방사광가속기 X선 흡수 미세구조(XAFS/EXAFS) 동역학 & 1,000Hz 0-Alloc C# 단일원자 촉매 배위구조 역산 엔진

using System;
using System.Runtime.CompilerServices;

namespace ZeliDesk.Stem.Synchrotron;

public readonly ref struct CatalystCoordinationState
{
    public readonly double PrimaryBondLengthAngstrom;
    public readonly double CoordinationNumber;
    public readonly double DebyeWallerFactor;
    public readonly double OxidationStateShiftEv;
    public readonly bool IsSinteringDegraded;

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public CatalystCoordinationState(double bondLength, double coordNum, double dwFactor, double shiftEv, bool degraded)
    {
        PrimaryBondLengthAngstrom = bondLength;
        CoordinationNumber = coordNum;
        DebyeWallerFactor = dwFactor;
        OxidationStateShiftEv = shiftEv;
        IsSinteringDegraded = degraded;
    }
}

public ref struct ExafsSpectroscopySimulator
{
    private const int EnergyBins = 32;
    private const double ElectronMass = 9.10938356e-31;
    private const double Hbar = 1.0545718e-34;
    private const double EvToJoules = 1.602176634e-19;

    private double _referenceEdgeEv;

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public ExafsSpectroscopySimulator(double edgeEv = 7112.0) // Fe K-edge
    {
        _referenceEdgeEv = edgeEv;
    }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public CatalystCoordinationState AnalyzeSpectrum(ReadOnlySpan<double> absorptionCoefficients, double currentEdgeEv)
    {
        if (absorptionCoefficients.Length < EnergyBins)
            throw new ArgumentException("Must supply 32 absorption bins.");

        // 1. 화학적 이동(Chemical Shift) 산출 -> 산화수 추정
        double edgeShiftEv = currentEdgeEv - _referenceEdgeEv;

        // 2. 주 결합 거리(Bond Length) 및 진동 위상 복조
        // 특정 k 파수 영역에서의 정현파 진동 주파수 추정 (간이 DFT 스택 연산)
        double maxPower = 0.0;
        double bestBondLength = 1.95; // 기본 1.95 옹스트롬 (M-O 결합)

        for (int rIdx = 0; rIdx < 20; rIdx++)
        {
            double testR = 1.5 + rIdx * 0.08; // 1.5 ~ 3.1 옹스트롬 탐색
            double sumCos = 0.0;
            double sumSin = 0.0;

            for (int kIdx = 0; kIdx < EnergyBins; kIdx++)
            {
                double k = 2.0 + kIdx * 0.3; // 2.0 ~ 11.3 Angstrom^-1
                double phase = 2.0 * k * testR;
                double chi = absorptionCoefficients[kIdx];
                sumCos += chi * Math.Cos(phase);
                sumSin += chi * Math.Sin(phase);
            }

            double power = sumCos * sumCos + sumSin * sumSin;
            if (power > maxPower)
            {
                maxPower = power;
                bestBondLength = testR;
            }
        }

        // 3. 배위수(Coordination Number) 추정 (진폭 비례)
        double rawAmplitude = Math.Sqrt(maxPower) / EnergyBins;
        double coordinationNumber = rawAmplitude * 12.0; // 0 ~ 12 스케일링
        if (coordinationNumber > 12.0) coordinationNumber = 12.0;

        // 4. 드바이-월러 인자 산출
        double debyeWaller = 0.003 + 0.005 * (1.0 / Math.Max(0.5, coordinationNumber));

        // 5. 소결(Sintering) 징후 감지: 단일원자(CN~4)에서 벌크 클러스터(CN > 8, 결합길이 2.5A Fe-Fe)로 전이
        bool sintering = bestBondLength > 2.4 && coordinationNumber > 7.5;

        return new CatalystCoordinationState(bestBondLength, coordinationNumber, debyeWaller, edgeShiftEv, sintering);
    }
}