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67度以上の熱を永続的に保存し、持ち運びできるセラミックが開発されました。(東大・パナソニックなど)
http://www.asyura2.com/16/eg3/msg/167.html
投稿者 ピノキ 日時 2020 年 11 月 22 日 00:05:42: /cgEbzQ/iEx0c g3ODbYNM
 


ひつじさん【明るいニュースch】


今回は、熱を永続的に保存できるセラミックが東大・パナソニックなどの研究グループにより発見されたので、まとめてみました。


普通熱は時間が経つと失われてしまい、その時に作られた熱をその場で使用しますよね。
しかし、今回開発された「スカンジウム置換型ラムダ5酸化3チタン」という物質は熱を保存したうえで保持することができます。
つまりこれまで立ちはだかっていた場所の障壁と時間の障壁がなくなり、いつでもどこでも熱を取り出せるようになりました。


これはほぼテレビでは報道されておりませんが、かなりすごいニュースです。
世界に先駆けた開発ですから日本がこの技術を売り込むことで経済的な恩恵にもつなげられる可能性が大いにあります。


今日はそんなセラミックについてサクッとまとめてみましたので、暇つぶしにどうぞ!


【出典】
@お湯の熱エネルギーを約一年間保存できるセラミックが発見される 。 水を温める手間がなくなるかも!? - ナゾロジー (nazology.net)
A東大、熱エネルギーを貯められる新材料「蓄熱セラミックス」発見 | ニュース | 環境ビジネスオンライン (kankyo-business.jp)
BLong-term heat-storage ceramics absorbing thermal energy from hot water | Science Advances (sciencemag.org)
C固体・液体・気体の違いとは?おもしろ話も一緒に徹底解説! | とはとは.net (towatowa.net)
D弱い圧力をかけるだけで熱を取り出せる蓄熱セラミックスを開発――自動車用の蓄熱材料として有効 東京大と筑波大 | fabcross for エンジニア
E固体 - Wikipedia
F「凍らない湖」が結氷・・・。 : Dr.MINO人生放談 (livedoor.jp)
G(1) Pinterest
H吉野彰氏が2019年ノーベル化学賞を受賞! | Nature ダイジェスト | Nature Research (natureasia.com)
I火力発電用タービンの大和機械メンテ株式会社 » 事業内容 (daiwa-ce.com)
J発電所の排水口 by クマ蔵 (ID:8900600) - 写真共有サイト:PHOTOHITO
K海を汚さないために | 環境への取り組み | JERA
L環境省_環境ビジネス FRONT RUNNER_鹿島建設 (env.go.jp)
M相転移 - Wikipedia
N通常種=酸化チタン説。チタンの語源がタイタンから (shingeki-kyojin.com)
O酸化チタンの新機能を発見 ―薄膜形状で超伝導を実現― | 東工大ニュース | 東京工業大学 (titech.ac.jp)
 

  拍手はせず、拍手一覧を見る

コメント
1. 2020年11月29日 19:20:27 : VTH59AY6XQ : WWk1VDA0bXVWVGM=[822] 報告
ある体積のセラミックにどんだけの熱量が保持できるのか
それはカップヌードルに70度のお湯が入ってるものが
1年間保持できるというイメージで大差ないだろう

じゃあトラックの大きさのセラミックに蓄えた熱量が
どんだけ有難く使えるかと考えると
北海道の家庭の1日分くらいの暖房に使えるだろうか
そんなものを運んでくるのも回収するのも大変だ

という部分で、使い道が限られそうだ
自販機とかに使えるかも?

2. 2021年3月06日 00:46:14 : A3vi7f7MBE : T2pDaGRZNDZvdUE=[201] 報告

更に効率の良い、断熱素材としては、利用価値は有ると思う。

コストから、AIP推進機関の断熱素材からかな?

火力発電所の発電効率40%超えを目標!?


