王 佳, 孫 澤, 路貴民, 于建國

(華東理工大學(xué)資源與環(huán)境工程學(xué)院,上海 200237)

堿金屬氯化物二元熔鹽密度的分子動力學(xué)模擬研究

王 佳, 孫 澤, 路貴民, 于建國

(華東理工大學(xué)資源與環(huán)境工程學(xué)院,上海 200237)

采用分子動力學(xué)模擬方法,計算了LiCl-NaCl、LiCl-KCl、LiCl-RbCl、LiCl-CsCl、NaCl-KCl、NaCl-RbCl以及NaCl-CsCl等堿金屬氯化物二元混合熔鹽在不同溫度和不同組分下的密度,證實了添加LiCl能夠降低NaCl、KCl、RbCl以及CsCl熔鹽的密度,添加NaCl則僅能夠降低RbCl和CsCl熔鹽的密度,而增大KCl熔鹽的密度。隨著溫度的逐漸升高,各混合熔鹽的密度逐漸減小。根據(jù)不同溫度、不同組分下的密度數(shù)據(jù),擬合得出了各混合熔鹽的密度關(guān)于溫度和組分含量的表達式。

堿金屬氯化物二元混合熔鹽; 密度; 分子動力學(xué)模擬

熔鹽在工業(yè)生產(chǎn)中具有廣泛的應(yīng)用,如熔鹽反應(yīng)堆[1]、核反應(yīng)中的冷卻劑[2]、金屬生產(chǎn)中或電沉積中的電解質(zhì)[3]以及傳熱蓄熱介質(zhì)[4]等。密度是熔鹽體系的一大重要性質(zhì),制約著熔鹽的實際應(yīng)用。在電解法生產(chǎn)金屬工藝過程中,金屬產(chǎn)物以及槽渣與電解質(zhì)熔鹽之間的分離效果受電解質(zhì)熔鹽的密度影響,在實際生產(chǎn)中常常會添加某種助劑來調(diào)整和改善電解質(zhì)熔鹽的密度。

堿金屬氯化物熔鹽是一類簡單的熔鹽,對該體系的研究比較廣泛,但是還不夠全面深入。有關(guān)堿金屬氯化物純?nèi)埯}的密度,已經(jīng)有了較為豐富的實驗數(shù)據(jù)[5],但關(guān)于堿金屬氯化物二元混合熔鹽密度的研究則相對比較離散,僅有少數(shù)的幾個體系在特定的溫度和組分下有相關(guān)的數(shù)據(jù)報道[5]。系統(tǒng)地研究堿金屬氯化物二元混合熔鹽的密度具有十分重要的理論價值和實際意義。

密度的實驗測定通常采用阿基米德法[6],由于熔鹽的腐蝕性以及高溫實驗的難操作性,測定各溫度、各組分下熔鹽的密度成本較高,因而較難實現(xiàn)。采用計算機模擬技術(shù)計算熔鹽的密度,成本低,操作簡便,還能實現(xiàn)任意溫度、任意組分下熔鹽密度的計算。本文采用分子動力學(xué)方法計算了不同溫度、不同組分下LiCl-NaCl、LiCl-KCl、LiCl-RbCl、LiCl-CsCl、NaCl-KCl、NaCl-RbCl與NaCl-CsCl等堿金屬氯化物二元混合熔鹽的密度,以完善堿金屬氯化物熔鹽密度數(shù)據(jù)庫,同時滿足工程實際應(yīng)用的需求。

1 計算方法

采用Fumi-Tosi勢函數(shù)[7]來描述離子之間的相互作用,前期研究表明,Fumi-Tosi勢函數(shù)可以準(zhǔn)確地預(yù)測堿金屬氯化物體系熔鹽的密度[8-9]。Fumi-Tosi勢函數(shù)的具體形式如下:

(1)

