Optimal bi-planar gradient coil configurations for diamond nitrogen-vacancy based diffusion-weighted NMR experiments

At a Glance

Metadata	Details
Publication Date	2023-08-14
Journal	Magnetic Resonance Materials in Physics Biology and Medicine
Authors	Philipp Amrein, Fleming Bruckmaier, Feng Jia, Dominik B. Bucher, Maxim Zaitsev
Institutions	University of Freiburg, University Medical Center Freiburg
Citations	2
Analysis	Full AI Review Included

Optimal Diamond Gradient Systems for NV-NMR: A 6CCVD Technical Analysis

This document analyzes the requirements and achievements detailed in the research paper “Optimal bi-planar gradient coil configurations for diamond nitrogen-vacancy based diffusion-weighted NMR experiments” and correlates them with the advanced material solutions offered by 6CCVD.

Executive Summary

The research successfully developed and validated a compact, high-sensitivity bi-planar gradient coil system essential for diffusion-weighted Nuclear Magnetic Resonance (NMR) utilizing Nitrogen-Vacancy (NV) centers in diamond.

Core Application: Diffusion-weighted NV-NMR for investigating microstructural properties in the biological micro- to nanoscale domain.
Material Requirement: High-quality, optically accessible Single Crystal Diamond (SCD) doped with NV centers serves as the quantum sensor.
Key Achievement: Implementation of a three-channel (G_x, G_y, G_z) bi-planar gradient system on PCBs, achieving high sensitivities (26-28.7 mT/m/A) within a 3 mm target volume.
Design Innovation: The optimal configuration required a specific 35° polar tilt of the bi-planar surfaces to align with the intrinsic 55° NV center quantization axis, maximizing transverse gradient efficiency.
Performance Validation: Measured field errors were low (below 8% for G_x/G_y and below 6% for G_z), confirming the effectiveness of the PCB-based design.
6CCVD Value Proposition: 6CCVD specializes in providing the necessary high-purity, custom-dimension Single Crystal Diamond (SCD) substrates and advanced metalization required to replicate and scale this cutting-edge quantum sensing platform.

Technical Specifications

The following hard data points were extracted from the optimized gradient coil design and experimental validation:

Parameter	Value	Unit	Context
Target Region Diameter	3	mm	Spherical volume for gradient linearity
Diamond Sensor Dimensions (Implied)	2 x 2 x 0.5	mm	High-quality SCD chip at the center of the ROI
Square Side Length ($l$)	5	cm	Final optimized bi-planar geometry
G_x Measured Sensitivity	28.7 ± 0.19	mT/m/A	Transverse gradient channel
G_y Measured Sensitivity	26.8 ± 0.12	mT/m/A	Transverse gradient channel
G_z Measured Sensitivity	26.0 ± 0.18	mT/m/A	Longitudinal gradient channel
G_x/G_y Max Field Error	8	%	Relative difference between measured and simulated data
G_z Max Field Error	6	%	Relative difference between measured and simulated data
Bi-planar Tilt (Chosen)	35	°	Polar angle relative to the MR scanner B₀ axis
Intrinsic NV Center Tilt	54.74 (≈ 55)	°	Relative to the diamond (100) surface normal
PCB Copper Thickness	35	µm	Used for double-layer coil fabrication
Required Current (100 mT/m)	3.8	A	Current needed to achieve high gradient strength
G_x Inductance	3.76	µH	Low inductance ensures no peak voltage limitations

Key Methodologies

The gradient coil design and validation process involved a rigorous computational search followed by PCB fabrication and experimental measurement.

Computational Geometry Search: Over 500 bi-planar surface configurations were generated and analyzed using the MATLAB-based open-source design tool, CoilGen.
Optimization Criteria: The search optimized three geometric parameters: planar surface separation ($d$), square side length ($l$), and surface normal orientation ($\vec{n}$) relative to the main magnetic field B₀.
Coil Layout Generation: The stream function approach was used to optimize the surface current density ($\vec{j}$) to achieve the desired linear magnetic target field within the 3 mm ROI.
Regularization: Tikhonov regularization ($\lambda = 100,000$) was applied during optimization to balance field accuracy against power dissipation (electric resistance).
Fabrication: The optimized stream function results were discretized into isocontour lines (wire turns) and implemented on double-layer Printed Circuit Boards (PCBs) with 35 µm copper thickness.
Experimental Validation: The fabricated three-channel system was tested in a clinical 3T MRI scanner using a copper sulfate phantom. Phase images were acquired using a double gradient echo sequence to measure field strengths and validate performance.

6CCVD Solutions & Capabilities

The success of this NV-NMR experiment hinges on the quality and precise integration of the diamond sensor. 6CCVD provides the specialized MPCVD diamond materials and engineering services necessary to replicate, optimize, and scale this research.

Applicable Materials

To replicate or extend this research, high-purity diamond material is critical for hosting stable, high-coherence NV centers.

