Size-dependent hysteresis and phase formation kinetics during temperature cycling of metal nanopowders

Abstract

We present a description of the evolution of a polymorphically transforming metal nanoparticle ensemble subjected to a temperature cycling with constant rates of temperature change. The calculations of the time dependence of the volume fraction of the new phase show the existence of size-dependent hysteresis and its main features. The statistical analysis makes it possible to introduce and determine the size-dependent superheating limit and supercooling limit.

Mercury Nanodrops and Nanocrystals

“…It is notable that a classical thermodynamic treatment including the effects of surface-induced order has predicted an energy barrier between surface melted state and the liquid droplet that decreases with particle size, causing the melt–freeze hysteresis also to decrease and vanish at very small sizes . Decrease of hysteresis with particle size has been discussed in connection with first-order crystallographic phase transitions, as well . Finally, we note that the SAED experiment on pure PVA film showed no hysteresis (Supporting Information, Figure S11).…”

“…54 Decrease of hysteresis with particle size has been discussed in connection with first-order crystallographic phase transitions, as well. 55 Finally, we note that the SAED experiment on pure PVA film showed no hysteresis (Supporting Information, Figure S11).…”

Phase stability of spherical Ferrum nanoparticles under radiation saturation with vacancies

“…Термодинамічні дані для заліза, поверхневі енергії  α ,   і міжфазні енергії визначено в праці [13]. Зміну ентальпії вакансії ΔH f можна оцінити з рівноважної температури плавлення, T пл , що дає значення ΔH f = 2,72•10 −19 Дж [14].…”

“…1, б. Щоб уникнути громіздкості формул, що враховують морфологію такого зародження, ми не наводимо математичний апарат і опис геометрії двофазних станів. Подібний аналіз можна знайти в нашій попередній роботі [13].…”