气体-表面相互作用中动量和能量分量间转化机制的分子动力学研究

于航; 张冉; 杨帆; 李桦

doi:10.7498/aps.70.20201192

摘要

气体分子与壁面之间的相互作用是影响稀薄气体流动状态的主要因素, 但是由于其物理上的复杂性和微观性, 这一过程的机理并没有得到充分揭示. 本文利用分子束法对Ar分子在金属Pt表面的碰撞过程进行了分子动力学模拟, 并探究了入射速度、角度和壁面粗糙度对动量、能量转化机制的影响. 结果表明, 当气体分子以$ 5^{\circ}$的极角入射时, 分子的法向速度分量占主导因素, 在与壁面发生碰撞之后, 分子的切向和法向动量都会损失, 法向动能会向切向转移, 并且当分子速度不低于2.0时, 切向和法向动能的比值会稳定在一个很小的区间, 而粗糙度对动量和能量转化的影响不明显. 与小角度入射时不同, 当气体分子以$ 75^{\circ} $的极角与金属表面碰撞时, 粗糙度的影响就不能再被忽略了. 大极角入射的气体分子在光滑壁面散射之后, 其运动规律基本符合Maxwell所假设的镜面反射, 动量和能量分量的变化都不明显. 而粗糙度的引入则会促进气体分子切向动量和能量向法向转移, 并且会使分子总能量的损失更加显著.

关键词:

Abstract

With the rapid development of micro-nano technology and aerospace technology, researches related to rarefied gas flows have received more and more attention. For micro-/nanoscale systems and spacecraft in a rarefied environment, the reduction in the frequency of intermolecular collisions in the flow field makes the interaction between gas molecules and the solid surface develop into a major factor affecting the flow state. However, the mechanism of gas-surface interaction in rarefied flow has not been fully revealed due to its microscopic nature and physical complexity, and the existing simulation methods cannot accurately reflect the effect of this process on the flow state. In this paper, molecular beam method is adopted to simulate the scattering process of argon molecules on platinum surface, and the impacts of incident velocity, angle and wall roughness on the momentum and energy conversion mechanism are explored. By simulating the molecular scattering process under the two incident angles of $ 5^{\circ} $ and $ 75^{\circ}$, the following conclusions are obtained. When colliding with the wall at an angle close to vertical, both components of the momentum of the gas molecules are lost. The normal energy transfers to the tangential direction, and when the molecular velocity is not less than 2.0, the transfer rate is not significantly affected by the incident energy of the molecule and the surface roughness. The total energy loss of gas molecules after scattering becomes significant with the increase of incident velocity, and it is not sensitive to changes of surface roughness. When the gas molecules are incident at $ 75^{\circ} $, the roughness of the surface has a significant impact on the conversion mechanism of molecular momentum and energy. After colliding with a smooth wall, the momentum and energy values of the gas molecules remain basically unchanged, only the direction of the momentum is reversed. The motion state of molecules is close to the mirror reflection, and the conversion between momentum and energy components is not obvious. The introduction of roughness enhances the degree of accommodation between gas molecules and metal surface, and promotes the transfer of molecular tangential momentum and kinetic energy to the normal direction. When incident at a large polar angle, as opposed to the small-angle cases, the total energy loss of molecules is not sensitive to changes of incident velocity, it goes up significantly with the surface roughness increasing. The research in this article not only explores the gas-surface interaction mechanism, but also provides a useful reference for the high-fidelity simulation of rare gas flow and the development of appropriate gas-surface interaction models.

