Anharmonicity and the low-temperature phase in lithium metal

McCarthy, C.M.; Tompson, C. W.; Werner, S. A.

doi:10.1103/physrevb.22.574

Cited by 55 publications

(19 citation statements)

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“…This is because the transverse displacement cannot be readily observed in the polycrystalline sample at this low L value. The outward shifts of the (104) and (1013) reflections and the inward shifts of the (105) and (1014) reflections are in qualitative agreement with the experimental and theoretical results of the polycrystalline studies, 6 but the shift of the (101) 9R and (T02) 9R reflections mentioned above are opposite to those calculated. The peak shifts and widths along with the diffuse streaking between reflections indicate a high degree of faulting, but weak extra peaks are observed which suggest a deviation from true rhombohedral symmetry.…”

Section: Martensitic Phase Transformation Of Single-crystal Lithium Fsupporting

confidence: 86%

Martensitic phase transformation of single-crystal lithium from bcc to a9R-related structure

Smith

1987

Phys. Rev. Lett.

118

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A neutron elastic-and inelastic-scattering study of single-crystal bcc lithium was performed above and below the martensitic phase transformation in the vicinity of 75 K. The transformation is abrupt and the bcc lattice partially transforms to a 9/?-related (Sm-type) structure. The 9R c* and a* axes of this variant are nearly along the [110] and [HO] bcc directions, respectively. The (10L) and (20L) 9R reflections were broadened and shifted from their ideal positions compared to the (00L) 9R reflections, indicative of numerous stacking faults. On warming, the sample reverts back to a single crystal with the same bcc orientation.PACS numbers: 61.50. Ks, 61.55.Fe, 64.70.Kb Lithium, in spite of its being the lightest metal and also having the smallest number of electrons, exhibits rather complex behavior in some of its physical properties. Barrett and Trautz 1 observed a partial structure change by x-ray diffraction in the vicinity of 75 K. It appeared to be a mixture of untransformed bcc lithium plus an hep phase. An fee phase could be obtained by cold working at low temperatures. 2 Specific-heat measurements by Martin 3 revealed a long hysteresis on warming from below the phase transition. Inelasticneutron-scattering studies of the lattice dynamics of Li 4,5 at 98 K showed an unusual crossing over of the LA[100] branch below the TA[100] branch.The present study of single-crystal lithium was undertaken for several reasons: (1) the discovery 6 " 8 of the 9R structure coexisting with the bcc lattice by a neutronscattering study of polycrystalline lithium at low temperatures; (2) the discovery of charge-density waves in potassium 9 ; and (3) the desire to extend the previous phonon measurements below the phase transition. In the meantime, a paper by Ernst et ai, l0 appeared describing a neutron-scattering study of single-crystal 7 Li above and below the phase transition. At 74 K they observed an extra reflection near the (110) bcc lattice point, which they indexed as (002) hep, but they conceded that it could be the (009) 9R or some other close-packed hexagonal lattice reflection. They also observed a softening of the entire Z 4 branch with a slight dip occurring at a q of (0.4,0.4,0)2/r/#.The previous inelastic neutronscattering studies did not show softening of the entire branch nor the dip at (0.4,0.4,0)2n/a\ indeed, a slight hardening of this branch at low q values had actually been observed.This study, using single crystals of natural lithium, confirms the growth and orientation of a 9/^-related (Sm-type) structure in the bcc lattice, and photographs of the Bragg reflections show that both types of reflections are coming from the entire crystal. The sample reverts to a single crystal of bcc Li on warming. These experiments and others are described below.Three single crystals of natural lithium of excellent quality (FWHM =0.2°, instrumental resolution plus mosaic width) were used. Crystal B (5 cm long by 1 cm diameter), obtained commercially, was the same one used in the lattice-dynamics study 4 nearly twenty...

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Section: Martensitic Phase Transformation Of Single-crystal Lithium Fsupporting

confidence: 86%

Martensitic phase transformation of single-crystal lithium from bcc to a9R-related structure

Smith

1987

Phys. Rev. Lett.

118

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“…3 for a range of temperatures between 0 and 350 K. The Murnaghan, Rose-Vinet and Poirier-Tarantola equations of state [31][32][33] give essentially identical results. A transition from the FCC to a BCC phase occurs upon heating at 217±13 K. This phase transition is observed on isobaric heating of the FCC phase experimentally; however, the calculated transition temperature is somewhat above the experimental range of 110-200 K [1,4,[34][35][36][37]. The reverse BCC → FCC transition is not seen experimentally upon isobaric cooling at ambient pressure.…”

Section: B Free Energy Calculationsmentioning

confidence: 80%

Structural and vibrational properties of lithium under ambient conditions within density functional theory

