Mastering XRR Fitting|Home/Introduction

Front Matter

Introduction

About This Book

This book shows you how to fit an X-ray reflectivity (XRR) curve. You start with a curve measured on your sample. At the end you have the thickness, roughness and density of each layer. You also have a report that another person can check.

All the work is done in one program, X-Ray Calc 3. Every step in the book is something you do in its window: a menu command, a dialog or a field you fill in. The book explains the physics you need for the next step in the program, and no more.

The steps come from a written fitting procedure of 13 steps (Penkov, Peng and Fu, 2026). It records how the author fits a curve in X-Ray Calc, with the reason for each step. It agrees with the author’s practice in 51 saved projects. Seven of its choices were tested against curves calculated from a known structure. Three failed and were replaced: the choices for the scale, for smoothing and for the end of the fitting range. The book teaches the tested version. Chapter 14: Four settings, in this order explains the three replacements.

The book has five Parts:

  • Part 1, Getting Started, says what fitting can tell you, introduces the program and takes you through a first quick fit.
  • Part 2, The Physics You Need, and No More, explains how X-rays reflect from thin films. It also explains how X-Ray Calc calculates a curve and how it searches for a fit.
  • Part 3, The Fitting Workflow, Step by Step, is the procedure itself, in the order you do it.
  • Part 4, Special Cases and Reporting, covers density, single films, graded multilayers and the final report.
  • Part 5, The Part of Tens, gives short lists to check a fit against.

Conventions used in this book

  • Menu commands are in bold, with > between the levels. Data > Normalize (Auto) means: open the Data menu and choose Normalize (Auto). Buttons, dialogs and fields are also in bold, spelled as the program shows them.
  • Every length is in ångströms (Å), including roughness and wavelength. Density is in g/cm³, and angles are in degrees. These are the program’s own units, so the numbers in the book match the numbers on your screen.
  • Every angle is labeled. The program’s chart shows the angle 2θ. The physics uses θ, the angle between the beam and the surface. So the book writes 2θ = 1.2° or θ = 0.6°, never a bare 0.6°. Chapter 2: 2θ or θ: the angle on your screen shows where the program sets the angle it displays.
  • Numbers from the author’s laboratory are marked as such. Each one is an example from one instrument. Your instrument needs its own value.

Each chapter works on its own. When a chapter needs an earlier one, it names it in one sentence with a link.

The book has a web edition and a PDF edition with the same text.

Foolish Assumptions

The book assumes a few things about you:

  • You have a measured XRR curve, or you’ll have one soon.
  • You know what a thin film is.
  • You have never fitted an XRR curve.
  • You haven’t taken a course in X-ray optics. Part 2 gives you the physics you need.
  • You have a PC with 64-bit Windows 10 or later.

You don’t need to program. You also don’t need to know how the fitting algorithm works inside. Chapter 9: How X-Ray Calc Finds a Fit explains the part of it you need.

Icons Used in This Book

Some paragraphs carry an icon. Each icon means one thing.

Going Deeper
The physics, the math or the reason behind a step. You can skip it and still do the fit. In the web edition this box stays closed until you open it.

Beyond the Book

X-Ray Calc has its own manual. It describes every dialog, including features this book doesn’t use.

The X-Ray Calc wiki covers the same ground for new users: getting started, manual fitting and working with measured data. It is at github.com/OleksiyPenkov/X-RayCalc3/wiki.

X-Ray Calc installs with demonstration projects in its Examples folder. Chapter 2: Opening a demo project opens one of them. The worked examples in this book use measured curves. They come with the book as X-Ray Calc projects (.xrcx files).

The web edition has figures that you can change. In Chapter 13: The Sensitivity Check, for example, a slider changes one parameter of a model, and you see which feature of the curve moves. The PDF shows the same figures as fixed panels.

Chapter 25: Ten Checks Before You Trust a Number is a one-page checklist. Print it and keep it next to the computer you fit on.

If you publish a result from X-Ray Calc, cite the two papers that describe the program: Penkov et al. (2020) and Penkov et al. (2024). The full references are in the Sources section.

Where to Go from Here

For the whole workflow on one page, see Chapter 1: The whole workflow on one page.

Sources
  • The fitting procedure: Penkov, O., Peng, J. & Fu, H. (2026). An XRR fitting procedure for a laboratory LLM agent. Zenodo, doi:10.5281/zenodo.22851595. It gives the 13 steps. The book returns each step to the X-Ray Calc action it came from.
  • How the procedure was recorded and tested: the methods paper on the procedure, Penkov, O. V., Peng, J. & Fu, H. (2026). Teaching an LLM agent to fit XRR curves with X-Ray Calc 3. arXiv preprint, arXiv:2609.28926, §3–4. §4 describes the recording while the author fitted in X-Ray Calc, and the audit against 51 of the author’s projects. Table 1 lists the nine conditioning decisions. Seven of them were tested against curves calculated from a known structure. Three were revised: the scale (now solved inside the fit), smoothing (now off) and the end of the fitting range (now at least the first seven predicted orders).
  • X-Ray Calc Help: Installation → System Requirements (Windows 10 or later); Quick Start → Exploring the Demo Projects (the Examples folder); Introduction (the reference to cite).
  • The X-Ray Calc 3 installer script (XRayCalc3Setup.iss): it installs only on 64-bit Windows. The Help says only that 64-bit is recommended, and the book follows the installer.
  • The X-Ray Calc 3 source, main window: the Help > User Manual command, its F1 shortcut, and the Data > Normalize (Auto) command used as the example of a menu path.
  • The papers that describe the program:
    • Penkov, O. V., Kopylets, I. A., Khadem, M. & Qin, T. (2020). X-Ray Calc: a software for the simulation of X-ray reflectivity. SoftwareX 12, 100528. doi:10.1016/j.softx.2020.100528
    • Penkov, O. V., Li, M., Mikki, S., Devizenko, A. & Kopylets, I. (2024). X-Ray Calc 3: improved software for simulation and inverse problem solving for X-ray reflectivity. J. Appl. Cryst. 57, 555–566. doi:10.1107/S1600576724001031

Cross-references: Chapter 1; Chapter 2; Chapter 3; Chapter 9; Chapter 10; Chapter 13; Chapter 14: Four settings, in this order; Chapter 18: Judging a Fit; Chapter 25: Ten Checks Before You Trust a Number; Appendix B: Menus, Buttons and Keys.

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