Triple Defect Research Articles

Origin of ordering in B2-type transition-metal aluminides: Comparative study of the defect properties of PdAl, NiAl, and FeAl.

The physical mechanism for ordering and the properties of lattice defects in {ital B}2-type transition-metal (TM) aluminides are presented. It is shown that the size effect is inadequate in explaining the defect structure (and ordering) in these intermetallics. Such is the case evident in the prototypical example of PdAl, which is found to exhibit all the physical characteristics of strongly ordered alloys even though the difference in atomic radii between constituent Pd and Al atoms is very small. We obtain a high heat of formation, high antiphase boundary energies associated with the partial 1/2{l_angle}111{r_angle} slip, and the existence of triple defect (for the point defect structure) in PdAl. Comparative analyses are presented for PdAl, NiAl, and FeAl, and results reveal that the electronic structure at the TM sites plays a decisive role in the energetics (and types) of defects. The strong ordering in late TM aluminides of the {ital B}2 type is due to the {ital lack} of electronic screening from the TM {ital d} band to compensate the energetically unfavorable nearest-neighbor interaction between Al atoms when ordering is disrupted.

Magnetothermal investigation of the kinetics of defect reaction in the CoGa intermetallic compound

The kinetics of the formation and of the annealing out of Co antistructure atoms in the CoGa intermetallic compound have been investigated by magnetothermal analysis. The annealing out was found to be influenced by a single defect type. A quantitative analysis of the susceptibility vs. temperature curve of quenched Co 50Ga 50 sample yielded the fraction of antistructure atoms. The triple defect model was used to calculate the amount of vacancies. The migration enthalpy H m was determined for the quenching temperatures 1000 °C, 900 °C, and 850 °C and found to be 1.78 ± 0.12 eV, 2.16 ± 0.12 eV, and 1.8 ± 0.2 eV respectively. The triple defect type, the amount of vacancies and the migration enthalpy for 1000 °C are in agreement with data reported in the literature.

Constitutional vacancies in NiAl

An explanation is offered, based on a simplified form of many-atom bonding theory, of why NiAl forms constitutional vacancies on its Ni sublattice when excess Al is present. The resultant increase in the number of Al atoms thereby able to bond with Ni atoms is only partially offset by the weakening of individual AlNi bonds, so that there is a net gain. Also, the NiNi bonds, being weak in NiAl, claim only a minor penalty when an Ni site is vacated. Other defects, i.e. antisite Ni atoms and triple defects, as well as ordering of vacancies, are briefly discussed.

Defect structure in Al-rich composition region in the β-NiAl intermetallic compound phase

Abstract The defect structure in the B2 type β-NiAl phase was investigated in the Al-rich composition region by means of powder X-ray diffractometry. In the analysis, earlier published density data were referred to for estimation of the total vacancy concentration in the alloy. As a result, the main constitutional defect was found to be the vacancy on the Ni-site (Ni-vacancy), supporting the defect structure model proposed previously by Bradley and Taylor. However, in a region of high Al concentration, some Al atoms substituted on the Ni-site, i.e. anti-structure defects of Al atoms (Al-ASD), as well as some vacancies on the Al-sites (Al-vacancies), were recognized to exist. Their amounts did not change with increasing temperature up to 1150 °C. These defect types of the Al-ASD and Al-vacancy had always been excluded in usual treatments based on the triple defect model. The reliability of the defect structure determined was examined by comparison with the triple defect model. Further, thermodynamic calculations based on the Bragg-Williams approximation were performed in order to reproduce the observations.

Ordering versus disordering tendencies in mechanically alloyed (NixFe1−x)Al alloys

(Ni[sub x]Fe[sub 1[minus]x])Al alloys (x = 0...1) were prepared by mechanical alloying of elemental powders and by intensive mechanical milling of master alloys for x = 0 and 1. Both mechanical-milling and mechanical alloying results in single phase alloy powders with highly strained nanometer sized crystals. The degree of long-range order after milling was found to vary with composition x. NiAl exhibited an almost completely ordered structure (B2-type). With increasing Fe content, the LRO parameter S drops continuously to S = 0 for FeAl. This difference in LRO is attributed to: (1) enhanced thermally activated reordering of the Ni-rich alloys during milling driven by the high ordering energy of these alloys; (2) enhanced disordering of the Fe-rich alloys by the introduction of defects due to a smaller difference in free energy between ordered and disordered state; and (3) enhanced disordering of the Fe-rich alloys due to different deformation mechanisms with respect to NiAl. The lattice parameter of disordered FeAl was found to be higher than that of ordered FeAl, which indicates the formation of substitutional defects by disordering. In contrast, mechanical alloying of NiAl leads to decreased lattice parameters, probably caused by the formation of triple defects.

