[Studio picture · a lens focusing a beam onto a thin metal film]
[09 / WHAT COMES NEXT]
What an experiment could test
The models make six predictions that a measurement could in principle look for. Three are firm outputs of the calculations, two rest on a number nobody has measured and one leans on extrapolation. This page sets them out, says what the team trusts and orders the next pass.
[IN SHORT]
In short
The models give numbers a measurement could look for: the energy of the vibration in which every hydrogen moves in step, how fast that vibration softens when the metal is stretched, and a response at exactly half the frequency of a pump.
The vibration energies and the response to stretch are firm outputs of the calculations. Whether a real pump would cross its threshold is not. That depends on how fast the vibration loses energy, and nobody has measured that rate.
Several soft spots the models found belong to hydrogens held on ideal positions, and where those hydrogens would actually rest has not been computed. Letting them settle is the first step of the next pass.
[09.1 · WHERE TO LOOK]
One vibration per material and a pump at twice its frequency
Each material has a collective mode, which is the vibration in which every hydrogen moves in step. The models put it at a definite frequency. A pump that shakes the stiffness of the wells would work at twice that frequency, and the lattice would answer at exactly half the pump frequency.
NiH
mode 85.6 meV · 20.7 THzpump 41.4 THzmeasured peak 89 meV
PdH
mode 62.3 meV · 15.1 THzpump 30.1 THzmeasured peak 55.8 meV
PdD
mode 39.8 meV · 9.6 THzpump 19.3 THzmeasured peak 37 meV
computed collective modepump at twice the modemeasured neutron peak (band average)
[H AGAINST D]
Swapping hydrogen for deuterium in palladium lowers the collective mode by a factor of 1.56 and the single-atom vibration by 1.51. The measured peaks differ by 1.51.
[ONE ATOM AGAINST ALL]
One hydrogen vibrating alone in its well sits higher, at 100.6 meV in NiH, 74.0 in PdH and 48.9 in PdD. The pull between neighbours brings the in-step mode down.
[THE PUMP BAND]
The three pump frequencies lie in the mid-infrared, from 19.3 to 41.4 THz. The open question of step 7 of the next pass is which physical drive would modulate the well stiffness there and by how much.
[09.2 · SIX PREDICTIONS]
What a measurement could look for
Each card names what to measure, the model's number, what that number rests on, which kind of measurement could see it, and how firm it is. Filter by material or by how firm the number is.
- Firm model outputcomputed directly for the inputs as declared
- Conditionalcomputed, but the size of the effect rests on an unmeasured input or a finite simulation
- Extrapolateduses laws far outside the range they were computed on
Showing all 6 predictions
-
01 NiHPdHPdD Firm model output The energy of the in-step vibration
Bars: computed collective mode. Ticks: measured neutron peak.
- [MEASURE]
- The energy of the vibration in which every hydrogen moves together in NiH, PdH and PdD, and its ratio between H and D.
- [MODEL]
- 85.6 meV (NiH), 62.3 (PdH), 39.8 (PdD). H to D ratio 1.56; 1.51 for one atom alone.
- [RESTS ON]
- The computed wells and neighbour couplings at full loading, with zero-point motion included. The PdD well was computed on a 3×3×3 k-point mesh and not converged further. Its collective stiffness sits 11 percent above the converged two-atom value.
- [TECHNIQUE]
- Inelastic neutron scattering resolved by wavevector, which separates the in-step mode from the rest of the band; optical vibrational spectroscopy.
- [HOW FIRM]
- Firm for the declared inputs. The measured peaks (89, 55.8, 37 meV) average a band of vibrations, so today they guide rather than test.
- [SHARPENED BY]
- Step 5
-
02 NiHPdD Firm model output Softening under stretch and its direction
Curvature lost at the well bottom per unit strain as a multiple of its unstrained value. A negative bar gains stiffness.
- [MEASURE]
- How the vibration energy of PdD and of NiH falls as the metal is stretched along and across the direction the hydrogen moves.
- [MODEL]
- Under uniform stretch PdD loses its curvature far faster than NiH: 113 against 22.0 times its unstrained value per unit strain. Along the motion the figures are 80.9 against 23.9. Across it PdD still softens (15.9) while NiH stiffens slightly. One percent of uniform stretch takes the bare PdD curvature to −0.013 eV/Ų.
