CN114678076B - A Data Calculation Method of Thermal Neutron Scattering Law Based on Atomic Trajectories - Google Patents
A Data Calculation Method of Thermal Neutron Scattering Law Based on Atomic Trajectories Download PDFInfo
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Abstract
Description
技术领域technical field
本发明涉及核数据处理和反应堆中子学计算领域，具体涉及一种基于原子轨迹的热中子散射律数据计算方法。The invention relates to the fields of nuclear data processing and reactor neutronics calculation, in particular to a data calculation method of thermal neutron scattering law based on atomic trajectory.
背景技术Background technique
在热中子占据重要作用的核设施中，需要对热中子在各种材料，特别是慢化材料中的散射行为有准确的描述。热中子的散射行为主要受三种效应的作用：材料中靶核的热运动，靶核的化学键作用和散射中子波的干涉效应。评价核数据库采用热中子散射律数据(以下简称热散射律数据)描述以上效应，热散射律数据是与散射的靶材料相关的。热散射律数据的精度对核反应堆设计、辐射屏蔽计算、核反应堆临界安全分析以及冷中子源设计等的计算结果具有重要影响，因此需要准确计算。In nuclear facilities where thermal neutrons play an important role, it is necessary to have an accurate description of the scattering behavior of thermal neutrons in various materials, especially moderator materials. The scattering behavior of thermal neutrons is mainly affected by three effects: the thermal motion of target nuclei in materials, the chemical bonding of target nuclei and the interference effect of scattered neutron waves. The evaluation nuclear database uses thermal neutron scattering law data (hereinafter referred to as heat scattering law data) to describe the above effects, and heat scattering law data is related to the scattering target material. The accuracy of heat scattering law data has an important impact on the calculation results of nuclear reactor design, radiation shielding calculation, nuclear reactor criticality safety analysis and cold neutron source design, so accurate calculation is required.
Van Hove从量子力学的角度出发，通过对散射原子时空关联函数的双重傅里叶变换推导得到了热散射律数据。然而，当时的计算条件难以直接得到量子力学下散射原子的时空关联函数。于是，Sjolander等人，基于立方近似和高斯近似，采用声子展开方法推导了由声子态密度表示的热散射律数据。这种方法后来成为国际上主流的处理热散射律数据的方法。近年来，美国、日本、阿根廷的研究人员陆续发现该方法的近似处理会对热散射律数据造成较大误差，采用一声子修正方法和德拜-沃勒矩阵等方法去除或减小其中的近似。但以上研究都是在传统理论框架下针对个别问题建立解决方案，不能从根本上解决传统方法精度低的问题。此外，该理论框架对于不同的液体还需要选择合适的扩散模型，适用性不广。From the perspective of quantum mechanics, Van Hove derived the data of the heat scattering law through the double Fourier transform of the space-time correlation function of the scattering atoms. However, the calculation conditions at that time were difficult to directly obtain the space-time correlation function of scattering atoms under quantum mechanics. Therefore, Sjolander et al., based on the cubic approximation and Gaussian approximation, used the phonon expansion method to derive the heat scattering law data represented by the phonon density of states. This method later became the mainstream method for processing heat scattering law data in the world. In recent years, researchers in the United States, Japan, and Argentina have successively found that the approximate processing of this method will cause large errors in the data of the heat scattering law, and the phonon correction method and the Debye-Waller matrix method are used to remove or reduce the approximation. . However, the above studies are based on the establishment of solutions to individual problems under the traditional theoretical framework, and cannot fundamentally solve the problem of low accuracy of traditional methods. In addition, this theoretical framework also needs to choose a suitable diffusion model for different liquids, which is not widely applicable.
