熱電材料中的晶格熱導(dǎo)率

沈家駿, 方騰, 傅鐵錚, 忻佳展, 趙新兵, 朱鐵軍

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熱電材料中的晶格熱導(dǎo)率

沈家駿, 方騰, 傅鐵錚, 忻佳展, 趙新兵, 朱鐵軍

(浙江大學(xué) 材料科學(xué)與工程學(xué)院, 硅材料國家重點實驗室, 杭州 310027)

隨著可再生能源及能源轉(zhuǎn)換技術(shù)的快速發(fā)展, 熱電材料在發(fā)電及制冷領(lǐng)域的應(yīng)用前景受到越來越廣泛的關(guān)注。發(fā)展具有高熱電優(yōu)值材料的重要性日益突出, 如何獲得低晶格熱導(dǎo)率是熱電材料的研究重點之一。本文闡述了熱容、聲速及弛豫時間對晶格熱導(dǎo)率的影響, 介紹了本征低熱導(dǎo)率熱電材料所具有的典型特征, 如強非諧性、弱化學(xué)鍵、本征共振散射及復(fù)雜晶胞結(jié)構(gòu)等, 并分析了通過多尺度聲子散射降低已有熱電材料晶格熱導(dǎo)率的方法, 其中包括點缺陷散射、位錯散射、晶界散射、共振散射、電聲散射等多種散射機制。此外, 總結(jié)了幾種預(yù)測材料最小晶格熱導(dǎo)率的理論模型, 對快速篩選具有低晶格熱導(dǎo)率的熱電材料具有一定的理論指導(dǎo)意義。最后, 展望了如何獲得低熱導(dǎo)率熱電材料的有效途徑。

熱電材料; 晶格熱導(dǎo)率; 熱容; 弛豫時間; 綜述

1 晶格熱導(dǎo)率的影響因素

1.1 熱容

從晶格熱導(dǎo)率的公式可以看出, 晶格熱導(dǎo)率與定容熱容V成正比, 所以降低V有利于獲得低晶格熱導(dǎo)率。杜隆-珀蒂定律指出構(gòu)成固體的各個原子在高溫時的熱容趨近于極限值3B, 其中B為玻爾茲曼常數(shù), 因此通過改變熱容來降低熱導(dǎo)率通常比較困難。然而研究人員發(fā)現(xiàn)中溫Cu2–xSe熱電材料的熱容隨著溫度升高會逐漸減小[10-11]。如圖1(a)所示, 固體的V為3B,為總原子數(shù)。而在液體中, 大部分橫向振動波無法傳遞,V減小到2~2.5B。隨著溫度升高, Cu2–xSe中Cu離子的高度離域性使材料在一定程度上表現(xiàn)出類液體的行為, 大大降低了橫向聲學(xué)波對熱容的貢獻(xiàn), 使得Cu2–xSe在高溫條件下的V接近2B。

根據(jù)德拜熱容模型, 熱導(dǎo)的貢獻(xiàn)主要來自于聲學(xué)波。這是由于光學(xué)波的波速趨近于0, 對熱導(dǎo)率的貢獻(xiàn)基本可以忽略[17]。對于多原子體系, 假設(shè)每個原胞中的原子數(shù)為, 總原胞數(shù)為, 則體系總的自由度為3。其中, 聲學(xué)支有3個, 光學(xué)支有3(-1)個[18]。根據(jù)能量均分原理可得, 聲學(xué)支貢獻(xiàn)的熱容為/, 光學(xué)支為(-1)/。因此, 原胞中原子數(shù)越多, 聲學(xué)支對總熱容的貢獻(xiàn)越小, 越有利于獲得低晶格熱導(dǎo)率。這在許多具有復(fù)雜晶胞結(jié)構(gòu)的熱電材料中得到了印證(如圖1(b)所示)。例如：Yb14MnSb11與PbTe具有相似的德拜溫度, 平均原子質(zhì)量, 熱容及格林內(nèi)森參數(shù)[19-20], 但是由于Yb14MnSb11原胞中原子數(shù)為104, 而PbTe只有2, 使得Yb14MnSb11的室溫晶格熱導(dǎo)率僅有0.6 W·m-1·K-1, 遠(yuǎn)低于PbTe的2 W·m-1·K-1[21]。

1.2 聲速

在熱導(dǎo)率公式中,g為聲子的群速度, 可以根據(jù)聲子譜中聲學(xué)支的斜率得到。在實際研究中, 為了便于測量, 通常假設(shè)群速度g與固體聲速s相等。研究表明具有弱化學(xué)鍵的化合物通常具有低聲速,例如,在-MgAgSb中由于Mg原子本身不存在d軌道, 無法與近鄰原子形成強d-d鍵, 導(dǎo)致Mg原子與Ag原子之間的共價鍵較弱, 晶格發(fā)生一定的扭曲[22]。這種弱鍵的存在使得-MgAgSb的聲速僅有1920 m/s。Ag8GeTe6等體系中也存在同樣的現(xiàn)象[23-24], 由于Ag原子與Te原子之間較弱的鍵合使得Ag8GeTe6聲速低至1000~1500 m/s。

