" itemprop="url" data-external="false">электрическое сопротивление</a> диэлектриков лежит в пределах 108–1017 Ом·см, металлов – 10–6–10–4 Ом·см.Количественное различие в электрической проводимости диэлектриков и металлов классическая физика пыталась объяснить тем, что в металлах есть свободные электроны, в то время как в диэлектриках все электроны связаны (принадлежат отдельным атомам) и электрическое поле их не отрывает, а лишь слегка смещает.Квантовая теория <a href="/c/tviordoe-telo-e5875e" class="bre-preview-link" itemprop="url" data-external="false">твёрдого тела</a> объясняет различие электрических свойств металлов и диэлектриков различным распределением электронов по энергетическим уровням. В диэлектриках верхний заполненный электронами энергетический уровень совпадает с верхней границей одной из <a href="/c/razreshionnaia-zona-74d72d" class="bre-preview-link" itemprop="url" data-external="false">разрешённых зон</a> (в металлах он лежит внутри разрешённой зоны), а ближайшие свободные уровни отделены от заполненных <a href="/c/zapreshchionnaia-zona-73a605" class="bre-preview-link" itemprop="url" data-external="false">запрещённой зоной</a>, преодолеть которую под действием не слишком сильных электрических полей электроны не могут (<a href="/c/zonnaia-teoriia-8a473a" class="bre-preview-link" itemprop="url" data-external="false">зонная теория</a>). Действие электрического поля сводится к перераспределению <a href="/c/elektronnaia-plotnost-a94534" class="bre-preview-link" itemprop="url" data-external="false">электронной плотности</a>, которое приводит к поляризации диэлектрика.<h2 id="h2_polyarizatsiya_dielektrikov">Поляризация диэлектриков</h2>Механизмы поляризации диэлектриков зависят от характера <a href="/c/khimicheskaia-sviaz-df39ab" class="bre-preview-link" itemprop="url" data-external="false">химической связи</a>, т. е. распределения электронной плотности в диэлектриках. В <a href="/c/ionnye-kristally-59353c" class="bre-preview-link" itemprop="url" data-external="false">ионных кристаллах</a> (например, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>NaCl</mtext></mrow><annotation encoding="application/x-tex">\text{NaCl}</annotation></semantics></math>NaCl) поляризация является результатом сдвига ионов относительно друг друга (ионная поляризация), а также деформации электронных оболочек отдельных ионов (электронная поляризация), т. е. суммой ионной и электронной поляризаций. В кристаллах с <a href="/c/kovalentnaia-sviaz-fb3867" class="bre-preview-link" itemprop="url" data-external="false">ковалентной связью</a> (например, <a href="/c/almaz-48db34" class="bre-preview-link" itemprop="url" data-external="false">алмаз</a>), где электронная плотность равномерно распределена между атомами, поляризация обусловлена главным образом смещением электронов, осуществляющих химическую связь. В т. н. полярных диэлектриках (например, твёрдый <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mtext>H</mtext><mn>2</mn></msub><mtext>S</mtext></mrow><annotation encoding="application/x-tex">\text{H}_2\text{S}</annotation></semantics></math>H2S) группы атомов представляют собой <a href="/c/elektricheskii-dipol-fee4cb" class="bre-preview-link" itemprop="url" data-external="false">электрические диполи</a>, которые ориентированы хаотически в отсутствии электрического поля, а в поле приобретают преимущественную ориентацию. Такая ориентационная поляризация типична для многих жидкостей и газов. Похожий механизм поляризации связан с «перескоком» под действием электрического поля отдельных ионов из одних положений равновесия в решётке в другие. Особенно часто такой механизм наблюдается в веществах с <a href="/c/vodorodnaia-sviaz-7f489c" class="bre-preview-link" itemprop="url" data-external="false">водородной связью</a> (например, <a href="/c/liod-834d88" class="bre-preview-link" itemprop="url" data-external="false">лёд</a>), где атомы водорода имеют несколько положений равновесия.