Rogl, Phase equilibria in ternary and higher order systems with rare earth elements and boron 335 50. Rogl, Phase equilibria in ternary and higher order systems with rare earth elements" and silicon 52.
Introduction
Physical properties of the most common rare earth elements and, for comparison, those of pure calcium, magnesium, aluminum, silicon and iron. The melting points and vapor pressures of rare earth metals differ from those of iron to the extent that problems arise in dissolving them.
Thermodynamic fundamentals
Temperature / °C
The standard free energies of formation of the more common interesting rare earth compounds are compared in fig. Standard free energies of compound formation for some rare earths and reactive metals in steelmaking are given in Table 2. Reciprocal values, K', of equil.
The melt composition then moves along the equilibrium line CE with the precipitation of both oxysulfide and sulfide. The sulfur level finally reached is determined by the initial conditions of the melt and the extent of the addition of rare earth elements.
Additional elements / wt %
Shape control of inclusions
The formation of rare earth compounds facilitates heterogeneous nucleation during solidification leading to grain refinement. Effect of rare earth addition on primary wing length distribution at different superheat temperatures.
Hydrogen embrittlement cracking
A maximum occurred at ultimate yield strength and 0.2% at approximately 0.1 w/o for both rare earth additions. This strengthening behavior is attributed to the deoxidizing and desulfurizing action of the rare earths.
Summary
Kippenhan, 1971, Thermochemistry of rare earth carbides, nitrides, and sulfides for steelmaking, Report IS-RIC-5 (Rare Earth Information Center, Iowa State University, Ames, IA). Me-Masters, 1973, Thermoehemistry of rare earths, Report 1S-R1C-6 (Rare Earth Information Center, Iowa State University, Ames, IA).
Introduction. General considerations
TERNARY AND HIGHER ORDER NITRIDE MATERIALS 53 material, especially in the area of ceramics and glasses, as exemplified by the R-Si-AI-O-N (R-sialon) systems. Finally, we would like to note that significant progress has been made recently in the study of nitrides, in general, and this is especially true in the case of rare-earth multinary nitride-type compounds.
Binary nitrides
Except in the case of nitride fluorides that exhibit clear salt behavior, nitrogen atoms generally do not play the same role as C1 or S2 anions; in some cases it is even difficult to know whether the boundary between a valence connection and a cluster connection has not been crossed. Many of the articles have appeared in recent years, often describing new types of materials.
2~/' (CvK~)
Ternary and higher (oxy)nitrides
The anti-La203 trigonal (P3ml) structure contains hexagonal close-packed nitrogen atoms with cerium in octahedral coordination forming filled layers of edge-sharing octahedra ~[CeN6/3], as in the CdI2 structure type. The corresponding rhombic crystal structure (R3c) appears as a combination of planar B3N3 hexagons stacked to form infinite columns along the [001] direction of the hexagonal unit cell, as in hexagonal BN, and of irregular bipyramidal [Pr»B] units centered by other nitrogen atoms, as in the Ce3B2N4 type. A partial oxygen/nitrogen replacement, with the formation of RlsBsN25-xOx oxynitrides, has been proven in the case of R = La and Ce (I2Haridon and Gaudé 1985, Klesnar et al. 1989).
In the face-centered cubic (Fm3m) structure of the Pauli paramagnetic nitride La3Cr9.24NI1, the lanthanum atoms are coordinated by nine nitrogen atoms, while the chromium and most of the nitrogen atoms form a three-dimensional infinite polyanionic network of corner- and edge-sharing CrN4 tetrahedra. Nitrogen atoms are located in interstitial octahedral sites N - 3 S c + 3Ta(Nb), with a random occupancy of 50%. They correspond to the partial solubilities of ScN in the fcc high-temperature phases 6-TaN and 6-NbN (Lengauer 1989).
![Fig. 3. Layers of condensed four- and eight- membered rings of corner-sharing SiN 4 tetrahedra in Ce3SiöNI~ as viewed along the [001] direction](https://thumb-ap.123doks.com/thumbv2/123dok/10272583.0/72.702.86.375.86.393/layers-condensed-membered-corner-sharing-tetrahedra-siöni-direction.webp)
MARCHAND
- Quaternary and higher oxynitrides
- Nitride halides and nitride sulfides
- Conclusion
- Transition mechanisms for lanthanide ions
- Definition of terms employed in intensity theory
Projection of the hexagonal apatite structure of Smr0Si6N2024 along the c-axis (Gaudé et al. 1975b). This is reminiscent of the existence of only metallic TiN and Ti2N in the binary Ti-N system. As noted by Meyer et al. 1989), the boundary between a cluster and a valence compound is not so clear, especially in the case of the [3-phases.
A more in-depth derivation of the basic formulas is given than in Judd's original article. Therefore, the kinetic and potential energy of the system will be higher than in the absence of light. Polarizability can be defined as the ratio between the induced torque and the applied electric field strength.
Since the intensity is proportional to the square of the transition dipole moment (see section 3), the intensity of the magnetic dipole transition is weak. Most of the optical transitions observed in lanthanide ions are induced electric dipole transitions.