  電磁推進機研究者談

3. 2021年5月20日 02:10:06 : jXbiWWJBCA : Rm5WWGpiTzAwU2c=[671] 報告

>熱を永続的に保存

悪く言えばデマ


大分前のフェイク記事の”永続的というコトバ”に騙されたようだが

英文紙を見れば、単にLong-termとしか言ってない


結局、潜熱を利用している蓄熱材であり

相転移のエネルギー障壁は単に大きいだけで無限大ではない

つまり常圧で永続的に位置エネルギーを保存できるわけではなく

原子レベルでは、徐々に熱揺らぎにより、相転移が進んでいく


実用性に関して言えば、単位体積あたりの蓄熱量や、エネルギー障壁の高さがどの程度か、

そして何より、製造コストが、どの程度かによるが

Scはレアアースだから結局、中国に握られる可能性もある


あまりはしゃぎすぎない方が賢いだろう

https://www.s.u-tokyo.ac.jp/ja/press/2020/6908/

https://advances.sciencemag.org/content/6/27/eaaz5264.full

Long-term heat-storage ceramics absorbing thermal energy from hot water
View ORCID ProfileYoshitaka Nakamura1,*, Yuki Sakai2,3, View ORCID ProfileMasaki Azuma2,3 and View ORCID ProfileShin-ichi Ohkoshi4,*
See all authors and affiliations

Science Advances 01 Jul 2020:
Vol. 6, no. 27, eaaz5264
DOI: 10.1126/sciadv.aaz5264
Article
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Abstract
In thermal and nuclear power plants, 70% of the generated thermal energy is lost as waste heat. The temperature of the waste heat is below the boiling temperature of water. Here, we show a long-term heat-storage material that absorbs heat energy at warm temperatures from 38°C (311 K) to 67°C (340 K). This unique series of material is composed of scandium-substituted lambda-trititanium-pentoxide (λ-ScxTi3−xO5). λ-ScxTi3−xO5 not only accumulates heat energy from hot water but also could release the accumulated heat energy by the application of pressure. λ-ScxTi3−xO5 has the potential to accumulate heat energy of hot water generated in thermal and nuclear power plants and to recycle the accumulated heat energy on demand by applying external pressure. Furthermore, it may be used to recycle waste heat in industrial factories and automobiles.

INTRODUCTION
Generated thermal energy cannot be efficiently converted to electric power at thermal and nuclear power plants. Seventy percent of the generated thermal energy is discarded as waste heat (1–4). The temperature of this waste heat is below the boiling temperature of water, i.e., 100°C (373 K) (5). The waste heat is currently released into the atmosphere through water or air, negatively affecting the environment (6–12). Storing and using this waste heat would provide numerous benefits due to the improved energy efficiency and environmental compliance. In the present paper, we report a long-term heat-storage ceramic, scandium-substituted lambda-trititanium-pentoxide, absorbing thermal energy by a solid-solid phase transition below boiling temperature of water. The ceramic can repeatedly use thermal energy by pressure and heating. This heat-storage performance could provide a sophisticated energy reuse technology for thermal and nuclear power plants and mitigate negative environmental impact of the waste heat.

RESULTS
First-principles calculations of formation energy
In an effort to realize heat-storage materials (13, 14) capable of absorbing low-temperature waste heat, our research has focused on metal-substituted lambda-trititanium-pentoxide (λ-MxTi3O5). λ-Ti3O5 exhibits photo- and pressure-induced phase transitions (15–19). To date, several types of metal-substituted λ-Ti3O5 have been reported (20–22). We surveyed metal cations suitable for metal substitution of the Ti ion in λ-Ti3O5. Specifically, we conducted first-principles calculations and determined the formation energies of the various λ-MxTi3O5 using 54 different elements. Figure 1A and fig. S1 show the results, where blue denotes that metallic ion substitution stabilizes the formation energy, while orange destabilizes the formation energy.


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Fig. 1 First-principles calculations of formation energies.
(A) Periodic table colored by the total electronic energies of λ-Ti3O5 with an elemental substitution. Blue elements are those where substituted λ-Ti3O5 shows a lower formation energy than that of pure λ-Ti3O5. Orange elements are those where substituted λ-Ti3O5 shows a higher formation energy. (B) Calculated total electronic energies of λ-AxTi3−xO5 (A, trivalent elements) and (C) λ-BxTi3-xO5 (B, tetravalent elements) in order of atomic number. One of three Ti sites in λ-Ti3O5 is substituted by a colored element for the first-principles calculations. Element A in λ-AxTi3−xO5 substitutes into the Ti1 site. Element B in λ-BxTi3-xO5 substitutes into the Ti2 site. Blue and orange squares represent that elemental substituted λ-Ti3O5 shows a lower formation and a higher formation energy, respectively. Black square denotes pure λ-Ti3O5.