Поляризация диэлектриков характеризуется вектором поляризации <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">P</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{P}</annotation></semantics></math>P, который представляет собой электрический дипольный момент единицы объёма диэлектрика:<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">P</mi><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></msubsup><msub><mi mathvariant="bold-italic">P</mi><mi>i</mi></msub><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">\boldsymbol{P}= \sum\limits_{i=1}^N \boldsymbol{P}_i,</annotation></semantics></math>P=i=1∑NPi,где <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold-italic">P</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\boldsymbol{P}_i</annotation></semantics></math>Pi – дипольные моменты частиц (атомов, ионов, молекул), <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext mathvariant="italic">N</mtext></mrow><annotation encoding="application/x-tex">\textit{N}</annotation></semantics></math>N – число частиц в единице объёма. Вектор <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">P</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{P}</annotation></semantics></math>P зависит от напряжённости электрического поля <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">E</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{E}</annotation></semantics></math>E. В слабых полях <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">P</mi><mo>=</mo><msub><mi>ε</mi><mn>0</mn></msub><mi><mrow><mtext mathvariant="bold">ϰ</mtext><mi mathvariant="bold-italic">E</mi></mrow></mi></mrow><annotation encoding="application/x-tex">\boldsymbol{P}={ε}_0\boldsymbol{ϰE}</annotation></semantics></math>P=ε0ϰE. Коэффициент пропорциональности <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold">ϰ</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{ϰ}</annotation></semantics></math>ϰ называется диэлектрической восприимчивостью. Часто вместо вектора <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">P</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{P}</annotation></semantics></math>P используют вектор электрической индукции в системе СИ:<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">D</mi><mo>=</mo><msub><mi>ε</mi><mn>0</mn></msub><mi mathvariant="bold-italic">E</mi><mo>+</mo><mi mathvariant="bold-italic">P</mi><mo>=</mo><msub><mi>ε</mi><mn>0</mn></msub><mi>ε</mi><mi mathvariant="bold-italic">E</mi><mo separator="true">,</mo><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\boldsymbol{D}={ε}_0\boldsymbol{E}+\boldsymbol{P}={ε}_0{ε}\boldsymbol{E}, (1)</annotation></semantics></math>D=ε0E+P=ε0εE,(1)где <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ε</mi></mrow><annotation encoding="application/x-tex">{ε}</annotation></semantics></math>ε – <a href="/c/dielektricheskaia-pronitsaemost-adb8e2" class="bre-preview-link" itemprop="url" data-external="false">диэлектрическая проницаемость</a>, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ε</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">{ε}_0</annotation></semantics></math>ε0 – <a href="/c/elektricheskaia-postoiannaia-978087" class="bre-preview-link" itemprop="url" data-external="false">электрическая постоянная</a>. Величины <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold">ϰ</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{ϰ}</annotation></semantics></math>ϰ и <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ε</mi></mrow><annotation encoding="application/x-tex">{ε}</annotation></semantics></math>ε – основные характеристики диэлектриков. В анизотропных диэлектриках (например, в некубических кристаллах) направление <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">P</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{P}</annotation></semantics></math>P определяется не только направлением поля <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">E</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{E}</annotation></semantics></math>E, но и направлением <a href="/c/simmetriia-kristallov-a007ea" class="bre-preview-link" itemprop="url" data-external="false">осей симметрии кристалла</a>. Поэтому вектор <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">P</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{P}</annotation></semantics></math>P будет составлять различные углы с вектором <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">E</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{E}</annotation></semantics></math>E в зависимости от ориентации <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">E</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{E}</annotation></semantics></math>E по отношению к осям симметрии кристалла. В этом случае вектор <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">D</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{D} </annotation></semantics></math>D будет определяться через вектор <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">E</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{E}</annotation></semantics></math>E с помощью не одной величины ε, а нескольких (в общем случае шести), образующих тензор диэлектрической проницаемости.