因此，针对以上存在的问题，需要发明一种适用性广、能准确地计算热散射律数据的方法。近年来，随着计算水平的发展，有研究人员通过采用基于经典力学的分子动力学方法(以下简称经典分子动力学方法)获得原子的轨迹，进而可以得到原子的时空关联函数，为通过原子轨迹计算热散射律数据提供了可能。然而，直接采用经典力学得到的原子轨迹，无法准确描述热中子与靶材料散射过程中的量子效应，其计算结果与慢化材料真实的热散射律数据存在差异。Therefore, in view of the above existing problems, it is necessary to invent a method that has wide applicability and can accurately calculate the heat scattering law data. In recent years, with the development of computing level, some researchers have obtained the trajectory of atoms by using the molecular dynamics method based on classical mechanics (hereinafter referred to as the classical molecular dynamics method), and then can obtain the space-time correlation function of atoms. It is possible to calculate the heat scattering law data. However, the atomic trajectories obtained directly from classical mechanics cannot accurately describe the quantum effects in the process of scattering thermal neutrons and target materials, and the calculation results are different from the real thermal scattering law data of moderator materials.
发明内容Contents of the invention
为了克服直接采用经典分子动力学得到的原子轨迹，无法准确描述热中子与靶材料散射过程中存在的量子效应，以及基于声子态密度的理论框架通用性不广等问题，本发明提出一种，利用经典分子动力学得到的原子轨迹，然后通过量子修正的方式考虑热中子与靶材料散射过程中的量子效应的通用的高精度的热散射律数据计算方法。In order to overcome the problems that the atomic trajectories obtained directly by classical molecular dynamics cannot accurately describe the quantum effects existing in the scattering process of thermal neutrons and target materials, and the theoretical framework based on the phonon density of state is not universal, etc., the present invention proposes a A general high-precision thermal scattering law data calculation method that uses the atomic trajectory obtained by classical molecular dynamics, and then considers the quantum effect during the scattering process of thermal neutrons and target materials through quantum correction.
为了实现以上目的，本发明采取如下的技术方案予以实施：In order to achieve the above object, the present invention takes the following technical solutions to implement:
一种基于原子轨迹的热中子散射律数据计算方法，包括如下步骤：A method for calculating thermal neutron scattering law data based on atomic trajectories, comprising the following steps:
步骤1：读取经典分子动力学软件计算得到的靶材料中各个原子随时间t变化的坐标信息其中j为原子的序数；Step 1: Read the coordinate information of each atom in the target material calculated by classical molecular dynamics software over time t Where j is the ordinal number of the atom;
步骤2：针对步骤1读取的坐标信息，按照自中间散射函数的定义，利用公式(1)计算得到基于经典力学的原子轨迹的自中间散射函数，即经典力学的自中间散射函数，以供后续步骤进行量子修正；公式(1)中对多个离散的时间步求平均的目的是，消除自中间散射函数的随机效应，保证结果的准确性；Step 2: For the coordinate information read in step 1, according to the definition of the self-intermediate scattering function, the formula (1) is used to calculate the self-intermediate scattering function of the atomic trajectory based on classical mechanics, that is, the self-intermediate scattering function of classical mechanics, for Subsequent steps carry out quantum correction; the purpose of averaging multiple discrete time steps in formula (1) is to eliminate the random effect of the self-intermediate scattering function and ensure the accuracy of the results;
式中：In the formula:
——倒晶格矢量长度为κ，时间为t的经典力学的自中间散射函数，其中c表示经典力学 ——The self-intermediate scattering function of the classical mechanics with the length of the inverted lattice vector κ and the time t, where c represents the classical mechanics
N——经典分子动力学计算体系中目标原子总个数N——The total number of target atoms in the classical molecular dynamics calculation system
L(t)——可用于时间t进行平均的总的离散时间步数L(t) - the total number of discrete time steps available for averaging at time t
k——离散时间步的序号k—the serial number of the discrete time step
j——经典分子动力学计算体系中目标原子的序号j—the serial number of the target atom in the classical molecular dynamics calculation system
