Size Effect on the Thermal Conductivity of a Type-I Clathrate
Wolfgang Löser
Round 1
Reviewer 1 Report
The manuscript reports on the synthesis of the type-I clathrate La1.2Ba6.8Au5.8Si38.8 Sq1.4 , where several mesoscopic wires with different widths, of the order of hundreds of nanometers, were cut from an oriented single crystal and as a consequence a size effect was observed as a decrease of the lattice thermal conductivity in the case of the of thinnest 600nm sample, as the authors expected from prior publications.
I recommend the acceptance of this manuscript for crystals after very minor revisions.
1- The manuscript is very interesting and is well written and is in the sequence of previous nice publications from these authors about the Kondo like phonon scattering observed in the lattice thermal conductivity on type-I clathrates.
2-.The interest of this manuscript is mainly from the point of view of fundamental research and confirms the prediction’s of the authors previous publications about the nature of the lattice thermal conductivity of this type of clathrates. The size effect observed bellow 600nm contributed to enhance ZT as expected due to decrease of the contribution of the long waveleght phonons to the lattice thermal conductivity. The only shortcoming is that this kind of samples can not be used directly into applications.
3-.The Seebeck coefficient has not been measured in the sample studied and the results used to calculate ZT were measured in a sample of slightly different Si composition, maybe a more direct reference about it should be made in the text, although the main conclusions are still valid of course.
Author Response
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Author Response.pdf
Reviewer 2 Report
Dear Authors,
I think your answers to the below questions add value to your manuscript and better draw the attention of readers. Please let me know
1- What is the zT value for the bulk crystal?
2- What was the reason for selecting the La1.2Ba6.8Au5.8Si38.8 1.4?
3- In clathrates the suppressed phonon lifetime is responsible for the reduction of lattice thermal conductivity, in addition to the decrease of phonon group velocity. Moreover, the hybridized modes dramatically suppress the acoustic phonon contribution to κl, that results in the non-negligible relative contribution from optical phonon to thermal transport in clathrates. The Callaway model is not able to capture these effects appropriately and further studies based on Boltzmann transport equation is necessary to help researchers design new thermoelectric materials. Additionally, I would like draw the attention of the authors to their report [ref 13] that states in the clathrates the strong Umklapp scattering dominates the lattice thermal conductivity in a wide temperature range while in the current manuscript the main suppressing scattering is considered the boundary scattering. My question is that for what wire size the boundary scattering starts to dominate over the Umklapp scattering based on your simulations?Could you please put more effort and plot it via your simulation?
Thanks.
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
The authors investigated the temperature dependence of thermal conductivity of nanowires of clathrate La-BAS with three diameters by 3 omega method. They analyzed the temperature dependence of thermal conductivity by Callaway model where Debye temperature is replaced by Einstein temperature. The authors claimed that better fit with by Callaway model with Einstein temperature proved the Kondo-like effect.
This topic is attracting the interest of the researcher about the heat conduction and thermoelectric studies. The experimental results are reliable. However, there are some concerns in reliability in analysis and conclusion.
In conclusion, the present manuscript does not have enough reliability to show the authors’ claim. Then, the present manuscript should be rejected.
(1) The authors fitted the temperature dependence of thermal conductivity. However, there is no discussion about fitting parameter results. No one can judge this fitting is correct or not although this fitting is key of this paper.
Not only discussion about fitted values but also discussion about each relaxation time using theoretical formulations should be done.
(2) Fitting validity is key in this manuscript. However, agreement is only above 270K.
This loses the reliability very much. The model should be proposed to explain in the low temperature range.
(3) To show Kondo-like effect from fitting, some more experiments should be done. For example, as vacancy amount is increased, tauD is changed.
The range of experimental lambda should be larger.
(4) The vacancy effect should be considered in discussion about tauD or something.
(5) Is blue line in energy dispersion in Figure 1(b) correct?
(6) The authors should discuss the results by comparing with the preceding nanowires result even if nanowire material is different.
Author Response
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Reviewer 4 Report
The manuscript investigated the size effect on the thermal conductivity of a type-I clathrate. The manuscript is well-written with enough literature background. The experiments have been conducted carefully, and the interpretation of the findings is reasonable.
The reviewer recommends acceptance in present form. One open question is whether the vacancy has an influence on the phonon. Is the impact of the vacancy's presence accounted for in the simulation?
Author Response
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Reviewer 5 Report
The authors have prepared mesoscopic wires of single crystalline Clathrates, prospective thermomagnetic materials with low thermal conductivity. The thermal conductivity from room temperature down to 80 K was measured with a self-heating 3w-technique. The phonon thermal conductivity has been reduced by 40 % (compared with the bulk material) for the thinnest wires of 600 nm diameter. The experimental findings reasonably agree with a modified Callaway model bearing in mind a suppression of high-frequency phonons. The size effect on the thermoelectric efficiency ZT, however, is small because it is partially counterbalanced by a decrease of the electrical conductivity for reduced wire diameters.
The paper provides new evidence for a size effect on the thermal conductivity of clathrates. It is clearly written and may be published in the present form.
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
The answer convinced me of the publication. The manuscript is properly revised. This meets the criteria for the publication.