<h2 id="h2_dielektriki_v_peremennom_pole">Диэлектрики в переменном поле</h2>Если поле <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">E</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{E}</annotation></semantics></math>E изменяется во времени <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>t</mtext></mrow><annotation encoding="application/x-tex">\text{t}</annotation></semantics></math>t, то поляризация диэлектриков не успевает следовать за ним, т. к. смещения зарядов не могут происходить мгновенно. Поскольку любое переменное поле можно представить в виде совокупности полей, меняющихся по <a href="/c/garmonicheskaia-funktsiia-86e8e0" class="bre-preview-link" itemprop="url" data-external="false">гармоническому закону</a>, то достаточно изучить поведение диэлектриков в поле <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">E</mi><mo>=</mo><msub><mi>E</mi><mn>0</mn></msub><mi>s</mi><mi>i</mi><mi>n</mi><mo stretchy="false">(</mo><mi>ω</mi><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\boldsymbol{E}={E}_0sin(ωt)</annotation></semantics></math>E=E0sin(ωt), где <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ω</mi></mrow><annotation encoding="application/x-tex">{ω}</annotation></semantics></math>ω – частота переменного поля, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold-italic">E</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">\boldsymbol{E}_0</annotation></semantics></math>E0 – амплитуда напряжённости поля. Под действием этого поля <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">D</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{D} </annotation></semantics></math>D и <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">P</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{P}</annotation></semantics></math>P будут колебаться тоже гармонически и с той же частотой. Однако между колебаниями <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">P</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{P}</annotation></semantics></math>P и <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">E</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{E}</annotation></semantics></math>E появляется разность фаз δ, что вызвано отставанием поляризации <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">P</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{P}</annotation></semantics></math>P от поля <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">E</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{E}</annotation></semantics></math>E. Гармонический закон можно представить в комплексном виде <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">E</mi><mo>=</mo><msub><mi mathvariant="bold-italic">E</mi><mn>0</mn></msub><mrow><mtext>е</mtext><mi>i</mi><mi>ω</mi><mi>t</mi></mrow></mrow><annotation encoding="application/x-tex">\boldsymbol{E}=\boldsymbol{E}_0{еiωt}</annotation></semantics></math>E=E0еiωt, тогда <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">D</mi><mo>=</mo><msub><mi mathvariant="bold-italic">D</mi><mn>0</mn></msub><mrow><mtext>е</mtext><mi>i</mi><mi>ω</mi><mi>t</mi></mrow></mrow><annotation encoding="application/x-tex">\boldsymbol{D}=\boldsymbol{D}_0{еiωt}</annotation></semantics></math>D=D0еiωt, причём <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold-italic">D</mi><mn>0</mn></msub><mo>=</mo><mrow><mi>ε</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow><msub><mi mathvariant="bold-italic">E</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">\boldsymbol{D}_0={ε(ω)}\boldsymbol{E}_0</annotation></semantics></math>D0=ε(ω)E0. Диэлектрическая проницаемость в этом случае является комплексной величиной: <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>ε</mtext><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>ε</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo>+</mo><msup><mrow><mi>i</mi><mi>ε</mi></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msup></mrow><annotation encoding="application/x-tex">\textε(ω)={ε}'+{iε}''</annotation></semantics></math>ε(ω)=ε′+iε′′; <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>ε</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">{ε'}</annotation></semantics></math>ε′ и <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>ε</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msup></mrow><annotation encoding="application/x-tex">{ε''}</annotation></semantics></math>ε′′ зависят от частоты переменного электрического поля <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ω</mi></mrow><annotation encoding="application/x-tex">{ω}</annotation></semantics></math>ω. Абсолютная величина<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∣</mi><mrow><mi>ε</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow><mi mathvariant="normal">∣</mi><mo>=</mo><mroot><mrow><mo stretchy="false">(</mo><msup><mi>ε</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mo>+</mo><mo stretchy="false">(</mo><msup><mi>ε</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msup><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><mrow></mrow></mroot></mrow><annotation encoding="application/x-tex">|{ε(ω)}|= \sqrt[]{(ε')^2+(ε'')^2} </annotation></semantics></math>∣ε(ω)∣=(ε′)2+(ε′′)2<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.28em' viewBox='0 0 400000 1296' preserveAspectRatio='xMinYMin slice'><path d='M263,681c0.7,0,18,39.7,52,119 c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120 c340,-704.7,510.7,-1060.3,512,-1067 l0 -0 c4.7,-7.3,11,-11,19,-11 H40000v40H1012.3 s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232 c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1 s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26 c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z M1001 80h400000v40h-400000z'/></svg>определяет амплитуду колебания <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">D</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{D} </annotation></semantics></math>D, а отношение <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><msup><mi>ε</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mi mathvariant="normal">/</mi><msup><mi>ε</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msup></mrow><mo>=</mo><mrow><mi>t</mi><mi>g</mi><mi>δ</mi></mrow></mrow><annotation encoding="application/x-tex">{ε'/ε''}={tgδ}</annotation></semantics></math>ε′/ε′′=tgδ – разность фаз между колебаниями <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">D</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{D} </annotation></semantics></math>D и <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">E</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{E}</annotation></semantics></math>E. Величина <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>δ</mi></mrow><annotation encoding="application/x-tex">{δ}</annotation></semantics></math>δ называется углом <a href="/c/dielektricheskie-poteri-b5c1a0" class="bre-preview-link" itemprop="url" data-external="false">диэлектрических потерь</a>. В постоянном электрическом поле <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ω</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">{ω=0}</annotation></semantics></math>ω=0, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>ε</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msup><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">{ε''=0}</annotation></semantics></math>ε′′=0, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>ε</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo>=</mo><mi>ε</mi></mrow><annotation encoding="application/x-tex">{ε'=ε}</annotation></semantics></math>ε′=ε.В переменных электрических полях высоких частот свойства диэлектрики характеризуются показателями преломления <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">{n}</annotation></semantics></math>n и поглощения <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">{k}</annotation></semantics></math>k (вместо <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>ε</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">{ε'}</annotation></semantics></math>ε′ и <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>ε</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msup></mrow><annotation encoding="application/x-tex">{ε''}</annotation></semantics></math>ε′′). Первый равен отношению скоростей распространения <a href="/c/elektromagnitnye-volny-22ae4f" class="bre-preview-link" itemprop="url" data-external="false">электромагнитных волн</a> в диэлектриках и в <a href="/c/vakuum-09e2ec" class="bre-preview-link" itemprop="url" data-external="false">вакууме</a>. Показатель поглощения <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">{k}</annotation></semantics></math>k характеризует затухание электромагнитных