Keywords:

作者及机构信息

1.
国防科技大学空天科学学院, 长沙　410073

2.
西北核技术研究所, 激光与物质相互作用国家重点实验室, 西安　710024

通信作者: 张冉, zr07024221@126.com

基金项目: 国家自然科学基金(批准号: 11472004)资助课题

Authors and contacts

1.
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China

2.
State Key Laboratory of Laser Interaction with Matter, Northwest Institute of Nuclear Technology, Xi’an 710024, China

Corresponding author: Zhang Ran, zr07024221@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11472004)

文章全文 : translate this paragraph

参考文献

[1]	Liang T, Li Q, Ye W 2017 J. Comput. Phys. 352 105 Google Scholar
[2]	曹炳阳, 陈民, 过增元 2006 物理学报 55 5305 Google Scholar Cao B Y, Chen M, Guo Z Y 2006 Acta Phys. Sin. 55 5305 Google Scholar
[3]	Sharipov F, Kalempa D 2005 Phys. Fluids 10 16 Google Scholar
[4]	Burnett D 1935 Proc. Lond. Math. Soc. 1 1 Google Scholar
[5]	Shavaliyev M S 1993 J. Appl. Math. Mech. 57 573 Google Scholar
[6]	Bird G A 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford: Oxford University Press) p199
[7]	Yuan Y D, Rahman S 2016 Phys. A 463 25 Google Scholar
[8]	Lockerby D A, Reese J M, Emerson D R, Barber R W 2004 Phys. Rev. E 70 017303 Google Scholar
[9]	Barber R W, Emerson D R 2006 Heat Transfer Eng. 27 3 Google Scholar
[10]	Lockerby D A, Reese J M, Gallis M A 2005 AIAA J. 43 1391 Google Scholar
[11]	Reese J M, Zheng Y, Lockerby D A 2007 J. Comput. Theor. Nanosci. 4 807 Google Scholar
[12]	Bruno D, Cacciatore M, Longo S, Rutigliano M 2000 Chem. Phys. Lett. 320 245 Google Scholar
[13]	Padilla, J F, Bo yd, Iain D 2009 J. Thermophys. Heat Transfer 23 96 Google Scholar
[14]	Liang T, Li Q, Ye W 2013 Phys. Rev. E 88 013009 Google Scholar
[15]	Woronowicz M S, Rault D F 1994 J. Spacecraft Rockets 31 532 Google Scholar
[16]	Myong R S 2004 J. Comput. Phys. 195 655 Google Scholar
[17]	Alder B J, Wainwright T E 1957 J. Chem. Phys. 27 1208 Google Scholar
[18]	Kovalev V, Yakunchikov A, Li F 2011 Acta Astronaut. 69 744 Google Scholar
[19]	张忠强, 刘汉伦, 范晋伟, 丁建宁, 程广贵 2019 物理学报 68 170202 Google Scholar Zhang Z Q, Liu H L, Fan J W, Ding J N, Cheng G G 2019 Acta Phys. Sin. 68 170202 Google Scholar
[20]	Chirita V, Pailthorpe B A, Collins R E 1997 Nucl. Instrum. Meth. B 129 465 Google Scholar
[21]	Yamanishi N, Matsumoto Y, Shobatake K 1999 Phys. Fluids 11 3540 Google Scholar
[22]	曹炳阳 2005 博士学位论文 (北京: 清华大学) Cao B Y 2005 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese)
[23]	Finger G W, Kapat J S, Bhattacharya A 2007 J. Fluids Eng-Trans. ASME 129 31 Google Scholar
[24]	Ozhgibesov M S, Leu T, Cheng C 2012 J. Mol. Graph. Model. 38 375 Google Scholar
[25]	Ozhgibesov M S, Leu T, Cheng C 2013 J. Mol. Graph. Model. 45 45 Google Scholar
[26]	Leu T, Cheng C, Ozhgibesov M S 2011 J. Mol. Graph. Model. 31 35 Google Scholar
[27]	Bao F, Mao Z, Qiu L 2014 Int. J. Numer. Methods Heat Fluid Flow 24 1338 Google Scholar
[28]	宋诚谦 2014 博士学位论文 (合肥: 中国科技大学) Song C Q 2014 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)
[29]	Cao B Y, Sun J, Chen M, Guo Z Y 2009 Int. J. Mol. Sci. 10 11 Google Scholar
[30]	Sun J, Li Z 2008 Mol. Phys. 106 2325 Google Scholar
[31]	Sun J, Li Z 2009 Mol. Simul. 35 228 Google Scholar
[32]	张冉, 常青, 李桦 2018 物理学报 67 223401 Google Scholar Zhang R, Chang Q, Li H 2018 Acta Phys. Sin. 67 223401 Google Scholar
[33]	Maruyama S 2000 Adv. Numer. Heat Transfer 2 189 Google Scholar
[34]	Wu L, Bogy D B 2002 J. Tribol.-Trans. ASME 124 562 Google Scholar
[35]	Swope W C, Andersen H C, Berens P H, Wilson K R 1982 J. Chem. Phys. 76 637 Google Scholar
[36]	Dongari N, Zhang Y H, Reese J M 2012 AIP Conf. Proc. 1501 895 Google Scholar
[37]	张烨, 张冉, 赖剑奇, 李桦 2019 物理学报 68 124702 Google Scholar Zhang Y, Zhang R, Lai J Q, Li H 2019 Acta Phys. Sin. 68 124702 Google Scholar
[38]	Chirita V, Pailthorpe B A, Collins R E 1993 J. Phys. D: Appl. Phys. 26 133 Google Scholar
[39]	Maxwell J C 1878 Proc. R. Soc. London 27 304 Google Scholar

