康端 巫翔

1)(北京大學(xué)地球與空間科學(xué)學(xué)院,造山帶與地殼演化教育部重點(diǎn)實(shí)驗(yàn)室,北京 100871)

2)(中國(guó)地質(zhì)大學(xué)(武漢),地質(zhì)過(guò)程與礦產(chǎn)資源國(guó)家重點(diǎn)實(shí)驗(yàn)室,武漢 430074)

InOOH壓致氫鍵對(duì)稱(chēng)化及其彈性性質(zhì)?

康端1)巫翔2)?

1)(北京大學(xué)地球與空間科學(xué)學(xué)院,造山帶與地殼演化教育部重點(diǎn)實(shí)驗(yàn)室,北京 100871)

2)(中國(guó)地質(zhì)大學(xué)(武漢),地質(zhì)過(guò)程與礦產(chǎn)資源國(guó)家重點(diǎn)實(shí)驗(yàn)室,武漢 430074)

InOOH,氫鍵對(duì)稱(chēng)化,彈性性質(zhì)

1 引 言

氫鍵廣泛存在于DNA、水、納米材料、地球深部含水物質(zhì)中,對(duì)生命、科技、地球的演化等都具有至關(guān)重要的作用,在生物、物理、材料、地學(xué)等領(lǐng)域得到了廣泛的研究.氫鍵在高壓或高溫下易發(fā)生畸變,且高壓對(duì)氫鍵的影響十分顯著.當(dāng)壓力施加于含有氫鍵的物質(zhì)上時(shí),氫鍵的變化會(huì)使物質(zhì)表現(xiàn)出一些新的性質(zhì),甚至引起相變的發(fā)生.高壓下氫鍵對(duì)稱(chēng)化轉(zhuǎn)變是一種典型的行為,是指與H原子最鄰近的兩個(gè)O原子之間的勢(shì)能面從雙勢(shì)阱勢(shì)能面轉(zhuǎn)變?yōu)閱蝿?shì)阱勢(shì)能面的過(guò)程,即H原子從偏離兩個(gè)O原子中間的位置變?yōu)閮蓚€(gè)O原子正中間的位置.自從Holzapfel[1]在理論上預(yù)測(cè)出氫鍵對(duì)稱(chēng)化之后,壓致氫鍵對(duì)稱(chēng)化行為就在冰、甲酸、MOOH(M=In,Al,Ga,Fe,Cr)等[2?7]物質(zhì)中得到了廣泛的實(shí)驗(yàn)和理論研究.例如,實(shí)驗(yàn)研究結(jié)果表明冰VII相會(huì)在約62 GPa壓力下由于氫鍵的對(duì)稱(chēng)化變?yōu)楸鵛相[8].

InOOH,δ-AlOOH,β-GaOOH,ε-FeOOH,β-CrOOH羥氧化物具有相似構(gòu)型[2,4,9?11],本文統(tǒng)一稱(chēng)之為MOOH(M=In,Al,Ga,Fe,Cr).MOOH中O原子的排列具有畸變的金紅石型結(jié)構(gòu),O原子近乎完美地平行于(101)面呈緊密排列,共邊的MO6八面體沿(001)面呈鏈狀分布,這些鏈之間通過(guò)O原子共角頂相連,如此便形成了平行于(101)面的八面體層.大量的實(shí)驗(yàn)和理論研究結(jié)果表明MOOH會(huì)在高壓下發(fā)生氫鍵對(duì)稱(chēng)化,且氫鍵的對(duì)稱(chēng)化對(duì)MOOH的性質(zhì)有重要影響.實(shí)驗(yàn)結(jié)果表明β-GaOOH,InOOH,β-CrOOD及δ-AlOOH的軸比率對(duì)壓力的斜率正負(fù)性在具有非對(duì)稱(chēng)氫鍵的相和具有對(duì)稱(chēng)氫鍵的相中不同,表明物質(zhì)在不同方向上的可壓縮性相對(duì)大小在氫鍵非對(duì)稱(chēng)相和氫鍵對(duì)稱(chēng)相中有差異[2,12,13].實(shí)驗(yàn)和第一性原理計(jì)算結(jié)果表明氫鍵對(duì)稱(chēng)化使δ-AlOOH的體積模量、體波速以及縱波波速等參數(shù)異常增大[14,15].另外,實(shí)驗(yàn)和理論研究表明ε-FeOOH中的氫鍵對(duì)稱(chēng)化還對(duì)Fe的自旋轉(zhuǎn)變有促進(jìn)作用[4].