Magnetothermal investigation of the kinetics of defect reaction in the FeAl intermetallic compound

The kinetics of the formation and of the annealing-out of Fe antistructure atoms in the FeAl intermetallic compound have been investigated by magnetothermal analysis. The annealing-out depends appreciably on the quenching temperature; at approximately 850 °C a transition from one defect type to another is obeyed. Quenching temperatures below 850 °C result in a late recovery, whereas quenching temperatures above 850 °C yield an earlier recovery. This behaviour is explained by assuming that triple defects dominate at low temperatures and that additional pairs of vacancies are formed above 850 °C. The kinetic parameters of the annealing-out of defects, as migration enthalpy and reaction order, have been determined.

Cholesterol nucleation time in gallbladder bile of patients with solitary or multiple cholesterol gallstones.

Patients with multiple cholesterol gallbladder stones have been found to be at a higher risk for the recurrence of gallstones after successful nonsurgical treatment than those with a solitary stone. Cholesterol gallstone recurrence, like primary gallstone formation, probably involves a triple defect with supersaturation, abnormally rapid nucleation of cholesterol in bile and altered gallbladder motor function. We investigated whether the increased recurrence rate of patients with multiple stones might be caused by more rapid nucleation. Therefore the time required for cholesterol monohydrate crystals to appear in ultracentrifuged bile of patients with solitary (n = 71) or multiple (n = 42) cholesterol gallstones was determined. The cholesterol nucleation time was significantly (p less than 0.01) longer in the bile from patients with solitary stones (less than 1 to 16 days, median = 2.0 days) than in the bile from patients with multiple stones (less than 1 to 8 days, median = 1.0 days). Moreover, 15 of 71 (21.1%) patients with solitary cholesterol stones but only 1 of 42 (2.4%) patients with multiple cholesterol stones showed a normal (greater than 4 days) nucleation time. However, no difference in the cholesterol saturation index was found between the bile samples from patients with solitary stones and the bile samples from patients with multiple stones (1.55 +/- 0.65 vs. 1.54 +/- 0.59, mean +/- S.D., respectively). The more rapid cholesterol nucleation in gallbladder bile may, therefore, be the major risk factor causing the higher percentage of stone recurrence in patients with multiple cholesterol stones as compared with patients with solitary cholesterol stones.

BaNdCe 0.9Fe 1+ xCu 1− xO 7−δ: An intergrowth of the BaYFeCuO 5 type and CeO 2 fluorite type structures

A new layered copper oxide BaNdCe 0.9Fe 1.1Cu 0.9O 7−δ has been isolated. Its tetragonal structure ( a = 3.902 Å, c = 20.895 Å) has been studied by X-ray powder diffraction and HREM. This oxide can be described as an intergrowth of the NdBaFeCuO 5 structure (isostructural with YBaFeCuO 5) and the CeO 2 fluorite structure. Thus it belongs to a series of oxides, characterized by double fluorite layers, resulting from the introduction of one additional [CeO 2] ∞ fluorite layer in mother structures involving double pyramidal copper layers [ A 2Cu 2O 5] ∞. The systematic HREM study of samples of nominal compositions “BaNdCe 0.9Fe 1.1Cu 0.9O 7” and “BaNdCeFeCuO 7” shows, besides regular crystals, extended intergrowth defects, i.e., mainly single fluorite-layered defects leading to intergrowths [NdBaFeCuO 5] m [L n 2BaFeCuO 7] n , triple fluorite-layered defects leading to possible intergrowths [ Ln 3BaFeCuO 9] m [ Ln 2BaFeCeO 7] n , and triple perovskite-layered defects suggesting the existence of possible intergrowths [Ba 2Ln 2 (Fe,Cu) 3O 9+δ] m [ Ln 2BaFeCuO 7] n . More complex intergrowth defects (multiple fluorite and perovskite layers, superdislocations) are also observed. These observations suggest that the systematic investigation of similar systems should allow complex disordered and ordered intergrowths [A 2Cu 2O 5] p h [ACuO 3− x ] p i [LnO 2] F j [A′O] RS k to be isolated.

Structural defects in Ni-Ti alloys in the region of B2-phase homogeneity

A comparison is made of the x-ray and pycnometric densities of Ti-Ni alloys, with a high nickel content relative to the equiatomic composition, when the alloys are quenched outside the region of Β-phase homogeneity. An analysis is made of the possibility of the formation of vacancies, interstitial atoms, triple defects, and substitutional defects in the alloys. It is concluded that substitutional defects are formed: nickel atoms which are “excess” atoms relative to those found at the lattice points in the CsCl superstructure are located in the titanium sublattice. An evaluation showed that in the formation of alloys near the equiatomic composition of TiNi, the atomic volumes of titanium and nickel are about 1.8 and 7.4% smaller than for the pure components, respectively.