施引文献

图 1 三种表面粗糙度构型

Fig. 1. Three surface roughness structures.

下载: 全尺寸图片幻灯片

图 2 气体分子的入射极角$ \theta$和反射速度的分解在笛卡尔坐标系下的示意图

Fig. 2. Schematic diagram of the incident polar angle $ \theta $ and the decompositions of molecular scattering velocity in Cartesian coordinate.

下载: 全尺寸图片幻灯片

图 3 入射角为$ 5^{\circ}$时, 气体分子与光滑表面碰撞中速度和能量随时间的变化　(a)速度随时间的变化; (b)能量随时间的变化

Fig. 3. When the incident angle is $ 5^{\circ} $, the variations of molecular velocity and energy in the collision with a smooth surface: (a) Variation of molecular velocity; (b) variation of molecular energy.

下载: 全尺寸图片幻灯片

图 4 以$ 5^{\circ}$极角入射时, 气体分子在不同粗糙表面的法向动量适应系数(NMAC)

Fig. 4. Normal momentum accommodation coefficient (NMAC) of gas molecules on different rough surfaces when the incident polar angle is $ 5^{\circ} $.

下载: 全尺寸图片幻灯片

图 5 以$ 5^{\circ} $极角入射时, 气体分子在不同粗糙表面的能量损失率

Fig. 5. Energy loss rate of gas molecules on different rough surfaces when the incident polar angle is $ 5^{\circ} $.

下载: 全尺寸图片幻灯片

图 6 入射角为$ 75^{\circ} $时, 气体分子与光滑表面碰撞中速度和能量随时间的变化　(a)速度随时间的变化; (b)能量随时间的变化

Fig. 6. When the incident angle is $ 75^{\circ}$, the variations of molecular velocity and energy in the collision with a smooth surface: (a) Variation of molecular velocity; (b) variation of molecular energy.

下载: 全尺寸图片幻灯片

图 7 入射角为$ 75^{\circ} $时, 气体分子与粗糙表面碰撞中速度和能量随时间的变化　(a)速度随时间的变化; (b)能量随时间的变化

Fig. 7. When the incident angle is $ 75^{\circ}$, the variations of molecular velocity and energy in the collision with a rough surface: (a) Variation of molecular velocity; (b) variation of molecular energy.

下载: 全尺寸图片幻灯片

图 8 以$ 75^{\circ}$极角入射时, 气体分子在不同粗糙表面的的切向动量适应系数(TMAC)

Fig. 8. Tangential momentum accommodation coefficient (TMAC) of gas molecules on different rough surfaces when the incident polar angle is $ 75^{\circ}$.