- [RESTS ON]
- Electronic-structure calculations at ±1 percent strain with every atom on its ideal position. The vibration itself softens more gently because zero-point motion in the steep walls adds stiffness back. In the model it reaches zero only at 5.3 percent stretch in PdD, 7.5 in PdH and 8.1 in NiH (0 K). Those points are extrapolated from ±1 percent.
- [TECHNIQUE]
- Vibrational spectroscopy (neutron or optical) on films or samples held at a known strain.
- [HOW FIRM]
- The contrast between the metals and the role of direction are firm within ±1 percent. The strain where the vibration vanishes is an extrapolation.
-
03 NiHPdHPdD Conditional An answer at exactly half the pump frequency
Threshold as a percentage modulation of the well stiffness, on a logarithmic scale.
- [MEASURE]
- Drive the metal at twice the mode frequency. Above a threshold the hydrogens should oscillate at exactly half the pump frequency, level off at a fixed amplitude, and ring down when the pump stops.
- [MODEL]
- The pump frequency is 41.4 THz (NiH), 30.1 (PdH) and 19.3 (PdD). With the loss rates assumed in the runs, the threshold is 1.9, 1.0 and 1.6 percent stiffness modulation and the ring-down is 1.6 ps (NiH) and 4.1 ps (PdH, PdD). The pumped NiH lattice levels off at 0.064 Å at 8 percent modulation.
- [RESTS ON]
- A loss rate nobody has measured for NiH, PdH or PdD. Across two labelled scenarios the threshold runs from 1.7 to about 23 percent and the ring-down from 1.6 to 0.16 ps. It is not established which drive produces the modulation or how much it gives per unit field.
- [TECHNIQUE]
- Pump-probe (time-resolved) spectroscopy with a pulsed mid-infrared pump, looking for the line at half the pump frequency and its threshold, saturation and decay.
- [HOW FIRM]
- The frequencies follow from firm mode energies. The threshold and ring-down are scenarios until the loss rate is known.
-
04 NiHPdD Conditional Nickel moves in step and palladium in patches
Share of the pumped motion in the single strongest pattern at 0 K and 8 percent stiffness modulation.
- [MEASURE]
- Whether the response to the same kind of pump at low temperature is one uniform motion in step (NiH) or a patchwork (PdD).
- [MODEL]
- In NiH with 110,592 sites, 99.8 percent of the pumped motion is in the uniform pattern, in step across the whole box. PdD at full loading has an in-step length of 1.38 nm, with 12 percent in the strongest pattern. At 300 K the pump adds nothing measurable in PdD (0.00915 Å without, 0.00919 Å with).
- [RESTS ON]
- Finite-time classical lattice simulations of the computed inputs, with an assumed loss rate and an imposed 8 percent modulation. The NiH in-step length of 3.85 nm is the size of the box, and NiH has not been run in a larger box or at 300 K on the corrected inputs.
- [TECHNIQUE]
- Time-resolved spectroscopy or diffraction, looking for one sharp in-step response in NiH against a broader and weaker one in PdD.
- [HOW FIRM]
- The contrast is a model result for the declared inputs. Its size and its survival at room temperature for NiH are open.
-
05 PdD Firm model output Deuterium pushed off-centre beside empty sites
Static displacement in the lattice with no pump at 0 K. The hollow point lies beyond the range the loading law was fitted on.
- [MEASURE]
- The static displacement of deuterium next to empty sites, how it grows as loading falls, and how it depends on the arrangement of the empty sites.
- [MODEL]
- A deuterium with two empty neighbours is pushed toward them with 0.070 eV/Å (0.109 when the vacancies are bunched, 0.136 with four). A linear estimate puts the shift near 0.13 Å. In the lattice the displacement is 0.072 Å at loading 0.875, 0.093 at 0.75 and 0.105 at 0.6. An ordered vacancy pattern cancels it, and clustered vacancies give 0.067 Å.
- [RESTS ON]
- Forces computed with every atom held on its ideal position. Where the deuterium settles was not computed. A fitted force law (0.0707 eV/Å per empty neighbour) with the second-neighbour term set to zero. Loading 0.6 lies outside the range the loading law was fitted on.
- [TECHNIQUE]
- Diffuse neutron or X-ray scattering and pair-distribution analysis of partially loaded samples.
- [HOW FIRM]
- The push and its dependence on arrangement are computed directly. The size of the shift is an estimate until the atoms are relaxed.
-
06 PdDNi on PdD Extrapolated A stronger response in the soft regions of an interface
Pumped amplitude in the interface layer of a Ni-on-Pd stack.