采用開源軟件LAMMPS進行分子動力學(xué)計算。計算元胞取為立方體,粒子數(shù)取1 024個,其中陰離子為512個,陽離子數(shù)目則按物質(zhì)的量之比分配,初始結(jié)構(gòu)為粒子隨機分布。粒子的初始速度設(shè)置為隨機分布,并符合高斯分布。為了消除邊界效應(yīng),計算采用周期性邊界條件。勢函數(shù)的截斷半徑設(shè)為L/2,其中L為體系弛豫平衡后模擬盒子的長度。為了消除截斷誤差,采用Ewald求和法處理長程作用力,即截斷半徑以內(nèi)的作用力直接計算,而截斷半徑以外的作用力則在倒易空間內(nèi)進行計算,Ewald求和法的計算精度設(shè)為1.0×10-6。用Verlet算法數(shù)值求解牛頓運動方程,時間步長設(shè)為1 fs。

體系首先在等溫等壓(NPT)系綜下平衡弛豫104步,采用Nose-Hoover控溫法和控壓法,恒溫和恒壓參數(shù)均設(shè)置為0.1 ps。待體系達到平衡后,在NPT系綜下進行計算,計算時間為5×105步,收集不同時刻下體系的體積信息,以計算體系的密度:

(2)

其中n是某種堿金屬氯化物“分子”的數(shù)目,M為分子的摩爾質(zhì)量,VE為模擬體系的平衡體積,NA為阿伏伽德羅常數(shù),其值為6.02×1023。

對所有的堿金屬氯化物二元混合熔鹽而言,密度計算的溫度范圍選取為近熔點處至1 500 K,計算間隔為20 K,計算溫度的下限根據(jù)體系的平衡相圖確定,組分質(zhì)量分?jǐn)?shù)為0～100%,計算間隔為6.25%。

2 結(jié)果與討論

2.1 LiCl-NaCl混合熔鹽

不同溫度、不同組分下LiCl-NaCl混合熔鹽的密度-溫度-組分關(guān)系如圖1所示。隨著LiCl摩爾分?jǐn)?shù)(x)的增加或者溫度的升高,LiCl-NaCl熔鹽的密度逐漸降低。不同溫度、不同組分下LiCl-NaCl混合熔鹽的密度值見表1。根據(jù)LiCl-NaCl混合熔鹽在不同溫度、不同組分下的密度,初始假設(shè)密度與溫度以及組分的一次項和二次項相關(guān),擬合得到LiCl-NaCl熔鹽的密度表達式為:

ρ(LiCl-NaCl)=1.907 5-3.797 5×10-4T-

5.662 1×10-4x-3.841 3×10-8T2-

5.866 8×10-6x2

(3)

式中:T表示溫度,單位為K;x為LiCl的摩爾分?jǐn)?shù)。由式(3)可以看出,溫度和組分的二次項在密度表達式中所占的比重很小,故舍棄二次項重新進行擬合,得到LiCl-NaCl熔鹽在860～1 500 K以及相應(yīng)組分范圍內(nèi)密度的表達式為:

ρ(LiCl-NaCl)=1.976 3-4.751 3×10-4T-

1.178 5×10-3x

(4)

圖1 不同溫度下LiCl-NaCl混合熔鹽的密度Fig.1 Densities of molten LiCl-NaCl at different temperatures表1 不同溫度下LiCl-NaCl混合熔鹽的密度Table 1 Densities of molten LiCl-NaCl at different temperatures