Of these elements, only six have a stabilizing effect: Sc, Nb, Ta, Zr, Hf, and W (Fig. 1, B and C). Thus, we synthesized these λ-MxTi3O5. Substituting with Nb, Ta, Zr, Hf, and W yields the β phase. However, Sc-substituted Ti3O5 assumes the λ phase (fig. S2). Here, we report the synthesis, crystal structure, and heat-storage properties of Sc-substituted λ-Ti3O5.

Crystal structure
We used an arc-melting technique to synthesize the Sc-substituted λ-Ti3O5 (23–27). Figure 2A overviews the synthetic procedure. Precursors of Sc2O3, TiO2, and Ti powders are mixed, and an 8-mm pellet of the mixture is prepared. Arc melting was used to melt the pellet in an Ar atmosphere. Then, the sample is shaped into a spherical ball (Fig. 2A). The obtained sample is milled by hand. The formula of the sample is determined to be Sc0.09Ti2.91O5 by x-ray fluorescent (XRF) measurements (see Materials and Methods). We performed synchrotron x-ray diffraction (SXRD) measurements using beamline BL02B2 at SPring-8 to determine the crystal structure (28). Figure 2B shows the SXRD pattern of the as-prepared sample at room temperature. From the Rietveld analysis, the crystal structure is monoclinic (space group C2/m) with lattice parameters of a = 9.84195 (4) Å, b = 3.79151 (1) Å, c = 9.98618 (4) Å, β = 91.1207 (3)°, and a unit cell volume of V = 372.572 (3) Å3 (fig. S3).


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Fig. 2 Synthesis, crystal structure, and morphology of λ-Sc0.09Ti2.91O5.
(A) λ-Sc0.09Ti2.91O5 sample synthesis. Pelletized mixture powder of Sc2O3, TiO2, and Ti metal with a diameter of 8 mm is prepared, melted, and rapidly cooled in an arc-melting process. After the melting process, the solidified (as-prepared) sample is milled by hand. Photo credit: Yoshitaka Nakamura, Panasonic Corporation. (B) Synchrotron x-ray diffraction (SXRD) pattern of the as-prepared Sc0.09Ti2.91O5 sample collected at room temperature with λ = 0.420111 Å. Upper blue and lower orange bars represent the calculated positions of the Bragg reflections of λ-Sc0.09Ti2.91O5 and β-Sc0.09Ti2.91O5. (C) Scanning electron microscopy (SEM) image of the powdered sample shows a grain size below 100 μm. Particle from the powdered sample is sliced by a focused ion beam. STEM image shows stripe-like domains with a size of about 100 nm × 200 nm. Scale bars show 100 μm in the SEM image and 100 nm in the STEM image.

These characteristics correspond to the crystal structure of λ-Ti3O5. λ-Sc0.09Ti2.91O5 has a slightly larger unit cell volume than that of λ-Ti3O5 with a 0.4% expansion. In addition, the β phase is present as the minor phase. The β phase adopts a monoclinic crystal structure (space group C2/m) with lattice parameters of a = 9.7930 (4) Å, b = 3.8064 (14) Å, c = 9.4375 (4) Å, β = 91.5611 (3)°, and V = 351.66 (2) Å3. The scanning transmission electron microscopy (STEM) image shows stripe-like domains measuring approximately 100 nm × 200 nm (Fig. 2C).

Pressure-induced phase transition
Next, we measured the pressure-induced phase transition using SXRD (fig. S4). The as-prepared sample was compressed by pressures of 0.2 to 1.7 GPa with a hydraulic press. As the pressure increases, the λ-phase fraction decreases, while the β-phase fraction increases (Fig. 3A). The crossover pressure is 670 MPa (Fig. 3B). The sample after the pressure-induced phase transition (Fig. 3A) was heated, and the temperature evolution of the SXRD patterns was collected (fig. S5). Figure 3C shows the peaks of λ-(203), λ- and β-(20-3), and α-(023). The λ and β peaks are constant until 50°C (323 K), and then the β phase decreases and the λ phase increases at 75°C (348 K), indicating reversibility due to pressure and heating. The λ phase transforms into the α phase above 175°C (448 K) but, upon cooling, returns to the λ phase in the absence of a transition back to the β phase (fig. S6).