——倒晶格矢量 - Inverted lattice vector
tk——离散时间步k对应的时间t k ——time corresponding to discrete time step k
——原子序号为j，时间为tk的坐标矢量 ——Coordinate vector with atomic number j and time t k
——原子序号为j，时间为tk+t的坐标矢量； ——coordinate vector with atomic number j and time t k + t;
步骤3：通过构造一个特征函数，建立经典力学的自中间散射函数和量子力学的自中间散射函数的联系，通过量子修正的方式考虑热中子与靶材料散射过程存在的量子效应；特征函数的表达式见公式(2)，基于步骤2得到的经典力学的自中间散射函数计算：Step 3: By constructing a characteristic function, establish the connection between the self-intermediate scattering function of classical mechanics and the self-intermediate scattering function of quantum mechanics, and consider the quantum effect existing in the scattering process of thermal neutrons and target materials through quantum correction; the characteristic function See formula (2) for the expression, based on the calculation of the self-intermediate scattering function of classical mechanics obtained in step 2:
f(β)——无量纲的能量转移量为β的特征函数f(β)——dimensionless energy transfer amount is the characteristic function of β
t'——约化的时间t' - reduced time
——倒晶格矢量长度为κ，约化时间为t'的经典力学的自中间散射函数，其中c表示经典力学 ——The self-intermediate scattering function of classical mechanics with the length of the inverted lattice vector κ and the reduced time t', where c represents the classical mechanics
α——无量纲的动量转移量α——dimensionless momentum transfer amount
λ——德拜-沃勒因子；λ——Debye-Waller factor;
步骤4：根据步骤3得到的特征函数，利用公式(3)计算得到考虑量子效应的量子力学的自中间散射函数：Step 4: According to the characteristic function obtained in step 3, use the formula (3) to calculate the self-intermediate scattering function of quantum mechanics considering the quantum effect:
——倒晶格矢量长度为κ，约化时间为t'的量子力学的自中间散射函数，其中q表示量子力学； ——The self-intermediate scattering function of quantum mechanics with the length of the inverted lattice vector κ and the reduced time t', where q represents quantum mechanics;
步骤5：根据步骤4得到的量子力学的自中间散射函数，按照自热散射律数据的定义，利用公式(4)计算量子力学的自热散射律数据：Step 5: According to the self-intermediate scattering function of quantum mechanics obtained in step 4, according to the definition of self-heating scattering law data, use formula (4) to calculate the self-heating scattering law data of quantum mechanics:
——量子力学的自热散射律数据 ——Self-heating scattering law data of quantum mechanics
步骤6：根据步骤1读取到的原子坐标信息，利用公式(5)计算经典力学的中间散射函数，包括相同原子贡献的自中间散射函数和不同原子贡献的相互散射函数两部分。Step 6: According to the atomic coordinate information read in step 1, use the formula (5) to calculate the intermediate scattering function of classical mechanics, including two parts: the self-intermediate scattering function contributed by the same atom and the mutual scattering function contributed by different atoms.
Ic(κ,t)——倒晶格矢量长度为κ，时间为t的经典力学的中间散射函数，其中c表示经典力学I c (κ,t)—the intermediate scattering function of classical mechanics with the length of inverted lattice vector κ and time t, where c represents classical mechanics
——原子序号为j'，时间为tk的坐标矢量 ——Coordinate vector with atomic number j' and time t k
步骤7：通过构造集体结构因子建立经典力学的自热散射律数据与经典力学的热散射律数据的联系。根据步骤2得到的经典力学的自中间散射函数，利用公式(6)计算经典力学的自热散射律数据；根据步骤6得到的经典力学的中间散射函数，利用公式(7)计算经典力学的热散射律数据；于是，经典力学的自热散射律数据和热散射律数据，可利用公式(8)表示。Step 7: Establish the connection between the self-heating scattering law data of classical mechanics and the heat scattering law data of classical mechanics by constructing the collective structure factor. According to the self-intermediate scattering function of classical mechanics obtained in step 2, use formula (6) to calculate the self-heating scattering law data of classical mechanics; according to the intermediate scattering function of classical mechanics obtained in step 6, use formula (7) to calculate the heat of classical mechanics The data of scattering law; thus, the data of self-heating scattering law and heat scattering law of classical mechanics can be expressed by formula (8).
