On the Relationship Between Entropy and Enthalpy of Grain Boundary Segregation

An extensive study of anisotropy of grain boundary segregation in -iron, performed in the last decade, confirmed the existence of a linear relationship between entropy and enthalpy of solute segregation at individual grain boundaries. A thermodynamic analysis of this relationship is performed in the present work. It is shown that this dependence defines a compensation temperature and an entropy-like parameter. The compensation temperature is not necessarily connected with a phase transformation, but it represents exclusively a mean temperature at which all boundaries approach to a mean value of the Gibbs free energy of segregation. The most important consequences of this dependence are outlined: a reversed anisotropy of grain boundary segregation at temperatures above the compensation temperature, and a new method for the prediction of the enthalpy and entropy of solute segregation at individual grain boundaries.     

Thermodynamics and structural aspects of grain boundary segregation

Physical and chemical properties of solid materials are strongly. influenced by the chemical composition of internal interfaces, One of the crucial parameters affecting interfacial chemistry is the atomic structure of the interface. Due to its importance. a considerable amount of work was done to elucidate the relationship between structure and chemical composition of interfaces. This article reviews the present understanding of an important and fundamental part of this relationship, namely, the structural aspects of grain boundary segregation. After a brief outline of grain boundary structure and geometry. thermodynamic approaches to describe grain boundary segregation are summarized and their application to materials is discussed. covering particular sites at a single grain boundary as well as the role of interfaces in polycrystals. Both the experimental evidence of grain boundary segregation anisotropy and the theoretical results of computer simulations of grain boundary segregation are summarized. Useful methods of predicting grain boundary segregation are presented. Finally, segregation behavior of solutes at grain boundaries is compared with that at free surfaces, and examples of chemical composition of intexphase boundaries are given.     

Thermodynamics of self-assembly of sodium octanoate: comparison with a fully fluorinated counterpart

The isotherms of conductivity of sodium octanoate were measured and the critical micelle concentration (cmc) and degree of ionization of the micelles, β, determined in a range of temperatures (273–343 K) above the Krafft point. The thermodynamic parameters, Gibbs free energy ΔG _m ⁰, enthalpy ΔH _m ⁰, and entropy ΔS _m ⁰ of micelle formation, were determined from polynomial adjustments of the temperature dependence of cmc and from a proposed thermodynamic model based on the works of Muller [1993, Langmuir, 9, 96] and Rodríguez et al. [2002, J. Colloid Interface Sci., 250, 438]. The increase in heat capacity upon micellization, ΔC _pm ⁰, was estimated from the parameters of the model and the enthalpy—entropy compensation phenomena discussed. Finally, for information on their structural differences, hence to understand their different behaviours, thermodynamic parameters are discussed, comparing the corresponding fluorocarbon compound. A remarkable shift in minimum temperature in the U-shaped curve of cmc versus temperature was found when hydrogen was substituted by fluorine in the hydrophobic chain of the surfactant. This behaviour is a consequence of the special characteristics of the fluorine substituent in the hydrophobic tail and was reflected in the thermodynamic parameters and in the enthalpy—entropy compensation parameters, presenting different intercepts at the same compensation temperature.     

On the relationship between the entropy and enthalpy of interfacial segregation

The general relationship between the excess entropy and enthalpy of segregation is elucidated in terms of basic thermodynamical principles applied to the bulk-interface equilibrium. The linearity reported in several studies of different grain boundary or surface orientations in alloys is accounted for in case at some temperature, the excess entropy varies much more strongly than the ideal solution configurational contribution to the segregation entropy. The theoretical analysis done for monolayer segregation (e.g., of non-metal impurity), shows that the linear relationship can be explicitly quantified by means of a quasi-isotropic interfacial segregation level and the corresponding temperature, and without introducing significant error in case of multilayer segregation.     

Solute segregation at 46.8°(111) twist grain boundary of a phosphorus doped Fe–2.3%V alloy

The Auger electron spectroscopy study on chemistry of the 46.8°(111) twist grain boundary of an Fe–2.3%V alloy showed an extended phosphorus enrichment at temperatures in range of 500 °C and 800 °C. Simultaneously, slight but nearly independent segregation of vanadium was also detected. The standard enthalpy and entropy of grain boundary segregation of phosphorus and vanadium were determined according to the Guttmann model of multicomponent interfacial segregation. Obtained data clearly show that this Σ = 19 coincidence boundary is special (i.e. low energy interface). The data also fit well with the predictive model of grain boundary segregation and confirm that phosphorus segregates interstitially at the grain boundary while vanadium substitutes iron atoms in the interface structure.     