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Fig. 3 Pressure-induced phase transition and heat-storage process.
(A) SXRD patterns of Sc0.09Ti2.91O5 measured at room temperature and ambient pressure after compression between 0.2 and 1.7 GPa with a hydraulic press (λ = 0.420111 Å). As the pressure increases, the λ-(20-3) and λ-(203) peaks (blue) decrease and the β-(20-3) peak (orange) increases, indicating a pressure-induced phase transition. a.u., arbitrary units. (B) Pressure dependence of the phase fractions of Sc0.09Ti2.91O5 calculated from the SXRD patterns in (A). Crossover pressure (phase transition pressure) occurs at 670 MPa. (C) SXRD patterns of Sc0.09Ti2.91O5 measured between 27°C (300 K) and 300°C (573 K; λ = 0.999255 Å). The λ and β peaks are constant until 50°C (323 K; orange), and then the β phase decreases and the λ phase increases at 75°C (348 K; blue). The λ phase transforms into the α phase above 175°C (448 K; black) but is restored upon cooling. (D) DSC chart of Sc0.09Ti2.91O5 shows an endothermic reaction at 67°C (340 K). Samples are compressed at 1.7 GPa before the variable temperature SXRD and DSC chart measurements.

Heat-storage property
We measured the heat absorption mass of the sample after the pressure-induced phase transition by differential scanning calorimetry (DSC). We swept the sample compressed at 1.7 GPa with 22.7% of the λ phase and 77.3% of the β phase from 0°C (273 K) to 300°C (573 K). Heat absorption is observed with an absorption peak at 67°C (340 K) (Fig. 3D). Considering the conversion of the λ and β phases, the heat absorption mass is 75 kJ liter−1. The pressure- and heat-induced phase transitions were repeatedly observed (fig. S7).

Compared to the previous work (16), the heat-storage temperature from the pressure-produced β phase to λ phase in the present study is 67°C, which is a remarkable reduction from 197°C. This reduction is attributed to the decrease in the formation energy difference between the two phases, which reduces the crossing temperature of the two Gibbs energy curves (29). First-principles calculations support these results. The Gibbs energy versus temperature is described in Fig. 4 and in Materials and Methods.


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Fig. 4 Mechanism for the decrease in transition temperature.
Calculated thermodynamic free energy of Ti3O5 and Sc0.09Ti2.91O5 with supercells (1 × 3 × 1). Sc substitution site for the calculation is set at Ti3, and 1 of 36 Ti atoms is substituted in λ- and β-Ti3O5. Difference of the free energies of the λ and β phases represents ΔG (ΔG = Gλ − Gβ). At ΔG = 0 (black dotted line), the free energies of the λ and β phases are equal, indicating the crossover temperature (calculated phase transition temperature). Normalized temperature of 1.0 is set at Tp1 = 848 K (575°C), which is the calculated crossover temperature of λ- and β-Ti3O5 (blue dotted line, ΔGTi3O5 = 0). Red dotted line represents the crossover temperature of λ- and β-Sc0.09Ti2.91O5 (ΔGSc0.09Ti2.91O5 = 0) at Tp2 = 614 K (341°C). Crossover temperature of Sc0.09Ti2.91O5 decreases about 27.6% from the temperature of Ti3O5. This temperature decrease ratio agreed well with the experimentally obtained decrease ratio of 27.7% calculated from the phase transition temperature of 470 K (197°C) reported in λ-Ti3O5 and 340 K (67°C) measured in λ-Sc0.09Ti2.91O5 (Fig. 3D).