The crystal structure of barium lead hexaaluminate phase II

A refinement was performed on the average crystal structure of barium lead hexaaluminate phase II ((Ba 0.8Pb 0.2) 2.34Al 21.0O 33.84) using single crystal X-ray diffraction data, giving a final R value of 0.030 with space group symmetry P 6m2 . The structure is essentially of a β-alumina type, but contains a lot of defects and interstitials. Inside the spinel block were found Ba(Pb) ions at 12-coordinated polyhedral sites, formed by complex defects, including triple Reidinger defects, in the same unit cell. Barium lead hexaaluminate phase II was found to consist of two kinds of unit cells with formulae “(BaPb) 3.0Al 20.0O 35.0” and “Ba 2.0Al 22.0O 34.0” in a 1 : 2 ratio; these three cells combine to form an a√3 × a√3 superstructure.

Diffusion kinetics and correlation effects for self-diffusion via vacancy pairs and triple defects in the sphalerite structure

In the present paper two possible mechanisms of self-diffusion in III-V compounds with the sphalerite structure, like GaSb, are considered in detail. (1) Expressions for the correlated diffusion coefficient of vacancy pairs and for the diffusion coefficients and correlation factors of tracer atoms diffusing via vacancy pairs are calculated. (2) It is pointed out that-as with triple-defect diffusion in intermetallic compounds with the CsCl structure discussed by Bakker et al. (1981)-the expressions for the self-diffusion coefficients and correlation factors via triple defects can be obtained from the vacancy-pair expressions.

Self-diffusion of gallium and antimony in GaSb

Abstract Self-diffusion of gallium and antimony in GaSb has been investigated in both Ga-saturated and Sb-saturated single crystals at temperatures ranging from 867 K to the temperature of congruent melting. The radio-isotopes 72Ga and I22 Sb were diffused simultaneously to avoid composition gradients. After sputter-sectioning, the penetration profiles for both isotopes were obtained by means of a Ge(Li) spectrometer. It is found that Ga diffuses slightly faster than Sb and that the composition plays an important role: Ga and Sb diffuse faster in Sb-rich than in Ga-rich samples. The temperature dependence of both diffusivities resembles that of the Sb partial pressure over the compound. Several mechanisms of diffusion are discussed in the light of these observations. The coupled diffusion of Ga and Sb leads us to conclude that both components diffuse via the same defect. In view of the special type of defect structure in GaSb, we propose that the triple defect is the predominant diffusion vehicle for both...

Diffusion kinetics and isotope effects for atomic migration via divacancies and triple defects in the CsCl (B2) structure

Abstract Expressions for the diffusion coefficients and correlation factors for diffusion by means of divacancies in ionic compounds with the CsCl (B2) structure are calculated. Values for the correlation factors as a function of the ratio of the defect-atom exchange frequencies of both components are tabulated. The correlation factors are obtained in explicit form. From this it turns out that a measurement of isotope effects would yield (in principle) the values of the correlation factors. It is demonstrated that, in a measurement of diffusion coefficients, differences in jump frequencies and activation energies between both components are decreased by correlation effects. For intermetallic compounds with the triple-defect B2 structure, atomic migration via triple defects has been proposed (Stolwijk, Van Gend and Bakker 1980). Expressions for the diffusion coefficients of both components via this defect are presented and it is shown how values for the correlation factors can be deduced from the divacancy...

Vacancies in CoGa

Thermal and constitutional vacancies are studied for five compositions of the intermetallic compound CoGa. Macroscopic density measurements are used to determine the structural and frozen-in thermal vacancy content. The formation of thermal vacancies is derived from thermal expansion measurements of the macroscopic length and the lattice parameter up to 900°C. The results of these vacancy concentration measurements are interpreted in terms of triple-defect formation. The temperature dependence of the creation of triple defects cannot be described by a simple Arrhenius behaviour. However a simple nearest-neighbour interaction model, with a Bragg-Williams approximation gives a very good description of all results both as a function of temperature and composition. From a simultaneous least-squares fit of all results with this model two energy parameters and a composition dependent triple-defect formation entropy are derived. In this way some insight into the interaction energies in CoGa is obtained.