Research Requirement	6CCVD Material Solution	Technical Rationale
NV Center Host Material	Optical Grade Single Crystal Diamond (SCD)	Provides the lowest defect density and highest purity required for long spin coherence times (T₂*) essential for high-sensitivity quantum sensing and NMR.
Diffusion-Weighted Imaging	Custom Nitrogen-Doped SCD	Precise control over nitrogen incorporation during MPCVD growth allows for optimization of NV center density and depth, balancing signal strength and proximity to the sample.
Future Microfluidic Integration	Heavy Boron Doped PCD (BDD)	For applications requiring integrated electrochemical sensing or high thermal conductivity substrates beneath the SCD sensor layer.

Customization Potential

The paper highlights the need for small, precisely dimensioned components integrated into a constrained setup. 6CCVD’s custom fabrication capabilities directly address these challenges.

Research Requirement	6CCVD Customization Service	Specification Match
Small Sensor Dimensions (2 x 2 x 0.5 mm)	Custom Dimensions & Laser Cutting	We provide SCD plates/wafers in custom sizes, including precise laser cutting to match the required millimeter-scale geometry for the NV-NMR setup.
Surface Quality for Optics	Ultra-Precision Polishing	SCD surfaces polished to Ra < 1 nm, minimizing optical scattering losses for the excitation laser and fluorescence readout system.
RF/Microwave Coil Integration (Fig. 1A, items 4, 5, 6)	In-House Metalization Services	We offer custom deposition of thin films (e.g., Ti/Pt/Au, W, Cu) directly onto the diamond surface, facilitating the integration of on-chip microwave/RF structures necessary for driving NV spin states.
Substrate Thickness	SCD/PCD Thickness Control	We offer SCD thicknesses from 0.1 µm up to 500 µm, and substrates up to 10 mm, allowing researchers to optimize thermal management and optical path length.

Engineering Support

The complexity of aligning the gradient system (35° tilt) with the NV center orientation (55° tilt) underscores the need for expert material selection and integration support.

Material Selection for Quantum Sensing: 6CCVD’s in-house PhD team specializes in the material science of diamond quantum defects. We assist researchers in selecting the optimal diamond specifications (crystal orientation, nitrogen concentration, and surface termination) for similar diffusion-weighted NV-NMR projects.
Global Supply Chain: We ensure reliable, global shipping (DDU default, DDP available) of sensitive diamond materials, supporting international research collaborations.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Abstract Introduction Diffusion weighting in optically detected magnetic resonance experiments involving diamond nitrogen-vacancy (NV) centers can provide valuable microstructural information. Bi-planar gradient coils employed for diffusion weighting afford excellent spatial access, essential for integrating the NV-NMR components. Nevertheless, owing to the polar tilt of roughly $$55^{\circ }$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:msup> <mml:mn>55</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> of the diamond NV center, the primary magnetic field direction must be taken into account accordingly. Methods To determine the most effective bi-planar gradient coil configurations, we conducted an investigation into the impact of various factors, including the square side length, surface separation, and surface orientation. This was accomplished by generating over 500 bi-planar surface configurations using automated methods. Results We successfully generated and evaluated coil layouts in terms of sensitivity and field accuracy. Interestingly, inclined bi-planar orientations close to the NV-NMR setup’s requirement, showed higher sensitivity for the transverse gradient channels than horizontal or vertical orientations. We fabricated a suitable solution as a three-channel bi-planar double-layered PCB system and experimentally validated the sensitivities at $$28.7 \mathrm mT/m/A$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:mrow> <mml:mn>28.7</mml:mn> <mml:mi>m</mml:mi> <mml:mi>T</mml:mi> <mml:mo>/</mml:mo> <mml:mi>m</mml:mi> <mml:mo>/</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> and $$26.8 \mathrm mT/m/A$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:mrow> <mml:mn>26.8</mml:mn> <mml:mi>m</mml:mi> <mml:mi>T</mml:mi> <mml:mo>/</mml:mo> <mml:mi>m</mml:mi> <mml:mo>/</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> for the transverse $$G_{x}$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>x</mml:mi> </mml:msub> </mml:math> and $$G_{y}$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>y</mml:mi> </mml:msub> </mml:math> gradients, and $$26 \mathrm mT/m/A$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:mrow> <mml:mn>26</mml:mn> <mml:mi>m</mml:mi> <mml:mi>T</mml:mi> <mml:mo>/</mml:mo> <mml:mi>m</mml:mi> <mml:mo>/</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> for the $$G_{z}$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>z</mml:mi> </mml:msub> </mml:math> gradient. Discussion We found that the chosen relative bi-planar tilt of $$35^{\circ }$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:msup> <mml:mn>35</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> represents a reasonable compromise in terms of overall performance and allows for easier coil implementation with a straight, horizontal alignment within the overall experimental setup.