双臂 XRD：原理与模型边界
本应用是参考 Bruker D8 θ–θ 双臂结构制作的独立教学仿真，不连接真实设备。设备外观、机械细节、光束亮度、动画速度和保护门联锁均为示意，不代表真实设备或安全培训认证。X 射线不可见；入射和出射束为伪色可视化，亮度随相对模拟信号非线性变化，束宽不是经过计算的仪器发散或聚焦。
外观修订与几何约束
根据用户提供的实机照片修订整圈测角仪、后置径向导轨、光源与探测器壳体；前方玻璃为中缝双扇，向左右平移开启。外形尺寸、导轨和门的行程用于教学展示，并非原厂工程尺寸。机械导轨位于散射平面后方且避开样品中心；粉末表面与测角原点重合，光束示意在水平样品表面终止。
测角几何
样品表面水平、中心固定；光源及探测器位于同一垂直散射平面，以样品中心为共同旋转中心。对称扫描时两臂分别与样品表面形成 θ，散射角为 2θ。使用单一波长，2d sinθ = λ。动画加速播放；估算时间为点数乘以每点计数时间，不包含机械运动、检测器窗口、准备和通信等时间。
粉末谱与强度
复用本站晶体衍射实验室的随机粉末计算：立方 SC、BCC、FCC、金刚石型结构为等权标量点散射体，枚举允许反射，采用文献所述理想 Lorentz–polarization 因子和 2θ 方向面积归一高斯峰形。背景和曲线标度是固定示意值；输出为相对强度，不是探测器计数，也未模拟计数噪声或计数时间与强度的关系。峰宽由用户指定，并非从粒径计算。未考虑真实原子散射因子、Kα 双峰、温度因子、吸收、择优取向、样品位移、仪器展宽或探测器响应。
适用范围
不能据此作物相鉴定、定量组成、Rietveld 精修或真实上机参数判断；布拉格公式显示的是当前角度所对应的晶面间距，不能单凭该值说明当前一定存在反射。内置安全状态仅是操作流程动画，实际 X 射线安全须遵循实验室与设备制造商的规程。
检查与依据
开发中以几何对称、角度范围、扫描点数及布拉格峰位数值测试检查模型。下列资料为几何和粉末计算依据；这些检查不是仪器厂商或领域专家认证。
Dual-arm XRD: scientific basis and limits
This is an independent educational simulation inspired by the Bruker D8 θ–θ arrangement; it does not connect to hardware. Enclosure, mechanical details, beam brightness, playback speed and interlock are illustrative and do not constitute equipment or safety training certification. X-rays are invisible: both beams use false colour, brightness changes nonlinearly with the relative simulated signal, and beam width is not a calculated divergence or focus.
Appearance revision and geometry constraints
User-supplied instrument photographs inform the full goniometer disc, rear radial rails and distinct source and detector housings. Two front glass leaves slide apart from the centre. Dimensions, rail layout and door travel are illustrative rather than manufacturer engineering dimensions. Mechanical rails sit behind the scattering plane and leave the sample centre clear. The powder surface coincides with the angular origin; beam overlays terminate on the horizontal sample surface.
Goniometer geometry
The sample surface remains horizontal and its centre stationary. Source and detector rotate in a vertical scattering plane around the common sample centre. In a symmetric scan both arms make θ to the sample plane and the scattering angle is 2θ. A single wavelength is used: 2d sinθ = λ. Animation runs faster than the simulated measurement; estimated time is point count × dwell, excluding motion, detector window, preparation and communication.
Powder profile and intensity
The existing crystal lab random-powder calculation is reused. Cubic SC, BCC, FCC and diamond prototypes use equal scalar point scatterers; allowed reflections are enumerated with an ideal Lorentz–polarization factor and area-normalized Gaussian peaks on the 2θ axis. Background and display scale are illustrative; output is relative intensity, not detector counts. Count noise and the relation between dwell and intensity are not modelled. Peak width is user supplied, not inferred from crystallite size. Atomic form factors, Kα doublet, thermal factors, absorption, preferred orientation, sample displacement, instrumental broadening and detector response are omitted.
Interpretation
Do not use the simulation for phase identification, quantitative composition, Rietveld refinement or setting a real instrument. The spacing shown corresponds to the current Bragg angle and does not by itself mean a reflection exists. The virtual interlock is an animation; actual X-ray safety follows laboratory and manufacturer procedures.
Checks and references
Development checks include symmetric geometry, angular bounds, scan point count and numerical Bragg-peak benchmarks. These checks are not manufacturer or domain-expert certification.