——经典力学的自热散射律数据 ——The self-heating scattering law data of classical mechanics
Sc(α,β)——经典力学的热散射律数据S c (α,β)——heat scattering law data of classical mechanics
Γ(α)——集体结构因子Γ(α)——collective structure factor
步骤8：近似的认为，量子力学的自热散射律数据和热散射律数据与经典力学的自热散射律数据和热散射律数据，满足同样的关系式；即根据步骤5得到的量子力学的自热散射律数据和步骤7得到的集体结构因子，利用公式(9)计算考虑量子效应的量子力学的热散射律数据Step 8: It is approximately considered that the self-heating scattering law data and heat scattering law data of quantum mechanics and the classical mechanics self-heating scattering law data and heat scattering law data satisfy the same relationship; that is, the quantum mechanics obtained according to step 5 From the heat scattering law data and the collective structure factor obtained in step 7, use the formula (9) to calculate the heat scattering law data of quantum mechanics considering quantum effects
Sq(α,β)——量子力学的热散射律数据S q (α,β)——The heat scattering law data of quantum mechanics
步骤9：根据步骤5得到的量子力学的自热散射律数据和步骤8得到的热散射律数据，利用公式(10)计算量子力学的总热散射律数据Step 9: According to the self-heat scattering law data of quantum mechanics obtained in step 5 and the heat scattering law data obtained in step 8, use formula (10) to calculate the total heat scattering law data of quantum mechanics
S(α,β)——量子力学的总热散射律数据S(α,β)——The total heat scattering law data of quantum mechanics
σcoh——束缚态相干散射截面σ coh ——Bound state coherent scattering cross section
σb——束缚态散射截面σ b ——bound state scattering cross section
σinc——束缚态非相干散射截面。σ inc —bound state incoherent scattering cross section.
与现有技术相比，本发明有如下突出的优点：Compared with the prior art, the present invention has the following prominent advantages:
1)相较于传统的根据原子运动模式将散射律分解的处理方法，本发明可直接实现热散射律的计算，彻底消除传统方法的非相干近似和立方近似；1) Compared with the traditional processing method of decomposing the scattering law according to the atomic motion mode, the present invention can directly realize the calculation of the heat scattering law, and completely eliminate the incoherent approximation and cubic approximation of the traditional method;
2)对于固体和液体采用同一套计算流程，且不需要对不同液体选取不同的扩散模型，具有通用性。2) The same set of calculation process is used for solid and liquid, and there is no need to select different diffusion models for different liquids, which is universal.
附图说明Description of drawings
图1为热中子散射律数据计算流程图。Figure 1 is a flow chart of thermal neutron scattering law data calculation.
具体实施方式Detailed ways
下面结合附图和具体实施方式对本发明做进一步详细说明。The present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments.
本发明一种基于原子轨迹的热中子散射律数据计算方法，包括如下步骤：The present invention a kind of thermal neutron scattering law data calculation method based on atomic track, comprises the following steps:
步骤1：读取经典分子动力学软件计算得到的靶材料中各个原子随时间t变化的坐标信息其中j为原子的序数；在本例中，分子动力学计算体系包含515个氢原子，1030个氧原子。需要计算的是轻水中氢原子的热中子散射律数据，因此目标原子为计算体系中所有的氢原子。Step 1: Read the coordinate information of each atom in the target material calculated by classical molecular dynamics software over time t Where j is the atomic number; in this example, the molecular dynamics calculation system contains 515 hydrogen atoms and 1030 oxygen atoms. What needs to be calculated is the thermal neutron scattering law data of hydrogen atoms in light water, so the target atoms are all hydrogen atoms in the calculation system.