Diffusion, Solute Segregations and Interfacial Energies in Some Material: An Overview

We have shown a connection among the three important properties of interfaces, namely, the free energy, diffusion and solute segregation through the conjecture that the interface free energy is the difference between those responsible for diffusion in the lattice and the interface itself. The interface energy is known to decrease upon solute additions. We discuss the methodology and the thermodynamical analysis of the diffusion parameters which enable extraction of the interfacial energies and illustrate them by results obtained in a wide variety of materials. Investigations carried out in pure polycrystalline metals have yielded grain boundary energies comparable to those directly measured. Furthermore, we discuss the role of solute segregation at grain boundaries in alloys in altering diffusion. From the perturbations caused, the solute segregation parameters—the enthalpy and the entropy of binding—have been extracted and levels of solute concentrations estimated. It is shown that similar analyses when applied to complex materials, e.g. the Pb–Sn eutectic alloy, several intermetallic compounds, and oxide systems, also result in acceptable values of interface energies and segregation factors. Finally, some ad-hoc guidelines are provided to alter diffusion in interfaces through solute additions in order to achieve some end use engineering objectives.     

Solute segregation to grain boundaries and free surfaces in an Fe---Si multicomponent alloy

Solute segregation was measured at both the {310} symmetrical tilt grain boundary and the (310) free surface of a sample of an Fe-6at%Si alloy containing traces of P, S, N and C at 873 K. Large phosphorus enrichment and silicon depletion characterize the grain boundary segregation in spite of a different bulk concentration of nitrogen. The surface segregation in nitrogen-containing samples is controlled by strong cosegregation of Si and N, resulting in the formation of a stable Si_xN_y 2D surface compound, whereas pronounced surface segregation of sulphur dominates in denitridized samples. The differences of grain boundary and surface segregation are discussed as a kind of “anisotropy of interfacial segregation” on the basis of Guttmann's theory with different values of free energies of segregation to grain boundary and free surface. They also suggest that the measurements of surface segregation cannot be unambiguously used for predicting the grain boundary segregation. In some non-brittle multicomponent systems, a better way of predicting segregation behavior at grain boundaries would be the measurement of grain boundary segregation in a related system with solute concentrations that cause embrittlement. The findings can then be applied to the required alloy composition on the basis of Guttmann's theory.     

Rotational statistics and thermodynamic functions of hydrogen peroxide

Partition functions for both the rotational modes (hindered internal rotation and overall rotation) of the hydrogen peroxide (H₂O₂) molecule in the ground electronic state are studied using quantum and classical Gibbsian statistical mechanics. The partition functions are used to calculate rotational thermodynamic functions (internal energy, enthalpy, Helmholtz free energy, Gibbs free energy and entropy) of a hydrogen peroxide gas of weakly interacting molecules at temperatures above 300 K.     

密度泛函理论研究LiX(X=H,D,T)体系的热力学性质

运用量子力学从头计算方法,计算了氢化锂(氘化锂、氚化锂)分子的部分热力学函数和力学、光谱学性质。基于准简谐Debye模型,计算了固体Li的振动内能、振动和电子熵,探讨了Li吸收氢同位素气体生成一氢化物的反应熵变、生成焓变和生成Gibbs自由能及氢同位素的平衡离解压。结果显示:在Li吸收同位素气体生成一氢化物的反应中,生成焓变和反应熵变均为负值,且随温度升高,绝对值越大,Gibbs自由能则向正的方向增加。热力学上,在相同温度和压力下,氢置换一氢化物中的氘和氚、及氘置换氚的反应更易发生。     

MAX相Nb2SnC和Nb2SnN的力学和热力学性质的第一性原理计算

利用基于密度泛函理论的第一性原理,在广义梯度近似下研究了MAX相Nb₂SnC和Nb₂SnN的力学、晶格动力学、电子以及热力学性质.通过弹性常数和声子的计算,研究了Nb₂SnC和Nb₂SnN两种结构的力学稳定性和动力学稳定性;通过对Nb₂SnC和Nb₂SnN的力学性质计算,证明了它们均具有较高的体积模量和剪切性,并且说明了Nb₂SnC和Nb₂SnN是具有弹性各向异性的韧性材料.此外,通过计算电子能带结构和态密度,研究了Nb₂SnC和Nb₂SnN的电子性质和成键性质,结果表明,两个化合物均具有金属导电性和较强的共价键,而且Nb₂SnN比Nb₂SnC具有更强的金属导电性.最后利用声子色散曲线预测了热容、自由能、焓和熵等热力学性质,结果标明,计算出的熵、焓和自由能值变化符合热力学第三定律.     