联合原理工作台：几何、干涉和峰形成
Unified principles workspace: geometry, interference and peak formation
联合工作台保留 D8 仪器和原有晶体、晶面、倒易空间与单晶探测器。两者共用晶体数学模型，但单晶取向与 D8 随机粉末扫描是不同实验；不把 Ewald 图中的单晶斑点当成双臂粉末扫描的实测信号。波矢采用 |k|=1/λ、g=k𝒇−kᵢ 的约定，无 2π 缩放。[3,6]
The suite retains the D8 instrument and the existing crystal, Miller-plane, reciprocal-space and single-crystal detector explorer. Both use shared crystal mathematics, but single-crystal orientation and a D8 random-powder scan are different experiments. Ewald spots are not labelled as acquired D8 powder signals. Wavevectors use |k|=1/λ and g=k𝒇−kᵢ without 2π scaling. [3,6]
几何动画保持水平样品与共同测角原点，光源及探测臂各与表面成 θ。2θ 为入射传播方向延长线与出射方向的夹角；从样品看光源头和探测头的内夹角为 180°−2θ。ki=(cosθ,−sinθ)/λ，kf=(cosθ,sinθ)/λ，故 g=(0,2sinθ/λ)。这里描述所选对称 θ–θ 配置，不声称所有 D8 配置都相同。[1,2]
The geometry animation keeps a horizontal sample and a common angular origin, with each arm at θ to the surface. 2θ is between the forward continuation of the incident propagation direction and the outgoing direction; the angle subtended by the two heads is 180°−2θ. ki=(cosθ,−sinθ)/λ and kf=(cosθ,sinθ)/λ give g=(0,2sinθ/λ). This describes the selected symmetric θ–θ configuration, not every D8 configuration. [1,2]
布拉格页使用 d=a/√(h²+k²+l²)，相邻晶面的光程差 Δ=2d sinθ、相位差 φ=2πΔ/λ。图中 C、D 是 A 到经过 B 的两条光线的垂足，CB+BD 为光程差。晶面是相位构造，不是实体反射镜。有限 N=4–32 层等幅波显示 |Σexp(ijφ)/N|²；还需检查等权基元结构因子，几何对准不保证峰存在。索引 hkl 采用 n=1，高阶反射通过成倍指数表示，避免重复计数。所示 |F(hkl)|² 仅适用于该索引反射；晶面相位和的高阶极大不是完整强度预测，须用 (mh,mk,ml) 重新计算基元。[2,5,6]
The Bragg page uses d=a/√(h²+k²+l²), adjacent-plane path difference Δ=2d sinθ and phase increment φ=2πΔ/λ. C and D are perpendicular projections of A onto the two rays through B, so CB+BD is the path difference. Planes are a phase construction rather than physical mirrors. A finite N=4–32 equal-amplitude stack displays |Σexp(ijφ)/N|²; the equal-scatterer unit-cell structure factor must also permit the reflection. Indexed hkl uses n=1, with multiplied indices representing higher orders to avoid double counting. The displayed |F(hkl)|² applies to that indexed reflection; higher-order maxima of the plane-only sum are not complete predicted intensities and require recalculating the basis at (mh,mk,ml). [2,5,6]
峰形成页分四步展示允许反射、同 d 反射的多重性与 LP 权重、面积归一高斯展宽和扫描步长采样。理论曲线与已采样点使用同一所选扫描范围的峰归一，避免范围改变导致相对强度尺度混淆。高斯 g(x)=√(4ln2/π)/w·exp[−4ln2((x−xB)/w)²] 在整个 2θ 轴的积分为 1，窗口边缘会截断部分尾部。FWHM 由用户独立设定；不由晶面演示 N 推算，也不模拟 Scherrer 粒径或真实仪器响应。窄峰可能被粗步长漏采。[3,4]
Four stages show allowed reflections, equal-d multiplicity and LP weighting, area-normalized Gaussian broadening and scan-step sampling. Theory and acquired points use the same selected scan range for peak normalization, avoiding incompatible relative-intensity scales. The Gaussian g(x)=√(4ln2/π)/w·exp[−4ln2((x−xB)/w)²] integrates to one over the entire 2θ axis; finite windows truncate tails. FWHM is independently specified, not calculated from the plane demonstrator's N; Scherrer size and real instrument response are not simulated. Coarse steps may miss narrow peaks. [3,4]
待采理论预览与已采原参数分别选择；完整蓝线不是已采数据，金色点只显示实际已采部分。为与原采集模型比较，图中从相对读数扣除固定背景 8 并除以显示倍率 2。动画播放、演示角度、hkl 和 N 不改变采集记录。无效待采参数保留上一组有效原理参数并提示。两个工作区只在显式应用时传递待采结构、a、λ、FWHM 和 hkl；范围限 a=3–12 Å、λ=1–2.2 Å、FWHM=0.15–1.2°、hkl=0–12 且非 000。超范围拒绝，不默默截断；扫描中拒绝应用，历史扫描保留原参数。
Pending theory and original acquired settings are selected separately. The full blue curve is not acquired data; gold points show only the acquired portion. For comparison with the original model, fixed background8 is subtracted and display factor2 removed. Playback, demo angle, hkl and N never change acquisition records. Invalid pending inputs retain the last valid principle parameters with a warning. The workspaces exchange pending structure, a, λ, FWHM and hkl only through explicit apply controls, within a=3–12 Å, λ=1–2.2 Å, FWHM=0.15–1.2° and integer hkl=0–12 excluding000. Out-of-range values are rejected rather than clamped; active scans reject transfers and historical scans retain original settings.
开发复核包括弹性波矢夹角与对称性、光程及同相/反相叠加、结构消光、几何不可达、高斯面积和半高宽、旧粉末剖面一致性以及参数传递边界。复核不是厂商或独立领域专家认证。
Development review covers elastic-vector angles and symmetry, path and constructive/destructive interference, systematic absences, inaccessible reflections, Gaussian area and half-height width, agreement with the original powder profile and transfer bounds. This review is not manufacturer or independent domain-expert certification.