- [MEASURE]
- Whether the pumped response in nickel grown on loaded palladium is stronger in the soft regions of the mismatch pattern between the two lattices.
- [MODEL]
- At the PdD spacing the pumped amplitude in the interface layer rises about tenfold from 0.0013 to 0.0146 Å and gathers in the soft regions (2.9 times enrichment) without copying the pattern's period (correlation 0.25). At the bare-palladium spacing the effect is negligible.
- [RESTS ON]
- A metal-only geometry from a simple interatomic potential with no hydrogen in it, and strain laws carried from the ±1 percent they were computed on to local strains of −18 to +8 percent. Every site is an extrapolation.
- [TECHNIQUE]
- Interface-sensitive vibrational spectroscopy on Ni/Pd multilayers, or nanometre-resolved vibrational mapping (the pattern repeats every 1.73 nm at the PdD spacing).
- [HOW FIRM]
- Low. It marks where to look.
No prediction matches both filters.
[09.3 · WHAT WE TRUST]
What the team stands behind and what it does not yet
One specialist for the electronic-structure calculations and one for the physics models each wrote a review of the results. The lead condensed them into two lists.
[STANDS BEHIND]
- The field alone does not order the hydrogens. When they are coupled to light with the same field in every term, they form no ordered state. This rules out only that one route.
- The computed wells and couplings. For NiH the on-site stiffness is 1.712 and the neighbour pull 0.676, which together give 1.036 eV/Ų. For PdD they are 0.591, 0.389 and 0.202.
- The stiffness under shear and in thin films and the way it is applied to any strain inside the computed range.
- What an empty site does. It softens its neighbours and pushes them toward itself. The arrangement of the empty sites matters as well as their count. The two-term loading law is a usable interpolation with a stated error.
- The vibration spectra for the declared inputs. The in-step modes of NiH, PdH and PdD sit at 85.6, 62.3 and 39.8 meV.
- The lattice runs as finite-time classical simulations. NiH moves in step across the whole 110,592-site box at 0 K, PdD is patchy, and the pump has no measurable effect in PdD at 300 K.
- The energy bookkeeping of pumps. A steady current gives no coherent gain. Modulating the well stiffness at twice the mode frequency is the route that remains.
[NOT YET]
- The Ni-on-Pd well map as a prediction. Every site lies outside the computed strain range, and the geometry has no hydrogen in it.
- The loading law below loading 0.75 or for any arrangement. The force from an empty site two neighbours away is undetermined, and it changes which pattern leads.
- The ordering strains of 5.3 to 8.8 percent as phase boundaries. They are extrapolated from ±1 percent and use a simplified self-consistent treatment.
- Any pump threshold as an experimental number. The loss rate is unmeasured, and nothing yet links an incident laser or current to the size of the stiffness modulation.
- The measured neutron peaks as a strict test. They average a band of vibrations, not the single in-step mode.
- The NiH in-step length as a domain size. It equals the box. There is no larger box and no 300 K run on the corrected inputs.
- A coherent domain at room temperature. This is not established.
[09.4 · THE NEXT PASS]
Seven steps that start with the top priority
The specialists named seven things to compute or measure next. They are listed in the order they were named, and the first is the top priority for both the strain and the loading results. Each block's length shows the compute it needs.
[FIG 2] Pass 4 in order. Block length shows the compute tier
-
1 [MODERATE TO HEAVY]
First priorityLet the hydrogens settle
- [SETTLES]
- Where the hydrogen comes to rest in a few representative strained, film and partially loaded cells, and how stiff its well is there. It decides which of the soft spots above are real.
- [TOOL]
- GPAW (electronic structure) with the hydrogen positions relaxed.
- [COMPUTE]
- The strained two-atom cells are cheap: the whole shear and film set cost 200 core-minutes. The 64-atom cells with empty sites are the costly part: the PdD loading set cost about 2,510.
[SHARPENS]Prediction 02Prediction 05Prediction 06
-
2 [HEAVY]
Check one soft patch of the interface with hydrogen in it
- [SETTLES]
- Whether a soft region of the Ni-on-Pd pattern survives when hydrogen is present and the electrons are computed. This replaces the metal-only geometry and the extrapolated strain law.
- [TOOL]
- GPAW on a cut-out of the interface, with the metal positions from ASE with EMT.