纳米多晶体的热力学函数及其在相变热力学中的应用

以往关于纳米材料热力学的研究，绝大多数以界面的热力学函数表征整体纳米材料的热力学性质，这种近似处理，对于尺寸超过几十纳米的较粗纳米材料，在相变热力学中对特征转变温度和临界尺寸等重要参量的预测，将导致很大误差. 应用“界面膨胀模型”和普适状态方程，研究了纳米晶界的热力学特性，进一步发展了纳米晶整体材料热力学函数的计算模型，给出了单相纳米多晶体的焓、熵和吉布斯自由能随界面过剩体积、温度，以及晶粒尺寸发生变化的明确表达式. 以Co纳米晶为例，分析了界面与整体纳米多晶体热力学函数的差异，确定了相变温度与晶粒尺寸的依赖关系，以及一定温度下可能发生相变的临界尺寸. 关键词： 纳米多晶体 热力学函数 相变热力学     

Criteria for the Occurrence of the Diffusion-Induced Grain Boundary Migration

Recent experimental data on diffusion-induced grain boundary migration (DIGM) are reviewed. For the case of the coherency strain driving force, quantitative criteria for the occurrence of DIGM are suggested, which establish the relationship between the net driving force for grain boundary migration, the diffusivity in the vicinity of the grain boundary, the enthalpy of the grain boundary segregation, the misfit parameter for the solute atoms in the matrix and the solubility of the diffusing element in the matrix. It is shown that an upper limit for the grain boundary velocity during DIGM exists due to the solute drag effect.     

Interaction of Solute Impurity with Grain Boundary: The Impurity Drag Effect

An equation of grain boundary motion in a binary polycrystal is derived. The derivation is based on minimization of free energy of the total systems. The equation takes into account an impurity segregation at the grain boundary, grain boundary curvature and energy.As an example, we apply this equation to the analysis of the impurity drag effect problem. It is shown, that the sign of the impurity effect on grain boundary velocity (delay or acceleration) does not depend on kinetic coefficients. The sign of the effect is determined by a thermodynamic function which combines the grain boundary segregation coefficient, the derivative of grain boundary energy with respect to absorbed impurity concentration, and the derivative of bulk free energy with respect to bulk impurity concentration.     

Computer simulation of solute segregation to a Σ = 5 tilt boundary in Au,Cu and Ni

A Lattice Energy Function that combines a Mie type interatomic potential and a free electron gas volume dependence has been applied to the study of grain boundary energy and structure of a Σ = 5 tilt boundary in Au, Cu and Ni and of solute segregation to the same. Interatomic potentials and volume dependencies of the solvent and solute were adjusted to fit the relative partial molar enthalpy and volume at infinite dilution order to construct a AB type potential and volume dependence. This AB interaction is then applied to calculate the binding energies of solute to various grain boundary sites and the resulting change in grain boundary energy. A relationship between the binding energy and change in grain boundary is derived. The relative values of the grain boundary energy are in agreement with experimental values of the average grain boundary energies. The relative binding energies of the tested solvent-solute systems are in agreemnet with expectations that certain systems should have larger binding energies than others. The behavior of solute binding energies and local relaxations are in agreement with other studies of grain boundary segregation which use different Lattice Energy Functions and relaxation algorithms. The change in grain boundary energy is shown to be directly proportional to the binding energy.     

Competing ordered structures formed by particles with a regular tetrahedral patch decoration

We study the ordered equilibrium structures of patchy particles where the patches are located on the surface of the colloid such that they form a regular tetrahedron. Using optimization techniques based on ideas of evolutionary algorithms we identify possible candidate structures. We retain not only the energetically most favourable lattices but also include a few energetically less favourable particle arrangements (i.e., local minima on the enthalpy landscape). Using suitably developed Monte Carlo based simulation techniques in an NPT ensemble we evaluate the thermodynamic properties of these candidate structures along selected isobars and isotherms and identify thereby the respective ranges of stability. We demonstrate on a quantitative level that the equilibrium structures at a given state point result from a delicate compromise between entropy, energy (i.e., the lattice sum) and packing.     