圖1 (a) Cu2-xSe化合物的熱容與溫度關(guān)系圖[11]和(b) 室溫晶格熱導(dǎo)率與原胞中原子數(shù)關(guān)系[12-16]

此外, 通過引入重原子的方式也能降低聲速,比較典型的例子有籠式化合物及填充方鈷礦[25-28]。如圖2(a)所示, 在Ba8Ga16Ge30籠式化合物中, Ba原子占據(jù)由Ga原子及Ge原子構(gòu)成的晶格間隙中。若將Ba原子單純看作散射中心, 則理論預(yù)測的聲子弛豫時間應(yīng)為0.18 ps。然而, 中子三軸光譜分析表明加入Ba原子僅僅使縱波弛豫時間L由2.6 ps降為1.3 ps。因此, 低晶格熱導(dǎo)率不能只歸因于弛豫時間的降低, 聲速的降低也起到了重要的作用。如圖2(b)和(c)所示, 在籠式結(jié)構(gòu)中, 由于聲學(xué)聲子模與填充原子產(chǎn)生的低頻光學(xué)支之間存在“避免交叉”現(xiàn)象, 使得聲學(xué)支的頻率進(jìn)一步降低, 從而具有更低的聲速[29]。

1.3 弛豫時間

圖2 (a)Ba8Ga16Ge30晶體結(jié)構(gòu)示意圖, (b)未填充及填充籠式結(jié)構(gòu)的彈簧模型及(c)色散關(guān)系[29]

點缺陷散射是一種非常有效的降低材料熱導(dǎo)率的方法, 包括質(zhì)量波動散射與應(yīng)力場波動散射[54], 二者分別與原子間質(zhì)量差和半徑差有關(guān), 原子間質(zhì)量差及半徑差越大, 點缺陷散射越強。合金化是目前應(yīng)用最廣的增強點缺陷散射的手段, 在Bi2Te3[55-56]、Pb(Te,Se)[57]、CuInTe2[58]、Mg2(Si,Sn)[59-60]、SiGe合金[61]以及Half-Heusler(HH)合金[62-69]中都有應(yīng)用。以FeNbSb基HH合金為例, 研究表明Nb位Ta合金化可以有效降低FeNbSb的晶格熱導(dǎo)率[70]。如圖4(a)及(b)所示, 雖然Nb和Ta之間較小的原子半徑差使應(yīng)力場波動散射較弱, 但兩者較大的原子質(zhì)量差可以引入強烈的質(zhì)量波動散射, 使其最小晶格熱導(dǎo)率降至1.3 W·m–1·K–1。除了合金化之外, 空位與間隙原子也屬于一種較為特殊的點缺陷散射機制。19電子HH合金Nb0.8CoSb中存在近20%的本征Nb空位,使Nb0.8CoSb合金具有相對較低的晶格熱導(dǎo)率[71]。Cu2SnSe4等熱電材料中也存在同樣的現(xiàn)象[72]。

晶界散射及位錯散射也是非常重要的降低晶格熱導(dǎo)率的方法[73]。常用的增強晶界散射的手段有球磨[74-75]和甩帶[76-79]兩種方法, 廣泛應(yīng)用于Bi2Te3[79]、SiGe[80]以及Half-Heusler合金[81]等熱電材料中。對于位錯散射, 有報道稱在Bi0.5Sb0.15Te3中通過過量Te液相燒結(jié)的手段可以增加晶界位錯陣列[8]。另外, 通過向材料中添加第二相的方式也能增加位錯密度[82], 這一現(xiàn)象在PbTe-PbS體系中得到了印證[83]。

圖3 格林內(nèi)森常數(shù)與室溫晶格熱導(dǎo)率的關(guān)系圖[6, 22, 39-53]

圖4 (a)(Nb0.6Ta0.4)0.8Ti0.2FeSb和Nb0.8Ti0.2FeSb的晶格熱導(dǎo)率與聲子頻率的依賴關(guān)系和(b)Ta摻雜量與無序散射因子及晶格熱導(dǎo)率的關(guān)系圖[70]