步骤2：针对步骤1读取的坐标信息，利用公式(1)计算得到基于经典力学的原子轨迹的自中间散射函数，即经典力学的自中间散射函数，以供后续步骤进行量子修正。公式(1)中对多个离散的时间步求平均的目的是，消除自中间散射函数的随机效应，保证结果的准确性。本例中，时间t的步长为0.0001ps，N的取值为515。Step 2: For the coordinate information read in step 1, use the formula (1) to calculate the self-intermediate scattering function of the atomic trajectory based on classical mechanics, that is, the self-intermediate scattering function of classical mechanics, for quantum correction in subsequent steps. The purpose of averaging multiple discrete time steps in formula (1) is to eliminate the random effect of the self-intermediate scattering function and ensure the accuracy of the result. In this example, the step size of time t is 0.0001ps, and the value of N is 515.
式中：In the formula:
——倒晶格矢量长度为κ，时间为t的经典力学的自中间散射函数，其中c表示经典力学 ——The self-intermediate scattering function of the classical mechanics with the length of the inverted lattice vector κ and the time t, where c represents the classical mechanics
N——经典分子动力学计算体系中目标原子总个数N——The total number of target atoms in the classical molecular dynamics calculation system
L(t)——可用于时间t进行平均的总的离散时间步数L(t) - the total number of discrete time steps available for averaging at time t
k——离散时间步的序号k—the serial number of the discrete time step
j——经典分子动力学计算体系中目标原子的序号j—the serial number of the target atom in the classical molecular dynamics calculation system
——倒晶格矢量 - Inverted lattice vector
tk——离散时间步k对应的时间t k ——time corresponding to discrete time step k
——原子序号为j，时间为tk的坐标矢量 ——Coordinate vector with atomic number j and time t k
——原子序号为j，时间为tk+t的坐标矢量 ——Coordinate vector with atomic number j and time t k +t
步骤3：计算轻水中氢原子的特征函数，β网格的步长由时间步长确定。特征函数的表达式见公式(2)，基于步骤2得到的经典力学的自中间散射函数计算：Step 3: Calculate the characteristic function of hydrogen atoms in light water, and the step size of the β grid is determined by the time step size. The expression of the characteristic function is shown in formula (2), based on the calculation of the self-intermediate scattering function of classical mechanics obtained in step 2:
f(β)——无量纲的能量转移量为β的特征函数f(β)——dimensionless energy transfer amount is the characteristic function of β
t'——约化的时间t' - reduced time
——倒晶格矢量长度为κ，约化时间为t'的经典力学的自中间散射函数，其中c表示经典力学 ——The self-intermediate scattering function of classical mechanics with the length of the inverted lattice vector κ and the reduced time t', where c represents the classical mechanics
α——无量纲的动量转移量α——dimensionless momentum transfer amount
λ——德拜-沃勒因子λ——Debye-Waller factor
步骤4：根据步骤3得到的特征函数，利用公式(3)计算得到轻水中氢原子考虑量子效应的量子力学的自中间散射函数：Step 4: According to the characteristic function obtained in step 3, use the formula (3) to calculate the self-intermediate scattering function of the quantum mechanics of the hydrogen atom in light water considering the quantum effect:
——倒晶格矢量长度为κ，约化时间为t'的量子力学的自中间散射函数，其中q表示量子力学 ——The self-intermediate scattering function of quantum mechanics with the length of the inverted lattice vector κ and the reduced time t', where q represents the quantum mechanics
步骤5：根据步骤4得到的量子力学的自中间散射函数，按照自热散射律数据的定义，利用公式(4)计算量子力学的自热散射律数据：Step 5: According to the self-intermediate scattering function of quantum mechanics obtained in step 4, according to the definition of self-heating scattering law data, use formula (4) to calculate the self-heating scattering law data of quantum mechanics:
——量子力学的自热散射律数据 ——Self-heating scattering law data of quantum mechanics
步骤6：根据步骤1读取到的原子坐标信息，采用与步骤2相似的方式，利用公式(5)计算经典力学的中间散射函数，包括相同原子贡献的自中间散射函数和不同原子贡献的相互散射函数两部分。Step 6: According to the atomic coordinate information read in step 1, use formula (5) to calculate the intermediate scattering function of classical mechanics in a similar manner to step 2, including the self-intermediate scattering function contributed by the same atom and the mutual scattering function contributed by different atoms The scatter function has two parts.
