Application of Bell-Shaped Functions in X-ray Diffraction Broadening Analysis

Graphical and analytical solutions for the crystallite size and strain parmneters, causing diffraction broadening, are given using two or more orders of the reflexion from the same set of crystal lattice planes and representing diffraction profiles with simple bell-shaped functions. The effect of the inevitable truncation of the profile tails on the derived values of the size and strain parameters is also discussed. It has been found that the truncation more considerably affects the functions describing the size parameter than the ones describing the strain parameter, this being in agreement with the experimental evidence

Dependence of microstructure of Al-44 at% and Al-48 at% zn alloys on temperature

The temperature dependence of microstructure of the title alloys was studied in situ by XRD. Each alloy had been subjected to two different thermal treatments: (i) rapid quenching from the solid-solution temperature, T_SS, in water at room temperature (RT) and ageing at RT (samples WQ) and (ii) cooling slowly from TSS to RT and ageing at RT (samples SC). As the samples SC were closer to the equilibrium state than the samples WQ, the microstructure of the two sets of samples dependeded on temperature in a different way. The solid solution, aSS, was formed at about 720 K for the samples SC, and at about 880 K for the samples WQ. During the slow cooling to RT the samples SC and WQ behaved in a similar way. Instead of the phase transitions expected according to the phase diagram, the following sequence of transitions was observed for both alloys: α(M/β)+β(Zn) - α¢+β(Zn)+a(M/α¢,β) - α_SS. A similar thermal behaviour was also found for the Zn-rich alloys, Al-54 at% Zn and Al-62 at% Zn

Temperature dependence of microstructure of (1-x)Al-xZn alloys, x = 0.44, 0.48, 0.54 and 0.62

The change of microstructure with temperature of the title alloys has been studied in situ by X-ray powder diffraction. It has been found that the temperature dependence of microstructure of the alloys, rapidly quenched from the solid-solution temperature, T_ss, to room temperature, RT, is quite different from that of the alloys slowly cooled from T_ss to RT. The area between two curves showing that dependence for the given phase during the first heating from RT to Tss and first cooling from T_ss to RT is much smaller for the slowly-cooled alloys than for the rapidly quenched alloys. That area slightly increases with the increase of the Zn content in the alloys. The temperature dependence of microstructure of the alloys during the second heating from RT to Tss and second cooling from Tss to RT differs little from that during the first cooling from T_ss to RT. The ideal equilibrium state cannot be reached either by slow cooling of the alloys from T_ss to RT, or by a prolonged ageing at RT of the rapidly quenched alloys. The observed sequence of phase transitions in alloys during heating from RT to T_ss is different from that which could be expected according to the phase diagram of the system Al-Zn accepted in the literature. During cooling from T_ss to RT, a temperature hysteresis is observed in reversal phase transitions

X-ray Diffraction Broadening Analysis

The microstructural parameters of a crystalline sample can be determined by a proper analysis of XRD line profile broadening. The observed XRD line profile, h(e), is the convolution of the instrumental profile, g(e), and pure diffraction profile, f(e), caused by small crystallite (coherent domain) sizes, by faultings in the sequence of the crystal lattice planes, and by the strains in the crystallites. Similarly, f(e) is the convolution of the crystallite size/faulting profile, p(e), and the strain profile, s(e). The derivation of f(e) can be performed from h(e) and g(e) by the Fourier transform method, which does not require mathematical assumptions. The analysis of f(e) can be done by the Warren-Averbach method applied to the obtained Fourier coefficients. Simplified methods based on integral widths may also be used in studies where a good relative accuracy suffices. The relation among integral widths of f(e), p(e) and s(e) can be obtained if one assumes bell-shaped functions for p(e) and s(e). Integral width methods overestimate both strain and crystallite size parameters in comparison to the Warren-Averbach method. The crystallite size parameter is more dependent on the accuracy in the diffraction profile measurement, than it is the strain parameter. The precautions necessary for minimization of errors are suggested through examples. The crystallite size and strain parameters obtained by means of integral widths are compared with those which follow from the Warren-Averbach method. Recent approaches in derivation of microstructure are also mentioned in short

Precipitation and Dissolution Phenomena in Al-Zn Alloys

The microstructure of Al-Zn alloys, with the Zn atom fraction, xZn 62%, has been studied in detail by XRD in dependence on the composition,temperature and previous thermal treatment. Precipitationphenomena in alloys, transferred to the supersaturated stateby rapid quenching from the solid solution temperature, Tss, in waterat RT, have been followed in dependence on the ageing time atRT or elevated temperature. The equilibrium state, reached by ageing,has been compared with that obtained by slow cooling from Tssto RT. Phase transitions, dissolution and precipitation processes inthe alloys, transferred to the equilibrium state, have been studiedin situ in dependence on temperature from RT to Tss. A temperaturehysteresis in reversal phase transitions has been observed oncooling from Tss to RT. Repeated heating and cooling cycles haverevealed different microstructure in alloys having undergone differentthermal treatments between RT and Tss. A change in thephase diagram of the Al-Zn system is necessary in the compositionregion xZn > 50%

Structures and Textures of Crystalline Phases and Lyotropic Mesophases of Alkylhenzenesulfonates