волн в диэлектриках. Величины <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">{n}</annotation></semantics></math>n, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">{k}</annotation></semantics></math>k, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>ε</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">{ε'}</annotation></semantics></math>ε′ и <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>ε</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msup></mrow><annotation encoding="application/x-tex">{ε''}</annotation></semantics></math>ε′′ связаны соотношением<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>+</mo><mrow><mi>i</mi><mi>k</mi></mrow><mo>=</mo><mroot><mrow><msup><mi>ε</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo>+</mo><mrow><mi>i</mi><msup><mi>ε</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msup></mrow></mrow><mrow></mrow></mroot><mi mathvariant="normal">.</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">{n}+{ik}= \sqrt[]{{ε'}+{iε''}}. (2)</annotation></semantics></math>n+ik=ε′+iε′′<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z'/></svg>.(2)<h2 id="h2_polyarizatsiya_dielektrikov_v_otsutstvii_elektricheskogo_polya">Поляризация диэлектриков в отсутствии электрического поля</h2>В ряде твёрдых диэлектриков (пироэлектриках, сегнетоэлектриках, пьезоэлектриках, электретах) поляризация может существовать и без электрического поля, т. е. может быть вызвана другими причинами. Так, в пироэлектриках заряды располагаются столь несимметрично, что центры тяжести зарядов противоположного знака не совпадают, т. е. диэлектрик спонтанно поляризован. Однако поляризация в пироэлектриках проявляется только при изменении температуры, когда компенсирующие поляризацию электрические заряды не успевают перестроиться. Разновидностью пироэлектриков являются сегнетоэлектрики, спонтанная поляризация которых может существенно изменяться под влиянием внешних воздействий (температуры, электрического поля). В пьезоэлектриках поляризация возникает при деформации кристалла, что связано с особенностями их кристаллической структуры. Поляризация в отсутствии поля может наблюдаться также в некоторых веществах типа смол и стёкол, называемых электретами.<h2 id="h2_elektricheskaya_provodimost'_dielektrikov">Электрическая проводимость диэлектриков</h2>Электрическая проводимость диэлектриков мала, но всегда отлична от нуля. Подвижными носителями заряда в диэлектриках могут быть электроны и ионы. В обычных условиях электронная проводимость диэлектриков мала по сравнению с ионной. <a href="/c/ionnaia-provodimost-b72191" class="bre-preview-link" itemprop="url" data-external="false">Ионная проводимость</a> может быть обусловлена перемещением как собственных ионов, так и примесных. Возможность перемещения ионов по кристаллу связана с наличием <a href="/c/defekty-v-kristallakh-fedef8" class="bre-preview-link" itemprop="url" data-external="false">дефектов в кристаллах</a>. Если, например, в кристалле есть <a href="/c/vakansiia-v-kristalle-e55659" class="bre-preview-link" itemprop="url" data-external="false">вакансия</a>, то под действием поля соседний ион может занять её, во вновь образовавшуюся вакансию может перейти следующий ион и т. д. В итоге происходит движение вакансий, которое приводит к переносу заряда через весь кристалл. Перемещение ионов происходит и в результате их перескоков по междоузлиям. С ростом температуры ионная проводимость возрастает. Заметный вклад в электрическую проводимость диэлектриков может вносить поверхностная проводимость (<a href="/c/poverkhnostnye-iavleniia-1ecbbd" class="bre-preview-link" itemprop="url" data-external="false">поверхностные явления</a>).<h2 id="h2_proбoi_dielektrikov">Пробой диэлектриков</h2>Плотность электрического тока <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">{j}</annotation></semantics></math>j через диэлектрик пропорциональна напряжённости электрического поля <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">E</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{E}</annotation></semantics></math>E (закон Ома): <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi><mo>=</mo><mi>σ</mi><mi mathvariant="bold-italic">E</mi></mrow><annotation encoding="application/x-tex">{j}=σ\boldsymbol{E}</annotation></semantics></math>j=σE, где <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">{σ}</annotation></semantics></math>σ – электрическая проводимость диэлектрика. Однако в достаточно сильных полях ток