Critical evaluation of (110) texture in lithium electrodeposits on isotropic Cu polycrystals

arising from Q. Zhao et al. Nature Communications https://doi.org/10.1038/s41467-021-26143-9 (2021)

In their paper, Zhao et al.¹ claimed enable to electrodeposit dominantly (110)-oriented lithium films on polycrystalline Cu foil of random orientation, and reported that the textured growth of metal Li electrode in battery enhances its cycling reversibility by regulating morphology. The crystallographic texture (preferred orientation) was quantified using the intensity fraction of 110 reflection in each θ–2θ scan of X-ray diffraction (XRD). There appear to be errors in methodology used for evaluating texture. Our interpretations on the XRD data don’t support the dominant (110) texture of lithium electrodeposits.

It is worth noting that the terminology of texture or preferred orientation is rarely seen in Zhao’s paper. The texture is instead described using various inappropriate phrases, including preferred crystal facet orientation, preferred crystal facets, crystal facet orientation, crystallographic facets, crystal facet, and crystallography.

The quantitation of (hkl) texture is measure of the volume fraction f_v(hkl) of crystallites having the orientation (hkl) within the spread of ΔΩ. Zhao et al.¹ claimed the Li electrodeposits of dominant (110) texture, meaning that the texture fraction f_v(110) of each Li film exceeds at least 50%. Before the conclusion was drawn, they should quantify the f_v(110) value of each Li film by calculating its crystallographic orientation distribution function (ODF). For this purpose, X-ray pole figure combined with electron diffraction (ED) and transmission electron microscopy (TEM) could be the preferred method^2,3,4,5,6,7. In Zhao’s paper, unfortunately, neither X-ray pole figure nor TEM/ED evidence is available. Instead, Zhao et al.¹ preferred θ–2θ scan XRD, which cannot give much information about ODF.

Based on the θ–2θ scans in Fig. S3 of their paper, Zhao et al.¹ emphasized the high intensity-fractions of 110 peak ranging from 88.3% to 91.2% (see supplementary Table 1 in Zhao’s paper) and then draw the conclusion of dominant (110) texture in their Li electrodeposits. Actually, they quantified (110) texture using the intensity fraction ${p}_{110}=\frac{\Sigma {I}_{{hh}0}}{\Sigma {I}_{{hkl}}}$⁸$,$ here I_hkl denotes the measured integrated intensity of hkl peak. From PDF #15-0401 for lithium powder, we know ${I}_{110}^{*}$/${I}_{200}^{*}$/${I}_{211}^{*}$ ≈ 100/30/40. Then we obtain ${p}_{110}^{*}$ of ≈51.5−58.8% for Li powder depending on the number of hkl peaks used, much higher than the expected ${f}_{{{{{{\rm{v}}}}}}}^{*}(110)$ value of ≈2.3% for Li powder when the maximum tilt deviation angle ψ_max of (110) orientation is 5°. Here

$${f}_{{{{{{\rm{v}}}}}}}^{*}\left(110\right)={m}_{110}\frac{\Delta \Omega }{4{{\pi }}}=6{{\times }}(1-{{{{{\rm{cos }}}}}}{{{\psi }}}_{{{{{{\rm{max }}}}}}}),$$

(1)

where m₁₁₀ = 12 is the multiplicity factor of {110} planes, ΔΩ is the solid angle of a spherical crown within the ψ_max and 4π the solid angle of the pole spherical surface. Therefore, it is totally wrong to quantify (110) texture with the intensity fraction ${p}_{110}$. As we know, it is unreliable and incorrect to make any quantitative assessment of (110) texture with the Lotgering degree of orientation ${f}_{110}=\frac{{p}_{110}-{p}_{110}^{*}}{1-{p}_{110}^{*}}$^9,10,11$.$ Such indiscriminate assessments give usually an overestimated value of texture^4,5,6,9. Quantifying (110) texture with the ${p}_{110}$ is even stray farther away, see Table 1.