Magnetic dipole (MD) transitions
Magnetic dipole matrix element for a single spectral line in a directional system. The calculated magnetic dipole strength for the transition between the state with the wave function (F v r SLJM I and the state with the wave function [l N r/S'L I J I M l) can be found by evaluating the matrix element in the dipole operator OMD. The calculation of the magnetic dipole matrix elements was discussed by Shortley (1940) and Pasternak (1940). The wave functions used to calculate the magnetic dipole strength are pure 4f N eigenfunctions of the even components (k = even) of the crystal field Hamilton±an.
In the Russell-Saunders coupling scheme, the magnetic dipole transition will be confined to J levels within a single 2S+~L term (i.e. the basis term for transitions observed in the absorption spectrum). Special Note: After evaluating the magnetic dipole matrix element and taking the absolute square, the calculated magnetic dipole strength is found, expressed in (Bohr magneton) 2 or/32. In practice, the magnetic dipole strength DMI~ for a randomly oriented system can be obtained from the formula.
Judd-Ofelt theory for induced electric dipole (ED) transitions
- First-order perturbation
- Matrix elements in the transition operator
- Approximations
- First approximation: J'~ and M" are degenerate
According to Judd-Ofelt theory (Judd 1962, Ofelt 1962), the mixing of electronic states of opposite parity in the 4f x electronic configuration of non-centrosymmetric lanthanide systems is induced by the odd-parity terms (k = odd) of the crystal. -field Hamiltonian. The crystal field is generated by point charges located at the atomic positions of the perturbing ligands. We choose here an expansion of the crystal field Hamiltonian in terms of Akq coefficients, instead of the B~ coefficients.
Note that the Akq are coefficients and are related to the angular part of the Bq. All approximations to the calculations of the matrix element are applied to the latter functions. The spin-orbit coupling is neglected in the excited configuration, and the energy of the excited configuration.
The expressions J~ and M can be either integers or half-integers, but if J " is an integer (half-integer), then M must also be an integer (half-integer).
Dieke (1968) has shown that the mean energetic position of the 4f N-15d configuration of all trivalent lanthanide ions is above 50 000 cm -1 . The second approach is adopted because it leads to a significant simplification of the mathematical expression for the electric dipole matrix element. The curly brace in the coefficient of fractional descent always points to the configuration with the largest number of electrons.
These states are the so-called parents of the state gt (12 SL) of the 1N configuration. Detailed information on the fractional descent coefficients is given by Judd (1963), and coefficients for all states of fN configurations with N ~< 7 have been tabulated by Nielson and Koster (1964). To obtain the coefficients for a configuration l N with N > 7, we can use the equation relating the coefficients of fractional origin to the configurations I N and 14l+2-N (Racah 1943):.
14'+2-NTSLI} 14'+2IN,SL)
- Third approximation: n I, l I, ~i and J~ are degenerate
- Fourth approximation: lN-l(nq¢) far above I N
- Calculation of the reduced matrix elements
- Matrix element of the electric dipole operator of a single line in an oriented system
- Intensity parametrization of transitions between J-multiplets
Because only the odd terms in the expansion of the crystal field potential are responsible for the mixing this produces. Matrix element of the electric dipole operator of a single line in an oriented system system. In the static coupling model, the electronic configuration of the lanthanide ion is disrupted by the ligands.
Transitions between these states can be directly induced by the electric dipole component of the incident light. Strictly speaking, it is only in the static coupling scheme that the A~ parameters can be related to the Bxk¢ parameters in the Judd-Ofelt-Axe parameterization scheme. A simplified parameterization scheme based on the idea of the angular overlap model (AOM) was introduced by Gajek (1993).
AI- (z'V, JMI aM,
For solutions, we must consider the random orientation of the molecules and the random orientation of the light polarization tensor. We will also sum all the polarizations and all the components (AJ and IA ~) of the final and initial level. Effect of random orientation on the crystal field operator Recall that the crystal field Hamiltonian is given by
The orientational dependence of the crystal field Hamiltonian V is obtained by taking into account the properties under rotation of the tensor (7~ k) and thus also of the tensor b~ k). Since the terms /~k) are components of an irreducible tensor operator of rank k, they satisfy the same commutation rule with respect to the angular momentum J as it does. SPECTRAL INTENSITIES OF f-f TRANSIENTS 157 spherical harmonics Yq(k), and therefore, have the same properties with respect to a rotation. If the crystal field Hamiltonian is initially specified for some reference orientation (0, 0, 0) as 170) After expanding the matrix element of the unit tensor and the modulus in the square, we get.
JIs JO~'IB')I 2
Carnall's ~z intensity parameters
- Definition
- Determination of f2~ intensity parameters
The actual values of the matrix elements depend on the calculation scheme, but the differences are not significant. Therefore, the f2x parameters depend largely on the relative magnitude of the oscillator (or dipole strengths) of the transitions used in the fit. The error for a parameter is given by the square root of the respective diagonal matrix element of the matrix (XTX) -1.
Second, in the case of overlapping bands, the matrix elements of each of the transitions contributing to the overlapping band can be added. Over the years, the Judd-Ofelt theory has been found to be quite successful for the intensity analysis of the trivalent lanthanide ions. The intensity of the transitions between J-multiplets in the spectrum can be rationalized in terms of just three parameters s'2x.
