ПОЧТИ АБСОЛЮТНЫЕ УРАВНЕНИЯ СОСТОЯНИЯ АЛМАЗА, Ag, Al, Au, Cu, Mo, Nb, Pt, Ta, W ДЛЯ КВАЗИГИДРОСТАТИЧЕСКИХ УСЛОВИЙ

По единой схеме с использованием модифицированного формализма из [Dorogokupets, Oganov, 2005, 2007] построены уравнения состояния алмаза, Ag, Al, Au, Cu, Mo, Nb, Pt, Ta, W путем одновременной оптимизации ударных данных, ультразвуковых, рентгеновских, дилатометрических и термохимических измерений в диапазоне температур от ~100 К до температуры плавления и до давлений несколько Mbar в зависимости от вещества. Комнатная изотерма была задана двумя формами: уравнением В. Хольцапфеля [Holzapfel, 2001, 2010], которое является интерполяционным между низкими давлениями (x≥1) и давлением при бесконечном сжатии (x=0), соответствующим модели Томаса-Ферми, и уравнением П. Вине [Vinet et al., 1987]. Объемная зависимость параметра Грюнейзена рассчитана по соотношениям из [Zharkov, Kalinin, 1971; Burakovsky, Preston, 2004], в которых параметры t и δ являются подгоночными. Комнатная изотерма и давление на ударной адиабате определяются тремя параметрами: K', t и δ, а параметр K0 рассчитывается из ультразвуковых измерений. В результате нам удалось с разумной точностью описать все основные термодинамические функции металлов в рамках простого уравнения состояния с минимальным набором подгоночных параметров.

Рассчитанное по комнатным изотермам давление можно сопоставить со сдвигом линии R1 люминесценции рубина, одновременные измерения которого и параметров ячейки металлов проведены в гелиевой [Dewaele et al., 2004b, 2008; Takemura, Dewaele, 2008; Takemura, Singh, 2006], водородной [Chijioke et al., 2005] и аргоновой средах [Tang et al., 2010]. Показано [Takemura, 2001], что гелиевая среда в алмазных наковальнях обеспечивает квазигидростатические условия, поэтому рубиновую шкалу, откалиброванную по десяти веществам, можно считать близкой к равновесной или почти абсолютной. Она имеет вид P(GPa)=1870⋅Δλ/λ0⋅(1+6⋅Δλ/λ0). Откорректированные по полученной рубиновой шкале комнатные изотермы других веществ также можно считать близкими к равновесным или почти абсолютным, поэтому построенные нами уравнения состояния девяти металлов и алмаза можно отнести к почти абсолютным уравнениям состояния для квазигидростатических условий. Другими словами, они являются взаимосогласованными между собой, с рубиновой шкалой давлений и близки к равновесным в термодинамическом смысле. Рассчитанные по ним P–V–T соотношения могут быть использованы в качестве взаимосогласованных шкал давления в алмазных наковальнях при изучении P–V–T свойств минералов в широкой области температур и давлений. Погрешность рекомендуемых уравнений состояния веществ и рубиновой шкалы составляет порядка 2–3 %. Расчет P–V–T соотношений и термодинамики доступен по адресу http://labpet.crust.irk.ru.

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