- [COMPUTE]
- No comparable step has been run. The closest is the NiH 64-atom check, which cost about 253 core-minutes for two calculations. A cut-out with nickel, palladium and hydrogen is larger.
[SHARPENS]Prediction 06
-
3 [HEAVY]
Pin down the pull of a more distant empty site
- [SETTLES]
- The force from an empty site at the second-neighbour distance, which the 64-atom cell cancels by symmetry. Setting it to plus or minus half the first-neighbour value moves the uniform share of the pumped PdD motion from 0.005 to 0.001 or 0.155.
- [TOOL]
- GPAW on a larger or differently shaped cell.
- [COMPUTE]
- Higher than for the 64-atom cells, whose loading set cost about 2,510 core-minutes.
[SHARPENS]Prediction 05Prediction 04
-
4 [LIGHT]
Rerun NiH in a larger box and at 300 K
- [SETTLES]
- The true in-step length of NiH, which the box now sets at 3.85 nm, and whether the locking survives room temperature.
- [TOOL]
- The lattice code (NumPy).
- [COMPUTE]
- The 110,592-site NiH run took 406 CPU-seconds on one core, which is under seven minutes. A million sites for 32 steps takes 12 seconds.
[SHARPENS]Prediction 04Prediction 03
-
5 [MODERATE TO HEAVY]
Converge the 64-atom mesh and recompute the last NiH input
- [SETTLES]
- The PdD collective stiffness and the NiH quartic along [111]. On the 3×3×3 mesh the stiffness sits 11 percent above the converged two-atom value, and the quartic still has the coarse value of 1.13 eV/Å⁴.
- [TOOL]
- GPAW with a denser k-point mesh in the 64-atom cell.
- [COMPUTE]
- One displaced NiH point cost about 107 core-minutes. A denser PdD mesh costs more than the 3×3×3 runs it checks.
[SHARPENS]Prediction 01
-
6 [HEAVY]
Treat the anharmonic lattice quantum mechanically
- [SETTLES]
- Whether the strains at which the hydrogens would order on their own (5.3 to 8.8 percent) are real phase boundaries. It replaces the simplified self-consistent treatment with a controlled one.
- [TOOL]
- A stochastic self-consistent harmonic approximation (SSCHA) or a similar method, on computed forces.
- [COMPUTE]
- Many force evaluations in large cells, which is heavy if the forces come from electronic structure.
[SHARPENS]Prediction 02
-
7 [MEASUREMENT AND HEAVY]
Establish the pump path and the loss rate
- [SETTLES]
- Which physical drive shakes the well stiffness at twice the mode frequency (for example a Raman-type optical process, which grows with the square of the field), how much modulation it gives per unit field and how far it reaches into a metal. It also settles the loss rate with a measured or defensible value. Without both, no threshold is an experimental number.
- [TOOL]
- A measurement of the mode's loss, and an electronic-structure calculation of the coupling between field and stiffness.
- [COMPUTE]
- The only loss value found is a published calculation for PdH, not a measurement.
[SHARPENS]Prediction 03Prediction 04
[09.5 · THE DETAIL]
Every prediction with its numbers and its source
| # | Prediction | Numbers on this page | How firm | Source in the repository |
|---|---|---|---|---|
| 01 | In-step vibration energy and H to D ratio | 85.6, 62.3, 39.8 meV (NiH, PdH, PdD); one atom alone 100.6, 74.0, 48.9 meV; ratio 1.56 collective, 1.51 single atom; measured 89, 55.8, 37 meV, ratio 1.51 | Firm | g3_lattice/rerun/part1/pd_x1_quantum/result.json, g3_lattice/rerun/part2/updated/ni_epoch/quantum.json, g3_lattice/README.md |
| 02 | Softening under stretch | −d ln K/dε: PdD 113.3, 80.9, 15.9; NiH 22.0, 23.9, −1.2 (uniform, along, across); PdD at +1%: −0.013 eV/Ų; ordering strains at 0 K / 300 K: NiH 8.1 / 8.2, PdH 7.5 / 8.8, PdD 5.3 / 7.1 percent | Firm within ±1%; ordering strains extrapolated | g2_input/adopted-strains.json, g3_lattice/rerun/part1/updated/part1.md, g3_lattice/rerun/part2/updated/part2.md |