Table 1 Comparison of the intensity fraction p₁₁₀ and the Lotgering degree of orientation f₁₁₀ as well as the possible texture fraction f_v(110) of the Li electrodeposits estimated from the intensity ratio I₂₀₀/I₂₁₁/I₁₁₀ in their θ−2θ scans

In a symmetric θ–2θ scan the lattice planes contributing to reflection I_hkl are all oriented parallel or nearly parallel to the film surface. Only a subset of grains is monitored, for which the plane normal lies in an angle window ΔΩ_w around the substrate normal, when ΔΩ_w characterizes the divergence of the X-ray beam received by the point detector. Here, ΔΩ_w ≈ πΔψΔω/4, where Δψ and Δω in unit of radian are the diameters of angle window parallel and perpendicular to the diffraction plane, respectively^12,13. If the ΔΩ_w covered the tilt spread ΔΩ of (110) texture, the f_v(110) values of the Li electrodeposits could be roughly estimated from the intensity ratio of the 110 peak to a nearby peak hkl¹¹. In order to balance the intensity fluctuation of weak 200 and 211 peaks, their total intensity is chosen to represent the diffraction contributions from the randomly oriented Li component. From Equation (10) in ref. 11. one can know $\frac{{I}_{200}+{I}_{211}}{{I}_{110}}{{\propto }}\frac{1-{f}_{{{{{{\rm{v}}}}}}}(110)}{{f}_{{{{{{\rm{v}}}}}}}(110)}$. Similarly, we can write $\frac{{I}_{200}^{*}+{I}_{211}^{*}}{{I}_{110}^{*}}{{\propto }}\frac{1-{f}_{{{{{{\rm{v}}}}}}}^{*}(110)}{{f}_{{{{{{\rm{v}}}}}}}^{*}(110)}$ for powder. Division of the two formulas yields

$$\frac{{I}_{200}+{I}_{211}}{{I}_{110}}\frac{{I}_{110}^{*}}{{I}_{200}^{*}+{I}_{211}^{*}}\frac{1-{f}_{{{{{{\rm{v}}}}}}}^{*}(110)}{{f}_{{{{{{\rm{v}}}}}}}^{*}(110)}=\frac{1-{f}_{{{{{{\rm{v}}}}}}}(110)}{{f}_{{{{{{\rm{v}}}}}}}(110)}.$$

(2)

Supposing that ΔψΔω ≈ 6° × 1.5°, which is a typical possible angle window of diffractometer¹², we can calculate ${f}_{{{{{{\rm{v}}}}}}}^{*}\left(110\right)={m}_{110}\frac{\Delta {\Omega }_{{{{{{\rm{w}}}}}}}}{4{{\pi }}}=\frac{3}{4}\Delta {\psi }\Delta {\omega }\,{{\approx }}\,0.21\%$. Then the possible f_v(110) values are estimated to be from 1.10% to 1.49% based on Eq. (2), see Table 1. Obviously, the θ–2θ scans with high ${p}_{110}$ of 88.3%–91.2% could come from the Li deposits of slight (110) texture, further confirming that it is incorrect to quantify (110) texture with ${p}_{110}$. It is easily understandable that the intensity ratio $\frac{{I}_{110}}{{I}_{200}+{I}_{211}}$ increases from 100/70 to 1000/79 as long as the f_v(110) value rises from 0.21% to 1.49% when the angle window ΔΩ_w covers the texture spread ΔΩ. For  evaluating the real (110) texture of each Li deposit, nevertheless, we have to know its ODF.

Generally, a two-dimensional (2D) XRD pattern provides much more information about ODF than a θ−2θ scan. The texture can be derived from analysis of the intensity variations along Debye-Scherrer rings⁷. Unfortunately, the 2D patterns shown in Zhao’s paper present a limited sector of the homogeneous diffraction rings without noticeable intensity change. This fact suggests intuitively that the Li deposits might be of nearly random orientation with slight (110) texture. This possibility would be more reasonable if some diffractometer-specific intensity corrections are considered when the f_v(110) values are estimated using Eq. (2). For example, the relative intensity of 110 peak from film sample increases significantly at lower 2θ angles due to the increment of diffraction volume, whereas such effect is generally very weak in the case of powder sample. Please note that the penetration thickness t₀ of Cu Kα radiation in metal Li is ≈2.63 cm, much thicker than the Li film thicknesses of 35−108 μm.