Thermodynamic mechanism of long-term heat storage and pressure-induced phase transition
According to previous reports on λ-Ti3O5 (15, 16), the reversible phase transition between the λ phase and β phase by pressure and heat is considered to be attributed to the energy barrier between the two phases, which originates from the elastic interaction within the material. To understand the mechanisms of long-term heat storage and the low pressure–induced heat energy release, we show the Gibbs free energy of the system (Gsys) using a thermodynamic model based on the Slichter and Drickamer mean-field model (SD model) (30) (see Materials and Methods). The Gibbs free energy in the SD model (Gsys) is described as Gsys = xΔH + γx(1 − x) + T{R[x ln x + (1 − x)ln(1 − x)] − xΔS}, with a cooperative interaction parameter (γ) between the λ phase and β phase due to the elastic interactions within the crystal. x is the ratio of λ phase, and R is the gas constant. From the result of the DSC measurement, the transition enthalpy (ΔH) is 75 kJ liter−1 (4.0 kJ mol−1), and the transition entropy (ΔS) is 0.22 kJ K−1 liter−1 (12 J K−1 mol−1). When the interaction parameters are set as a particular combination of values, the SD model calculation well reproduces the measurement data (i.e., the phase transition of β phase → λ phase occurs around 350 K). Then, the thermally produced λ phase is maintained even at low temperatures in the cooling process (Fig. 5, A and B). Thus, the reason why the λ phase is maintained for a long period is that the presence of the energy barrier between the λ and β phases prevents the transformation of the λ phase into the β phase. The prepared λ-Sc0.09Ti2.91O5 shows good stability; i.e., λ-Sc0.09Ti2.91O5 is perfectly maintained after 248 days (about 8 months) and 367 days (1 year) from the XRD measurement.


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Fig. 5 Mechanism of long-term heat storage and pressure-induced phase transition.
(A) Gibbs free energy (Gsys) versus λ phase fraction (x) curves from 420 to 200 K with a 20 K interval, calculated by the SD model. Blue spheres indicate the thermal population of the λ phase. (B) Temperature dependence of the calculated λ phase (blue) and β phase (red) fractions. (C) Gsys versus x under ambient pressures of 0.1, 400, and 700 MPa at 300 K.

Furthermore, we reproduced the pressure-induced phase transition from the λ phase to β phase. Applying pressure to the system causes the energy barrier to disappear and induces a phase transition from the λ phase to β phase (Fig. 5C). This pressure-induced phase transition is caused by the change in the γ value upon applying external pressure (see Materials and Methods). Therefore, the system is trapped as the λ phase at room temperature, but applying pressure overcomes the energy barrier, resulting in a phase transition to the β phase.

DISCUSSION
Figure 6 schematically illustrates the heat-storage system using Sc-substituted λ-Ti3O5. Cooling water for a turbine in a power plant is pumped from a river or sea. As the water passes through the turbine, the water temperature increases due to heat exchange. The energy of hot water is transferred to Sc-substituted λ-Ti3O5 in tanks. Subsequently, water with a reduced thermal energy returns to the river or the sea. This system can mitigate the rise of river or sea water temperature. Energy-stored Sc-substituted λ-Ti3O5 can release its stored thermal energy by application of pressure, allowing energy to be used on demand. For example, the stored thermal energy can be supplied to buildings or industrial plants that are close to power plants, without using electricity. Moreover, taking advantage of the characteristic of holding the latent heat energy until pressure application, if energy-stored Sc-substituted λ-Ti3O5 is transported by truck, the heat energy can be used at a distant location. As for the efficiency, the transformation energy efficiency (e) value is evaluated on the basis of the temperature dependence of the enthalpy for the λ phase and β phase obtained by first-principles calculations and DSC measurements (fig. S8). For example, when the heat release temperature is 15°C (288 K) and the temperature increase is 1 K, the efficiency is 93%. When the temperature increase is 5 K, the efficiency is 77% (table S1).


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Fig. 6 Application of Sc-substituted λ-Ti3O5 for power plants.
Schematic illustration of a heat energy recycling system using Sc-substituted λ-Ti3O5 heat-storage ceramics. Cooling water for a turbine in a power plant is pumped from a river or sea. Water becomes hot after heat exchange through the turbine. This hot water energy is stored in tanks containing Sc-substituted λ-Ti3O5 heat-storage ceramics. Water with a reduced heat energy returns to the river or the sea, mitigating the rise of the sea temperature. Energy-stored Sc-substituted λ-Ti3O5 heat-storage ceramics can supply heat energy to buildings or industrial plants by applying pressure. Furthermore, the energy-stored ceramics can be transported to distant locations by a truck.