Nuclear relaxation and motional anisotropy of liquid s-triazine

The dynamic structure of liquid s-triazine has been studied by analysing the deuterium and nitrogen-14 quadrupolar relaxation data of d ₃-s-triazine.

The molecular motions are markedly anisotropic with: (a) fast, large angle jump, inertial type in-plane motions of almost zero activation enthalpy and large negative activation entropy; (b) comparatively slow, small angle jump, rotational diffusion type, out of plane motions of higher activation enthalpy and small activation entropy. Comparison of the data on the dynamic behaviour of pyridine [3] and benzene [4] with the present ones on s-triazine leads to a general picture of molecular motions of planar hexagonal rotors in the liquid state (at atmospheric pressure). The behaviour of pyridine, which has a dipole moment departs somewhat from the more similar (and more anisotropic) behaviour of benzene and s-triazine. These results also support our previous finding of motional anisotropy in liquid pyridine [3].

A pictorial representation of the motional anisotropy in benzene, pyridine and s-triazine is giving using motional ellipsoids whose axes lengths are proportional to the diffusion constants.     

Interfacial segregation in Ag-Au,Au-Pd,and Cu-Ni alloys: II. [001] Σ5 twist grain boundaries

Atomistic simulations of segregation to [001] 5 twist boundaries in Cu–Ni, Au–Pd, and Ag–Au alloy systems have been performed for a wide range of temperatures and compositions within the solid solution region of these alloy phase diagrams. In addition to the grain boundary segregation profiles, grain boundary free energies, enthalpies, and entropies were determined. These simulations were performed within the framework of the free energy simulation method, in which an approximate free energy functional is minimized with respect to atomic coordinates and atomic site occupation. For all alloy bulk compositions (0.05 C 0.95) and temperatures (400 T (K) 1,100) examined, Cu and Au segregates to the boundary in the Cu–Ni and Au–Pd alloy systems, respectively; although in the Ag–Au alloys, the majority element segregates to the boundary. The width of the segregation profile is limited to approximately three to four (002) atomic planes. The classical theories for the segregation, and the effects of the relaxation with respect to either the atomic positions or the atomic concentrations, are discussed. The boundary thermodynamic properties depend sensitively on the magnitude of the boundary segregation, and some of them are shown to vary linearly with the magnitude of the grain boundary segregation.     

Monte Carlo simulations of neon and argon using ab initio potentials

Gibbs ensemble Monte Carlo simulations of neon and argon have been performed with pair potentials taken from literature as well as with new ab initio potentials from just above the triple point to close to the critical point. The densities of the coexisting phases, their pair correlation functions, the vapour pressure and the enthalpy and entropy of vaporization have been calculated. The influence of the potential choice and of the addition of the Axilrod-Teller (AT) three-body potential on the above mentioned properties have been investigated. It turns out that an accurate ab initio two-body potential in connection with the AT potential yields very good results for thermodynamic properties of phase equilibria.     

Application of automated crystallography for transmission electron microscopy in the study of grain-boundary segregation

Analytical Electron Microscopy (AEM) has brought significant progress in the study of grain-boundary segregation. Using X-ray energy-dispersive spectrometry (XEDS) in the AEM, elemental segregation information can be related to the crystallographic character of the same boundary via conventional Transmission Electron Microscope (TEM) diffraction techniques. While significant efforts have been made to improve XEDS analysis of sub-nanometer segregation layers, the methods for crystallographic characterization of grain boundaries have remained the same for several decades and labor-intensive processes. Recently, a method termed Automated Crystallography for TEM (ACT) was developed, which automates crystallographic characterization of grains under TEM observation. In the present work, we combine ACT and X-ray mapping via EDS in AEM for the study of Sb grain-boundary segregation in a rapidly solidified Cu-0.08 wt % Sb alloy. In contrast with previous reports, a large degree of anisotropy in Sb segregation level between different boundaries is found. ACT results suggest that one of the several grain boundaries observed with no detectable Sb segregation is very close to a Sigma 3 coincidence-site lattice structure. The reason for the observed anisotropy in the present alloy is discussed, based upon McLean's theory of segregation.