此外, 位錯還可以通過自身空位的聚集產(chǎn)生。如圖5所示, 在Mg2Si1–xSb材料[84]中, Sb的高劑量合金化產(chǎn)生大量Mg空位, 使得空位濃度遠(yuǎn)高于平衡空位密度, 多余的Mg空位自發(fā)地發(fā)生聚集從而形成位錯。在Mg2Si0.5Sb0.5中, 位錯密度高達(dá)2.8×1016m?2。圖5(b)為Sn及Sb元素合金化對Mg2Si晶格熱導(dǎo)率的不同影響。由于Sn元素的加入不會增加Mg空位的濃度從而產(chǎn)生位錯, 晶格熱導(dǎo)率的降低主要來自點缺陷散射的作用。而Sb合金化不僅能增強點缺陷散射, 而且能增強位錯散射, 因此具有更低的晶格熱導(dǎo)率。此外, 在NaEu0.03Pb0.97–yTe體系[7]中也觀察到類似的現(xiàn)象。研究表明隨著Na摻雜量的增加, 體系中的主要微觀缺陷由點缺陷逐步過渡到位錯及納米顆粒。位錯散射使PbTe的晶格熱導(dǎo)率下降到0.4 W·m-1·K-1以下。

圖5 (a) Mg2Si0.5Sb0.5中位錯的IFFT圖及相應(yīng)的應(yīng)力掃描圖, (b) Mg2Si1-xSbx及Mg2Si1–zSnz的室溫晶格熱導(dǎo)率對比圖[84]

除此之外, 共振散射一般出現(xiàn)在具有特殊晶體結(jié)構(gòu)的熱電材料中, 如籠式化合物及方鈷礦等[29, 85-86]。通過加入填充原子, 可以引入特定頻率的共振譜, 從而降低材料熱導(dǎo)率。在S0.5Co4Sb10.5Te1.5中S作為填充原子, 可以在聲子譜中引入一段頻率較低的光學(xué)支, 與聲學(xué)支發(fā)生光聲耦合現(xiàn)象, 增強共振散射, 最終使得CoSb3材料獲得極低的晶格熱導(dǎo)率[87]。另外, 最近的研究表明一些具有拓?fù)浣^緣性的熱電材料中也存在共振散射。如圖6所示, 在BiSe材料中額外的Bi2原子層同樣可以引起局域共振效應(yīng), 強烈的光聲耦合顯著降低了BiSe的晶格熱導(dǎo)率, 使其室溫晶格熱導(dǎo)率僅為0.6 W×m-1×K-1[88]。

相比于其他類型的散射機制, 電聲散射的研究相對較少。然而, 對于具有較大載流子有效質(zhì)量的體系, 通常需要較高的載流子濃度使其電性能達(dá)到最佳[89-92]。因此, 在這些體系中需要考慮電聲散射對晶格熱導(dǎo)率的影響。如圖7所示, 在多晶硅中摻入P使其晶格熱導(dǎo)率顯著降低, 0.1at%的P摻雜量就可以使多晶硅室溫時的晶格熱導(dǎo)率降低60%。但由于P與Si在元素周期表中的位置接近, 具有相似的質(zhì)量和半徑, 因此點缺陷散射不足以解釋其晶格熱導(dǎo)率的大幅度降低, 必然存在其他散射機制的作用。研究表明P元素的摻雜作用可以引起多晶硅中載流子濃度的增加, 使電聲相互作用顯著增強。當(dāng)摻入6at%的P時, 電聲散射對晶格熱導(dǎo)率的降低作用占所有散射機制的36%, 接近晶界散射的作用[93]。

圖6 BiSe晶體結(jié)構(gòu)示意圖(a)和Bi2Se3及BiSe的晶格熱導(dǎo)率對比圖(b)[88]

圖7 電聲散射示意圖(a)和硅樣品晶格熱導(dǎo)率的實驗值與Callaway模型計算值的對比圖(b)[93]

2 最小晶格熱導(dǎo)率

圖8 (a)擴散子模型及聲子模型的差別示意圖和(b)Cahill模型及擴散子模型預(yù)測的最小晶格熱導(dǎo)率對比圖

雖然最小晶格熱導(dǎo)率的計算模型有所不同, 但不同模型預(yù)測出的結(jié)果大都比較接近。這主要由兩方面原因造成的：首先, 大多數(shù)材料達(dá)到最小晶格熱導(dǎo)率時, 溫度均遠(yuǎn)遠(yuǎn)高于德拜溫度, 此時, 熱容已經(jīng)趨近于極限值3; 其次, 所有模型都假設(shè)對熱導(dǎo)率的貢獻(xiàn)全部由平均自由程等于原子間距尺度的聲子貢獻(xiàn), 這一假設(shè)使得晶體中尺度大于原子間距的缺陷, 如位錯、第二相等不會對最小晶格熱導(dǎo)率的預(yù)測產(chǎn)生影響。