Ic(κ,t)——倒晶格矢量长度为κ，时间为t的经典力学的中间散射函数，其中c表示经典力学I c (κ,t)—the intermediate scattering function of classical mechanics with the length of inverted lattice vector κ and time t, where c represents classical mechanics
——原子序号为j'，时间为tk的坐标矢量 ——Coordinate vector with atomic number j' and time t k
步骤7：通过构造集体结构因子建立经典力学的自热散射律数据与经典力学的热散射律数据的联系。根据步骤2得到的经典力学的自中间散射函数，利用公式(6)计算经典力学的自热散射律数据；根据步骤6得到的经典力学的中间散射函数，利用公式(7)计算经典力学的热散射律数据；于是，经典力学的自热散射律数据和热散射律数据，可利用公式(8)的表示。Step 7: Establish the connection between the self-heating scattering law data of classical mechanics and the heat scattering law data of classical mechanics by constructing the collective structure factor. According to the self-intermediate scattering function of classical mechanics obtained in step 2, use formula (6) to calculate the self-heating scattering law data of classical mechanics; according to the intermediate scattering function of classical mechanics obtained in step 6, use formula (7) to calculate the heat of classical mechanics Scattering law data; therefore, the self-heating scattering law data and heat scattering law data of classical mechanics can be represented by formula (8).
——经典力学的自热散射律数据 ——The self-heating scattering law data of classical mechanics
Sc(α,β)——经典力学的热散射律数据S c (α,β)——heat scattering law data of classical mechanics
Γ(α)——集体结构因子Γ(α)——collective structure factor
步骤8：根据步骤5得到的量子力学的自热散射律数据和步骤7得到的集体结构因子，利用公式(9)计算轻水中氢原子考虑量子效应的量子力学的热散射律数据Step 8: According to the self-heat scattering law data of quantum mechanics obtained in step 5 and the collective structure factor obtained in step 7, use formula (9) to calculate the heat scattering law data of quantum mechanics of hydrogen atoms in light water considering quantum effects
Sq(α,β)——量子力学的热散射律数据S q (α,β)——The heat scattering law data of quantum mechanics
步骤9：根据步骤5得到的量子力学的自热散射律数据和步骤8得到的热散射律数据，利用公式(10)计算量子力学的总热散射律数据Step 9: According to the self-heat scattering law data of quantum mechanics obtained in step 5 and the heat scattering law data obtained in step 8, use formula (10) to calculate the total heat scattering law data of quantum mechanics
S(α,β)——量子力学的总热散射律数据S(α,β)——The total heat scattering law data of quantum mechanics
σcoh——束缚态相干散射截面σ coh ——Bound state coherent scattering cross section
σb——束缚态散射截面σ b ——bound state scattering cross section
σinc——束缚态非相干散射截面σ inc ——Bound state incoherent scattering cross section
在本发明中，原子的位置信息由步骤1读入，位置信息由分子动力学软件计算得到。本发明对计算原子位置信息的方法没有限制，且对位置信息的表达格式没有限制。In the present invention, the position information of atoms is read in step 1, and the position information is calculated by molecular dynamics software. The present invention has no limitation on the method of calculating the atomic position information, and has no limitation on the expression format of the position information.
步骤7中，通过经典力学的热散射律数据和经典力学的自热散射律数据，计算得到集体结构因子。在步骤2计算经典力学的自中间散射函数和步骤6计算经典力学的中间散射函数时，可采用不同程度的近似，本发明对其是否采用近似，以及采用近似的程度没有限制。In step 7, the collective structure factor is calculated through the heat scattering law data of classical mechanics and the self-heating scattering law data of classical mechanics. When calculating the self-intermediate scattering function of classical mechanics in step 2 and calculating the intermediate scattering function of classical mechanics in step 6, different degrees of approximation can be used, and the present invention has no limitation on whether or not the approximation is used and the degree of approximation.
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