Meanwhile, we need consider another possibility that the (110) texture is so scattered that the intensity variations along the Debye rings occur beyond the sector available, see our analysis in Fig. 1, although the well-distributed intensity along the 110 ring in Fig. 1e disagrees with the gradual intensity change in usual textured cases. In this possible case, the absence of intensity variation along the weak 211 ring within |χ| ≤ 5° demonstrates that the tilt spread Δψ of (110) texture should be ≤15°. This means that the 2D detector employed is large enough for collecting the intensity variations along the Debye rings. We encourage Zhao et al.¹ collect two 2D frames with either 110 or 211 ring in the middle of the 2D detector, and then merge them into a diffraction pattern⁷. The homogeneous 110 ring in Fig. 1e might indicate that the Li deposit has well-distributed pole density within the ${{\psi }}_{{{{{{\rm{max }}}}}}}$ of 10°. In this possible case, we could calculate ${f}_{{{{{{\rm{v}}}}}}}^{*}\left(110\right)$ using Formula (1) and then estimate the possible f_v(110) values with Eq. (2), see Table 1. At this moment, the estimated f_v(110) values of 34.7%–41.9% may not be true because no ODF of any Li deposit can be unambiguously derived from the 2D patterns in Zhao’s paper.

Fig. 1: XRD analyses of crystallographic orientation distribution in deposited lithium on isotropic polycrystalline Cu.

a–d Schematic drawings in reciprocal space to show the geometry requirement producing diffraction with intensity variation from polycrystal Li, which is a mixture of randomly oriented grains and (110)-textured grains with the tilt spread Δψ of ≤15°. a Superimposing the reciprocal lattice of a dominantly (110)-textured polycrystal Li on the reflecting sphere construction demonstrates the geometric conditions producing Debye diffraction cones of intensity variation. A set of homocentric spherical surfaces display raised red spherical crowns or broad latitude-zones denoting enhanced orientation density due to the scattered (110) texture. They intersect with the reflecting sphere at a set of coaxial circles χ representing the allowed Bragg reflections. The incident angle ω ≈ 18.1° was told by the first author Zhao. b {110} orientation hemisphere showing the tilt scatter of (110) fiber texture and the relation between the tilt angle ψ and the diffraction azimuth χ. The gray denotes well-distributed random orientation of low pole density while the red arctic area the scattered texture of enhanced pole density. c {211} orientation hemisphere showing the broadenings and overlapping of four latitude-zones centered at ψ = 30°, 54.74°, 73.22°, and 90°, corresponding to the interplane angles ∠{211}:(110). The χ–ψ relation indicates that ψ shifts from 14.84° to 15.09° with increasing χ from 4° to 5°. The latitude-zone centered at ψ = 30° with Δψ of ≥15° can broaden to the position of ψ = 15°. Thus, (211) diffraction intensity enhances when χ  ≥ 5° due to the contribution of near-(110)-oriented grains. d Schematic 2D XRD pattern from polycrystalline Li of dominant (110) texture. The weak rings come from Li grains of random orientation while the strong spots elongated along the 110 and 211 rings from near-(110)-oriented grains. The two yellow spots elongated along the 211 ring would contact and even overlap when the tilt spread Δψ ≥ 15.6°. e 2D XRD pattern of a Li film deposited on Cu foil with an areal capacity of 20 mAh cm⁻², reproduced from Fig. 2d in Zhao’s paper. The Li(110) ring presents homogeneous intensity while both the Li{200} and Li{211} rings are weak.

In summary, it is incorrect to quantify (110) texture with the intensity fraction ${p}_{110}$. The XRD data in Zhao’s paper are insufficient to support the Li electrodeposition of dominant (110) texture. Zhao et al.¹ need provide new convincing evidences to prove their claim of dominant (110) texture in the electrodeposited Li films on isotropic Cu polycrystals.