# Debye Continuous Phonon Spectrum Thermal State Functions Calculator

> Debye Continuous Phonon Spectrum Thermal State Functions Calculator is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).

Computes thermal state functions (energy, heat capacity, entropy) of an explicit continuous Debye phonon spectrum given a Debye temperature and a set of sample temperatures.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B009/debye-continuous-phonon-density-energy-heat-capacity-entropy?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-04
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/debye-continuous-phonon-spectrum-thermal-state-functions-calculator-b20fb38d
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_zIn-9519XyfR1van6-Igp

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability debye-continuous-phonon-spectrum-thermal-state-functions-calculator-b20fb38d -d '<json body>'
```

Example prompt: Compute the Debye thermal state functions — energy, heat capacity, and entropy — for a material with a Debye temperature of 345 K at the following sample temperatures: 10, 50, 100, 200, 300, and 400 Kelvin.

## When to prefer this

Use this endpoint when you need analytically rigorous thermodynamic state functions (energy, Cv, entropy) under the continuous Debye phonon model for a single material characterized by its Debye temperature, evaluated over a custom temperature grid of up to 32 points. Prefer this over Einsten-model or discrete-spectrum endpoints when the continuous Debye approximation is physically appropriate (most elemental solids and simple compounds).

## Known failure modes

- temperatures_kelvin array is empty or exceeds 32 items — schema validation error
- Debye temperature or any sample temperature outside allowed range (0.1–5000 K or 0.1–10000 K) — validation failure
- Missing required fields debye_temperature_kelvin or temperatures_kelvin — 400 Bad Request
- Payment not provided or insufficient USDC — 402 Payment Required
- Numerical instability at extreme low temperatures approaching absolute zero

## How this service works

Compute the thermal state functions of an explicit continuous Debye phonon spectrum.

## Output

Returns computed thermodynamic quantities derived from the continuous Debye phonon density of states: internal (phonon) energy, constant-volume heat capacity, and entropy — each evaluated at every requested sample temperature, grounded in the specified Debye temperature.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "artifact": {
   "type": "object",
   "required": [
    "debyeHeat"
   ],
   "properties": {
    "debyeHeat": {
     "type": "object",
     "required": [
      "data",
      "claim"
     ],
     "properties": {
      "data": {
       "type": "object",
       "required": [
        "debye_temperature_kelvin",
        "temperatures_kelvin"
       ],
       "properties": {
        "temperatures_kelvin": {
         "type": "array",
         "items": {
          "type": "number",
          "maximum": 10000,
          "minimum": 0.1
         },
         "maxItems": 32,
         "minItems": 1
        },
        "debye_temperature_kelvin": {
         "type": "number",
         "maximum": 5000,
         "minimum": 0.1
        }
       },
       "additionalProperties": false
      },
      "claim": {}
     },
     "additionalProperties": false
    }
   },
   "additionalProperties": false
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/debye-continuous-phonon-spectrum-thermal-state-functions-calculator-b20fb38d/health.json
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