Half-Heusler-like compounds with wide continuous compositions and tunable p- to n-type semiconducting thermoelectrics

Half-Heusler and full-Heusler compounds were considered as independent phases with a natural composition gap. Here we report the discovery of TiRu1+xSb (x = 0.15 ~ 1.0) solid solution with wide homogeneity range and tunable p- to n-type semiconducting thermoelectrics, which bridges the composition gap between half- and full-Heusler phases. At the high-Ru end, strange glass-like thermal transport behavior with unusually low lattice thermal conductivity (~1.65 Wm−1K−1 at 340 K) is observed for TiRu1.8Sb, being the lowest among reported half-Heusler phases. In the composition range of 0.15 < x < 0.50, TiRu1+xSb shows abnormal semiconducting behaviors because tunning Ru composition results in band structure change and carrier-type variation simultaneously, which seemingly correlates with the localized d electrons. This work reveals the possibility of designing fascinating half-Heusler-like materials by manipulating the tetrahedral site occupancy, and also demonstrates the potential of tuning crystal and electronic structures simultaneously to realize intriguing physical properties.

significant changes in the calculated band structures as a function of Ru content, and occurrence of Schottky effect in heat capacity only in one of the Ru-poor sample. The above arguments are qualitative. Attempt of more precise explanation of this important and rather surprising effect is likely to attract attention of the scientific community.
The thermoelectric properties are described briefly. One of the critical information missing in the manuscript is the value of the ab-initio effective masses, which could be useful for assessing opportunities of performance optimization e.g. via parabolic band modelling. At very least, the authors should provide value of the density of effective (DOS) effective mass for Ti1.15Ru1.2Sb sample, for which DOS data is explicitly shown in Fig. S6; preferentially the effective mass should be shown for all the compositions, for which DOS was calculated. The manuscript contains two more findings that were only scarcely discussed, and might be of interest for detailed studies in the next articles: (1) rising anharmonicity quantified by Gruneisen parameter towards ruthenium-rich compositions, (2) breakdown of 18-valence electron scheme in half-Heusler-like phase while maintaining semiconducting transport properties. ZT of 0.4 at elevated temperatures seems promising from perspective of further optimization e.g. tuning of carrier concentration by aliovalent doping.
Overall, the manuscript is free from major flaws and provides information important for scientific communities focused on solid state crystallography and applied thermoelectricity. Hence, I recommend it for publication in Nature Communications after two more technical remarks are incorporated: 1. Beginning of 7th page " Figure 2b shows an atom-resolved high-angle annular dark field (HAADF) image and its corresponding atomic-scale EDS maps projected along a [100] direction, which indicate that Ti and Sb atoms respectively locate at the 4a and 4b sites of the F-43m structure, and Ru atoms occupy the 4c and/or 4d site." I understand that off-centering of Sb atoms to 16e positions might be too small to be unequivocally confirmed by TEM imaging, yet I suggest maintaining the notation of Sb atoms residing on 16e Wyckoff slot, rather than 4b. This a minuscule issue, yet consistent notation will make manuscript easier to follow for the reader.
2. 2nd paragraph on 12th page "As discussed later, the picture is even complex because adding Ru revises the band structure and tunes carrier concentration simultaneously." Correct version: "As discussed later, the picture is even more complex (...)" Reviewer #3 (Remarks to the Author): Half-Heulser compound family offers a series of promising potential semiconductors for future electronic devices. I am glad to see a comprehensive study of Ru(1+x)TiSb compounds.
In this work, the authors successfully fabricated the Ru(1+x)TiSb from x=0.15 to 1.0 and prove the tunable phase region from half-Heusler to full-Heusler. The extremely low total and lattice thermal conductivities is really impressive, much better than any other half-Heulser compounds so far. The temperature-dependent Seebeck coefficients of the samples show the great potential as p-/n-type thermoelectric semiconductors. First-principle calculation also explains the different semiconducting behaviour with different Ru doping, supporting the experimental results that the filling of Ru changes the carrier concentration and band structure of compounds very well. Finally, the appreciable thermoelectric power factor at 340K suggests Ru(1+x)TiSb compounds also perform well in the electrical conductivities.
The authors offer systematic and reasonable exerimental and theoretical results to support their claims. The organization of paper is clear. I strongly support the paper to be published, but I still think some minor revisions are necessary in the next step.
1. The crystal structure is not plotted well in Fig. 1. Please add a legend with fraction coordinates in unit cell to indicate the atomic sites. Replace X, Y and Z by Ru, Ti and Sb, since you only analyze one element for each atomic site.
2. The authors use single-phase Ru1.5TiSb as the typical sample through the paper, and I appreciate it. I further suggest the authors cite and discuss the reference(Synthesis and characterization of Fe-Ti-Sb intermetallic compounds: Discovery of a new Slater-Pauling phase, PHYSICAL REVIEW B 93, 104424 (2016)). The team in this reference systematically discuss the fabrication and electronics property of Fe(1+x)TiSb (x=0, 0.5, 1). Because Ru has the same valence electron numbers with Fe, I think the Ru1.5TiSb and Fe1.5TiSb may have the same crystal structure and behave similarly in the semiconducting. In the reference, the author claims the Fe1.5TiSb is the layered structure of FeTiSb and Fe2TiSb in R3m phase, and it has 21 electrons per formula, matching the Slater-Pauling rule that 3 electrons per atom in each spin channel. The gap of Fe1.5TiSb is 0.64eV, closed to 0.614eV in Ru1.5TiSb. I suggest the author add a crystal figure of Ru1.5TiSb along with Fig. 5S in Supplementary to show whether it is a layered structure of Ru2TiSb and RuTiSb. Also add some sentences about electron numbers in the main paper, comparing it to Fe1.5TiSb. Fig. 5 makes the bands unclear. There are some 'watermark' in band structure of Ru1.5TiSb. Please remove the blue background and replot the figures in a clearer format. Fig. 7, I suggest to add some power factors or zT of other typical half-Heusler semiconductors to compare and discuss.