Self-diffusion in the intermetallic compound CoGa

Abstract In the ordered B2 compound CoGa, self-diffusion coefficients of both 60Co and 67Ga have been measured for five compositions, namely 60·0, 56·0, 50·0, 48·0 and 45·2 at.% Co, covering a large diffusivity range from 10−8 to 10−14 cm2/s. In addition, a small number of self-diffusion coefficients has been determined for four intermediate compositions, namely 58·0, 54·0, 52·0 and 47·0 at.% Co. The Arrhenius plots for the Co and Ga diffusion in every composition are curved and can be fitted to the sum of two exponentials: D = D 0a exp (-Q a/kT) + D 0b exp (-Q b/kT). The lower activation energies and frequency factors for Co diffusion have average values of 2·4 eV and 0·7 cm2/s respectively. This Co process has been attributed to diffusion via single vacancies and nearest-neighbour jumps. For every composition the other Co activation energy equals one of the Ga activation energies, within error limits, at values of about 3·1 eV. The associated Co frequency factors are of the order of 1000 cm2/s and the Ca frequency factors are smaller by a factor of about four. These processes have been identified as representing coupled diffusion of Co and Ga via divacancies. The second exponentials of the Ga diffusion are characterized by very large activation energies of about 4·4 eV and very large frequency factors of the order of 107 cm2/s. The relation between the logarithm of the frequency factor and the activation energy turns out to be almost linear for all components, diffusion mechanisms and compositions involved. The combined diffusion of Co and Ga has been worked out in more detail in view of the special type of defect structure in CoGa. This leads to the concept of the triple defect as a special and predominant type of divacancy. Finally the triple defect is discussed as an alternative to the six-jump cycle for the interpretation of diffusion measurements in intermetallic compounds with the B2 structure.

On the occurrence of substitutional and triple defects in intermetallic phases with the B2 structure

Theoretical models for the thermodynamic properties of intermetallic B2 phases are employed to explain a priori the empirical observation that B2 phases with a small enthalpy of formation exhibit substitutional defects, whereas B2 phases with a large enthalpy of formation exhibit triple defects. The following expressions for the concentration of anti-structure atoms ( N β A / N) as a function of the enthalpy of formation ΔH ∝ of the stoichiometric compound, the enthalpy of formation of vacancies ΔH v , and the temperature T, are derived: substitutional defects: ( N β A / N) s = 0.5 exp[( ΔH ∝)(2/ RT)] triple defects: (N β A/N) t = 0.315 exp[( 2 3 ΔH ∝ − 1 3 ΔH v)2/RT)] . These equations indicate that the formation of substitutional defects, which depends solely on ΔH ∝, becomes more difficult with increasing ΔH ∝. On the other hand, the formation of triple defects, which depends on both ΔH ∝ and ΔH v , becomes comparatively easier, assuming that ΔH v has approximately the same value for all B2 phases. It is predicted that some B2 phases might exhibit a hybrid behavior, with both defect types occurring in comparable concentrations.

On the Vacancy Concentration in B2 Phases Exhibiting Triple Defects

On the Vacancy Concentration in B2 Phases Exhibiting Triple Defects

Microfracture from thermal expansion anisotropy—I. Single phase systems

The onset of the mode of microfracture associated with thermal expansion anisotropy has been calculated for single phase polycrystals. The calculations include estimates of the thermal stress in single grains and in polycrystalline aggregates, emphasizing the grain orientations and shapes that yield the maximum stress intensification at boundary located defects. The largest stress intensification was found to occur at triple points, emphasizing that triple point defects are the most likely sites for microfracture initiation. Critical grain facet sizes for microfracture initiation have been predicted as functions of the elastic, viscoelastic and thermal properties of the material, the defect size distribution, and the boundary fracture energy. Although a wide statistical variability in the microfracture condition is anticipated, the predictions can be shown to conform reasonably well with data for magnesium titanate and results obtained for alumina.

A thermodynamic analysis ofβ′-PdIn

A recently developed model for the thermodynamic properties of intermetallic B2 phases with triple defects is applied to Β′-PdIn. The values of the disorder parameter α, obtained independently from measurements of the activity and the partial enthalpy, are in reasonable agreement. The validity of a theoretical expression, which describes the temperature dependence of the disorder parameter, is confirmed experimentally. It is shown that the equations by Libowitz for triple defect B2 phases can be reduced to the less cumbersome, yet continuous, expressions by Neumann, Chang, and Lee.

Crystal field splitting of 5d states in Ce 3+ : YPO 4

The kinetics of the formation and of the annealing out of Co antistructure atoms in the CoGa intermetallic compound have been investigated by magnetothermal analysis. The annealing out was found to be influenced by a single defect type. A quantitative analysis of the susceptibility vs. temperature curve of quenched Co50Ga50 sample yielded the fraction of antistructure atoms. The triple defect model was used to calculate the amount of vacancies. The migration enthalpy Hm was determined for the quenching temperatures 1000 °C, 900 °C, and 850 °C and found to be 1.78 ± 0.12 eV, 2.16 ± 0.12 eV, and 1.8 ± 0.2 eV respectively. The triple defect type, the amount of vacancies and the migration enthalpy for 1000 °C are in agreement with data reported in the literature.