нарастает быстрее, чем по закону Ома. При некотором критическом значении <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold-italic">E</mi><mtext>пр</mtext></msub></mrow><annotation encoding="application/x-tex">\boldsymbol{E}_{пр}</annotation></semantics></math>Eпр наступает электрический пробой диэлектрика. Величина <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold-italic">E</mi><mtext>пр</mtext></msub></mrow><annotation encoding="application/x-tex">\boldsymbol{E}_{пр}</annotation></semantics></math>Eпр называется <a href="/c/elektricheskaia-prochnost-d7565a" class="bre-preview-link" itemprop="url" data-external="false">электрической прочностью диэлектрика</a>. При пробое почти весь ток течёт по узкому каналу (<a href="/c/shnurovanie-toka-2394bd" class="bre-preview-link" itemprop="url" data-external="false">шнурование тока</a>). В этом канале <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">{j}</annotation></semantics></math>j достигает больших величин, что может привести к разрушению диэлектрика: образуется сквозное отверстие или диэлектрик проплавляется по каналу. В канале могут протекать химические реакции; например, в органических диэлектриках осаждается углерод, в ионных кристаллах – металл (металлизация канала) и т. п. Пробою способствуют всегда присутствующие в диэлектрике неоднородности, поскольку в местах неоднородностей поле <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">E</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{E}</annotation></semantics></math>E может локально возрастать.В твёрдых диэлектриках различают тепловой и электрический пробои. При тепловом пробое с ростом <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">{j}</annotation></semantics></math>j растёт количество теплоты, выделяемое в диэлектрике, и, следовательно, температура диэлектрика, что приводит к увеличению числа носителей заряда <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">{n}</annotation></semantics></math>n и уменьшению удельного электрического сопротивления <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ρ</mi></mrow><annotation encoding="application/x-tex">{ρ}</annotation></semantics></math>ρ. При электрическом пробое с ростом поля возрастает генерация носителей заряда под действием поля и <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ρ</mi></mrow><annotation encoding="application/x-tex">{ρ}</annotation></semantics></math>ρ тоже уменьшается.Электрическая прочность жидких диэлектриков в сильной степени зависит от чистоты жидкости. Наличие примесей и загрязнений существенно понижает <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold-italic">E</mi><mtext>пр</mtext></msub></mrow><annotation encoding="application/x-tex">\boldsymbol{E}_{пр}</annotation></semantics></math>Eпр. Для чистых однородных жидких диэлектриков <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold-italic">E</mi><mtext>пр</mtext></msub></mrow><annotation encoding="application/x-tex">\boldsymbol{E}_{пр}</annotation></semantics></math>Eпр близка к <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold-italic">E</mi><mtext>пр</mtext></msub></mrow><annotation encoding="application/x-tex">\boldsymbol{E}_{пр}</annotation></semantics></math>Eпр твёрдых диэлектриков. Пробой в газе связан с ударной ионизацией и проявляется в виде электрического разряда.<h2 id="h2_nelineinыe_svoistva_dielektrikov">Нелинейные свойства диэлектриков</h2>Линейная зависимость <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">P</mi><mo>=</mo><msub><mi>ε</mi><mn>0</mn></msub><mi><mrow><mtext mathvariant="bold">ϰ</mtext><mi mathvariant="bold-italic">E</mi></mrow></mi></mrow><annotation encoding="application/x-tex">\boldsymbol{P}={ε}_0\boldsymbol{ϰE}</annotation></semantics></math>P=ε0ϰE справедлива только для полей <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold-italic">E</mi></mrow><annotation encoding="application/x-tex">\boldsymbol{E}</annotation></semantics></math>E, значительно меньших внутрикристаллических полей <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold-italic">E</mi><mtext>кр</mtext></msub></mrow><annotation encoding="application/x-tex">\boldsymbol{E}_{кр} </annotation></semantics></math>Eкр (<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold-italic">E</mi><mtext>кр</mtext></msub></mrow><annotation encoding="application/x-tex">\boldsymbol{E}_{кр} </annotation></semantics></math>Eкр порядка 108 В/см). Так как <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold-italic">E</mi><mtext>пр</mtext></msub><mo>≪</mo><msub><mi