圖9 獲得低晶格熱導(dǎo)率的幾種途徑

3 結(jié)束語

晶格熱導(dǎo)率是一個可以相對獨立調(diào)控的影響材料熱電性能的參數(shù)。本文分別闡述了熱容、聲速及弛豫時間等三個物理量對晶格熱導(dǎo)率的影響, 并介紹了幾種不同類型的預(yù)測材料最小晶格熱導(dǎo)率的理論模型, 對降低材料的晶格熱導(dǎo)率具有重要的指導(dǎo)意義。那么如何從實驗上獲得較低的晶格熱導(dǎo)率呢? 主要可以從以下兩方面考慮：

第一、尋找并制備具有本征低熱導(dǎo)率的熱電材料。具有本征低熱導(dǎo)率的熱電材料一般具有以下幾個特征：1. 強非諧性。非諧性強弱主要與化學(xué)鍵及原子平衡位置的對稱性有關(guān)。原子在振動過程中, 若其對稱中心發(fā)生偏移越大, 則非對稱性越強。具有孤對電子的材料往往由于電子云分布不均勻, 晶體結(jié)構(gòu)會發(fā)生一定的變形, 非對稱性顯著增強, 有利于獲得強非諧性; 2. 弱化學(xué)鍵。化學(xué)鍵弱的材料具有較低的聲速, 原子在其平衡位置附近具有更大的活動空間, 電子云分布更為彌散。在聲子譜中, 弱化學(xué)鍵往往對應(yīng)一些低頻段的聲子模, 更容易與聲學(xué)支發(fā)生耦合作用, 從而進(jìn)一步降低聲學(xué)支對熱導(dǎo)的貢獻(xiàn); 3. 復(fù)雜的晶胞結(jié)構(gòu)。一方面可以降低聲學(xué)支對總熱容的貢獻(xiàn)比重, 另一方面可以降低聲學(xué)支聲子的群速。

第二、通過多尺度聲子散射降低已有熱電材料的熱導(dǎo)率。由于在德拜溫度以上, 聲子頻率分布在0到德拜頻率之間, 同時抑制所有波長段的聲子模能夠有效降低晶格熱導(dǎo)率, 如點缺陷散射、位錯散射、晶界散射、共振散射和電聲散射等(如圖9所示)。

近年來有研究表明, 弱拓?fù)浣^緣體能實現(xiàn)極低的晶格熱導(dǎo)率[101-103], 并且其特殊的表面?zhèn)鲗?dǎo)特性有望沖破半導(dǎo)體基熱電材料的禁錮, 實現(xiàn)電性能及熱性能的真正解耦。然而, 拓?fù)浣^緣體的晶格動力學(xué)、聲子輸運等機制仍需要人們進(jìn)一步研究與探索[104-105]?？偟膩碚f, 不論是研究發(fā)現(xiàn)新型的具有本征低晶格熱導(dǎo)率的熱電材料, 還是對現(xiàn)有的熱電材料熱導(dǎo)率進(jìn)一步的降低, 通過多種手段的并用, 一定會對未來的熱電材料領(lǐng)域的可持續(xù)發(fā)展產(chǎn)生實質(zhì)的積極促進(jìn)作用。

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Lattice Thermal Conductivity in Thermoelectric Materials

SHEN Jia-Jun, FANG Teng, FU Tie-Zheng, XIN Jia-Zhan, ZHAO Xin-Bing, ZHU Tie-Jun

(State Key Laboratory of Silicon Materials, School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China)

With rapid development of sustainable energies and energy conversion technologies, application prospect of thermoelectric (TE) materials in power generation and cooling has received increasing attention. The requirement of improving TE materials with high figure of merit becomes much more important. How to obtain the low lattice thermal conductivity is one of the main concerns in TE materials. In this review, the influences of specific heat, phonon group velocity and relaxation time on the lattice thermal conductivity are discussed, respectively. Several typical features of TE materials with intrinsic low lattice thermal conductivity are introduced, such as strong anharmonicity, weak chemical bonds and complex primitive cells. Introducing multiscale phonon scatterings to reduce the lattice thermal conductivity of known TE materials is also presented and discussed, including but not limited to point defect scattering, dislocation scattering, boundary scattering, resonance scattering and electron-phonon scattering. In addition, some theoretical models of the minimum lattice thermal conductivity are analyzed, which has certain theoretical significance for rapid screening of TE materials with low lattice thermal conductivity. Finally, the efficient ways to obtain the low lattice thermal conductivity for TE property optimization are proposed.

thermoelectric materials; lattice thermal conductivity; specific heat; relaxation time; review

TB34

A

1000-324X(2019)03-0260-09

10.15541/jim20180320

2018-07-16;

2018-09-03

國家自然科學(xué)基金(51725102, 51761135127, 11574267) National Natural Science Foundation of China (51725102, 51761135127, 11574267)

沈家駿(1992-), 男, 博士研究生. E-mail: 11626058@zju.edu.cn

朱鐵軍, 教授. E-mail: zhutj@zju.edu.cn