Predicting equilibrium shape of precipitates as function of coherency state

Shi, Rongpei; Ma, Ning; Wang, Y.

doi:10.1016/j.actamat.2012.04.019

Cited by 163 publications

(80 citation statements)

References 35 publications

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“…Formation of line defects, such as misfit dislocations and structure ledges, within the interface relieves misfit stress at the expense of increasing interfacial energy. 2 By introducing the structure ledges, the interfacial coherency can be significantly increased. 6,7 The coherent interface can be investigated by methods based on density functional theory (DFT), however, without considering the lattice mismatch or lattice relaxation.…”

Section: Introductionmentioning

confidence: 99%

“…It has been shown that the interfacial energy is a key parameter determining the nucleation barrier and also the shapes of precipitates. [1][2][3] However, the interfacial energy is often not experimentally accessible. Due to the lack of measured data, ab initio calculations have been extensively applied to determine the metal-ceramic interfacial energy.…”

Section: Introductionmentioning

confidence: 99%

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First-principles study of fcc-Ag/bcc-Fe interfaces

Punkkinen

et al. 2013

Phys. Rev. B

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Ab initio calculations are employed to determine the lower and upper bounds of the interfacial energy and work of separation of a fcc-Ag/bcc-Fe interface. The strain-free interfacial energy of the coherent interface is taken as the lower bound and the interfacial energy of the commensurate incoherent interface as the upper bound of the interfacial energy of a realistic semicoherent interface. The latter is estimated by applying an averaging scheme based on the interfacial energies obtained for the coherent interfaces. Similar calculations are performed for determining the bounds of the work of separation. We justify the use of the averaging scheme by carrying out large supercell calculations for a semicoherent interface. For a Fe(110)/Ag(111) semicoherent interface, we show that taking either Fe or Ag as the underlying lattice, our averaging scheme can yield a reasonable estimation of the work of separation of the semicoherent interface. However, when taking Ag as the underlying lattice, the averaged interfacial energy of the semicoherent interface is significantly underestimated due to the magnetism. The structure and magnetism at the coherent and semicoherent interfaces are discussed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

First-principles study of fcc-Ag/bcc-Fe interfaces

Punkkinen

et al. 2013

Phys. Rev. B

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“…Во всем интервале температур развития β / α превращения коэффициент анизотропии удельной меж-фазной поверхностной энергии (K = E max / E min ) близок к 2. Полученные значения энергии удовлетворительно согла-суются с данными, приводимыми в литературе [9], где энергия межфазных границ оценивалась как доля энер-гии высокоугловых границ зерен.…”

Section: A) все эти плоскости содержат направле-ние [0001] α || [110]unclassified

“…Поскольку прямых экспериментальных мето-дов измерения энергии межфазных границ нет, за ве-личину энергии межфазных границ часто принимают долю энергии высокоугловых границ зерен (High angle boundaries -Е HAB ) одной из фаз. Считают, что энер-гия некогерентных межфазных границ составляет (0.7 -1) Е HAB , а полукогерентных -(0.4 -0.5) Е HAB [1,2,9]. В то же время известно, что энергия межфазных границ определяется их строением, и строение разных граней сопрягающихся фаз существенно различается, особен-но в тех случаях, когда между фазами существует опре-деленное кристаллографическое ориентационное соот-ветствие [1 -4].…”

Section: Introductionunclassified

Effect of temperature on the specific energy of β / α interfaces in Ti-6Al-4V alloy