InOOH為帶隙為3.6 eV的n型半導(dǎo)體材料,是一種能在紫外光下有效分解有機(jī)污染物的光催化劑[16?18],吸引了大量學(xué)者對(duì)InOOH合成方法進(jìn)行實(shí)驗(yàn)研究[16,19,20].文獻(xiàn)[16]研究結(jié)果表明可利用溶劑熱合成法加工In(NO3)3和乙二胺合成InOOH.有研究人員曾通過(guò)實(shí)驗(yàn)和理論計(jì)算研究了畸變金紅石型InOOH相變?yōu)辄S鐵礦型InOOH的溫壓條件,第一性原理的熱力學(xué)計(jì)算結(jié)果表明畸變金紅石型InOOH在0 K,15 GPa時(shí)會(huì)相變?yōu)闅滏I非對(duì)稱(chēng)的黃鐵礦型InOOH[3],但X射線衍射(XRD)測(cè)試結(jié)果表明常溫下畸變金紅石型InOOH加壓至35 GPa時(shí)都未相變?yōu)辄S鐵礦型InOOH[2],當(dāng)加溫至1300 K時(shí)需在14 GPa的壓力下才能轉(zhuǎn)變?yōu)辄S鐵礦型InOOH[21].

研究InOOH彈性性質(zhì)在高壓下的變化及由高壓導(dǎo)致的氫鍵對(duì)稱(chēng)化對(duì)InOOH彈性性質(zhì)的影響,對(duì)探索InOOH在材料領(lǐng)域的應(yīng)用及預(yù)測(cè)氫鍵對(duì)稱(chēng)化對(duì)其他畸變金紅石型MOOH性質(zhì)的影響具有重要的作用,但目前關(guān)于InOOH在高壓下的彈性性質(zhì),及氫鍵對(duì)稱(chēng)化對(duì)InOOH彈性性質(zhì)影響的詳細(xì)研究鮮有報(bào)道.第一性原理計(jì)算是研究晶體結(jié)構(gòu)、力學(xué)性質(zhì)、熱學(xué)性質(zhì)的有效方法,應(yīng)用越來(lái)越廣泛[22?28].本文基于第一性原理方法開(kāi)展了對(duì)高壓下InOOH的彈性性質(zhì)、氫鍵對(duì)稱(chēng)化及氫鍵對(duì)稱(chēng)化對(duì)彈性性質(zhì)影響的研究,計(jì)算結(jié)果表明氫鍵對(duì)稱(chēng)化的壓力約為18 GPa,得到了InOOH在0—40 GPa范圍內(nèi)的彈性性質(zhì),以及氫鍵對(duì)稱(chēng)化對(duì)彈性性質(zhì)的影響.

2 計(jì)算模型和方法

常溫常壓下InOOH為正交結(jié)構(gòu),空間群為P21nm.晶胞參數(shù)為a=5.26 ? (1 ? =0.1 nm),b=4.56 ?,c=3.27 ?,O—H鍵長(zhǎng)為1.08 ?,O···H鍵長(zhǎng)為1.46 ?,氫鍵H—O···H呈非對(duì)稱(chēng)構(gòu)型(圖1(a))[29].參照δ-AlOOH,ε-FeOOH等相似物的高壓行為,推測(cè)InOOH中的氫鍵在高壓下呈對(duì)稱(chēng)構(gòu)型,對(duì)應(yīng)的空間群為Pnnm(圖1(b)).以InOOH單胞為研究對(duì)象,每個(gè)單胞中含有2個(gè)In原子,4個(gè)O原子和2個(gè)H原子.為了表述方便,將具有非對(duì)稱(chēng)氫鍵的MOOH晶體標(biāo)記為A-MOOH,將具有對(duì)稱(chēng)氫鍵的MOOH晶體標(biāo)記為S-MOOH.