下载: 全尺寸图片幻灯片

图 9 以$ 75^{\circ} $极角入射时, 气体分子在不同粗糙表面的能量损失率

Fig. 9. Energy loss rate of gas molecules on different rough surfaces when the incident polar angle is $ 75^{\circ} $.

下载: 全尺寸图片幻灯片

表 1 入射极角为$ 5^{\circ}$时, 不同速度的气体分子在不同表面上散射后的平均速度和能量

Table 1. When the incident polar angle is $ 5^{\circ}$, the mean velocity and energy of gas molecules that with different velocities after scattering on different surfaces.

${V_{\rm{i}}}$/$\sqrt {2{k_{\rm{B}}}T} $	States	${V_{\rm{t}}}$/($\sigma \cdot {\tau^{-1}}$)	${V_{\rm{n}}}$/($\sigma \cdot {\tau^{-1}}$)	${E_{{\rm{t}}}}$/$\varepsilon $	${E_{{\rm{n}}}}$/$\varepsilon $	E/$\varepsilon $
1.0	Incident	3.0566	–0.8191	4.6720	0.3355	5.0083
	Re-R = 0 Å	2.1165	1.8812	3.1534	2.0912	5.2478
	Re-R = 0.5 Å	0.2948	1.8122	2.2248	1.9670	4.1892
	Re-R = 1.0 Å	0.1625	1.7772	1.9206	1.9334	3.8632
2.0	Incident	6.1133	–1.6382	18.692	1.3420	20.034
	Re-R = 0 Å	5.6211	2.2725	16.724	3.1156	19.829
	Re-R = 0.5 Å	2.0090	2.9777	9.8840	5.6781	15.547
	Re-R = 1.0 Å	0.2579	3.3517	7.4644	6.7519	14.216
4.0	Incident	12.226	–3.2766	74.766	5.3679	80.135
	Re-R = 0.0 Å	11.937	3.0014	72.802	5.1488	78.079
	Re-R = 0.5 Å	5.7585	5.6367	34.796	18.909	62.501
	Re-R = 1.0 Å	1.0305	6.6301	26.878	25.619	52.504
8.0	Incident	24.452	–6.5532	299.06	21.472	320.54
	Re-R = 0 Å	24.021	6.0509	293.14	19.210	312.38
	Re-R = 0.5 Å	16.386	9.6325	209.77	49.747	259.52
	Re-R = 1.0 Å	2.0656	12.770	117.64	95.714	213.20
16.0	Incident	48.906	–13.106	1196.3	85.880	1282.1
	Re-R = 0 Å	47.378	12.256	1143.2	79.050	1220.8
	Re-R = 0.5 Å	32.525	16.818	832.86	177.59	1009.5
	Re-R = 1.0 Å	2.9900	23.156	474.64	318.22	790.68

下载: 导出CSV

表 2 入射极角为$ 75^{\circ}$时, 不同速度的气体分子在不同表面上散射后的平均速度和能量

Table 2. When the incident polar angle is $ 75^{\circ} $, the mean velocity and energy of gas molecules that with different velocities after scattering on different surfaces.