Murzinova¹

2017

LoM

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Most of titanium alloys contain two phases at temperatures of processing and exploitation: α-phase with HCP lattice and β-phase with BCC lattice. Stability of two-phase structure and thermodynamics of β / α transformation, which occurs in a wide range of temperatures, considerably depend on the specific energy of interphase boundaries, and, consequently, on their structure. Basing on the literature data, four schemes of "planar" semicoherent interfaces, in which mismatches in interatomic distances are accommodated by two or three sets of edge misfit dislocations, were plotted. Such types of conjugation are observed on side and end interfaces of lamellas in titanium alloys. The procedure developed by J. H. van der Merwe and G. J. Shiflet was used for estimation of specific energy of interphase boundaries in Ti-6Al-4V alloy. Effect of temperature and content of alloying elements on lattice parameters and elastic properties of the α-and β-phases in Ti-6Al-4V alloy was taken into account for calculations. This approach allowed one to estimate the change in the energy of interphase boundaries in the alloy in temperature interval 600 -975°C, where diffusion β / α transformation and enrichment of β-phase by vanadium are observed. It was shown that the energy of interphase boundaries in Ti-6Al-4V alloy decreased by 1.3 -1.5 times with increasing temperature from 600 to 975°C at all examined types of conjugation. Depending on the structure the energy of interphase boundaries can vary from 0.201 to 0.337 J / m 2 at 975°C and from 0.298 to 0.429 J / m 2 at 600°C. Во многих титановых сплавах при температурах обработки и эксплуатации присутствуют две фазы: α-фаза с ГПУ решеткой и β-фаза с ОЦК решеткой. Стабильность двухфазной структуры и термодинамика фазового β / α превра-щения, которое протекает в широком интервале температур, во многом зависят от удельной энергии межфазных границ, и, следовательно, их строения. На основе обобщения литературных данных об атомном и дислокационном строении границ между фазами с ОЦК и ГПУ решетками предложены четыре схемы строения «плоских» полукоге-рентных межфазных границ, на которых несоответствия межатомных расстояний компенсируются двумя или тремя рядами краевых дислокаций несоответствия. Границы сопряжения такого типа наблюдаются на боковых и торцевых гранях пластин в титановых сплавах. По методике, разработанной ван дер Мерве и Шифлитом, выполнена оценка удельной энергии межфазных границ разного типа в сплаве Ti-6Al-4V. Расчеты проводились с учетом литературных данных о влиянии содержания легирующих элементов и температуры на параметры решеток и упругие свойства фаз сплава Ti-6Al-4V. Это позволило оценить изменение энергии межфазных границ в сплаве Ti-6Al-4V в интер-вале температур 600 -975°С, при которых наблюдается развитие диффузионного β / α превращения и интенсивное обогащение β-фазы ванадием. Показано, что при всех вариантах сопряжения энергия межфазных границ в сплаве Ti-6Al-4V монотонно уменьшается в 1,3 -1,5 раза с повышением температуры от 600 до 975°С. При постоянной тем-пер...

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“…[1][2][3] Computer simulations of microstructures generated from solid-state phase transformations have also achieved a certain degree of success. [4][5][6][7][8] The orientations of the predicted faceted interfaces are a key parameter that can be used to check whether a simulated morphology actually resembles what is observed in a real material. Simulation results are generally in excellent agreement with experimental results if the two phases are related by a rational OR and have a rational HP.…”

Section: Introductionmentioning

confidence: 99%

Faceted interfaces: a key feature to quantitative understanding of transformation morphology

Zhang

Dai

2016

npj Comput Mater

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Faceted interfaces are a typical key feature of the morphology of many microstructures generated from solid-state phase transformations. Interpretation, prediction and simulation of this faceted morphology remain a challenge, especially for systems where irrational orientation relationships (ORs) between two phases and irrational interface orientations (IOs) are preferred. In terms of structural singularities, this work suggests an integrated framework, which possibly encompasses all candidates of faceted interfaces. The structural singularities are identified from a matching pattern, a dislocation structure and/or a ledge structure. The resultant singular interfaces have discrete IOs, described with low-index g's (rational orientations) and/or Δg's (either rational or irrational orientations). Various existing models are grouped according to their determined results regarding the OR and IO, and the links between the models are clarified in the integrated framework. Elimination of defect types as far as possible in a dominant singular interface often exerts a central restriction on the OR. An irrational IO is usually due to the elimination of dislocations in one direction, i.e., an O-line interface. Analytical methods using both three-dimensional and two-dimensional models for quantitative determinations of O-line interfaces are reviewed, and a detailed example showing the calculation for an irrational interface is given. The association between structural singularities and local energy minima is verified by atomistic calculations of interfacial energies in fcc/bcc alloys where it is found that the calculated equilibrium cross-sections are in a good agreement with observations from selected alloys.

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Predicting equilibrium shape of precipitates as function of coherency state

Cited by 163 publications

References 35 publications

First-principles study of fcc-Ag/bcc-Fe interfaces

First-principles study of fcc-Ag/bcc-Fe interfaces

Effect of temperature on the specific energy of β / α interfaces in Ti-6Al-4V alloy

Faceted interfaces: a key feature to quantitative understanding of transformation morphology

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