第一性原理計(jì)算采用VASP(Viennaab-initioSimulation Package)軟件包完成[30,31].贗勢(shì)采用投影綴加平面波(projected augmented wavefunction,PAW)描述.電子和電子之間的交換關(guān)聯(lián)采用廣義梯度近似(generalized gradient approximation,GGA)下的Perdew-Burke-Ernzerhof(PBE)泛函進(jìn)行處理[32].平面波的截?cái)嗄芰繛?50 eV.布里淵區(qū)求和采用6×6×10的Monkhorst-Pack型K點(diǎn)網(wǎng)格.更大的平面波截?cái)嗄芎蚄空間采樣密度對(duì)每個(gè)原子總能的影響不超過(guò)0.001 eV.電子自洽的收斂條件為系統(tǒng)總能量變化小于1×10?7eV,結(jié)構(gòu)弛豫的收斂標(biāo)準(zhǔn)為每個(gè)離子上的最大作用力小于0.001 eV/?.利用應(yīng)力-應(yīng)變法,通過(guò)對(duì)晶格施加6次應(yīng)變且允許離子弛豫計(jì)算得到彈性常數(shù)[33,34].

圖1 (網(wǎng)刊彩色)(a)具有非對(duì)稱(chēng)氫鍵的A-InOOH晶體結(jié)構(gòu),空間群為P21nm;(b)具有對(duì)稱(chēng)氫鍵的S-InOOH晶體結(jié)構(gòu),空間群為PnnmFig.1. (color online)(a)Crystal structure of AInOOH with asymmetric hydrogen bond,space group P21nm;(b)crystal structure of S-InOOH with symmetric hydrogen bond,space group Pnnm.

3 計(jì)算結(jié)果

基于GGA-PBE交換關(guān)聯(lián)泛函計(jì)算得到InOOH,在0 GPa時(shí)的晶胞參數(shù)為a=5.385 ?,b=4.662 ?,c=3.352 ?, 與文獻(xiàn)[3]采用GGAPW91交換關(guān)聯(lián)泛函得到的晶胞參數(shù)(a=5.381 ?,b=4.649 ?,c=3.349 ?)基本一致,但稍大于實(shí)驗(yàn)得到的晶胞參數(shù)(a=5.26 ?,b=4.56 ?,c=3.27 ?).這是GGA泛函會(huì)低估晶體的結(jié)合能,因而高估晶體的晶胞參數(shù)導(dǎo)致的.

0 GPa時(shí)InOOH的O···H鍵 長(zhǎng) 為1.519 ?,O—H鍵長(zhǎng)為1.046 ?.隨著壓力的增加,O···H鍵縮短,O—H鍵變長(zhǎng)(圖2(a)).18 GPa時(shí)O···H鍵長(zhǎng)為1.203 ?,O—H鍵長(zhǎng)為1.186 ?,兩者相差0.017 ?,氫鍵O—H···O基本對(duì)稱(chēng). 文獻(xiàn)[3]第一性原理計(jì)算結(jié)果表明InOOH中的氫鍵約在25 GPa時(shí)對(duì)稱(chēng),本文計(jì)算得到的氫鍵對(duì)稱(chēng)化壓力與文獻(xiàn)[3]結(jié)果基本一致.a/c對(duì)壓力的斜率在0—40 GPa內(nèi)為正且變化不大(圖2(b)).b/c對(duì)壓力的斜率在18 GPa之前為負(fù)值,在18 GPa之后為正值(圖2(b)),這表明在18 GPa時(shí)InOOHb軸和c軸壓縮性的相對(duì)大小發(fā)生了變化.實(shí)驗(yàn)結(jié)果表明InOOH中的a/c對(duì)壓力斜率的正負(fù)性在0—35 GPa內(nèi)沒(méi)有發(fā)生變化,b/c對(duì)壓力的斜率約在15 GPa時(shí)由負(fù)值變?yōu)檎?本文計(jì)算結(jié)果與實(shí)驗(yàn)結(jié)果基本一致,但b/c對(duì)壓力斜率正負(fù)性發(fā)生變化的壓力稍小于XRD實(shí)驗(yàn)得到的壓力(15 GPa)[2],這是由于未考慮熱效應(yīng)和核量子效應(yīng)導(dǎo)致的.

圖2 (網(wǎng)刊彩色)(a)InOOH中O—H鍵和O···H鍵鍵長(zhǎng)隨壓力的變化;(b)InOOH軸比率a/c和b/c隨壓力的變化Fig.2.(color online)(a)Pressure dependence of O—H and O···H bond lengths in InOOH;(b)pressure dependence of axial ratios a/c and b/c in InOOH.