T/Kρ(LiCl-NaCl)/(g·cm-3)06.25%12.50%18.75%25.00%31.25%37.50%43.75%50.00%56.25%62.50%68.75%75.00%81.25%87.50%93.75%100%860-----------1.4881.4761.467---880----------1.4881.4791.4701.4581.445--900---------1.4891.4781.4691.4591.4461.4361.4241.411920--------1.4891.4781.4671.4591.4501.4381.4281.4161.402940-------1.4871.4791.4691.4601.4501.4421.4291.4171.4051.395960-------1.4781.4671.4611.4521.4411.4301.4191.4101.3991.384980------1.4761.4681.4591.4501.4411.4311.4221.4091.4011.3871.3761000-----1.4731.4651.4561.4481.4401.4341.4211.4111.4031.3911.3811.3681020----1.4701.4621.4571.4471.4401.4301.4221.4121.4031.3921.3821.3731.3591040---1.4661.4601.4521.4451.4391.4291.4211.4111.4021.3931.3851.3731.3631.3501060--1.4641.4571.4501.4411.4341.4271.4191.4141.4031.3931.3841.3751.3631.3551.3411080-1.4581.4531.4431.4371.4331.4241.4181.4121.4011.3941.3861.3751.3651.3541.3441.33311001.4531.4481.4411.4351.4311.4231.4151.4081.3991.3921.3851.3751.3671.3561.3451.3351.32211201.4421.4381.4321.4251.4191.4121.4051.3991.3911.3841.3731.3661.3561.3481.3371.3261.31311401.4331.4261.4211.4161.4081.4031.3941.3891.3821.3711.3661.3581.3461.3381.3291.3181.30511601.4221.4161.4121.4051.4001.3901.3861.3791.3721.3631.3561.3461.3381.3281.3181.3091.29811801.4101.4071.4011.3941.3891.3821.3771.3721.3621.3551.3471.3371.3281.3181.3111.2991.28612001.3971.3971.3911.3861.3801.3731.3651.3581.3531.3441.3361.3281.3201.3101.3021.2921.27912201.3891.3841.3801.3761.3681.3611.3561.3491.3421.3371.3281.3211.3121.3021.2921.2821.27212401.3801.3751.3711.3641.3581.3521.3461.3411.3341.3271.3191.3101.3001.2931.2831.2731.26312601.3701.3651.3591.3561.3491.3431.3381.3311.3211.3171.3081.3011.2931.2841.2751.2641.25312801.3601.3551.3481.3441.3381.3351.3291.3251.3121.3081.2991.2911.2841.2741.2651.2561.24313001.3461.3431.3381.3361.3291.3241.3181.3101.3031.2971.2891.2801.2731.2651.2551.2461.23713201.3371.3341.3271.3221.3191.3141.3071.3011.2941.2891.2811.2731.2651.2561.2461.2371.22613401.3291.3221.3211.3141.3091.3031.2961.2911.2841.2781.2681.2631.2541.2471.2381.2291.21713601.3191.3111.3101.3051.3001.2931.2881.2821.2731.2711.2621.2531.2471.2391.2301.2201.20913801.3071.3051.2971.2941.2891.2831.2781.2741.2661.2591.2521.2451.2381.2291.2221.2111.20114001.2981.2931.2891.2821.2781.2741.2671.2621.2571.2491.2441.2341.2281.2191.2101.2001.19214201.2871.2831.2771.2751.2681.2641.2581.2531.2451.2421.2341.2281.2181.2091.2001.1931.18314401.2771.2741.2681.2651.2591.2531.2491.2421.2381.2311.2241.2171.2081.2011.1921.1831.17614601.2671.2631.2571.2521.2481.2451.2391.2331.2261.2221.2151.2071.2001.1921.1841.1751.16614801.2561.2531.2501.2441.2391.2331.2271.2241.2161.2131.2051.1981.1921.1821.1741.1651.15615001.2471.2421.2401.2331.2281.2241.2191.2171.2091.2011.1961.1891.1831.1751.1631.1551.144

2.2 LiCl-KCl混合熔鹽

不同溫度、不同組分下LiCl-KCl混合熔鹽的溫度-組分-密度關(guān)系如圖2所示,具體的密度值見表2。隨著LiCl摩爾分?jǐn)?shù)的增加或者溫度的升高,LiCl-KCl熔鹽的密度逐漸減小。根據(jù)LiCl-KCl混合熔鹽在不同溫度、不同組分下的密度值,初步擬合得到LiCl-KCl熔鹽密度的表達式為:

ρ(LiCl-KCl)=1.915 1-5.213 7×10-4T-

2.231 9×10-4x+8.127 3×10-9T2-

2.347 5×10-7x2

(5)

圖2 不同溫度下LiCl-KCl混合熔鹽的密度Fig.2 Densities of molten LiCl-KCl at different temperatures表2 不同溫度下LiCl-KCl混合熔鹽的密度Table 2 Densities of molten LiCl-KCl at different temperatures