| 03 | Response at half the pump frequency | Pump 41.4, 30.1, 19.3 THz; thresholds 1.9, 1.0, 1.6%; ring-down 1.6, 4.1, 4.1 ps; scenarios 1.7% and about 23%; NiH amplitude 0.064 Å | Conditional | g3_lattice/loss_table.json, g3_lattice/rerun/part1/pd_x1_quantum/result.json, g3_lattice/rerun/part2/updated/ni_epoch/ |
| 04 | NiH in step and PdD in patches | NiH 99.8% uniform, 3.85 nm (box), 110,592 sites; PdD 1.38 nm, share 0.12; PdD 300 K 0.00915 / 0.00919 Å | Conditional | g3_lattice/rerun/part2/updated/part2.md, ni_epoch/phase_summary.json |
| 05 | Off-centre deuterium beside empty sites | Forces 0.070, 0.109, 0.136 eV/Å; shift about 0.13 Å; static 1.0: 0.000, 0.875 random: 0.072, 0.75 random: 0.093, 0.6 random: 0.105, 0.875 ordered: 0.000, 0.875 clustered: 0.067 Å; force law 0.0707 eV/Å, RMS 0.0041 over 80 force vectors | Firm (forces); sizes estimated | g3_loading/README.md, g3_lattice/README.md (Part 1), g3_lattice/rerun/part2/updated/part2.md |
| 06 | Stronger response in soft interface regions | 0.0013 → 0.0146 Å; enrichment 2.86; correlation 0.248; bare Pd 0.00006 → 0.00010 Å; pattern 1.73 nm | Extrapolated | g3_lattice/rerun/part2/updated/part2.md, g3_skew/README.md |
The pumped mode
q is the amplitude of the collective mode, Ω its angular frequency (2π times the mode frequency in THz) and κ the loss rate (ps⁻¹), which is the rate at which friction drains the motion. The pump modulates the well stiffness by a fraction h at angular frequency 2ωp. This is the oscillator of the loss table with the pump fully projected on the mode.
The threshold
When the pump is on resonance at twice the mode frequency, the motion grows once h exceeds hth and then oscillates at exactly half the pump frequency. The threshold is proportional to the loss rate, which is why it cannot be stated as an experimental number.
The ring-down
For pure friction loss, τ is the time for the amplitude to fall by a factor e once the pump stops. Extra loss of phase without loss of energy would shorten the decay of the coherent signal further.
Inputs and results eqs. (2) and (3)
| Case | Mode (THz) | Pump (THz) | κ (ps⁻¹) | hth | τ (ps) |
|---|---|---|---|---|---|
| NiH · loss assumed in the runs | 20.70 | 41.39 | 1.259 | 1.94% | 1.59 |
| PdH · loss assumed in the runs | 15.06 | 30.11 | 0.484 | 1.02% | 4.14 |
| PdD · loss assumed in the runs | 9.63 | 19.26 | 0.484 | 1.60% | 4.14 |
| Scenario A · exploratory loss of the earlier lattice runs | 23.44 | 46.87 | 1.259 | 1.71% | 1.59 |
| Scenario B · calculated loss for PdH at 295 K (Paulatto et al.) | about 16.9 | about 33.9 | 12.47 | about 23% | 0.16 |
Neither scenario is a measurement. They are labels rather than bounds, and the loss table says the real value need not lie between them. Scenario B is a published calculation (arXiv:1411.5628). No measured homogeneous loss was found for NiH, PdH or PdD. The published neutron data give the width of a whole band or the instrument resolution. Scenario A was computed for an earlier NiH reference mode, so its mode frequency differs from the rerun. ↳g3_lattice/loss_table.json
Vibration energies Fig. 1
| Material | One atom alone, meV | Collective, meV | Collective, THz | Measured peak, meV |
|---|---|---|---|---|
| NiH | 100.6 | 85.6 | 20.7 | 89 |
| PdH | 74.0 | 62.3 | 15.1 | 55.8 |
| PdD | 48.9 | 39.8 | 9.6 | 37 |
One atom alone is the first excitation of one hydrogen in its computed anharmonic well with its neighbours held. Collective means every hydrogen moves in step, with the neighbour couplings included. The NiH row used the earlier NiH quartic coefficients. With the recomputed one along [100] the single-atom value moves by −1.3 percent.
[WHAT THIS MEANS FOR THE NEXT MODEL]
Start where the hydrogens rest
The next model starts from where each hydrogen actually settles. That decides which soft spots are real, and every prediction that leans on one moves with it. The pump threshold stays a pair of scenarios until someone measures how fast the vibration loses energy.