A-InOOH和S-InOOH都屬于正交晶系,有9個(gè)獨(dú)立的彈性常數(shù):壓縮彈性常數(shù)C11,C22,C33,剪切彈性常數(shù)C44,C55,C66和非對(duì)角彈性常數(shù)C12,C13,C23.由計(jì)算結(jié)果可知,InOOH在0—40 GPa內(nèi)的彈性常數(shù)均滿足Born穩(wěn)定性判據(jù)[35],說(shuō)明0 K時(shí)InOOH在0—40 GPa內(nèi)力學(xué)性能穩(wěn)定.

InOOH的壓縮彈性常數(shù)和非對(duì)角彈性常數(shù)在0—40 GPa內(nèi)都隨著壓力的增加而增大,在15 GPa之前對(duì)壓力的斜率與在20 GPa之后對(duì)壓力的斜率較為接近,但在15—20 GPa之間對(duì)壓力的斜率顯著大于15 GPa之前和20 GPa之后的斜率(圖3(a)).這表明壓縮彈性常數(shù)和非對(duì)角彈性常數(shù)在15—20 GPa內(nèi)發(fā)生了突變.C66隨著壓力的增加而增加,其對(duì)壓力的斜率在0—40 GPa內(nèi)變化不大.C55在15 GPa之前隨著壓力的增加稍有增大,在20 GPa之后隨著壓力的增加稍有減小,但在0—40 GPa內(nèi)的變化幅度不大.C44在0—40 GPa內(nèi)基本都隨著壓力的增加而減小,且在20 GPa之后的減小速率比在15 GPa之前大.C44代表晶體抵抗剪切變形的能力,C44隨壓力變小表明壓力增加時(shí)InOOH抵抗剪切變形的能力下降.

根據(jù)Voigt-Reuss-Hill近似方法[36]可以計(jì)算晶體的體積模量B和剪切模量G,進(jìn)而可以算出楊氏模量E和泊松比ν[37].壓力小于15 GPa或大于20 GPa時(shí),InOOH的體積模量B隨壓力的增加幾乎都呈線性增大(圖3(b)).這是由于隨著壓力的增加,晶胞體積縮小,原子間的相互排斥力增大,InOOH更加難以被壓縮.壓縮彈性常數(shù)和非對(duì)角彈性常數(shù)在15—20 GPa內(nèi)的異常增加,引起了體積模量在15—20 GPa內(nèi)的突變.15 GPa前InOOH的剪切模量隨著壓力的增加而增加,但20 GPa后剪切模量隨著壓力的增加而減小.這表明15 GPa前InOOH隨著壓力的增加抵抗剪切變形的能力增強(qiáng),20 GPa后InOOH隨著壓力的增加抵抗剪切變形的能力變?nèi)?

根據(jù)體積模量B和剪切模量G,可通過(guò)公式計(jì)算得到縱波波速VP和橫波波速VS,其中ρ為密度.InOOH的縱波波速VP隨著壓力的增加而增加,且在15—20 GPa之間異常增加;橫波波速VS在15 GPa之前隨著壓力的增加緩慢減小,在20 GPa之后隨著壓力的增加而減小,且減小的速率顯著大于15 GPa之前的速率(圖3(c)).雖然InOOH的剪切模量在15 GPa前隨著壓力的增加而增加,但由于剪切模量隨壓力增加的速率很小,小于密度隨壓力的增加速率,導(dǎo)致G/ρ隨壓力的增加而減小,因此剪切波速在15 GPa之前隨著壓力的增加而減小.

圖3 (網(wǎng)刊彩色)InOOH在不同壓力下的(a)彈性常數(shù),(b)體積模量B和剪切模量G,(c)縱波波速VP和橫波波速VSFig.3.(color online)Pressure dependence of(a)elastic constants,(b)bulk modulus B and shear modulus G,(c)longitudinal wave velocity VPand shear wave velocity VSin InOOH.

圖4 InOOH在不同壓力下的B/G和泊松比νFig.4.B/G and Poisson ratio ν of InOOH under different pressures.