T/Kρ(LiCl-KCl)/(g·cm-3)06.25%12.50%18.75%25.00%31.25%37.50%43.75%50.00%56.25%62.50%68.75%75.00%81.25%87.50%93.75%680----------1.553-----700---------1.5511.543-----720---------1.5401.532-----740---------1.5291.5211.516----760--------1.5241.5181.5111.504----780--------1.5131.5051.4981.4951.486---800--------1.5001.4941.4911.4821.478---820-------1.4971.4881.4841.4771.4731.4681.461--840-------1.4841.4781.4731.4661.4631.4571.451--860-------1.4731.4681.4621.4571.4531.4471.4421.438-880------1.4661.4611.4561.4531.4481.4421.4361.4331.4291.424900------1.4541.4491.4461.4421.4381.4321.4281.4231.4191.416920-----1.4471.4441.4401.4331.4301.4251.4231.4181.4141.4101.406940-----1.4361.4311.4261.4251.4201.4141.4111.4101.4041.4011.397960----1.4281.4241.4211.4161.4131.4091.4061.4031.3981.3961.3911.387980----1.4161.4141.4101.4061.4021.3991.3951.3911.3891.3851.3821.3791000---1.4091.4051.4011.3981.3961.3931.3881.3851.3801.3801.3751.3731.3691020--1.4001.3981.3951.3901.3881.3871.3811.3781.3741.3711.3691.3671.3611.3621040-1.3911.3901.3861.3841.3791.3761.3741.3721.3691.3641.3621.3581.3561.3531.35310601.3791.3801.3781.3741.3721.3691.3671.3651.3601.3571.3541.3531.3491.3471.3441.34210801.3691.3681.3661.3641.3611.3611.3551.3511.3501.3471.3441.3421.3391.3371.3361.33511001.3601.3561.3551.3521.3511.3481.3441.3431.3411.3371.3351.3321.3301.3281.3261.32511201.3471.3471.3451.3421.3401.3371.3351.3331.3311.3271.3261.3231.3201.3201.3171.31611401.3351.3351.3321.3321.3281.3261.3241.3211.3181.3181.3141.3151.3121.3101.3061.30811601.3241.3231.3211.3181.3171.3171.3131.3111.3081.3061.3051.3021.3001.3011.2991.29811801.3131.3131.3121.3091.3061.3041.3021.2991.2991.2971.2931.2941.2921.2911.2881.28812001.3031.3001.2991.3001.2951.2941.2921.2911.2871.2871.2861.2831.2801.2801.2811.28212201.2921.2891.2881.2881.2851.2851.2811.2801.2771.2761.2751.2741.2721.2701.2711.27012401.2801.2801.2801.2781.2761.2731.2711.2681.2681.2671.2651.2661.2631.2611.2611.26312601.2701.2721.2711.2661.2641.2641.2601.2581.2571.2561.2561.2531.2541.2521.2531.25212801.2591.2591.2551.2541.2551.2511.2511.2511.2491.2471.2451.2441.2441.2421.2431.24513001.2501.2481.2471.2461.2431.2401.2401.2391.2391.2361.2351.2361.2341.2341.2341.23513201.2381.2361.2351.2321.2341.2301.2301.2271.2281.2261.2261.2271.2241.2241.2241.22613401.2261.2261.2231.2231.2221.2201.2181.2181.2151.2171.2151.2171.2151.2151.2141.21813601.2181.2151.2151.2111.2121.2111.2071.2091.2061.2071.2051.2061.2041.2061.2061.20913801.2061.2041.2031.2031.1991.2011.1981.1981.1961.1971.1981.1931.1971.1961.1961.19814001.1951.1931.1941.1921.1921.1891.1891.1881.1861.1871.1851.1871.1861.1881.1871.18914201.1841.1831.1831.1811.1801.1791.1781.1761.1781.1781.1751.1761.1781.1791.1781.18214401.1721.1711.1721.1691.1681.1661.1681.1671.1681.1661.1681.1671.1671.1651.1671.17214601.1631.1621.1601.1591.1581.1591.1581.1581.1561.1571.1571.1551.1571.1611.1581.16314801.1501.1501.1501.1501.1491.1481.1471.1441.1451.1491.1461.1461.1481.1501.1511.15315001.1411.1391.1391.1371.1381.1371.1361.1351.1361.1361.1371.1351.1401.1391.1401.142