In conclusion, we demonstrate heat-storage ceramics based on Sc-substituted λ-Ti3O5, which absorb heat from hot water. After conducting first-principles calculations, we synthesize Sc-substituted λ-Ti3O5 ceramics with a heat absorption below 100°C (373 K). This heat absorption material below 100°C can recover the thermal energy from cooling water in power plant turbines, mitigating the rise in sea water temperatures. Moreover, the heat absorption temperature can be easily controlled by changing the Sc content in λ-Ti3O5 in accordance to the target application.

These heat absorption temperature changes are attributed to the crossover temperature change of Gibbs energies. We successfully synthesize λ-Sc0.105Ti2.895O5 with a heat absorption temperature at 45°C (318 K) and λ-Sc0.108Ti2.892O5 with a heat absorption temperature at 38°C (311 K; see Materials and Methods and fig. S9). Sc-substituted λ-Ti3O5 will expand opportunities to use thermal energy as it can use thermal energy that is currently in the unused temperature range. In addition to electric power plants, other applications of the present material such as heat-storage usage to collect waste heat from factories, transportation vehicles, mobile phones, and electronic devices should be possible.

MATERIALS AND METHODS
First-principles calculations
In consideration of the valences between six-coordinated Ti3+ and Ti4+ in λ-Ti3O5 (15, 16, 31), the total electronic energies of λ-Ti3O5 substituted by trivalent or tetravalent elements from one of three Ti sites were calculated by first-principles calculations using the Vienna ab initio simulation package (VASP) code. The crystal structure of λ-Ti3O5 shown in (16) was used as calculation models for the initial structure. The lattice parameters and atomic positions were optimized at standard pressure with a cutoff energy of 500 eV and a k-mesh of 7 × 7 × 2 until the electronic iterations converged below 10−5 eV. On the basis of first-principles calculations, we focused on the synthesis of Sc-substituted Ti3O5 because Sc takes Sc3+ with a six- or eight-coordinated geometry, which hinders the higher valence states in Ti sites observed in β-Ti3O5.

Material synthesis by arc melting
Sc-substituted λ-Ti3O5 samples were synthesized by an arc-melting method with a pelletized mixture powder of Ti metal (99.9% purity), TiO2 (99.9% purity), and Sc2O3 (99.99% purity) in an Ar atmosphere at 0.05 MPa. Ti metal, TiO2, and Sc2O3 powders were mixed in a molar ratio of Ti:TiO2:Sc2O3 = 0.478:2.433:0.045. In this method, samples were melted and turned over three or four times on a copper cooling stage after solidification. These solidified samples were milled by hand before the measurements. The composition was confirmed by XRF, and the formula was determined to be Sc0.09Ti2.91O5: calcd: Ti, 62.4; O, 35.8; Sc, 1.8%; found: Ti, 62.0; O, 36.0; Sc, 2.0%, which is identical to the mixed ratio of the starting materials. Sc0.105Ti2.895O5 and Sc0.108Ti2.892O5 samples were also synthesized, and we measured the x-ray diffraction patterns (fig. S9). Moreover, Ti3O5 samples, substituted by 3 atomic % (at %) of Zr, Nb, Hf, Ta, and W, were synthesized and their x-ray diffraction patterns were measured (fig. S2). They mainly showed β-Ti3O5 patterns.

SXRD measurement
Crystal structures of Sc-substituted Ti3O5 samples were determined by Rietveld analysis of the SXRD data collected in beamline BL02B2 at SPring-8 (28). The samples were sealed in glass capillaries for the SXRD measurements. The RIETAN-FP program was used to refine the structural parameters (32).

Thermal property measurement
The heat absorption properties of Sc-substituted Ti3O5 samples were measured by DSC (Seiko Instruments, DSC 220C) at a heating-cooling rate of 10 K/min and an air gas flow of 100 ml/min. Before DSC measurements, the samples containing both the λ phase and the β phase were compressed at 1.7 GPa to transform them from the λ phase to the β phase. In addition, the thermal properties of λ-Sc0.105Ti2.895O5 and λ-Sc0.108Ti2.892O5 samples were measured (fig. S9).