${V_{\rm{i}}}$/$\sqrt {2{k_{\rm{B}}}T} $	States	${V_{\rm{t}}}$/($\sigma \cdot {\tau^{-1} }$)	${V_{\rm{n}}}$/($\sigma \cdot {\tau^{-1}}$)	${E_{{\rm{t}}}}$/$\varepsilon$	${E_{{\rm{n}}}}$/$\varepsilon $	E/$\varepsilon $
1.0	Incident	3.0566	–0.8191	4.6720	0.3355	5.0083
	Re-R = 0 Å	2.1165	1.8812	3.1534	2.0912	5.2478
	Re-R = 0.5 Å	0.2948	1.8122	2.2248	1.9670	4.1892
	Re-R = 1.0 Å	0.1625	1.7772	1.9206	1.9334	3.8632
2.0	Incident	6.1133	–1.6382	18.692	1.3420	20.034
	Re-R = 0 Å	5.6211	2.2725	16.724	3.1156	19.829
	Re-R = 0.5 Å	2.0090	2.9777	9.8840	5.6781	15.547
	Re-R = 1.0 Å	0.2579	3.3517	7.4644	6.7519	14.216
4.0	Incident	12.226	–3.2766	74.766	5.3679	80.135
	Re-R = 0.0 Å	11.937	3.0014	72.802	5.1488	78.079
	Re-R = 0.5 Å	5.7585	5.6367	34.796	18.909	62.501
	Re-R = 1.0 Å	1.0305	6.6301	26.878	25.619	52.504
8.0	Incident	24.452	–6.5532	299.06	21.472	320.54
	Re-R = 0 Å	24.021	6.0509	293.14	19.210	312.38
	Re-R = 0.5 Å	16.386	9.6325	209.77	49.747	259.52
	Re-R = 1.0 Å	2.0656	12.770	117.64	95.714	213.20
16.0	Incident	48.906	–13.106	1196.3	85.880	1282.1
	Re-R = 0 Å	47.378	12.256	1143.2	79.050	1220.8
	Re-R = 0.5 Å	32.525	16.818	832.86	177.59	1009.5
	Re-R = 1.0 Å	2.9900	23.156	474.64	318.22	790.68