由式(5)可以看出,溫度和組分的二次項在密度表達式中所占的比重很小,故舍棄二次項重新進行擬合,得到LiCl-KCl熔鹽在680～1 500 K溫度區(qū)間以及相應(yīng)組分范圍內(nèi)的密度的表達式為:

ρ(LiCl-KCl)=1.905 3-5.028 3×10-4T-

2.465 4×10-4x

(6)

2.3 LiCl-RbCl混合熔鹽

不同溫度不同組分下LiCl-RbCl混合熔鹽的溫度-組分-密度關(guān)系如圖3所示,具體的密度值見表3。

表3 不同溫度下LiCl-RbCl混合熔鹽的密度Table 3 Densities of molten LiCl-RbCl at different temperatures

圖3 不同溫度下LiCl-RbCl混合熔鹽的密度Fig.3 Densities of molten LiCl-RbCl at different temperatures

隨著LiCl摩爾分?jǐn)?shù)的增加或溫度的升高,體系的密度逐漸減小。根據(jù)計算結(jié)果,初步擬合得到LiCl-RbCl熔鹽密度的表達式為:

ρ(LiCl-RbCl)=2.723 6-7.474 8×10-4T-

1.851 4×10-3x+3.691 4×10-8T2-

4.122 2×10-5x2

(7)

由式(7)可以看出,溫度的二次項在密度表達式中所占的比重很小,故舍棄溫度的二次項,增加組分的三次項,重新進行擬合,得到的表達式為:

ρ(LiCl-RbCl)=2.680 3-6.634 0×10-4T-

2.291 2×10-3x-2.949 3×10-5x2-

7.998 7×10-8x3

(8)

由式(8)則可以看出,組分的三次項所占的比重也很小,故舍棄組分的三次項,再次擬合,得到LiCl-RbCl混合熔鹽在620～1 500 K溫度區(qū)間以及相應(yīng)組分范圍內(nèi)密度的表達式為:

ρ(LiCl-RbCl)=2.677 1-6.638 1×10-4T-

1.808 2×10-3x-4.161 9×10-5x2

(9)

2.4 LiCl-CsCl混合熔鹽

計算得到不同溫度、不同組分下LiCl-CsCl混合熔鹽的密度,其溫度-組分-密度關(guān)系如圖4所示,具體的密度值見表4。

圖4 不同溫度下LiCl-CsCl混合熔鹽的密度Fig.4 Densities of molten LiCl-CsCl at different temperatures

由圖4可以看出,隨著LiCl摩爾分?jǐn)?shù)的增加或者溫度的升高,LiCl-CsCl熔鹽的密度逐漸減小。此外,還可以看到,與LiCl-NaCl和LiCl-KCl等熔鹽不同,LiCl-CsCl混合熔鹽的溫度-組分-密度關(guān)系圖明顯呈曲面,說明該混合熔鹽的密度與溫度或者組分的高次項相關(guān)。根據(jù)LiCl-CsCl混合熔鹽在不同溫度、不同組分下的密度,初步擬合得到LiCl-CsCl熔鹽密度的表達式為:

ρ(LiCl-CsCl)=3.461 2-1.056 0×10-3T-

3.226 2×10-3x+1.028 9×10-7T2-

7.246 0×10-5x2

(10)

由式(10)可以看出,溫度的二次項在密度表達式中所占的比重很小,故舍棄溫度的二次項,同時增加組分的三次項,重新進行擬合得到的表達式為:

ρ(LiCl-CsCl)=3.345 4-8.226 3×10-4T-

4.961 5×10-3x-2.645 2×10-5x2-

3.132 8×10-7x3

(11)

由式(11)則可以看出,組分的三次項所占的比重也很小,故舍棄組分的三次項,再次擬合得到LiCl-CsCl混合熔鹽在640～1 500 K溫度區(qū)間以及相應(yīng)組分范圍內(nèi)密度的表達式為:

ρ(LiCl-CsCl)=3.332 7-8.236 1×10-4T-

3.105 3×10-3x-7.360 9×10-5x2

(12)

2.5 NaCl-KCl混合熔鹽

不同溫度、不同組分下NaCl-KCl混合熔鹽的溫度-組分-密度關(guān)系如圖5所示,其詳細密度值見表5。

圖5 不同溫度下NaCl-KCl混合熔鹽的密度Fig.5 Densities of molten NaCl-KCl at different temperatures

隨著NaCl摩爾分?jǐn)?shù)的降低或者溫度的升高,NaCl-KCl熔鹽的密度逐漸減小。根據(jù)計算結(jié)果初步擬合得到NaCl-KCl熔鹽密度的表達式為:

ρ(NaCl-KCl)=1.990 7-6.097 3×10-4T+

5.797 0×10-4x+3.035 5×10-8T2+

4.038 5×10-6x2

(13)

表4 不同溫度下LiCl-CsCl混合熔鹽的密度Table 4 Densities of molten LiCl-CsCl at different temperatures

表5 不同溫度下NaCl-KCl混合熔鹽的密度Table 5 Densities of molten NaCl-KCl at different temperatures

其中,x為NaCl的摩爾分?jǐn)?shù)。由式(13)可以看出,溫度和組分的二次項在密度表達式中所占的比重均很小,故舍棄二次項,重新進行擬合,得到NaCl-KCl混合熔鹽在960～1 500 K溫度區(qū)間以及相應(yīng)組分范圍內(nèi)密度的表達式為:

ρ(NaCl-KCl)=1.933 7-5.307 8×10-4T+

9.796 7×10-4x

(14)

2.6 NaCl-RbCl混合熔鹽

不同溫度、不同組分下NaCl-RbCl混合熔鹽的溫度-組分-密度關(guān)系如圖6所示,詳細的密度值見表6。隨著NaCl摩爾分?jǐn)?shù)的增加或者溫度的升高,NaCl-RbCl混合熔鹽的密度逐漸降低。根據(jù)NaCl-RbCl混合熔鹽在不同溫度、不同組分下的密度,初步擬合得到NaCl-RbCl熔鹽的密度表達式為:

ρ(NaCl-RbCl)=2.903 1-9.890 0×10-4T-

3.094 8×10-3x+1.178 8×10-7T2-

1.582 4×10-5x2

(15)

圖6 不同溫度下NaCl-RbCl混合熔鹽的密度Fig.6 Densities of molten NaCl-RbCl at different temperatures

由式(15)可以看出,溫度的二次項在密度表達式中所占的比重均很小,故舍棄溫度的二次項,同時添加組分的三次項,重新進行擬合,得到的密度表達式為:

ρ(NaCl-RbCl)=2.729 5-7.009 6×10-4T-

由式(16)可以看出,組分的三次項在密度表達式中所占的比重也很小,故舍棄組分的三次項,再次擬合,得到NaCl-RbCl混合熔鹽在860～1 500 K溫度區(qū)間以及相應(yīng)組分范圍內(nèi)密度的表達式為:

ρ(NaCl-RbCl)=2.729 7-7.009 7×10-4T-

3.037 3×10-3x-1.646 9×10-5x2

(17)表6 不同溫度下NaCl-RbCl混合熔鹽的密度Table 6 Densities of molten NaCl-RbCl at different temperatures

2.7 NaCl-CsCl混合熔鹽

不同溫度、不同組分下NaCl-CsCl熔鹽的溫度-組分-密度關(guān)系如圖7所示,詳細的密度值見表7。隨著NaCl摩爾分?jǐn)?shù)的增加或者溫度的升高,NaCl-CsCl熔鹽的密度降低。此外,與LiCl-CsCl相似,NaCl-CsCl混合熔鹽的溫度-組分-密度關(guān)系圖明顯呈曲面,說明該混合熔鹽的密度與溫度或者組分的高次項相關(guān)。根據(jù)密度數(shù)據(jù)初步擬合得到NaCl-CsCl熔鹽的密度表達式為:

ρ(NaCl-CsCl)=3.744 8-1.460 3×10-3T-

5.465 6×10-3x+2.481 1×10-7T2-

3.634 1×10-5x2

(18)

由式(18)可以看出,溫度的二次項在密度表達式中所占的比重均很小,故舍棄溫度的二次項,同時添加組分的三次項,重新進行擬合,得到的密度表達式為:

ρ(NaCl-CsCl)=3.403 0-8.679 9×10-4T-

5.910 2×10-3x-2.357 5×10-5x2-

9.469 3×10-8x3

(19)

圖7 不同溫度下NaCl-CsCl混合熔鹽的密度Fig.7 Densities of molten NaCl-CsCl at different temperatures表7 不同溫度下NaCl-CsCl混合熔鹽的密度Table 7 Densities of molten NaCl-CsCl at different temperatures

T/Kρ(NaCl-RbCl)/(g·cm-3)6.25%12.50%18.75%25.00%31.25%37.50%43.75%50.00%56.25%62.50%68.75%75.00%81.25%87.50%93.75%800----2.5272.464---------820----2.5072.445---------840---2.5472.4912.4282.364--------860--2.5812.5242.4682.4072.3472.279-------880--2.5622.5092.4502.3892.3282.263-------900-2.5922.5422.4882.4292.3702.3102.2422.175------9202.6192.5692.5202.4642.4102.3512.2902.2282.161------9402.5962.5512.4982.4462.3952.3352.2712.2122.1442.076-----9602.5772.5272.4792.4242.3722.3172.2562.1932.1282.0581.985----9802.5522.5052.4582.4072.3522.2992.2352.1762.1122.0441.971----10002.5332.4892.4342.3882.3352.2782.2202.1592.0952.0251.9561.876---10202.5102.4652.4182.3682.3172.2582.2042.1422.0782.0111.9401.8631.782--10402.4922.4452.3942.3452.2962.2422.1862.1242.0611.9961.9241.8481.767--10602.4682.4262.3792.3292.2782.2222.1712.1072.0441.9831.9101.8351.7541.672-10802.4472.4022.3552.3102.2572.2042.1522.0942.0311.9631.8971.8181.7431.6571.56311002.4282.3812.3352.2912.2372.1872.1322.0752.0131.9491.8801.8071.7271.6441.55311202.4062.3622.3162.2732.2222.1712.1142.0571.9981.9311.8641.7951.7151.6331.54011402.3832.3402.2982.2502.2042.1462.0982.0421.9811.9151.8501.7781.7031.6211.53011602.3632.3222.2752.2312.1822.1342.0822.0241.9671.9031.8391.7671.6891.6041.51811802.3462.3022.2612.2132.1672.1182.0632.0071.9481.8871.8241.7491.6761.5941.50612002.3182.2802.2402.1942.1482.0982.0471.9921.9361.8721.8041.7381.6641.5831.49612202.3042.2632.2182.1752.1272.0802.0291.9771.9191.8581.7931.7221.6511.5711.48412402.2822.2422.2002.1572.1132.0632.0131.9601.9031.8421.7791.7101.6361.5571.47112602.2632.2232.1792.1382.0912.0461.9941.9421.8861.8271.7641.6951.6231.5471.46212802.2392.2002.1632.1202.0752.0261.9751.9241.8711.8121.7491.6851.6111.5351.44913002.2202.1812.1432.0982.0512.0101.9631.9081.8551.7981.7371.6711.5981.5231.43913202.2002.1592.1212.0792.0371.9931.9441.8931.8381.7821.7211.6551.5821.5091.42613402.1792.1412.1062.0602.0201.9711.9271.8791.8251.7641.7061.6431.5721.5011.41613602.1552.1192.0852.0452.0011.9571.9061.8601.8091.7521.6931.6291.5581.4851.40313802.1392.1042.0612.0231.9821.9381.8941.8491.7911.7361.6761.6131.5461.4781.39514002.1172.0792.0522.0091.9611.9221.8791.8291.7791.7231.6631.6031.5341.4601.38414202.0982.0632.0261.9851.9441.9031.8601.8101.7571.7061.6471.5881.5241.4491.37214402.0792.0442.0081.9691.9341.8871.8421.7951.7441.6931.6351.5761.5061.4371.35914602.0582.0231.9891.9491.9061.8691.8291.7791.7311.6781.6171.5601.4981.4251.35014802.0352.0051.9681.9331.8931.8511.8061.7611.7121.6621.6101.5461.4811.4151.33815002.0171.9861.9531.9071.8761.8351.7921.7431.6981.6461.5921.5341.4701.4021.330

