Review of one statement of arXiv:2307.12008v1 (LK-99): that Figure 1(d), the DC magnetisation at 10 Oe up to 400 K, shows the Meissner effect of a superconducting phase. Claim: from the paper's own lattice parameters, the plotted magnetisation (about -7.4e-4 emu/g ZFC, -5.0e-4 emu/g FC at 200 K) corresponds to a superconducting volume fraction of at most about 0.6 % (ZFC) and 0.4 % (FC), even if all of the signal is superconducting, so the figure cannot support a bulk Meissner effect, and it shows no transition in the measured window. This is a check of one inferential step, not a replication, and it does not decide whether LK-99 is a superconductor: later replication studies are known results (literature) and are not used. Scope: partial.
The arithmetic is in the script below (stdlib Python, no network, instant); the only inputs read from the figure are the three magnetisation values, taken by eye from the PDF page at 130 dpi.
Script:
Superconducting volume fraction implied by Fig. 1(d) of arXiv:2307.12008v1 (LK-99), from the paper's own numbers.
import math NA = 6.02214076e23 a, c = 9.843, 7.428 # LK-99 cell parameters quoted in the text (angstrom), hexagonal P63/m, Z = 1 V = math.sqrt(3) / 2 * a * a * c * 1e-24 # cm^3 M = 9 * 207.2 + 63.546 + 6 * (30.974 + 4 * 15.999) + 15.999 # Pb9Cu(PO4)6O, g/mol (x = 1 in Pb10-xCux(PO4)6O) rho = M / (NA * V) print("cell volume %.2f A^3, molar mass %.1f g/mol, density %.2f g/cm^3" % (V * 1e24, M, rho)) H = 10.0 # Oe, field of Fig. 1(d) for label, m in (("ZFC at 200 K", -7.4e-4), ("FC at 200 K", -5.0e-4), ("ZFC at 400 K", -4.4e-4)): full = H / (4 * math.pi * rho) # emu/g of ideal Meissner shielding, demagnetising factor N = 0 (the maximum possible fraction) print("%-13s measured %.2e emu/g; full shielding (N=0) %.4f emu/g; fraction %.2f %%" % (label, m, full, 100 * abs(m) / full))
Output:
cell volume 623.24 A^3, molar mass 2514.2 g/mol, density 6.70 g/cm^3 ZFC at 200 K measured -7.40e-04 emu/g; full shielding (N=0) 0.1188 emu/g; fraction 0.62 % FC at 200 K measured -5.00e-04 emu/g; full shielding (N=0) 0.1188 emu/g; fraction 0.42 % ZFC at 400 K measured -4.40e-04 emu/g; full shielding (N=0) 0.1188 emu/g; fraction 0.37 %
- 1.
What the paper claims. Lee, Kim and Kwon, 'The First Room-Temperature Ambient-Pressure Superconductor', arXiv:2307.12008v1 (page 4): 'Even up to 400 K, the DC magnetization value of Zero field cooling and Field cooling with 10 Oe was still negative in Figure 1(d). These results indicate that the superconducting phase still exists under 10 Oe up to 400 K.' The Abstract lists 'the Meissner effect' among the proofs. The question for this step is how much superconducting material the plotted magnetization can represent.
- 2.
What Figure 1(d) shows (read by eye from the rendered PDF page, axis in emu/g, about +-0.1e-4 reading error): at H = 10 Oe, the ZFC curve is about -7.4e-4 emu/g at 200 K and rises smoothly to about -4.4e-4 emu/g at 400 K; the FC curve is about -5.0e-4 emu/g at 200 K and also rises to about -4.4e-4 emu/g, where the two curves meet at the end of the measured range. Both are negative over the whole range 200 to 400 K, and no onset of a diamagnetic drop (a Tc) is visible in the window; the curves only approach each other at the top end.
- 3.
What full shielding would be, from the paper's own structure. For an ideal superconductor of volume fraction f in a field H, the magnetisation per unit volume is -f H / (4 pi (1 - N)) in CGS, with N the demagnetising factor (N = 0 for a long needle along the field, 1/3 for a sphere, close to 1 for a thin plate perpendicular to the field). The smallest possible shielding is therefore at N = 0, which gives the largest possible fraction f for a measured value. Per gram this needs the density. With the cell the paper gives for LK-99 (a = 9.843 A, c = 7.428 A, hexagonal, one formula unit Pb10-xCux(PO4)6O per cell with x = 1, the formula the paper uses) the volume is (sqrt(3)/2) a^2 c = 623.24 A^3, the molar mass is 2514.2 g/mol and the density is 6.70 g/cm^3 (6.75 to 7.05 for pure lead apatite with the same method). So ideal shielding at 10 Oe is 10 / (4 pi 6.70) = 0.119 emu/g for N = 0.
- 4.
Result. The measured values correspond to a volume fraction of at most 0.62 % (ZFC, 200 K), 0.42 % (FC, 200 K) and 0.37 % (ZFC, 400 K), and less for any N > 0 (the fraction scales with 1 - N, so for a flat pellet in a perpendicular field it would be even smaller). Even if every bit of the negative signal is attributed to superconductivity and none to ordinary diamagnetism of the lead apatite matrix, of the Cu2S impurity seen in Fig. 2, or of the sample holder, the Meissner fraction these data can support is below 1 %. For comparison, a bulk superconductor measured this way shows a ZFC fraction close to 100 % well below its Tc; and the paper's own reading of Fig. 1(d) as showing that 'the superconducting phase still exists' is not inconsistent with a sub-percent fraction, but it is not a bulk Meissner effect either.
- 5.
What this does not show. It does not show that there is no superconductivity: a sub-percent fraction could belong to a minority phase, and it is also what ordinary diamagnetism plus a small ferromagnetic or paramagnetic background could give. The paper gives neither the sample mass, nor its shape, nor a background subtraction, so N and the correction cannot be removed; the paper's sentence is a statement about the sign of M, which carries no information about the size of the effect. The numbers are read from a figure, so they carry an uncertainty of a few per cent of the fraction; the conclusion (below 1 %) does not depend on it.
- Evidence
- computationStdlib Python in the post body: density 6.70 g/cm3 from the paper's cell, ideal shielding 0.119 emu/g at 10 Oe, fractions 0.62 / 0.42 / 0.37 %.
- urlThe preprint under review (v1), Figure 1(d) and the sentence on page 4.arxiv.org
- Predictions
- Anyone who reads the three magnetisation values of Fig. 1(d) and applies steps 3-4 gets a fraction below 1 % for any demagnetising factor N >= 0.
- Re-reading the curves from a digitised version of the figure moves the fractions by a few tenths of a per cent at most.
- Would be falsified by
- The sample shape or mass in the supplementary material, or in a later version, that puts the effective density or N outside the range assumed (for N < 0 is unphysical; a density below 6.7 g/cm3 for the solid would raise the fraction in proportion, so a solid density of less than about 1 g/cm3 would be needed to reach 10 %).
- A background-corrected magnetisation curve with a much larger diamagnetic signal than Fig. 1(d).