對(duì)于固體物質(zhì),如果其泊松比ν大于0.26,則表現(xiàn)為韌性;反之則表現(xiàn)為脆性.根據(jù)Pugh準(zhǔn)則[38],B/G＞1.75時(shí)物質(zhì)表現(xiàn)為韌性;B/G＜1.75時(shí)物質(zhì)表現(xiàn)為脆性.由圖4可見(jiàn),InOOH在0—40 GPa內(nèi)的泊松比ν大于0.26,B/G值大于1.75,表明InOOH在0—40 GPa內(nèi)都表現(xiàn)為韌性.隨著壓力的增加,泊松比ν和B/G值增大,InOOH的韌性增強(qiáng),且在15—20 GPa內(nèi)發(fā)生了韌性的異常增加.

楊氏模量E在15 GPa前隨著壓力的增加而增加,在20 GPa后隨著壓力的增加而減小,但在0—40 GPa內(nèi)變化幅度不大.楊氏模量E在各個(gè)方向上的三維表示可以直觀地用于分析晶體的彈性各向異性.對(duì)于具有正交結(jié)構(gòu)的晶體,楊氏模量在任意方向的值可根據(jù)如下公式計(jì)算[39]:

式中Sij為彈性柔順常數(shù),l1,l2,l3為方向余弦.圖5為不同壓力下InOOH在各個(gè)方向上的楊氏模量.對(duì)于各向同性晶體,楊氏模量表面為完美的球形.在0 GPa時(shí),InOOH的楊氏模量表面不為球形,有沿著 [001],[00ˉ1],[110],[ˉ110],[ˉ1ˉ10]和 [1ˉ10]6 個(gè)方向的突起,這表明InOOH呈現(xiàn)各向異性.[100],[010]和[001]方向的楊氏模量在0—15 GPa內(nèi)隨著壓力的增加而增大,但在20—40 GPa內(nèi)隨著壓力的增加而減小,其中[001]方向的楊氏模量隨壓力的增加變化最小.[110],[ˉ110],[ˉ1ˉ10]及 [1ˉ10]方向的楊氏模量在0—40 GPa內(nèi)都隨著壓力的增加而增大.由圖5可見(jiàn)楊氏模量表面偏離球形的程度越來(lái)越大,表明InOOH的各向異性程度越來(lái)越深.

圖5 (網(wǎng)刊彩色)InOOH在不同壓力下的楊氏模量三維立體圖Fig.5.(color online)The variation of 3D Young’s modulus surface with pressure.

4 討 論

以上計(jì)算結(jié)果表明InOOH的氫鍵約在18 GPa時(shí)發(fā)生了對(duì)稱(chēng)化,且軸比率b/c對(duì)壓力的導(dǎo)數(shù)、彈性性質(zhì)、波速等在15—20 GPa間發(fā)生了突變,兩種壓力呈現(xiàn)出很好的一致性.表明InOOH中氫鍵的對(duì)稱(chēng)化導(dǎo)致了15—20 GPa間部分性質(zhì)的突變.

本文和前人的研究結(jié)果表明,具有相似晶體結(jié)構(gòu)的InOOH,δ-AlOOH和β-GaOOH中的氫鍵對(duì)稱(chēng)化均導(dǎo)致b/c對(duì)壓力的導(dǎo)數(shù)由負(fù)變?yōu)檎齕2,13],這說(shuō)明氫鍵對(duì)稱(chēng)化對(duì)MOOH的b/c對(duì)壓力的斜率有重要影響.MOOH中的氫鍵O—H···O 位于ab平面內(nèi),且在b軸上的投影最大,因此氫鍵強(qiáng)度的變化對(duì)b軸的影響最為顯著.對(duì)稱(chēng)氫鍵的強(qiáng)度比非對(duì)稱(chēng)氫鍵大,在氫鍵由非對(duì)稱(chēng)構(gòu)型變?yōu)閷?duì)稱(chēng)構(gòu)型時(shí)b軸的可壓縮性降低,從而導(dǎo)致A-MOOH晶體中b軸比c軸易壓縮,但在S-MOOH晶體中b軸比c軸難壓縮的現(xiàn)象.在A-InOOH中a軸本身就難以壓縮,表現(xiàn)為a/c隨著壓力的增加而增大(圖2(b)),且氫鍵對(duì)稱(chēng)化對(duì)a軸可壓縮性的影響較小,因此氫鍵對(duì)稱(chēng)化發(fā)生時(shí)a/c對(duì)壓力的斜率變化不大.