In the
5. Please clean out the atoms outside the unit cell in Fig. S6. It is hard to understand the crystal structure with so many redundant atoms.
Here are my suggestion. Thank you Response to the referee Thanks to all the referees for their insightful and constructive comments. We have seriously considered all the comments from the reviewers and carefully revised the manuscript. Our replies and changes are listed in detail by following the referees' listing. The corresponding revision is also highlighted in the text.

Reviewer #1:
Half-Heusler-like compounds with wide continuous compositions and tuneable p-to n-type semiconducting thermoelectrics, by Z. Dong, C. Wang, Y. Jiang, S. Tan, Y. Zhang, Y. Grin, Z. Yu, K. Guo, J. Zhang and W. Zhang is an interesting paper, dealing with materials "between" full and half Heuslers, p-and n-type, however, this manuscript is not outstanding enough to be published in a high-ranking journal as Nature Communications and should be transferred to a lower ranking (impact factor <10) journal. As reader one expects that any article published in Nature Communications presents either something new, which is scientifically important, or it shows outstanding results. Both is not the case in the current manuscript.
Compounds tunable between p-and n-type are common among thermoelectric materials since years, not only for Heuslers and half Heuslers but also for skutterudites, clathrates… Reply: Thanks sincerely to the referee for ranking our work interesting because of our discovery of something unusual, that is, novel materials "between" full and half Heuslers, pand n-type. Actually, reviewers 2 & 3 also caught and addressed this point of our work for bridging the composition "gap".
Our work provides the first solid proof that the long-existing composition gap between the half-Heusler (HH) and full-Heusler (FH) compounds can be bridged by continuously filling the vacant tetrahedral interstitial 4c/4d sites in a series compounds TiRu 1+x Sb with appropriate atoms, which has never been known and realized before. The HH-like TiRu 1+x Sb covers a surprisingly wide composition range of x = 0.15 ~ 1.0. Previous literatures did report that the vacant 4d sites in a few HH compounds could be filled to some extent, always in a much narrow composition range, such as TiFe It is true that different doping (or substitution or filling, etc) can tune a thermoelectric material between p-type and n-type. This is the classical approach in optimizing the performance of typical thermoelectric materials. The doping method usually only optimizes the performance of a given material at a nearly fixed band structure (rigid band approach) and a given conduction type, which also shows a limited composition/concentration range. In contrast, competitive p-and n-type thermoelectric properties can be achieved in the TiRu 1+x Sb systems by adjusting the filled Ru content in a wide range. Different from the conventional doping, our approach simultaneously reveals novel compounds with versatile structures, revises electronic bands, and leads to n-type or p-type transports. At each given Ru composition, there is still large space to optimize the TE performance by following the classical approaches.
The TiRu 1+x Sb system, due to the widely tunable compositions and electronic band structures, exhibits versatile and fascinating physical properties. We have mainly demonstrated the surprising thermoelectric properties of the novel TiRu 1+x Sb systems in this work. The thermoelectric properties of the system show many interesting and usual aspects, such as the increased anharmonicity at Ru-rich compositions, violation of 18 valence electrons rule in forming HH-like semiconductors (also mentioned by the reviewer 2), and abnormal semiconducting behaviors in the composition range of 0.15 < x < 0.50 possibly due to the localized d