Comment on "Colossal Pressure-Induced Softening in Scandium Fluoride"
CComment on “Colossal Pressure-Induced Softening in Scandium Fluoride”
I. A. Zaliznyak, ∗ E. Bozin, and A. V. Tkachenko Condensed Matter Physics and Materials Science Division,Brookhaven National Laboratory, Upton, NY 11973, USA CFN, Brookhaven National Laboratory, Upton, New York 11973, USA (Dated: September 28, 2020)
In a recent Letter [1], Wei et al. report neutron powderdiffraction measurements at variable temperature and pres-sure of negative thermal expansion material, scandium fluo-ride ScF [2]. The diffraction patterns were fitted using theRietveld method to refine the lattice and the atomic displace-ment parameters, with other aspects of the crystal structurefixed by P m ¯3 m cubic symmetry. From the structural refine-ment of the measured diffraction patterns, authors obtain theisothermal compressibility curves. These results thoroughlycharacterize the equation of state of this material in the low-pressure cubic phase (with increasing pressure, ScF under-goes a structural transition to the rhombohedral structure).The results reported by Wei et al. [1] are indeed very inter-esting and important because these results can be confrontedwith predictive, quantitative theories of NTE and pressure-induced softening and allow to corroborate, or invalidate cer-tain approaches. Wei et al. discuss their observations in thecontext of model molecular dynamics simulations and simpleone-dimensional models, which capture qualitative features ofthe observed phenomena, but do not provide a quantitativetheory. On the other hand, a microscopic theory of vibrationaland thermomechanical properties of empty perovskite crystalswith ReO structure (also rooted in neutron diffraction results[3]) has recently been proposed. This theory describes emptyperovslkite structures with strong nearest-neighbor bonds asCoulomb Floppy Networks (CFNs, floppy networks of rigidlinks stabilized by Coulomb interaction) and provides a veryaccurate quantitative description of NTE in ScF [3, 4].Motivated to further corroborate the CFN theory, we com-pared its prediction for the mean-squared transverse displace-ment of the F atoms, U perp ≡ (cid:104) u perp (cid:105) , with that obtained byWei et al. , and observed a marked discrepancy. The experi-mental values are much smaller than those expected from the-ory (Fig. 1). In fact, the U perp values of Wei et al. appear un-physically small, falling for T (cid:46) K well below the quan-tum limit for the Fluorine mean-squared transverse displace-ment due to zero-point motion at T = 0, (cid:104) u (cid:105) = (cid:126) /m F ω + ≈ . ˚A (dashed line in Fig. 1; (cid:126) is Planck constant, m F ismass of the F ion, and (cid:126) ω + ≈ meV is the transverse Fphonon bandwidth). We then compared these results with thepreviously published X-ray diffraction data of Greve, et al. [2]and the neutron diffraction data of Wendt, et al. [3]. We foundthe latter two data sets to be in a good agreement with eachother, as well as with the prediction of CFN theory (Fig. 1).We thus conclude that U perp values reported in Fig. 5 ofRef. 1 are substantially incorrect. In our experience, suchan underestimate of atomic displacement parameters can be T (K) U ( A ) pe r p2 Greve, etal [2]Wendt, etal [3]Wei, etal [1]
FIG. 1. Mean-squared transverse displacement of the F atoms ob-tained from refinement of the crystal structure at P ≈ . The tri-angles show the results of Rietveld refinement of neutron diffractiondata measured on NPDF diffractometer at LANSCE (down triangles)and NOMAD diffractometer at Spallation Neutron Source (up trian-gles) from Fig. 4b of Wendt, et al. [3]. The circles and squarescorrespond to the Xray data from Supplementary Figure 1 of Greve, et al. [2]. The (red) diamonds are the data of Wei et al. [1]. Thesolid line is theoretical prediction of Ref. 4; the horizontal brokenline shows the quantum limit for the Fluorine mean-squared trans-verse displacement due to zero-point motion at T = 0. caused by an incorrect accounting for the effects of beam ab-sorption in/transmission through the sample and sample envi-ronment (such as pressure cell in measurements of Wei et al. )in the Rietveld treatment of the diffraction data. This wouldalso explain unphysical negative atomic displacement param-eters reported in Supplementary Figs. S7 and S8 of Ref. 1,where authors indeed write, “the negative values are consis-tent with not including the effects of beam attenuation in therefinement process, which at this point could be taken into ac-count by a positive constant shift of all values”. Whether thesystematic error of U perp in Fig. 5 of Ref. 1 can be some-how accounted by a simple shift, is unclear. We believe thatthe data are of sufficient interest and importance to deservean analysis better accounting for the absorption/transmissioneffects, which would eliminate, or markedly reduce the sys-tematic error that is currently present in Fig. 5 of Ref. 1.The purpose of this Comment is twofold: (i) to caution theresearchers against using the U perp data of Wei et al. [1] forquantitative comparisons with theory, and (ii) to encouragethe authors of Ref. 1 to reconsider their analysis and obtain areliable U perp data by better accounting for the beam trans-mission and attenuation effects.Work at Brookhaven National Laboratory was supported a r X i v : . [ c ond - m a t . m t r l - s c i ] S e p by Office of Basic Energy Sciences (BES), Division of Ma-terials Sciences and Engineering, U.S. Department of Energy(DOE), under contract DE-SC0012704. Work at BNL’s Cen-ter for Functional Nanomaterials (CFN) was sponsored by theScientific User Facilities Division, Office of Basic Energy Sci-ences, U.S. Department of Energy, under the same contract. ∗ [email protected] [1] Z. Wei, L. Tan, G. Cai, A. E. Phillips, I. da Silva, M. G. Kibble,and M. T. Dove, Phys. Rev. Lett. , 255502 (2020).[2] B. K. Greve, K. L. Martin, P. L. Lee, P. J. Chupas, K. W. Chap-man, and A. P. Wilkinson, Journal of the American ChemicalSociety , 15496 (2010).[3] D. Wendt, E. Bozin, J. Neuefeind, K. Page, W. Ku, L. Wang,B. Fultz, A. V. Tkachenko, and I. A. Zaliznyak, Science Ad-vances5