mathvariant="bold-italic">E</mi><mtext>кр</mtext></msub></mrow><annotation encoding="application/x-tex">\boldsymbol{E}_{пр}≪\boldsymbol{E}_{кр}</annotation></semantics></math>Eпр≪Eкр, то в большинстве диэлектриков не удаётся наблюдать нелинейную зависимость <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi><mrow><mi mathvariant="bold-italic">P</mi><mo stretchy="false">(</mo><mi mathvariant="bold-italic">E</mi><mo stretchy="false">)</mo></mrow></mi></mrow><annotation encoding="application/x-tex">\boldsymbol{P(E)}</annotation></semantics></math>P(E) в постоянном электрическом поле. Исключение составляют <a href="/c/segnetoelektriki-b88eeb" class="bre-preview-link" itemprop="url" data-external="false">сегнетоэлектрики</a>, в которых в сегнетоэлектрические области и вблизи точек <a href="/c/fazovyi-perekhod-002599" class="bre-preview-link" itemprop="url" data-external="false">фазовых переходов</a> наблюдается сильная нелинейная зависимость <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi><mrow><mi mathvariant="bold-italic">P</mi><mo stretchy="false">(</mo><mi mathvariant="bold-italic">E</mi><mo stretchy="false">)</mo></mrow></mi></mrow><annotation encoding="application/x-tex">\boldsymbol{P(E)}</annotation></semantics></math>P(E). При высоких частотах электрическая прочность диэлектриков повышается, поэтому нелинейные свойства любых диэлектриков проявляются в ВЧ-полях больших амплитуд. В частности, в луче лазера могут быть созданы электрические поля напряжённостью порядка 108 В/см, в которых становятся существенными нелинейные свойства диэлектриков, что позволяет осуществить преобразование частоты света, <a href="/c/samofokusirovka-sveta-5cc915" class="bre-preview-link" itemprop="url" data-external="false">самофокусировку света</a> и другие нелинейные эффекты (<a href="/c/nelineinaia-optika-8987ad" class="bre-preview-link" itemprop="url" data-external="false">нелинейная оптика</a>).<h2 id="h2_primenenie_dielektrikov">Применение диэлектриков</h2>Диэлектрики используются главным образом как электроизоляционные материалы. <a href="/c/p-ezoelektriki-5a5199" class="bre-preview-link" itemprop="url" data-external="false">Пьезоэлектрики</a> применяются для преобразования механических сигналов (перемещений, <a href="/c/deformatsiia-92bf2c" class="bre-preview-link" itemprop="url" data-external="false">деформаций</a>, <a href="/c/akustika-95eeec" class="bre-preview-link" itemprop="url" data-external="false">звуковых колебаний</a>) в электрические и наоборот (пьезоэлектрический преобразователь); <a href="/c/piroelektriki-15fe2b" class="bre-preview-link" itemprop="url" data-external="false">пироэлектрики</a> – как тепловые детекторы различных излучений, особенно ИК-излучения; <a href="/c/segnetoelektriki-b88eeb" class="bre-preview-link" itemprop="url" data-external="false">сегнетоэлектрики</a>, будучи также пьезоэлектриками и пироэлектриками, применяются, кроме того, как конденсаторные материалы (из-за высокой диэлектрической проницаемости), а также как нелинейные элементы и элементы памяти в разнообразных устройствах. Большинство <a href="/c/opticheskie-materialy-ad9576" class="bre-preview-link" itemprop="url" data-external="false">оптических материалов</a> является диэлектриками.<a href="/a/ap-levanyuk-911d28" class="">Леванюк Аркадий Петрович</a>, <a href="/a/dg-sannikov-0f5a5d" class="">Санников Дмитрий Германович</a></section></section></div><meta itemprop="description" content="Диэле́ктрики, вещества, плохо проводящие электрический ток. Термин «диэлектрики» введён М. Фарадеем для обозначения веществ, в которые проникает...">Опубликовано 16 декабря 2022 г. в 21:00 (GMT+3). Последнее обновление 16 декабря 2022 г. в 21:00 (GMT+3).<button type="button" class="b-button tw-gap-2 b-button--link -text-button-text tw-rounded-lg tw-cursor-pointer" data-v-cfbedafc>Связаться с редакцией</button></div></div><div class="bre-tags-wrap"><a href="/l/fizika-dielektrikov-e7e56b" class="bre-article-tag bre-article-tag__link _default _no-border" data-v-063d9480>#Физика диэлектриков</a><a href="/l/fizicheskaia-elektronika-ab7e51" class="bre-article-tag bre-article-tag__link _default _no-border" data-v-063d9480>#Физическая электроника</a></div></div><aside class="bre-article-page__sidebar -show-on-desktop-s" style=""><nav class="bre-article-loc lg:tw-sticky"><div class="bre-article-loc-button">Содержание<svg viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path d="M6 9l6 