electrons. These are all new to HH and Heusler materials. We believe that the rich and fascinating properties of TiRu 1+x Sb will attract great attention from scientists in various research fields. Reply: The focus of this work is to demonstrate that the natural composition gap between HH and FH can be bridged and to show the fascinating properties of the newly-found HH-like TiRu 1+x Sb systems. We report the very low lattice thermal conductivities of the TiRu 1+x Sb samples because the high Ru composition (TiRu 1.8 Sb) shows a glass-like thermal transport properties, even though the XRD pattern of the system still shows clear diffraction peaks of crystallinity. Optimizing zT of TiRu 1+x Sb is not the focus of the current work. In fact, at each composition, the TiRu 1+x Sb solid solution can be treated as a single material, whose properties can be further regulated by doping, substituting, and so on for further work.
Besides that, even for a publication in an other journal some improvements are necessary: (1) The English needs improvement, therefore a native English-speaking person should correct the text. Some (out of many) mistakes: Reply: Thanks a lot. We have checked the manuscript carefully, corrected these mistakes mentioned above, and tried our best to polish the language. The corresponding changes have been highlighted in the text.
1) A sentence should never start with "however"!

Reply:
We have revised according to your suggestion.
.…..no diffraction peaks from impurity phase are detected (from an impurity phase OR from impurity phases)

Reply:
We have changed it into "……no diffraction peaks from impurity phases……" according to your suggestion.

Reply:
We have corrected according to your suggestion.

Similar off-center location of atoms (A similar…)
3

) The κL decreases significantly with the increasing of filled Ru content (no proper English!)
And so on.

Reply:
We have changed the sentence into "κ L decreases dramatically with the increasing Ru content." (2) The authors should measure the density of each sample and calculate the relative density as densities influence physical properties like electrical or thermal conductivity.
Reply: Thank the referee. We have measured and calculated the densities of the samples, which are now presented in the supporting information as Table S5. x = 0.5 9.13 x = 0.6 9.40 x = 0.7 9.66 x = 0.8 9.89 x = 0.9 10.15 x = 1.0 10.38 * The measured mass density of the sample with x = 0.1 is higher than its theoretical mass density because it is a multi-phase sample. The relative densities of the sample with x = 0.7 ~ 1.0 are slightly lower than 98%, which could be ascribed to the presence of trace amounts of RuSb 2 impurities.
(3) Tavassoli (ref. 6) published also very thermal and lattice thermal conductivities. Please read and compare and add.
Reply: Thank the referee. We have added the total and lattice thermal conductivities reported in ref.6 into our Fig. 3a and 3c for comparison. The following discussions have also been added in the text: "The HH-like TiFe 1.33 Sb sample shows also pretty low total and lattice thermal conductivies 6 , further confirming that the filling of vacant 4d site of the HH compound can effectively reduce the thermal transport." Reply: Thank the referee. We have added the highest zT of ref. 6 into our Fig. 7b for comparison.
The following discussions have also been added in the text: "In comparison with typical HH thermoelectric semiconductors (See Supplementary Fig. S10), the power factors and zT values of our TiRu 1+x Sb samples are much lower. Meanwhile, the zT value of our p-type TiRu 1.2 Sb sample is nearly identical to that of the p-type TiFe 0.29 Co 0.78 Sb while much higher than that of the p-type TiFe 1.33 Sb 6 , which also implies that the thermoelectric properties of the TiRu 1+x Sb samples can be further improved by doping, substituting, and so on."