下载: 导出CSV

[1]	Liang T, Li Q, Ye W 2017 J. Comput. Phys. 352 105 Google Scholar
[2]	曹炳阳, 陈民, 过增元 2006 物理学报 55 5305 Google Scholar Cao B Y, Chen M, Guo Z Y 2006 Acta Phys. Sin. 55 5305 Google Scholar
[3]	Sharipov F, Kalempa D 2005 Phys. Fluids 10 16 Google Scholar
[4]	Burnett D 1935 Proc. Lond. Math. Soc. 1 1 Google Scholar
[5]	Shavaliyev M S 1993 J. Appl. Math. Mech. 57 573 Google Scholar
[6]	Bird G A 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford: Oxford University Press) p199
[7]	Yuan Y D, Rahman S 2016 Phys. A 463 25 Google Scholar
[8]	Lockerby D A, Reese J M, Emerson D R, Barber R W 2004 Phys. Rev. E 70 017303 Google Scholar
[9]	Barber R W, Emerson D R 2006 Heat Transfer Eng. 27 3 Google Scholar
[10]	Lockerby D A, Reese J M, Gallis M A 2005 AIAA J. 43 1391 Google Scholar
[11]	Reese J M, Zheng Y, Lockerby D A 2007 J. Comput. Theor. Nanosci. 4 807 Google Scholar
[12]	Bruno D, Cacciatore M, Longo S, Rutigliano M 2000 Chem. Phys. Lett. 320 245 Google Scholar
[13]	Padilla, J F, Bo yd, Iain D 2009 J. Thermophys. Heat Transfer 23 96 Google Scholar
[14]	Liang T, Li Q, Ye W 2013 Phys. Rev. E 88 013009 Google Scholar
[15]	Woronowicz M S, Rault D F 1994 J. Spacecraft Rockets 31 532 Google Scholar
[16]	Myong R S 2004 J. Comput. Phys. 195 655 Google Scholar
[17]	Alder B J, Wainwright T E 1957 J. Chem. Phys. 27 1208 Google Scholar
[18]	Kovalev V, Yakunchikov A, Li F 2011 Acta Astronaut. 69 744 Google Scholar
[19]	张忠强, 刘汉伦, 范晋伟, 丁建宁, 程广贵 2019 物理学报 68 170202 Google Scholar Zhang Z Q, Liu H L, Fan J W, Ding J N, Cheng G G 2019 Acta Phys. Sin. 68 170202 Google Scholar
[20]	Chirita V, Pailthorpe B A, Collins R E 1997 Nucl. Instrum. Meth. B 129 465 Google Scholar
[21]	Yamanishi N, Matsumoto Y, Shobatake K 1999 Phys. Fluids 11 3540 Google Scholar
[22]	曹炳阳 2005 博士学位论文 (北京: 清华大学) Cao B Y 2005 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese)
[23]	Finger G W, Kapat J S, Bhattacharya A 2007 J. Fluids Eng-Trans. ASME 129 31 Google Scholar
[24]	Ozhgibesov M S, Leu T, Cheng C 2012 J. Mol. Graph. Model. 38 375 Google Scholar
[25]	Ozhgibesov M S, Leu T, Cheng C 2013 J. Mol. Graph. Model. 45 45 Google Scholar
[26]	Leu T, Cheng C, Ozhgibesov M S 2011 J. Mol. Graph. Model. 31 35 Google Scholar
[27]	Bao F, Mao Z, Qiu L 2014 Int. J. Numer. Methods Heat Fluid Flow 24 1338 Google Scholar
[28]	宋诚谦 2014 博士学位论文 (合肥: 中国科技大学) Song C Q 2014 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)
[29]	Cao B Y, Sun J, Chen M, Guo Z Y 2009 Int. J. Mol. Sci. 10 11 Google Scholar
[30]	Sun J, Li Z 2008 Mol. Phys. 106 2325 Google Scholar
[31]	Sun J, Li Z 2009 Mol. Simul. 35 228 Google Scholar
[32]	张冉, 常青, 李桦 2018 物理学报 67 223401 Google Scholar Zhang R, Chang Q, Li H 2018 Acta Phys. Sin. 67 223401 Google Scholar
[33]	Maruyama S 2000 Adv. Numer. Heat Transfer 2 189 Google Scholar
[34]	Wu L, Bogy D B 2002 J. Tribol.-Trans. ASME 124 562 Google Scholar
[35]	Swope W C, Andersen H C, Berens P H, Wilson K R 1982 J. Chem. Phys. 76 637 Google Scholar
[36]	Dongari N, Zhang Y H, Reese J M 2012 AIP Conf. Proc. 1501 895 Google Scholar
[37]	张烨, 张冉, 赖剑奇, 李桦 2019 物理学报 68 124702 Google Scholar Zhang Y, Zhang R, Lai J Q, Li H 2019 Acta Phys. Sin. 68 124702 Google Scholar
[38]	Chirita V, Pailthorpe B A, Collins R E 1993 J. Phys. D: Appl. Phys. 26 133 Google Scholar
[39]	Maxwell J C 1878 Proc. R. Soc. London 27 304 Google Scholar