The molecular arrays in crystalline n-alkylbenzenesulfonates (CS-C12) were determined by X-ray diffraction and found to be lamellar bilayers with the basic lamellar thickness of 30.1-36.9 A for single-tailed, and 22.25-30.0A for C12 double-tailed surfactants, depending on the length of surfactant molecule. In the colloid dispersions of metal dodecylbenzenesulfonates as well as in the systems of double-tailed C12-isomers, microscopic investigations of liquid crystal textures showed the characteristic lyotropic nematic, lamellar, pseudo-isotropic and transient phases with batonnents

Ovisnost mikrostrukture slitina Al-44 at% Zn i Al-48 at% Zn o temperaturi

The temperature dependence of microstructure of the title alloys was studied in situ by XRD. Each alloy had been subjected to two different thermal treatments: (i) rapid quenching from the solid-solution temperature, TSS, in water at room temperature (RT) and ageing at RT (samples WQ) and (ii) cooling slowly from TSS to RT and ageing at RT (samples SC). As the samples SC were closer to the equilibrium state than the samples WQ, the microstructure of the two sets of samples dependeded on temperature in a different way. The solid solution, αSS, was formed at about 720 K for the samples SC, and at about 880 K for the samples WQ. During the slow cooling to RT the samples SC and WQ behaved in a similar way. Instead of the phase transitions expected according to the phase diagram, the following sequence of transitions was observed for both alloys: α(M/β)+β(Zn) – α0 +β(Zn)+α(M/α0 ,β) – αSS. A similar thermal behaviour was also found for the Zn-rich alloys, Al-54 at% Zn and Al-62 at% Zn.Primjenom rentgenske difrakcije in situ istraživali smo temperaturnu ovisnost mikrostrukture navedenih slitina. Slitine su bile prethodno podvrgnute različitim termičkim obradama: (i) brzom kaljenju s temperature čvrste otopine, TSS, u vodi pri sobnoj temperaturi (uzorci WQ); (ii) sporom hlađenju od TSS do sobne temperature i starenju pri sobnoj temperaturi (uzorci SC). Budući da su nakon starenja uzorci SC bili bliži ravnotežnom stanju nego uzorci WQ, mikrostruktura dviju skupina uzoraka ovisila je o temperaturi na različit način. Uzorci SC bili su prevedeni u stanje čvrste otopine, αSS, na temperaturi oko 720 K, a uzorci WQ na oko 880 K. Umjesto faznih pretvorbi koje bi se očekivale prema faznom dijagramu, opazili smo ovaj niz pretvorbi za obje slitine: α(M/β)+β(Zn) – α0 +β(Zn)+α(M/α0 ,β) – αSS. Slično ponašanje nađeno je i za slitine bogatije cinkom, Al-54 at% Zn i Al-62 at% Zn

Temperaturna ovisnost mikrostrukture slitina (1−x)Al–xZn, x = 0.44, 0.48, 0.54 i 0.62

The change of microstructure with temperature of the title alloys has been studied in situ by X-ray powder diffraction. It has been found that the temperature dependence of microstructure of the alloys, rapidly quenched from the solid-solution temperature, Tss, to room temperature, RT, is quite different from that of the alloys slowly cooled from Tss to RT. The area between two curves showing that dependence for the given phase during the first heating from RT to Tss and first cooling from Tss to RT is much smaller for the slowly-cooled alloys than for the rapidly quenched alloys. That area slightly increases with the increase of the Zn content in the alloys. The temperature dependence of microstructure of the alloys during the second heating from RT to Tss and second cooling from Tss to RT differs little from that during the first cooling from Tss to RT. The ideal equilibrium state cannot be reached either by slow cooling of the alloys from Tss to RT, or by a prolonged ageing at RT of the rapidly quenched alloys. The observed sequence of phase transitions in alloys during heating from RT to Tss is different from that which could be expected according to the phase diagram of the system Al-Zn accepted in the literature. During cooling from Tss to RT, a temperature hysteresis is observed in reversal phase transitions.Istraživali smo ovisnost mikrostrukture navedenih slitina o temperaturi in situ pomoću rentgenske difrakcije u prahu. Pokazali smo da je temperaturna ovisnost mikrostrukture slitina, brzo kaljenih s temperature čvrste otopine, Tss, na sobnu temperaturu, RT, bitno različita od one za slitine, koje su sporo hlađene s Tss na RT. Površina između dviju krivulja, koje pokazuju tu ovisnost tijekom prvog grijanja slitine od RT do Tss i prvog hlađenja od Tss do RT, mnogo je manja za sporo hlađene slitine nego za brzo kaljene slitine. Ta površina lagano raste s udjelom Zn u slitinama. Temperaturna ovisnost mikrostrukture slitina tijekom drugog grijanja od RT do Tss i drugog hlađenja od Tss do RT malo se razlikuje od ovisnosti tijekom prvog hlađenja od Tss do RT. Idealno ravnotežno stanje ne može se postići niti sporim hlađenjem slitina od Tss do RT niti dugim starenjem pri RT slitina brzo kaljenih od Tss na RT. Opaženi niz faznih pretvorbi u slitinama tijekom grijanja od RT do Tss razlikuje se od onoga koji bi se očekivao prema faznom dijagramu sustava Al–Zn, prihvaćnog u literaturi. Tijekom hlađenja slitine od Tss do RT uočili smo temperaturnu histerezu za obrnute fazne pretvorbe