由式(19)可以看出,組分的三次項在密度表達式中所占的比重也很小,故舍棄組分的三次項,再次擬合,得到NaCl-CsCl混合熔鹽在800～1 500 K溫度區(qū)間以及相應(yīng)組分范圍內(nèi)密度的表達式為:

ρ(NaCl-CsCl)=3.398 3-8.672 8×10-4T-

5.377 3×10-3x-3.754 9×10-5x2

(20)

堿金屬氯化物二元混合熔鹽的密度隨著組分的變化關(guān)系與其微觀結(jié)構(gòu)的變化密切相關(guān)。以LiCl-NaCl為例,前期研究表明[9],隨著LiCl摩爾分?jǐn)?shù)的增加,混合熔鹽中Na-Cl和Na-Na離子對之間的相互作用逐漸減弱,離子趨向于分散分布,因而LiCl-NaCl體系的宏觀密度逐漸降低。對于NaCl-KCl體系而言,隨著NaCl摩爾分?jǐn)?shù)的增加,熔鹽中離子對之間的相互作用亦逐漸減弱,但程度輕微,而離子間的緊密堆積度逐漸增大,即原子的排列更加趨于緊湊,因此體系的密度逐漸增大。

3 結(jié) 論

本文采用分子動力學(xué)方法,計算了不同溫度、不同組分下LiCl-NaCl、LiCl-KCl、LiCl-RbCl、LiCl-CsCl、NaCl-KCl、NaCl-RbCl以及NaCl-CsCl等堿金屬氯化物二元混合熔鹽體系的密度,同時根據(jù)計算結(jié)果,擬合得到了LiCl-NaCl、LiCl-KCl、LiCl-RbCl、LiCl-CsCl、NaCl-KCl、NaCl-RbCl以及NaCl-CsCl等體系熔鹽的密度表達式。計算結(jié)果表明,隨著溫度的逐漸升高,各混合熔鹽的密度逐漸減小;隨著LiCl摩爾分?jǐn)?shù)的增加,LiCl-NaCl,LiCl-KCl,LiCl-RbCl和LiCl-CsCl等混合熔鹽的密度逐漸下降;隨著NaCl摩爾分?jǐn)?shù)的增加,NaCl-KCl熔鹽的密度逐漸增大,而NaCl-RbCl和NaCl-CsCl體系熔鹽的密度逐漸減小。

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Molecular Dynamics Simulation for the Densities of Molten Binary Alkali Metal Chlorides

WANG Jia, SUN Ze, LU Gui-min, YU Jian-guo

(School of Resources and Environmental Engineering,East China University of Science and Technology,Shanghai 200237,China)

The densities of molten LiCl-NaCl,LiCl-KCl,LiCl-RbCl,LiCl-CsCl,NaCl-KCl,NaCl-RbCl and NaCl-CsCl at different temperatures were calculated by molecular dynamics simulation within the full composition range.The addition of LiCl could reduce the densities of molten NaCl,KCl,RbCl and CsCl.NaCl could also reduce the densities of molten RbCl and CsCl,but increase the density of molten KCl.The densities of these mixtures all reduced with the increasing of temperature.In addition,the expression of density on temperatune and composition for these melts were fitted according to the calculated results.

molten binary alkali metal chlorides; densities; molecular dynamics simulation

1006-3080(2016)06-0771-11

10.14135/j.cnki.1006-3080.2016.06.005

2016-09-18

國家自然科學(xué)基金(U1407202)

王 佳(1989-),女,江蘇人,博士生，主要從事氯化物熔鹽的相關(guān)模擬計算。 E-mail:10072157@mail.ecust.edu.cn

路貴民,E-mail:gmlu@ecust.edu.cn

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