Reviewer #2:
The manuscript reports on finding of high structural flexibility in half-Heusler-like compound TiRu1+xSb. The tetrahedral Wyckoff positions 4c and 4d are shown to be continuously filled by ruthenium in range, x = 0.15 -1. Ru-rich samples exhibit one of the lowest thermal conductivities reported within Heusler family (c.a. 1.7 W/mK at proximity of room temperature). Filling of the ruthenium sites leads to transition from p-to n-type conductivity. Eventually, maximum ZT of 0.4 at 800-1000 K is reported for sample TiRu1.2Sb.
The core part of the manuscript, i.e. report of the unusual structural properties, is based on high quality data: synchrotron radiation XRD, quantitative mapping of chemical composition (EPMA), and atomic-resolution TEM. The performed Rietveld analysis carefully considered different possible types of crystallographic disorder. The authors justify the effect of p-to n-type conductivity transition by significant changes in the calculated band structures as a function of Ru content, and occurrence of Schottky effect in heat capacity only in one of the Ru-poor sample. The above arguments are qualitative. Attempt of more precise explanation of this important and rather surprising effect is likely to attract attention of the scientific community.
The thermoelectric properties are described briefly. One of the critical information missing in the manuscript is the value of the ab-initio effective masses, which could be useful for assessing opportunities of performance optimization e.g. via parabolic band modelling. At very least, the authors should provide value of the density of effective (DOS) effective mass for Ti1.15Ru1.2Sb sample, for which DOS data is explicitly shown in Fig. S6; preferentially the effective mass should be shown for all the compositions, for which DOS was calculated. The manuscript contains two more findings that were only scarcely discussed, and might be of interest for detailed studies in the next articles: (1) rising anharmonicity quantified by Gruneisen parameter towards ruthenium-rich compositions, (2) breakdown of 18-valence electron scheme in half-Heusler-like phase while maintaining semiconducting transport properties. ZT of 0.4 at elevated temperatures seems promising from perspective of further optimization e.g. tuning of carrier concentration by aliovalent doping.
Overall, the manuscript is free from major flaws and provides information important for scientific communities focused on solid state crystallography and applied thermoelectricity. Hence, I recommend it for publication in Nature Communications after two more technical remarks are incorporated: Reply: Thank the referee for the positive and insightful comments. We agree with the referee that many interest aspects of the TiRu 1+x Sb system deserve to be further studied, and we are moving on in this direction. According to the suggestion of the referee, we have added the ab-initio effective masses in the supporting information as Table S4.  Figure 2b shows an atom-resolved high-angle annular dark field (HAADF) image and its corresponding atomic-scale EDS maps projected along a [100] direction, which indicate that Ti and Sb atoms respectively locate at the 4a and 4b sites of the F-43m structure, and Ru atoms occupy the 4c and/or 4d site." I understand that off-centering of Sb atoms to 16e positions might be too small to be unequivocally confirmed by TEM imaging, yet I suggest maintaining the notation of Sb atoms residing on 16e Wyckoff slot, rather than 4b. This a minuscule issue, yet consistent notation will make manuscript easier to follow for the reader.
Reply: Thank the referee. We have made the change accordingly.
2. 2nd paragraph on 12th page "As discussed later, the picture is even complex because adding Ru revises the band structure and tunes carrier concentration simultaneously." Correct version: "As discussed later, the picture is even more complex (...)" Reply: Thanks a lot for pointing out our language mistake. We have checked the manuscript carefully, corrected these mistakes mentioned above, and polished the language.

