New High Pressure Form of Calcium Disilicide

Silverman, M. S.; Soulen, J. R.

doi:10.1021/j100803a505

Cited by 13 publications

(11 citation statements)

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“…At high pressures, CaSi 2 shows polymorphic behaviour and forms high-pressure modifications with crystal structures of the ThSi 2 type (4 GPa and 1270 K to 8.7 GPa and 1770 K [21][22][23][24][25]), with trigonal symmetry (9 GPaoPo16 GPa at ambient temperature [26,27]) and with an AlB 2 -like pattern (P416 GPa and ambient temperature [26,27]). …”

Section: Article In Pressmentioning

confidence: 99%

High-pressure synthesis of the electron-excess compound CaSi₆

Wosylus

Prots

Burkhardt

et al. 2007

Science and Technology of Advanced Materials

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The binary phase CaSi 6 is prepared at a pressure of 10(1) GPa and a temperature of 1520(150) K. X-ray single-crystal structure refinements and powder diffraction data of quenched samples reveal that the compound crystallizes in the orthorhombic crystal system (space group Cmcm, a ¼ 4.4953(5) Å , b ¼ 10.078(1) Å , c ¼ 11.469(1) Å ). At ambient pressure, exothermic decomposition into CaSi 2 and Si at 737(5) K indicates that the compound is a metastable high-pressure phase. Physical property measurements reveal that the new hexasilicide is diamagnetic and a bad metallic conductor, with resistivity rE900 mO cm at 300 K. r

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Section: Article In Pressmentioning

confidence: 99%

High-pressure synthesis of the electron-excess compound CaSi₆

Wosylus

Prots

Burkhardt

et al. 2007

Science and Technology of Advanced Materials

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“…(i) The most obvious numerical application is to compute eL, aeL/aA, and a2EL/dA2, respectively, via (8), (14), and (19) over a wide range of A values; note that for a given A, the same eigenvector C L is used in all three calculations. Since the behavior of a functional is largely determined by the behavior of its leading derivatives, this procedure affords a far more sensitive test of the influence of the perturbation than the customary calculation of e L alone; for some systems, it may be of interest to investigate in this manner the effect of different selections of the perturbation, that is, of varying the choice of A.…”

Section: Discussionmentioning

confidence: 99%

“…Using (1 1) again, one obtains Solution of (13) for &"/ah using (10) and (7b) yields the matrix formulation of the generalized Hellmann-Feynman theorem, valid for all states. The formal equivalent of (14) was previously derived by Lowdin [27] for the more specialized quantum mechanical matrix eigenvalue equation constructed with a A dependent nonorthonormal basis set (see footnote on p. 918). Now proceed to second order by differentiating (13) in respect to A and solving for a2c"/dA2.…”

Section: A Exact and Rr Solutionsmentioning

confidence: 99%

“…Aside from its theoretical import, the bound of (19) is much simpler to compute than the exact (15) because the inaccessible A derivatives of the eigenvectors have been eliminated. The generalized matrix theorems, (14) and (19), are valid in both classical and quantum mechanics for all cases where (9b) holds, regardless of how the A dependency enters the latter (see footnote on p. 918). Finally, note that if S is independent of A , (14) and ('l9), respectively, reduce to the matrix formulations of the original quantum mechanical Hellmann-Feynman theorem [ 11, and curvature theorem [5],…”

Section: A Exact and Rr Solutionsmentioning

confidence: 99%

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Generalized Hellmann–Feynman and curvature theorems in classical and quantum mechanics

Silverman

1984

Int J of Quantum Chemistry

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The generalized Hellmann-Feynman and curvature theorems are derived for the generalized Sturm-Liouville-type eigenvalue equation which is widely encountered in many branches of physics. In classical mechanics, the Sturm-Liouville eigenvalue equation primarily arises from applying the theory of small oscillations to vibration problems while, in quantum mechanics, the most important example is the time-independent Schrodinger equation. The generalized theorems, respectively, provide simple useful expressions for the first and second A derivatives of the eigenvalue where h is an arbitrary real parameter appearing in the eigenvalue equation. These results, which apply to both classical and quanta1 systems, include as special cases the well-known quantum mechanical HellmannFeynman and curvature theorems for the time-independent Schrodinger equation, thus unifying the formalism. This connection between classical and quantum mechanics is of interest per se, and also because classical eigenvalue equations find application in the treatment of some quantum chemical problems. Two derivations of both generalizations are presented, the first proof applying to exact and Rayleigh-Ritz (linear variational) solutions of the eigenvalue problem, and the second, more general one, to arbitrary optimal variational as well as exact solutions. Necessary and sufficient conditions for the validity of the results are discussed. To demonstrate the insight they afford, several applications of the theorems in conjunction with perturbation theory are described.

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“…A similar calculation was later performed by Ledovskaya (1969). A useful sum rule for (r -1) has been given by Silverman & Obata (1963): this quantifies the correspondence between 'contraction in r-space' and 'increase' of atomic scattering factors and between 'dilation in r space' and 'decrease' of atomic scattering factors. The rule has been applied by Ruffa (1967) to MgO, with the conclusion that the extension of the charge cloud of Mg 2+ in the crystal is slightly greater than in the free ion.…”

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confidence: 99%