First-principles calculation of Gibbs free energy
To interpret the phase transition temperature, the Gibbs free energies of Sc-substituted λ-Ti3O5 and β-Ti3O5 with supercells (1 × 3 × 1) and a k-mesh of 2 × 2 × 2 of the optimized structures were calculated using the Phonopy code in cooperation with the VASP code for the interatomic force constants calculations (33, 34). The Sc substitution ratio was set to about 3 at % (Sc0.09Ti2.91O5). That is, 1 of 36 Ti atoms was substituted by an Sc atom in the supercells. The differential energy of λ and β phase was calculated (ΔG = Gλ − Gβ). The calculated ΔG of Ti3O5 and Sc-substituted Ti3O5 are shown in Fig. 4. Ti3O5 shows ΔG = 0 at 575°C (848 K), which is the crossover temperature of the calculated free energies corresponding to the phase transition temperature (29). Sc-substituted Ti3O5 showed ΔG = 0 at 341°C (614 K). The normalized temperature in Fig. 4 was set at 575°C (848 K), which is the crossover temperature of the free energies of Ti3O5. The crossover temperature of Sc-substituted Ti3O5 decreased about 27.6% from the temperature of Ti3O5. This temperature decrease ratio agreed well with the experimentally obtained decrease ratio of 27.7% calculated from the phase transition temperature of 470 K (197°C) reported in λ-Ti3O5 (16) and 340 K (67°C) measured in λ-Sc0.09Ti2.91O5. The calculated crossover temperature was overestimated compared with the phase transition temperature, which was likely because the magnetic interaction was not taken into account during the phonon calculations. The formation energies corresponding to the Gibbs free energies (G) at 0 K were −2362.47 eV (λ-Ti3O5), −2376.44 eV (Sc-substituted λ-Ti3O5), −2372.45 eV (β-Ti3O5), and −2381.65 eV (Sc-substituted β-Ti3O5).

Thermodynamic analysis
In the SD model calculations, the γ value depends on the temperature and pressure (i.e., γ = γa + γbT + γcP). From the DSC measurement result, the ΔH value was 4.0 kJ mol−1, and the ΔS value was 11.7 J K−1 mol−1. When the parameters of γ were set as γa = 7 kJ mol−1, γb = −1.2 J K−1 mol−1, and γc = −0.37 J MPa−1 mol−1, the SD model calculations reproduced the long-term heat storage and pressure-induced phase transition, as shown in Fig. 5.

SUPPLEMENTARY MATERIALS
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/27/eaaz5264/DC1

https://creativecommons.org/licenses/by/4.0/
This is an open-access article distributed under the terms of the Creative Commons Attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Acknowledgments: Funding: This work was supported, in part, by JSPS Grant-in-Aid for Specially Promoted Research (grant 15H05697), Grant-in-Aid for Scientific Research(A) (grant 20H00369), and Collaborative Research Projects, Laboratory for Materials and Structures, Tokyo Institute of Technology. The synchrotron-radiation experiments were performed at SPring-8 with the approval of Japan Synchrotron Radiation Research Institute (JASRI; Proposal nos. 2018A1642 and 2018B1797). We are grateful to T. Takizawa (Panasonic Corporation) for setting up the first-principles calculation using VASP and Phonopy codes, H. Tamaki (Panasonic Corporation) for use of the arc-melting equipment, H. Kataoka (Panasonic Corporation) for use of a hydraulic press, and F. Shinsyu (Panasonic Corporation) for collecting the SEM and STEM images. We are grateful to F. Jia (The University of Tokyo) and H. Tokoro (University of Tsukuba) for the thermodynamic calculation, K. Imoto (The University of Tokyo) for the enthalpy calculation, K. Nakagawa (The University of Tokyo) for XRF measurement, and M. Yoshikiyo (The University of Tokyo) for the discussion of the manuscript. Author contributions: Y.N. designed and coordinated this study, contributed to all the measurements and calculations, and wrote the paper. Y.S. and M.A. conducted the SXRD measurements. S.O. designed this study and wrote the paper. All the authors discussed the results and commented on the manuscript. Competing interests: Y.N. is author on a patent filed by Panasonic Intellectual Property Management Co. Ltd. (no. PCT/JP2019/010402, published on 19 September 2019). Y.N. is author on a patent application filed by Panasonic Intellectual Property Management Co. Ltd. (no. JP 2019-124064, filed on |2 July 2019). The others declare no other competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.
Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY).
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