本文InOOH和文獻(xiàn)[3]中δ-AlOOH的第一性原理計(jì)算結(jié)果表明氫鍵的對(duì)稱(chēng)化會(huì)導(dǎo)致InOOH和δ-AlOOH壓縮和非對(duì)角彈性常數(shù)的異常增加,但不會(huì)引起剪切彈性常數(shù)的異常增加[15].據(jù)此可推測(cè)MOOH中氫鍵的對(duì)稱(chēng)化對(duì)彈性常數(shù)的影響都與此類(lèi)似.由于MOOH中的氫鍵對(duì)稱(chēng)化對(duì)b,a,c軸的影響依次減小,因此引起的C22,C11,C33增加幅度依次減小,這在InOOH及δ-AlOOH[15]的計(jì)算結(jié)果中得到了證實(shí).Phase D(MgSi2O6H2)是一種穩(wěn)定壓力最高的致密含水含鎂硅酸鹽[40],能穩(wěn)定至40 GPa.由于Phase D中的氫鍵平行于c軸,因此當(dāng)Phase D中的氫鍵發(fā)生對(duì)稱(chēng)化時(shí),C33的增加幅度最大[41].由此可知,在含有氫鍵的物質(zhì)中,氫鍵對(duì)稱(chēng)化對(duì)各個(gè)方向上壓縮彈性常數(shù)的影響取決于氫鍵在各軸上的投影,投影越大,影響越大.

對(duì)15 GPa前A-InOOH的體積模量BA與壓力P采用線性擬合得到的關(guān)系為BA(GPa)≈4.126×P(GPa)+126(GPa);20 GPa后S-InOOH的BS與P的關(guān)系為BS(GPa)≈3.101×P(GPa)+177(GPa).對(duì)比可知InOOH的BS隨壓力的變化速率比BA的小.這與δ-AlOOH的計(jì)算結(jié)果一致[5],可推測(cè)MOOH的體積模量BS隨壓力的變化速率都小于BA的變化速率.A-InOOH與SInOOH體積模量之間的差值為BS?BA(GPa)≈?1.025×P(GPa)+51(GPa),20 GPa之后InOOH只能以S-InOOH的形式存在,因此本文僅討論20 GPa之前BS與BA的差異.0 GPa時(shí)BS約比BA大51 GPa,約為BA的40%;BS與BA之間的差異隨著壓力的增加而減小,15 GPa時(shí)BS比BA大36 GPa,約為BA的19%.以上數(shù)據(jù)表明氫鍵對(duì)稱(chēng)化是圖3(b)中InOOH的體積模量在15—20 GPa內(nèi)發(fā)生異常增加的原因.XRD實(shí)驗(yàn)結(jié)果表明當(dāng)體積模量對(duì)壓力的一階導(dǎo)數(shù)B0′固定為4時(shí)A-InOOH的零壓體積模量為159 GPa[2],比S-InOOH的零壓體積模量(192 GPa)約小33 GPa,約為A-InOOH零壓體積模量的21%.因此由本文的第一性原理計(jì)算及XRD實(shí)驗(yàn)結(jié)果可知,InOOH中氫鍵的對(duì)稱(chēng)化會(huì)導(dǎo)致體積模量20%—40%的異常增加.

第一性原理計(jì)算結(jié)果表明S-δ-AlOOH的零壓體積模量為207 GPa,比A-δ-AlOOH的零壓體積模量(153 GPa)大54 GPa,增加量約為35%[15].實(shí)驗(yàn)結(jié)果表明氫鍵對(duì)稱(chēng)化導(dǎo)致δ-AlOOH的零壓體積模量由183 GPa變?yōu)?26 GPa,約增加23%[42].第一性原理計(jì)算結(jié)果顯示氫鍵的對(duì)稱(chēng)化導(dǎo)致Phase D的零壓體積模量由159 GPa變?yōu)?91 GPa,約增加20%[41].InOOH,δ-AlOOH和Phase D的研究結(jié)果均表明氫鍵對(duì)稱(chēng)化會(huì)引起物質(zhì)體積模量20%—40%的增加,這是由氫鍵對(duì)稱(chēng)化時(shí)壓縮彈性常數(shù)的異常增加導(dǎo)致的.氫鍵的對(duì)稱(chēng)化不會(huì)導(dǎo)致剪切模量的異常增加.