6 6-6" stroke="currentColor" stroke-width="1.5" stroke-linecap="round"/></svg> <div class="bre-article-loc-short">Поляризация диэлектриков</div></div></nav><div class="bre-article-page__sidebar-wrapper"><div class="article-sidebar"><div class="article-sidebar-button -show-on-tablet -hide-on-desktop-s">Информация<svg viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"><path d="M6 9l6 6 6-6" stroke="currentColor" stroke-width="1.5" stroke-linecap="round"/></svg> <div class="article-sidebar-text -show-on-tablet -hide-on-desktop-s"></div></div><div class="article-sidebar-wrapper -hide-on-tablet"><meta itemprop="name" content="Физика"><meta itemprop="caption" content="Физика. Научно-образовательный портал «Большая российская энциклопедия»"><img src="https://i.bigenc.ru/resizer/resize?sign=7JK17_fgqWlQEFIk2cRkfA&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=120" onerror="this.setAttribute('data-error', 1)" alt="Физика" data-nuxt-img sizes="320px" srcset="https://i.bigenc.ru/resizer/resize?sign=7JK17_fgqWlQEFIk2cRkfA&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=120 120w,https://i.bigenc.ru/resizer/resize?sign=Jf8Ovt6NK1CJRMEXmLmu9w&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=320 320w,https://i.bigenc.ru/resizer/resize?sign=9FmjZNIS1_JG-eBy3nkCow&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=480 480w,https://i.bigenc.ru/resizer/resize?sign=W0YAxakNej-ihBYTmKOUhA&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=640 640w,https://i.bigenc.ru/resizer/resize?sign=bU5vxPnJKBxMhvgLEjl-uA&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=768 768w,https://i.bigenc.ru/resizer/resize?sign=CO7eqX0CglCAJmsuCYDJxQ&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=1024 1024w,https://i.bigenc.ru/resizer/resize?sign=SNrDJXfJeDUaOjs9TGABPA&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=1280 1280w,https://i.bigenc.ru/resizer/resize?sign=A65s2m2zZF6hgTDDppMoDA&filename=vault/2a7425e2f5716d70117aeb7f30155e04.webp&width=1920 1920w" title="Физика" class="" itemprop="contentUrl"><div class="article-sidebar-meta"><dl class="tw-mt-0"><dt>Области знаний:</dt><dd>Диэлектрики и их свойства</dd></dl></div></div></div></div></aside></div></article></div></div><div></div></main><footer class="bre-footer" itemscope itemprop="hasPart" itemtype="https://schema.org/WPFooter"><meta itemprop="copyrightNotice" content="&copy;&nbsp;АНО БРЭ, 2022&nbsp;&mdash;&nbsp;2024. 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Однако поляризация в пироэлектриках проявляется только при изменении температуры, когда компенсирующие поляризацию электрические заряды не успевают перестроиться. Разновидностью пироэлектриков являются сегнетоэлектрики, спонтанная поляризация которых может существенно изменяться под влиянием внешних воздействий (температуры, электрического поля). В пьезоэлектриках поляризация возникает при деформации кристалла, что связано с особенностями их кристаллической структуры. 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Исключение составляют ",{"attrs":10,"content":10,"marks":1357,"text":1363,"type":48},[1358],{"attrs":1359,"content":10,"marks":10,"text":13,"type":62},{"content_id":1360,"external":12,"graph_link":6,"href":56,"kind_id":57,"link":1361,"link_type":306,"navigation_value":10,"target":13,"version":45},"b88eeb57-fccc-43ac-bf68-61b3c8a93671",{"slug":1362,"type":60},"segnetoelektriki-b88eeb","сегнетоэлектрики",{"attrs":10,"content":10,"marks":10,"text":1365,"type":48},", в которых в сегнетоэлектрические области и вблизи точек ",{"attrs":10,"content":10,"marks":1367,"text":1373,"type":48},[1368],{"attrs":1369,"content":10,"marks":10,"text":13,"type":62},{"content_id":1370,"external":12,"graph_link":6,"href":56,"kind_id":57,"link":1371,"link_type":105,"navigation_value":10,"target":13,"version":45},"0025995d-5950-43ba-898c-460a4e70d38f",{"slug":1372,"type":60},"fazovyi-perekhod-002599","фазовых переходов",{"attrs":10,"content":10,"marks":10,"text":1375,"type":48}," наблюдается сильная нелинейная зависимость ",{"attrs":1377,"content":10,"marks":1378,"text":13,"type":287},{"display":285,"displayMode":13,"src":1350,"title":13},[1379],{"attrs":1380,"content":10,"marks":10,"text":13,"type":357},{"version":45},{"attrs":10,"content":10,"marks":10,"text":1382,"type":48},". При высоких частотах электрическая прочность диэлектриков повышается, поэтому нелинейные свойства любых диэлектриков проявляются в ВЧ-полях больших амплитуд. 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