Hutcheon¹,

Needs²

2019

Phys. Rev. B

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We apply a general first-principles approach to derive the phase diagram of metallic Lithium at ambient pressure between 0 and 350 K, including identification of candidate phases. We use ab initio random structure searching (AIRSS) to identify competing phases and supplement the results with calculations of vibrational properties and relevant derived neutron diffraction patterns. Strong quantum nuclear effects are present, prompting a careful treatment of vibrations. We directly map the Born-Oppenheimer surface of Li for the first time, allowing the extention of the normal quasi-harmonic treatment of vibrations to a "quasi-anharmonic" approach, where the effects of anharmonicity are included. The Gibbs free energies of the FCC, BCC, HCP and 9R phases are derived using a variety of equations of state. We find that the anharmonic contribution to the Gibbs free energies of Li phases is of the same order as the differences between phases. Anharmonicity also makes a noticeable difference to the 0 K phonon dispersion of the BCC phase, with the largest difference at the N-point phonon. The ordering of phase transitions that we find agrees with the calculations of Ackland et al. [Science 356, 1254[Science 356, -1259[Science 356, (2017], even when anharmonic effects are included, suggesting that a quasi-harmonic treatment is sufficient for correct phase behaviour. We show explicitly that the Martensitic phase transition from close-packed to BCC lithium upon heating is driven by entropic contributions to the phonon free energy. * mjh261@cam.ac.uk † rn11@cam.ac.uk

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“…In pure metals, besides in Sm itself, the structure has been seen in quenched, ultrafine Co particles [11], in Cu precipitates in a-Fe [12], and in our own work on Cu and Ag twin boundaries to be reported. Furthermore, the 9R structure has received increasing attention recently from the physics community since it was identified by Overhauser [13] from neutron scattering data [14] as a stable structure of Li below 75 K. Subsequent work by Smith and others confirmed that there is a 9R phase, albeit heavily faulted, in Li below 75 K [15] and also in Na below 35 K [16]. The evidence that it exists at all in K appears to be weaker [16,17].…”

Section: Theoretical Prediction and Direct Observation Of The 9r Strumentioning

confidence: 90%

Theoretical prediction and direct observation of the 9Rstructure in Ag

et al. 1992

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Molecular-dynamics simulations of the Z3< 110X211) twin boundary in Ag predict a thin (1 nm) boundary phase of the 9R (a-Sm) structure. High-resolution electron microscopy shows the presence of the predicted structure. We also calculate the energy ab initio for several hypothetical structures of Cu and Ag. Low energies of the 9R structure and other polytypes, low experimental stacking-fault energies, and the hcp-fcc energy difference are correlated and explained in terms of an effective nearest-neighbor Ising interaction. PACS numbers: 61.16.Di, 61.70.Ng, 68.35.Bs It has been recognized for some time that the 9R polytype or a-Sm structure occurs as a martensitic product in a number of alloys [1-7] and compounds [8][9][10]. In pure metals, besides in Sm itself, the structure has been seen in quenched, ultrafine Co particles [11], in Cu precipitates in a-Fe [12], and in our own work on Cu and Ag twin boundaries to be reported. Furthermore, the 9R structure has received increasing attention recently from the physics community since it was identified by Overhauser [13] from neutron scattering data [14] as a stable structure of Li below 75 K. Subsequent work by Smith and others confirmed that there is a 9R phase, albeit heavily faulted, in Li below 75 K [15] and also in Na below 35 K [16]. The evidence that it exists at all in K appears to be weaker [16,17]. From a theoretical point of view firstprinciples calculations for metallic hydrogen have shown [18] that, among several candidate structures, the 9R is the most stable.We report here the first observation of the 9R structure in pure Ag. It occurs in a rather special situation, namely, at a S3 (211) twin boundary, where a thin (1 nm) layer of the phase appears as a means to ease the reversal of the stacking sequence ABC...to CBA . . . from grain to grain. Its structure is appropriate for this purpose since it can be thought of as fee with a stacking fault on every third close-packed plane. However, to occur at the boundary it is necessary that 9R be only slightly higher in energy than fee, and as we shall show this is enabled by the low stacking-fault energy of Ag. The boundary structure was predicted by computer simulation, as described below. It has also been predicted and found in Cu [19]. Evidence has been published that it appears in Au [20], although it was not recognized at the time as such. Our direct experimental evidence for the structure was obtained by high-resolution transmission electron microscopy (HRTEM). We have also made first-principles total-energy calculations for polytypes and obtained stacking-fault energies which support our interpretation.To understand the geometry of the 97? and other polytype structures it is helpful to note that the possible stacking sequences of close-packed planes are isomorphic to the Ising model. This is a useful way to think about polytypes [21-23]. The familiar notation ABCABC. . . for the stacking sequence in fee, for example, obscures the fact that each close-packed plane has the same translation with respect ...

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Anharmonicity and the low-temperature phase in lithium metal

Cited by 55 publications

References 4 publications

Martensitic phase transformation of single-crystal lithium from bcc to a9R-related structure

Martensitic phase transformation of single-crystal lithium from bcc to a9R-related structure

Structural and vibrational properties of lithium under ambient conditions within density functional theory

Theoretical prediction and direct observation of the 9Rstructure in Ag

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