[1]	邢赫威, 陈占秀, 杨历, 苏瑶, 李源华, 呼和仓. 不凝性气体对纳米通道内水分子流动传热影响的分子动力学模拟. 物理学报, 2024, 73(9): 094701. doi: 10.7498/aps.73.20240192
[2]	丁业章, 叶寅, 李多生, 徐锋, 朗文昌, 刘俊红, 温鑫. WC-Co硬质合金表面石墨烯沉积生长分子动力学仿真研究. 物理学报, 2023, 72(6): 068703. doi: 10.7498/aps.72.20221332
[3]	赵中华, 渠广昊, 姚佳池, 闵道敏, 翟鹏飞, 刘杰, 李盛涛. 热峰作用下单斜ZrO₂相变过程的分子动力学模拟. 物理学报, 2021, 70(13): 136101. doi: 10.7498/aps.70.20201861
[4]	常旭. 多层石墨烯的表面起伏的分子动力学模拟. 物理学报, 2014, 63(8): 086102. doi: 10.7498/aps.63.086102
[5]	肖红星, 龙冲生. UO2 晶体中低密勒指数晶面表面能的分子动力学模拟. 物理学报, 2013, 62(10): 103104. doi: 10.7498/aps.62.103104
[6]	柯川, 赵成利, 苟富均, 赵勇. 分子动力学模拟H原子与Si的表面相互作用. 物理学报, 2013, 62(16): 165203. doi: 10.7498/aps.62.165203
[7]	贺平逆, 宁建平, 秦尤敏, 赵成利, 苟富均. 低能Cl原子刻蚀Si(100)表面的分子动力学模拟. 物理学报, 2011, 60(4): 045209. doi: 10.7498/aps.60.045209
[8]	贺平逆, 吕晓丹, 赵成利, 宁建平, 秦尤敏, 苟富均. F原子与SiC(100)表面相互作用的分子动力学模拟. 物理学报, 2011, 60(9): 095203. doi: 10.7498/aps.60.095203
[9]	宁建平, 吕晓丹, 赵成利, 秦尤敏, 贺平逆, Bogaerts A., 苟富君. 样品温度对CF3+ 与Si表面相互作用影响的分子动力学模拟. 物理学报, 2010, 59(10): 7225-7231. doi: 10.7498/aps.59.7225
[10]	张林, 张彩碚, 祁阳. 低温下Au959团簇负载于MgO(100)表面后结构变化的分子动力学研究. 物理学报, 2009, 58(13): 53-S57. doi: 10.7498/aps.58.53
[11]	张宗宁, 刘美林, 李蔚, 耿长建, 赵骞, 张林. 熔融Cu55团簇在Cu(010)表面上凝固过程的分子动力学模拟. 物理学报, 2009, 58(13): 67-S71. doi: 10.7498/aps.58.67
[12]	刘建廷, 段海明. 不同势下铱团簇结构和熔化行为的分子动力学模拟. 物理学报, 2009, 58(7): 4826-4834. doi: 10.7498/aps.58.4826
[13]	刘美林, 张宗宁, 李蔚, 赵骞, 祁阳, 张林. MgO（001）表面上沉积MgO薄膜过程的分子动力学模拟. 物理学报, 2009, 58(13): 199-S203. doi: 10.7498/aps.58.199
[14]	张超, 王永亮, 颜超, 张庆瑜. 替位杂质对低能Pt原子与Pt(111)表面相互作用影响的分子动力学模拟. 物理学报, 2006, 55(6): 2882-2891. doi: 10.7498/aps.55.2882
[15]	杨全文, 朱如曾, 文玉华. 纳米铜团簇在常温和升温过程中能量特征的分子动力学研究. 物理学报, 2005, 54(1): 89-95. doi: 10.7498/aps.54.89
[16]	王海龙, 王秀喜, 梁海弋. 应变效应对金属Cu表面熔化影响的分子动力学模拟. 物理学报, 2005, 54(10): 4836-4841. doi: 10.7498/aps.54.4836
[17]	谢国锋, 王德武, 应纯同. 分子动力学模拟Gd原子在Cu(110)表面的扩散过程. 物理学报, 2003, 52(9): 2254-2258. doi: 10.7498/aps.52.2254
[18]	胡晓君, 戴永兵, 何贤昶, 沈荷生, 李荣斌. 空位在金刚石近(001)表面扩散的分子动力学模拟. 物理学报, 2002, 51(6): 1388-1392. doi: 10.7498/aps.51.1388
[19]	陈军, 经福谦, 张景琳, 陈栋泉. 冲击作用下金属表面微喷射的分子动力学模拟. 物理学报, 2002, 51(10): 2386-2392. doi: 10.7498/aps.51.2386
[20]	张超, 吕海峰, 张庆瑜. 低能Pt原子与Pt(111)表面相互作用的分子动力学模拟. 物理学报, 2002, 51(10): 2329-2334. doi: 10.7498/aps.51.2329

计量

文章访问数: 5799
PDF下载量: 90
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板