Reviewer #3:
Half-Heulser compound family offers a series of promising potential semiconductors for future electronic devices. I am glad to see a comprehensive study of Ru(1+x)TiSb compounds.
In this work, the authors successfully fabricated the Ru(1+x)TiSb from x=0.15 to 1.0 and prove the tunable phase region from half-Heusler to full-Heusler. The extremely low total and lattice thermal conductivities is really impressive, much better than any other half-Heulser compounds so far. The temperature-dependent Seebeck coefficients of the samples show the great potential as p-/n-type thermoelectric semiconductors. First-principle calculation also explains the different semiconducting behaviour with different Ru doping, supporting the experimental results that the filling of Ru changes the carrier concentration and band structure of compounds very well. Finally, the appreciable thermoelectric power factor at 340K suggests Ru(1+x)TiSb compounds also perform well in the electrical conductivities.
The authors offer systematic and reasonable experimental and theoretical results to support their claims. The organization of paper is clear. I strongly support the paper to be published, but I still think some minor revisions are necessary in the next step.
Reply: Thank the referee for the positive comments.
1. The crystal structure is not plotted well in Fig. 1. Please add a legend with fraction coordinates in unit cell to indicate the atomic sites. Replace X, Y and Z by Ru, Ti and Sb, since you only analyze one element for each atomic site.
Reply: Thank the referee. We have made the change accordingly in our revised version.

Fig. R3
Schematic crystal structure of Heusler compounds.
2. The authors use single-phase Ru1.5TiSb as the typical sample through the paper, and I appreciate it. I further suggest the authors cite and discuss the reference (Synthesis and characterization of Fe-Ti-Sb intermetallic compounds: Discovery of a new Slater-Pauling phase, PHYSICAL REVIEW B 93, 104424 (2016)). The team in this reference systematically discuss the fabrication and electronics property of Fe(1+x)TiSb (x=0, 0.5, 1). Because Ru has the same valence electron numbers with Fe, I think the Ru1.5TiSb and Fe1.5TiSb may have the same crystal structure and behave similarly in the semiconducting. In the reference, the author claims the Fe1.5TiSb is the layered structure of FeTiSb and Fe2TiSb in R3m phase, and it has 21 electrons per formula, matching the Slater-Pauling rule that 3 electrons per atom in each spin channel. The gap of Fe1.5TiSb is 0.64eV, closed to 0.614eV in Ru1.5TiSb. I suggest the author add a crystal figure of Ru1.5TiSb along with Fig. 5S in Supplementary to show whether it is a layered structure of Ru2TiSb and RuTiSb. Also add some sentences about electron numbers in the main paper, comparing it to Fe1.5TiSb.
Reply: Thank the referee. In our calculation, the TiRu 1.5 Sb structure was found by the structure search through the cluster expansion included in the Alloy Theoretic Automated Toolkit (see detail information in the Methods part of our manuscript). The referee is right that the most stable TiRu 1.5 Sb structure found by our calculation is a layered structure of TiRuSb and TiRu 2 Sb with the space group R3m, which is the same as that of TiFe 1.5 Sb reported by Naghibolashraf et al. (Phys. Rev. B 2016, 93, 104424). We have added the crystal structure of TiRu 1.5 Sb into Fig. S5 according to your kind advice. We have also added several sentence to discuss the crystal structure and valence electrons number in the text: "The calculations reveal two different regions showing different characteristics of band structures, with the composition TiRu 1.5 Sb as the divided line. TiRu 1.5 Sb is the most stable composition obtained from the cluster expansion. In the TiRu 1.5 Sb sample, the HH TiRuSb and FH TiRu 2 Sb blocks stack alternatively to form the layered structure with the space group R3m. According to our theoretical calculation, the TiRu 1.5 Sb sample with 21 valence electrons is a Slater-Pauling semiconductor, which is very similar to the previously reported TiFe 1.5 Sb 25 ."

Fig. R4.
(a-f) Calculated electronic band structure and (g) crystal structure of TiRu 1.5 Sb. The most stable TiRu 1.5 Sb sample has a layered structure of TiRuSb and TiRu 2 Sb with the space group R3m according to our theoretical calculation.