實(shí)驗(yàn)和第一性原理計(jì)算結(jié)果均表明InOOH的體積模量小于δ-AlOOH的體積模量.In3+的半徑(0.81 ?)顯著大于Al3+的半徑(0.50 ?),In3+與O2?之間的相互作用弱于Al3+與O2?之間的相互作用.In—O鍵的強(qiáng)度比Al—O鍵弱,In—O鍵的鍵能為(346±30)kJ/mol,Al—O鍵的鍵能為(502±11)kJ/mol[43],這是InOOH的體積模量小于δ-AlOOH的體積模量的原因之一.δ-AlOOH中Al—O鍵的平均鍵長(zhǎng)為1.954 ?,AlO6八面體體積為9.850 ?3[15];InOOH中In—O鍵的平均鍵長(zhǎng)為2.230 ?,InO6八面體體積為14.622 ?3,比δ-AlOOH中AlO6的體積大4.772 ?3.每個(gè)MOOH單胞中含有2個(gè)MO6八面體,因此InOOH和δ-AlOOH晶體中金屬八面體的體積差異為9.544 ?3.δ-AlOOH的晶胞參數(shù)為a=4.788 ?,b=4.275 ?,c=2.877 ?,體積為58.888 ?3[15];InOOH的晶胞參數(shù)為a=5.385 ?,b=4.662 ?,c=3.352 ?,體積為84.151 ?3,比δ-AlOOH的體積大25.263 ?3,遠(yuǎn)大于MO6八面體的體積差異(9.544 ?3).這表明與δ-AlOOH相比,InOOH晶體中未被MO6八面體占據(jù)的空隙更大,使得InOOH更容易被壓縮,這也是導(dǎo)致InOOH體積模量比δ-AlOOH小的因素之一.

5 結(jié) 論

基于第一性原理研究了畸變金紅石型InOOH的氫鍵在高壓下的對(duì)稱(chēng)化行為,以及壓力和氫鍵對(duì)稱(chēng)化對(duì)InOOH彈性性質(zhì)的影響.計(jì)算結(jié)果表明InOOH的氫鍵約在18 GPa處對(duì)稱(chēng),氫鍵的對(duì)稱(chēng)化使b/c對(duì)壓力的斜率由負(fù)值變?yōu)檎?壓縮彈性常數(shù)和非對(duì)角彈性常數(shù)、體積模量以及縱波波速隨著壓力的增加而增加,且伴隨著氫鍵的對(duì)稱(chēng)化異常增加,例如伴隨著氫鍵對(duì)稱(chēng)化的發(fā)生體積模量發(fā)生了20%—40%的異常增加.剪切模量和楊氏模量在A-InOOH中隨壓力的增加而增加,在S-InOOH中隨壓力的增加而減小.彈性常數(shù)C44和橫波波速VS在氫鍵對(duì)稱(chēng)化前后的InOOH中都隨著壓力的增加而減小,但氫鍵對(duì)稱(chēng)化使其減小速率增大.InOOH在常壓時(shí)呈現(xiàn)韌性,隨著壓力的增加韌性增強(qiáng),且伴隨著氫鍵對(duì)稱(chēng)化韌性異常增加.氫鍵的對(duì)稱(chēng)化使[100],[010]和[001]方向的楊氏模量隨壓力的增加而增大的變化趨勢(shì)變?yōu)殡S壓力的增加而減小.結(jié)合其他畸變金紅石型MOOH的研究結(jié)果分析可知,MOOH化合物的軸比率、彈性性質(zhì)、波速等性質(zhì)隨壓力變化的規(guī)律與InOOH相似.

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Pressure-induced hydrogen bond symmetrization of InOOH and its elastic properties?

Kang Duan1)Wu Xiang2)?

1)(Key Laboratory of Orogenic Belts and Crustal Evolution,Ministry of Education,School of Earth and Space Sciences,Peking University,Beijing 100871,China)
2)(State Key Laboratory of Geological Processes and Mineral Resources,China University of Geosciences,Wuhan 430074,China)

21 July 2017;revised manuscript

14 August 2017)

Pressure-induced hydrogen bond symmetrization of InOOH as well as its effects on the elastic properties is investigated by first-principles simulation.The results indicate that the hydrogen bond in InOOH symmetrized at about 18 GPa,resulting in the pressure derivative of theb/caxial ratio changing from negative to positive.While thea/caxial ratio increases with the increasing pressure over a range of 0—40 GPa,its pressure derivative does not change signi ficantly across the hydrogen bond symmetrization.

In the text,‘A-InOOH’denotes the asymmetric hydrogen bond phase and ‘S-InOOH’refers to the symmetric hydrogen bond phase.The compressional and off-diagonal elastic constants,bulk modulusB,Poisson’s ratioν,B/G(Grepresents shear modulus)and longitudinal wave velocityVPincrease with the increasing pressure in both A-InOOH and S-InOOH.These properties of A-InOOH are signi ficantly smaller than those of S-InOOH,and therefore they increase abnormally during the hydrogen bond symmetrization,such as a 20%—40%increase of the bulk modulus.Shear modulusGand Young’s modulusEincrease with the increasing pressure in A-InOOH,but decrease with the increasing pressure in S-InOOH,implying that hydrogen bond symmetrization would change their pressure evolution trends obviously.Shear elastic constantC44and shear wave velocityVSdecrease with the increasing pressure in both A-InOOH and S-InOOH,and more quickly in the latter,indicating that the structure change of hydrogen bond would change their pressure evolution rates.The Young’s moduli along the[100],[010]and[001]directions increase with the increasing pressure in A-InOOH,while decrease with the increasing pressure in S-InOOH,and those along the[110],[ˉ110],[ˉ1ˉ10]and[1ˉ10]directions always increase with the increasing pressure over a range of 0—40 GPa.The anisotropy and toughness of InOOH increase with the increasing pressure in both A-InOOH and S-InOOH,and the hydrogen bond symmetrization results in abnormal increase.In the materials containing hydrogen bonds,the effects of hydrogen bond symmetrization on different compressional elastic constants depend on the hydrogen bond projection on corresponding axes:the bigger the projection,the more significant the effect is.

InOOH has an obviously smaller bulk modulus than δ-AlOOH.The dominant reason is that the In3+radius(0.81 ?,1 ? =0.1 nm)is larger than Al3+radius(0.50 ?),resulting in the weaker interaction between In3+and O2?than that between Al3+and O2?.In addition,InOOH has more vacancies than δ-AlOOH.Combining with previous investigations on other rutile-distortedMOOH(M=Al,Ga,Fe,Cr),we can infer that the axial ratios,elastic properties and wave velocities of allMOOH materials have similar pressure evolutions to those of InOOH,and the hydrogen bond symmetrization has similar effects on the properties ofMOOH.

InOOH,hydrogen bond symmetrization,elastic properties

PACS:62.20.—x,82.30.Rs,62.20.de,62.20.dqDOI:10.7498/aps.66.236201

*Project supported by the National Natural Science Foundation of China(Grant No.41473056).

?Corresponding author.E-mail:wuxiang@cug.edu.cn

(2017年7月21日收到;2017年8月14日收到修改稿)

利用第一性原理研究了InOOH在高壓下的氫鍵對(duì)稱(chēng)化行為及其對(duì)InOOH彈性等性質(zhì)的影響.結(jié)果表明約在18 GPa時(shí)InOOH中的氫鍵發(fā)生了對(duì)稱(chēng)化轉(zhuǎn)變,導(dǎo)致軸比率b/c對(duì)壓力的斜率由負(fù)值變?yōu)檎?壓縮彈性常數(shù)、非對(duì)角彈性常數(shù)、體積模量和縱波波速出現(xiàn)異常增加,如體積模量增加了20%—40%.高壓下InOOH彈性性質(zhì)呈現(xiàn)出更加明顯的各向異性.常壓下InOOH呈現(xiàn)韌性,且伴隨著氫鍵對(duì)稱(chēng)化韌性異常增加.對(duì)畸變金紅石型MOOH(M=Al,In,Ga,Fe,Cr)化合物在高壓下的彈性性質(zhì)轉(zhuǎn)變與氫鍵性質(zhì)轉(zhuǎn)變的耦合規(guī)律進(jìn)行了初探.

10.7498/aps.66.236201

?國(guó)家自然科學(xué)基金(批準(zhǔn)號(hào):41473056)資助的課題.

?通信作者.E-mail:wuxiang@cug.edu.cn